From 478daf71a645b925b4affdda76fe6f315aacc0b6 Mon Sep 17 00:00:00 2001
From: Yifan Wang <yifan.wang@aei.mpg.de>
Date: Mon, 24 Feb 2020 22:02:56 +0100
Subject: [PATCH] upload SEOBNREv1
---
SEOBNREv1/DIY_SEOBNRE_ALL.h | 1175 +++++
SEOBNREv1/DIY_SEOBNRE_main.c | 385 ++
SEOBNREv1/LALSimSEOBNRE_DIY.c | 8566 +++++++++++++++++++++++++++++++++
SEOBNREv1/readme.txt | 11 +
4 files changed, 10137 insertions(+)
create mode 100755 SEOBNREv1/DIY_SEOBNRE_ALL.h
create mode 100755 SEOBNREv1/DIY_SEOBNRE_main.c
create mode 100755 SEOBNREv1/LALSimSEOBNRE_DIY.c
create mode 100755 SEOBNREv1/readme.txt
diff --git a/SEOBNREv1/DIY_SEOBNRE_ALL.h b/SEOBNREv1/DIY_SEOBNRE_ALL.h
new file mode 100755
index 0000000..3110c96
--- /dev/null
+++ b/SEOBNREv1/DIY_SEOBNRE_ALL.h
@@ -0,0 +1,1175 @@
+#ifndef _DATETYPES_H
+#define _DATETYPES_H
+
+#ifdef newc
+#include <ccomplex>
+#include <cstdint>
+#include <cstdlib>
+#include <cstring>
+#include <cmath>
+
+using namespace std;
+#else
+#include <complex.h>
+#include <stdint.h>
+#include <stdlib.h>
+#include <string.h>
+#include <math.h>
+#endif
+#include <gsl/gsl_odeiv.h>
+#include <gsl/gsl_spline.h>
+#include <gsl/gsl_matrix.h>
+
+
+/* Integer types */
+typedef unsigned int UINT4; /**< Four-byte unsigned integer. */
+
+/* Real types */
+typedef float REAL4; /**< Single precision real floating-point number (4 bytes). */
+typedef double REAL8; /**< Double precision real floating-point number (8 bytes). */
+typedef double complex COMPLEX16;
+//typedef struct tagCOMPLEX16 { REAL8 re; REAL8 im; } COMPLEX16;
+
+typedef int16_t INT2; /**< Two-byte signed integer */
+typedef int32_t INT4; /**< Four-byte signed integer. */
+typedef int64_t INT8; /**< Eight-byte signed integer; on some platforms this is equivalent to <tt>long int</tt> instead. */
+typedef uint16_t UINT2; /**< Two-byte unsigned integer. */
+typedef uint64_t UINT8; /**< Eight-byte unsigned integer; on some platforms this is equivalent to <tt>unsigned long int</tt> instead. */
+
+
+
+//#define LAL_INT8_C INT64_C
+#define LAL_INT8_C long int
+
+//#define I (XLALCOMPLEX16Rect(0.0,1.0))
+#define XLAL_BILLION_REAL8 1e9
+#define XLAL_BILLION_INT8 LAL_INT8_C( 1000000000 )
+#define EOB_RD_EFOLDS 10.0
+#define LAL_MTSUN_SI 4.92549095e-6 /**< Geometrized solar mass, s */
+#define LAL_PI_2 1.5707963267948966192313216916397514 /**< pi/2 */
+#define LAL_1_PI 0.3183098861837906715377675267450287 /**< 1/pi */
+#define LAL_MSUN_SI 1.98892e30 /**< Solar mass, kg */
+#define LAL_GAMMA 0.5772156649015328606065120900824024 /**< gamma */
+#define LAL_E 2.7182818284590452353602874713526625 /**< e */
+#define LAL_MRSUN_SI 1.47662504e3 /**< Geometrized solar mass, m */
+#define LAL_TWOPI 6.2831853071795864769252867665590058 /**< 2*pi */
+
+#define LALFree(p) free(p)
+
+
+typedef struct tagGSParams {
+ int ampO; /**< twice PN order of the amplitude */
+ REAL8 phiRef; /**< phase at fRef */
+ REAL8 deltaT; /**< sampling interval */
+ REAL8 m1; /**< mass of companion 1 */
+ REAL8 m2; /**< mass of companion 2 */
+ REAL8 f_min; /**< start frequency */
+ REAL8 e0; /**< eccentricity at start frequency */
+ REAL8 f_max; /**< end frequency */
+ REAL8 distance; /**< distance of source */
+ REAL8 inclination; /**< inclination of L relative to line of sight */
+ REAL8 s1x; /**< (x,y,z) components of spin of m1 body */
+ REAL8 s1y; /**< z-axis along line of sight, L in x-z plane */
+ REAL8 s1z; /**< dimensionless spin, Kerr bound: |s1| <= 1 */
+ REAL8 s2x; /**< (x,y,z) component ofs spin of m2 body */
+ REAL8 s2y; /**< z-axis along line of sight, L in x-z plane */
+ REAL8 s2z; /**< dimensionless spin, Kerr bound: |s2| <= 1 */
+ int output; /**< out put to file or not(0 if do not write to file) */
+ char outname[256]; /**< file to which output should be written */
+ int ampPhase;
+ int verbose;
+ char jobtag[256];
+} GSParams;
+
+typedef struct
+tagLALUnit
+{
+ int unitNumerator[7]; /**< Array of unit power numerators. */
+ int unitDenominatorMinusOne[7]; /**< Array of unit power denominators-minus-one. */
+}
+LALUnit;
+
+/** Vector of type REAL8, see \ref ss_Vector for more details. */
+typedef struct tagREAL8Vector
+{
+ UINT4 length; /**< Number of elements in array. */
+ REAL8 *data; /**< Pointer to the data array. */
+}
+REAL8Vector;
+
+typedef REAL8Vector REAL8Sequence; /**< See \ref ss_Sequence for documentation */
+
+typedef struct
+tagLIGOTimeGPS
+{
+ int gpsSeconds; /**< Seconds since 0h UTC 6 Jan 1980. */
+ int gpsNanoSeconds; /**< Residual nanoseconds. */
+}
+LIGOTimeGPS;
+
+
+/** Time series of REAL8 data, see \ref ss_TimeSeries for more details. */
+typedef struct
+tagREAL8TimeSeries
+{
+ char name[64]; /**< The name of the time series. */
+ LIGOTimeGPS epoch; /**< The start time of the time series. */
+ REAL8 deltaT; /**< The time step between samples of the time series in seconds. */
+ REAL8 f0; /**< The heterodyning frequency, in Hertz (zero if not heterodyned). */
+ LALUnit sampleUnits; /**< The physical units of the quantity being sampled. */
+ //REAL8Sequence *data; /**< The sequence of sampled data. */
+ REAL8Vector *data; /**< The sequence of sampled data. */
+}
+REAL8TimeSeries;
+
+typedef struct tagCOMPLEX16Vector
+{
+ UINT4 length; /**< Number of elements in array. */
+ COMPLEX16 *data; /**< Pointer to the data array. */
+}
+COMPLEX16Vector;
+
+typedef struct
+tagEOBNonQCCoeffs
+{
+ REAL8 a1;
+ REAL8 a2;
+ REAL8 a3;
+ REAL8 a3S;
+ REAL8 a4;
+ REAL8 a5;
+ REAL8 b1;
+ REAL8 b2;
+ REAL8 b3;
+ REAL8 b4;
+} EOBNonQCCoeffs;
+
+typedef struct
+tagark4GSLIntegrator
+{
+ gsl_odeiv_step *step;
+ gsl_odeiv_control *control;
+ gsl_odeiv_evolve *evolve;
+
+ gsl_odeiv_system *sys;
+
+ int (* dydt) (double t, const double y[], double dydt[], void * params);
+ int (* stop) (double t, const double y[], double dydt[], void * params);
+
+ int retries; /* retries with smaller step when derivatives encounter singularity */
+ int stopontestonly; /* stop only on test, use tend to size buffers only */
+
+ int returncode;
+} ark4GSLIntegrator;
+
+typedef struct
+tagUINT4Vector
+{
+ UINT4 length; /**< Number of elements in array. */
+ UINT4 *data; /**< Pointer to the data array. */
+}
+UINT4Vector;
+
+/** Multidimentional array of REAL8, see \ref ss_Array for more details. */
+typedef struct
+tagREAL8Array
+{
+ UINT4Vector *dimLength; /**< Vector of array dimensions. */
+ REAL8 *data; /**< Pointer to the data array. */
+}
+REAL8Array;
+
+typedef struct
+tagEOBACoefficients
+{
+ REAL8 n4;
+ REAL8 n5;
+ REAL8 d0;
+ REAL8 d1;
+ REAL8 d2;
+ REAL8 d3;
+ REAL8 d4;
+ REAL8 d5;
+}
+EOBACoefficients;
+
+typedef struct
+tagFacWaveformCoeffs
+{
+ REAL8 delta22vh3;
+ REAL8 delta22vh6;
+ REAL8 delta22v8;
+ REAL8 delta22vh9;
+ REAL8 delta22v5;
+
+ REAL8 rho22v2;
+ REAL8 rho22v3;
+ REAL8 rho22v4;
+ REAL8 rho22v5;
+ REAL8 rho22v6;
+ REAL8 rho22v6l;
+ REAL8 rho22v7;
+ REAL8 rho22v8;
+ REAL8 rho22v8l;
+ REAL8 rho22v10;
+ REAL8 rho22v10l;
+
+ REAL8 delta21vh3;
+ REAL8 delta21vh6;
+ REAL8 delta21vh7;
+ REAL8 delta21vh9;
+ REAL8 delta21v5;
+ REAL8 delta21v7;
+
+ REAL8 rho21v1;
+ REAL8 rho21v2;
+ REAL8 rho21v3;
+ REAL8 rho21v4;
+ REAL8 rho21v5;
+ REAL8 rho21v6;
+ REAL8 rho21v6l;
+ REAL8 rho21v7;
+ REAL8 rho21v7l;
+ REAL8 rho21v8;
+ REAL8 rho21v8l;
+ REAL8 rho21v10;
+ REAL8 rho21v10l;
+
+ REAL8 f21v1;
+
+ REAL8 delta33vh3;
+ REAL8 delta33vh6;
+ REAL8 delta33vh9;
+ REAL8 delta33v5;
+ REAL8 delta33v7;
+
+ REAL8 rho33v2;
+ REAL8 rho33v3;
+ REAL8 rho33v4;
+ REAL8 rho33v5;
+ REAL8 rho33v6;
+ REAL8 rho33v6l;
+ REAL8 rho33v7;
+ REAL8 rho33v8;
+ REAL8 rho33v8l;
+
+ REAL8 f33v3;
+
+ REAL8 delta32vh3;
+ REAL8 delta32vh4;
+ REAL8 delta32vh6;
+ REAL8 delta32vh9;
+
+ REAL8 rho32v;
+ REAL8 rho32v2;
+ REAL8 rho32v3;
+ REAL8 rho32v4;
+ REAL8 rho32v5;
+ REAL8 rho32v6;
+ REAL8 rho32v6l;
+ REAL8 rho32v8;
+ REAL8 rho32v8l;
+
+ REAL8 delta31vh3;
+ REAL8 delta31vh6;
+ REAL8 delta31vh7;
+ REAL8 delta31vh9;
+ REAL8 delta31v5;
+
+ REAL8 rho31v2;
+ REAL8 rho31v3;
+ REAL8 rho31v4;
+ REAL8 rho31v5;
+ REAL8 rho31v6;
+ REAL8 rho31v6l;
+ REAL8 rho31v7;
+ REAL8 rho31v8;
+ REAL8 rho31v8l;
+
+ REAL8 f31v3;
+
+ REAL8 delta44vh3;
+ REAL8 delta44vh6;
+ REAL8 delta44v5;
+
+ REAL8 rho44v2;
+ REAL8 rho44v3;
+ REAL8 rho44v4;
+ REAL8 rho44v5;
+ REAL8 rho44v6;
+ REAL8 rho44v6l;
+
+ REAL8 delta43vh3;
+ REAL8 delta43vh4;
+ REAL8 delta43vh6;
+
+ REAL8 rho43v;
+ REAL8 rho43v2;
+ REAL8 rho43v4;
+ REAL8 rho43v5;
+ REAL8 rho43v6;
+ REAL8 rho43v6l;
+
+ REAL8 f43v;
+
+ REAL8 delta42vh3;
+ REAL8 delta42vh6;
+
+ REAL8 rho42v2;
+ REAL8 rho42v3;
+ REAL8 rho42v4;
+ REAL8 rho42v5;
+ REAL8 rho42v6;
+ REAL8 rho42v6l;
+
+ REAL8 delta41vh3;
+ REAL8 delta41vh4;
+ REAL8 delta41vh6;
+
+ REAL8 rho41v;
+ REAL8 rho41v2;
+ REAL8 rho41v4;
+ REAL8 rho41v5;
+ REAL8 rho41v6;
+ REAL8 rho41v6l;
+
+ REAL8 f41v;
+
+ REAL8 delta55vh3;
+ REAL8 delta55v5;
+ REAL8 rho55v2;
+ REAL8 rho55v3;
+ REAL8 rho55v4;
+ REAL8 rho55v5;
+ REAL8 rho55v6;
+
+ REAL8 delta54vh3;
+ REAL8 delta54vh4;
+ REAL8 rho54v2;
+ REAL8 rho54v3;
+ REAL8 rho54v4;
+
+ REAL8 delta53vh3;
+ REAL8 rho53v2;
+ REAL8 rho53v3;
+ REAL8 rho53v4;
+ REAL8 rho53v5;
+
+ REAL8 delta52vh3;
+ REAL8 delta52vh4;
+ REAL8 rho52v2;
+ REAL8 rho52v3;
+ REAL8 rho52v4;
+
+ REAL8 delta51vh3;
+ REAL8 rho51v2;
+ REAL8 rho51v3;
+ REAL8 rho51v4;
+ REAL8 rho51v5;
+
+ REAL8 delta66vh3;
+ REAL8 rho66v2;
+ REAL8 rho66v3;
+ REAL8 rho66v4;
+
+ REAL8 delta65vh3;
+ REAL8 rho65v2;
+ REAL8 rho65v3;
+
+ REAL8 delta64vh3;
+ REAL8 rho64v2;
+ REAL8 rho64v3;
+ REAL8 rho64v4;
+
+ REAL8 delta63vh3;
+ REAL8 rho63v2;
+ REAL8 rho63v3;
+
+ REAL8 delta62vh3;
+ REAL8 rho62v2;
+ REAL8 rho62v3;
+ REAL8 rho62v4;
+
+ REAL8 delta61vh3;
+ REAL8 rho61v2;
+ REAL8 rho61v3;
+
+ REAL8 delta77vh3;
+ REAL8 rho77v2;
+ REAL8 rho77v3;
+
+ REAL8 rho76v2;
+
+ REAL8 delta75vh3;
+ REAL8 rho75v2;
+ REAL8 rho75v3;
+
+ REAL8 rho74v2;
+
+ REAL8 delta73vh3;
+ REAL8 rho73v2;
+ REAL8 rho73v3;
+
+ REAL8 rho72v2;
+
+ REAL8 delta71vh3;
+ REAL8 rho71v2;
+ REAL8 rho71v3;
+
+ REAL8 rho88v2;
+ REAL8 rho87v2;
+ REAL8 rho86v2;
+ REAL8 rho85v2;
+ REAL8 rho84v2;
+ REAL8 rho83v2;
+ REAL8 rho82v2;
+ REAL8 rho81v2;
+}
+FacWaveformCoeffs;
+
+typedef
+struct tagNewtonMultipolePrefixes
+{
+ COMPLEX16 values[8+1][8+1];
+}
+NewtonMultipolePrefixes;
+
+typedef
+struct tagEOBParams
+{
+ REAL8 eta;
+ REAL8 omega;
+ REAL8 m1;
+ REAL8 m2;
+ EOBACoefficients *aCoeffs;
+ FacWaveformCoeffs *hCoeffs;
+ EOBNonQCCoeffs *nqcCoeffs;
+ NewtonMultipolePrefixes *prefixes;
+}
+EOBParams;
+
+typedef struct
+tagSpinEOBHCoeffs
+{
+ double KK;
+ double k0;
+ double k1;
+ double k2;
+ double k3;
+ double k4;
+ double b3;
+ double bb3;
+}
+SpinEOBHCoeffs;
+
+typedef struct
+tagSpinEOBParams
+{
+ EOBParams *eobParams;
+ SpinEOBHCoeffs *seobCoeffs;
+ REAL8Vector *sigmaStar;
+ REAL8Vector *sigmaKerr;
+ REAL8 a;
+ int alignedSpins;
+ int tortoise;
+
+ // we assume m1>m2
+ REAL8Vector *Spin1;
+ REAL8Vector *Spin2;
+}
+SpinEOBParams;
+
+typedef
+struct tagSEOBRootParams
+{
+ REAL8 values[12]; /**<< Dynamical variables, x, y, z, px, py, pz, S1x, S1y, S1z, S2x, S2y and S2z */
+ SpinEOBParams *params; /**<< Spin EOB parameters -- physical, pre-computed, etc. */
+ REAL8 omega; /**<< Orbital frequency */
+}
+SEOBRootParams;
+
+
+/* We need to encapsulate the data for the GSL derivative function */
+typedef
+struct tagHcapDerivParams
+{
+ const REAL8 *values;
+ SpinEOBParams *params;
+ UINT4 varyParam;
+}
+HcapDerivParams;
+
+#define XLAL_REAL8_FAIL_NAN_INT LAL_INT8_C(0x7ff80000000001a1) /**< Hexadecimal representation of <tt>REAL8</tt> NaN failure bit pattern */
+#define XLAL_IS_REAL8_FAIL_NAN(val) XLALIsREAL8FailNaN(val) /**< Tests if <tt>val</tt> is a XLAL <tt>REAL8</tt> failure NaN. */
+
+/* We need to encapsulate the data for calculating spherical 2nd derivatives */
+typedef
+struct tagHcapSphDeriv2Params
+{
+ const REAL8 *sphValues;
+ SpinEOBParams *params;
+ UINT4 varyParam1;
+ UINT4 varyParam2;
+}
+HcapSphDeriv2Params;
+
+
+/** XLAL error numbers and return values. */
+enum XLALErrorValue {
+ XLAL_SUCCESS = 0, /**< Success return value (not an error number) */
+ XLAL_FAILURE = -1, /**< Failure return value (not an error number) */
+
+ /* these are standard error numbers */
+ XLAL_EIO = 5, /**< I/O error */
+ XLAL_ENOMEM = 12, /**< Memory allocation error */
+ XLAL_EFAULT = 14, /**< Invalid pointer */
+ XLAL_EINVAL = 22, /**< Invalid argument */
+ XLAL_EDOM = 33, /**< Input domain error */
+ XLAL_ERANGE = 34, /**< Output range error */
+
+ /* extended error numbers start at 128 ...
+ * should be beyond normal errnos */
+
+ /* these are common errors for XLAL functions */
+ XLAL_EFAILED = 128, /**< Generic failure */
+ XLAL_EBADLEN = 129, /**< Inconsistent or invalid length */
+ XLAL_ESIZE = 130, /**< Wrong size */
+ XLAL_EDIMS = 131, /**< Wrong dimensions */
+ XLAL_ETYPE = 132, /**< Wrong or unknown type */
+ XLAL_ETIME = 133, /**< Invalid time */
+ XLAL_EFREQ = 134, /**< Invalid freqency */
+ XLAL_EUNIT = 135, /**< Invalid units */
+ XLAL_ENAME = 136, /**< Wrong name */
+ XLAL_EDATA = 137, /**< Invalid data */
+
+ /* user-defined errors */
+ XLAL_EUSR0 = 200, /**< User-defined error 0 */
+ XLAL_EUSR1 = 201, /**< User-defined error 1 */
+ XLAL_EUSR2 = 202, /**< User-defined error 2 */
+ XLAL_EUSR3 = 203, /**< User-defined error 3 */
+ XLAL_EUSR4 = 204, /**< User-defined error 4 */
+ XLAL_EUSR5 = 205, /**< User-defined error 5 */
+ XLAL_EUSR6 = 206, /**< User-defined error 6 */
+ XLAL_EUSR7 = 207, /**< User-defined error 7 */
+ XLAL_EUSR8 = 208, /**< User-defined error 8 */
+ XLAL_EUSR9 = 209, /**< User-defined error 9 */
+
+ /* external or internal errors */
+ XLAL_ESYS = 254, /**< System error */
+ XLAL_EERR = 255, /**< Internal error */
+
+ /* specific mathematical and numerical errors start at 256 */
+
+ /* IEEE floating point errors */
+ XLAL_EFPINVAL = 256, /**< IEEE Invalid floating point operation, eg sqrt(-1), 0/0 */
+ XLAL_EFPDIV0 = 257, /**< IEEE Division by zero floating point error */
+ XLAL_EFPOVRFLW = 258, /**< IEEE Floating point overflow error */
+ XLAL_EFPUNDFLW = 259, /**< IEEE Floating point underflow error */
+ XLAL_EFPINEXCT = 260, /**< IEEE Floating point inexact error */
+
+ /* numerical algorithm errors */
+ XLAL_EMAXITER = 261, /**< Exceeded maximum number of iterations */
+ XLAL_EDIVERGE = 262, /**< Series is diverging */
+ XLAL_ESING = 263, /**< Apparent singularity detected */
+ XLAL_ETOL = 264, /**< Failed to reach specified tolerance */
+ XLAL_ELOSS = 265, /**< Loss of accuracy */
+
+ /* failure from within a function call: "or" error number with this */
+ XLAL_EFUNC = 1024 /**< Internal function call failed bit: "or" this with existing error number */
+};
+
+typedef struct
+tagREAL8VectorSequence
+{
+ UINT4 length; /**< The number \a l of vectors. */
+ UINT4 vectorLength; /**< The length \a n of each vector. */
+ REAL8 *data; /**< Pointer to the data array. Element \a i of vector \a j is \c data[ \a jn + \a i \c ]. */
+}
+REAL8VectorSequence;
+
+enum
+{
+ LALUnitIndexMeter, /**< The meter index. */
+ LALUnitIndexKiloGram, /**< The kilogram index. */
+ LALUnitIndexSecond, /**< The second index. */
+ LALUnitIndexAmpere, /**< The ampere index. */
+ LALUnitIndexKelvin, /**< The kelvin index. */
+ LALUnitIndexStrain, /**< The strain index. */
+ LALUnitIndexADCCount, /**< The ADC counts index. */
+ LALNumUnits /**< The number of units. */
+};
+
+#define LAL_PI 3.1415926535897932384626433832795029 /**< pi */
+
+enum enumLALNameLength { LALNameLength = 64 };
+
+#endif /* _DATE_H */
+
+
+
+
+#ifndef _LALCONSTANTS_H
+#define _LALCONSTANTS_H
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+ /** \name Floating-point constants
+ * The following constants define the precision and range of
+ * floating-point arithmetic in LAL. They are taken from the IEEE
+ * standard 754 for binary arithmetic. All numbers are dimensionless. */
+ /*@{*/
+#define LAL_REAL4_MANT 24 /**< Bits of precision in the mantissa of a REAL4 */
+#define LAL_REAL4_MAX 3.40282347e+38 /**< Largest REAL4 */
+#define LAL_REAL4_MIN 1.17549435e-38 /**< Smallest nonzero REAL4 */
+#define LAL_REAL4_EPS 1.19209290e-07 /**< 0.5^(LAL_REAL4_MANT-1), ie the difference between 1 and the next resolveable REAL4 */
+#define LAL_REAL8_MANT 53 /**< Bits of precision in the mantissa of a REAL8 */
+#define LAL_REAL8_MAX 1.7976931348623157e+308 /**< Largest REAL8 */
+#define LAL_REAL8_MIN 2.2250738585072014e-308 /**< Smallest nonzero REAL8 */
+#define LAL_REAL8_EPS 2.2204460492503131e-16 /**< 0.5^(LAL_REAL8_MANT-1), ie the difference between 1 and the next resolveable REAL8 */
+ /*@}*/
+
+ /** \name Mathematical constants
+ * The following are fundamental mathematical constants. They are mostly
+ * taken from the GNU C <tt>math.h</tt> header (with the exception of
+ * <tt>LAL_TWOPI</tt>, which was computed using Maple). All numbers are
+ * dimensionless. The value of exp(gamma) is taken from
+ * http://www.research.att.com/~njas/sequences/A073004 */
+ /*@{*/
+#define LAL_E 2.7182818284590452353602874713526625 /**< e */
+#define LAL_LOG2E 1.4426950408889634073599246810018922 /**< log_2 e */
+#define LAL_LOG10E 0.4342944819032518276511289189166051 /**< log_10 e */
+#define LAL_LN2 0.6931471805599453094172321214581766 /**< log_e 2 */
+#define LAL_LN10 2.3025850929940456840179914546843642 /**< log_e 10 */
+#define LAL_SQRT2 1.4142135623730950488016887242096981 /**< sqrt(2) */
+#define LAL_SQRT1_2 0.7071067811865475244008443621048490 /**< 1/sqrt(2) */
+#define LAL_GAMMA 0.5772156649015328606065120900824024 /**< gamma */
+#define LAL_EXPGAMMA 1.7810724179901979852365041031071795 /**< exp(gamma) */
+ /* Assuming we're not near a black hole or in Tennessee... */
+#define LAL_PI 3.1415926535897932384626433832795029 /**< pi */
+#define LAL_TWOPI 6.2831853071795864769252867665590058 /**< 2*pi */
+#define LAL_PI_2 1.5707963267948966192313216916397514 /**< pi/2 */
+#define LAL_PI_4 0.7853981633974483096156608458198757 /**< pi/4 */
+#define LAL_1_PI 0.3183098861837906715377675267450287 /**< 1/pi */
+#define LAL_2_PI 0.6366197723675813430755350534900574 /**< 2/pi */
+#define LAL_2_SQRTPI 1.1283791670955125738961589031215452 /**< 2/sqrt(pi) */
+#define LAL_PI_180 1.7453292519943295769236907684886127e-2 /**< pi/180 */
+#define LAL_180_PI 57.295779513082320876798154814105170 /**< 180/pi */
+ /*@}*/
+
+ /** \name Exact physical constants
+ * The following physical constants are defined to have exact values.
+ * The values of \f$c\f$ and \f$g\f$ are taken from \ref Barnet_1996,
+ * \f$p_\mathrm{atm}\f$ is from \ref Lang_1992, while \f$\epsilon_0\f$ and
+ * \f$\mu_0\f$ are computed from \f$c\f$ using exact formulae. The use
+ * of a Julian year (365.25 days) as standard is specified by the IAU.
+ * They are given in the SI units shown. */
+ /*@{*/
+#define LAL_C_SI 299792458 /**< Speed of light in vacuo, m s^-1 */
+#define LAL_EPSILON0_SI 8.8541878176203898505365630317107503e-12 /**< Permittivity of free space, C^2 N^-1 m^-2 */
+#define LAL_MU0_SI 1.2566370614359172953850573533118012e-6 /**< Permeability of free space, N A^-2 */
+#define LAL_GEARTH_SI 9.80665 /**< Standard gravity, m s^-2 */
+#define LAL_PATM_SI 101325 /**< Standard atmosphere, Pa */
+#define LAL_YRJUL_SI 31557600 /**< Julian year, s */
+#define LAL_LYR_SI 9.4607304725808e15 /**< (Julian) Lightyear, m */
+ /*@}*/
+
+ /** \name Physical constants
+ * The following are measured fundamental physical constants, with values
+ * given in \ref Barnet_1996. When not dimensionless, they are given
+ * in the SI units shown. */
+ /*@{*/
+#define LAL_G_SI 6.67259e-11 /**< Gravitational constant, N m^2 kg^-2 */
+#define LAL_H_SI 6.6260755e-34 /**< Planck constant, J s */
+#define LAL_HBAR_SI 1.05457266e-34 /**< Reduced Planck constant, J s */
+#define LAL_MPL_SI 2.17671e-8 /**< Planck mass, kg */
+#define LAL_LPL_SI 1.61605e-35 /**< Planck length, m */
+#define LAL_TPL_SI 5.39056e-44 /**< Planck time, s */
+#define LAL_K_SI 1.380658e-23 /**< Boltzmann constant, J K^-1 */
+#define LAL_R_SI 8.314511 /**< Ideal gas constant, J K^-1 */
+#define LAL_MOL 6.0221367e23 /**< Avogadro constant, dimensionless */
+#define LAL_BWIEN_SI 2.897756e-3 /**< Wien displacement law constant, m K */
+#define LAL_SIGMA_SI 5.67051e-8 /**< Stefan-Boltzmann constant, W m^-2 K^-4 */
+#define LAL_AMU_SI 1.6605402e-27 /**< Atomic mass unit, kg */
+#define LAL_MP_SI 1.6726231e-27 /**< Proton mass, kg */
+#define LAL_ME_SI 9.1093897e-31 /**< Electron mass, kg */
+#define LAL_QE_SI 1.60217733e-19 /**< Electron charge, C */
+#define LAL_ALPHA 7.297354677e-3 /**< Fine structure constant, dimensionless */
+#define LAL_RE_SI 2.81794092e-15 /**< Classical electron radius, m */
+#define LAL_LAMBDAE_SI 3.86159323e-13 /**< Electron Compton wavelength, m */
+#define LAL_AB_SI 5.29177249e-11 /**< Bohr radius, m */
+#define LAL_MUB_SI 9.27401543e-24 /**< Bohr magneton, J T^-1 */
+#define LAL_MUN_SI 5.05078658e-27 /**< Nuclear magneton, J T^-1 */
+ /*@}*/
+
+ /** \name Astrophysical parameters
+ * The following parameters are derived from measured properties of the
+ * Earth and Sun. The values are taken from \ref Barnet_1996, except
+ * for the obliquity of the ecliptic plane and the eccentricity of
+ * Earth's orbit, which are taken from \ref Lang_1992. All values are
+ * given in the SI units shown. Note that the ``year'' and
+ * ``light-year'' have exactly defined values, and appear under
+ * ``Exact physical constants''.
+ */
+ /*@{*/
+#define LAL_REARTH_SI 6.378140e6 /**< Earth equatorial radius, m */
+#define LAL_AWGS84_SI 6.378137e6 /**< Semimajor axis of WGS-84 Reference Ellipsoid, m */
+#define LAL_BWGS84_SI 6.356752314e6 /**< Semiminor axis of WGS-84 Reference Ellipsoid, m */
+#define LAL_MEARTH_SI 5.97370e24 /**< Earth mass, kg */
+#define LAL_IEARTH 0.409092804 /**< Earth inclination (2000), radians */
+#define LAL_EEARTH 0.0167 /**< Earth orbital eccentricity */
+#define LAL_RSUN_SI 6.960e8 /**< Solar equatorial radius, m */
+#define LAL_MSUN_SI 1.98892e30 /**< Solar mass, kg */
+#define LAL_MRSUN_SI 1.47662504e3 /**< Geometrized solar mass, m */
+#define LAL_MTSUN_SI 4.92549095e-6 /**< Geometrized solar mass, s */
+#define LAL_LSUN_SI 3.846e26 /**< Solar luminosity, W */
+#define LAL_AU_SI 1.4959787066e11 /**< Astronomical unit, m */
+#define LAL_PC_SI 3.0856775807e16 /**< Parsec, m */
+#define LAL_YRTROP_SI 31556925.2 /**< Tropical year (1994), s */
+#define LAL_YRSID_SI 31558149.8 /**< Sidereal year (1994), s */
+#define LAL_DAYSID_SI 86164.09053 /**< Mean sidereal day, s */
+ /*@}*/
+
+ /** \name Cosmological parameters
+ * The following cosmological parameters are derived from measurements of
+ * the Hubble expansion rate and of the cosmic background radiation
+ * (CBR). Data are taken from \ref Barnet_1996. In what follows, the
+ * normalized Hubble constant \f$h_0\f$ is equal to the actual Hubble
+ * constant \f$H_0\f$ divided by \f$\langle H
+ * \rangle=100\,\mathrm{km}\,\mathrm{s}^{-1}\mathrm{Mpc}^{-1}\f$. Thus the
+ * Hubble constant can be written as:
+ * \f$H_0 = \langle H \rangle h_0\f$.
+ * Similarly, the critical energy density \f$\rho_c\f$ required for spatial
+ * flatness is given by: \f$\rho_c = \langle\rho\rangle h_0^2\f$.
+ * Current estimates give \f$h_0\f$ a value of around 0.65, which is what is
+ * assumed below. All values are in the SI units shown. */
+ /*@{*/
+#define LAL_H0FAC_SI 3.2407792903e-18 /**< Hubble constant prefactor, s^-1 */
+#define LAL_H0_SI 2e-18 /**< Approximate Hubble constant, s^-1 */
+ /* Hubble constant H0 = h0*HOFAC, where h0 is around 0.65 */
+#define LAL_RHOCFAC_SI 1.68860e-9 /**< Critical density prefactor, J m^-3 */
+#define LAL_RHOC_SI 7e-10 /**< Approximate critical density, J m^-3 */
+ /* Critical density RHOC = h0*h0*RHOCFAC, where h0 is around 0.65 */
+#define LAL_TCBR_SI 2.726 /**< Cosmic background radiation temperature, K */
+#define LAL_VCBR_SI 3.695e5 /**< Solar velocity with respect to CBR, m s^-1 */
+#define LAL_RHOCBR_SI 4.177e-14 /**< Energy density of CBR, J m^-3 */
+#define LAL_NCBR_SI 4.109e8 /**< Number density of CBR photons, m^-3 */
+#define LAL_SCBR_SI 3.993e-14 /**< Entropy density of CBR, J K^-1 m^-3 */
+ /*@}*/
+
+ /*@}*/
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* _LALCONSTANTS_H */
+
+#define PI M_PI
+
+
+REAL8 XLALGPSGetREAL8( const LIGOTimeGPS *epoch );
+
+COMPLEX16Vector* XLALCreateCOMPLEX16Vector(UINT4 length);
+void XLALDestroyCOMPLEX16Vector(COMPLEX16Vector* v);
+
+REAL8Vector* XLALCreateREAL8Vector(UINT4 length);
+void XLALDestroyREAL8Vector(REAL8Vector* v);
+
+UINT4Vector* XLALCreateUINT4Vector(UINT4 length);
+void XLALDestroyUINT4Vector(UINT4Vector* v);
+
+REAL8Array* XLALCreateREAL8ArrayL(UINT4 ndim,...);
+void XLALDestroyREAL8Array(REAL8Array* v);
+
+REAL8VectorSequence * XLALCreateREAL8VectorSequence ( UINT4 length, UINT4 veclen );
+void XLALDestroyREAL8VectorSequence ( REAL8VectorSequence * vseq );
+
+REAL8TimeSeries *XLALCreateREAL8TimeSeries ( const char *name, const LIGOTimeGPS *epoch, REAL8 f0, REAL8 deltaT, const LALUnit *sampleUnits, int length );
+void XLALDestroyREAL8TimeSeries( REAL8TimeSeries * series );
+
+int XLALSimIMREOBFinalMassSpin_re(
+ REAL8 *finalMass, /**<< OUTPUT, the final mass (scaled by original total mass) */
+ REAL8 *finalSpin, /**<< OUTPUT, the final spin (scaled by final mass) */
+ const REAL8 mass1, /**<< The mass of the 1st component of the system */
+ const REAL8 mass2, /**<< The mass of the 2nd component of the system */
+ const REAL8 spin1[3], /**<< The spin of the 1st object; only needed for spin waveforms */
+ const REAL8 spin2[3] /**<< The spin of the 2nd object; only needed for spin waveforms */
+);
+
+int XLALSimIMREOBGenerateQNMFreqV2_re(
+ COMPLEX16Vector *modefreqs, /**<< OUTPUT, complex freqs of overtones in unit of Hz */
+ const REAL8 mass1, /**<< The mass of the 1st component (in Solar masses) */
+ const REAL8 mass2, /**<< The mass of the 2nd component (in Solar masses) */
+ const REAL8 spin1[3], /**<< The spin of the 1st object; only needed for spin waveforms */
+ const REAL8 spin2[3], /**<< The spin of the 2nd object; only needed for spin waveforms */
+ UINT4 l, /**<< The l value of the mode in question */
+ UINT4 m, /**<< The m value of the mode in question */
+ UINT4 nmodes /**<< The number of overtones that should be included (max 8) */
+);
+
+int XLALSimIMRSpinEOBCalculateSigmaStar(
+ REAL8Vector *sigmaStar, /**<< OUTPUT, normalized (to total mass) spin of test particle */
+ REAL8 mass1, /**<< mass 1 */
+ REAL8 mass2, /**<< mass 2 */
+ REAL8Vector *s1, /**<< spin vector 1 */
+ REAL8Vector *s2 /**<< spin vector 2 */);
+
+int XLALSimIMRSpinEOBCalculateSigmaKerr(
+ REAL8Vector *sigmaKerr, /**<< OUTPUT, normalized (to total mass) spin of deformed-Kerr */
+ REAL8 mass1, /**<< mass 1 */
+ REAL8 mass2, /**<< mass 2 */
+ REAL8Vector *s1, /**<< spin vector 1 */
+ REAL8Vector *s2 /**<< spin vector 2 */);
+
+int XLALSimIMREOBCalcSpinFacWaveformCoefficients(
+ FacWaveformCoeffs * const coeffs, /**< OUTPUT, pre-computed waveform coefficients */
+ const REAL8 m1, /**< mass 1 */
+ const REAL8 m2, /**< mass 2 */
+ const REAL8 eta, /**< symmetric mass ratio */
+ const REAL8 a, /**< Kerr spin parameter for test-particle terms */
+ const REAL8 chiS, /**< (chi1+chi2)/2 */
+ const REAL8 chiA /**< (chi1-chi2)/2 */
+);
+
+int XLALSimIMREOBComputeNewtonMultipolePrefixes(
+ NewtonMultipolePrefixes *prefix, /**<< OUTPUT Structure containing the coeffs */
+ const REAL8 m1, /**<< Mass of first component */
+ const REAL8 m2 /**<< Nass of second component */
+);
+
+int XLALSimIMRSpinEOBInitialConditions(
+ REAL8Vector *initConds, /**<< OUTPUT, Initial dynamical variables */
+ const REAL8 mass1, /**<< mass 1 */
+ const REAL8 mass2, /**<< mass 2 */
+ const REAL8 fMin, /**<< Initial frequency (given) */
+ const REAL8 e0, /**<< eccentricity at starting GW frequency (Hz) */
+ const REAL8 inc, /**<< Inclination */
+ const REAL8 spin1[], /**<< Initial spin vector 1 */
+ const REAL8 spin2[], /**<< Initial spin vector 2 */
+ SpinEOBParams *params /**<< Spin EOB parameters */
+);
+
+int
+CalculateRotationMatrix(
+ gsl_matrix *rotMatrix, /**< OUTPUT, rotation matrix */
+ gsl_matrix *rotInverse, /**< OUTPUT, rotation matrix inversed */
+ REAL8 r[], /**< position vector */
+ REAL8 v[], /**< velocity vector */
+ REAL8 L[] /**< orbital angular momentum */
+);
+REAL8 CalculateCrossProduct( const int i, const REAL8 a[], const REAL8 b[] );
+
+int NormalizeVector( REAL8 a[] );
+int ApplyRotationMatrix(
+ gsl_matrix *rotMatrix, /**< rotation matrix */
+ REAL8 a[] /**< OUTPUT, vector rotated */
+);
+
+int
+XLALFindSphericalOrbit( const gsl_vector *x, /**<< Parameters requested by gsl root finder */
+ void *params, /**<< Spin EOB parameters */
+ gsl_vector *f /**<< Function values for the given parameters */
+);
+
+REAL8 XLALSpinHcapNumDerivWRTParam(
+ const INT4 paramIdx, /**<< Index of the parameters */
+ const REAL8 values[], /**<< Dynamical variables */
+ SpinEOBParams *funcParams /**<< EOB Parameters */
+);
+double GSLSpinHamiltonianWrapper( double x, void *params );
+
+int XLALSimIMRCalculateSpinEOBHCoeffs(
+ SpinEOBHCoeffs *coeffs, /**<< OUTPUT, EOB parameters including pre-computed coefficients */
+ const REAL8 eta, /**<< symmetric mass ratio */
+ const REAL8 a /**<< Normalized deformed Kerr spin */
+);
+
+
+REAL8 XLALSimIMRSpinEOBHamiltonian(
+ const REAL8 eta, /**<< Symmetric mass ratio */
+ REAL8Vector *x, /**<< Position vector */
+ REAL8Vector *p, /**<< Momentum vector (tortoise radial component pr*) */
+ REAL8Vector *sigmaKerr, /**<< Spin vector sigma_kerr */
+ REAL8Vector *sigmaStar, /**<< Spin vector sigma_star */
+ INT4 tortoise, /**<< flag to state whether the momentum is the tortoise co-ord */
+ SpinEOBHCoeffs *coeffs /**<< Structure containing various coefficients */
+);
+
+
+int XLALSimIMRSpinEOBGetSpinFactorizedWaveform(
+ COMPLEX16 * hlm, /**< OUTPUT, hlm waveforms */
+ REAL8Vector * values, /**< dyanmical variables */
+ const REAL8 v, /**< velocity */
+ const REAL8 Hreal, /**< real Hamiltonian */
+ const int l, /**< l mode index */
+ const int m, /**< m mode index */
+ SpinEOBParams * params /**< Spin EOB parameters */
+);
+
+REAL8 XLALCalculateSphHamiltonianDeriv2(
+ const int idx1, /**<< Derivative w.r.t. index 1 */
+ const int idx2, /**<< Derivative w.r.t. index 2 */
+ const REAL8 values[], /**<< Dynamical variables in spherical coordinates */
+ SpinEOBParams *params /**<< Spin EOB Parameters */
+);
+int SphericalToCartesian(
+ REAL8 qCart[], /**<< OUTPUT, position vector in Cartesean coordinates */
+ REAL8 pCart[], /**<< OUTPUT, momentum vector in Cartesean coordinates */
+ const REAL8 qSph[], /**<< position vector in spherical coordinates */
+ const REAL8 pSph[] /**<< momentum vector in spherical coordinates */
+);
+double GSLSpinHamiltonianDerivWrapper( double x, /**<< Derivative at x */
+ void *params /**<< Function parameters */);
+REAL8 XLALInspiralSpinFactorizedFlux(
+ REAL8Vector *values, /**< dynamical variables */
+ const REAL8 omega, /**< orbital frequency */
+ SpinEOBParams *ak, /**< physical parameters */
+ const REAL8 H, /**< real Hamiltonian */
+ const int lMax /**< upper limit of the summation over l */
+);
+
+
+int
+XLALSimIMRSpinEOBCalculateNewtonianMultipole(
+ COMPLEX16 *multipole, /**<< OUTPUT, Newtonian multipole */
+ REAL8 x, /**<< Dimensionless parameter \f$\equiv v^2\f$ */
+ REAL8 r, /**<< Orbital separation (units of total mass M */
+ REAL8 phi, /**<< Orbital phase (in radians) */
+ UINT4 l, /**<< Mode l */
+ int m, /**<< Mode m */
+ EOBParams *params /**<< Pre-computed coefficients, parameters, etc. */
+);
+int
+XLALScalarSphHarmThetaPiBy2(
+ COMPLEX16 *y, /**<< OUTPUT, Ylm(0,phi) */
+ int l, /**<< Mode l */
+ int m, /**<< Mode m */
+ REAL8 phi /**<< Orbital phase (in radians) */
+);
+REAL8
+XLALAssociatedLegendreXIsZero( const int l,
+ const int m );
+
+REAL8 XLALSimIMRSpinEOBHamiltonianDeltaR(
+ SpinEOBHCoeffs *coeffs, /**<< Pre-computed coefficients which appear in the function */
+ const REAL8 r, /**<< Current orbital radius (in units of total mass) */
+ const REAL8 eta, /**<< Symmetric mass ratio */
+ const REAL8 a /**<< Normalized deformed Kerr spin */
+);
+
+REAL8 XLALSimIMRSpinEOBHamiltonianDeltaT(
+ SpinEOBHCoeffs *coeffs, /**<< Pre-computed coefficients which appear in the function */
+ const REAL8 r, /**<< Current orbital radius (in units of total mass) */
+ const REAL8 eta, /**<< Symmetric mass ratio */
+ const REAL8 a /**<< Normalized deformed Kerr spin */
+);
+ark4GSLIntegrator *XLALAdaptiveRungeKutta4Init( int dim,
+ int (* dydt) (double t, const double y[], double dydt[], void * params), /* These are XLAL functions! */
+ int (* stop) (double t, const double y[], double dydt[], void * params),
+ double eps_abs, double eps_rel
+ );
+void XLALAdaptiveRungeKutta4Free( ark4GSLIntegrator *integrator );
+int XLALSpinAlignedHcapDerivative(
+ double t, /**< UNUSED */
+ const REAL8 values[], /**< dynamical varables */
+ REAL8 dvalues[], /**< time derivative of dynamical variables */
+ void *funcParams /**< EOB parameters */
+);
+double GSLSpinAlignedHamiltonianWrapper( double x, void *params );
+
+int
+XLALEOBSpinAlignedStopCondition(double t, /**< UNUSED */
+ const double values[], /**< dynamical variable values */
+ double dvalues[], /**< dynamical variable time derivative values */
+ void *funcParams /**< physical parameters */
+);
+
+int XLALAdaptiveRungeKutta4( ark4GSLIntegrator *integrator,
+ void *params,
+ REAL8 *yinit,
+ REAL8 tinit, REAL8 tend, REAL8 deltat,
+ REAL8Array **yout
+ );
+int XLALSpinAlignedHiSRStopCondition(double t, /**< UNUSED */
+ const double values[], /**< dynamical variable values */
+ double dvalues[], /**< dynamical variable time derivative values */
+ void *funcParams /**< physical parameters */
+);
+// scaling omega with (vy/(vy+vx))^gamma
+REAL8
+XLALSimIMRSpinAlignedEOBCalcOmega(
+ const REAL8 values[], /**<< Dynamical variables */
+ SpinEOBParams *funcParams /**<< EOB parameters */
+);
+REAL8
+XMYSimIMRSpinAlignedEOBCalcOmega(
+ const REAL8 values[], /**<< Dynamical variables */
+ SpinEOBParams *funcParams /**<< EOB parameters */
+);
+LIGOTimeGPS * XLALGPSAdd( LIGOTimeGPS *epoch, REAL8 dt );
+LIGOTimeGPS * XLALGPSSetREAL8( LIGOTimeGPS *epoch, REAL8 t );
+LIGOTimeGPS * XLALGPSAddGPS( LIGOTimeGPS *epoch, const LIGOTimeGPS *dt );
+LIGOTimeGPS * XLALGPSSet( LIGOTimeGPS *epoch, INT4 gpssec, INT8 gpsnan );
+LIGOTimeGPS * XLALINT8NSToGPS( LIGOTimeGPS *epoch, INT8 ns );
+INT8 XLALGPSToINT8NS( const LIGOTimeGPS *epoch );
+
+int XLALSimIMRGetEOBCalibratedSpinNQC( EOBNonQCCoeffs *coeffs,
+ INT4 l,
+ INT4 m,
+ REAL8 eta,
+ REAL8 a );
+int XLALSimIMRSpinEOBCalculateNQCCoefficients(
+ REAL8Vector *amplitude, /**<< Waveform amplitude, func of time */
+ REAL8Vector *phase, /**<< Waveform phase(rad), func of time */
+ REAL8Vector *rVec, /**<< Position-vector, function of time */
+ REAL8Vector *prVec, /**<< Momentum vector, function of time */
+ REAL8Vector *orbOmegaVec, /**<< Orbital frequency, func of time */
+ INT4 l, /**<< Mode index l */
+ INT4 m, /**<< Mode index m */
+ REAL8 timePeak, /**<< Time of peak orbital frequency */
+ REAL8 deltaT, /**<< Sampling interval */
+ REAL8 eta, /**<< Symmetric mass ratio */
+ REAL8 a, /**<< Normalized spin of deformed-Kerr */
+ EOBNonQCCoeffs *coeffs /**<< OUTPUT, NQC coefficients */);
+
+
+REAL8 XLALSimIMREOBGetNRSpinPeakDeltaT(
+ INT4 l, /**<< Mode l */
+ INT4 m, /**<< Mode m */
+ REAL8 eta, /**<< Symmetric mass ratio */
+ REAL8 a /**<< Dimensionless spin */
+);
+REAL8 GetNRSpinPeakOmega( INT4 l, INT4 m, REAL8 eta, REAL8 a );
+
+REAL8 GetNRSpinPeakOmegaDot( INT4 l, INT4 m, REAL8 eta, REAL8 a );
+
+int XLALSimIMREOBNonQCCorrection(
+ COMPLEX16 *nqc, /**<< OUTPUT, The NQC correction */
+ REAL8Vector *values, /**<< Dynamics r, phi, pr, pphi */
+ const REAL8 omega, /**<< Angular frequency */
+ EOBNonQCCoeffs *coeffs /**<< NQC coefficients */
+);
+
+INT4 XLALGenerateHybridWaveDerivatives (
+ REAL8Vector *rwave, /**<< OUTPUT, values of the waveform at comb points */
+ REAL8Vector *dwave, /**<< OUTPUT, 1st deriv of the waveform at comb points */
+ REAL8Vector *ddwave, /**<< OUTPUT, 2nd deriv of the waveform at comb points */
+ REAL8Vector *timeVec, /**<< Vector containing the time */
+ REAL8Vector *wave, /**<< Last part of inspiral waveform */
+ REAL8Vector *matchrange, /**<< Times which determine the size of the comb */
+ REAL8 dt, /**<< Sample time step */
+ REAL8 mass1, /**<< First component mass (in Solar masses) */
+ REAL8 mass2 /**<< Second component mass (in Solar masses) */
+);
+
+COMPLEX16 XLALSpinWeightedSphericalHarmonic(
+ REAL8 theta, /**< polar angle (rad) */
+ REAL8 phi, /**< azimuthal angle (rad) */
+ int s, /**< spin weight */
+ int l, /**< mode number l */
+ int m /**< mode number m */
+);
+
+int
+CalculateThisMultipolePrefix(
+ COMPLEX16 *prefix, /**<< OUTPUT, Prefix value */
+ const REAL8 m1, /**<< mass 1 */
+ const REAL8 m2, /**<< mass 2 */
+ int l, /**<< Mode l */
+ int m /**<< Mode m */
+);
+int XLALIsREAL8FailNaN(REAL8 val);
+int CartesianToSpherical(
+ REAL8 qSph[], /**<< OUTPUT, position vector in spherical coordinates */
+ REAL8 pSph[], /**<< OUTPUT, momentum vector in Cartesean coordinates */
+ const REAL8 qCart[], /**<< position vector in spherical coordinates */
+ const REAL8 pCart[] /**<< momentum vector in Cartesean coordinates */
+);
+REAL8
+XLALSimIMRSpinAlignedEOBNonKeplerCoeff(
+ const REAL8 values[], /**<< Dynamical variables */
+ SpinEOBParams *funcParams /**<< EOB parameters */
+);
+REAL8 GetNRSpinPeakAmplitude( INT4 l, INT4 m, REAL8 eta, REAL8 a );
+REAL8 GetNRSpinPeakADDot( INT4 l, INT4 m, REAL8 eta, REAL8 a );
+
+COMPLEX16 XLALCOMPLEX16Rect (REAL8 x, REAL8 y);
+double MYlog2(double x);
+double MYcbrt(double x);
+double carg (COMPLEX16 z);
+COMPLEX16 cexp (COMPLEX16 a);
+COMPLEX16 CX16polar(double r,double phi);
+COMPLEX16 MYcpow(COMPLEX16 a,UINT4 n);
+double cabs(COMPLEX16 z);
+
+int XLALSimInspiralChooseTDWaveform(
+ REAL8TimeSeries **hplus, /**< +-polarization waveform */
+ REAL8TimeSeries **hcross, /**< x-polarization waveform */
+ REAL8 phiRef, /**< reference orbital phase (rad) */
+ REAL8 deltaT, /**< sampling interval (s) */
+ REAL8 m1, /**< mass of companion 1 (kg) */
+ REAL8 m2, /**< mass of companion 2 (kg) */
+ REAL8 S1x, /**< x-component of the dimensionless spin of object 1 */
+ REAL8 S1y, /**< y-component of the dimensionless spin of object 1 */
+ REAL8 S1z, /**< z-component of the dimensionless spin of object 1 */
+ REAL8 S2x, /**< x-component of the dimensionless spin of object 2 */
+ REAL8 S2y, /**< y-component of the dimensionless spin of object 2 */
+ REAL8 S2z, /**< z-component of the dimensionless spin of object 2 */
+ REAL8 f_min, /**< starting GW frequency (Hz) */
+ REAL8 e0, /**< eccentricity at starting GW frequency (Hz) */
+ REAL8 r, /**< distance of source (m) */
+ REAL8 i, /**< inclination of source (rad) */
+ char *jobtag
+);
+
+
+int XLALSimSEOBNRE(
+ REAL8TimeSeries **hplus, /**<< OUTPUT, +-polarization waveform */
+ REAL8TimeSeries **hcross, /**<< OUTPUT, x-polarization waveform */
+ const REAL8 phiC, /**<< coalescence orbital phase (rad) */
+ REAL8 deltaT, /**<< sampling time step */
+ const REAL8 m1SI, /**<< mass-1 in SI unit */
+ const REAL8 m2SI, /**<< mass-2 in SI unit */
+ const REAL8 fMin, /**<< starting frequency (Hz) */
+ const REAL8 e0, /**<< eccentricity at starting GW frequency (Hz) */
+ const REAL8 r, /**<< distance in SI unit */
+ const REAL8 inc, /**<< inclination angle */
+ const REAL8 spin1z, /**<< z-component of spin-1, dimensionless */
+ const REAL8 spin2z, /**<< z-component of spin-2, dimensionless */
+ const char *jobtag
+);
+
+INT4 XLALSimIMREOBHybridRingdownWave(
+ REAL8Vector *rdwave1, /**<< OUTPUT, Real part of ringdown waveform */
+ REAL8Vector *rdwave2, /**<< OUTPUT, Imag part of ringdown waveform */
+ const REAL8 dt, /**<< Sampling interval */
+ const REAL8 mass1, /**<< First component mass (in Solar masses) */
+ const REAL8 mass2, /**<< Second component mass (in Solar masses) */
+ REAL8VectorSequence *inspwave1, /**<< Values and derivs of real part inspiral waveform */
+ REAL8VectorSequence *inspwave2, /**<< Values and derivs of imag part inspiral waveform */
+ COMPLEX16Vector *modefreqs, /**<< Complex freqs of ringdown (scaled by total mass) */
+ REAL8Vector *matchrange /**<< Times which determine the comb of ringdown attachment */
+);
+INT4 XLALSimIMREOBHybridAttachRingdown(
+ REAL8Vector *signal1, /**<< OUTPUT, Real of inspiral waveform to which we attach ringdown */
+ REAL8Vector *signal2, /**<< OUTPUT, Imag of inspiral waveform to which we attach ringdown */
+ const INT4 l, /**<< Current mode l */
+ const INT4 m, /**<< Current mode m */
+ const REAL8 dt, /**<< Sample time step (in seconds) */
+ const REAL8 mass1, /**<< First component mass (in Solar masses) */
+ const REAL8 mass2, /**<< Second component mass (in Solar masses) */
+ const REAL8 spin1x, /**<<The spin of the first object; only needed for spin waveforms */
+ const REAL8 spin1y, /**<<The spin of the first object; only needed for spin waveforms */
+ const REAL8 spin1z, /**<<The spin of the first object; only needed for spin waveforms */
+ const REAL8 spin2x, /**<<The spin of the second object; only needed for spin waveforms */
+ const REAL8 spin2y, /**<<The spin of the second object; only needed for spin waveforms */
+ const REAL8 spin2z, /**<<The spin of the second object; only needed for spin waveforms */
+ REAL8Vector *timeVec, /**<< Vector containing the time values */
+ REAL8Vector *matchrange /**<< Time values chosen as points for performing comb matching */
+);
+
+void PNwaveformPRD544813rdotc_22mode(double *hr,double *hi,
+ const double x1,const double x2,const double x3, // test particle position
+ const double v1,const double v2,const double v3, // test particle velocity
+ const double eta); // symmetric mass ratio
diff --git a/SEOBNREv1/DIY_SEOBNRE_main.c b/SEOBNREv1/DIY_SEOBNRE_main.c
new file mode 100755
index 0000000..3564dec
--- /dev/null
+++ b/SEOBNREv1/DIY_SEOBNRE_main.c
@@ -0,0 +1,385 @@
+// $Id: Panyimain.cpp,v 1.1.1.1 2016/12/30 06:03:09 zjcao Exp $
+// Ref PRD 96, 044028 (2017)
+#ifdef newc
+#include <cstdio>
+#include <ctime>
+#include <cstring>
+#include <cstdlib>
+#else
+#include <stdio.h>
+#include <time.h>
+#include <string.h>
+#include <stdlib.h>
+#endif
+#include "DIY_SEOBNRE_ALL.h"
+
+
+int XLALREAL8VectorUnwrapAngle( REAL8Vector *out, const REAL8Vector *in );
+int output_waveform(REAL8TimeSeries * h_plus, REAL8TimeSeries * h_cross, int ampPhase);
+
+const char * usage =
+"Generate a simulation using the lalsimulation library\n\n"
+"The following options can be given (will assume a default value if omitted):\n"
+//"--domain DOM 'TD' for time domain (default) or 'FD' for frequency\n"
+//" domain; not all approximants support all domains\n"
+"--amp-phase If given, will output:\n"
+" |h+ - i hx|, Arg(h+ - i hx) (TD) or\n"
+" |h+(f)|, Arg(h+(f)), |hx(f)|, Arg(hx(f)) (FD)\n"
+" If not given, will output h+ and hx (TD and FD)\n"
+
+" NOTE: Other approximants may be available if the\n"
+" developer forgot to edit this help message\n"
+//"--phase-order ORD Twice PN order of phase (default ORD=7 <==> 3.5PN)\n"
+"--amp-order ORD Twice PN order of amplitude (default 0 <==> Newt.)\n"
+"--phiRef phiRef Phase at the reference frequency (default 0)\n"
+//"--fRef FREF Reference frequency in Hz\n"
+" (default: 0)\n"
+"--sample-rate SRATE Sampling rate of TD approximants in Hz (default 4096)\n"
+//"--deltaF DF Frequency bin size for FD approximants in Hz (default 1/8)\n"
+"--m1 M1 Mass of the 1st object in solar masses (default 10)\n"
+"--m2 M2 Mass of the 2nd object in solar masses (default 1.4)\n"
+"--inclination IOTA Angle in radians between line of sight (N) and \n"
+" orbital angular momentum (L) at the reference\n"
+" (default 0, face on)\n"
+"--spin1x S1X Vector components for spin of mass1 (default all 0)\n"
+"--spin1y S1Y z-axis=line of sight, L in x-z plane at reference\n"
+"--spin1z S1Z Kerr limit: s1x^2 + s1y^2 + s1z^2 <= 1\n"
+"--spin2x S2X Vector components for spin of mass2 (default all 0)\n"
+"--spin2y S2Y z-axis=line of sight, L in x-z plane at reference\n"
+"--spin2z S2Z Kerr limit: s2x^2 + s2y^2 + s2z^2 <= 1\n"
+//"--tidal-lambda1 L1 (tidal deformability of mass 1) / (mass of body 1)^5\n"
+//" (~128-2560 for NS, 0 for BH) (default 0)\n"
+//"--tidal-lambda2 L2 (tidal deformability of mass 2) / (mass of body 2)^5\n"
+//" (~128-2560 for NS, 0 for BH) (default 0)\n"
+//"--spin-order ORD Twice PN order of spin effects\n"
+//" (default ORD=-1 <==> All spin effects)\n"
+//"--tidal-order ORD Twice PN order of tidal effects\n"
+//" (default ORD=-1 <==> All tidal effects)\n"
+"--f-min FMIN Lower frequency to start waveform in Hz (default 40)\n"
+"--f-max FMAX Frequency at which to stop waveform in Hz\n"
+" (default: generate as much as possible)\n"
+"--e0 e0 eccentricity at FMIN (default 0)\n"
+"--distance D Distance in Mpc (default 100)\n"
+//"--axis AXIS for PhenSpin: 'View' (default), 'TotalJ', 'OrbitalL'\n"
+"--output Do not out put to file\n"
+"--outname FNAME Output to file FNAME (default 'simulation.dat')\n"
+"--verbose If included, add verbose output\n"
+"--jobtag If not equal to \"None\", print dynamics as XX_jobtag.txt\n"
+" (default None: no output)\n"
+" Formation: \"time, omega, r, pr, phi, pphi \"\n"
+;
+
+/* Parse command line, sanity check arguments, and return a newly
+ * allocated GSParams object */
+
+GSParams *parse_args(unsigned int argc, char **argv) {
+ unsigned int i;
+ GSParams *params;
+ params = (GSParams *) malloc(sizeof(GSParams));
+ memset(params, 0, sizeof(GSParams));
+
+ /* Set default values to the arguments */
+ params->ampO = 0;
+ params->phiRef = 0.;
+ params->deltaT = 1./4096.;
+ params->m1 = 10 * LAL_MSUN_SI;
+ params->m2 = 1.4 * LAL_MSUN_SI;
+ params->f_min = 40;
+ params->f_max = 0.; /* Generate as much as possible */
+ params->e0 = 0.;
+ params->distance = 100. * 1e6 * LAL_PC_SI;
+ params->inclination = 0.;
+ params->s1x = 0.;
+ params->s1y = 0.;
+ params->s1z = 0.;
+ params->s2x = 0.;
+ params->s2y = 0.;
+ params->s2z = 0.;
+ params->verbose = 0; /* No verbosity */
+ params->output = 1;
+ strncpy(params->outname, "simulation.dat", 256); /* output to this file */
+ params->ampPhase = 0; /* output h+ and hx */
+ strncpy(params->jobtag, "None", 256);
+
+ /* consume command line */
+ for (i = 1; i < argc; ++i) {
+ if ((strcmp(argv[i], "-h") == 0) || (strcmp(argv[i], "--help") == 0)) {
+ goto fail;
+
+ } else if (strcmp(argv[i], "--amp-order") == 0) {
+ params->ampO = atof(argv[++i]);
+ } else if (strcmp(argv[i], "--phiRef") == 0) {
+ params->phiRef = atof(argv[++i]);
+ } else if (strcmp(argv[i], "--sample-rate") == 0) {
+ params->deltaT = 1./atof(argv[++i]);
+ } else if (strcmp(argv[i], "--m1") == 0) {
+ params->m1 = atof(argv[++i]) * LAL_MSUN_SI;
+ } else if (strcmp(argv[i], "--m2") == 0) {
+ params->m2 = atof(argv[++i]) * LAL_MSUN_SI;
+ } else if (strcmp(argv[i], "--spin1x") == 0) {
+ params->s1x = atof(argv[++i]);
+ } else if (strcmp(argv[i], "--spin1y") == 0) {
+ params->s1y = atof(argv[++i]);
+ } else if (strcmp(argv[i], "--spin1z") == 0) {
+ params->s1z = atof(argv[++i]);
+ } else if (strcmp(argv[i], "--spin2x") == 0) {
+ params->s2x = atof(argv[++i]);
+ } else if (strcmp(argv[i], "--spin2y") == 0) {
+ params->s2y = atof(argv[++i]);
+ } else if (strcmp(argv[i], "--spin2z") == 0) {
+ params->s2z = atof(argv[++i]);
+ } else if (strcmp(argv[i], "--f-min") == 0) {
+ params->f_min = atof(argv[++i]);
+ fprintf(stderr,"f_0 = %eHz (%e[1/M])\n", params->f_min,params->f_min*((params->m1+params->m2)/LAL_MSUN_SI*LAL_MTSUN_SI));
+ } else if (strcmp(argv[i], "--f-max") == 0) {
+ params->f_max = atof(argv[++i]);
+ } else if (strcmp(argv[i], "--e0") == 0) {
+ params->e0 = atof(argv[++i]);
+ } else if (strcmp(argv[i], "--distance") == 0) {
+ params->distance = atof(argv[++i]) * 1e6 * LAL_PC_SI;
+ } else if (strcmp(argv[i], "--inclination") == 0) {
+ params->inclination = atof(argv[++i]);
+ } else if (strcmp(argv[i], "--output") == 0 ) {
+ params->output = 0;
+ } else if (strcmp(argv[i], "--outname") == 0) {
+ strncpy(params->outname, argv[++i], 256);
+ } else if (strcmp(argv[i], "--amp-phase") == 0) {
+ params->ampPhase = 1;
+ } else if (strcmp(argv[i], "--verbose") == 0) {
+ params->verbose = 1;
+ } else if (strcmp(argv[i], "--jobtag") == 0) {
+ strncpy(params->jobtag, argv[++i], 256);
+ } else {
+ fprintf(stderr,"Error: invalid option: %s\n", argv[i]);
+ goto fail;
+ }
+ }
+
+ //printf("M=m1+m2=%e(s), M/R=%e\n",(params->m1+params->m2)/LAL_MSUN_SI*LAL_MTSUN_SI,(params->m1+params->m2)/LAL_MSUN_SI*LAL_MRSUN_SI/params->distance);
+
+ return params;
+
+ fail:
+ fprintf(stderr,"%s", usage);
+ exit(1);
+}
+int dump_TD(FILE *f, REAL8TimeSeries *hplus, REAL8TimeSeries *hcross) {
+ size_t i;
+ REAL8 t0 = XLALGPSGetREAL8(&(hplus->epoch));
+ if (hplus->data->length != hcross->data->length) {
+ fprintf(stderr,"Error: hplus and hcross are not the same length\n");
+ return 1;
+ } else if (hplus->deltaT != hcross->deltaT) {
+ fprintf(stderr,"Error: hplus and hcross do not have the same sample rate\n");
+ return 1;
+ }
+
+ fprintf(f, "# t hplus hcross\n");
+ for (i=0; i < hplus->data->length; i++)
+ fprintf(f, "%.16e %.16e %.16e\n", t0 + i * hplus->deltaT,
+ hplus->data->data[i], hcross->data->data[i]);
+
+ return 0;
+}
+
+int dump_convertTD(GSParams *params, REAL8TimeSeries *hplus, REAL8TimeSeries *hcross) {
+ size_t i;
+ if (hplus->data->length != hcross->data->length) {
+ fprintf(stderr, "Error: hplus and hcross are not the same length\n");
+ return 1;
+ } else if (hplus->deltaT != hcross->deltaT) {
+ fprintf(stderr,"Error: hplus and hcross do not have the same sample rate\n");
+ return 1;
+ }
+
+ const REAL8 UM = (params->m1+params->m2)/LAL_MSUN_SI*LAL_MTSUN_SI;
+ const REAL8 UMoR = (params->m1+params->m2)/LAL_MSUN_SI*LAL_MRSUN_SI/params->distance;
+
+ FILE *f;
+ f = fopen(params->outname, "w");
+ fprintf(f, "# t hplus hcross\n");
+ for (i=0; i < hplus->data->length; i++)
+ // convert to [M] for t and [M/R] for h
+ fprintf(f, "%.16e %.16e %.16e\n", (i * hplus->deltaT)/UM,
+ (hplus->data->data[i])/UMoR, (hcross->data->data[i])/UMoR);
+
+ fclose(f);
+
+ return 0;
+}
+
+int main (int argc , char **argv) {
+
+ FILE *f;
+
+ int start_time;
+ REAL8TimeSeries *hplus = NULL;
+ REAL8TimeSeries *hcross = NULL;
+ GSParams *params;
+
+ /* parse commandline */
+ params = parse_args(argc, argv);
+
+ /* generate waveform */
+ start_time = time(NULL);
+
+ // in Panyi_elip.cpp
+ XLALSimInspiralChooseTDWaveform(&hplus, &hcross, params->phiRef,
+ params->deltaT, params->m1, params->m2, params->s1x,
+ params->s1y, params->s1z, params->s2x, params->s2y,
+ params->s2z, params->f_min, params->e0,
+ params->distance, params->inclination, params->jobtag
+ );
+
+ if (params->verbose)
+ fprintf(stderr,"Generation took %.0f seconds\n",
+ difftime(time(NULL), start_time));
+
+ /* dump file */
+ if(params->output)
+ {
+ f = fopen(params->outname, "w");
+ dump_TD(f, hplus, hcross);
+ fclose(f);
+ }
+ else
+ {
+ output_waveform(hplus, hcross, params->ampPhase);
+ }
+
+ return 1;
+}
+
+int output_waveform(REAL8TimeSeries * h_plus, REAL8TimeSeries * h_cross, int ampPhase)
+{
+ double t0, t_end;
+ int j;
+ t0 = XLALGPSGetREAL8(&(h_plus->epoch));
+ t_end = t0 + (h_plus->data->length - 1) * h_plus->deltaT;
+ if (ampPhase)
+ {
+ REAL8Vector *amp;
+ REAL8Vector *phi;
+ amp->length = h_plus->data->length;
+ phi->length = h_plus->data->length;
+ double phi0;
+
+ for (j = 0; j < h_plus->data->length; ++j)
+ {
+ double complex z = h_plus->data->data[j] - I * h_cross->data->data[j];
+ amp->data[j] = cabs(z);
+ phi->data[j] = carg(z);
+ }
+
+ XLALREAL8VectorUnwrapAngle(phi, phi);
+
+ phi0 = 2 * phi->data[phi->length - 1] - phi->data[phi->length - 2];
+ phi0 -= fmod(phi0 + copysign(LAL_PI, phi0), 2.0 * LAL_PI) - copysign(LAL_PI, phi0);
+ for ( j = 0; j < phi->length; ++j )
+ phi->data[j] -= phi0;
+
+ fprintf(stdout, " # time (s)\th_abs (strain)\t h_arg (rad)\n ");
+ for ( j=0; j < h_plus->data->length; ++j )
+ fprintf(stdout, "%.9f\t%e\t%e\n", t0 + j * h_plus->deltaT, amp->data[j], phi->data[j] );
+
+ XLALDestroyREAL8Vector(phi);
+ XLALDestroyREAL8Vector(amp);
+ } else
+ {
+ fprintf(stdout, "# time (s)\th_+ (strain)\th_x (strain)\n" );
+ for ( j=0; j < h_plus->data->length; ++j )
+ fprintf(stdout, "%.9f\t%e\t%e\n" , t0 + j * h_plus->deltaT, h_plus->data->data[j], h_cross->data->data[j] );
+ }
+ return 0;
+}
+
+int XLALREAL8VectorUnwrapAngle( REAL8Vector *out, const REAL8Vector *in )
+{
+ REAL8 prev;
+ REAL8 diff;
+ INT4 wrap;
+ UINT4 i;
+ if ( ! out || ! in )
+ return XLAL_EFAULT;
+ if ( ! out->data || ! in->data || in->length == 0 )
+ return XLAL_EINVAL;
+ if ( out->length != in->length )
+ return XLAL_EBADLEN;
+ wrap = 0;
+ prev = out->data[0] = in->data[0];
+ for ( i = 1; i < in->length; ++i ) {
+ diff = in->data[i] - prev;
+ prev = in->data[i];
+ wrap += (diff < -LAL_PI) - (diff > LAL_PI);
+ out->data[i] = in->data[i] + wrap * LAL_TWOPI;
+ }
+ return 0;
+}
+
+int XLALSimInspiralChooseTDWaveform(
+ REAL8TimeSeries **hplus, /**< +-polarization waveform */
+ REAL8TimeSeries **hcross, /**< x-polarization waveform */
+ REAL8 phiRef, /**< reference orbital phase (rad) */
+ REAL8 deltaT, /**< sampling interval (s) */
+ REAL8 m1, /**< mass of companion 1 (kg) */
+ REAL8 m2, /**< mass of companion 2 (kg) */
+ REAL8 S1x, /**< x-component of the dimensionless spin of object 1 */
+ REAL8 S1y, /**< y-component of the dimensionless spin of object 1 */
+ REAL8 S1z, /**< z-component of the dimensionless spin of object 1 */
+ REAL8 S2x, /**< x-component of the dimensionless spin of object 2 */
+ REAL8 S2y, /**< y-component of the dimensionless spin of object 2 */
+ REAL8 S2z, /**< z-component of the dimensionless spin of object 2 */
+ REAL8 f_min, /**< starting GW frequency (Hz) */
+ REAL8 e0, /**< eccentricity at starting GW frequency (Hz) */
+ REAL8 r, /**< distance of source (m) */
+ REAL8 i, /**< inclination of source (rad) */
+ char *jobtag
+)
+{
+
+ int ret;
+ /* N.B. the quadrupole of a spinning compact body labeled by A is
+ * Q_A = - quadparam_A chi_A^2 m_A^3 (see gr-qc/9709032)
+ * where quadparam = 1 for BH ~= 4-8 for NS.
+ * This affects the quadrupole-monopole interaction.
+ * For now, hardcode quadparam1,2 = 1.
+ * Will later add ability to set via LALSimInspiralTestGRParam
+ */
+ REAL8 v0 = 1., quadparam1 = 1., quadparam2 = 1.;
+
+ /* General sanity checks that will abort */
+ /*
+ * If non-GR approximants are added, change the below to
+ * if( nonGRparams && approximant != nonGR1 && approximant != nonGR2 )
+ */
+
+ /* General sanity check the input parameters - only give warnings! */
+ if( deltaT > 1. )
+ fprintf(stderr,"XLAL Warning - : Large value of deltaT = %e requested.\nPerhaps sample rate and time step size were swapped?\n", deltaT);
+ if( deltaT < 1./16385. )
+ fprintf(stderr,"XLAL Warning - : Small value of deltaT = %e requested.\nCheck for errors, this could create very large time series.\n", deltaT);
+ if( m1 < 0.09 * LAL_MSUN_SI )
+ fprintf(stderr,"XLAL Warning - : Small value of m1 = %e (kg) = %e (Msun) requested.\nPerhaps you have a unit conversion error?\n", m1, m1/LAL_MSUN_SI);
+ if( m2 < 0.09 * LAL_MSUN_SI )
+ fprintf(stderr,"XLAL Warning - : Small value of m2 = %e (kg) = %e (Msun) requested.\nPerhaps you have a unit conversion error?\n", m2, m2/LAL_MSUN_SI);
+ if( m1 + m2 > 1000. * LAL_MSUN_SI )
+ fprintf(stderr,"XLAL Warning - : Large value of total mass m1+m2 = %e (kg) = %e (Msun) requested.\nSignal not likely to be in band of ground-based detectors.\n", m1+m2, (m1+m2)/LAL_MSUN_SI);
+ if( S1x*S1x + S1y*S1y + S1z*S1z > 1.000001 )
+ fprintf(stderr,"XLAL Warning - : S1 = (%e,%e,%e) with norm > 1 requested.\nAre you sure you want to violate the Kerr bound?\n", S1x, S1y, S1z);
+ if( S2x*S2x + S2y*S2y + S2z*S2z > 1.000001 )
+ fprintf(stderr,"XLAL Warning - : S2 = (%e,%e,%e) with norm > 1 requested.\nAre you sure you want to violate the Kerr bound?\n", S2x, S2y, S2z);
+ if( f_min < 1. )
+ fprintf(stderr,"XLAL Warning - : Small value of fmin = %e requested.\nCheck for errors, this could create a very long waveform.\n",f_min);
+ if( f_min > 40.000001 )
+ fprintf(stderr,"XLAL Warning - : Large value of fmin = %e requested.\nCheck for errors, the signal will start in band.\n", f_min);
+ if( e0 < 0 || e0 > 1 )
+ fprintf(stderr,"XLAL Warning - : unphysical e0 = %e.\n", e0);
+
+
+
+ /* Call the waveform driver routine */
+ ret = XLALSimSEOBNRE(hplus, hcross, phiRef,
+ deltaT, m1, m2, f_min, e0, r, i, S1z, S2z, jobtag); // in current file
+
+ return ret;
+}
diff --git a/SEOBNREv1/LALSimSEOBNRE_DIY.c b/SEOBNREv1/LALSimSEOBNRE_DIY.c
new file mode 100755
index 0000000..baa6475
--- /dev/null
+++ b/SEOBNREv1/LALSimSEOBNRE_DIY.c
@@ -0,0 +1,8566 @@
+// $Id: Panyicomm_elip.cpp,v 1.1.1.1 2017/09/25 02:35:55 zjcao Exp $
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_multiroots.h>
+#include <gsl/gsl_integration.h>
+#include <gsl/gsl_sf_gamma.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_deriv.h>
+#include <gsl/gsl_errno.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_interp.h>
+#include <gsl/gsl_spline.h>
+#include "DIY_SEOBNRE_ALL.h"
+
+#ifdef newc
+#include <complex>
+#include <iostream>
+#include <iomanip>
+#include <fstream>
+#include <cstdlib>
+#include <cstdarg>
+#include <cstring>
+#include <cmath>
+using namespace std;
+#else
+#include <complex.h>
+#include <stdlib.h>
+#include <stdarg.h>
+#include <string.h>
+#include <math.h>
+#endif
+
+#define debugOutput 0
+#define outputh22 1
+#define outputOmega 1
+/* Function Declaration */
+
+const LALUnit lalStrainUnit = {{ 0, 0, 0, 0, 0, 1, 0}, { 0, 0, 0, 0, 0, 0, 0} }; /**< Strain [1] */
+
+
+void PNwaveformPRD544813rdotc_22mode(double *hr,double *hi,
+ const double x1,const double x2,const double x3, // test particle position
+ const double v1,const double v2,const double v3, // test particle velocity
+ const double eta) // symmetric mass ratio
+{
+ const double dm = sqrt(1-4*eta);
+ double r = sqrt(x1*x1+x2*x2+x3*x3);
+ double n1 = x1/r,n2 = x2/r,n3 = x3/r;
+ double rdot = v1*n1+v2*n2+v3*n3;
+ double vsqr = v1*v1+v2*v2+v3*v3;
+
+ double vn1,vn2,vn3;
+ vn1 = rdot*n1;
+ vn2 = rdot*n2;
+ vn3 = rdot*n3;
+ double lambda1,lambda2,lambda3;
+ lambda1 = v1-vn1;
+ lambda2 = v2-vn2;
+ lambda3 = v3-vn3;
+ double ln = sqrt(lambda1*lambda1+lambda2*lambda2+lambda3*lambda3);
+ lambda1 = lambda1/ln;
+ lambda2 = lambda2/ln;
+ lambda3 = lambda3/ln;
+
+ double complex hm22;
+
+ double complex h11,h12,h13,h22,h23,h33;
+ double complex Q11,Q12,Q13,Q22,Q23,Q33;
+
+ ///////////////////////////////////////00 part///////////////////////////////////////
+ Q11 = sqrt(M_PI/5)/3;
+ Q12 = -sqrt(M_PI/5)/3*I;
+ Q13 = 0;
+ Q22 = -sqrt(M_PI/5)/3;
+ Q23 = 8/sqrt(5*M_PI)/3;
+ Q33 = 0;
+
+ h11 = 0;
+ h12 = 0;
+ h13 = 0;
+ h22 = 0;
+ h23 = 0;
+ h33 = 0;
+
+ h11 += 1.0/3*(2/r*rdot*(5+3*eta)*(n1*v1+v1*n1)+(3*(1-3*eta)*rdot*rdot)/r*n1*n1);
+ h12 += 1.0/3*(2/r*rdot*(5+3*eta)*(n1*v2+v1*n2)+(3*(1-3*eta)*rdot*rdot)/r*n1*n2);
+ h13 += 1.0/3*(2/r*rdot*(5+3*eta)*(n1*v3+v1*n3)+(3*(1-3*eta)*rdot*rdot)/r*n1*n3);
+ h22 += 1.0/3*(2/r*rdot*(5+3*eta)*(n2*v2+v2*n2)+(3*(1-3*eta)*rdot*rdot)/r*n2*n2);
+ h23 += 1.0/3*(2/r*rdot*(5+3*eta)*(n2*v3+v2*n3)+(3*(1-3*eta)*rdot*rdot)/r*n2*n3);
+ h33 += 1.0/3*(2/r*rdot*(5+3*eta)*(n3*v3+v3*n3)+(3*(1-3*eta)*rdot*rdot)/r*n3*n3);
+
+ hm22 = Q11*h11+Q22*h22+Q33*h33+2.*(Q12*h12+Q13*h13+Q23*h23);
+
+ ///////////////////////////////////////10 part///////////////////////////////////////
+ Q11 = 0;
+ Q12 = 0;
+ Q13 = -sqrt(M_PI/5)*(x1 - I*x2)/(3.*r);
+ Q22 = 0;
+ Q23 = sqrt(M_PI/5)*(I*x1 + x2)/(3.*r);
+ Q33 = 0;
+
+ h11 = dm*3/r*(-rdot*n1*n1);
+ h12 = dm*3/r*(-rdot*n1*n2);
+ h13 = dm*3/r*(-rdot*n1*n2);
+ h22 = dm*3/r*(-rdot*n2*n2);
+ h23 = dm*3/r*(-rdot*n2*n3);
+ h33 = dm*3/r*(-rdot*n3*n3);
+
+ h11 += dm/12/r*((n1*v1+v1*n1)*(rdot*rdot*(63+54*eta))
+ +n1*n1*rdot*(rdot*rdot*(15-90*eta)-vsqr*(63-54*eta)+(242-24*eta)/r)-rdot*v1*v1*(186+24*eta));
+ h12 += dm/12/r*((n1*v2+v1*n2)*(rdot*rdot*(63+54*eta))
+ +n1*n2*rdot*(rdot*rdot*(15-90*eta)-vsqr*(63-54*eta)+(242-24*eta)/r)-rdot*v1*v2*(186+24*eta));
+ h13 += dm/12/r*((n1*v3+v1*n3)*(rdot*rdot*(63+54*eta))
+ +n1*n3*rdot*(rdot*rdot*(15-90*eta)-vsqr*(63-54*eta)+(242-24*eta)/r)-rdot*v1*v3*(186+24*eta));
+ h22 += dm/12/r*((n2*v2+v2*n2)*(rdot*rdot*(63+54*eta))
+ +n2*n2*rdot*(rdot*rdot*(15-90*eta)-vsqr*(63-54*eta)+(242-24*eta)/r)-rdot*v2*v2*(186+24*eta));
+ h23 += dm/12/r*((n2*v3+v2*n3)*(rdot*rdot*(63+54*eta))
+ +n2*n3*rdot*(rdot*rdot*(15-90*eta)-vsqr*(63-54*eta)+(242-24*eta)/r)-rdot*v2*v3*(186+24*eta));
+ h33 += dm/12/r*((n3*v3+v3*n3)*(rdot*rdot*(63+54*eta))
+ +n3*n3*rdot*(rdot*rdot*(15-90*eta)-vsqr*(63-54*eta)+(242-24*eta)/r)-rdot*v3*v3*(186+24*eta));
+
+ hm22 += Q11*h11+Q22*h22+Q33*h33+2.*(Q12*h12+Q13*h13+Q23*h23);
+
+ ///////////////////////////////////////01 part///////////////////////////////////////
+ Q11 = 0;
+ Q12 = 0;
+ Q13 = -sqrt(M_PI/5)*(v1 - I*v2)/3.;
+ Q22 = 0;
+ Q23 = sqrt(M_PI/5)*(I*v1 + v2)/3.;
+ Q33 = 0;
+
+ h11 = 0;
+ h12 = 0;
+ h13 = 0;
+ h22 = 0;
+ h23 = 0;
+ h33 = 0;
+
+ h11 += dm*(-(n1*v1+v1*n1)/2/r*rdot*(7+4*eta)
+ -n1*n1/r*(0.75*(1-2*eta)*rdot*rdot));
+ h12 += dm*(-(n1*v2+v1*n2)/2/r*rdot*(7+4*eta)
+ -n1*n2/r*(0.75*(1-2*eta)*rdot*rdot));
+ h13 += dm*(-(n1*v3+v1*n3)/2/r*rdot*(7+4*eta)
+ -n1*n3/r*(0.75*(1-2*eta)*rdot*rdot));
+ h22 += dm*(-(n2*v2+v2*n2)/2/r*rdot*(7+4*eta)
+ -n2*n2/r*(0.75*(1-2*eta)*rdot*rdot));
+ h23 += dm*(-(n2*v3+v2*n3)/2/r*rdot*(7+4*eta)
+ -n2*n3/r*(0.75*(1-2*eta)*rdot*rdot));
+ h33 += dm*(-(n3*v3+v3*n3)/2/r*rdot*(7+4*eta)
+ -n3*n3/r*(0.75*(1-2*eta)*rdot*rdot));
+
+ hm22 += Q11*h11+Q22*h22+Q33*h33+2.*(Q12*h12+Q13*h13+Q23*h23);
+
+ ///////////////////////////////////////20 part///////////////////////////////////////
+ Q11 = -sqrt(M_PI/5)*(x1*x1-8.*I*x1*x2-7*x2*x2-x3*x3)/21./r/r;
+ Q12 = -I*sqrt(M_PI/5)*(3*(x1*x1+x2*x2)+x3*x3)/21./r/r;
+ Q13 = 2*sqrt(M_PI/5)*(x1-I*x2)*x3/21./r/r;
+ Q22 = sqrt(M_PI/5)*(-7*x1*x1+8.*I*x1*x2+x2*x2-x3*x3)/21./r/r;
+ Q23 = -2.*I*sqrt(M_PI/5)*(x1-I*x2)*x3/21./r/r;
+ Q33 = 8*sqrt(M_PI/5)*pow(x1-I*x2,2)/21./r/r;
+
+ h11 = (1-3*eta)/3/r*((-15*rdot*rdot)*n1*n1+15*rdot*(n1*v1+v1*n1));
+ h12 = (1-3*eta)/3/r*((-15*rdot*rdot)*n1*n2+15*rdot*(n1*v2+v1*n2));
+ h13 = (1-3*eta)/3/r*((-15*rdot*rdot)*n1*n3+15*rdot*(n1*v3+v1*n3));
+ h22 = (1-3*eta)/3/r*((-15*rdot*rdot)*n2*n2+15*rdot*(n2*v2+v2*n2));
+ h23 = (1-3*eta)/3/r*((-15*rdot*rdot)*n2*n3+15*rdot*(n2*v3+v2*n3));
+ h33 = (1-3*eta)/3/r*((-15*rdot*rdot)*n3*n3+15*rdot*(n3*v3+v3*n3));
+
+ hm22 += Q11*h11+Q22*h22+Q33*h33+2.*(Q12*h12+Q13*h13+Q23*h23);
+
+ ///////////////////////////////////////11 part///////////////////////////////////////
+ Q11 = sqrt(M_PI/5)*(-v1*x1+4.*I*v2*x1+4.*I*v1*x2+7*v2*x2+v3*x3)/21./r;
+ Q12 = -I*sqrt(M_PI/5)*(3*v1*x1+3*v2*x2+v3*x3)/21./r;
+ Q13 = sqrt(M_PI/5)*(v3*(x1-I*x2)+x3*(v1-I*v2))/21./r;
+ Q22 = sqrt(M_PI/5)*(-7*v1*x1+4.*I*v2*x1+4.*I*v1*x2+v2*x2-v3*x3)/21./r;
+ Q23 = -sqrt(M_PI/5)*(v3*(I*x1+x2)+x3*(I*v1+v2))/21./r;
+ Q33 = 8*sqrt(M_PI/5)*(v1-I*v2)*(x1-I*x2)/21./r;
+
+ h11 = (1-3*eta)/3/r*(12*rdot*n1*n1);
+ h12 = (1-3*eta)/3/r*(12*rdot*n1*n2);
+ h13 = (1-3*eta)/3/r*(12*rdot*n1*n3);
+ h22 = (1-3*eta)/3/r*(12*rdot*n2*n2);
+ h23 = (1-3*eta)/3/r*(12*rdot*n2*n3);
+ h33 = (1-3*eta)/3/r*(12*rdot*n3*n3);
+
+ hm22 += Q11*h11+Q22*h22+Q33*h33+2.*(Q12*h12+Q13*h13+Q23*h23);
+
+ ///////////////////////////////////////02 part///////////////////////////////////////
+ Q11 = sqrt(M_PI/5)*(-v1*v1+8.*I*v1*v2+7*v2*v2+v3*v3)/21.;
+ Q12 = -I*sqrt(M_PI/5)*(3*(v1*v1+v2*v2)+v3*v3)/21.;
+ Q13 = 2*sqrt(M_PI/5)*(v1-I*v2)*v3/21.;
+ Q22 = sqrt(M_PI/5)*(-7*v1*v1+8.*I*v1*v2+v2*v2-v3*v3)/21.;
+ Q23 = -2.*I*sqrt(M_PI/5)*(v1-I*v2)*v3/21.;
+ Q33 = 8*sqrt(M_PI/5)*pow(v1-I*v2,2)/21.;
+
+ h11 = 0;
+ h12 = 0;
+ h13 = 0;
+ h22 = 0;
+ h23 = 0;
+ h33 = 0;
+
+ hm22 += Q11*h11+Q22*h22+Q33*h33+2.*(Q12*h12+Q13*h13+Q23*h23);
+
+ ///////////////////////////////////////30 part///////////////////////////////////////
+ Q11 = sqrt(M_PI/5)*pow(x1-I*x2,2)*x3/7./r/r/r;
+ Q12 = 0;
+ Q13 = -sqrt(M_PI/5)*(x1-I*x2)*(2.*x1*x1+5.*I*x1*x2+7*x2*x2+3*x3*x3)/21./r/r/r;
+ Q22 = sqrt(M_PI/5)*pow(x1-I*x2,2)*x3/7./r/r/r;
+ Q23 = sqrt(M_PI/5)*(I*x1+x2)*(7*x1*x1-5.*I*x1*x2+2*x2*x2+3*x3*x3)/21./r/r/r;
+ Q33 = -2*sqrt(M_PI/5)*pow(x1-I*x2,2)*x3/7./r/r/r;
+
+ h11 = dm*(1-2*eta)/r*(1.25*(3*vsqr-7*rdot*rdot+6/r)*rdot*n1*n1-8.5*rdot*v1*v1-(-105*rdot*rdot)/12*(n1*v1+v1*n1));
+ h12 = dm*(1-2*eta)/r*(1.25*(3*vsqr-7*rdot*rdot+6/r)*rdot*n1*n2-8.5*rdot*v1*v2-(-105*rdot*rdot)/12*(n1*v2+v1*n2));
+ h13 = dm*(1-2*eta)/r*(1.25*(3*vsqr-7*rdot*rdot+6/r)*rdot*n1*n3-8.5*rdot*v1*v3-(-105*rdot*rdot)/12*(n1*v3+v1*n3));
+ h22 = dm*(1-2*eta)/r*(1.25*(3*vsqr-7*rdot*rdot+6/r)*rdot*n2*n2-8.5*rdot*v2*v2-(-105*rdot*rdot)/12*(n2*v2+v2*n2));
+ h23 = dm*(1-2*eta)/r*(1.25*(3*vsqr-7*rdot*rdot+6/r)*rdot*n2*n3-8.5*rdot*v2*v3-(-105*rdot*rdot)/12*(n2*v3+v2*n3));
+ h33 = dm*(1-2*eta)/r*(1.25*(3*vsqr-7*rdot*rdot+6/r)*rdot*n3*n3-8.5*rdot*v3*v3-(-105*rdot*rdot)/12*(n3*v3+v3*n3));
+
+ hm22 += Q11*h11+Q22*h22+Q33*h33+2.*(Q12*h12+Q13*h13+Q23*h23);
+
+ ///////////////////////////////////////21 part///////////////////////////////////////
+ Q11 = sqrt(M_PI/5)*(x1-I*x2)*(v3*(x1-I*x2)+2.*(v1-I*v2)*x3)/21./r/r;
+ Q12 = 0;
+ Q13 = -sqrt(M_PI/5)*((x1-I*x2)*(2*v1*x1+I*x1*v2+4.*I*v1*x2+7*x2*v2)+2*v3*(x1-I*x2)*x3+(v1-I*v2)*x3*x3)/21./r/r;
+ Q22 = sqrt(M_PI/5)*(x1-I*x2)*(v3*(x1-I*x2)+2.*(v1-I*v2)*x3)/21./r/r;
+ Q23 = sqrt(M_PI/5)*((x1-I*x2)*(v2*(4*x1+2.*I*x2)+v1*(7.*I*x1+x2))+2*v3*(I*x1+x2)*x3+(I*v1+v2)*x3*x3)/21./r/r;
+ Q33 = -2*sqrt(M_PI/5)*(x1-I*x2)*(v3*(x1-I*x2)+2.*(v1-I*v2)*x3)/21./r/r;
+
+ h11 = dm*(1-2*eta)/4/r*((45*rdot*rdot)*n1*n1-54*rdot*(n1*v1+v1*n1));
+ h12 = dm*(1-2*eta)/4/r*((45*rdot*rdot)*n1*n2-54*rdot*(n1*v2+v1*n2));
+ h13 = dm*(1-2*eta)/4/r*((45*rdot*rdot)*n1*n3-54*rdot*(n1*v3+v1*n3));
+ h22 = dm*(1-2*eta)/4/r*((45*rdot*rdot)*n2*n2-54*rdot*(n2*v2+v2*n2));
+ h23 = dm*(1-2*eta)/4/r*((45*rdot*rdot)*n2*n3-54*rdot*(n2*v3+v2*n3));
+ h33 = dm*(1-2*eta)/4/r*((45*rdot*rdot)*n3*n3-54*rdot*(n3*v3+v3*n3));
+
+ hm22 += Q11*h11+Q22*h22+Q33*h33+2.*(Q12*h12+Q13*h13+Q23*h23);
+
+ ///////////////////////////////////////12 part///////////////////////////////////////
+ Q11 = sqrt(M_PI/5)*(v1-I*v2)*(2*v3*(x1-I*x2)+(v1-I*v2)*x3)/21./r;
+ Q12 = 0;
+ Q13 = -sqrt(M_PI/5)*(v3*v3*(x1-I*x2)+v1*v1*(2*x1+I*x2)+v2*v2*(4*x1-7.*I*x2)-2.*I*v2*v3*x3+2*v1*(I*v2*x1+4*v2*x2+v3*x3))/21./r;
+ Q22 = sqrt(M_PI/5)*(v1-I*v2)*(2*v3*(x1-I*x2)+(v1-I*v2)*x3)/21./r;
+ Q23 = sqrt(M_PI/5)*(v3*v3*(I*x1+x2)+v2*v2*(-I*x1+2*x2)+v1*v1*(7.*I*x1+4*x2)+2*v2*v3*x3+v1*(8*v2*x1-2.*I*v2*x2+2.*I*v3*x3))/21./r;
+ Q33 = -2*sqrt(M_PI/5)*(v1-I*v2)*(2*v3*(x1-I*x2)+(v1-I*v2)*x3)/21./r;
+
+ h11 = dm*(1-2*eta)*1.5/r*(-3*rdot*n1*n1);
+ h12 = dm*(1-2*eta)*1.5/r*(-3*rdot*n1*n2);
+ h13 = dm*(1-2*eta)*1.5/r*(-3*rdot*n1*n3);
+ h22 = dm*(1-2*eta)*1.5/r*(-3*rdot*n2*n2);
+ h23 = dm*(1-2*eta)*1.5/r*(-3*rdot*n2*n3);
+ h33 = dm*(1-2*eta)*1.5/r*(-3*rdot*n3*n3);
+
+ hm22 += Q11*h11+Q22*h22+Q33*h33+2.*(Q12*h12+Q13*h13+Q23*h23);
+
+ ///////////////////////////////////////03 part///////////////////////////////////////
+ Q11 = sqrt(M_PI/5)*pow(v1-I*v2,2)*v3/7.;
+ Q12 = 0;
+ Q13 = -sqrt(M_PI/5)*(v1-I*v2)*(2*v1*v1+5.*I*v1*v2+7*v2*v2+3*v3*v3)/21.;
+ Q22 = sqrt(M_PI/5)*pow(v1-I*v2,2)*v3/7.;
+ Q23 = sqrt(M_PI/5)*(I*v1+v2)*(7*v1*v1-5.*I*v1*v2+2*v2*v2+3*v3*v3)/21.;
+ Q33 = -2*sqrt(M_PI/5)*pow(v1-I*v2,2)*v3/7.;
+
+ h11 = 0;
+ h12 = 0;
+ h13 = 0;
+ h22 = 0;
+ h23 = 0;
+ h33 = 0;
+
+ hm22 += Q11*h11+Q22*h22+Q33*h33+2.*(Q12*h12+Q13*h13+Q23*h23);
+ //-----------------------------------complete-----------------------------------------
+
+ hm22 = hm22*2.*eta;
+ *hr = creal(hm22);
+ *hi = cimag(hm22);
+ //exit(0);
+}
+
+
+
+
+
+/**��Ҫ�ļ��������
+ * This function generates spin-aligned SEOBNRv1 waveforms h+ and hx.
+ * Currently, only the h22 harmonic is available.
+ * STEP 0) Prepare parameters, including pre-computed coefficients
+ * for EOB Hamiltonian, flux and waveform
+ * STEP 1) Solve for initial conditions
+ * STEP 2) Evolve EOB trajectory until reaching the peak of orbital frequency
+ * STEP 3) Step back in time by tStepBack and volve EOB trajectory again
+ * using high sampling rate, stop at 0.3M out of the "EOB horizon".
+ * STEP 4) Locate the peak of orbital frequency for NQC and QNM calculations
+ * STEP 5) Calculate NQC correction using hi-sampling data
+ * STEP 6) Calculate QNM excitation coefficients using hi-sampling data
+ * STEP 7) Generate full inspiral waveform using desired sampling frequency
+ * STEP 8) Generate full IMR modes -- attaching ringdown to inspiral
+ * STEP 9) Generate full IMR hp and hx waveforms
+ */
+int XLALSimSEOBNRE(
+ REAL8TimeSeries **hplus, /**<< OUTPUT, +-polarization waveform */
+ REAL8TimeSeries **hcross, /**<< OUTPUT, x-polarization waveform */
+ const REAL8 phiC, /**<< coalescence orbital phase (rad) */
+ REAL8 deltaT, /**<< sampling time step */
+ const REAL8 m1SI, /**<< mass-1 in SI unit */
+ const REAL8 m2SI, /**<< mass-2 in SI unit */
+ const REAL8 fMin, /**<< starting frequency (Hz) */
+ const REAL8 e0, /**<< eccentricity at starting GW frequency (Hz) */
+ const REAL8 r, /**<< distance in SI unit */
+ const REAL8 inc, /**<< inclination angle */
+ const REAL8 spin1z, /**<< z-component of spin-1, dimensionless */
+ const REAL8 spin2z, /**<< z-component of spin-2, dimensionless */
+ const char *jobtag
+)
+{
+ /* If either spin > 0.6, model not available, exit */
+ if ( spin1z > 0.6 || spin2z > 0.6 )
+ {
+ fprintf(stderr, "XLAL Error -: Component spin larger than 0.6!\nSEOBNRv1 is only available for spins in the range -1 < a/M < 0.6.\n");
+ }
+
+ int i;
+
+ REAL8Vector *values = NULL;
+ REAL8 fini = fMin;
+ /* elip correction for initial frequency */
+ fini /= pow(1-e0*e0, 1.5);
+
+ /* EOB spin vectors used in the Hamiltonian */
+ REAL8Vector *sigmaStar = NULL;
+ REAL8Vector *sigmaKerr = NULL;
+ REAL8 a;
+ REAL8 chiS, chiA;
+
+ /* Wrapper spin vectors used to calculate sigmas */
+ REAL8Vector s1Vec;
+ REAL8Vector s2Vec;
+ REAL8 spin1[3] = {0, 0, spin1z};
+ REAL8 spin2[3] = {0, 0, spin2z};
+ REAL8 s1Data[3], s2Data[3];
+
+ /* Parameters of the system */
+ REAL8 m1, m2, mTotal, eta, mTScaled;
+ REAL8 amp0;
+ REAL8 sSub = 0.0;
+ LIGOTimeGPS tc = { 0, 0 };
+
+ /* Dynamics of the system */
+ REAL8Vector rVec, phiVec, prVec, pPhiVec;
+ REAL8 omega, v, ham;
+
+ /* Cartesian vectors needed to calculate Hamiltonian */
+ REAL8Vector cartPosVec, cartMomVec;
+ REAL8 cartPosData[3], cartMomData[3];
+
+ /* Signal mode */
+ COMPLEX16 hLM;
+ REAL8Vector *sigReVec = NULL, *sigImVec = NULL;
+
+ /* Non-quasicircular correction */
+ EOBNonQCCoeffs nqcCoeffs;
+ COMPLEX16 hNQC;
+ REAL8Vector *ampNQC = NULL, *phaseNQC = NULL;
+
+ /* Ringdown freq used to check the sample rate */
+ COMPLEX16Vector modefreqVec;
+ COMPLEX16 modeFreq;
+
+ /* Spin-weighted spherical harmonics */
+ COMPLEX16 MultSphHarmP;
+ COMPLEX16 MultSphHarmM;
+
+ /* We will have to switch to a high sample rate for ringdown attachment */
+ REAL8 deltaTHigh;
+ UINT4 resampFac;
+ UINT4 resampPwr;
+ REAL8 resampEstimate;
+
+ /* How far will we have to step back to attach the ringdown? */
+ REAL8 tStepBack;
+ int nStepBack;
+
+ /* Dynamics and details of the high sample rate part used to attach the ringdown */
+ UINT4 hiSRndx;
+ REAL8Vector timeHi, rHi, phiHi, prHi, pPhiHi;
+ REAL8Vector *sigReHi = NULL, *sigImHi = NULL;
+ REAL8Vector *omegaHi = NULL;
+
+ /* Indices of peak frequency and final point */
+ /* Needed to attach ringdown at the appropriate point */
+ UINT4 peakIdx = 0, finalIdx = 0;
+
+ /* (2,2) and (2,-2) spherical harmonics needed in (h+,hx) */
+ REAL8 y_1, y_2, z1, z2;
+
+ /* Variables for the integrator */
+ ark4GSLIntegrator *integrator = NULL;
+ REAL8Array *dynamics = NULL;
+ REAL8Array *dynamicsHi = NULL;
+ int retLen;
+
+
+ /* Accuracies of adaptive Runge-Kutta integrator */
+ const REAL8 EPS_ABS = 1.0e-10;
+ const REAL8 EPS_REL = 1.0e-9;
+
+ /**
+ * STEP 0) Prepare parameters, including pre-computed coefficients
+ * for EOB Hamiltonian, flux and waveform
+ */
+
+ /* Parameter structures containing important parameters for the model */
+ SpinEOBParams seobParams;
+ SpinEOBHCoeffs seobCoeffs;
+ EOBParams eobParams;
+ FacWaveformCoeffs hCoeffs;
+ NewtonMultipolePrefixes prefixes;
+
+ /* Initialize parameters */
+ m1 = m1SI / LAL_MSUN_SI;
+ m2 = m2SI / LAL_MSUN_SI;
+ mTotal = m1 + m2;
+ mTScaled = mTotal * LAL_MTSUN_SI;
+ eta = m1 * m2 / (mTotal*mTotal);
+
+ amp0 = mTotal * LAL_MRSUN_SI / r;
+
+ /* TODO: Insert potentially necessary checks on the arguments */
+
+ /* Calculate the time we will need to step back for ringdown */
+ tStepBack = 50. * mTScaled;
+ nStepBack = ceil( tStepBack / deltaT );
+
+ /* Calculate the resample factor for attaching the ringdown */
+ /* We want it to be a power of 2 */
+ /* If deltaT > Mtot/50, reduce deltaT by the smallest power of two for which deltaT < Mtot/50 */
+ resampEstimate = 50. * deltaT / mTScaled;
+ resampFac = 1;
+ //resampFac = 1 << (UINT4)ceil(MYlog2(resampEstimate));
+
+ if ( resampEstimate > 1. )
+ {
+ resampPwr = (UINT4)ceil( MYlog2( resampEstimate ) );
+ while ( resampPwr-- )
+ {
+ resampFac *= 2u;
+ }
+ }
+
+
+ /* Allocate the values vector to contain the initial conditions */
+ /* Since we have aligned spins, we can use the 4-d vector as in the non-spin case */
+ if ( !(values = XLALCreateREAL8Vector( 4 )) )
+ {
+ return 0;
+ }
+ memset ( values->data, 0, values->length * sizeof( REAL8 ));
+
+ /* Set up structures and calculate necessary PN parameters */
+ /* Unlike the general case, we only need to calculate these once */
+ memset( &seobParams, 0, sizeof(seobParams) );
+ memset( &seobCoeffs, 0, sizeof(seobCoeffs) );
+ memset( &eobParams, 0, sizeof(eobParams) );
+ memset( &hCoeffs, 0, sizeof( hCoeffs ) );
+ memset( &prefixes, 0, sizeof( prefixes ) );
+
+ /* Before calculating everything else, check sample freq is high enough */
+ modefreqVec.length = 1;
+ modefreqVec.data = &modeFreq;
+
+ if ( XLALSimIMREOBGenerateQNMFreqV2_re( &modefreqVec, m1, m2, spin1, spin2, 2, 2, 1) == -1 )
+ {
+ XLALDestroyREAL8Vector( values );
+ return -1;
+ }
+
+
+ /* If Nyquist freq < 220 QNM freq, exit */
+ if ( deltaT > LAL_PI / creal(modeFreq) )
+ {
+ fprintf( stderr,"XLAL Error -: Ringdown frequency > Nyquist frequency = %f!\nAt present this situation is not supported.\n", LAL_PI / creal(modeFreq));
+ XLALDestroyREAL8Vector( values );
+ return -1;
+ }
+
+ if ( !(sigmaStar = XLALCreateREAL8Vector( 3 )) )
+ {
+ XLALDestroyREAL8Vector( values );
+ return -1;
+ }
+
+ if ( !(sigmaKerr = XLALCreateREAL8Vector( 3 )) )
+ {
+ XLALDestroyREAL8Vector( sigmaStar );
+ XLALDestroyREAL8Vector( values );
+ return -1;
+ }
+
+ seobParams.alignedSpins = 1;
+ seobParams.tortoise = 1;
+ seobParams.sigmaStar = sigmaStar;
+ seobParams.sigmaKerr = sigmaKerr;
+ seobParams.seobCoeffs = &seobCoeffs;
+ seobParams.eobParams = &eobParams;
+ seobParams.Spin1 = XLALCreateREAL8Vector( 3 );
+ seobParams.Spin2 = XLALCreateREAL8Vector( 3 );
+ eobParams.hCoeffs = &hCoeffs;
+ eobParams.prefixes = &prefixes;
+
+ eobParams.m1 = m1;
+ eobParams.m2 = m2;
+ eobParams.eta = eta;
+
+ s1Vec.length = s2Vec.length = 3;
+ s1Vec.data = s1Data;
+ s2Vec.data = s2Data;
+
+ /* copy the spins into the appropriate vectors, and scale them by the mass */
+ memcpy( s1Data, spin1, sizeof( s1Data ) );
+ memcpy( s2Data, spin2, sizeof( s2Data ) );
+
+ /* Calculate chiS and chiA */
+
+
+ chiS = 0.5 * (spin1[2] + spin2[2]);
+ chiA = 0.5 * (spin1[2] - spin2[2]);
+
+ for( i = 0; i < 3; i++ )
+ {
+ s1Data[i] *= m1*m1;
+ s2Data[i] *= m2*m2;
+ }
+
+ cartPosVec.length = cartMomVec.length = 3;
+ cartPosVec.data = cartPosData;
+ cartMomVec.data = cartMomData;
+ memset( cartPosData, 0, sizeof( cartPosData ) );
+ memset( cartMomData, 0, sizeof( cartMomData ) );
+
+ /* Populate the initial structures */
+ if ( XLALSimIMRSpinEOBCalculateSigmaStar( sigmaStar, m1, m2, &s1Vec, &s2Vec ) == -1 )
+ {
+ XLALDestroyREAL8Vector( sigmaKerr );
+ XLALDestroyREAL8Vector( sigmaStar );
+ XLALDestroyREAL8Vector( values );
+ return -1;
+ }
+
+ if ( XLALSimIMRSpinEOBCalculateSigmaKerr( sigmaKerr, m1, m2, &s1Vec, &s2Vec ) == -1 )
+ {
+ XLALDestroyREAL8Vector( sigmaKerr );
+ XLALDestroyREAL8Vector( sigmaStar );
+ XLALDestroyREAL8Vector( values );
+ return -1;
+ }
+
+ /* Calculate the value of a */
+ /* XXX I am assuming that, since spins are aligned, it is okay to just use the z component XXX */
+ /* TODO: Check this is actually the way it works in LAL */
+ a = 0.0;
+ /*for ( i = 0; i < 3; i++ )
+ {
+ a += sigmaKerr->data[i]*sigmaKerr->data[i];
+ }
+ a = sqrt( a );*/
+ seobParams.a = a = sigmaKerr->data[2];
+ /* a set to zero in SEOBNRv1, didn't know yet a good mapping from two physical spins to the test-particle limit Kerr spin */
+ if ( XLALSimIMREOBCalcSpinFacWaveformCoefficients( &hCoeffs, m1, m2, eta, /*a*/0.0, chiS, chiA ) == -1 )
+ {
+ XLALDestroyREAL8Vector( sigmaKerr );
+ XLALDestroyREAL8Vector( sigmaStar );
+ XLALDestroyREAL8Vector( values );
+ return -1;
+ }
+
+ if ( XLALSimIMREOBComputeNewtonMultipolePrefixes( &prefixes, eobParams.m1, eobParams.m2 )
+ == -1 )
+ {
+ XLALDestroyREAL8Vector( sigmaKerr );
+ XLALDestroyREAL8Vector( sigmaStar );
+ XLALDestroyREAL8Vector( values );
+ return -1;
+ }
+
+ /**
+ * STEP 1) Solve for initial conditions
+ */
+
+ /* Set the initial conditions. For now we use the generic case */
+ /* Can be simplified if spin-aligned initial conditions solver available. The cost of generic code is negligible though. */
+ REAL8Vector *tmpValues = XLALCreateREAL8Vector( 14 );
+ if ( !tmpValues )
+ {
+ XLALDestroyREAL8Vector( sigmaKerr );
+ XLALDestroyREAL8Vector( sigmaStar );
+ XLALDestroyREAL8Vector( values );
+ return -1;
+ }
+
+ memset( tmpValues->data, 0, tmpValues->length * sizeof( REAL8 ) );
+
+ /* We set inc zero here to make it easier to go from Cartesian to spherical coords */
+ /* No problem setting inc to zero in solving spin-aligned initial conditions. */
+ /* inc is not zero in generating the final h+ and hx */
+ if ( XLALSimIMRSpinEOBInitialConditions( tmpValues, m1, m2, fini, e0, 0, s1Data, s2Data, &seobParams ) == XLAL_FAILURE )
+ {
+ XLALDestroyREAL8Vector( tmpValues );
+ XLALDestroyREAL8Vector( sigmaKerr );
+ XLALDestroyREAL8Vector( sigmaStar );
+ XLALDestroyREAL8Vector( values );
+ return -1;
+ }
+
+ /*fprintf( stderr, "ICs = %.16e %.16e %.16e %.16e %.16e %.16e %.16e %.16e %.16e %.16e %.16e %.16e\n", tmpValues->data[0], tmpValues->data[1], tmpValues->data[2],
+ tmpValues->data[3], tmpValues->data[4], tmpValues->data[5], tmpValues->data[6], tmpValues->data[7], tmpValues->data[8],
+ tmpValues->data[9], tmpValues->data[10], tmpValues->data[11] );*/
+
+ /* Taken from Andrea's code */
+ /* memset( tmpValues->data, 0, tmpValues->length*sizeof(tmpValues->data[0]));*/
+ /*
+ tmpValues->data[0] = 12.983599142327673;
+ tmpValues->data[3] = -0.002383249720459786;
+ tmpValues->data[4] = 4.3204065947459735/tmpValues->data[0];
+ */
+ /* Now convert to Spherical */
+ /* The initial conditions code returns Cartesian components of four vectors x, p, S1 and S2,
+ * in the special case that the binary starts on the x-axis and the two spins are aligned
+ * with the orbital angular momentum along the z-axis.
+ * Therefore, in spherical coordinates the initial conditions are
+ * r = x; phi = 0.; pr = px; pphi = r * py.
+ */
+ values->data[0] = tmpValues->data[0];
+ values->data[1] = 0.;
+ values->data[2] = tmpValues->data[3];
+ values->data[3] = tmpValues->data[0] * tmpValues->data[4];
+
+ //fprintf( stderr, "Spherical initial conditions: %e %e %e %e\n", values->data[0], values->data[1], values->data[2], values->data[3] );
+
+ /* Now compute the spinning H coefficients and store them in seobCoeffs */
+ if ( XLALSimIMRCalculateSpinEOBHCoeffs( &seobCoeffs, eta, a ) == -1 )
+ {
+ XLALDestroyREAL8Vector( tmpValues );
+ XLALDestroyREAL8Vector( sigmaKerr );
+ XLALDestroyREAL8Vector( sigmaStar );
+ XLALDestroyREAL8Vector( values );
+ return -1;
+ }
+
+ /**
+ * STEP 2) Evolve EOB trajectory until reaching the peak of orbital frequency
+ */
+
+ /* Now we have the initial conditions, we can initialize the adaptive integrator */
+ /* XLALAdaptiveRungeKutta4Init is in Panyicomm_elip.cpp */
+ /* XLALSpinAlignedHcapDerivative is in Panyicomm_elip.cpp */
+ /* XLALEOBSpinAlignedStopCondition is in Panyicomm_elip.cpp */
+ if (!(integrator = XLALAdaptiveRungeKutta4Init(4, XLALSpinAlignedHcapDerivative, XLALEOBSpinAlignedStopCondition, EPS_ABS, EPS_REL)))
+ {
+ XLALDestroyREAL8Vector( values );
+ }
+
+ integrator->stopontestonly = 1;
+ integrator->retries = 1;
+
+ retLen = XLALAdaptiveRungeKutta4( integrator, &seobParams, values->data, 0., 20./mTScaled, deltaT/mTScaled, &dynamics );
+#if debugOutput
+ fprintf(stderr, "DEBUG:retLen=%d\n", retLen);
+#endif
+ if ( retLen == XLAL_FAILURE )
+ {
+ fprintf(stderr,"Error!");
+ }
+
+ /* Set up pointers to the dynamics */
+ rVec.length = phiVec.length = prVec.length = pPhiVec.length = retLen;
+ rVec.data = dynamics->data+retLen;
+ phiVec.data = dynamics->data+2*retLen;
+ prVec.data = dynamics->data+3*retLen;
+ pPhiVec.data = dynamics->data+4*retLen;
+
+ //printf( "We think we hit the peak at time %e\n", dynamics->data[retLen-1] );
+ //fprintf(stderr, "r0 = %.16e pphi0 = %.16e\n", rVec.data[i], pPhiVec.data[i]);
+ /* TODO : Insert high sampling rate / ringdown here */
+#if 0
+ FILE *out = fopen( "dynamics_v1_debug.txt", "w" );
+ for ( i = 0; i < retLen - nStepBack; i++ )
+ {
+ fprintf( out, "%.16e %.16e %.16e %.16e %.16e\n", dynamics->data[i], rVec.data[i], phiVec.data[i], prVec.data[i], pPhiVec.data[i] );
+ }
+ fclose(out);
+#endif
+ /**
+ * STEP 3) Step back in time by tStepBack and volve EOB trajectory again
+ * using high sampling rate, stop at 0.3M out of the "EOB horizon".
+ */
+
+ /* Set up the high sample rate integration */
+ hiSRndx = retLen - nStepBack;
+ deltaTHigh = deltaT / (REAL8)resampFac;
+#if debugOutput
+ fprintf(stderr, "DEBUG:hiSRndx=%d\n", hiSRndx);
+ fprintf(stderr, "DEBUG:deltaTHigh=%f\n", deltaTHigh);
+#endif
+ /*fprintf( stderr, "Stepping back %d points - we expect %d points at high SR\n", nStepBack, nStepBack*resampFac );
+ fprintf( stderr, "Commencing high SR integration... from %.16e %.16e %.16e %.16e %.16e\n",
+ (dynamics->data)[hiSRndx],rVec.data[hiSRndx], phiVec.data[hiSRndx], prVec.data[hiSRndx], pPhiVec.data[hiSRndx] );*/
+
+ values->data[0] = rVec.data[hiSRndx];
+ values->data[1] = phiVec.data[hiSRndx];
+ values->data[2] = prVec.data[hiSRndx];
+ values->data[3] = pPhiVec.data[hiSRndx];
+ /* For HiSR evolution, we stop at a radius 0.3M from the deformed Kerr singularity,
+ * or when any derivative of Hamiltonian becomes nan */
+ integrator->stop = XLALSpinAlignedHiSRStopCondition;
+
+ retLen = XLALAdaptiveRungeKutta4( integrator, &seobParams, values->data, 0., 20./mTScaled, deltaTHigh/mTScaled, &dynamicsHi );
+#if debugOutput
+ fprintf(stderr, "DEBUG:retLen=%d\n", retLen);
+#endif
+ if ( retLen == XLAL_FAILURE )
+ {
+ fprintf(stderr,"Error!");
+ }
+
+ //fprintf( stderr, "We got %d points at high SR\n", retLen );
+
+ /* Set up pointers to the dynamics */
+ rHi.length = phiHi.length = prHi.length = pPhiHi.length = timeHi.length = retLen;
+ timeHi.data = dynamicsHi->data;
+ rHi.data = dynamicsHi->data+retLen;
+ phiHi.data = dynamicsHi->data+2*retLen;
+ prHi.data = dynamicsHi->data+3*retLen;
+ pPhiHi.data = dynamicsHi->data+4*retLen;
+
+#if debugOutput
+ FILE *out1 = fopen( "dynamicsHi_v1.txt", "w" );
+ for ( i = 0; i < retLen; i++ )
+ {
+ fprintf( out1 , "%.16e %.16e %.16e %.16e %.16e\n", dynamics->data[hiSRndx]+timeHi.data[i], rHi.data[i], phiHi.data[i], prHi.data[i], pPhiHi.data[i] );
+ }
+ fclose(out1);
+#endif
+ //printf("retLen = %d\n", retLen);
+ /* Allocate the high sample rate vectors */
+ sigReHi = XLALCreateREAL8Vector( retLen + (UINT4)ceil( 20 / ( cimag(modeFreq) * deltaTHigh )) );
+ sigImHi = XLALCreateREAL8Vector( retLen + (UINT4)ceil( 20 / ( cimag(modeFreq) * deltaTHigh )) );
+ omegaHi = XLALCreateREAL8Vector( retLen + (UINT4)ceil( 20 / ( cimag(modeFreq) * deltaTHigh )) );
+ ampNQC = XLALCreateREAL8Vector( retLen );
+ phaseNQC = XLALCreateREAL8Vector( retLen );
+
+ if ( !sigReHi || !sigImHi || !omegaHi || !ampNQC || !phaseNQC )
+ {
+ //XLAL_ERROR( XLAL_ENOMEM );
+ fprintf(stderr,"Error!");
+ }
+
+ memset( sigReHi->data, 0, sigReHi->length * sizeof( sigReHi->data[0] ));
+ memset( sigImHi->data, 0, sigImHi->length * sizeof( sigImHi->data[0] ));
+
+ /* Populate the high SR waveform */
+ REAL8 omegaOld = 0.0;
+ INT4 phaseCounter = 0;
+
+ for ( i = 0; i < retLen; i++ )
+ {
+ values->data[0] = rHi.data[i];
+ values->data[1] = phiHi.data[i];
+ values->data[2] = prHi.data[i];
+ values->data[3] = pPhiHi.data[i];
+
+ omegaHi->data[i] = omega = XLALSimIMRSpinAlignedEOBCalcOmega( values->data, &seobParams );
+
+ v = MYcbrt( omega );
+
+ /* Calculate the value of the Hamiltonian */
+ cartPosVec.data[0] = values->data[0];
+ cartMomVec.data[0] = values->data[2];
+ cartMomVec.data[1] = values->data[3] / values->data[0];
+
+ ham = XLALSimIMRSpinEOBHamiltonian( eta, &cartPosVec, &cartMomVec, sigmaKerr, sigmaStar, seobParams.tortoise, &seobCoeffs );
+
+ if ( XLALSimIMRSpinEOBGetSpinFactorizedWaveform( &hLM, values, v, ham, 2, 2, &seobParams )
+ == XLAL_FAILURE )
+ {
+ /* TODO: Clean-up */
+ fprintf(stderr,"Error!");
+ }
+
+ ampNQC->data[i] = cabs( hLM );
+ sigReHi->data[i] = (REAL4)(amp0 * creal(hLM));
+ sigImHi->data[i] = (REAL4)(amp0 * cimag(hLM));
+ phaseNQC->data[i]= carg( hLM ) + phaseCounter * LAL_TWOPI;
+
+ if ( i && phaseNQC->data[i] > phaseNQC->data[i-1] )
+ {
+ phaseCounter--;
+ phaseNQC->data[i] -= LAL_TWOPI;
+ }
+
+ if ( omega <= omegaOld && !peakIdx )
+ {
+
+ peakIdx = i;
+ }
+ omegaOld = omega;
+ }
+
+
+
+ //printf( "We now think the peak is at %d\n", peakIdx );
+ finalIdx = retLen - 1;
+#if debugOutput
+ fprintf(stderr, "DEBUG:peakIdx=%d\n", peakIdx);
+#endif
+ /**
+ * STEP 4) Locate the peak of orbital frequency for NQC and QNM calculations
+ */
+
+ /* Stuff to find the actual peak time */
+ gsl_spline *spline = NULL;
+ gsl_interp_accel *acc = NULL;
+ REAL8 omegaDeriv1; //, omegaDeriv2;
+ REAL8 time1, time2;
+ REAL8 timePeak, timewavePeak = 0., omegaDerivMid;
+ REAL8 sigAmpSqHi = 0., oldsigAmpSqHi = 0.;
+ INT4 peakCount = 0;
+
+ spline = gsl_spline_alloc( gsl_interp_cspline, retLen );
+ acc = gsl_interp_accel_alloc();
+
+ time1 = dynamicsHi->data[peakIdx];
+
+ gsl_spline_init( spline, dynamicsHi->data, omegaHi->data, retLen );
+ omegaDeriv1 = gsl_spline_eval_deriv( spline, time1, acc );
+ if ( omegaDeriv1 > 0. )
+ {
+ time2 = dynamicsHi->data[peakIdx+1];
+ //omegaDeriv2 = gsl_spline_eval_deriv( spline, time2, acc );
+ }
+ else
+ {
+ //omegaDeriv2 = omegaDeriv1;
+ time2 = time1;
+ time1 = dynamicsHi->data[peakIdx-1];
+ peakIdx--;
+ omegaDeriv1 = gsl_spline_eval_deriv( spline, time1, acc );
+ }
+#if debugOutput
+ fprintf(stderr, "DEBUG:time1=%f, time2=%f\n", time1, time2);
+#endif
+ do
+ {
+ timePeak = ( time1 + time2 ) / 2.;
+ omegaDerivMid = gsl_spline_eval_deriv( spline, timePeak, acc );
+
+ if ( omegaDerivMid * omegaDeriv1 < 0.0 )
+ {
+ //omegaDeriv2 = omegaDerivMid;
+ time2 = timePeak;
+ }
+ else
+ {
+ omegaDeriv1 = omegaDerivMid;
+ time1 = timePeak;
+ }
+ }
+ while ( time2 - time1 > 1.0e-5 );
+#if debugOutput
+ fprintf(stderr, "DEBUG:omegaDeriv1=%f\n", omegaDeriv1);
+ fprintf(stderr, "DEBUG:timePeak=%f\n", timePeak);
+#endif
+ /*gsl_spline_free( spline );
+ gsl_interp_accel_free( acc );
+ */
+
+
+ //printf( "Estimation of the peak is now at time %.16e\n", timePeak );
+
+ /* Having located the peak of orbital frequency, we set time and phase of coalescence */
+ XLALGPSAdd( &tc, -mTScaled * (dynamics->data[hiSRndx] + timePeak));
+ gsl_spline_init( spline, dynamicsHi->data, phiHi.data, retLen );
+#if 1
+ sSub = gsl_spline_eval( spline, timePeak, acc ) - phiC;
+#else
+ sSub = -phiC;
+#endif
+ gsl_spline_free( spline );
+ gsl_interp_accel_free( acc );
+ /* Apply phiC to hi-sampling waveforms */
+ REAL8 thisReHi, thisImHi;
+ REAL8 csSub2 = cos(2.0 * sSub);
+ REAL8 ssSub2 = sin(2.0 * sSub);
+ for ( i = 0; i < retLen; i++)
+ {
+ thisReHi = sigReHi->data[i];
+ thisImHi = sigImHi->data[i];
+ sigReHi->data[i] = thisReHi * csSub2 - thisImHi * ssSub2; //set the phase of waveform at peak orbital frequancy as 0, C*exp(i 2*sSub)
+ sigImHi->data[i] = thisReHi * ssSub2 + thisImHi * csSub2;
+ }
+
+ /**
+ * STEP 5) Calculate NQC correction using hi-sampling data
+ */
+
+ /* Calculate nonspin and amplitude NQC coefficients from fits and interpolation table */
+#if debugOutput
+ fprintf
+ (stderr,"NQC should be 0 here: a1=%.16e, a2=%.16e\na3= %.16e,a3S= %.16e\na4= %.16e, a5= %.16e\nb1= %.16e,b2= %.16e\nb3= %.16e, b4= %.16e\n",
+ nqcCoeffs.a1, nqcCoeffs.a2, nqcCoeffs.a3, nqcCoeffs.a3S, nqcCoeffs.a4,
+ nqcCoeffs.a5, nqcCoeffs.b1, nqcCoeffs.b2, nqcCoeffs.b3, nqcCoeffs.b4);
+ fprintf (stderr,"timePeak %.16e\n", timePeak);
+#endif
+
+ if ( XLALSimIMRGetEOBCalibratedSpinNQC( &nqcCoeffs, 2, 2, eta, a ) == XLAL_FAILURE )
+ {
+ fprintf(stderr,"Error(%d)", XLAL_EFUNC );
+ }
+
+ /* Calculate phase NQC coefficients */
+ if ( XLALSimIMRSpinEOBCalculateNQCCoefficients( ampNQC, phaseNQC, &rHi, &prHi, omegaHi,
+ 2, 2, timePeak, deltaTHigh/mTScaled, eta, a, &nqcCoeffs ) == XLAL_FAILURE )
+ {
+ fprintf(stderr,"Error(%d)", XLAL_EFUNC );
+ }
+#if debugOutput
+ fprintf
+ (stderr, "Only spin NQC should be 0 here:a1= %.16e, a2= %.16e\na3= %.16e, a3S= %.16e\na4= %.16e, a5= %.16e\nb1= %.16e, b2= %.16e\nb3= %.16e, b4= %.16e\n",
+ nqcCoeffs.a1, nqcCoeffs.a2, nqcCoeffs.a3, nqcCoeffs.a3S, nqcCoeffs.a4,
+ nqcCoeffs.a5, nqcCoeffs.b1, nqcCoeffs.b2, nqcCoeffs.b3, nqcCoeffs.b4);
+#endif
+
+ /* Calculate the time of amplitude peak. Despite the name, this is in fact the shift in peak time from peak orb freq time */
+ timewavePeak = XLALSimIMREOBGetNRSpinPeakDeltaT(2, 2, eta, a);
+#if debugOutput
+ fprintf(stderr, "DEBUG:timewavePeak=%f\n", timewavePeak);
+#endif
+ /* Apply to the high sampled part */
+ //out = fopen( "saWavesHi.dat", "w" );
+ for ( i = 0; i < retLen; i++ )
+ {
+ values->data[0] = rHi.data[i];
+ values->data[1] = phiHi.data[i] - sSub;
+ values->data[2] = prHi.data[i];
+ values->data[3] = pPhiHi.data[i];
+
+ //printf("NQCs entering hNQC: %.16e, %.16e, %.16e, %.16e, %.16e, %.16e\n", nqcCoeffs.a1, nqcCoeffs.a2,nqcCoeffs.a3, nqcCoeffs.a3S, nqcCoeffs.a4, nqcCoeffs.a5 );
+ if ( XLALSimIMREOBNonQCCorrection( &hNQC, values, omegaHi->data[i], &nqcCoeffs ) == XLAL_FAILURE )
+ {
+ fprintf(stderr,"Error(%d)", XLAL_EFUNC );
+ }
+
+ hLM = sigReHi->data[i];
+ hLM += I * sigImHi->data[i];
+ //fprintf( out, "%.16e %.16e %.16e %.16e %.16e\n", timeHi.data[i], hLM.re, hLM.im, hNQC.re, hNQC.im );
+
+ hLM *= hNQC;
+ //if ( l == 2 && m == 2 ) elliptic correction
+ {
+ double r,phi,pr,pphi,rdot,phidot;
+ values->data[1] += sSub;
+ r = values->data[0];
+ phi = values->data[1];
+ pr = values->data[2];
+ pphi = values->data[3];
+ double dydt[4],ttmp=0;
+ XLALSpinAlignedHcapDerivative(ttmp, values->data, dydt, &seobParams);
+ values->data[1] -= sSub;
+ rdot = dydt[0];
+ phidot = dydt[1];
+
+ double x1,x2,x3;
+ x1 = r*cos(phi);
+ x2 = r*sin(phi);
+ x3 = 0;
+ double v1,v2,v3;
+ v1 = rdot*cos(phi)-r*phidot*sin(phi);
+ v2 = rdot*sin(phi)+r*phidot*cos(phi);
+ v3 = 0;
+
+ double hp,hc;
+ PNwaveformPRD544813rdotc_22mode(&hp,&hc,x1,x2,x3,v1,v2,v3,eta);
+
+ hLM = hLM*exp(-I*2.0*sSub);
+#if 1
+ hLM += amp0*(hp+I*hc);
+#else
+ hLM += amp0*(hp+I*hc)/cabs(hNQC); // relax by hNQC for late inspiral
+#endif
+ hLM = hLM*exp(I*2.0*sSub);
+ }
+ sigReHi->data[i] = (REAL4) creal(hLM);
+ sigImHi->data[i] = (REAL4) cimag(hLM);
+ sigAmpSqHi = creal(hLM)*creal(hLM)+cimag(hLM)*cimag(hLM);
+ if (sigAmpSqHi < oldsigAmpSqHi && peakCount == 0 && (i-1)*deltaTHigh/mTScaled < timePeak - timewavePeak)
+ {
+ timewavePeak = (i-1)*deltaTHigh/mTScaled;
+ peakCount += 1;
+ }
+ oldsigAmpSqHi = sigAmpSqHi;
+ }
+#if 0
+ fclose(out);
+#endif
+#if debugOutput
+ fprintf(stderr, "DEBUG:timewavePeak=%f, peakCount=%d\n", timewavePeak, peakCount);
+#endif
+ if (timewavePeak < 1.0e-16 || peakCount == 0 )
+ {
+#if debugOutput
+ fprintf(stderr,"YP::warning: could not locate mode peak, use calibrated time shift of amplitude peak instead.\n");
+#endif
+ /* NOTE: instead of looking for the actual peak, use the calibrated value, */
+ /* ignoring the error in using interpolated NQC instead of iterated NQC */
+ timewavePeak = timePeak - timewavePeak;
+ }
+
+ /**
+ * STEP 6) Calculate QNM excitation coefficients using hi-sampling data
+ */
+
+ /*out = fopen( "saInspWaveHi.dat", "w" );
+ for ( i = 0; i < retLen; i++ )
+ {
+ fprintf( out, "%.16e %.16e %.16e\n", timeHi.data[i], sigReHi->data[i], sigImHi->data[i] );
+ }
+ fclose( out );*/
+
+ /* Attach the ringdown at the time of amplitude peak */
+ REAL8 combSize = 7.5; /* Eq. 34 */
+ REAL8 timeshiftPeak;
+ timeshiftPeak = timePeak - timewavePeak;
+
+ //printf("YP::timePeak and timewavePeak: %.16e and %.16e\n",timePeak,timewavePeak);
+
+ REAL8Vector *rdMatchPoint = XLALCreateREAL8Vector( 3 );
+ if ( !rdMatchPoint )
+ {
+ fprintf(stderr,"Error(%d)", XLAL_ENOMEM );
+ }
+
+ if ( combSize > timePeak - timeshiftPeak )
+ {
+ fprintf( stderr,"The comb size looks to be too big!!!\n" );
+ }
+
+ rdMatchPoint->data[0] = combSize < timePeak - timeshiftPeak ? timePeak - timeshiftPeak - combSize : 0;
+ rdMatchPoint->data[1] = timePeak - timeshiftPeak;
+ rdMatchPoint->data[2] = dynamicsHi->data[finalIdx];
+#if 0
+ fprintf( out, "#match to inspiral at t = %.16e (%.16e)\n", dynamics->data[hiSRndx]+rdMatchPoint->data[1],rdMatchPoint->data[1]);
+ fclose( out );
+#endif
+ //printf("Get combine range: [%.5f, %.5f], now let's attach ringdown...\n", rdMatchPoint->data[0], rdMatchPoint->data[1]);
+ //XLALSimIMREOBHybridAttachRingdown locates in the current file
+ if ( XLALSimIMREOBHybridAttachRingdown( sigReHi, sigImHi, 2, 2,
+ deltaTHigh, m1, m2, spin1[0], spin1[1], spin1[2], spin2[0], spin2[1], spin2[2],
+ &timeHi, rdMatchPoint)
+ == XLAL_FAILURE )
+ {
+
+ fprintf(stderr,"Error(%d)", XLAL_EFUNC );
+ }
+
+ /**
+ * STEP 7) Generate full inspiral waveform using desired sampling frequency
+ */
+
+ /* Now create vectors at the correct sample rate, and compile the complete waveform */
+ sigReVec = XLALCreateREAL8Vector( rVec.length + (UINT4)ceil( sigReHi->length / (double)resampFac ) );
+ sigImVec = XLALCreateREAL8Vector( sigReVec->length );
+
+ memset( sigReVec->data, 0, sigReVec->length * sizeof( REAL8 ) );
+ memset( sigImVec->data, 0, sigImVec->length * sizeof( REAL8 ) );
+
+ /* Generate full inspiral waveform using desired sampling frequency */
+ /* TODO - Check vectors were allocated */
+
+ REAL8Vector *omegaPrint = NULL, *rVecPrint = NULL, *phiVecPrint = NULL, *prVecPrint = NULL, *pPhiVecPrint = NULL;
+ REAL8Vector *timePrint = NULL;
+ omegaPrint = XLALCreateREAL8Vector( (INT4)rVec.length );
+ rVecPrint = XLALCreateREAL8Vector( (INT4)rVec.length );
+ phiVecPrint = XLALCreateREAL8Vector( (INT4)rVec.length );
+ prVecPrint = XLALCreateREAL8Vector( (INT4)rVec.length );
+ pPhiVecPrint = XLALCreateREAL8Vector( (INT4)rVec.length );
+ timePrint = XLALCreateREAL8Vector( (INT4)rVec.length );
+ double t_ini;
+ t_ini = XLALGPSGetREAL8(&tc);
+
+ for ( i = 0; i < (INT4)rVec.length; i++ )
+ {
+ rVecPrint->data[i] = values->data[0] = rVec.data[i];
+ phiVecPrint->data[i] = values->data[1] = phiVec.data[i] - sSub;
+ prVecPrint->data[i] = values->data[2] = prVec.data[i];
+ pPhiVecPrint->data[i] = values->data[3] = pPhiVec.data[i];
+
+ omegaPrint->data[i] = omega = XLALSimIMRSpinAlignedEOBCalcOmega( values->data, &seobParams );
+ timePrint->data[i] = i * deltaT;
+ v = MYcbrt( omega );
+
+ /* Calculate the value of the Hamiltonian */
+ cartPosVec.data[0] = values->data[0];
+ cartMomVec.data[0] = values->data[2];
+ cartMomVec.data[1] = values->data[3] / values->data[0];
+
+ ham = XLALSimIMRSpinEOBHamiltonian( eta, &cartPosVec, &cartMomVec, sigmaKerr, sigmaStar, seobParams.tortoise, &seobCoeffs );
+
+ // printf("%f,%f,%f,%f\n",values->data[0],values->data[1],values->data[2],values->data[3]); exit(0);
+
+ if ( XLALSimIMRSpinEOBGetSpinFactorizedWaveform( &hLM, values, v, ham, 2, 2, &seobParams )
+ == XLAL_FAILURE )
+ {
+ /* TODO: Clean-up */
+ fprintf(stderr,"Error(%d)", XLAL_EFUNC );
+ }
+
+ if ( XLALSimIMREOBNonQCCorrection( &hNQC, values, omega, &nqcCoeffs ) == XLAL_FAILURE )
+ {
+ fprintf(stderr,"Error(%d)", XLAL_EFUNC );
+ }
+
+ hLM *= hNQC;
+
+ sigReVec->data[i] = amp0 * creal(hLM);
+ sigImVec->data[i] = amp0 * cimag(hLM);
+ }
+
+ // Print out dynamics to file XXX_v1_jobtag.txt....
+ if (strcmp(jobtag, "None") != 0)
+ {
+ char dynamicout[256];
+ sprintf(dynamicout, "%s%s%s", "dynamic_v1_", jobtag, ".txt");
+ FILE *out1 = fopen( dynamicout, "w" );
+ for ( i = 0; i < (INT4)rVec.length; i++ )
+ {
+ // time, omega, r, pr, phi, pphi
+ fprintf( out1 , "%.16e %.16e %.16e %.16e %.16e %.16e\n",timePrint->data[i] + t_ini , omegaPrint->data[i] ,rVecPrint->data[i], prVecPrint->data[i], phiVecPrint->data[i], pPhiVecPrint->data[i]);
+ }
+ fclose(out1);
+ }
+ XLALDestroyREAL8Vector(omegaPrint);
+ XLALDestroyREAL8Vector(timePrint);
+ XLALDestroyREAL8Vector(rVecPrint);
+ XLALDestroyREAL8Vector(prVecPrint);
+ XLALDestroyREAL8Vector(phiVecPrint);
+ XLALDestroyREAL8Vector(pPhiVecPrint);
+ //mTScaled*(timeHi.data[i]-(dynamics->data[hiSRndx] + timePeak))
+
+ /**
+ * STEP 8) Generate full IMR modes -- attaching ringdown to inspiral
+ */
+
+ /* Attach the ringdown part to the inspiral */
+ for ( i = 0; i < (INT4)(sigReHi->length / resampFac); i++ )
+ {
+ sigReVec->data[i+hiSRndx] = sigReHi->data[i*resampFac]; // right hand side include high resolution inspiral and ringdown
+ sigImVec->data[i+hiSRndx] = sigImHi->data[i*resampFac];
+ }
+
+ /**
+ * STEP 9) Generate full IMR hp and hx waveforms
+ */
+
+ /* For now, let us just try to create a waveform */
+ REAL8TimeSeries *hPlusTS = XLALCreateREAL8TimeSeries( "H_PLUS", &tc, 0.0, deltaT, &lalStrainUnit, sigReVec->length );
+ REAL8TimeSeries *hCrossTS = XLALCreateREAL8TimeSeries( "H_CROSS", &tc, 0.0, deltaT, &lalStrainUnit, sigImVec->length );
+
+ /* TODO change to using XLALSimAddMode function to combine modes */
+ /* For now, calculate -2Y22 * h22 + -2Y2-2 * h2-2 directly (all terms complex) */
+ /* Compute spin-weighted spherical harmonics and generate waveform */
+ REAL8 coa_phase = 0.0;
+
+ MultSphHarmP = XLALSpinWeightedSphericalHarmonic( inc, coa_phase, -2, 2, 2 ); // -2Y22(inc, coa_phase)
+ MultSphHarmM = XLALSpinWeightedSphericalHarmonic( inc, coa_phase, -2, 2, -2 ); // -2Y2-2(inc, coa_phase)
+
+ y_1 = creal(MultSphHarmP) + creal(MultSphHarmM);
+ y_2 = cimag(MultSphHarmM) - cimag(MultSphHarmP) ;
+ z1 = - cimag(MultSphHarmM) - cimag(MultSphHarmP) ;
+ z2 = creal(MultSphHarmM) - creal(MultSphHarmP);
+
+ for ( i = 0; i < (INT4)sigReVec->length; i++ )
+ {
+ REAL8 x1 = sigReVec->data[i];
+ REAL8 x2 = sigImVec->data[i];
+#if outputh22
+ // output h22
+ hPlusTS->data->data[i] = x1;
+ hCrossTS->data->data[i] = x2;
+#else
+ // output h_+-i*h_x=-2Y22 * h22 + -2Y2-2 * h2-2 while h2-2 = h22^(*)
+ // h_+ = y1*x1 + y2*x2
+ // h_x = z1*x1 + z2*x2
+ hPlusTS->data->data[i] = y_1*x1 + y_2*x2;
+ hCrossTS->data->data[i] = z1*x1 + z2*x2;
+#endif
+ }
+
+ /* Point the output pointers to the relevant time series and return */
+ (*hplus) = hPlusTS;
+ (*hcross) = hCrossTS;
+
+ /* Free memory */
+ XLALDestroyREAL8Vector( tmpValues );
+ XLALDestroyREAL8Vector( sigmaKerr );
+ XLALDestroyREAL8Vector( sigmaStar );
+ XLALDestroyREAL8Vector( values );
+ XLALDestroyREAL8Vector( rdMatchPoint );
+ XLALDestroyREAL8Vector( ampNQC );
+ XLALDestroyREAL8Vector( phaseNQC );
+ XLALDestroyREAL8Vector( sigReVec );
+ XLALDestroyREAL8Vector( sigImVec );
+ XLALAdaptiveRungeKutta4Free( integrator );
+ XLALDestroyREAL8Array( dynamics );
+ XLALDestroyREAL8Array( dynamicsHi );
+ XLALDestroyREAL8Vector( sigReHi );
+ XLALDestroyREAL8Vector( sigImHi );
+ XLALDestroyREAL8Vector( omegaHi );
+
+ return XLAL_SUCCESS;
+}
+
+
+/**
+ * The main workhorse function for performing the ringdown attachment for EOB
+ * models EOBNRv2 and SEOBNRv1. This is the function which gets called by the
+ * code generating the full IMR waveform once generation of the inspiral part
+ * has been completed.
+ * The ringdown is attached using the hybrid comb matching detailed in
+ * The method is describe in Sec. II C of Pan et al. PRD 84, 124052 (2011),
+ * specifically Eqs. 30 - 32.. Further details of the
+ * implementation of the found in the DCC document T1100433.
+ * In SEOBNRv1, the last physical overtone is replace by a pseudoQNM. See
+ * Taracchini et al. PRD 86, 024011 (2012) for details.
+ * STEP 1) Get mass and spin of the final black hole and the complex ringdown frequencies
+ * STEP 2) Based on least-damped-mode decay time, allocate memory for rigndown waveform
+ * STEP 3) Get values and derivatives of inspiral waveforms at matching comb points
+ * STEP 4) Solve QNM coefficients and generate ringdown waveforms
+ * STEP 5) Stitch inspiral and ringdown waveoforms
+ */
+INT4 XLALSimIMREOBHybridAttachRingdown(
+ REAL8Vector *signal1, /**<< OUTPUT, Real of inspiral waveform to which we attach ringdown */
+ REAL8Vector *signal2, /**<< OUTPUT, Imag of inspiral waveform to which we attach ringdown */
+ const INT4 l, /**<< Current mode l */
+ const INT4 m, /**<< Current mode m */
+ const REAL8 dt, /**<< Sample time step (in seconds) */
+ const REAL8 mass1, /**<< First component mass (in Solar masses) */
+ const REAL8 mass2, /**<< Second component mass (in Solar masses) */
+ const REAL8 spin1x, /**<<The spin of the first object; only needed for spin waveforms */
+ const REAL8 spin1y, /**<<The spin of the first object; only needed for spin waveforms */
+ const REAL8 spin1z, /**<<The spin of the first object; only needed for spin waveforms */
+ const REAL8 spin2x, /**<<The spin of the second object; only needed for spin waveforms */
+ const REAL8 spin2y, /**<<The spin of the second object; only needed for spin waveforms */
+ const REAL8 spin2z, /**<<The spin of the second object; only needed for spin waveforms */
+ REAL8Vector *timeVec, /**<< Vector containing the time values */
+ REAL8Vector *matchrange /**<< Time values chosen as points for performing comb matching */
+)
+{
+
+ COMPLEX16Vector *modefreqs;
+ UINT4 Nrdwave;
+ UINT4 j;
+
+ UINT4 nmodes;
+ REAL8Vector *rdwave1;
+ REAL8Vector *rdwave2;
+ REAL8Vector *rinspwave;
+ REAL8Vector *dinspwave;
+ REAL8Vector *ddinspwave;
+ REAL8VectorSequence *inspwaves1;
+ REAL8VectorSequence *inspwaves2;
+ REAL8 eta, a, NRPeakOmega22; /* To generate pQNM frequency */
+ REAL8 mTot; /* In geometric units */
+ REAL8 spin1[3] = { spin1x, spin1y, spin1z };
+ REAL8 spin2[3] = { spin2x, spin2y, spin2z };
+ REAL8 finalMass, finalSpin;
+
+ mTot = (mass1 + mass2) * LAL_MTSUN_SI;
+ eta = mass1 * mass2 / ( (mass1 + mass2) * (mass1 + mass2) );
+
+ /**
+ * STEP 1) Get mass and spin of the final black hole and the complex ringdown frequencies
+ */
+
+ /* Create memory for the QNM frequencies */
+ nmodes = 8;
+ modefreqs = XLALCreateCOMPLEX16Vector( nmodes );
+ if ( !modefreqs )
+ {
+ fprintf(stderr,"Error(%d)", XLAL_ENOMEM );
+ }
+
+ if ( XLALSimIMREOBGenerateQNMFreqV2_re( modefreqs, mass1, mass2, spin1, spin2, l, m, nmodes ) == XLAL_FAILURE )
+ {
+ XLALDestroyCOMPLEX16Vector( modefreqs );
+
+ fprintf(stderr,"Error(%d)", XLAL_EFUNC );
+ }
+ //printf("mode0 = %f + i%f\n", creal(modefreqs->data[0]), cimag(modefreqs->data[0]));
+
+ /* Call XLALSimIMREOBFinalMassSpin_re() to get mass and spin of the final black hole */
+ if ( XLALSimIMREOBFinalMassSpin_re(&finalMass, &finalSpin, mass1, mass2, spin1, spin2) == XLAL_FAILURE )
+ {
+ fprintf(stderr,"Error(%d)", XLAL_EFUNC );
+ }
+
+ //if ( approximant == SEOBNRv1 )
+ //{
+ /* Replace the last QNM with pQNM */
+ /* We assume aligned/antialigned spins here */
+ a = (spin1[2] + spin2[2]) / 2. * (1.0 - 2.0 * eta) + (spin1[2] - spin2[2]) / 2. * (mass1 - mass2) / (mass1 + mass2);
+ NRPeakOmega22 = GetNRSpinPeakOmega( l, m, eta, a ) / mTot;
+ /*printf("a and NRomega in QNM freq: %.16e %.16e %.16e %.16e %.16e\n",spin1[2],spin2[2],
+ mTot/LAL_MTSUN_SI,a,NRPeakOmega22*mTot);*/
+ modefreqs->data[7] = (NRPeakOmega22/finalMass + creal(modefreqs->data[0])) / 2.;
+ modefreqs->data[7] += I * 10./3. * cimag(modefreqs->data[0]);
+ //}
+
+ /*for (j = 0; j < nmodes; j++)
+ {
+ printf("QNM frequencies: %d %d %d %e %e\n",l,m,j,modefreqs->data[j].re*mTot,1./modefreqs->data[j].im/mTot);
+ }*/
+
+ /* Ringdown signal length: 10 times the decay time of the n=0 mode */
+ Nrdwave = (INT4) (EOB_RD_EFOLDS / cimag(modefreqs->data[0]) / dt);
+
+ /* Check the value of attpos, to prevent memory access problems later */
+ if ( matchrange->data[0] * mTot / dt < 5 || matchrange->data[1]*mTot/dt > matchrange->data[2] *mTot/dt - 2 )
+ {
+ fprintf(stderr, "More inspiral points needed for ringdown matching.\n" );
+ //printf("%.16e,%.16e,%.16e\n",matchrange->data[0] * mTot / dt, matchrange->data[1]*mTot/dt, matchrange->data[2] *mTot/dt - 2);
+ XLALDestroyCOMPLEX16Vector( modefreqs );
+
+ fprintf(stderr,"Error(%d)", XLAL_EFAILED );
+ }
+
+ /**
+ * STEP 2) Based on least-damped-mode decay time, allocate memory for rigndown waveform
+ */
+
+ /* Create memory for the ring-down and full waveforms, and derivatives of inspirals */
+
+ rdwave1 = XLALCreateREAL8Vector( Nrdwave );
+ rdwave2 = XLALCreateREAL8Vector( Nrdwave );
+ rinspwave = XLALCreateREAL8Vector( 6 );
+ dinspwave = XLALCreateREAL8Vector( 6 );
+ ddinspwave = XLALCreateREAL8Vector( 6 );
+ inspwaves1 = XLALCreateREAL8VectorSequence( 3, 6 );
+ inspwaves2 = XLALCreateREAL8VectorSequence( 3, 6 );
+
+ /* Check memory was allocated */
+ if ( !rdwave1 || !rdwave2 || !rinspwave || !dinspwave
+ || !ddinspwave || !inspwaves1 || !inspwaves2 )
+ {
+ XLALDestroyCOMPLEX16Vector( modefreqs );
+ if (rdwave1) XLALDestroyREAL8Vector( rdwave1 );
+ if (rdwave2) XLALDestroyREAL8Vector( rdwave2 );
+ if (rinspwave) XLALDestroyREAL8Vector( rinspwave );
+ if (dinspwave) XLALDestroyREAL8Vector( dinspwave );
+ if (ddinspwave) XLALDestroyREAL8Vector( ddinspwave );
+ if (inspwaves1) XLALDestroyREAL8VectorSequence( inspwaves1 );
+ if (inspwaves2) XLALDestroyREAL8VectorSequence( inspwaves2 );
+ fprintf(stderr,"Error(%d)", XLAL_ENOMEM );
+ }
+
+ memset( rdwave1->data, 0, rdwave1->length * sizeof( REAL8 ) );
+ memset( rdwave2->data, 0, rdwave2->length * sizeof( REAL8 ) );
+
+ /**
+ * STEP 3) Get values and derivatives of inspiral waveforms at matching comb points
+ */
+
+ /* Generate derivatives of the last part of inspiral waves */
+ /* Get derivatives of signal1 */
+ if ( XLALGenerateHybridWaveDerivatives( rinspwave, dinspwave, ddinspwave, timeVec, signal1,
+ matchrange, dt, mass1, mass2 ) == XLAL_FAILURE )
+ {
+ XLALDestroyCOMPLEX16Vector( modefreqs );
+ XLALDestroyREAL8Vector( rdwave1 );
+ XLALDestroyREAL8Vector( rdwave2 );
+ XLALDestroyREAL8Vector( rinspwave );
+ XLALDestroyREAL8Vector( dinspwave );
+ XLALDestroyREAL8Vector( ddinspwave );
+ XLALDestroyREAL8VectorSequence( inspwaves1 );
+ XLALDestroyREAL8VectorSequence( inspwaves2 );
+ fprintf(stderr,"Error(%d)", XLAL_EFUNC );
+ }
+ for (j = 0; j < 6; j++)
+ {
+ inspwaves1->data[j] = rinspwave->data[j];
+ inspwaves1->data[j + 6] = dinspwave->data[j];
+ inspwaves1->data[j + 12] = ddinspwave->data[j];
+ }
+
+ /* Get derivatives of signal2 */
+ if ( XLALGenerateHybridWaveDerivatives( rinspwave, dinspwave, ddinspwave, timeVec, signal2,
+ matchrange, dt, mass1, mass2 ) == XLAL_FAILURE )
+ {
+ XLALDestroyCOMPLEX16Vector( modefreqs );
+ XLALDestroyREAL8Vector( rdwave1 );
+ XLALDestroyREAL8Vector( rdwave2 );
+ XLALDestroyREAL8Vector( rinspwave );
+ XLALDestroyREAL8Vector( dinspwave );
+ XLALDestroyREAL8Vector( ddinspwave );
+ XLALDestroyREAL8VectorSequence( inspwaves1 );
+ XLALDestroyREAL8VectorSequence( inspwaves2 );
+ fprintf(stderr,"Error(%d)", XLAL_EFUNC );
+ }
+ for (j = 0; j < 6; j++)
+ {
+ inspwaves2->data[j] = rinspwave->data[j];
+ inspwaves2->data[j + 6] = dinspwave->data[j];
+ inspwaves2->data[j + 12] = ddinspwave->data[j];
+ }
+
+
+ /**
+ * STEP 4) Solve QNM coefficients and generate ringdown waveforms
+ */
+
+ /* Generate ring-down waveforms */
+ //XLALSimIMREOBHybridRingdownWave locates in the current file
+ if ( XLALSimIMREOBHybridRingdownWave( rdwave1, rdwave2, dt, mass1, mass2, inspwaves1, inspwaves2,
+ modefreqs, matchrange ) == XLAL_FAILURE )
+ {
+ XLALDestroyCOMPLEX16Vector( modefreqs );
+ XLALDestroyREAL8Vector( rdwave1 );
+ XLALDestroyREAL8Vector( rdwave2 );
+ XLALDestroyREAL8Vector( rinspwave );
+ XLALDestroyREAL8Vector( dinspwave );
+ XLALDestroyREAL8Vector( ddinspwave );
+ XLALDestroyREAL8VectorSequence( inspwaves1 );
+ XLALDestroyREAL8VectorSequence( inspwaves2 );
+ fprintf(stderr,"Error(%d)", XLAL_EFUNC );
+ }
+
+ /**
+ * STEP 5) Stitch inspiral and ringdown waveoforms
+ */
+
+ /* Generate full waveforms, by stitching inspiral and ring-down waveforms */
+ UINT4 attachIdx = (UINT4)(matchrange->data[1] * mTot / dt);
+ //printf("attachIdx = %d\n", attachIdx);
+ //printf("len(signal1) = %d\n", signal1->length);
+ //printf("Nrdwave = %d\n", Nrdwave);
+
+ for (j = 1; j < Nrdwave; ++j)
+ {
+ signal1->data[j + attachIdx] = rdwave1->data[j];
+ signal2->data[j + attachIdx] = rdwave2->data[j];
+ }
+
+ memset( signal1->data+Nrdwave+attachIdx, 0, (signal1->length - Nrdwave - attachIdx)*sizeof(REAL8) );
+ memset( signal2->data+Nrdwave+attachIdx, 0, (signal2->length - Nrdwave - attachIdx)*sizeof(REAL8) );
+
+ /* Free memory */
+ XLALDestroyCOMPLEX16Vector( modefreqs );
+ XLALDestroyREAL8Vector( rdwave1 );
+ XLALDestroyREAL8Vector( rdwave2 );
+ XLALDestroyREAL8Vector( rinspwave );
+ XLALDestroyREAL8Vector( dinspwave );
+ XLALDestroyREAL8Vector( ddinspwave );
+ XLALDestroyREAL8VectorSequence( inspwaves1 );
+ XLALDestroyREAL8VectorSequence( inspwaves2 );
+
+ return XLAL_SUCCESS;
+}
+
+/**
+ * Generates the ringdown wave associated with the given real
+ * and imaginary parts of the inspiral waveform. The parameters of
+ * the ringdown, such as amplitude and phase offsets, are determined
+ * by solving the linear equations defined in the DCC document T1100433.
+ * In the linear equations Ax=y,
+ * A is a 16-by-16 matrix depending on QNM (complex) frequencies,
+ * x is a 16-d vector of the 8 unknown complex QNM amplitudes,
+ * y is a 16-d vector depending on inspiral-plunge waveforms and their derivatives near merger.
+ */
+INT4 XLALSimIMREOBHybridRingdownWave(
+ REAL8Vector *rdwave1, /**<< OUTPUT, Real part of ringdown waveform */
+ REAL8Vector *rdwave2, /**<< OUTPUT, Imag part of ringdown waveform */
+ const REAL8 dt, /**<< Sampling interval */
+ const REAL8 mass1, /**<< First component mass (in Solar masses) */
+ const REAL8 mass2, /**<< Second component mass (in Solar masses) */
+ REAL8VectorSequence *inspwave1, /**<< Values and derivs of real part inspiral waveform */
+ REAL8VectorSequence *inspwave2, /**<< Values and derivs of imag part inspiral waveform */
+ COMPLEX16Vector *modefreqs, /**<< Complex freqs of ringdown (scaled by total mass) */
+ REAL8Vector *matchrange /**<< Times which determine the comb of ringdown attachment */
+)
+{
+#if debugOutput
+ fprintf(stderr,"matchrange = %f, %f, %f\n",matchrange->data[0],matchrange->data[1],matchrange->data[2]);
+#endif
+ /* XLAL error handling */
+ INT4 errcode = XLAL_SUCCESS;
+
+ /* For checking GSL return codes */
+ INT4 gslStatus;
+
+ UINT4 i, j, k, nmodes = 8;
+
+ /* Sampling rate from input */
+ REAL8 t1, t2, t3, t4, t5, rt;
+ gsl_matrix *coef;
+ gsl_vector *hderivs;
+ gsl_vector *x;
+ gsl_permutation *p;
+ REAL8Vector *modeamps;
+ int s;
+ REAL8 tj;
+ REAL8 m;
+
+ /* mass in geometric units */
+ m = (mass1 + mass2) * LAL_MTSUN_SI;
+ t5 = (matchrange->data[0] - matchrange->data[1]) * m;
+ rt = -t5 / 5.;
+
+ t4 = t5 + rt;
+ t3 = t4 + rt;
+ t2 = t3 + rt;
+ t1 = t2 + rt;
+
+ if ( inspwave1->length != 3 || inspwave2->length != 3 ||
+ modefreqs->length != nmodes )
+ {
+ fprintf(stderr,"Error(%d)", XLAL_EBADLEN );
+ }
+
+ /* Solving the linear system for QNMs amplitude coefficients using gsl routine */
+ /* Initiate matrices and supporting variables */
+ //XLAL_CALLGSL( coef = (gsl_matrix *) gsl_matrix_alloc(2 * nmodes, 2 * nmodes) );
+ coef = (gsl_matrix *) gsl_matrix_alloc(2 * nmodes, 2 * nmodes);
+ //XLAL_CALLGSL( hderivs = (gsl_vector *) gsl_vector_alloc(2 * nmodes) );
+ hderivs = (gsl_vector *) gsl_vector_alloc(2 * nmodes);
+ //XLAL_CALLGSL( x = (gsl_vector *) gsl_vector_alloc(2 * nmodes) );
+ x = (gsl_vector *) gsl_vector_alloc(2 * nmodes);
+ //XLAL_CALLGSL( p = (gsl_permutation *) gsl_permutation_alloc(2 * nmodes) );
+ p = (gsl_permutation *) gsl_permutation_alloc(2 * nmodes);
+
+ /* Check all matrices and variables were allocated */
+ if ( !coef || !hderivs || !x || !p )
+ {
+ if (coef) gsl_matrix_free(coef);
+ if (hderivs) gsl_vector_free(hderivs);
+ if (x) gsl_vector_free(x);
+ if (p) gsl_permutation_free(p);
+ fprintf(stderr,"Error(%d)", XLAL_ENOMEM );
+ }
+
+ /* Define the linear system Ax=y */
+ /* Matrix A (2*n by 2*n) has block symmetry. Define half of A here as "coef" */
+ /* The half of A defined here corresponds to matrices M1 and -M2 in the DCC document T1100433 */
+ /* Define y here as "hderivs" */
+ for (i = 0; i < nmodes; ++i)
+ {
+ gsl_matrix_set(coef, 0, i, 1);
+ gsl_matrix_set(coef, 1, i, - cimag(modefreqs->data[i]));
+ gsl_matrix_set(coef, 2, i, exp(-cimag(modefreqs->data[i])*t1) * cos(creal(modefreqs->data[i])*t1));
+ gsl_matrix_set(coef, 3, i, exp(-cimag(modefreqs->data[i])*t2) * cos(creal(modefreqs->data[i])*t2));
+ gsl_matrix_set(coef, 4, i, exp(-cimag(modefreqs->data[i])*t3) * cos(creal(modefreqs->data[i])*t3));
+ gsl_matrix_set(coef, 5, i, exp(-cimag(modefreqs->data[i])*t4) * cos(creal(modefreqs->data[i])*t4));
+ gsl_matrix_set(coef, 6, i, exp(-cimag(modefreqs->data[i])*t5) * cos(creal(modefreqs->data[i])*t5));
+ gsl_matrix_set(coef, 7, i, exp(-cimag(modefreqs->data[i])*t5) *
+ (-cimag(modefreqs->data[i]) * cos(creal(modefreqs->data[i])*t5)
+ -creal(modefreqs->data[i]) * sin(creal(modefreqs->data[i])*t5)));
+ gsl_matrix_set(coef, 8, i, 0);
+ gsl_matrix_set(coef, 9, i, - creal(modefreqs->data[i]));
+ gsl_matrix_set(coef, 10, i, -exp(-cimag(modefreqs->data[i])*t1) * sin(creal(modefreqs->data[i])*t1));
+ gsl_matrix_set(coef, 11, i, -exp(-cimag(modefreqs->data[i])*t2) * sin(creal(modefreqs->data[i])*t2));
+ gsl_matrix_set(coef, 12, i, -exp(-cimag(modefreqs->data[i])*t3) * sin(creal(modefreqs->data[i])*t3));
+ gsl_matrix_set(coef, 13, i, -exp(-cimag(modefreqs->data[i])*t4) * sin(creal(modefreqs->data[i])*t4));
+ gsl_matrix_set(coef, 14, i, -exp(-cimag(modefreqs->data[i])*t5) * sin(creal(modefreqs->data[i])*t5));
+ gsl_matrix_set(coef, 15, i, exp(-cimag(modefreqs->data[i])*t5) *
+ (cimag(modefreqs->data[i]) * sin(creal(modefreqs->data[i])*t5)
+ -creal(modefreqs->data[i]) * cos(creal(modefreqs->data[i])*t5)));
+ }
+ for (i = 0; i < 2; ++i)
+ {
+ gsl_vector_set(hderivs, i, inspwave1->data[(i + 1) * inspwave1->vectorLength - 1]);
+ gsl_vector_set(hderivs, i + nmodes, inspwave2->data[(i + 1) * inspwave2->vectorLength - 1]);
+ gsl_vector_set(hderivs, i + 6, inspwave1->data[i * inspwave1->vectorLength]);
+ gsl_vector_set(hderivs, i + 6 + nmodes, inspwave2->data[i * inspwave2->vectorLength]);
+ }
+ gsl_vector_set(hderivs, 2, inspwave1->data[4]);
+ gsl_vector_set(hderivs, 2 + nmodes, inspwave2->data[4]);
+ gsl_vector_set(hderivs, 3, inspwave1->data[3]);
+ gsl_vector_set(hderivs, 3 + nmodes, inspwave2->data[3]);
+ gsl_vector_set(hderivs, 4, inspwave1->data[2]);
+ gsl_vector_set(hderivs, 4 + nmodes, inspwave2->data[2]);
+ gsl_vector_set(hderivs, 5, inspwave1->data[1]);
+ gsl_vector_set(hderivs, 5 + nmodes, inspwave2->data[1]);
+
+ /* Complete the definition for the rest half of A */
+ for (i = 0; i < nmodes; ++i)
+ {
+ for (k = 0; k < nmodes; ++k)
+ {
+ gsl_matrix_set(coef, i, k + nmodes, - gsl_matrix_get(coef, i + nmodes, k));
+ gsl_matrix_set(coef, i + nmodes, k + nmodes, gsl_matrix_get(coef, i, k));
+ }
+ }
+
+#if 0
+ /* print ringdown-matching linear system: coefficient matrix and RHS vector */
+ fprintf(stderr,"\nRingdown matching matrix:\n");
+ for (i = 0; i < 16; ++i)
+ {
+ for (j = 0; j < 16; ++j)
+ {
+ fprintf(stderr,"%.12e ",gsl_matrix_get(coef,i,j));
+ }
+ fprintf(stderr, "\n");
+ }
+ fprintf(stderr,"RHS: ");
+ for (i = 0; i < 16; ++i)
+ {
+ fprintf(stderr,"%.12e ",gsl_vector_get(hderivs,i));
+ }
+ fprintf(stderr,"\n");
+#endif
+
+ /* Call gsl LU decomposition to solve the linear system */
+ //XLAL_CALLGSL( gslStatus = gsl_linalg_LU_decomp(coef, p, &s) );
+ gslStatus = gsl_linalg_LU_decomp(coef, p, &s) ;
+ if ( gslStatus == GSL_SUCCESS )
+ {
+ //XLAL_CALLGSL( gslStatus = gsl_linalg_LU_solve(coef, p, hderivs, x) );
+ gslStatus = gsl_linalg_LU_solve(coef, p, hderivs, x);
+ }
+ if ( gslStatus != GSL_SUCCESS )
+ {
+ gsl_matrix_free(coef);
+ gsl_vector_free(hderivs);
+ gsl_vector_free(x);
+ gsl_permutation_free(p);
+
+ fprintf(stderr,"Error(%d)", XLAL_EFUNC );
+ }
+
+ /* Putting solution to an XLAL vector */
+ modeamps = XLALCreateREAL8Vector(2 * nmodes);
+
+ if ( !modeamps )
+ {
+ gsl_matrix_free(coef);
+ gsl_vector_free(hderivs);
+ gsl_vector_free(x);
+ gsl_permutation_free(p);
+
+ fprintf(stderr,"Error(%d)", XLAL_ENOMEM );
+ }
+
+ for (i = 0; i < nmodes; ++i)
+ {
+ modeamps->data[i] = gsl_vector_get(x, i);
+ modeamps->data[i + nmodes] = gsl_vector_get(x, i + nmodes);
+ }
+#if debugOutput
+ fprintf(stderr,"using 20Msun to do scaling.\n");
+
+ for (i = 0; i < nmodes; ++i)
+ {
+ fprintf(stderr,"%d-th amps = %e+i %e, freq = %e+i %e\n",i,modeamps->data[i],
+ modeamps->data[i + nmodes],creal(modefreqs->data[i])*20*4.92549095e-6,cimag(modefreqs->data[i])*20*4.92549095e-6);
+ }
+
+ fprintf(stderr,"using Mtotal to do scaling.\n");
+ for (i = 0; i < nmodes; ++i)
+ {
+ fprintf(stderr,"%d-th amps = %e+i %e, freq = %e+i %e\n",i,modeamps->data[i],
+ modeamps->data[i + nmodes],creal(modefreqs->data[i])*m,cimag(modefreqs->data[i])*m);
+ }
+#endif
+ /* Free all gsl linear algebra objects */
+ gsl_matrix_free(coef);
+ gsl_vector_free(hderivs);
+ gsl_vector_free(x);
+ gsl_permutation_free(p);
+
+ /* Build ring-down waveforms */
+
+ REAL8 timeOffset = fmod( matchrange->data[1], dt/m) * dt;
+
+ for (j = 0; j < rdwave1->length; ++j)
+ {
+ tj = j * dt - timeOffset;
+ rdwave1->data[j] = 0;
+ rdwave2->data[j] = 0;
+ for (i = 0; i < nmodes; ++i)
+ {
+ rdwave1->data[j] += exp(- tj * cimag(modefreqs->data[i]))
+ * ( modeamps->data[i] * cos(tj * creal(modefreqs->data[i]))
+ + modeamps->data[i + nmodes] * sin(tj * creal(modefreqs->data[i])) );
+ rdwave2->data[j] += exp(- tj * cimag(modefreqs->data[i]))
+ * (- modeamps->data[i] * sin(tj * creal(modefreqs->data[i]))
+ + modeamps->data[i + nmodes] * cos(tj * creal(modefreqs->data[i])) );
+ }
+ }
+
+ XLALDestroyREAL8Vector(modeamps);
+ return errcode;
+}
+
+
+
+ REAL8 XLALInspiralSpinFactorizedFlux_elip(
+ REAL8Vector *values, /**< dynamical variables */
+ const REAL8 rphivalues[], /**< dynamical varables, r, phi, pr, pphi */
+ const REAL8 drphivalues[], /**< dot dynamical varables, r, phi, pr, pphi */
+ const REAL8 omega, /**< orbital frequency */
+ SpinEOBParams *ak, /**< physical parameters */
+ const REAL8 H, /**< real Hamiltonian */
+ const int lMax /**< upper limit of the summation over l */
+ )
+
+{
+
+ REAL8 flux = 0.0;
+ REAL8 v;
+ REAL8 omegaSq;
+ COMPLEX16 hLM;
+ int l, m;
+
+ EOBNonQCCoeffs nqcCoeffs;
+
+
+ if ( lMax < 2 )
+ {
+ return -1;
+ }
+
+ /* Omegs is the derivative of phi */
+ omegaSq = omega*omega;
+
+ v = MYcbrt( omega );
+// printf( "v = %.16e\n", v );
+ for ( l = 2; l <= lMax; l++ )
+ {
+ for ( m = 1; m <= l; m++ )
+ {
+
+ if ( XLALSimIMRSpinEOBGetSpinFactorizedWaveform( &hLM, values, v, H, l, m, ak )
+ == -1 )
+ {
+ fprintf(stderr,"Error!(%d)", XLAL_EFUNC );
+ }
+ /* For the 2,2 mode, we apply NQC correction to the flux */
+ if ( l == 2 && m == 2 )
+ {
+ COMPLEX16 hNQC;
+ XLALSimIMRGetEOBCalibratedSpinNQC( &nqcCoeffs, l, m, ak->eobParams->eta, ak->a );
+ XLALSimIMREOBNonQCCorrection( &hNQC, values, omega, &nqcCoeffs );
+ /* Eq. 16 */
+ hLM *= hNQC;
+
+ double r,phi,prt,pphi,rdot,phidot;
+ r = rphivalues[0];
+ prt = rphivalues[2];
+ phi = rphivalues[1];
+ phidot = drphivalues[3];
+ pphi = rphivalues[3];
+ rdot = drphivalues[0];
+
+ double x1,x2,x3;
+ x1 = r*cos(phi);
+ x2 = r*sin(phi);
+ x3 = 0;
+ double v1,v2,v3;
+ v1 = rdot*cos(phi)-r*phidot*sin(phi);
+ v2 = rdot*sin(phi)+r*phidot*cos(phi);
+ v3 = 0;
+
+ double hp,hc;
+ PNwaveformPRD544813rdotc_22mode(&hp,&hc,x1,x2,x3,v1,v2,v3,ak->eobParams->eta);
+
+ const double complex CI = I;
+#if 1
+ hLM += hp+CI*hc;
+#else
+ hLM += (hp+CI*hc)/cabs(hNQC); // relax by hNQC for late inspiral
+#endif
+ }
+ // printf( "l = %d, m = %d, mag(hLM) = %.17e\n", l, m, XLALCOMPLEX16Abs2( hLM ) );
+ /* Eq. 13, Eq.(12) of PRD 84, 124052 (2011)*/
+ flux += (REAL8)(m * m) * omegaSq * ( creal(hLM)*creal(hLM) + cimag(hLM)*cimag(hLM));
+ }
+ }
+ return flux * LAL_1_PI / 8.0;
+}
+/*
+double EOBPNflux(const double m1,const double m2, // we assume m1>m2
+ const double s1x,const double s1y,const double s1z,
+ const double s2x,const double s2y,const double s2z,
+ const double x1,const double x2,const double x3, // relative position
+ const double v1,const double v2,const double v3, // relative velocity
+ double *EOBPNfluxwoNQC=0);
+*/
+double EOBPNflux(const double m1,const double m2, // we assume m1>m2
+ const double s1x,const double s1y,const double s1z,
+ const double s2x,const double s2y,const double s2z,
+ const double x1,const double x2,const double x3, // relative position
+ const double v1,const double v2,const double v3, // relative velocity
+ double *EOBPNfluxwoNQC)
+{
+ double tpt;
+ if(EOBPNfluxwoNQC == 0) EOBPNfluxwoNQC = &tpt;
+ const double chi1x = s1x/m1/m1;
+ const double chi1y = s1y/m1/m1;
+ const double chi1z = s1z/m1/m1;
+ const double chi2x = s2x/m2/m2;
+ const double chi2y = s2y/m2/m2;
+ const double chi2z = s2z/m2/m2;
+ const double m=m1+m2;
+ const double eta=m1*m2/m/m;
+
+ const double r=sqrt(x1*x1+x2*x2+x3*x3);
+ const double v=sqrt(v1*v1+v2*v2+v3*v3);
+ const double n1 = x1/r,n2 = x2/r,n3 = x3/r;
+ const double rd = v1*n1+v2*n2+v3*n3;
+ const double dm = m1-m2;
+ const double ncv1=n2*v3-n3*v2;
+ const double ncv2=n3*v1-n1*v3;
+ const double ncv3=n1*v2-n2*v1;
+
+ const double chis1=(chi1x+chi2x)/2;
+ const double chis2=(chi1y+chi2y)/2;
+ const double chis3=(chi1z+chi2z)/2;
+ const double chia1=(chi1x-chi2x)/2;
+ const double chia2=(chi1y-chi2y)/2;
+ const double chia3=(chi1z-chi2z)/2;
+ const double chissqr = chis1*chis1+chis2*chis2+chis3*chis3;
+ const double chiasqr = chia1*chia1+chia2*chia2+chia3*chia3;
+ const double ndchis = chis1*n1+chis2*n2+chis3*n3;
+ const double ndchia = chia1*n1+chia2*n2+chia3*n3;
+ const double vdchis = chis1*v1+chis2*v2+chis3*v3;
+ const double vdchia = chia1*v1+chia2*v2+chia3*v3;
+
+ double flux;
+#if 0
+ flux = 8./15*eta*eta*pow(m/r,4)*(
+ (12*v*v-11*rd*rd) // (6.13a) of PRD 54, 4813 (1996); (3.25a) of PRD 52, 821 (1995)
+ +((785-852*eta)*pow(v,4)-2*(1487-1392*eta)*v*v*rd*rd
+ +3*(687-620*eta)*pow(rd,4)-160*(17-eta)*m/r*v*v
+ +8*(367-15*eta)*m/r*rd*rd+16*(1-4*eta)*pow(m/r,2))/28 // (6.13b) of PRD 54, 4813 (1996); (3.25b) of PRD 52, 821 (1995)
+ +(18*(1692-5497*eta+4430*eta*eta)*pow(v,6)-54*(1719-10278*eta+6292*eta*eta)*pow(v,4)*rd*rd
+ +54*(2018-15207*eta+7572*eta*eta)*v*v*pow(rd,4)-18*(2501-20234*eta+8404*eta*eta)*pow(rd,6)
+ -12*(33510-60971*eta+14290*eta*eta)*m/r*pow(rd,4)-36*(4446-5237*eta+1393*eta*eta)*m/r*pow(v,4)
+ +108*(4987-8513*eta+2165*eta*eta)*m/r*rd*rd*v*v-3*(106319+9798*eta+5376*eta*eta)*m/r*m/r*rd*rd
+ +(281473+81828*eta+4368*eta*eta)*m/r*m/r*v*v-24*(253-1026*eta+56*eta*eta)*pow(m/r,3))/756 // (6.13d) of PRD 54, 4813 (1996)
+ +m/r*((27*rd*rd-37*v*v-12*m/r)*(ncv1*(chis1+dm/m*chia1)+ncv2*(chis2+dm/m*chia2)+ncv3*(chis3+dm/m*chia3))
+ +4*eta*(12*rd*rd-3*v*v+8*m/r)*(ncv1*chis1+ncv2*chis2+ncv3*chis3)) // (F16) of PRD 54, 4813 (1996)
+ +m*m/r/r*eta*(3*(chissqr-chiasqr)*(47*v*v-55*rd*rd)
+ -3*(ndchis*ndchis+ndchia*ndchia)*(168*v*v-269*rd*rd)
+ +71*(vdchis*vdchis+vdchia*vdchia)
+ -342*rd*(vdchis*ndchis-vdchia*ndchia)) // (F17) of PRD 54, 4813 (1996)
+ );
+#else
+ const double omega=sqrt(ncv1*ncv1+ncv2*ncv2+ncv3*ncv3)/r;
+ const double x=pow(MYcbrt( omega ),2);
+ const double a0 = 153.8803;
+ const double a1 = -55.13;
+ const double a2 = 588;
+ const double a3 = -1144;
+ const double EulerGamma = 0.57721566490153286060651209008240243104215933593992;
+ flux = 32.0/5*eta*eta*pow(x,5)*(1
+ -(1247+980*eta)/336*x
+ +4*M_PI*pow(x,1.5)
+ +(-4.928461199294532 + (9271*eta)/504. + (65*pow(eta,2))/18.)*pow(x,2)
+ -(8191/672. + 583*eta/24.)*M_PI*pow(x,2.5)
+ +(95.10839000836025 - (1712*EulerGamma)/105. + (16*pow(M_PI,2))/3.
+ - (134543*eta)/7776. + (41*pow(M_PI,2)*eta)/48. - (94403*pow(eta,2))/3024.
+ - (775*pow(eta,3))/324. - (856*log(16))/105. - (856*log(x))/105.)*pow(x,3)
+ +(-16285/504. + 214745*eta/1728. + 27755*pow(eta,2)/432.)*M_PI*pow(x,3.5)
+ +(-257.36874820698483 + (856*EulerGamma)/35. - 8*pow(M_PI,2)
+ - (59292668653*eta)/8.382528e8 + 5*a0*eta + (856*EulerGamma*eta)/315.
+ + (31495*pow(M_PI,2)*eta)/8064. - (54732199*pow(eta,2))/93312.
+ + (3157*pow(M_PI,2)*pow(eta,2))/144. + (18929389*pow(eta,3))/435456.
+ + (97*pow(eta,4))/3888. + (428*log(16))/35. + (428*eta*log(16))/315.
+ + (428*log(x))/35. + (47468*eta*log(x))/315.)*pow(x,4)
+ +(-104.44401041666667 + (51438847*eta)/48384. - (205*pow(M_PI,2)*eta)/6.
+ - (42745411*pow(eta,2))/145152. - (4199*pow(eta,3))/576.)*M_PI*pow(x,4.5)
+ +(-1466.6353720117309 + (5778*EulerGamma)/35. - 54*pow(M_PI,2)
+ + (4820443583363*eta)/1.2573792e9 - (3715*a0*eta)/336. + 6*a1*eta
+ - (4066*EulerGamma*eta)/35. - (31869941*pow(M_PI,2)*eta)/435456.
+ - (2006716046219*pow(eta,2))/3.3530112e9 - (55*a0*pow(eta,2))/4.
+ + (214*EulerGamma*pow(eta,2))/105. + (406321*pow(M_PI,2)*pow(eta,2))/48384.
+ + (2683003625*pow(eta,3))/3.359232e6 - (100819*pow(M_PI,2)*pow(eta,3))/3456.
+ - (192478799*pow(eta,4))/5.225472e6 + (33925*pow(eta,5))/186624.
+ + (2889*log(16))/35. - (2033*eta*log(16))/35. + (107*pow(eta,2)*log(16))/105.
+ + (2889*log(x))/35. - (391669*eta*log(x))/315. - (122981*pow(eta,2)*log(x))/105.)*pow(x,5)
+ +(-347.97154017857144 - (235274549*eta)/241920. + 20*a0*eta + (852595*pow(M_PI,2)*eta)/16128.
+ - (187219705*pow(eta,2))/32256. + (12915*pow(M_PI,2)*pow(eta,2))/64.
+ + (503913815*pow(eta,3))/870912. - (24065*pow(eta,4))/3456. + (1792*eta*log(x))/3.)*M_PI*pow(x,5.5)
+ +(-5876.793546111627 + (4815*EulerGamma)/7. - 225*pow(M_PI,2) + (45811843687349*eta)/1.14960384e9
+ + (170515*a0*eta)/18144. - (743*a1*eta)/56. + 7*a2*eta + a3*eta - (737123*EulerGamma*eta)/189.
+ - (84643435883*pow(M_PI,2)*eta)/6.7060224e8 + (8774*EulerGamma*pow(M_PI,2)*eta)/63.
+ - (410*pow(M_PI,4)*eta)/9. - (37516325949517*pow(eta,2))/6.03542016e8
+ + (68305*a0*pow(eta,2))/2016. - (33*a1*pow(eta,2))/2. + (6634*EulerGamma*pow(eta,2))/63.
+ + (23084972185*pow(M_PI,2)*pow(eta,2))/5.225472e6 - (92455*pow(M_PI,4)*pow(eta,2))/1152.
+ + (6069288163291*pow(eta,3))/2.58660864e9 + (295*a0*pow(eta,3))/18. + (107*EulerGamma*pow(eta,3))/243.
+ - (114930545*pow(M_PI,2)*pow(eta,3))/1.741824e6 - (145089945295*pow(eta,4))/2.82175488e8
+ + (141655*pow(M_PI,2)*pow(eta,4))/7776. + (6942085*pow(eta,5))/497664. + (196175*pow(eta,6))/3.359232e6
+ + (4815*log(16))/14. - (737123*eta*log(16))/378. + (4387*pow(M_PI,2)*eta*log(16))/63.
+ + (3317*pow(eta,2)*log(16))/63. + (107*pow(eta,3)*log(16))/486. + (4815*log(x))/14.
+ + (13185899*eta*log(x))/59535. + 7*a3*eta*log(x) + (4387*pow(M_PI,2)*eta*log(x))/63.
+ + (963937*pow(eta,2)*log(x))/189. + (6279367*pow(eta,3)*log(x))/2430.)*pow(x,6));
+
+ // NQC correction
+ flux += (8*pow(m,4)*pow(eta,2)*((64*pow(m,8)*pow(rd,6)*pow(eta,4)*(44 - 25*eta - 67*pow(eta,2)))/21. + (64*pow(m,8)*pow(rd,4)*pow(eta,4)*
+ (-1965*m - 288*r + 65*m*eta + 162*r*eta + 1016*m*pow(eta,2) + 1224*pow(r,3)*pow(omega,2) - 666*pow(r,3)*eta*pow(omega,2)
+ - 2619*pow(r,3)*pow(eta,2)*pow(omega,2)))/(63.*r) + (32*pow(m,8)*pow(rd,2)*pow(eta,4)*(-18742*pow(m,2) + 2916*m*r
+ + 378*pow(r,2) + 26217*pow(m,2)*eta + 540*m*r*eta - 5880*pow(m,2)*pow(eta,2) + 109242*m*pow(r,3)*pow(omega,2)
+ - 18954*pow(r,4)*pow(omega,2) - 271170*m*pow(r,3)*eta*pow(omega,2) + 14580*pow(r,4)*eta*pow(omega,2)
+ + 66762*m*pow(r,3)*pow(eta,2)*pow(omega,2) - 729*pow(r,6)*pow(omega,4)
+ + 129087*pow(r,6)*eta*pow(omega,4) - 50274*pow(r,6)*pow(eta,2)*pow(omega,4)))/(189.*pow(r,2))))/(15.*pow(r,4));
+#endif
+
+ return flux;
+}
+/** Returns the GPS time as a REAL8. */
+REAL8 XLALGPSGetREAL8( const LIGOTimeGPS *epoch )
+{
+ return epoch->gpsSeconds + (epoch->gpsNanoSeconds / 1e9);
+}
+COMPLEX16Vector* XLALCreateCOMPLEX16Vector(UINT4 length)
+{
+ COMPLEX16Vector* vector;
+ vector = (COMPLEX16Vector*)malloc(sizeof(*vector));
+ vector->length = length;
+ if ( ! length ) /* zero length: set data pointer to be NULL */
+ {
+ vector->data = NULL;
+ }
+ else /* non-zero length: allocate memory for data */
+ {
+ vector->data = (COMPLEX16 *)malloc(length * sizeof( *vector->data));
+ }
+
+ return vector;
+}
+
+void XLALDestroyCOMPLEX16Vector(COMPLEX16Vector* v)
+{
+ if(NULL == v)
+ {
+ return;
+ }
+ if(v->data)
+ {
+ v->length = 0;
+ free(v->data);
+ }
+ v->data = NULL;
+ free(v);
+
+ return;
+}
+
+REAL8Vector* XLALCreateREAL8Vector(UINT4 length)
+{
+ REAL8Vector* vector;
+ vector = (REAL8Vector*)malloc(sizeof(*vector));
+ vector->length = length;
+ if ( ! length ) /* zero length: set data pointer to be NULL */
+ {
+ vector->data = NULL;
+ }
+ else /* non-zero length: allocate memory for data */
+ {
+ vector->data = (REAL8 *)malloc(length * sizeof( *vector->data));
+ }
+
+ return vector;
+}
+
+void XLALDestroyREAL8Vector(REAL8Vector* v)
+{
+ if(NULL == v)
+ {
+ return;
+ }
+ if(v->data)
+ {
+ v->length = 0;
+ free(v->data);
+ }
+ v->data = NULL;
+ free(v);
+
+ return;
+}
+UINT4Vector* XLALCreateUINT4Vector(UINT4 length)
+{
+ UINT4Vector* vector;
+ vector = (UINT4Vector*)malloc(sizeof(*vector));
+ vector->length = length;
+ if ( ! length ) /* zero length: set data pointer to be NULL */
+ {
+ vector->data = NULL;
+ }
+ else /* non-zero length: allocate memory for data */
+ {
+ vector->data = (UINT4 *)malloc(length * sizeof( *vector->data));
+ }
+
+ return vector;
+}
+
+void XLALDestroyUINT4Vector(UINT4Vector* v)
+{
+ if(NULL == v)
+ {
+ return;
+ }
+ if(v->data)
+ {
+ v->length = 0;
+ free(v->data);
+ }
+ v->data = NULL;
+ free(v);
+
+ return;
+}
+
+REAL8Array* XLALCreateREAL8ArrayL(UINT4 ndim,...)
+{
+
+ enum { maxdim = 16 };
+ va_list ap;
+ REAL8Array *arr;
+ UINT4 dims[maxdim];
+ UINT4 dim;
+
+ UINT4 size = 1;
+
+ UINT4Vector dimLength;
+
+ //����������uint4����
+ va_start( ap, ndim );
+ for ( dim = 0; dim < ndim; ++dim )
+ dims[dim] = va_arg( ap, UINT4 );
+ va_end( ap );
+
+ //��������Ϊά��������Ϊ�����������
+ dimLength.length = ndim;
+ dimLength.data = dims;
+
+ //Array�����ݴ洢�ռ�Ĵ�СΪ����n�������ij˻�
+ for ( dim = 0; dim < ndim; ++dim )
+ size *= dimLength.data[dim];
+
+ /* create array */
+ arr = (REAL8Array *)malloc( sizeof( *arr ) );//Ϊָ���������ռ�
+ /* create array dimensions */
+ arr->dimLength = XLALCreateUINT4Vector( ndim );
+ if ( ! arr->dimLength )
+ {
+ free( arr );
+ }
+ /* copy dimension lengths */
+ memcpy( arr->dimLength->data, dimLength.data,
+ ndim * sizeof( *arr->dimLength->data ) );
+ /* allocate data storage */
+ arr->data = (REAL8 *)malloc( size * sizeof( *arr->data ) );
+ if ( ! arr->data )
+ {
+ XLALDestroyUINT4Vector( arr->dimLength );
+ free( arr );
+ }
+
+ return arr;
+}
+
+void XLALDestroyREAL8Array(REAL8Array* array)
+{
+ XLALDestroyUINT4Vector( array->dimLength );
+ free( array->data );
+ free( array );
+}
+
+REAL8VectorSequence * XLALCreateREAL8VectorSequence ( UINT4 length, UINT4 veclen )
+{
+
+ REAL8VectorSequence *seq;
+
+ seq = (REAL8VectorSequence *)malloc( sizeof( *seq ) );
+ if ( ! seq )
+ fprintf(stderr,"Error(%d)", XLAL_ENOMEM );
+
+ seq->length = length;
+ seq->vectorLength = veclen;
+
+ if ( ! length || ! veclen )
+ seq->data = NULL;
+ else
+ {
+ seq->data = (REAL8 *)malloc( length * veclen * sizeof( *seq->data ) );
+ if ( ! seq )
+ {
+ free( seq );
+ fprintf(stderr,"Error(%d)",XLAL_ENOMEM );
+ }
+ }
+
+ return seq;
+}
+void XLALDestroyREAL8VectorSequence ( REAL8VectorSequence * vseq )
+{
+ if ( ! vseq )
+ return;
+ if ( ( ! vseq->length || ! vseq->vectorLength ) && vseq->data )
+ fprintf(stderr,"Error(%d)", XLAL_EINVAL );
+ if ( ! vseq->data && ( vseq->length || vseq->vectorLength ) )
+ fprintf(stderr,"Error(%d)" ,XLAL_EINVAL );
+ if ( vseq->data )
+ free( vseq->data );
+ vseq->data = NULL; /* leave lengths as they are to indicate freed vector */
+ free( vseq );
+ return;
+}
+
+REAL8TimeSeries *XLALCreateREAL8TimeSeries ( const char *name, const LIGOTimeGPS *epoch, REAL8 f0, REAL8 deltaT, const LALUnit *sampleUnits, int length )
+{
+ REAL8TimeSeries *r8ts;
+ REAL8Vector *r8sequence;
+
+ r8ts = (REAL8TimeSeries *)malloc(sizeof(*r8ts));
+ r8sequence = XLALCreateREAL8Vector(length);
+ if(!r8ts || !r8sequence) {
+ free(r8ts);
+ XLALDestroyREAL8Vector (r8sequence);
+ }
+
+ if(name)
+ strncpy(r8ts->name, name, LALNameLength);
+ else
+ r8ts->name[0] = '\0';
+ r8ts->epoch = *epoch;
+ r8ts->f0 = f0;
+ r8ts->deltaT = deltaT;
+ r8ts->sampleUnits = *sampleUnits;
+ r8ts->data = r8sequence;
+
+ return r8ts;
+}
+
+void XLALDestroyREAL8TimeSeries( REAL8TimeSeries * series )
+{
+ if(series)
+ XLALDestroyREAL8Vector(series->data);
+ free(series);
+}
+
+
+int XLALSimIMREOBGenerateQNMFreqV2_re(
+ COMPLEX16Vector *modefreqs, /**<< OUTPUT, complex freqs of overtones in unit of Hz */
+ const REAL8 mass1, /**<< The mass of the 1st component (in Solar masses) */
+ const REAL8 mass2, /**<< The mass of the 2nd component (in Solar masses) */
+ const REAL8 spin1[3], /**<< The spin of the 1st object; only needed for spin waveforms */
+ const REAL8 spin2[3], /**<< The spin of the 2nd object; only needed for spin waveforms */
+ UINT4 l, /**<< The l value of the mode in question */
+ UINT4 m, /**<< The m value of the mode in question */
+ UINT4 nmodes /**<< The number of overtones that should be included (max 8) */
+ )
+{
+
+ /* Data for interpolating the quasinormal mode frequencies is taken from
+ * The webpage of Vitor Cardoso, http://centra.ist.utl.pt/~vitor/?page=ringdown
+ * In the spin range of (-0.995, 0.999),
+ * interpolation error within 5e-5 for the first 3 overtones of the 22 mode
+ * interpolation error within 0.005 for the first 8 overtones of the 22 mode
+ * On the data points, interpolation error is within 1e-5, except for the
+ * highest overtone of the (4,4) and (5,5) modes.
+ */
+
+// a/M with M is the mass of the final black hole
+ const double afinallist[107] = {-0.9996, -0.9995, -0.9994, -0.9992, -0.999, -0.9989, -0.9988,
+ -0.9987, -0.9986, -0.9985, -0.998, -0.9975, -0.997, -0.996, -0.995, -0.994, -0.992, -0.99, -0.988,
+ -0.986, -0.984, -0.982, -0.98, -0.975, -0.97, -0.96, -0.95, -0.94, -0.92, -0.9, -0.88, -0.86, -0.84,
+ -0.82, -0.8, -0.78, -0.76, -0.74, -0.72, -0.7, -0.65, -0.6, -0.55, -0.5, -0.45, -0.4, -0.35, -0.3,
+ -0.25, -0.2, -0.15, -0.1, -0.05, 0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6,
+ 0.65, 0.7, 0.72, 0.74, 0.76, 0.78, 0.8, 0.82, 0.84, 0.86, 0.88, 0.9, 0.92, 0.94, 0.95, 0.96, 0.97,
+ 0.975, 0.98, 0.982, 0.984, 0.986, 0.988, 0.99, 0.992, 0.994, 0.995, 0.996, 0.997, 0.9975, 0.998,
+ 0.9985, 0.9986, 0.9987, 0.9988, 0.9989, 0.999, 0.9992, 0.9994, 0.9995, 0.9996};
+
+ /* 2, 0 mode */
+// M\omega_R with M is the mass of the final black hole
+ const double reomegaqnm20[8][107] = {{0.4247721439,0.4247863113,0.4247985972,0.4248325877,0.4248584259,0.4248659433,0.4248700764,
+0.4248712306,0.4248698326,0.4248662798,0.4248267198,0.4247676547,0.4247005042,0.4245577530,0.4244119723,0.4242658712,
+0.4239745379,0.4236846241,0.4233960302,0.4231086991,0.4228226189,0.4225377956,0.4222542405,0.4215509794,0.4208558870,0.4194906865,
+0.4181592598,0.4168617799,0.4143677184,0.4120044663,0.4097658509,0.4076448500,0.4056343086,0.4037273098,0.4019173509,
+0.4001984114,0.3985649653,0.3970119631,0.3955348022,0.3941292897,0.3909047276,0.3880539184,0.3855360484,0.3833182760,
+0.3813740024,0.3796815867,0.3782233906,0.3769850625,0.3759550001,0.3751239445,0.3744846758,0.3740317881,0.3737615278,
+0.3736716844,0.3737615278,0.3740317881,0.3744846758,0.3751239445,0.3759550001,0.3769850625,0.3782233906,0.3796815867,
+0.3813740024,0.3833182760,0.3855360484,0.3880539184,0.3909047276,0.3941292897,0.3955348022,0.3970119631,0.3985649653,
+0.4001984114,0.4019173509,0.4037273098,0.4056343086,0.4076448500,0.4097658509,0.4120044663,0.4143677184,0.4168617799,
+0.4181592598,0.4194906865,0.4208558870,0.4215509794,0.4222542405,0.4225377956,0.4228226189,0.4231086991,0.4233960302,
+0.4236846241,0.4239745379,0.4242658712,0.4244119723,0.4245577530,0.4247005042,0.4247676547,0.4248267198,0.4248662798,
+0.4248698326,0.4248712306,0.4248700764,0.4248659433,0.4248584259,0.4248325877,0.4247985972,0.4247863113,0.4247721439},
+ {0.4022595044,0.4025176372,0.4026385253,0.4027146550,0.4027157267,0.4027081834,0.4026990446,0.4026895027,
+0.4026801424,0.4026712204,0.4026338048,0.4026034279,0.4025749860,0.4025177609,0.4024587579,0.4023983315,0.4022740572,
+0.4021454680,0.4020126089,0.4018755539,0.4017344007,0.4015892521,0.4014402120,0.4010512734,0.4006403236,0.3997591492,
+0.3988102405,0.3978068020,0.3956841928,0.3934728792,0.3912313515,0.3889989525,0.3868012743,0.3846545743,0.3825688955,
+0.3805501632,0.3786015741,0.3767245157,0.3749191785,0.3731849675,0.3691526314,0.3655335386,0.3623007731,0.3594283374,
+0.3568927266,0.3546733772,0.3527526583,0.3511156895,0.3497501098,0.3486458530,0.3477949500,0.3471913675,0.3468308827,
+0.3467109969,0.3468308827,0.3471913675,0.3477949500,0.3486458530,0.3497501098,0.3511156895,0.3527526583,0.3546733772,
+0.3568927266,0.3594283374,0.3623007731,0.3655335386,0.3691526314,0.3731849675,0.3749191785,0.3767245157,0.3786015741,
+0.3805501632,0.3825688955,0.3846545743,0.3868012743,0.3889989525,0.3912313515,0.3934728792,0.3956841928,0.3978068020,
+0.3988102405,0.3997591492,0.4006403236,0.4010512734,0.4014402120,0.4015892521,0.4017344007,0.4018755539,0.4020126089,
+0.4021454680,0.4022740572,0.4023983315,0.4024587579,0.4025177609,0.4025749860,0.4026034279,0.4026338048,0.4026712204,
+0.4026801424,0.4026895027,0.4026990446,0.4027081834,0.4027157267,0.4027146550,0.4026385253,0.4025176372,0.4022595044},
+ {0.3587631202,0.3586562755,0.3585571621,0.3584767648,0.3584871698,0.3585031359,0.3585201960,0.3585364516,
+0.3585511443,0.3585641498,0.3586123314,0.3586525789,0.3586945293,0.3587812110,0.3588663108,0.3589493444,0.3591108827,
+0.3592664061,0.3594155854,0.3595583252,0.3596945387,0.3598241205,0.3599469676,0.3602240117,0.3604570682,0.3607872733,
+0.3609323176,0.3608910420,0.3602774401,0.3590639204,0.3574099949,0.3554578534,0.3533158689,0.3510620393,0.3487514511,
+0.3464228554,0.3441035438,0.3418127732,0.3395641339,0.3373671870,0.3321397710,0.3273292258,0.3229529922,0.3190100679,
+0.3154913069,0.3123844448,0.3096766084,0.3073555756,0.3054103975,0.3038316900,0.3026117559,0.3017446212,0.3012260348,
+0.3010534545,0.3012260348,0.3017446212,0.3026117559,0.3038316900,0.3054103975,0.3073555756,0.3096766084,0.3123844448,
+0.3154913069,0.3190100679,0.3229529922,0.3273292258,0.3321397710,0.3373671870,0.3395641339,0.3418127732,0.3441035438,
+0.3464228554,0.3487514511,0.3510620393,0.3533158689,0.3554578534,0.3574099949,0.3590639204,0.3602774401,0.3608910420,
+0.3609323176,0.3607872733,0.3604570682,0.3602240117,0.3599469676,0.3598241205,0.3596945387,0.3595583252,0.3594155854,
+0.3592664061,0.3591108827,0.3589493444,0.3588663108,0.3587812110,0.3586945293,0.3586525789,0.3586123314,0.3585641498,
+0.3585511443,0.3585364516,0.3585201960,0.3585031359,0.3584871698,0.3584767648,0.3585571621,0.3586562755,0.3587631202},
+ {0.2955931981,0.2956911763,0.2959013663,0.2960902804,0.2960805341,0.2960706030,0.2960715835,0.2960841755,
+0.2961057593,0.2961328408,0.2962715691,0.2963767257,0.2964791366,0.2967001479,0.2969184558,0.2971346512,0.2975687544,
+0.2980006488,0.2984308575,0.2988593119,0.2992856405,0.2997097563,0.3001315265,0.3011744976,0.3021986114,0.3041793062,
+0.3060420460,0.3077622800,0.3106733357,0.3125253856,0.3131974762,0.3128916813,0.3118658660,0.3103333453,0.3084523863,
+0.3063370790,0.3040694520,0.3017088670,0.2992986826,0.2968708711,0.2908660077,0.2851210461,0.2797541132,0.2748239607,
+0.2703586352,0.2663699371,0.2628610658,0.2598308118,0.2572759173,0.2551924300,0.2535764879,0.2524247751,0.2517347842,
+0.2515049622,0.2517347842,0.2524247751,0.2535764879,0.2551924300,0.2572759173,0.2598308118,0.2628610658,0.2663699371,
+0.2703586352,0.2748239607,0.2797541132,0.2851210461,0.2908660077,0.2968708711,0.2992986826,0.3017088670,0.3040694520,
+0.3063370790,0.3084523863,0.3103333453,0.3118658660,0.3128916813,0.3131974762,0.3125253856,0.3106733357,0.3077622800,
+0.3060420460,0.3041793062,0.3021986114,0.3011744976,0.3001315265,0.2997097563,0.2992856405,0.2988593119,0.2984308575,
+0.2980006488,0.2975687544,0.2971346512,0.2969184558,0.2967001479,0.2964791366,0.2963767257,0.2962715691,0.2961328408,
+0.2961057593,0.2960841755,0.2960715835,0.2960706030,0.2960805341,0.2960902804,0.2959013663,0.2956911763,0.2955931981},
+ {0.2265759655,0.2263134666,0.2259201107,0.2260332610,0.2263091114,0.2263241376,0.2262966437,0.2262653635,
+0.2262534991,0.2262677342,0.2264910301,0.2266045970,0.2267226381,0.2270204493,0.2272816677,0.2275628966,0.2281119757,
+0.2286682789,0.2292233708,0.2297821291,0.2303431133,0.2309055008,0.2314706692,0.2328917020,0.2343288764,0.2372425752,
+0.2401516712,0.2432064357,0.2490028794,0.2551643774,0.2609821536,0.2649179918,0.2670263535,0.2677578325,0.2675054998,
+0.2665561482,0.2651128405,0.2633200598,0.2612820783,0.2590753625,0.2531607164,0.2470884185,0.2411635985,0.2355561825,
+0.2303648137,0.2256486007,0.2214438733,0.2177734415,0.2146518936,0.2120886995,0.2100900575,0.2086599993,0.2078010452,
+0.2075145798,0.2078010452,0.2086599993,0.2100900575,0.2120886995,0.2146518936,0.2177734415,0.2214438733,0.2256486007,
+0.2303648137,0.2355561825,0.2411635985,0.2470884185,0.2531607164,0.2590753625,0.2612820783,0.2633200598,0.2651128405,
+0.2665561482,0.2675054998,0.2677578325,0.2670263535,0.2649179918,0.2609821536,0.2551643774,0.2490028794,0.2432064357,
+0.2401516712,0.2372425752,0.2343288764,0.2328917020,0.2314706692,0.2309055008,0.2303431133,0.2297821291,0.2292233708,
+0.2286682789,0.2281119757,0.2275628966,0.2272816677,0.2270204493,0.2267226381,0.2266045970,0.2264910301,0.2262677342,
+0.2262534991,0.2262653635,0.2262966437,0.2263241376,0.2263091114,0.2260332610,0.2259201107,0.2263134666,0.2265759655},
+ {0.1624677140,0.1634934248,0.1638277421,0.1630968281,0.1635010049,0.1636759976,0.1636803676,0.1635845741,
+0.1634883150,0.1634553864,0.1638050393,0.1637918910,0.1639844275,0.1642094594,0.1645146073,0.1647460864,0.1652882910,
+0.1658098185,0.1663401778,0.1668757036,0.1674133259,0.1679475306,0.1685023684,0.1698847398,0.1712487246,0.1741108365,
+0.1768267467,0.1804631771,0.1863051500,0.1935771765,0.1987452707,0.2093226733,0.2181547856,0.2237317269,0.2269036596,
+0.2284118203,0.2287563990,0.2282723907,0.2271898972,0.2256715181,0.2206696442,0.2147729564,0.2085926425,0.2024747303,
+0.1966287474,0.1911890101,0.1862461282,0.1818640842,0.1780897950,0.1749585446,0.1724970437,0.1707251041,0.1696565048,
+0.1692994034,0.1696565048,0.1707251041,0.1724970437,0.1749585446,0.1780897950,0.1818640842,0.1862461282,0.1911890101,
+0.1966287474,0.2024747303,0.2085926425,0.2147729564,0.2206696442,0.2256715181,0.2271898972,0.2282723907,0.2287563990,
+0.2284118203,0.2269036596,0.2237317269,0.2181547856,0.2093226733,0.1987452707,0.1935771765,0.1863051500,0.1804631771,
+0.1768267467,0.1741108365,0.1712487246,0.1698847398,0.1685023684,0.1679475306,0.1674133259,0.1668757036,0.1663401778,
+0.1658098185,0.1652882910,0.1647460864,0.1645146073,0.1642094594,0.1639844275,0.1637918910,0.1638050393,0.1634553864,
+0.1634883150,0.1635845741,0.1636803676,0.1636759976,0.1635010049,0.1630968281,0.1638277421,0.1634934248,0.1624677140},
+ {0.1150947175,0.1136995811,0.1144317617,0.1145108329,0.1143223733,0.1147075752,0.1148529865,0.1147211083,
+0.1145101899,0.1144146127,0.1148757124,0.1147623558,0.1150527078,0.1152162011,0.1153522163,0.1156670599,0.1160937605,
+0.1165085059,0.1169521137,0.1174121457,0.1178333408,0.1183089991,0.1188779907,0.1199614936,0.1212661221,0.1229079880,
+0.1252696237,0.1300527498,0.1363714850,0.1365743504,0.1502937555,0.1499042247,0.1576063359,0.1737999474,0.1840565193,
+0.1901954481,0.1937178657,0.1954878977,0.1960322476,0.1956928755,0.1923495252,0.1869716004,0.1806432357,0.1739650338,
+0.1673020380,0.1608944901,0.1549126532,0.1494856455,0.1447169546,0.1406923509,0.1374833382,0.1351476926,0.1337284518,
+0.1332523443,0.1337284518,0.1351476926,0.1374833382,0.1406923509,0.1447169546,0.1494856455,0.1549126532,0.1608944901,
+0.1673020380,0.1739650338,0.1806432357,0.1869716004,0.1923495252,0.1956928755,0.1960322476,0.1954878977,0.1937178657,
+0.1901954481,0.1840565193,0.1737999474,0.1576063359,0.1499042247,0.1502937555,0.1365743504,0.1363714850,0.1300527498,
+0.1252696237,0.1229079880,0.1212661221,0.1199614936,0.1188779907,0.1183089991,0.1178333408,0.1174121457,0.1169521137,
+0.1165085059,0.1160937605,0.1156670599,0.1153522163,0.1152162011,0.1150527078,0.1147623558,0.1148757124,0.1144146127,
+0.1145101899,0.1147211083,0.1148529865,0.1147075752,0.1143223733,0.1145108329,0.1144317617,0.1136995811,0.1150947175},
+ {0.07824594797,0.07897765236,0.07781656751,0.07894919224,0.07811549687,0.07852555182,0.07887349260,0.07877853969,
+0.07846824390,0.07832233515,0.07872416680,0.07887758159,0.07876636539,0.07904172864,0.07931185989,0.07935962619,0.07970963786,
+0.08015321455,0.08049831171,0.08098647273,0.08113113975,0.08171084479,0.08245975407,0.08198058103,0.08310489532,0.08636947463,
+0.08742026462,0.09301825285,0.09708260702,0.10449211510,0.09410791221,0.1163296909,0.1194610774,0.1071758642,0.1310599660,
+0.1479210288,0.1575029326,0.1631326584,0.1662931627,0.1677797021,0.1669344646,0.1623398390,0.1558069565,0.1482827082,
+0.1403267639,0.1323069592,0.1244931384,0.1171075385,0.1103537661,0.1044314061,0.09954024628,0.09587287090,0.09359533547,
+0.09282239791,0.09359533547,0.09587287090,0.09954024628,0.1044314061,0.1103537661,0.1171075385,0.1244931384,0.1323069592,
+0.1403267639,0.1482827082,0.1558069565,0.1623398390,0.1669344646,0.1677797021,0.1662931627,0.1631326584,0.1575029326,
+0.1479210288,0.1310599660,0.1071758642,0.1194610774,0.1163296909,0.09410791221,0.10449211510,0.09708260702,0.09301825285,
+0.08742026462,0.08636947463,0.08310489532,0.08198058103,0.08245975407,0.08171084479,0.08113113975,0.08098647273,0.08049831171,
+0.08015321455,0.07970963786,0.07935962619,0.07931185989,0.07904172864,0.07876636539,0.07887758159,0.07872416680,0.07832233515,
+0.07846824390,0.07877853969,0.07887349260,0.07852555182,0.07811549687,0.07894919224,0.07781656751,0.07897765236,0.07824594797}};
+
+// M\omega_I with M is the mass of the final black hole
+ const double imomegaqnm20[8][107] = {{0.06956111286,0.07057665227,0.07109516199,0.07156667263,0.07176004502,0.07181519360,
+0.07185564256,0.07188639200,0.07191058835,0.07193027264,0.07199608801,0.07204342275,0.07208725348,0.07217445117,
+0.07226259362,0.07235103048,0.07252698509,0.07270070919,0.07287193971,0.07304067834,0.07320697034,0.07337086430,
+0.07353240627,0.07392625431,0.07430631954,0.07502754477,0.07570073722,0.07633017500,0.07747297842,0.07848269543,
+0.07938083725,0.08018464701,0.08090799941,0.08156214052,0.08215626528,0.08269795953,0.08319353674,0.08364829544,
+0.08406671695,0.08445261881,0.08529549690,0.08599466937,0.08657885062,0.08706905134,0.08748097560,0.08782655405,
+0.08811495632,0.08835327799,0.08854701612,0.08870040374,0.08881664656,0.08889809023,0.08894633586,0.08896231569,
+0.08894633586,0.08889809023,0.08881664656,0.08870040374,0.08854701612,0.08835327799,0.08811495632,0.08782655405,
+0.08748097560,0.08706905134,0.08657885062,0.08599466937,0.08529549690,0.08445261881,0.08406671695,0.08364829544,
+0.08319353674,0.08269795953,0.08215626528,0.08156214052,0.08090799941,0.08018464701,0.07938083725,0.07848269543,
+0.07747297842,0.07633017500,0.07570073722,0.07502754477,0.07430631954,0.07392625431,0.07353240627,0.07337086430,
+0.07320697034,0.07304067834,0.07287193971,0.07270070919,0.07252698509,0.07235103048,0.07226259362,0.07217445117,
+0.07208725348,0.07204342275,0.07199608801,0.07193027264,0.07191058835,0.07188639200,0.07185564256,0.07181519360,
+0.07176004502,0.07156667263,0.07109516199,0.07057665227,0.06956111286},
+ {0.2185411094,0.2185862168,0.2185760597,0.2185502469,0.2185551556,0.2185670597,0.2185832072,0.2186023833,
+0.2186236698,0.2186463949,0.2187689601,0.2188938400,0.2190172960,0.2192613118,0.2195038699,0.2197457780,0.2202276534,
+0.2207065981,0.2211824488,0.2216551307,0.2221245734,0.2225907052,0.2230534566,0.2241951244,0.2253143564,0.2274827082,
+0.2295545126,0.2315282566,0.2351860943,0.2384795534,0.2414444658,0.2441189781,0.2465387707,0.2487354182,0.2507361819,
+0.2525643629,0.2542398214,0.2557795018,0.2571979034,0.2585074823,0.2613723978,0.2637535915,0.2657465547,0.2674214198,
+0.2688307276,0.2700144584,0.2710033792,0.2718213228,0.2724867699,0.2730139630,0.2734136955,0.2736938697,0.2738598819,
+0.2739148753,0.2738598819,0.2736938697,0.2734136955,0.2730139630,0.2724867699,0.2718213228,0.2710033792,0.2700144584,
+0.2688307276,0.2674214198,0.2657465547,0.2637535915,0.2613723978,0.2585074823,0.2571979034,0.2557795018,0.2542398214,
+0.2525643629,0.2507361819,0.2487354182,0.2465387707,0.2441189781,0.2414444658,0.2384795534,0.2351860943,0.2315282566,
+0.2295545126,0.2274827082,0.2253143564,0.2241951244,0.2230534566,0.2225907052,0.2221245734,0.2216551307,0.2211824488,
+0.2207065981,0.2202276534,0.2197457780,0.2195038699,0.2192613118,0.2190172960,0.2188938400,0.2187689601,0.2186463949,
+0.2186236698,0.2186023833,0.2185832072,0.2185670597,0.2185551556,0.2185502469,0.2185760597,0.2185862168,0.2185411094},
+ {0.3746283234,0.3744760286,0.3744655082,0.3745713459,0.3746804416,0.3747239651,0.3747616125,0.3747951976,
+0.3748262688,0.3748559959,0.3750036033,0.3751595179,0.3753190966,0.3756378976,0.3759558332,0.3762746082,0.3769149521,
+0.3775582079,0.3782042318,0.3788529456,0.3795041978,0.3801578285,0.3808136809,0.3824619707,0.3841204813,0.3874566765,
+0.3907983942,0.3941199491,0.4005962971,0.4067113438,0.4123795696,0.4175861754,0.4223525880,0.4267144430,0.4307106786,
+0.4343787455,0.4377527783,0.4408631174,0.4437364171,0.4463959791,0.4522370945,0.4571173234,0.4612213527,0.4646855141,
+0.4676122255,0.4700795615,0.4721476900,0.4738632779,0.4752625561,0.4763734789,0.4772172535,0.4778094206,0.4781606008,
+0.4782769831,0.4781606008,0.4778094206,0.4772172535,0.4763734789,0.4752625561,0.4738632779,0.4721476900,0.4700795615,
+0.4676122255,0.4646855141,0.4612213527,0.4571173234,0.4522370945,0.4463959791,0.4437364171,0.4408631174,0.4377527783,
+0.4343787455,0.4307106786,0.4267144430,0.4223525880,0.4175861754,0.4123795696,0.4067113438,0.4005962971,0.3941199491,
+0.3907983942,0.3874566765,0.3841204813,0.3824619707,0.3808136809,0.3801578285,0.3795041978,0.3788529456,0.3782042318,
+0.3775582079,0.3769149521,0.3762746082,0.3759558332,0.3756378976,0.3753190966,0.3751595179,0.3750036033,0.3748559959,
+0.3748262688,0.3747951976,0.3747616125,0.3747239651,0.3746804416,0.3745713459,0.3744655082,0.3744760286,0.3746283234},
+ {0.5488977566,0.5492725578,0.5493796167,0.5493030521,0.5492800515,0.5493081779,0.5493493533,0.5493946353,
+0.5494384190,0.5494780738,0.5496229054,0.5497549686,0.5499025591,0.5501989882,0.5504901744,0.5507853393,0.5513807914,
+0.5519818189,0.5525897750,0.5532041749,0.5538251797,0.5544529382,0.5550874672,0.5567036937,0.5583633611,0.5618146957,
+0.5654450115,0.5692386679,0.5773386388,0.5859421423,0.5945472028,0.6027877630,0.6105064194,0.6176644895,0.6242770530,
+0.6303804075,0.6360171698,0.6412297490,0.6460576806,0.6505367243,0.6604082105,0.6686938222,0.6756913514,0.6816215439,
+0.6866504101,0.6909045159,0.6944813958,0.6974567098,0.6998892223,0.7018243015,0.7032963922,0.7043307557,0.7049446682,
+0.7051482024,0.7049446682,0.7043307557,0.7032963922,0.7018243015,0.6998892223,0.6974567098,0.6944813958,0.6909045159,
+0.6866504101,0.6816215439,0.6756913514,0.6686938222,0.6604082105,0.6505367243,0.6460576806,0.6412297490,0.6360171698,
+0.6303804075,0.6242770530,0.6176644895,0.6105064194,0.6027877630,0.5945472028,0.5859421423,0.5773386388,0.5692386679,
+0.5654450115,0.5618146957,0.5583633611,0.5567036937,0.5550874672,0.5544529382,0.5538251797,0.5532041749,0.5525897750,
+0.5519818189,0.5513807914,0.5507853393,0.5504901744,0.5501989882,0.5499025591,0.5497549686,0.5496229054,0.5494780738,
+0.5494384190,0.5493946353,0.5493493533,0.5493081779,0.5492800515,0.5493030521,0.5493796167,0.5492725578,0.5488977566},
+ {0.7501379784,0.7495636806,0.7496503080,0.7501258019,0.7500613683,0.7499927446,0.7499667401,0.7499862570,
+0.7500353707,0.7500943083,0.7502378208,0.7502955686,0.7504262429,0.7506329733,0.7508454096,0.7510636293,0.7514901194,
+0.7519267005,0.7523658758,0.7528118500,0.7532615237,0.7537170118,0.7541777199,0.7553533494,0.7565672969,0.7591011388,
+0.7618191441,0.7646738706,0.7712404750,0.7783465723,0.7875759366,0.7980345082,0.8085705185,0.8186647248,0.8281387322,
+0.8369567431,0.8451396344,0.8527290961,0.8597724928,0.8663164947,0.8807666598,0.8929239587,0.9032139277,0.9119531958,
+0.9193796679,0.9256743556,0.9309764881,0.9353939337,0.9390104311,0.9418906437,0.9440837035,0.9456256811,0.9465412730,
+0.9468448909,0.9465412730,0.9456256811,0.9440837035,0.9418906437,0.9390104311,0.9353939337,0.9309764881,0.9256743556,
+0.9193796679,0.9119531958,0.9032139277,0.8929239587,0.8807666598,0.8663164947,0.8597724928,0.8527290961,0.8451396344,
+0.8369567431,0.8281387322,0.8186647248,0.8085705185,0.7980345082,0.7875759366,0.7783465723,0.7712404750,0.7646738706,
+0.7618191441,0.7591011388,0.7565672969,0.7553533494,0.7541777199,0.7537170118,0.7532615237,0.7528118500,0.7523658758,
+0.7519267005,0.7514901194,0.7510636293,0.7508454096,0.7506329733,0.7504262429,0.7502955686,0.7502378208,0.7500943083,
+0.7500353707,0.7499862570,0.7499667401,0.7499927446,0.7500613683,0.7501258019,0.7496503080,0.7495636806,0.7501379784},
+ {0.9742529776,0.9747874524,0.9741123398,0.9741101898,0.9745054107,0.9743713094,0.9742131924,0.9741459996,
+0.9741878531,0.9742927333,0.9744241227,0.9744440584,0.9745998745,0.9746798313,0.9748508069,0.9749764636,0.9752738201,
+0.9755817532,0.9758699637,0.9761776339,0.9764736452,0.9767861418,0.9770899129,0.9778706747,0.9786413703,0.9802309584,
+0.9821505190,0.9839171716,0.9872274650,0.9938892699,0.9973348177,1.0029600920,1.0137082960,1.0258619280,1.0379031380,
+1.0493556480,1.0600886610,1.0700928400,1.0794025970,1.0880666360,1.1072318520,1.1233872540,1.1370869350,1.1487453930,
+1.1586731910,1.1671054460,1.1742220930,1.1801619460,1.1850324510,1.1889164550,1.1918768980,1.1939600320,1.1951975740,
+1.1956080540,1.1951975740,1.1939600320,1.1918768980,1.1889164550,1.1850324510,1.1801619460,1.1742220930,1.1671054460,
+1.1586731910,1.1487453930,1.1370869350,1.1233872540,1.1072318520,1.0880666360,1.0794025970,1.0700928400,1.0600886610,
+1.0493556480,1.0379031380,1.0258619280,1.0137082960,1.0029600920,0.9973348177,0.9938892699,0.9872274650,0.9839171716,
+0.9821505190,0.9802309584,0.9786413703,0.9778706747,0.9770899129,0.9767861418,0.9764736452,0.9761776339,0.9758699637,
+0.9755817532,0.9752738201,0.9749764636,0.9748508069,0.9746798313,0.9745998745,0.9744440584,0.9744241227,0.9742927333,
+0.9741878531,0.9741459996,0.9742131924,0.9743713094,0.9745054107,0.9741101898,0.9741123398,0.9747874524,0.9742529776},
+ {1.2115268570,1.2119224830,1.2127581510,1.2117269920,1.2124824650,1.2124753940,1.2122054860,1.2120007160,
+1.2120183490,1.2121990080,1.2122129970,1.2124447280,1.2123706080,1.2125862000,1.2126197320,1.2127468970,1.2129846840,
+1.2132075340,1.2134023920,1.2136367370,1.2138479250,1.2141571580,1.2143110530,1.2150808200,1.2157732190,1.2167214260,
+1.2186909060,1.2196006930,1.2213948240,1.2231508920,1.2289533870,1.2368231740,1.2309780760,1.2383599140,1.2512352410,
+1.2647465460,1.2777995720,1.2901129870,1.3016351760,1.3123895010,1.3362428600,1.3564067550,1.3735550870,1.3881973760,
+1.4007134530,1.4113878280,1.4204352180,1.4280186030,1.4342618660,1.4392588030,1.4430794470,1.4457744710,1.4473782250,
+1.4479106320,1.4473782250,1.4457744710,1.4430794470,1.4392588030,1.4342618660,1.4280186030,1.4204352180,1.4113878280,
+1.4007134530,1.3881973760,1.3735550870,1.3564067550,1.3362428600,1.3123895010,1.3016351760,1.2901129870,1.2777995720,
+1.2647465460,1.2512352410,1.2383599140,1.2309780760,1.2368231740,1.2289533870,1.2231508920,1.2213948240,1.2196006930,
+1.2186909060,1.2167214260,1.2157732190,1.2150808200,1.2143110530,1.2141571580,1.2138479250,1.2136367370,1.2134023920,
+1.2132075340,1.2129846840,1.2127468970,1.2126197320,1.2125862000,1.2123706080,1.2124447280,1.2122129970,1.2121990080,
+1.2120183490,1.2120007160,1.2122054860,1.2124753940,1.2124824650,1.2117269920,1.2127581510,1.2119224830,1.2115268570},
+ {1.4571663840,1.4557744370,1.4561406500,1.4561633880,1.4563989150,1.4567024440,1.4564520290,1.4561110480,
+1.4560841830,1.4563431260,1.4562032670,1.4566118340,1.4564050080,1.4564957940,1.4567084750,1.4568561130,1.4570324500,
+1.4571992550,1.4572168310,1.4577583970,1.4580789520,1.4583441320,1.4581619640,1.4585416390,1.4580717000,1.4621403950,
+1.4642010920,1.4637245060,1.4685741490,1.4643467300,1.4727222970,1.4673766030,1.4833905610,1.4800758950,1.4701776130,
+1.4825655120,1.4971099840,1.5114169920,1.5249950640,1.5377449720,1.5661545750,1.5902726720,1.6108788240,1.6285796450,
+1.6438274760,1.6569573710,1.6682159440,1.6777810640,1.6857758350,1.6922778140,1.6973286180,1.7009421340,1.7031156000,
+1.7038413270,1.7031156000,1.7009421340,1.6973286180,1.6922778140,1.6857758350,1.6777810640,1.6682159440,1.6569573710,
+1.6438274760,1.6285796450,1.6108788240,1.5902726720,1.5661545750,1.5377449720,1.5249950640,1.5114169920,1.4971099840,
+1.4825655120,1.4701776130,1.4800758950,1.4833905610,1.4673766030,1.4727222970,1.4643467300,1.4685741490,1.4637245060,
+1.4642010920,1.4621403950,1.4580717000,1.4585416390,1.4581619640,1.4583441320,1.4580789520,1.4577583970,1.4572168310,
+1.4571992550,1.4570324500,1.4568561130,1.4567084750,1.4564957940,1.4564050080,1.4566118340,1.4562032670,1.4563431260,
+1.4560841830,1.4561110480,1.4564520290,1.4567024440,1.4563989150,1.4561633880,1.4561406500,1.4557744370,1.4571663840}};
+
+ /* 2, 2 mode */
+
+ const double reomegaqnm22[8][107] = {{0.270228, 0.276562, 0.280636, 0.285234, 0.287548, 0.288282,
+ 0.288845, 0.289287, 0.289639, 0.289924, 0.290781, 0.291189, 0.291418, 0.291658, 0.291785, 0.29187,
+ 0.291998, 0.292111, 0.292221, 0.292331, 0.292441, 0.292552, 0.292664, 0.292943, 0.293223, 0.293787, 0.294354, 0.294925, 0.296077, 0.297244, 0.298426, 0.299624, 0.300837, 0.302067, 0.303313, 0.304577, 0.305857, 0.307156, 0.308473, 0.309808, 0.313232, 0.316784, 0.320473, 0.324307, 0.328299, 0.332458, 0.336798, 0.341333, 0.346079, 0.351053, 0.356275, 0.361768, 0.367557, 0.373672, 0.380146, 0.387018, 0.394333, 0.402145, 0.410518, 0.419527, 0.429264, 0.439842, 0.451402, 0.464123, 0.478235, 0.494045, 0.511969, 0.5326, 0.541794, 0.55163, 0.562201, 0.573616, 0.586017, 0.59958, 0.614539, 0.631206, 0.650018, 0.671614, 0.696995, 0.727875, 0.74632, 0.767674, 0.793208, 0.808235, 0.825429, 0.8331, 0.841343, 0.850272, 0.860046, 0.870893, 0.883162, 0.897446, 0.905664, 0.914902, 0.925581, 0.931689, 0.938524, 0.946385, 0.948123, 0.949929, 0.951813, 0.953784, 0.955854, 0.960358, 0.965514, 0.968438, 0.97169},
+{0.243689, 0.247076, 0.248937, 0.250577, 0.251041, 0.251088, 0.251073, 0.251023, 0.250952, 0.250874,
+ 0.25052, 0.250339, 0.250292, 0.250359, 0.250463, 0.250549, 0.250686, 0.250814, 0.250945, 0.251079, 0.251214, 0.251349, 0.251484, 0.25182, 0.252158, 0.252836, 0.253519, 0.254205, 0.255591, 0.256994, 0.258413, 0.259851, 0.261306, 0.26278, 0.264273, 0.265785, 0.267317, 0.268869, 0.270442, 0.272036, 0.276117, 0.280342, 0.284721, 0.289262, 0.293978, 0.29888, 0.303981, 0.309295, 0.314838, 0.320629, 0.326687, 0.333036, 0.339701, 0.346711, 0.354101, 0.36191, 0.370183, 0.378976, 0.388353, 0.39839, 0.409183, 0.420847, 0.433527, 0.447407, 0.462728, 0.479807, 0.499079, 0.521161, 0.53097, 0.541447, 0.552684, 0.564795, 0.577922, 0.592247, 0.608001, 0.625499, 0.645173, 0.667658, 0.693938, 0.725708, 0.744582, 0.766349, 0.792272, 0.807482, 0.824852, 0.832591, 0.840901, 0.849896, 0.859735, 0.870645, 0.882977, 0.897322, 0.905568, 0.914834, 0.925538, 0.931657, 0.938502, 0.946371, 0.94811, 0.949919, 0.951804, 0.953776, 0.955847, 0.960353, 0.96551, 0.968435, 0.971688},
+{0.191626, 0.188311, 0.185222, 0.182107, 0.182532, 0.183173, 0.183784, 0.184279, 0.184634, 0.18486,
+ 0.184811, 0.184353, 0.184263, 0.184581, 0.184713, 0.18472, 0.184862, 0.185055, 0.185205, 0.185357, 0.185521, 0.185687, 0.18585, 0.18625, 0.186658, 0.187473, 0.188294, 0.189121, 0.190789, 0.192478, 0.194189, 0.195923, 0.19768, 0.19946, 0.201263, 0.203092, 0.204945, 0.206823, 0.208728, 0.210659, 0.215608, 0.220737, 0.226056, 0.231577, 0.237312, 0.243272, 0.249472, 0.255926, 0.262651, 0.269665, 0.276988, 0.284642, 0.292654, 0.301053, 0.309873, 0.319153, 0.328939, 0.339285, 0.350255, 0.361927, 0.374396, 0.387779, 0.402225, 0.417925, 0.43513, 0.454179, 0.475545, 0.499906, 0.510701, 0.522217, 0.534557, 0.547847, 0.56224, 0.577926, 0.595148, 0.614222, 0.635576, 0.659827, 0.687923, 0.721496, 0.741239, 0.763831, 0.790516, 0.806079, 0.823779, 0.831643, 0.840075, 0.849189, 0.859144, 0.870168, 0.882612, 0.897067, 0.905368, 0.914687, 0.925444, 0.931587, 0.938454, 0.946343, 0.948085, 0.949897, 0.951785, 0.95376, 0.955833, 0.960343, 0.965503, 0.96843, 0.971683},
+{0.127766, 0.134925, 0.137314, 0.135026, 0.132545, 0.132613, 0.133213, 0.133927, 0.134502, 0.134846, 0.134197,
+0.133839, 0.134383, 0.134311, 0.134305, 0.134548, 0.134538, 0.134764, 0.134855, 0.13499, 0.135153, 0.135276, 0.135401, 0.13576, 0.136094, 0.136791, 0.137494, 0.138199, 0.139634, 0.141097, 0.142587, 0.144106, 0.145656, 0.147236, 0.148849, 0.150493, 0.152171, 0.153884, 0.155632, 0.157416, 0.162043, 0.16692, 0.172065, 0.177495, 0.183228, 0.18928, 0.19567, 0.202416, 0.209537, 0.217053, 0.224984, 0.233352, 0.242183, 0.251505, 0.261348, 0.271749, 0.282749, 0.294397, 0.306753, 0.319886, 0.333884, 0.348856, 0.364938, 0.382309, 0.40121, 0.421977, 0.445099, 0.471336, 0.482957, 0.495375, 0.508729, 0.523187, 0.538956, 0.556285, 0.575464, 0.59683, 0.620788, 0.647869, 0.678894, 0.715333, 0.736426, 0.760279, 0.788101, 0.804173, 0.822338, 0.830374, 0.83897, 0.848242, 0.858347, 0.869515, 0.8821, 0.896696, 0.905068, 0.91446, 0.925289, 0.931468, 0.938371, 0.946292, 0.948041, 0.949858, 0.951752, 0.953732, 0.955811, 0.960329, 0.965496, 0.968424, 0.971679},
+{0.111845, 0.106167, 0.107777, 0.111206, 0.108936, 0.108364, 0.108639, 0.109304, 0.109887, 0.110167,
+ 0.109102, 0.109714, 0.109696, 0.109638, 0.109676, 0.109676, 0.109779, 0.109961, 0.109986, 0.110136, 0.11021, 0.110304, 0.110427, 0.110658, 0.110906, 0.111408, 0.111916, 0.112428, 0.113458, 0.114508, 0.115576, 0.116663, 0.117771, 0.118902, 0.120054, 0.12123, 0.122431, 0.123659, 0.124914, 0.126199, 0.12955, 0.133123, 0.136951, 0.141068, 0.145514, 0.150331, 0.155561, 0.161252, 0.167448, 0.174197, 0.18154, 0.189518, 0.198166, 0.207515, 0.217594, 0.228433, 0.24006, 0.252511, 0.265825, 0.280057, 0.295269, 0.311546, 0.328992, 0.347741, 0.367967, 0.389902, 0.413872, 0.440385, 0.451887, 0.464034, 0.476972, 0.490925, 0.506263, 0.523592, 0.543861, 0.568205, 0.597077, 0.629836, 0.666171, 0.707148, 0.730203, 0.755806, 0.785154, 0.801892, 0.82065, 0.828901, 0.837698, 0.847157, 0.857436, 0.868766, 0.881504, 0.896248, 0.904696, 0.914167, 0.925079, 0.931302, 0.938248, 0.946214, 0.947971, 0.949797, 0.951699, 0.953687, 0.955773, 0.960306, 0.965484, 0.968417, 0.971675},
+{0.0973518, 0.0987518, 0.0952128, 0.097231, 0.0968051, 0.0959061, 0.0958383, 0.0963991, 0.0969597, 0.0971588, 0.0962907, 0.0968828, 0.0964446, 0.0967173, 0.0968133, 0.0967445, 0.0968961, 0.0970152, 0.0970355, 0.0971754, 0.0972259, 0.0973507, 0.097408, 0.0976397, 0.0978753, 0.0983115, 0.0987594, 0.099209, 0.100108, 0.101005, 0.101904, 0.102805, 0.103707, 0.104611, 0.10552, 0.106431, 0.107346, 0.108266, 0.109192, 0.110125, 0.112493, 0.114931, 0.117463, 0.120121, 0.122943, 0.125975, 0.129278, 0.132931, 0.137032, 0.14171, 0.147116, 0.153415, 0.160767, 0.169299, 0.179085, 0.19014, 0.202441, 0.215947, 0.230623, 0.246457, 0.263464, 0.281691, 0.301218, 0.322157, 0.344655, 0.368896, 0.39509, 0.42345, 0.43543, 0.447764, 0.460418, 0.473311, 0.486283, 0.499037,
+0.511101, 0.522095, 0.532461, 0.536917, 0.527548, 0.521465, 0.518438, 0.515417, 0.51241, 0.510911, 0.509415, 0.508818, 0.508221, 0.507624, 0.507028, 0.506432, 0.505837, 0.505242, 0.504944, 0.504647, 0.50435, 0.504202, 0.504054, 0.503904, 0.503874, 0.503845, 0.503817, 0.503789, 0.50376, 0.503692, 0.503638, 0.503632, 0.503585},
+{0.084098, 0.0868741, 0.0879148, 0.0858816, 0.0871769, 0.0862173, 0.0858779, 0.0863779, 0.0869438, 0.0870509, 0.0866021, 0.0864788, 0.0867758, 0.0866752, 0.0866613, 0.0868868, 0.086965, 0.0870574, 0.0871075, 0.0872251, 0.0873545, 0.0874293, 0.087563, 0.0878271, 0.088086, 0.0886037, 0.0891314, 0.0896576, 0.0906978, 0.0917299, 0.0927446, 0.093744, 0.0947274, 0.0956935, 0.0966414, 0.0975719, 0.0984848, 0.0993786, 0.100255, 0.101113, 0.103185, 0.105155, 0.107036, 0.108838, 0.110571, 0.112244, 0.113866, 0.115452, 0.117034, 0.118689, 0.120596, 0.123138, 0.127029, 0.133252, 0.142539, 0.154841, 0.169536, 0.185971, 0.203721, 0.222585, 0.242517, 0.263571, 0.285865, 0.309569, 0.334899, 0.362133, 0.391629, 0.423854, 0.437641, 0.45201, 0.467014, 0.482713, 0.499165, 0.516428, 0.534543, 0.553525, 0.573596, 0.602227, 0.649295, 0.697231, 0.722841, 0.750611, 0.781797, 0.799333,
+0.818797, 0.827303, 0.836336, 0.846012, 0.856487, 0.867993, 0.880887, 0.895775, 0.904293, 0.913837, 0.92483, 0.931097, 0.938091, 0.946107, 0.947875, 0.949711, 0.951623, 0.953621, 0.955717, 0.960269, 0.965464, 0.968404, 0.971669},
+{0.0783357, 0.0733796, 0.0766204, 0.0744319, 0.0764107, 0.0754793, 0.0749396, 0.0755031, 0.0761004,
+ 0.0760294, 0.0759874, 0.075511, 0.0757765, 0.0758322, 0.0759714, 0.0759232, 0.0761145, 0.0762289, 0.0763205, 0.0764184, 0.0765972, 0.0767207, 0.0768409, 0.0771736, 0.0775187, 0.07821, 0.0789117, 0.0796137, 0.0810158, 0.0824117, 0.0837964, 0.0851528, 0.0864792, 0.0877698, 0.0890208, 0.0902295, 0.0913937, 0.0925132, 0.0935883, 0.0946171, 0.0969926, 0.0990908, 0.100921, 0.102489, 0.103795, 0.104821, 0.10553, 0.105854, 0.105679, 0.104817, 0.102968, 0.0997112, 0.094996, 0.0928224, 0.102996, 0.122468, 0.144233, 0.166117, 0.187881, 0.209753, 0.232042, 0.255048, 0.279057, 0.304354, 0.331244, 0.360084, 0.391319, 0.425537, 0.440234, 0.455604, 0.471729, 0.488705, 0.506652, 0.52572, 0.546107, 0.568081, 0.592057, 0.618799, 0.650217, 0.691189, 0.716737, 0.745623, 0.778341, 0.796657, 0.816858, 0.825638, 0.834931, 0.844846, 0.855539, 0.867237, 0.880294, 0.895318, 0.903898, 0.913504, 0.924565, 0.930871, 0.93791, 0.945976, 0.947755, 0.949602, 0.951525, 0.953535, 0.955643, 0.960217, 0.965434, 0.968355, 0.971639}};
+
+ const double imomegaqnm22[8][107] = {{0.0784607, 0.0801007, 0.0816472, 0.0840037, 0.0854954,
+ 0.0860129, 0.0864215, 0.0867455, 0.0870035, 0.08721, 0.0877802, 0.0879878, 0.088065, 0.0880965,
+ 0.0880878, 0.0880757, 0.0880612, 0.0880574, 0.0880589, 0.0880627, 0.0880675, 0.0880727, 0.088078, 0.0880913, 0.0881045, 0.0881304, 0.088156, 0.0881813, 0.0882315, 0.0882807, 0.0883289, 0.0883763, 0.0884226, 0.0884679, 0.0885122, 0.0885555, 0.0885976, 0.0886386, 0.0886785, 0.0887172, 0.0888085, 0.0888917, 0.0889663, 0.0890315, 0.0890868, 0.0891313, 0.0891643, 0.0891846, 0.0891911, 0.0891825, 0.0891574, 0.0891138, 0.0890496, 0.0889623, 0.0888489, 0.0887057, 0.0885283, 0.0883112, 0.0880477, 0.0877293, 0.0873453, 0.086882, 0.0863212, 0.0856388, 0.0848021, 0.0837652, 0.0824618, 0.0807929, 0.0799908, 0.0790927, 0.0780817, 0.0769364, 0.0756296, 0.0741258, 0.072378, 0.0703215, 0.0678642, 0.0648692, 0.0611186, 0.0562313, 0.053149, 0.0494336, 0.0447904, 0.0419586, 0.0386302, 0.0371155, 0.0354676, 0.033659, 0.0316516, 0.0293904, 0.0267908, 0.0237095, 0.0219107, 0.0198661, 0.0174737, 0.0160919, 0.014534, 0.0127274, 0.0123259, 0.0119077, 0.0114708, 0.0110127, 0.0105306, 0.00947799, 0.00826689, 0.00757704, 0.0068074},
+{0.284478, 0.282567, 0.281162, 0.279245, 0.278072, 0.27767, 0.277358, 0.277118, 0.276936, 0.2768,
+ 0.276536, 0.276565, 0.276647, 0.276753, 0.276778, 0.276775, 0.276764, 0.276768, 0.276776, 0.276784, 0.276791, 0.276797, 0.276803, 0.276818, 0.276834, 0.276864, 0.276893, 0.276922, 0.276977, 0.277028, 0.277076, 0.27712, 0.27716, 0.277197, 0.27723, 0.277259, 0.277283, 0.277304, 0.277321, 0.277333, 0.277344, 0.277326, 0.277278, 0.277196, 0.27708, 0.276926, 0.276732, 0.276495, 0.276212, 0.275877, 0.275486, 0.275033, 0.274512, 0.273915, 0.273232, 0.272452, 0.271562, 0.270546, 0.269383, 0.268049, 0.266512, 0.264733, 0.262661, 0.260225, 0.257331, 0.253847, 0.24958, 0.244238, 0.241705, 0.238888, 0.235736, 0.232183, 0.228149, 0.223524, 0.218165, 0.211876, 0.204376, 0.195252, 0.183847, 0.169019, 0.159687, 0.148458, 0.134453, 0.125927, 0.115917, 0.111365, 0.106415, 0.100985, 0.0949599, 0.0881754, 0.080377, 0.0711342, 0.0657383, 0.0596046, 0.0524264, 0.04828, 0.043605, 0.0381837, 0.0369789, 0.0357239, 0.0344128, 0.0330384, 0.0315916, 0.0284334, 0.0247999, 0.0227304, 0.0204216},
+{0.504534, 0.501693, 0.501238, 0.503711, 0.506007, 0.50649, 0.506633, 0.506559, 0.506365, 0.50612,
+ 0.505173, 0.50512, 0.505381, 0.505519, 0.505371, 0.505318, 0.505354, 0.505311, 0.505262, 0.505236, 0.50521, 0.505177, 0.505141, 0.505059, 0.504978, 0.504812, 0.504645, 0.504476, 0.504135, 0.503786, 0.503432, 0.50307, 0.502702, 0.502326, 0.501944, 0.501554, 0.501156, 0.500751, 0.500338, 0.499917, 0.498828, 0.497686, 0.496488, 0.49523, 0.49391, 0.492523, 0.491065, 0.489531, 0.487913, 0.486206, 0.484399, 0.482484, 0.480448, 0.478277, 0.475955, 0.473463, 0.470778, 0.467872, 0.464713, 0.46126, 0.457463, 0.453259, 0.448569, 0.443287, 0.437269, 0.430315, 0.422131, 0.412262, 0.407689, 0.402664, 0.397103, 0.390894, 0.383895, 0.375919, 0.366715, 0.35594, 0.34311, 0.327518, 0.308058, 0.282827, 0.266998, 0.248008, 0.22441, 0.210086, 0.193307, 0.18569, 0.177413, 0.16834, 0.158283, 0.146966, 0.133965, 0.118563, 0.109572, 0.0993515, 0.0873891, 0.0804781, 0.0726848, 0.0636465, 0.0616378, 0.0595453, 0.0573593, 0.0550676, 0.0526555, 0.0473899, 0.0413327, 0.037883, 0.0340348},
+{0.777682, 0.77817, 0.774907, 0.771079, 0.772456, 0.773571, 0.774249, 0.774423, 0.774236, 0.773865,
+ 0.772678, 0.773376, 0.773489, 0.77299, 0.773229, 0.773121, 0.773005, 0.772942, 0.772818, 0.772776, 0.77268, 0.772579, 0.772506, 0.772294, 0.772084, 0.771654, 0.771224, 0.770787, 0.7699, 0.768995, 0.768072, 0.767129, 0.766168, 0.765187, 0.764186, 0.763165, 0.762123, 0.761061, 0.759977, 0.758872, 0.756015, 0.75302, 0.749885, 0.746606, 0.743182, 0.739611, 0.735891, 0.732017, 0.727985, 0.723788, 0.719419, 0.714865, 0.710114, 0.705148, 0.699946, 0.694481, 0.688721, 0.682628, 0.676155, 0.669243, 0.661823, 0.653808, 0.645091, 0.635536, 0.624969, 0.613154, 0.599764, 0.584301, 0.577364, 0.569885, 0.561756, 0.552827, 0.542888, 0.531648, 0.518699, 0.50348, 0.485224, 0.462864, 0.434823, 0.398473, 0.375741, 0.348572, 0.314974, 0.294663, 0.270945, 0.2602, 0.248542, 0.235779, 0.221649, 0.205769, 0.187547, 0.16598, 0.153396, 0.139094, 0.122354, 0.112682, 0.101773, 0.0891181, 0.0863053, 0.0833752, 0.0803139, 0.0771045, 0.0737264, 0.0663517, 0.0578682, 0.053037, 0.0476481},
+{1.04431, 1.0466, 1.05065, 1.04828, 1.04719, 1.04809, 1.04894, 1.04925, 1.04906, 1.04863, 1.04812,
+ 1.04862, 1.04806, 1.04843, 1.04808, 1.04824, 1.04803, 1.04799, 1.04788, 1.04781, 1.04768, 1.04762, 1.04752, 1.04729, 1.04704, 1.04657, 1.04609, 1.0456, 1.0446, 1.04357, 1.04251, 1.04141, 1.04028, 1.03911, 1.03791, 1.03667, 1.03539, 1.03406, 1.0327, 1.03129, 1.02756, 1.02353, 1.01918, 1.01448, 1.00943, 1.004, 0.9982, 0.992012, 0.985437, 0.978476, 0.971133, 0.963412, 0.955317, 0.946845, 0.937987, 0.928725, 0.919026, 0.908845, 0.898118, 0.886764, 0.874681, 0.861738, 0.847776, 0.832595, 0.815947, 0.797527, 0.776957, 0.7538, 0.74371, 0.733106, 0.721967, 0.710268, 0.697962, 0.684902, 0.670601, 0.65375, 0.632042, 0.603295, 0.56587, 0.517102, 0.486783, 0.450771, 0.406552, 0.379969, 0.349048, 0.33508, 0.319949, 0.303412, 0.285135, 0.264631, 0.241142, 0.213382, 0.197201, 0.178818, 0.157307, 0.144878, 0.130859, 0.114594, 0.110978, 0.107211, 0.103275, 0.099148, 0.0948041, 0.0853202, 0.0744092, 0.0681953, 0.0612642},
+{1.32188, 1.31695, 1.31668, 1.31947, 1.31731, 1.3177, 1.31852, 1.31894, 1.31877, 1.31831, 1.31844,
+ 1.31807, 1.31822, 1.318, 1.3182, 1.318, 1.31792, 1.31791, 1.31782, 1.3177, 1.31764, 1.31754, 1.31745, 1.31723, 1.31701, 1.31656, 1.31612, 1.31566, 1.31474, 1.31378, 1.3128, 1.31179, 1.31075, 1.30967, 1.30856, 1.3074, 1.3062, 1.30495, 1.30366, 1.30231, 1.2987, 1.2947, 1.29025, 1.2853, 1.2798, 1.27368, 1.26687, 1.25931, 1.25091, 1.24163, 1.23143, 1.22032, 1.20835, 1.19561, 1.18221, 1.16825, 1.15377, 1.13878, 1.1232, 1.10691, 1.08976, 1.07153, 1.05194, 1.03067, 1.0073, 0.981265, 0.951825, 0.91795, 0.902851, 0.886706, 0.869389, 0.850781, 0.830803, 0.809534, 0.787531, 0.766572, 0.750871, 0.748723, 0.741744, 0.732374, 0.728044, 0.723765, 0.719565, 0.717492, 0.715438, 0.714621, 0.713807, 0.712996, 0.712188, 0.711383, 0.710581, 0.709781, 0.709382, 0.708984, 0.708587, 0.708388, 0.70819, 0.707992, 0.707952, 0.707911, 0.707871, 0.707832, 0.707796, 0.70772, 0.70762, 0.707592, 0.707598},
+{1.58204, 1.58635, 1.58318, 1.58511, 1.58355, 1.58343, 1.58418, 1.58468, 1.58448, 1.58398, 1.58441,
+ 1.58383, 1.58417, 1.5841, 1.58387, 1.58384, 1.58373, 1.58367, 1.58357, 1.58342, 1.58336, 1.58323, 1.58315, 1.58289, 1.58264, 1.58213, 1.58164, 1.58114, 1.58016, 1.57919, 1.57821, 1.57723, 1.57624, 1.57524, 1.57422, 1.57317, 1.5721, 1.57099, 1.56984, 1.56865, 1.56545, 1.56189, 1.55789, 1.55337, 1.54825, 1.54244, 1.53582, 1.52823, 1.51949, 1.50932, 1.49738, 1.48328, 1.46673, 1.44791, 1.42768, 1.40711, 1.38682, 1.36683, 1.34689, 1.32662, 1.30561, 1.28347, 1.25976, 1.234, 1.20558, 1.17376, 1.13753, 1.09541, 1.07645, 1.05602, 1.03387, 1.0097, 0.983084, 0.953463, 0.919986, 0.881204, 0.833927, 0.770337, 0.707988, 0.641106, 0.601525, 0.555418, 0.499613, 0.466355, 0.427874, 0.41055, 0.391822, 0.371395, 0.348864, 0.323638, 0.2948, 0.260789, 0.240992, 0.218519, 0.192238, 0.177057, 0.159933, 0.140065, 0.135647, 0.131044, 0.126235, 0.121193, 0.115884, 0.104293, 0.0909554, 0.0833586, 0.0748845},
+{1.84957, 1.84968, 1.85134, 1.85007, 1.84983, 1.84929, 1.85004, 1.8506, 1.85027, 1.84968, 1.85008,
+ 1.85008, 1.84964, 1.84961, 1.84963, 1.84966, 1.84941, 1.84923, 1.84906, 1.84884, 1.84864, 1.84851, 1.84829, 1.84788, 1.84746, 1.84662, 1.84583, 1.84506, 1.84361, 1.84225, 1.84097, 1.83975, 1.83859, 1.83747, 1.83638, 1.8353, 1.83424, 1.83317, 1.8321, 1.831, 1.82815, 1.82502, 1.82153, 1.81757, 1.81306, 1.8079, 1.80199, 1.79518, 1.78728, 1.77801, 1.76686, 1.75278, 1.73323, 1.70384, 1.66882, 1.63893, 1.61423, 1.59206, 1.57064, 1.54892, 1.52619, 1.5019, 1.47555, 1.44657, 1.41428, 1.37781, 1.33598, 1.28712, 1.26509, 1.24133, 1.21558, 1.18751, 1.15671, 1.12263, 1.08453, 1.04141, 0.991742, 0.933178, 0.861906, 0.773444, 0.721837, 0.663505, 0.594647, 0.554166, 0.507666, 0.486825, 0.464348, 0.439888, 0.412969, 0.382898, 0.348601, 0.308246, 0.284798, 0.25821, 0.227147, 0.209213, 0.188989, 0.165524, 0.160306, 0.15487, 0.149189, 0.143232, 0.136961, 0.123266, 0.107504, 0.113694, 0.102135}};
+
+ /* 2, 1 mode */
+
+ const double reomegaqnm21[8][107] = {{0.336609, 0.339386, 0.340852, 0.342219, 0.342818, 0.343002,
+ 0.343143, 0.343254, 0.343344, 0.343417, 0.343641, 0.343748,
+ 0.343804, 0.343853, 0.343871, 0.343879, 0.343886, 0.343891,
+ 0.343896, 0.343902, 0.343909, 0.343915, 0.343922, 0.343941, 0.34396,
+ 0.344002, 0.344049, 0.344101, 0.34422, 0.344359, 0.344517,
+ 0.344696, 0.344896, 0.345115, 0.345356, 0.345617, 0.345899,
+ 0.346201, 0.346525, 0.34687, 0.347824, 0.348911, 0.350132, 0.351491,
+ 0.35299, 0.354633, 0.356423, 0.358366, 0.360469, 0.362738,
+ 0.365183, 0.367812, 0.370637, 0.373672, 0.376931, 0.380432,
+ 0.384197, 0.388248, 0.392615, 0.39733, 0.402436, 0.407979, 0.41402,
+ 0.420632, 0.427909, 0.435968, 0.444968, 0.455121, 0.459569,
+ 0.464271, 0.469259, 0.474564, 0.480231, 0.486308, 0.492859,
+ 0.499965, 0.507729, 0.516291, 0.525845, 0.536673, 0.542693,
+ 0.549213, 0.556329, 0.560146, 0.564155, 0.565814, 0.567505,
+ 0.569227, 0.570976, 0.572749, 0.574535, 0.576322, 0.577208,
+ 0.578084, 0.578948, 0.579374, 0.579795, 0.580212, 0.580295,
+ 0.580377, 0.58046, 0.580541, 0.580623, 0.580784, 0.580942, 0.581018,
+ 0.581093}, {0.313486, 0.314984, 0.315748, 0.31636, 0.316504,
+ 0.316512, 0.316502, 0.316483, 0.31646, 0.316436, 0.316347, 0.316311,
+ 0.316305, 0.316315, 0.316325, 0.31633, 0.316338, 0.316345,
+ 0.316352, 0.31636, 0.316368, 0.316375, 0.316383, 0.316401, 0.316419,
+ 0.316455, 0.316491, 0.316527, 0.316602, 0.316682, 0.316772,
+ 0.316874, 0.316989, 0.317122, 0.317273, 0.317444, 0.317636,
+ 0.317851, 0.31809, 0.318353, 0.319124, 0.320064, 0.321179, 0.322476,
+ 0.32396, 0.325636, 0.327508, 0.329582, 0.331865, 0.334364,
+ 0.337088, 0.340045, 0.343249, 0.346711, 0.350448, 0.354478,
+ 0.358823, 0.363506, 0.368558, 0.374014, 0.379916, 0.386313,
+ 0.393268, 0.400856, 0.409172, 0.418337, 0.428509, 0.439897,
+ 0.444855, 0.450076, 0.455587, 0.46142, 0.467612, 0.474208, 0.481261,
+ 0.488834, 0.497004, 0.505862, 0.515506, 0.526011, 0.531572,
+ 0.537263, 0.542874, 0.545479, 0.547723, 0.548438, 0.548984, 0.54929,
+ 0.549241, 0.548642, 0.54714, 0.544185, 0.542606, 0.542325,
+ 0.541626, 0.540962, 0.540617, 0.540156, 0.540066, 0.539986,
+ 0.539906, 0.539818, 0.539726, 0.539553, 0.539377, 0.539288,
+ 0.539198}, {0.270281, 0.269419, 0.268655, 0.267935, 0.267923,
+ 0.268009, 0.268102, 0.268185, 0.268251, 0.268297, 0.268334,
+ 0.268285, 0.268273, 0.268312, 0.268342, 0.268359, 0.268398,
+ 0.268442, 0.268483, 0.268523, 0.268562, 0.268601, 0.26864, 0.268733,
+ 0.268822, 0.268989, 0.269141, 0.26928, 0.26952, 0.269718, 0.269881,
+ 0.270016, 0.270132, 0.270235, 0.270333, 0.270431, 0.270536,
+ 0.270653, 0.270785, 0.270937, 0.271426, 0.2721, 0.272992, 0.274121,
+ 0.275504, 0.277153, 0.279078, 0.281288, 0.283792, 0.286598,
+ 0.289716, 0.293156, 0.296931, 0.301053, 0.30554, 0.31041, 0.315684,
+ 0.321389, 0.327554, 0.334218, 0.341421, 0.349217, 0.357668,
+ 0.366852, 0.376864, 0.387825, 0.39989, 0.413261, 0.419032, 0.425075,
+ 0.431414, 0.438075, 0.445088, 0.452488, 0.46031, 0.468593,
+ 0.477369, 0.48665, 0.49639, 0.506348, 0.511184, 0.515607, 0.51903,
+ 0.519992, 0.5201, 0.51983, 0.519361, 0.51871, 0.517943, 0.517204,
+ 0.516728, 0.516696, 0.516098, 0.513376, 0.509813, 0.508083,
+ 0.506412, 0.504789, 0.504468, 0.504148, 0.50383, 0.503511, 0.503194,
+ 0.502559, 0.501923, 0.501605, 0.501286}, {0.21269, 0.214089,
+ 0.215208, 0.215364, 0.21474, 0.214584, 0.21456, 0.214625, 0.21473,
+ 0.214837, 0.214992, 0.214885, 0.214922, 0.215045, 0.215071,
+ 0.215139, 0.215267, 0.215383, 0.215507, 0.215624, 0.215741,
+ 0.215858, 0.215974, 0.216256, 0.216533, 0.217064, 0.217566, 0.21804,
+ 0.218903, 0.219653, 0.220295, 0.220836, 0.221285, 0.22165,
+ 0.221945, 0.22218, 0.222368, 0.22252, 0.222647, 0.222759, 0.223032,
+ 0.223383, 0.2239, 0.224647, 0.225672, 0.22701, 0.228689, 0.23073,
+ 0.233151, 0.235969, 0.239199, 0.242854, 0.246951, 0.251505,
+ 0.256534, 0.262058, 0.268101, 0.274689, 0.281852, 0.289628,
+ 0.298059, 0.307197, 0.317104, 0.327855, 0.339542, 0.352278,
+ 0.366207, 0.38151, 0.388065, 0.394895, 0.402017, 0.409454, 0.417227,
+ 0.425361, 0.433878, 0.442797, 0.452127, 0.461855, 0.471918,
+ 0.482195, 0.48739, 0.49271, 0.498495, 0.501813, 0.5056, 0.507251,
+ 0.508939, 0.510585, 0.512031, 0.513028, 0.513289, 0.512758,
+ 0.512367, 0.512091, 0.511921, 0.51135, 0.5096, 0.50715, 0.50665,
+ 0.506154, 0.505662, 0.505175, 0.504694, 0.503744, 0.502809,
+ 0.502344, 0.50188}, {0.171239, 0.169224, 0.168634, 0.170053,
+ 0.169938, 0.169613, 0.169418, 0.169408, 0.169531, 0.169696,
+ 0.169825, 0.169724, 0.16992, 0.169916, 0.170075, 0.17014, 0.170344,
+ 0.170511, 0.17071, 0.170886, 0.171073, 0.171258, 0.171437, 0.171892,
+ 0.172337, 0.173213, 0.174064, 0.174889, 0.176453, 0.177895,
+ 0.179203, 0.180372, 0.181395, 0.182273, 0.183007, 0.183606,
+ 0.184081, 0.184444, 0.18471, 0.184896, 0.185105, 0.18512, 0.185113,
+ 0.185222, 0.18555, 0.186176, 0.187164, 0.188562, 0.190413, 0.192751,
+ 0.195604, 0.199, 0.202962, 0.207515, 0.212679, 0.21848, 0.224939,
+ 0.232083, 0.23994, 0.248543, 0.257928, 0.268139, 0.279228, 0.291258,
+ 0.304303, 0.318456, 0.33383, 0.350563, 0.357675, 0.365045,
+ 0.372687, 0.380617, 0.388855, 0.397422, 0.406346, 0.41567, 0.425462,
+ 0.435857, 0.447149, 0.45999, 0.467349, 0.475546, 0.484594,
+ 0.489367, 0.494295, 0.496339, 0.498459, 0.500692, 0.50308, 0.505635,
+ 0.508214, 0.510197, 0.510572, 0.510387, 0.509864, 0.509635,
+ 0.509456, 0.50879, 0.508443, 0.507999, 0.50747, 0.506881, 0.506257,
+ 0.504974, 0.503704, 0.503082, 0.502466}, {0.136159, 0.137914,
+ 0.137016, 0.136626, 0.137329, 0.137055, 0.136755, 0.136667,
+ 0.136793, 0.136997, 0.136954, 0.137117, 0.137154, 0.137279, 0.1373,
+ 0.13747, 0.137649, 0.137842, 0.138069, 0.138258, 0.138476, 0.138671,
+ 0.138881, 0.139389, 0.139898, 0.14091, 0.14191, 0.142898, 0.144829,
+ 0.146684, 0.148447, 0.150099, 0.151622, 0.153001, 0.154221,
+ 0.15527, 0.156142, 0.156839, 0.157368, 0.15774, 0.158094, 0.157845,
+ 0.15725, 0.156526, 0.155847, 0.155354, 0.155162, 0.155369, 0.156061,
+ 0.157316, 0.159206, 0.161795, 0.165143, 0.169299, 0.174306,
+ 0.180192, 0.186977, 0.194671, 0.203282, 0.212811, 0.223263,
+ 0.234649, 0.246985, 0.260297, 0.274622, 0.290009, 0.306518,
+ 0.324226, 0.331666, 0.339322, 0.347205, 0.355332, 0.363727,
+ 0.372432, 0.381518, 0.391111, 0.401435, 0.412868, 0.425995,
+ 0.441563, 0.45052, 0.460463, 0.471717, 0.477974, 0.484665, 0.487438,
+ 0.490248, 0.493085, 0.49596, 0.498923, 0.502084, 0.505527,
+ 0.507222, 0.508526, 0.508875, 0.508627, 0.508251, 0.507926,
+ 0.507863, 0.507785, 0.50767, 0.507484, 0.507181, 0.506113, 0.504624,
+ 0.503839, 0.50306}, {0.114342, 0.113963, 0.115141, 0.114074,
+ 0.11486, 0.114789, 0.114485, 0.114338, 0.114452, 0.114665, 0.114512,
+ 0.114807, 0.11467, 0.114821, 0.114995, 0.115025, 0.115231,
+ 0.115438, 0.115661, 0.115846, 0.11605, 0.116249, 0.116452, 0.116951,
+ 0.117454, 0.118454, 0.11946, 0.120464, 0.122464, 0.124443,
+ 0.126383, 0.128266, 0.130073, 0.131781, 0.133368, 0.134813, 0.13609,
+ 0.137179, 0.138065, 0.138742, 0.139567, 0.139335, 0.138333,
+ 0.136834, 0.135064, 0.133208, 0.131418, 0.129826, 0.128564,
+ 0.127775, 0.127629, 0.128336, 0.130133, 0.133252, 0.137863,
+ 0.144021, 0.151672, 0.160684, 0.170902, 0.182186, 0.194429,
+ 0.207556, 0.221528, 0.236327, 0.251955, 0.268421, 0.285744, 0.30395,
+ 0.311492, 0.319195, 0.327076, 0.335168, 0.343522, 0.352232,
+ 0.361443, 0.371382, 0.382361, 0.394771, 0.409089, 0.426092,
+ 0.436065, 0.4474, 0.460415, 0.467675, 0.475563, 0.478922, 0.482402,
+ 0.485993, 0.489665, 0.493377, 0.497113, 0.500995, 0.503086,
+ 0.505273, 0.507186, 0.507677, 0.507628, 0.507177, 0.507077,
+ 0.506981, 0.506892, 0.506806, 0.506714, 0.506383, 0.505391,
+ 0.504576, 0.503665}, {0.0996362, 0.098809, 0.0988228, 0.0989612,
+ 0.0991812, 0.0993225, 0.0990912, 0.0989133, 0.0990066, 0.0992056,
+ 0.0990844, 0.0992013, 0.0993046, 0.0993698, 0.0994135, 0.0995406,
+ 0.0997102, 0.0999057, 0.100109, 0.100292, 0.100464, 0.100668,
+ 0.100843, 0.10132, 0.101793, 0.102742, 0.103705, 0.104671, 0.106617,
+ 0.108576, 0.11054, 0.112492, 0.114417, 0.116296, 0.118106,
+ 0.119822, 0.121422, 0.122876, 0.12415, 0.125214, 0.12686, 0.127085,
+ 0.126123, 0.124264, 0.121765, 0.118824, 0.115576, 0.112102, 0.10844,
+ 0.104598, 0.100602, 0.0966436, 0.0934548, 0.0928224, 0.0967608,
+ 0.105267, 0.116748, 0.129817, 0.143719, 0.158124, 0.17292, 0.188094,
+ 0.203673, 0.219697, 0.236201, 0.253208, 0.270727, 0.288784,
+ 0.296181, 0.303707, 0.311404, 0.319342, 0.327628, 0.336416,
+ 0.345907, 0.35633, 0.367923, 0.380968, 0.395965, 0.413866, 0.424377,
+ 0.436366, 0.450442, 0.458506, 0.467375, 0.471171, 0.475126,
+ 0.479254, 0.483568, 0.488052, 0.492639, 0.497232, 0.499557,
+ 0.501993, 0.504598, 0.505838, 0.506697, 0.506742, 0.506649,
+ 0.506536, 0.50641, 0.506281, 0.506156, 0.505924, 0.505541, 0.505047,
+ 0.504219}};
+
+ const double imomegaqnm21[8][107] = {{0.0743116, 0.0772659, 0.0791824, 0.0812815, 0.0822652, 0.082556,
+ 0.0827684, 0.082926, 0.0830445, 0.0831347, 0.0833596, 0.0834304,
+ 0.0834555, 0.0834714, 0.0834806, 0.0834917, 0.0835195, 0.0835507,
+ 0.0835831, 0.0836156, 0.0836481, 0.0836804, 0.0837126, 0.083792,
+ 0.0838704, 0.0840241, 0.0841737, 0.0843193, 0.0845994, 0.084865,
+ 0.085117, 0.0853561, 0.0855831, 0.0857987, 0.0860035, 0.086198,
+ 0.0863828, 0.0865584, 0.0867253, 0.086884, 0.087247, 0.0875662,
+ 0.0878462, 0.0880906, 0.0883025, 0.088484, 0.088637, 0.0887628,
+ 0.0888621, 0.0889354, 0.0889828, 0.0890037, 0.0889973, 0.0889623,
+ 0.0888968, 0.0887983, 0.0886636, 0.0884885, 0.0882679, 0.0879952,
+ 0.0876618, 0.0872571, 0.086767, 0.086173, 0.0854501, 0.0845642,
+ 0.0834665, 0.0820852, 0.0814304, 0.0807035, 0.0798926, 0.0789827,
+ 0.077955, 0.0767847, 0.0754394, 0.0738744, 0.072027, 0.0698043,
+ 0.067061, 0.0635492, 0.0613721, 0.058791, 0.0556436, 0.0537759,
+ 0.0516427, 0.0506978, 0.0496908, 0.0486136, 0.0474565, 0.0462084,
+ 0.0448564, 0.0433879, 0.0426068, 0.0417939, 0.0409501, 0.0405173,
+ 0.0400777, 0.0396319, 0.039542, 0.0394519, 0.0393616, 0.039271,
+ 0.0391802, 0.0389974, 0.0388111, 0.038714, 0.0386091}, {0.258785,
+ 0.258526, 0.258215, 0.257703, 0.257385, 0.257284, 0.25721, 0.257158,
+ 0.257123, 0.257101, 0.257089, 0.257133, 0.257178, 0.257248,
+ 0.257304, 0.257357, 0.257465, 0.257574, 0.257683, 0.257791,
+ 0.257898, 0.258005, 0.258112, 0.258376, 0.258637, 0.259149,
+ 0.259649, 0.260137, 0.261076, 0.261967, 0.262812, 0.263613,
+ 0.264372, 0.265089, 0.265768, 0.26641, 0.267016, 0.267589, 0.26813,
+ 0.26864, 0.269792, 0.270782, 0.271629, 0.272346, 0.272945, 0.273434,
+ 0.273821, 0.274112, 0.274309, 0.274415, 0.27443, 0.274354,
+ 0.274183, 0.273915, 0.273543, 0.273058, 0.272452, 0.271711,
+ 0.270819, 0.269754, 0.268489, 0.266992, 0.265218, 0.263108,
+ 0.260587, 0.257547, 0.253838, 0.249238, 0.247078, 0.244692,
+ 0.242045, 0.239089, 0.235766, 0.231999, 0.227686, 0.222686, 0.2168,
+ 0.209731, 0.201006, 0.189803, 0.18282, 0.174484, 0.164205, 0.158029,
+ 0.150891, 0.1477, 0.14428, 0.140606, 0.136657, 0.132444, 0.128112,
+ 0.124511, 0.123925, 0.123321, 0.12167, 0.121162, 0.120732, 0.12014,
+ 0.120048, 0.119951, 0.119844, 0.119734, 0.119631, 0.119429,
+ 0.119227, 0.119127, 0.119027}, {0.451082, 0.450126, 0.449946,
+ 0.450393, 0.450836, 0.450954, 0.451016, 0.451037, 0.451032,
+ 0.451015, 0.450927, 0.450953, 0.451028, 0.451151, 0.451242,
+ 0.451336, 0.451538, 0.451736, 0.451932, 0.452129, 0.452326,
+ 0.452521, 0.452716, 0.453201, 0.453683, 0.454634, 0.45557, 0.456489,
+ 0.458275, 0.459989, 0.461626, 0.463185, 0.464665, 0.466067,
+ 0.46739, 0.468636, 0.469808, 0.470906, 0.471935, 0.472897, 0.475022,
+ 0.476783, 0.478216, 0.479352, 0.48022, 0.48084, 0.481231, 0.481407,
+ 0.481377, 0.481149, 0.480726, 0.480109, 0.479294, 0.478277,
+ 0.477047, 0.475592, 0.473893, 0.471929, 0.469669, 0.467076,
+ 0.464104, 0.460691, 0.456761, 0.45221, 0.446903, 0.440653, 0.433196,
+ 0.424144, 0.419951, 0.415358, 0.4103, 0.404693, 0.398434, 0.391383,
+ 0.383355, 0.374094, 0.363227, 0.350188, 0.334044, 0.313093,
+ 0.299808, 0.283583, 0.262719, 0.249472, 0.233119, 0.225306,
+ 0.216483, 0.206365, 0.194563, 0.180538, 0.16345, 0.141483, 0.12731,
+ 0.111596, 0.0954876, 0.0868316, 0.0774193, 0.066857, 0.0645541,
+ 0.0621712, 0.0596988, 0.057125, 0.0544355, 0.0486318, 0.0420655,
+ 0.0383765, 0.0343031}, {0.670736, 0.672092, 0.671812, 0.670663,
+ 0.670549, 0.67073, 0.670927, 0.671078, 0.671164, 0.671189, 0.671021,
+ 0.671075, 0.671219, 0.67131, 0.671427, 0.671572, 0.671807,
+ 0.672062, 0.672309, 0.672557, 0.672808, 0.673057, 0.673305,
+ 0.673929, 0.674552, 0.675799, 0.677043, 0.678283, 0.680743,
+ 0.683166, 0.685536, 0.68784, 0.690067, 0.692205, 0.694247, 0.696187,
+ 0.69802, 0.699744, 0.701359, 0.702865, 0.706165, 0.708833,
+ 0.710915, 0.71246, 0.71351, 0.714105, 0.714277, 0.714053, 0.713452,
+ 0.71249, 0.711176, 0.709516, 0.707509, 0.705148, 0.702423, 0.699317,
+ 0.695803, 0.691851, 0.687416, 0.682445, 0.676867, 0.670592,
+ 0.663504, 0.655451, 0.646227, 0.635554, 0.623036, 0.60809, 0.601244,
+ 0.593791, 0.58563, 0.576638, 0.566651, 0.555455, 0.54276, 0.528156,
+ 0.511038, 0.490465, 0.464847, 0.431189, 0.409563, 0.382936,
+ 0.348824, 0.32773, 0.302947, 0.291759, 0.279694, 0.26659, 0.252176,
+ 0.235931, 0.216835, 0.192946, 0.178198, 0.160681, 0.138951,
+ 0.125667, 0.110911, 0.095128, 0.0917732, 0.0883219, 0.0847576,
+ 0.0810612, 0.0772103, 0.0689279, 0.0595841, 0.0543422,
+ 0.048559}, {0.910592, 0.910063, 0.91138, 0.911832, 0.911012,
+ 0.911003, 0.911199, 0.911439, 0.911606, 0.91166, 0.911352, 0.911585,
+ 0.911648, 0.911704, 0.911854, 0.911933, 0.912192, 0.912425,
+ 0.912663, 0.912897, 0.913141, 0.913376, 0.913616, 0.91422, 0.91483,
+ 0.916061, 0.917309, 0.918574, 0.921148, 0.923769, 0.92642, 0.929083,
+ 0.931738, 0.934365, 0.936941, 0.939446, 0.941862, 0.944173,
+ 0.946367, 0.948436, 0.953025, 0.956761, 0.959656, 0.961747, 0.96308,
+ 0.963701, 0.963651, 0.962967, 0.96168, 0.959815, 0.957389,
+ 0.954417, 0.950902, 0.946845, 0.942236, 0.937057, 0.931283,
+ 0.924873, 0.917775, 0.909918, 0.901208, 0.891524, 0.880707,
+ 0.868545, 0.854753, 0.838939, 0.820547, 0.798756, 0.788822,
+ 0.778034, 0.76625, 0.75329, 0.738922, 0.722836, 0.704612, 0.683652,
+ 0.659084, 0.629562, 0.592913, 0.54542, 0.515651, 0.480063, 0.436051,
+ 0.409334, 0.377864, 0.363486, 0.347803, 0.330563, 0.311454,
+ 0.290066, 0.265802, 0.237412, 0.220683, 0.201065, 0.17693, 0.162373,
+ 0.145371, 0.124789, 0.120176, 0.115422, 0.110541, 0.105527,
+ 0.100358, 0.0893955, 0.0771778, 0.0703585, 0.0628494}, {1.16313,
+ 1.16205, 1.16102, 1.16236, 1.1618, 1.16155, 1.16165, 1.16191,
+ 1.16212, 1.16217, 1.16185, 1.16214, 1.162, 1.16222, 1.16228, 1.1624,
+ 1.16261, 1.16279, 1.163, 1.16321, 1.16342, 1.16362, 1.16384,
+ 1.16436, 1.16489, 1.16598, 1.1671, 1.16824, 1.1706, 1.17306,
+ 1.17562, 1.17826, 1.18098, 1.18376, 1.18658, 1.18941, 1.19222,
+ 1.19499, 1.19769, 1.20029, 1.20624, 1.21127, 1.21528, 1.21824,
+ 1.22017, 1.2211, 1.22105, 1.22006, 1.21814, 1.21533, 1.21164,
+ 1.20711, 1.20176, 1.19561, 1.18868, 1.18098, 1.17251, 1.16324,
+ 1.15314, 1.14213, 1.13009, 1.11686, 1.10224, 1.08592, 1.06753,
+ 1.04652, 1.02214, 0.993243, 0.980058, 0.965724, 0.950047, 0.932779,
+ 0.913601, 0.892095, 0.867699, 0.839644, 0.806856, 0.767797,
+ 0.720146, 0.659944, 0.622848, 0.578732, 0.524237, 0.491317,
+ 0.452927, 0.435542, 0.416661, 0.395943, 0.372912, 0.346898,
+ 0.316949, 0.28167, 0.261342, 0.238436, 0.211307, 0.195088, 0.176156,
+ 0.153337, 0.148132, 0.142654, 0.136869, 0.130747, 0.124273,
+ 0.110319, 0.0949385, 0.0864639, 0.0771851}, {1.41428, 1.41604,
+ 1.4156, 1.41536, 1.4156, 1.41524, 1.41519, 1.41543, 1.41565,
+ 1.41568, 1.41551, 1.41554, 1.41563, 1.41566, 1.41579, 1.41591,
+ 1.41608, 1.41624, 1.41643, 1.41663, 1.4168, 1.417, 1.41717, 1.41765,
+ 1.41813, 1.41911, 1.42011, 1.42114, 1.42328, 1.42554, 1.42792,
+ 1.43041, 1.43303, 1.43576, 1.4386, 1.44152, 1.44453, 1.44758,
+ 1.45065, 1.45369, 1.46099, 1.46752, 1.473, 1.47733, 1.48042,
+ 1.48226, 1.48282, 1.48207, 1.47997, 1.47646, 1.4715, 1.46505,
+ 1.45715, 1.44791, 1.43752, 1.42619, 1.41412, 1.4014, 1.38801,
+ 1.37384, 1.35872, 1.34237, 1.32445, 1.30456, 1.28213, 1.25643,
+ 1.22645, 1.19065, 1.17422, 1.15628, 1.13659, 1.11481, 1.09053,
+ 1.06323, 1.03225, 0.996712, 0.955487, 0.906959, 0.848541, 0.775494,
+ 0.730792, 0.678016, 0.613349, 0.574379, 0.528885, 0.508284,
+ 0.485946, 0.461517, 0.434493, 0.404108, 0.369135, 0.327547,
+ 0.303278, 0.275875, 0.244209, 0.225953, 0.204982, 0.179727,
+ 0.173965, 0.167908, 0.161519, 0.154752, 0.147552, 0.131555,
+ 0.113035, 0.102763, 0.09161}, {1.6695, 1.6684, 1.66944, 1.66866,
+ 1.66927, 1.66897, 1.66882, 1.66899, 1.6692, 1.66921, 1.66919,
+ 1.66906, 1.66925, 1.66933, 1.66938, 1.66941, 1.6696, 1.66977,
+ 1.66995, 1.67014, 1.67031, 1.67048, 1.67066, 1.6711, 1.67155,
+ 1.67246, 1.6734, 1.67436, 1.67635, 1.67846, 1.68069, 1.68303,
+ 1.68552, 1.68814, 1.69089, 1.69379, 1.69681, 1.69996, 1.70322,
+ 1.70655, 1.71494, 1.72293, 1.73008, 1.73612, 1.7409, 1.74437,
+ 1.74645, 1.74707, 1.74612, 1.74337, 1.73845, 1.73073, 1.71933,
+ 1.70384, 1.68568, 1.6674, 1.65022, 1.63402, 1.61822, 1.60219,
+ 1.58534, 1.56716, 1.54712, 1.52462, 1.49894, 1.46917, 1.43397,
+ 1.39142, 1.37171, 1.35009, 1.32623, 1.29974, 1.27014, 1.23683,
+ 1.19912, 1.15609, 1.10649, 1.04841, 0.97878, 0.892317, 0.839828,
+ 0.778168, 0.702974, 0.657884, 0.605411, 0.581667, 0.555906,
+ 0.527711, 0.496517, 0.46151, 0.421398, 0.373867, 0.346042, 0.314367,
+ 0.277467, 0.25637, 0.232725, 0.204918, 0.198597, 0.191947,
+ 0.184925, 0.177485, 0.169568, 0.151985, 0.131247, 0.119312,
+ 0.106197}};
+
+ /* 3, 3 mode */
+ const double reomegaqnm33[8][107] = {{0.445768, 0.452799, 0.456948, 0.460943, 0.462462, 0.462842,
+ 0.463095, 0.463269, 0.463394, 0.463488, 0.463746, 0.463886,
+ 0.463989, 0.464144, 0.464267, 0.464374, 0.464572, 0.464763,
+ 0.464952, 0.46514, 0.465329, 0.465518, 0.465707, 0.466182, 0.466657,
+ 0.467612, 0.468573, 0.46954, 0.471491, 0.473465, 0.475464,
+ 0.477487, 0.479535, 0.481609, 0.483709, 0.485837, 0.487991,
+ 0.490174, 0.492386, 0.494627, 0.500363, 0.5063, 0.512449, 0.518826,
+ 0.525445, 0.532323, 0.539479, 0.546934, 0.55471, 0.562834, 0.571335,
+ 0.580244, 0.5896, 0.599443, 0.609823, 0.620796, 0.632425, 0.644787,
+ 0.657972, 0.672086, 0.68726, 0.70365, 0.721455, 0.740921, 0.762369,
+ 0.786223, 0.813057, 0.843687, 0.857254, 0.871717, 0.887201,
+ 0.90386, 0.921885, 0.941521, 0.963088, 0.987016, 1.01391, 1.04464,
+ 1.08058, 1.1241, 1.14998, 1.17986, 1.21547, 1.23637, 1.26023,
+ 1.27086, 1.28227, 1.29462, 1.30812, 1.32308, 1.33999, 1.35965,
+ 1.37094, 1.38363, 1.39829, 1.40666, 1.41603, 1.42679, 1.42917,
+ 1.43164, 1.43422, 1.43692, 1.43975, 1.44591, 1.45295, 1.45695,
+ 1.46139}, {0.428357, 0.432238, 0.434351, 0.436362, 0.437184,
+ 0.437404, 0.437552, 0.437654, 0.437725, 0.437773, 0.437868,
+ 0.437898, 0.437929, 0.438015, 0.438115, 0.438217, 0.438421,
+ 0.438623, 0.438826, 0.43903, 0.439233, 0.439437, 0.439641, 0.440152,
+ 0.440665, 0.441694, 0.442729, 0.443771, 0.445872, 0.447999,
+ 0.45015, 0.452328, 0.454532, 0.456764, 0.459023, 0.461311, 0.463627,
+ 0.465974, 0.46835, 0.470758, 0.476918, 0.483289, 0.489884,
+ 0.496717, 0.503805, 0.511164, 0.518814, 0.526776, 0.535074,
+ 0.543734, 0.552785, 0.562261, 0.5722, 0.582644, 0.593642, 0.60525,
+ 0.617535, 0.630573, 0.644453, 0.659285, 0.675198, 0.692352,
+ 0.710943, 0.731221, 0.753507, 0.778225, 0.805952, 0.837504,
+ 0.851449, 0.866295, 0.882167, 0.89922, 0.917645, 0.937687, 0.959667,
+ 0.984015, 1.01133, 1.0425, 1.07889, 1.12285, 1.14897, 1.17907,
+ 1.21491, 1.23591, 1.25988, 1.27055, 1.28201, 1.2944, 1.30794,
+ 1.32294, 1.33989, 1.35958, 1.37089, 1.38359, 1.39826, 1.40664,
+ 1.41601, 1.42678, 1.42916, 1.43163, 1.43421, 1.43691, 1.43974,
+ 1.4459, 1.45295, 1.45695, 1.46139}, {0.390162, 0.390933, 0.390855,
+ 0.39013, 0.389593, 0.389452, 0.389377, 0.389349, 0.389352, 0.389374,
+ 0.389533, 0.389627, 0.38968, 0.38978, 0.389896, 0.390013, 0.390243,
+ 0.390473, 0.390704, 0.390935, 0.391167, 0.391398, 0.39163,
+ 0.392211, 0.392793, 0.393963, 0.395139, 0.396321, 0.398706,
+ 0.401118, 0.403557, 0.406025, 0.408522, 0.411048, 0.413604,
+ 0.416191, 0.41881, 0.42146, 0.424144, 0.426861, 0.433807, 0.44098,
+ 0.448397, 0.456071, 0.464019, 0.47226, 0.480815, 0.489704, 0.498954,
+ 0.50859, 0.518645, 0.529153, 0.540151, 0.551685, 0.563804,
+ 0.576567, 0.590041, 0.604302, 0.619445, 0.635578, 0.652833,
+ 0.671371, 0.691391, 0.713145, 0.736956, 0.763249, 0.792606,
+ 0.825846, 0.840483, 0.856032, 0.872619, 0.890397, 0.90956, 0.930355,
+ 0.953102, 0.978234, 1.00636, 1.03835, 1.07558, 1.12042, 1.14697,
+ 1.17752, 1.21379, 1.23502, 1.2592, 1.26995, 1.28149, 1.29396,
+ 1.30758, 1.32266, 1.33967, 1.35943, 1.37078, 1.38351, 1.3982,
+ 1.4066, 1.41598, 1.42676, 1.42914, 1.43162, 1.4342, 1.4369, 1.43973,
+ 1.44589, 1.45294, 1.45694, 1.46139}, {0.332321, 0.329612, 0.329447,
+ 0.330998, 0.331533, 0.331485, 0.331367, 0.331244, 0.331151,
+ 0.331101, 0.331226, 0.331354, 0.331387, 0.331504, 0.331643,
+ 0.331766, 0.332024, 0.33228, 0.332537, 0.332795, 0.333053, 0.333311,
+ 0.333569, 0.334216, 0.334865, 0.336168, 0.337478, 0.338796,
+ 0.341454, 0.344143, 0.346863, 0.349614, 0.352398, 0.355215,
+ 0.358066, 0.360951, 0.363872, 0.366829, 0.369823, 0.372855,
+ 0.380605, 0.388612, 0.39689, 0.405455, 0.414327, 0.423525, 0.43307,
+ 0.442986, 0.4533, 0.464039, 0.475237, 0.486928, 0.499155, 0.511962,
+ 0.525402, 0.539534, 0.554428, 0.570163, 0.586836, 0.604556, 0.62346,
+ 0.643711, 0.665511, 0.689115, 0.71485, 0.743145, 0.774586,
+ 0.809998, 0.82553, 0.841991, 0.859506, 0.878231, 0.898362, 0.920146,
+ 0.943908, 0.970086, 0.999286, 1.0324, 1.0708, 1.11686, 1.14404,
+ 1.17523, 1.21215, 1.23369, 1.25818, 1.26906, 1.28072, 1.2933,
+ 1.30704, 1.32223, 1.33936, 1.35922, 1.37061, 1.38339, 1.39812,
+ 1.40653, 1.41593, 1.42673, 1.42911, 1.43159, 1.43418, 1.43688,
+ 1.43971, 1.44588, 1.45294, 1.45694, 1.46138}, {0.279748, 0.281425,
+ 0.280003, 0.278496, 0.279479, 0.279701, 0.279679, 0.279534, 0.27938,
+ 0.279284, 0.279511, 0.279556, 0.279569, 0.279745, 0.279852,
+ 0.279994, 0.280246, 0.280507, 0.280766, 0.281026, 0.281285,
+ 0.281546, 0.281806, 0.282459, 0.283115, 0.284431, 0.285757,
+ 0.287091, 0.289787, 0.292519, 0.295288, 0.298095, 0.30094, 0.303825,
+ 0.306751, 0.309717, 0.312725, 0.315776, 0.318871, 0.322011,
+ 0.330062, 0.338415, 0.347087, 0.356096, 0.365463, 0.37521, 0.385359,
+ 0.395936, 0.406968, 0.418488, 0.430528, 0.443126, 0.456326,
+ 0.470174, 0.484725, 0.500042, 0.516195, 0.533269, 0.551359,
+ 0.570583, 0.591077, 0.61301, 0.636588, 0.662069, 0.689786, 0.720173,
+ 0.753822, 0.791564, 0.808064, 0.825515, 0.844044, 0.863808,
+ 0.885005, 0.907885, 0.932779, 0.960131, 0.990559, 1.02497, 1.06475,
+ 1.11229, 1.14026, 1.17226, 1.21, 1.23195, 1.25686, 1.26789, 1.2797,
+ 1.29245, 1.30633, 1.32167, 1.33893, 1.35893, 1.37038, 1.38322,
+ 1.39801, 1.40645, 1.41587, 1.42669, 1.42908, 1.43156, 1.43415,
+ 1.43685, 1.43969, 1.44587, 1.45293, 1.45693, 1.46137}, {0.239992,
+ 0.240995, 0.242946, 0.24156, 0.241854, 0.242213, 0.242269, 0.242117,
+ 0.241939, 0.241855, 0.242174, 0.24208, 0.242226, 0.242298,
+ 0.242438, 0.242546, 0.242783, 0.243024, 0.243261, 0.243498,
+ 0.243736, 0.243974, 0.244213, 0.244811, 0.245412, 0.246621, 0.24784,
+ 0.249069, 0.251558, 0.254089, 0.256662, 0.259279, 0.26194,
+ 0.264647, 0.2674, 0.2702, 0.273049, 0.275948, 0.278897, 0.281899,
+ 0.289636, 0.297725, 0.306186, 0.315041, 0.324312, 0.334027, 0.34421,
+ 0.354891, 0.366101, 0.377873, 0.390245, 0.403257, 0.416954,
+ 0.431386, 0.446612, 0.462696, 0.479713, 0.49775, 0.516906, 0.537303,
+ 0.559082, 0.582416, 0.607517, 0.634649, 0.66415, 0.696462,
+ 0.732182, 0.77215, 0.789586, 0.807999, 0.827516, 0.848298, 0.870543,
+ 0.894505, 0.920521, 0.949042, 0.980704, 1.01643, 1.05767, 1.10684,
+ 1.1357, 1.16864, 1.20737, 1.22983, 1.25522, 1.26646, 1.27846,
+ 1.29139, 1.30546, 1.32098, 1.33842, 1.35857, 1.3701, 1.38301,
+ 1.39787, 1.40634, 1.41579, 1.42664, 1.42903, 1.43152, 1.43411,
+ 1.43682, 1.43966, 1.44585, 1.45291, 1.45692, 1.46137}, {0.21884,
+ 0.216298, 0.216633, 0.217244, 0.216888, 0.217233, 0.217329,
+ 0.217189, 0.217034, 0.217006, 0.217217, 0.217255, 0.217293,
+ 0.217414, 0.217505, 0.217599, 0.217807, 0.218016, 0.218223,
+ 0.218427, 0.218635, 0.218841, 0.21905, 0.21957, 0.220094, 0.221148,
+ 0.222212, 0.223288, 0.22547, 0.227696, 0.229966, 0.232282, 0.234646,
+ 0.237057, 0.239517, 0.242028, 0.244591, 0.247207, 0.249877,
+ 0.252604, 0.259674, 0.267128, 0.274991, 0.283291, 0.292057,
+ 0.301319, 0.31111, 0.321465, 0.332419, 0.344012, 0.356285, 0.369284,
+ 0.383057, 0.39766, 0.413152, 0.429604, 0.447094, 0.465712,
+ 0.485563, 0.506772, 0.529486, 0.553883, 0.580183, 0.608655,
+ 0.639647, 0.673609, 0.711146, 0.753105, 0.771386, 0.790674,
+ 0.811095, 0.832808, 0.856013, 0.880965, 0.908002, 0.937583,
+ 0.970359, 1.00729, 1.04987, 1.10064, 1.13044, 1.16442, 1.20427,
+ 1.22731, 1.2533, 1.26476, 1.27699, 1.29015, 1.30444, 1.32016,
+ 1.3378, 1.35815, 1.36977, 1.38276, 1.3977, 1.40621, 1.4157, 1.42658,
+ 1.42898, 1.43147, 1.43407, 1.43678, 1.43963, 1.44582, 1.4529,
+ 1.45691, 1.46135}, {0.199814, 0.201353, 0.200132, 0.200956,
+ 0.200467, 0.200722, 0.200829, 0.200716, 0.200604, 0.200626,
+ 0.200705, 0.200826, 0.200822, 0.200914, 0.201004, 0.201103,
+ 0.201273, 0.201448, 0.201625, 0.2018, 0.201975, 0.202153, 0.202329,
+ 0.202773, 0.20322, 0.204121, 0.205032, 0.205953, 0.207826, 0.209742,
+ 0.211702, 0.213706, 0.215757, 0.217854, 0.220001, 0.222198,
+ 0.224447, 0.226749, 0.229105, 0.231518, 0.237809, 0.244492,
+ 0.251597, 0.25916, 0.267216, 0.275804, 0.284965, 0.294742, 0.305178,
+ 0.316322, 0.328221, 0.340928, 0.354499, 0.368992, 0.384475,
+ 0.401019, 0.418708, 0.437635, 0.45791, 0.479661, 0.50304, 0.528232,
+ 0.555461, 0.585008, 0.617226, 0.652577, 0.691676, 0.735379,
+ 0.754411, 0.774477, 0.795706, 0.818253, 0.842317, 0.868149,
+ 0.896082, 0.926573, 0.960272, 0.998162, 1.04182, 1.09394, 1.1246,
+ 1.15963, 1.20071, 1.22441, 1.25107, 1.2628, 1.2753, 1.28872,
+ 1.30326, 1.31923, 1.3371, 1.35766, 1.36938, 1.38248, 1.39751,
+ 1.40606, 1.41559, 1.4265, 1.42891, 1.43141, 1.43401, 1.43673,
+ 1.43959, 1.44579, 1.45288, 1.45689, 1.46134}};
+
+ const double imomegaqnm33[8][107] = {{0.068612, 0.0735351, 0.0774984, 0.0829193, 0.0860369, 0.0870572,
+ 0.0878377, 0.0884398, 0.0889085, 0.0892767, 0.0902685, 0.0906386,
+ 0.0907974, 0.0909101, 0.0909414, 0.090952, 0.0909603, 0.0909664,
+ 0.0909729, 0.0909798, 0.090987, 0.0909942, 0.0910015, 0.0910197,
+ 0.0910378, 0.091074, 0.09111, 0.0911457, 0.0912166, 0.0912867,
+ 0.091356, 0.0914243, 0.0914917, 0.0915582, 0.0916236, 0.091688,
+ 0.0917514, 0.0918136, 0.0918746, 0.0919344, 0.0920784, 0.0922137,
+ 0.0923394, 0.0924547, 0.0925583, 0.0926492, 0.0927258, 0.0927867,
+ 0.0928302, 0.0928541, 0.0928562, 0.0928338, 0.092784, 0.092703,
+ 0.0925869, 0.0924305, 0.0922281, 0.0919726, 0.0916556, 0.0912666,
+ 0.0907928, 0.0902179, 0.0895213, 0.0886763, 0.087647, 0.0863849,
+ 0.0848213, 0.0828557, 0.0819248, 0.0808922, 0.0797413, 0.0784512,
+ 0.0769953, 0.075339, 0.0734361, 0.0712234, 0.0686106, 0.0654629,
+ 0.0615646, 0.056537, 0.0533881, 0.0496087, 0.0449046, 0.0420439,
+ 0.0386881, 0.0371631, 0.0355053, 0.0336873, 0.0316714, 0.0294027,
+ 0.0267968, 0.023711, 0.0219107, 0.0198652, 0.0174725, 0.0160908,
+ 0.014533, 0.0127266, 0.0123252, 0.011907, 0.0114701, 0.011012,
+ 0.0105299, 0.00947732, 0.00826624, 0.0075764,
+ 0.00680679}, {0.277496, 0.278402, 0.278809, 0.278955, 0.278824,
+ 0.278742, 0.278664, 0.278594, 0.278534, 0.278482, 0.278334,
+ 0.278289, 0.278281, 0.278294, 0.278307, 0.278318, 0.278336,
+ 0.278354, 0.278373, 0.278391, 0.278409, 0.278427, 0.278446,
+ 0.278491, 0.278537, 0.278627, 0.278716, 0.278805, 0.27898, 0.279153,
+ 0.279323, 0.279489, 0.279653, 0.279813, 0.27997, 0.280123,
+ 0.280273, 0.280419, 0.280561, 0.280699, 0.281026, 0.281324,
+ 0.281591, 0.281825, 0.28202, 0.282175, 0.282285, 0.282345, 0.28235,
+ 0.282293, 0.282168, 0.281967, 0.281681, 0.281298, 0.280807,
+ 0.280191, 0.279434, 0.278515, 0.277407, 0.27608, 0.274494, 0.272602,
+ 0.27034, 0.26763, 0.264363, 0.260394, 0.255518, 0.249435, 0.246568,
+ 0.243397, 0.239871, 0.235928, 0.231489, 0.226451, 0.220675,
+ 0.213971, 0.206071, 0.19657, 0.184822, 0.169692, 0.160224, 0.148867,
+ 0.134739, 0.12615, 0.116076, 0.111499, 0.106524, 0.101069,
+ 0.0950193, 0.088212, 0.0803933, 0.0711348, 0.0657335, 0.0595967,
+ 0.0524182, 0.0482728, 0.0435993, 0.03818, 0.0369756, 0.0357211,
+ 0.0344103, 0.0330362, 0.0315898, 0.028432, 0.0247987, 0.0227292,
+ 0.0204204}, {0.486993, 0.484741, 0.483427, 0.482389, 0.482301,
+ 0.482372, 0.48246, 0.482542, 0.482611, 0.482664, 0.482744, 0.482718,
+ 0.482702, 0.482709, 0.482722, 0.482729, 0.482743, 0.482759,
+ 0.482774, 0.482789, 0.482804, 0.482819, 0.482834, 0.482871,
+ 0.482907, 0.48298, 0.483051, 0.483121, 0.483256, 0.483386, 0.483511,
+ 0.48363, 0.483742, 0.483849, 0.483949, 0.484043, 0.48413, 0.48421,
+ 0.484283, 0.484348, 0.484477, 0.484555, 0.484575, 0.484535,
+ 0.484428, 0.484247, 0.483987, 0.483638, 0.483192, 0.48264, 0.481968,
+ 0.481164, 0.480211, 0.479093, 0.477786, 0.476267, 0.474506,
+ 0.472466, 0.470105, 0.467369, 0.464195, 0.4605, 0.456181, 0.451103,
+ 0.44509, 0.437899, 0.42919, 0.418467, 0.413455, 0.407937, 0.401829,
+ 0.39503, 0.387407, 0.37879, 0.36895, 0.357573, 0.344212, 0.328195,
+ 0.308447, 0.283082, 0.267235, 0.248247, 0.224647, 0.210309,
+ 0.193501, 0.185866, 0.177568, 0.168469, 0.158382, 0.147032,
+ 0.133998, 0.118564, 0.10956, 0.0993313, 0.0873659, 0.0804562,
+ 0.0726665, 0.0636339, 0.0616265, 0.0595355, 0.0573509, 0.0550606,
+ 0.0526499, 0.0473868, 0.0413313, 0.0378821, 0.034034}, {0.709974,
+ 0.711601, 0.713499, 0.714385, 0.713785, 0.713546, 0.713418,
+ 0.713383, 0.713411, 0.713468, 0.713655, 0.713595, 0.713563,
+ 0.713584, 0.713571, 0.713561, 0.71355, 0.713535, 0.713522, 0.713507,
+ 0.713493, 0.713479, 0.713465, 0.713428, 0.713392, 0.713317,
+ 0.713241, 0.713162, 0.712999, 0.712828, 0.712649, 0.712461,
+ 0.712264, 0.712058, 0.711843, 0.711618, 0.711383, 0.711138,
+ 0.710882, 0.710616, 0.709899, 0.709105, 0.708229, 0.707264,
+ 0.706201, 0.705033, 0.703748, 0.702336, 0.700785, 0.699079,
+ 0.697202, 0.695135, 0.692855, 0.690337, 0.68755, 0.684459, 0.68102,
+ 0.677183, 0.672887, 0.668056, 0.662599, 0.656401, 0.649315,
+ 0.641153, 0.631664, 0.620511, 0.607221, 0.591101, 0.583641,
+ 0.575473, 0.566484, 0.556529, 0.545428, 0.532943, 0.518759,
+ 0.502439, 0.48336, 0.460589, 0.432625, 0.396831, 0.37452, 0.347819,
+ 0.314676, 0.294558, 0.270986, 0.260282, 0.248651, 0.235902,
+ 0.221769, 0.20587, 0.187614, 0.166001, 0.153393, 0.13907, 0.122317,
+ 0.112642, 0.101735, 0.0890889, 0.0862783, 0.0833507, 0.080292,
+ 0.0770855, 0.0737103, 0.0663418, 0.057864, 0.053035,
+ 0.0476477}, {0.972477, 0.969229, 0.96766, 0.969029, 0.969442,
+ 0.969155, 0.968886, 0.968746, 0.968738, 0.968815, 0.969029,
+ 0.968878, 0.968919, 0.968877, 0.968857, 0.968828, 0.968768,
+ 0.968706, 0.968649, 0.968589, 0.968529, 0.96847, 0.96841, 0.96826,
+ 0.96811, 0.967806, 0.9675, 0.96719, 0.966561, 0.96592, 0.965265,
+ 0.964597, 0.963916, 0.96322, 0.962509, 0.961784, 0.961043, 0.960287,
+ 0.959514, 0.958725, 0.956678, 0.954518, 0.952237, 0.949827,
+ 0.947277, 0.944577, 0.941715, 0.938677, 0.935446, 0.932005,
+ 0.928331, 0.924401, 0.920185, 0.915649, 0.910755, 0.905456,
+ 0.899695, 0.893406, 0.88651, 0.878908, 0.870479, 0.861073, 0.850501,
+ 0.838516, 0.824795, 0.808901, 0.790225, 0.767883, 0.757639,
+ 0.746483, 0.73427, 0.720819, 0.7059, 0.689212, 0.670355, 0.648776,
+ 0.623682, 0.593881, 0.557455, 0.511016, 0.482143, 0.44764, 0.404868,
+ 0.378929, 0.348555, 0.334768, 0.319791, 0.303378, 0.285189,
+ 0.264731, 0.241246, 0.213447, 0.197233, 0.178815, 0.157271,
+ 0.144831, 0.130807, 0.114545, 0.110932, 0.107167, 0.103234,
+ 0.0991113, 0.0947715, 0.0852972, 0.0743968, 0.068188,
+ 0.0612614}, {1.23488, 1.2385, 1.23757, 1.23638, 1.23735, 1.23719,
+ 1.23689, 1.23671, 1.23672, 1.23684, 1.23689, 1.23686, 1.23687,
+ 1.23681, 1.23674, 1.23671, 1.2366, 1.23651, 1.23641, 1.23631,
+ 1.23622, 1.23612, 1.23602, 1.23578, 1.23553, 1.23504, 1.23454,
+ 1.23403, 1.23301, 1.23196, 1.23088, 1.22979, 1.22867, 1.22753,
+ 1.22637, 1.22518, 1.22396, 1.22272, 1.22145, 1.22016, 1.21681,
+ 1.21328, 1.20956, 1.20564, 1.20152, 1.19717, 1.19258, 1.18775,
+ 1.18264, 1.17724, 1.17153, 1.16546, 1.15902, 1.15215, 1.14481,
+ 1.13695, 1.12848, 1.11934, 1.10942, 1.09859, 1.08672, 1.07361,
+ 1.05902, 1.04265, 1.02409, 1.00282, 0.978074, 0.948772, 0.935434,
+ 0.920971, 0.905209, 0.887929, 0.868853, 0.847622, 0.823753,
+ 0.796583, 0.765161, 0.728048, 0.682917, 0.625639, 0.590118,
+ 0.547732, 0.49525, 0.463448, 0.42623, 0.409344, 0.391005, 0.370913,
+ 0.348652, 0.323623, 0.294897, 0.260904, 0.241081, 0.218564,
+ 0.192229, 0.177023, 0.159881, 0.140004, 0.135587, 0.130985,
+ 0.126178, 0.121138, 0.115834, 0.104253, 0.09093, 0.0833412,
+ 0.0748751}, {1.50812, 1.50714, 1.50886, 1.50765, 1.50833, 1.50831,
+ 1.50805, 1.5079, 1.50794, 1.50808, 1.50796, 1.50805, 1.50794,
+ 1.50791, 1.50787, 1.50779, 1.50768, 1.50756, 1.50745, 1.50733,
+ 1.50721, 1.50709, 1.50697, 1.50667, 1.50637, 1.50577, 1.50515,
+ 1.50453, 1.50326, 1.50195, 1.50061, 1.49924, 1.49784, 1.49639,
+ 1.49491, 1.4934, 1.49185, 1.49025, 1.48862, 1.48695, 1.4826,
+ 1.47798, 1.47308, 1.46789, 1.46239, 1.45657, 1.45042, 1.44391,
+ 1.43702, 1.42973, 1.42201, 1.41383, 1.40515, 1.39591, 1.38607,
+ 1.37555, 1.36428, 1.35215, 1.33904, 1.32481, 1.30928, 1.29221,
+ 1.27333, 1.25226, 1.22852, 1.20145, 1.17016, 1.13335, 1.11668,
+ 1.09865, 1.07906, 1.05766, 1.03413, 1.00803, 0.978819, 0.945725,
+ 0.907651, 0.862934, 0.808869, 0.7406, 0.698384, 0.648072, 0.585828,
+ 0.54813, 0.50403, 0.484027, 0.462309, 0.43852, 0.412171, 0.382553,
+ 0.348572, 0.308374, 0.284937, 0.258319, 0.227191, 0.209218,
+ 0.188957, 0.165464, 0.160243, 0.154805, 0.149123, 0.143167,
+ 0.136898, 0.123211, 0.107464, 0.0984948, 0.102103}, {1.77947,
+ 1.77829, 1.77828, 1.77845, 1.7786, 1.77868, 1.7785, 1.77838,
+ 1.77844, 1.77854, 1.77842, 1.77841, 1.77841, 1.77834, 1.77827,
+ 1.7782, 1.77808, 1.77795, 1.77783, 1.7777, 1.77757, 1.77744,
+ 1.77732, 1.77699, 1.77667, 1.77601, 1.77534, 1.77466, 1.77327,
+ 1.77183, 1.77035, 1.76883, 1.76726, 1.76564, 1.76398, 1.76226,
+ 1.7605, 1.75868, 1.75682, 1.75489, 1.74985, 1.74445, 1.73867,
+ 1.73249, 1.72589, 1.71886, 1.71137, 1.7034, 1.69493, 1.68592,
+ 1.67635, 1.66618, 1.65536, 1.64384, 1.63157, 1.61846, 1.60441,
+ 1.58931, 1.57303, 1.55539, 1.53617, 1.5151, 1.49185, 1.46597,
+ 1.43689, 1.40384, 1.36575, 1.32111, 1.30093, 1.27916, 1.25555,
+ 1.22981, 1.20156, 1.17032, 1.13545, 1.09609, 1.05101, 0.998352,
+ 0.935078, 0.85569, 0.806777, 0.748562, 0.676569, 0.632966, 0.58196,
+ 0.558828, 0.533715, 0.506213, 0.475757, 0.441533, 0.40228, 0.355861,
+ 0.328804, 0.29808, 0.262156, 0.241415, 0.218035, 0.190926,
+ 0.184902, 0.178626, 0.17207, 0.165197, 0.157962, 0.142169, 0.123998,
+ 0.113649, 0.115718}};
+
+
+ /* 4, 4 mode */
+ const double reomegaqnm44[8][107] = {{0.603485, 0.613847, 0.619636, 0.623952, 0.624219, 0.623894,
+ 0.623504, 0.623122, 0.62278, 0.622487, 0.621648, 0.621375, 0.621309,
+ 0.621365, 0.621483, 0.621613, 0.621877, 0.622141, 0.622404,
+ 0.622667, 0.62293, 0.623194, 0.623458, 0.624119, 0.624781, 0.626113,
+ 0.627452, 0.628799, 0.631518, 0.634269, 0.637054, 0.639872,
+ 0.642726, 0.645615, 0.648541, 0.651503, 0.654504, 0.657544,
+ 0.660623, 0.663743, 0.671728, 0.679989, 0.688543, 0.697411,
+ 0.706611, 0.716168, 0.726107, 0.736455, 0.747243, 0.758508,
+ 0.770286, 0.782624, 0.795569, 0.809178, 0.823517, 0.83866, 0.854693,
+ 0.871718, 0.889853, 0.909242, 0.930054, 0.9525, 0.976839, 1.0034,
+ 1.03259, 1.06498, 1.10131, 1.14265, 1.16092, 1.18036, 1.20114,
+ 1.22345, 1.24755, 1.27374, 1.30245, 1.33422, 1.36984, 1.41042,
+ 1.45773, 1.51478, 1.54862, 1.58759, 1.6339, 1.66102, 1.69194,
+ 1.7057, 1.72045, 1.73641, 1.75384, 1.77314, 1.79492, 1.82022,
+ 1.83474, 1.85104, 1.86985, 1.8806, 1.8926, 1.9064, 1.90945, 1.91261,
+ 1.91592, 1.91937, 1.92299, 1.93088, 1.93989, 1.945,
+ 1.95068}, {0.59231, 0.596523, 0.598412, 0.599977, 0.600617,
+ 0.600806, 0.600947, 0.601053, 0.601136, 0.601202, 0.601389,
+ 0.601485, 0.601558, 0.601693, 0.601828, 0.601964, 0.602238,
+ 0.602511, 0.602785, 0.60306, 0.603334, 0.603609, 0.603884, 0.604574,
+ 0.605265, 0.606653, 0.60805, 0.609455, 0.61229, 0.615158, 0.618061,
+ 0.620998, 0.623972, 0.626982, 0.630029, 0.633115, 0.63624,
+ 0.639405, 0.64261, 0.645858, 0.654166, 0.662758, 0.671651, 0.680865,
+ 0.69042, 0.700341, 0.710653, 0.721383, 0.732565, 0.744232,
+ 0.756425, 0.769188, 0.782571, 0.796632, 0.811434, 0.827055,
+ 0.843581, 0.861114, 0.879773, 0.899703, 0.921074, 0.944098,
+ 0.969034, 0.996209, 1.02604, 1.05909, 1.09611, 1.13816, 1.15671,
+ 1.17644, 1.19752, 1.22013, 1.24453, 1.27103, 1.30005, 1.33214,
+ 1.36806, 1.40896, 1.45658, 1.51396, 1.54795, 1.58707, 1.63353,
+ 1.66073, 1.69172, 1.7055, 1.72028, 1.73626, 1.75372, 1.77304,
+ 1.79485, 1.82017, 1.8347, 1.85101, 1.86983, 1.88058, 1.89259,
+ 1.90639, 1.90944, 1.91261, 1.91591, 1.91936, 1.92299, 1.93087,
+ 1.93989, 1.945, 1.95068}, {0.559386, 0.561881, 0.562985, 0.563673,
+ 0.563747, 0.563732, 0.563712, 0.563695, 0.563683, 0.563678,
+ 0.563718, 0.563794, 0.563872, 0.564021, 0.564168, 0.564316,
+ 0.564612, 0.564908, 0.565204, 0.565501, 0.565798, 0.566096,
+ 0.566394, 0.567139, 0.567887, 0.56939, 0.570901, 0.57242, 0.575484,
+ 0.578584, 0.58172, 0.584892, 0.588102, 0.59135, 0.594637, 0.597965,
+ 0.601333, 0.604743, 0.608195, 0.611692, 0.62063, 0.629865, 0.639415,
+ 0.649299, 0.65954, 0.670161, 0.681189, 0.692653, 0.704586,
+ 0.717023, 0.730006, 0.743579, 0.757794, 0.77271, 0.788392, 0.804918,
+ 0.822375, 0.840868, 0.860518, 0.88147, 0.903897, 0.928012,
+ 0.954076, 0.982419, 1.01346, 1.04777, 1.08608, 1.12947, 1.14857,
+ 1.16887, 1.19051, 1.21369, 1.23867, 1.26576, 1.29538, 1.32806,
+ 1.36459, 1.4061, 1.45434, 1.51232, 1.54662, 1.58604, 1.6328,
+ 1.66014, 1.69127, 1.70511, 1.71994, 1.73598, 1.75348, 1.77286,
+ 1.79471, 1.82008, 1.83463, 1.85096, 1.8698, 1.88055, 1.89257,
+ 1.90638, 1.90943, 1.9126, 1.9159, 1.91935, 1.92298, 1.93087,
+ 1.93989, 1.945, 1.95068}, {0.514416, 0.513669, 0.512866, 0.5122,
+ 0.512256, 0.512336, 0.512404, 0.512455, 0.512488, 0.51251, 0.512565,
+ 0.51264, 0.512726, 0.512889, 0.513051, 0.513214, 0.51354, 0.513866,
+ 0.514193, 0.51452, 0.514848, 0.515175, 0.515503, 0.516325,
+ 0.517149, 0.518804, 0.520467, 0.522139, 0.525511, 0.52892, 0.532367,
+ 0.535852, 0.539377, 0.542943, 0.546549, 0.550198, 0.553889,
+ 0.557625, 0.561406, 0.565233, 0.575009, 0.585097, 0.595517,
+ 0.606289, 0.617438, 0.628986, 0.640963, 0.653399, 0.666327,
+ 0.679785, 0.693815, 0.708464, 0.723784, 0.739837, 0.75669, 0.774421,
+ 0.793122, 0.812899, 0.833875, 0.856197, 0.880043, 0.905628,
+ 0.933216, 0.96314, 0.995828, 1.03184, 1.07193, 1.11717, 1.13703,
+ 1.1581, 1.18052, 1.20451, 1.2303, 1.25821, 1.28866, 1.32219,
+ 1.35958, 1.40195, 1.45106, 1.50993, 1.54467, 1.58453, 1.63172,
+ 1.65927, 1.69061, 1.70453, 1.71944, 1.73555, 1.75313, 1.77258,
+ 1.79451, 1.81994, 1.83452, 1.85088, 1.86975, 1.88051, 1.89254,
+ 1.90636, 1.90941, 1.91258, 1.91589, 1.91934, 1.92297, 1.93086,
+ 1.93988, 1.94499, 1.95068}, {0.454601, 0.454746, 0.455842, 0.456343,
+ 0.456046, 0.455998, 0.456018, 0.456071, 0.456127, 0.456171,
+ 0.456246, 0.456327, 0.456423, 0.456596, 0.456773, 0.456949,
+ 0.457302, 0.457655, 0.458009, 0.458363, 0.458717, 0.459072,
+ 0.459427, 0.460317, 0.461208, 0.462999, 0.464799, 0.466609,
+ 0.470257, 0.473946, 0.477675, 0.481446, 0.485259, 0.489115,
+ 0.493016, 0.496962, 0.500954, 0.504993, 0.509081, 0.513219,
+ 0.523786, 0.534689, 0.545948, 0.557585, 0.569625, 0.582093, 0.59502,
+ 0.608436, 0.622378, 0.636885, 0.652, 0.667772, 0.684256, 0.701516,
+ 0.71962, 0.738651, 0.758702, 0.779882, 0.802317, 0.82616, 0.851591,
+ 0.878829, 0.908143, 0.939873, 0.974449, 1.01244, 1.05461, 1.10202,
+ 1.12279, 1.14477, 1.16814, 1.19308, 1.21984, 1.24875, 1.28021,
+ 1.31477, 1.35322, 1.39666, 1.44687, 1.50684, 1.54214, 1.58256,
+ 1.63031, 1.65813, 1.68974, 1.70376, 1.71878, 1.73499, 1.75267,
+ 1.77222, 1.79424, 1.81975, 1.83438, 1.85077, 1.86967, 1.88046,
+ 1.8925, 1.90633, 1.90939, 1.91256, 1.91587, 1.91932, 1.92296,
+ 1.93085, 1.93987, 1.94499, 1.95067}, {0.405546, 0.404573, 0.403366,
+ 0.404025, 0.404115, 0.403989, 0.40394, 0.403971, 0.404037, 0.404098,
+ 0.40416, 0.404265, 0.404355, 0.404535, 0.404715, 0.404897, 0.40526,
+ 0.405624, 0.405988, 0.406353, 0.406718, 0.407083, 0.407449,
+ 0.408365, 0.409284, 0.411129, 0.412986, 0.414853, 0.418619, 0.42243,
+ 0.426286, 0.430188, 0.434137, 0.438134, 0.44218, 0.446277,
+ 0.450425, 0.454625, 0.458878, 0.463187, 0.474206, 0.485594,
+ 0.497376, 0.509573, 0.522212, 0.535321, 0.54893, 0.563075, 0.577791,
+ 0.593121, 0.609109, 0.625808, 0.643274, 0.661572, 0.680777,
+ 0.700971, 0.722252, 0.744732, 0.768542, 0.793839, 0.820807,
+ 0.849672, 0.880708, 0.914263, 0.950774, 0.990817, 1.03516, 1.0849,
+ 1.10664, 1.12961, 1.15399, 1.17998, 1.20782, 1.23782, 1.27041,
+ 1.30613, 1.34576, 1.39042, 1.44188, 1.50314, 1.53909, 1.58017,
+ 1.62858, 1.65673, 1.68866, 1.70281, 1.71796, 1.7343, 1.7521,
+ 1.77176, 1.7939, 1.81952, 1.83419, 1.85064, 1.86958, 1.88039,
+ 1.89245, 1.9063, 1.90936, 1.91253, 1.91584, 1.9193, 1.92294,
+ 1.93083, 1.93986, 1.94498, 1.95067}, {0.35976, 0.362048, 0.362088,
+ 0.361405, 0.361838, 0.361724, 0.361635, 0.361653, 0.361731,
+ 0.361798, 0.361829, 0.361951, 0.362022, 0.362204, 0.362384,
+ 0.362559, 0.362914, 0.363269, 0.363624, 0.36398, 0.364336, 0.364693,
+ 0.36505, 0.365945, 0.366843, 0.368648, 0.370465, 0.372293,
+ 0.375986, 0.379729, 0.383522, 0.387367, 0.391264, 0.395214, 0.39922,
+ 0.403281, 0.4074, 0.411576, 0.415813, 0.42011, 0.431129, 0.44256,
+ 0.454427, 0.466756, 0.479575, 0.492914, 0.506807, 0.521289,
+ 0.536401, 0.552185, 0.568691, 0.585972, 0.604089, 0.623109,
+ 0.643109, 0.664176, 0.686412, 0.709933, 0.734875, 0.761399,
+ 0.789696, 0.819999, 0.85259, 0.887824, 0.92615, 0.968153, 1.01462,
+ 1.06665, 1.08936, 1.11334, 1.13875, 1.16581, 1.19475, 1.22589,
+ 1.25966, 1.29659, 1.33748, 1.38345, 1.43625, 1.49892, 1.53559,
+ 1.57741, 1.62657, 1.6551, 1.6874, 1.7017, 1.717, 1.73348, 1.75142,
+ 1.77123, 1.79349, 1.81924, 1.83398, 1.85048, 1.86948, 1.8803,
+ 1.89239, 1.90626, 1.90932, 1.9125, 1.91581, 1.91928, 1.92291,
+ 1.93082, 1.93985, 1.94497, 1.95066},
+{0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72, 0.72}};
+
+ const double imomegaqnm44[8][107] = {{0.0472887, 0.0570846, 0.0652857, 0.0769202, 0.0835313, 0.0855743,
+ 0.0870596, 0.0881437, 0.0889418, 0.0895359, 0.0909619, 0.0914196,
+ 0.0916056, 0.091741, 0.0917845, 0.0918026, 0.0918186, 0.0918281,
+ 0.0918366, 0.0918448, 0.0918531, 0.0918614, 0.0918696, 0.0918903,
+ 0.0919109, 0.0919521, 0.0919931, 0.092034, 0.0921151, 0.0921956,
+ 0.0922753, 0.0923543, 0.0924324, 0.0925097, 0.0925861, 0.0926616,
+ 0.0927361, 0.0928096, 0.0928821, 0.0929535, 0.0931268, 0.093292,
+ 0.0934484, 0.0935949, 0.0937302, 0.0938532, 0.0939623, 0.0940559,
+ 0.0941321, 0.0941887, 0.0942233, 0.094233, 0.0942145, 0.094164,
+ 0.0940768, 0.0939478, 0.0937705, 0.0935374, 0.0932393, 0.092865,
+ 0.0924006, 0.0918287, 0.0911274, 0.0902679, 0.0892124, 0.0879094,
+ 0.086287, 0.0842401, 0.0832692, 0.0821917, 0.0809905, 0.0796442,
+ 0.0781255, 0.0763992, 0.0744185, 0.0721192, 0.0694103, 0.066156,
+ 0.0621396, 0.056982, 0.0537633, 0.0499111, 0.0451315, 0.0422323,
+ 0.0388376, 0.037297, 0.0356236, 0.0337901, 0.0317587, 0.0294747,
+ 0.0268536, 0.0237529, 0.0219453, 0.0198926, 0.0174928, 0.0161075,
+ 0.0145463, 0.0127365, 0.0123344, 0.0119155, 0.0114779, 0.0110192,
+ 0.0105364, 0.00948248, 0.00827008, 0.00757959,
+ 0.00680933}, {0.267496, 0.27243, 0.275117, 0.277412, 0.278166,
+ 0.278332, 0.278431, 0.278489, 0.278523, 0.278542, 0.278554,
+ 0.278543, 0.278539, 0.278544, 0.278555, 0.278567, 0.27859, 0.278613,
+ 0.278636, 0.278659, 0.278682, 0.278704, 0.278727, 0.278784,
+ 0.278841, 0.278955, 0.279068, 0.27918, 0.279403, 0.279623, 0.279841,
+ 0.280057, 0.28027, 0.28048, 0.280687, 0.280892, 0.281093, 0.281291,
+ 0.281485, 0.281676, 0.282137, 0.282572, 0.282979, 0.283355,
+ 0.283696, 0.283998, 0.284257, 0.284467, 0.284624, 0.284721,
+ 0.284749, 0.284701, 0.284567, 0.284334, 0.28399, 0.283519, 0.282901,
+ 0.282113, 0.281129, 0.279913, 0.278426, 0.276614, 0.274412,
+ 0.271733, 0.268465, 0.264452, 0.25948, 0.253233, 0.250278, 0.247003,
+ 0.243357, 0.239276, 0.234678, 0.229458, 0.223476, 0.216539,
+ 0.208375, 0.198576, 0.186494, 0.170992, 0.161324, 0.149756,
+ 0.135408, 0.126707, 0.116519, 0.111896, 0.106875, 0.101374,
+ 0.0952787, 0.0884259, 0.0805622, 0.0712595, 0.0658364, 0.0596782,
+ 0.0524786, 0.0483228, 0.043639, 0.0382095, 0.0370031, 0.0357465,
+ 0.0344338, 0.0330576, 0.0316092, 0.0284475, 0.0248103, 0.0227388,
+ 0.020428}, {0.476992, 0.476552, 0.476059, 0.475354, 0.475023,
+ 0.474945, 0.474902, 0.47488, 0.474873, 0.474873, 0.474904, 0.474923,
+ 0.474932, 0.474945, 0.47496, 0.474975, 0.475006, 0.475036,
+ 0.475066, 0.475097, 0.475127, 0.475157, 0.475187, 0.475263,
+ 0.475338, 0.475487, 0.475635, 0.475782, 0.476073, 0.476359,
+ 0.476641, 0.476918, 0.47719, 0.477456, 0.477718, 0.477973, 0.478223,
+ 0.478467, 0.478704, 0.478936, 0.479483, 0.479984, 0.480434,
+ 0.480828, 0.48116, 0.481423, 0.48161, 0.481712, 0.481721, 0.481624,
+ 0.48141, 0.481064, 0.48057, 0.479908, 0.479056, 0.477986, 0.476666,
+ 0.47506, 0.47312, 0.470791, 0.468003, 0.464669, 0.460679, 0.45589,
+ 0.450113, 0.44309, 0.434465, 0.423712, 0.41865, 0.413055, 0.406842,
+ 0.399905, 0.392108, 0.383276, 0.373175, 0.361487, 0.347759,
+ 0.331313, 0.311071, 0.28514, 0.268985, 0.249669, 0.225726, 0.21121,
+ 0.194221, 0.186512, 0.17814, 0.168968, 0.158807, 0.147383, 0.134275,
+ 0.118768, 0.109729, 0.099465, 0.0874652, 0.0805385, 0.072732,
+ 0.0636828, 0.0616721, 0.0595777, 0.0573898, 0.0550962, 0.0526822,
+ 0.0474125, 0.0413505, 0.037898, 0.0340467}, {0.688887, 0.687276,
+ 0.68687, 0.687194, 0.687484, 0.687529, 0.687535, 0.687523, 0.687504,
+ 0.687487, 0.687464, 0.68748, 0.687488, 0.687497, 0.687509,
+ 0.687521, 0.687544, 0.687567, 0.68759, 0.687613, 0.687636, 0.687658,
+ 0.687681, 0.687738, 0.687794, 0.687905, 0.688015, 0.688122,
+ 0.688333, 0.688537, 0.688734, 0.688923, 0.689105, 0.689278,
+ 0.689444, 0.689601, 0.689749, 0.689889, 0.690018, 0.690138,
+ 0.690394, 0.690579, 0.69069, 0.690717, 0.690652, 0.690487, 0.690211,
+ 0.689812, 0.689276, 0.688589, 0.687732, 0.686685, 0.685425,
+ 0.683924, 0.682151, 0.680068, 0.677629, 0.674782, 0.671462,
+ 0.667589, 0.663066, 0.657772, 0.651551, 0.644203, 0.635463,
+ 0.624972, 0.612229, 0.596503, 0.589146, 0.581044, 0.572077,
+ 0.562097, 0.550915, 0.538287, 0.523888, 0.507273, 0.48781, 0.464555,
+ 0.436002, 0.399509, 0.376808, 0.349693, 0.316109, 0.295761,
+ 0.271954, 0.261154, 0.249426, 0.236578, 0.222347, 0.206349,
+ 0.187993, 0.166281, 0.153625, 0.139254, 0.122453, 0.112755,
+ 0.101826, 0.0891563, 0.0863413, 0.0834091, 0.080346, 0.0771349,
+ 0.0737552, 0.0663776, 0.0578907, 0.0530572, 0.0476654}, {0.918235,
+ 0.920515, 0.920895, 0.920137, 0.920012, 0.920094, 0.920167,
+ 0.920207, 0.920214, 0.920202, 0.920149, 0.920166, 0.920164, 0.92016,
+ 0.920158, 0.920156, 0.920152, 0.920148, 0.920144, 0.92014,
+ 0.920136, 0.920132, 0.920127, 0.920116, 0.920104, 0.920079,
+ 0.920051, 0.920022, 0.919956, 0.919881, 0.919796, 0.919702,
+ 0.919597, 0.919482, 0.919356, 0.919218, 0.919069, 0.918908,
+ 0.918734, 0.918547, 0.91802, 0.917401, 0.916681, 0.915851, 0.9149,
+ 0.913815, 0.912584, 0.91119, 0.909617, 0.907843, 0.905847, 0.903603,
+ 0.901078, 0.898239, 0.895043, 0.891442, 0.887378, 0.88278,
+ 0.877566, 0.871633, 0.864855, 0.857075, 0.848091, 0.837647, 0.8254,
+ 0.81089, 0.79347, 0.772205, 0.762324, 0.751485, 0.739534, 0.72628,
+ 0.711484, 0.694831, 0.675907, 0.654142, 0.628729, 0.598457, 0.5614,
+ 0.514171, 0.484847, 0.449863, 0.406581, 0.380377, 0.349729,
+ 0.335831, 0.32074, 0.304211, 0.285904, 0.265327, 0.24172, 0.213799,
+ 0.197524, 0.179045, 0.157442, 0.144973, 0.13092, 0.11463, 0.111011,
+ 0.107241, 0.103302, 0.0991739, 0.0948285, 0.0853429, 0.0744311,
+ 0.0682165, 0.0612841}, {1.17243, 1.17025, 1.17072, 1.17153, 1.17109,
+ 1.17107, 1.17115, 1.17122, 1.17125, 1.17124, 1.17116, 1.17118,
+ 1.17115, 1.17114, 1.17112, 1.17109, 1.17105, 1.171, 1.17096,
+ 1.17092, 1.17087, 1.17083, 1.17078, 1.17067, 1.17055, 1.17033,
+ 1.17009, 1.16986, 1.16938, 1.16889, 1.16838, 1.16786, 1.16733,
+ 1.16679, 1.16622, 1.16565, 1.16506, 1.16445, 1.16382, 1.16318,
+ 1.1615, 1.15969, 1.15776, 1.15567, 1.15344, 1.15103, 1.14843,
+ 1.14562, 1.14259, 1.1393, 1.13573, 1.13184, 1.12761, 1.12298,
+ 1.1179, 1.11232, 1.10615, 1.09933, 1.09174, 1.08325, 1.07371,
+ 1.06294, 1.05067, 1.0366, 1.0203, 1.00121, 0.97854, 0.951144,
+ 0.9385, 0.92468, 0.909499, 0.892724, 0.874063, 0.853135, 0.829435,
+ 0.802272, 0.770663, 0.733138, 0.687353, 0.629184, 0.593147,
+ 0.550213, 0.497162, 0.465071, 0.427558, 0.410551, 0.392089,
+ 0.371872, 0.349482, 0.32432, 0.295457, 0.261323, 0.241428, 0.218839,
+ 0.192433, 0.177192, 0.160015, 0.140105, 0.135681, 0.131073,
+ 0.126259, 0.121213, 0.115902, 0.104308, 0.0909715, 0.0833759,
+ 0.0749029}, {1.43411, 1.43505, 1.43374, 1.43433, 1.43411, 1.43401,
+ 1.43406, 1.43415, 1.43418, 1.43415, 1.4341, 1.43407, 1.43405,
+ 1.43401, 1.43397, 1.43393, 1.43384, 1.43376, 1.43367, 1.43359,
+ 1.4335, 1.43342, 1.43333, 1.43312, 1.4329, 1.43247, 1.43203,
+ 1.43159, 1.43069, 1.42978, 1.42884, 1.42789, 1.42691, 1.42592,
+ 1.4249, 1.42387, 1.42281, 1.42173, 1.42062, 1.41949, 1.41656,
+ 1.41345, 1.41017, 1.4067, 1.40302, 1.39911, 1.39496, 1.39054,
+ 1.38582, 1.38079, 1.3754, 1.36961, 1.36339, 1.35669, 1.34943,
+ 1.34155, 1.33296, 1.32356, 1.31324, 1.30183, 1.28915, 1.27497,
+ 1.259, 1.24085, 1.22004, 1.19589, 1.16745, 1.13339, 1.11775,
+ 1.10072, 1.08207, 1.06154, 1.03877, 1.01331, 0.984584, 0.951766,
+ 0.913705, 0.868675, 0.81392, 0.744589, 0.701738, 0.650764, 0.587868,
+ 0.549856, 0.505448, 0.485323, 0.46348, 0.439564, 0.413085,
+ 0.383331, 0.349205, 0.308853, 0.285337, 0.258637, 0.227427,
+ 0.209413, 0.189112, 0.16558, 0.160352, 0.154906, 0.149217, 0.143253,
+ 0.136976, 0.123274, 0.107512, 0.0985354, 0.0885218},
+{0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28,
+ 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28}};
+
+ /* 5, 5 mode */
+ const double reomegaqnm55[8][107] = {{0.752532, 0.769133, 0.779179, 0.78709, 0.786149, 0.784329, 0.782338,
+ 0.780485, 0.778903, 0.777615, 0.774286, 0.773282, 0.772966,
+ 0.77289, 0.772999, 0.773149, 0.773476, 0.77381, 0.774145, 0.77448,
+ 0.774816, 0.775152, 0.775488, 0.776331, 0.777176, 0.778874,
+ 0.780582, 0.782299, 0.785766, 0.789274, 0.792825, 0.79642, 0.800059,
+ 0.803743, 0.807474, 0.811253, 0.81508, 0.818956, 0.822883,
+ 0.826863, 0.837046, 0.847582, 0.858493, 0.869802, 0.881536,
+ 0.893724, 0.906398, 0.919594, 0.93335, 0.947712, 0.962728, 0.978454,
+ 0.994953, 1.0123, 1.03056, 1.04985, 1.07027, 1.09194, 1.11502,
+ 1.13968, 1.16614, 1.19467, 1.22558, 1.25928, 1.29631, 1.33734,
+ 1.38332, 1.43555, 1.45861, 1.48313, 1.50932, 1.53742, 1.56774,
+ 1.60067, 1.63671, 1.67655, 1.72115, 1.77188, 1.83092, 1.90197,
+ 1.94403, 1.99239, 2.04977, 2.08333, 2.12154, 2.13852, 2.15673,
+ 2.17641, 2.1979, 2.22168, 2.24849, 2.27961, 2.29746, 2.31749,
+ 2.34058, 2.35377, 2.3685, 2.38542, 2.38915, 2.39303, 2.39708,
+ 2.40131, 2.40575, 2.41541, 2.42645, 2.43271, 2.43967}, {0.753001,
+ 0.757208, 0.757533, 0.756804, 0.756468, 0.756414, 0.756397,
+ 0.756401, 0.756417, 0.756438, 0.756561, 0.756667, 0.756761,
+ 0.756937, 0.757109, 0.75728, 0.757623, 0.757967, 0.758311, 0.758656,
+ 0.759001, 0.759346, 0.759692, 0.760558, 0.761427, 0.763172,
+ 0.764927, 0.766693, 0.770255, 0.77386, 0.777508, 0.7812, 0.784938,
+ 0.788722, 0.792553, 0.796433, 0.800362, 0.804341, 0.808372,
+ 0.812456, 0.822904, 0.833711, 0.844898, 0.85649, 0.868513, 0.880997,
+ 0.893974, 0.90748, 0.921555, 0.936243, 0.951594, 0.967664,
+ 0.984515, 1.00222, 1.02086, 1.04054, 1.06135, 1.08343, 1.10693,
+ 1.13203, 1.15894, 1.18793, 1.21932, 1.25352, 1.29105, 1.33262,
+ 1.37915, 1.43196, 1.45525, 1.48001, 1.50644, 1.53478, 1.56534,
+ 1.59852, 1.63481, 1.67491, 1.71976, 1.77074, 1.83004, 1.90134,
+ 1.94352, 1.992, 2.0495, 2.08311, 2.12137, 2.13838, 2.15661, 2.17631,
+ 2.19781, 2.22161, 2.24844, 2.27957, 2.29743, 2.31747, 2.34057,
+ 2.35376, 2.36849, 2.38541, 2.38915, 2.39303, 2.39708, 2.40131,
+ 2.40575, 2.41541, 2.42645, 2.43271, 2.43967}, {0.7196, 0.722567,
+ 0.723924, 0.725024, 0.725386, 0.725467, 0.725518, 0.725552,
+ 0.725576, 0.725595, 0.725675, 0.72576, 0.725849, 0.72603, 0.726211,
+ 0.726392, 0.726754, 0.727117, 0.72748, 0.727843, 0.728207, 0.728571,
+ 0.728936, 0.729849, 0.730765, 0.732605, 0.734456, 0.736316,
+ 0.740071, 0.743868, 0.747711, 0.751599, 0.755534, 0.759516,
+ 0.763547, 0.767627, 0.771759, 0.775942, 0.780178, 0.784469,
+ 0.795442, 0.806783, 0.818514, 0.830662, 0.843253, 0.856316,
+ 0.869886, 0.883998, 0.898692, 0.914015, 0.930016, 0.946752,
+ 0.964288, 0.982696, 1.00206, 1.02247, 1.04405, 1.06692, 1.09123,
+ 1.11716, 1.14494, 1.17482, 1.20713, 1.24229, 1.28082, 1.32342,
+ 1.37101, 1.42493, 1.44867, 1.47389, 1.50078, 1.5296, 1.56064,
+ 1.5943, 1.63108, 1.67167, 1.71702, 1.7685, 1.82829, 1.90008, 1.9425,
+ 1.99122, 2.04895, 2.08267, 2.12104, 2.13809, 2.15636, 2.1761,
+ 2.19764, 2.22147, 2.24834, 2.27951, 2.29738, 2.31743, 2.34054,
+ 2.35374, 2.36848, 2.3854, 2.38914, 2.39302, 2.39707, 2.4013,
+ 2.40575, 2.41541, 2.42645, 2.43271, 2.43966}, {0.680361, 0.681655,
+ 0.681927, 0.681788, 0.681669, 0.681657, 0.681664, 0.681682,
+ 0.681705, 0.681729, 0.681838, 0.681934, 0.682031, 0.682225, 0.68242,
+ 0.682614, 0.683004, 0.683394, 0.683784, 0.684175, 0.684566,
+ 0.684957, 0.685349, 0.686331, 0.687316, 0.689293, 0.69128, 0.693279,
+ 0.69731, 0.701387, 0.705509, 0.709679, 0.713897, 0.718164,
+ 0.722481, 0.72685, 0.731271, 0.735746, 0.740276, 0.744863, 0.756582,
+ 0.768683, 0.781187, 0.794122, 0.807514, 0.821395, 0.835799,
+ 0.850762, 0.866327, 0.88254, 0.899452, 0.917122, 0.935614, 0.955004,
+ 0.975376, 0.996827, 1.01947, 1.04344, 1.06888, 1.09599, 1.12497,
+ 1.1561, 1.18971, 1.22621, 1.26614, 1.31018, 1.35928, 1.41476,
+ 1.43915, 1.46502, 1.49258, 1.52208, 1.5538, 1.58816, 1.62564,
+ 1.66694, 1.713, 1.76521, 1.82572, 1.89823, 1.941, 1.99007, 2.04813,
+ 2.08202, 2.12055, 2.13766, 2.15599, 2.17578, 2.19738, 2.22127,
+ 2.24819, 2.2794, 2.2973, 2.31737, 2.34051, 2.35371, 2.36846,
+ 2.38539, 2.38913, 2.39301, 2.39706, 2.40129, 2.40574, 2.4154,
+ 2.42645, 2.43271, 2.43966}, {0.630475, 0.629154, 0.628652, 0.628812,
+ 0.628995, 0.62902, 0.629028, 0.629035, 0.629045, 0.629061,
+ 0.629172, 0.629277, 0.629381, 0.629592, 0.629802, 0.630012,
+ 0.630433, 0.630855, 0.631277, 0.631699, 0.632122, 0.632545,
+ 0.632968, 0.634029, 0.635093, 0.637229, 0.639376, 0.641534,
+ 0.645886, 0.650284, 0.65473, 0.659225, 0.66377, 0.668366, 0.673014,
+ 0.677716, 0.682472, 0.687284, 0.692153, 0.69708, 0.709663, 0.722641,
+ 0.73604, 0.749885, 0.764206, 0.779035, 0.794407, 0.81036, 0.826938,
+ 0.844188, 0.862164, 0.880925, 0.900539, 0.921082, 0.94264,
+ 0.965314, 0.989218, 1.01449, 1.04128, 1.06978, 1.1002, 1.13284,
+ 1.168, 1.20613, 1.24774, 1.29355, 1.34449, 1.4019, 1.42708, 1.45377,
+ 1.48215, 1.51248, 1.54506, 1.58029, 1.61866, 1.66085, 1.70782,
+ 1.76095, 1.82238, 1.89581, 1.93904, 1.98856, 2.04706, 2.08116,
+ 2.1199, 2.13709, 2.1555, 2.17537, 2.19704, 2.221, 2.24799, 2.27927,
+ 2.29719, 2.31729, 2.34045, 2.35367, 2.36843, 2.38537, 2.38911,
+ 2.39299, 2.39704, 2.40128, 2.40573, 2.41539, 2.42644, 2.4327,
+ 2.43966}, {0.571708, 0.573132, 0.573635, 0.573297, 0.573329,
+ 0.573398, 0.573443, 0.573465, 0.573477, 0.573488, 0.5736, 0.573712,
+ 0.573823, 0.574048, 0.574272, 0.574496, 0.574944, 0.575393,
+ 0.575843, 0.576292, 0.576743, 0.577194, 0.577645, 0.578775,
+ 0.579908, 0.582183, 0.58447, 0.586768, 0.591402, 0.596085, 0.600818,
+ 0.605603, 0.61044, 0.61533, 0.620276, 0.625278, 0.630337, 0.635455,
+ 0.640632, 0.645871, 0.659247, 0.673038, 0.687272, 0.701975,
+ 0.717178, 0.732914, 0.74922, 0.766136, 0.783707, 0.801983, 0.821018,
+ 0.840873, 0.86162, 0.883336, 0.90611, 0.930046, 0.955261, 0.981893,
+ 1.0101, 1.04008, 1.07205, 1.10629, 1.14315, 1.18304, 1.22651,
+ 1.27427, 1.32727, 1.38685, 1.41293, 1.44053, 1.46986, 1.50115,
+ 1.53471, 1.57094, 1.61033, 1.65357, 1.70161, 1.75581, 1.81834,
+ 1.89287, 1.93665, 1.98671, 2.04575, 2.08011, 2.1191, 2.13638,
+ 2.15489, 2.17486, 2.19662, 2.22067, 2.24774, 2.2791, 2.29706,
+ 2.31719, 2.34039, 2.35362, 2.36839, 2.38534, 2.38909, 2.39297,
+ 2.39703, 2.40126, 2.40571, 2.41538, 2.42643, 2.4327,
+ 2.43966}, {0.522196, 0.520579, 0.52057, 0.521087, 0.52093, 0.520981,
+ 0.521047, 0.521087, 0.521102, 0.52111, 0.521228, 0.521338,
+ 0.521456, 0.521686, 0.521918, 0.522149, 0.522613, 0.523077,
+ 0.523541, 0.524006, 0.524471, 0.524937, 0.525404, 0.526572,
+ 0.527743, 0.530095, 0.53246, 0.534837, 0.539631, 0.544478, 0.549379,
+ 0.554335, 0.559348, 0.564418, 0.569547, 0.574737, 0.579987,
+ 0.585301, 0.590679, 0.596123, 0.61003, 0.624382, 0.639206, 0.654532,
+ 0.670391, 0.686819, 0.703853, 0.721535, 0.739912, 0.759036,
+ 0.778963, 0.799758, 0.821493, 0.844248, 0.868117, 0.893205,
+ 0.919633, 0.947544, 0.977101, 1.0085, 1.04198, 1.07781, 1.11634,
+ 1.15802, 1.20338, 1.25315, 1.30829, 1.37015, 1.39719, 1.42578,
+ 1.45611, 1.48844, 1.52307, 1.56039, 1.6009, 1.64529, 1.69451,
+ 1.74992, 1.81368, 1.88946, 1.93386, 1.98455, 2.0442, 2.07886,
+ 2.11815, 2.13555, 2.15417, 2.17425, 2.19612, 2.22028, 2.24745,
+ 2.2789, 2.29691, 2.31708, 2.34031, 2.35356, 2.36835, 2.38531,
+ 2.38906, 2.39295, 2.39701, 2.40125, 2.4057, 2.41537, 2.42643,
+ 2.43269, 2.43965},
+{0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9,
+ 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9}};
+
+ const double imomegaqnm55[8][107] = {{0.0151971, 0.02987, 0.0432352, 0.064849, 0.0789971, 0.0834521,
+ 0.0865117, 0.0885261, 0.0898184, 0.090638, 0.0919286, 0.0920896,
+ 0.0921222, 0.0921485, 0.0921652, 0.0921765, 0.092191, 0.0922013,
+ 0.0922106, 0.0922195, 0.0922283, 0.0922371, 0.0922459, 0.0922679,
+ 0.0922898, 0.0923335, 0.092377, 0.0924205, 0.0925068, 0.0925926,
+ 0.0926777, 0.092762, 0.0928457, 0.0929286, 0.0930106, 0.0930918,
+ 0.0931722, 0.0932516, 0.09333, 0.0934074, 0.0935961, 0.0937773,
+ 0.09395, 0.0941133, 0.094266, 0.0944066, 0.0945339, 0.094646,
+ 0.0947411, 0.0948169, 0.0948709, 0.0949002, 0.0949014, 0.0948705,
+ 0.094803, 0.0946932, 0.0945348, 0.0943198, 0.0940389, 0.0936804,
+ 0.0932301, 0.09267, 0.0919774, 0.0911228, 0.0900671, 0.0887575,
+ 0.0871199, 0.0850466, 0.0840612, 0.0829665, 0.0817451, 0.0803751,
+ 0.0788289, 0.0770706, 0.0750526, 0.0727103, 0.0699513, 0.0666388,
+ 0.0625545, 0.0573174, 0.054054, 0.0501531, 0.0453206, 0.0423931,
+ 0.038969, 0.0374162, 0.0357305, 0.0338844, 0.0318402, 0.0295431,
+ 0.0269089, 0.0237947, 0.0219803, 0.0199207, 0.017514, 0.0161252,
+ 0.0145605, 0.0127472, 0.0123443, 0.0119247, 0.0114865, 0.011027,
+ 0.0105435, 0.00948819, 0.00827437, 0.00758316,
+ 0.00681219}, {0.25166, 0.264251, 0.270831, 0.275931, 0.277491,
+ 0.277846, 0.278073, 0.278222, 0.278323, 0.278391, 0.278527,
+ 0.278556, 0.278565, 0.278576, 0.278588, 0.2786, 0.278625, 0.27865,
+ 0.278676, 0.278701, 0.278726, 0.278751, 0.278776, 0.278839,
+ 0.278901, 0.279026, 0.27915, 0.279273, 0.279519, 0.279763, 0.280005,
+ 0.280244, 0.280481, 0.280716, 0.280948, 0.281177, 0.281404,
+ 0.281627, 0.281847, 0.282065, 0.282593, 0.283097, 0.283575,
+ 0.284023, 0.284438, 0.284817, 0.285154, 0.285444, 0.285682,
+ 0.285862, 0.285974, 0.286011, 0.285963, 0.285817, 0.28556, 0.285175,
+ 0.284643, 0.28394, 0.283038, 0.281902, 0.280489, 0.278746,
+ 0.276603, 0.273974, 0.27074, 0.266744, 0.261763, 0.255474, 0.252491,
+ 0.249179, 0.245488, 0.24135, 0.236685, 0.231383, 0.225304,
+ 0.218251, 0.20995, 0.199989, 0.187715, 0.171984, 0.162185, 0.150475,
+ 0.135971, 0.127186, 0.116912, 0.112252, 0.107194, 0.101656,
+ 0.0955223, 0.0886307, 0.0807275, 0.0713845, 0.0659411, 0.0597624,
+ 0.0525421, 0.0483758, 0.0436815, 0.0382415, 0.037033, 0.0357743,
+ 0.0344594, 0.0330811, 0.0316306, 0.0284646, 0.0248231, 0.0227495,
+ 0.0204366}, {0.467579, 0.470028, 0.470942, 0.471348, 0.471322,
+ 0.47129, 0.471261, 0.471239, 0.471223, 0.471213, 0.471201, 0.47121,
+ 0.471221, 0.47124, 0.471258, 0.471277, 0.471314, 0.471351, 0.471388,
+ 0.471425, 0.471462, 0.471499, 0.471536, 0.471628, 0.47172,
+ 0.471904, 0.472086, 0.472268, 0.472628, 0.472984, 0.473336,
+ 0.473684, 0.474028, 0.474367, 0.474701, 0.475031, 0.475355,
+ 0.475674, 0.475987, 0.476294, 0.477036, 0.477735, 0.478387,
+ 0.478987, 0.479529, 0.480006, 0.480411, 0.480735, 0.480968,
+ 0.481101, 0.481119, 0.481008, 0.480751, 0.480328, 0.479717,
+ 0.478889, 0.477812, 0.476446, 0.474745, 0.472651, 0.470091,
+ 0.466978, 0.463197, 0.4586, 0.452993, 0.446112, 0.437588, 0.426883,
+ 0.421821, 0.416213, 0.409971, 0.402987, 0.395124, 0.386201,
+ 0.375984, 0.364147, 0.350231, 0.333554, 0.313026, 0.286746,
+ 0.270386, 0.250845, 0.226651, 0.212, 0.194868, 0.1871, 0.178668,
+ 0.169434, 0.15921, 0.147722, 0.134549, 0.118976, 0.109903,
+ 0.0996047, 0.0875705, 0.0806266, 0.0728027, 0.063736, 0.0617217,
+ 0.0596238, 0.0574324, 0.0551353, 0.0527177, 0.047441, 0.0413719,
+ 0.0379158, 0.034061}, {0.676801, 0.675633, 0.67493, 0.67443, 0.6744,
+ 0.674422, 0.674445, 0.674462, 0.674474, 0.674481, 0.67449,
+ 0.674497, 0.674508, 0.674528, 0.674548, 0.674568, 0.674609,
+ 0.674649, 0.674689, 0.674729, 0.674769, 0.674809, 0.674849,
+ 0.674948, 0.675048, 0.675245, 0.675441, 0.675635, 0.67602, 0.676399,
+ 0.676771, 0.677137, 0.677496, 0.677847, 0.678192, 0.678529,
+ 0.678858, 0.679179, 0.679492, 0.679795, 0.680514, 0.681168,
+ 0.681753, 0.68226, 0.682681, 0.683008, 0.683228, 0.683332, 0.683303,
+ 0.683128, 0.682788, 0.682263, 0.681529, 0.680557, 0.679315,
+ 0.677766, 0.675862, 0.673549, 0.67076, 0.667416, 0.663415, 0.658633,
+ 0.65291, 0.64604, 0.637751, 0.627674, 0.615292, 0.599856, 0.592588,
+ 0.584557, 0.575639, 0.565684, 0.554498, 0.541831, 0.527355,
+ 0.510615, 0.490971, 0.467468, 0.438585, 0.401662, 0.378702,
+ 0.351292, 0.317377, 0.296847, 0.272846, 0.261966, 0.250155,
+ 0.237224, 0.222906, 0.20682, 0.188374, 0.16657, 0.153867, 0.139448,
+ 0.1226, 0.112878, 0.101924, 0.0892306, 0.0864106, 0.0834736,
+ 0.0804055, 0.0771896, 0.0738049, 0.0664175, 0.0579207, 0.0530822,
+ 0.0476854}, {0.891895, 0.89147, 0.891863, 0.892311, 0.89227,
+ 0.892236, 0.892217, 0.892213, 0.892217, 0.892223, 0.892242,
+ 0.892246, 0.892254, 0.892269, 0.892283, 0.892298, 0.892327,
+ 0.892357, 0.892386, 0.892415, 0.892444, 0.892473, 0.892502,
+ 0.892574, 0.892646, 0.892788, 0.892927, 0.893065, 0.893335,
+ 0.893597, 0.89385, 0.894094, 0.894329, 0.894554, 0.89477, 0.894975,
+ 0.89517, 0.895353, 0.895526, 0.895686, 0.896031, 0.896291, 0.896458,
+ 0.896521, 0.89647, 0.896292, 0.895974, 0.895501, 0.894855,
+ 0.894014, 0.892957, 0.891657, 0.890083, 0.888198, 0.88596, 0.88332,
+ 0.880219, 0.876586, 0.872336, 0.867364, 0.86154, 0.854705, 0.846653,
+ 0.83712, 0.825754, 0.812083, 0.795442, 0.774871, 0.765236,
+ 0.754619, 0.742864, 0.729775, 0.715106, 0.698537, 0.679644,
+ 0.657847, 0.632324, 0.601851, 0.564477, 0.516789, 0.487173,
+ 0.451846, 0.408167, 0.381741, 0.350856, 0.336857, 0.321664, 0.30503,
+ 0.286614, 0.265926, 0.242205, 0.214167, 0.197833, 0.179293,
+ 0.15763, 0.14513, 0.131046, 0.114725, 0.1111, 0.107324, 0.103379,
+ 0.099244, 0.0948923, 0.085394, 0.0744695, 0.0682486,
+ 0.0613098}, {1.12614, 1.12697, 1.12642, 1.12612, 1.12629, 1.12629,
+ 1.12627, 1.12625, 1.12624, 1.12624, 1.12626, 1.12625, 1.12626,
+ 1.12626, 1.12626, 1.12626, 1.12626, 1.12626, 1.12627, 1.12627,
+ 1.12627, 1.12627, 1.12628, 1.12628, 1.12628, 1.12629, 1.12629,
+ 1.1263, 1.12629, 1.12628, 1.12625, 1.12622, 1.12617, 1.12611,
+ 1.12604, 1.12595, 1.12586, 1.12574, 1.12562, 1.12548, 1.12505,
+ 1.12453, 1.12388, 1.1231, 1.12219, 1.12111, 1.11986, 1.11841,
+ 1.11675, 1.11485, 1.11267, 1.1102, 1.10738, 1.10418, 1.10054,
+ 1.09641, 1.0917, 1.08634, 1.08021, 1.07319, 1.06513, 1.05582,
+ 1.04501, 1.03238, 1.0175, 0.999787, 0.978439, 0.952276, 0.940091,
+ 0.926705, 0.911928, 0.895521, 0.877184, 0.856528, 0.833035, 0.806,
+ 0.774421, 0.736806, 0.690779, 0.632177, 0.595837, 0.552533,
+ 0.499038, 0.466693, 0.428905, 0.411781, 0.393199, 0.372856,
+ 0.350338, 0.325043, 0.296043, 0.261768, 0.241802, 0.219141,
+ 0.192661, 0.177383, 0.160169, 0.140221, 0.135789, 0.131174,
+ 0.126352, 0.121299, 0.11598, 0.104371, 0.0910184, 0.083415,
+ 0.0749342}, {1.3749, 1.37446, 1.37529, 1.37504, 1.37506, 1.37511,
+ 1.37511, 1.37508, 1.37506, 1.37506, 1.37507, 1.37505, 1.37505,
+ 1.37503, 1.37501, 1.37499, 1.37496, 1.37492, 1.37488, 1.37485,
+ 1.37481, 1.37478, 1.37474, 1.37465, 1.37456, 1.37437, 1.37418,
+ 1.37399, 1.37359, 1.37319, 1.37277, 1.37233, 1.37188, 1.37142,
+ 1.37094, 1.37045, 1.36993, 1.36941, 1.36886, 1.36829, 1.3668,
+ 1.36517, 1.36339, 1.36145, 1.35934, 1.35704, 1.35452, 1.35177,
+ 1.34875, 1.34544, 1.3418, 1.33779, 1.33338, 1.3285, 1.32309,
+ 1.31709, 1.3104, 1.30292, 1.29452, 1.28507, 1.27436, 1.26216,
+ 1.24818, 1.23202, 1.2132, 1.19101, 1.1645, 1.13228, 1.11735,
+ 1.10101, 1.08301, 1.06309, 1.04089, 1.01595, 0.987663, 0.955194,
+ 0.917365, 0.872418, 0.817554, 0.747869, 0.704729, 0.653377,
+ 0.590005, 0.551715, 0.507, 0.486743, 0.464764, 0.440707, 0.41408,
+ 0.384173, 0.34989, 0.309375, 0.285775, 0.25899, 0.227694, 0.209637,
+ 0.189292, 0.165716, 0.160479, 0.155024, 0.149326, 0.143353,
+ 0.137067, 0.123347, 0.107567, 0.0985815, 0.0885587},
+{0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28,
+ 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28, 0.28}};
+
+ /* To actually calculate the ringdown, we will use the following pointers to point to the correct mode */
+ const double (*reomegaqnm)[107] = NULL;
+ const double (*imomegaqnm)[107] = NULL;
+
+ REAL8 totalMass, finalMass, finalSpin;
+
+ /* Stuff for interpolating the data */
+ gsl_spline *spline = NULL;
+ gsl_interp_accel *acc = NULL;
+
+ UINT4 i;
+
+ /* Check we do not require more overtones than we have */
+#if debugOutput
+ if ( nmodes > 8 )
+ {
+ fprintf( stderr,"Requesting more overtones than we have data to generate!\n");
+ }
+#endif
+
+ /* Choose the appropriate data bases on the user requested l an m */
+ switch ( l )
+ {
+ case 2:
+ if ( m == 2 )
+ {
+ reomegaqnm = reomegaqnm22;
+ imomegaqnm = imomegaqnm22;
+ }
+ else if ( m == 1 )
+ {
+ reomegaqnm = reomegaqnm21;
+ imomegaqnm = imomegaqnm21;
+ }
+ else if ( m == 0 )
+ {
+ reomegaqnm = reomegaqnm20;
+ imomegaqnm = imomegaqnm20;
+ }
+ else
+ {
+ fprintf( stderr,"Unsupported combination of l, m (%d, %d)\n", l, m );
+ return -1;
+ }
+ break;
+ case 3:
+ if ( l == 3 )
+ {
+ reomegaqnm = reomegaqnm33;
+ imomegaqnm = imomegaqnm33;
+ }
+ else
+ {
+ fprintf( stderr,"Unsupported combination of l, m (%d, %d)\n", l, m );
+ return -1;
+ }
+ break;
+ case 4:
+ if ( l == 4 )
+ {
+ reomegaqnm = reomegaqnm44;
+ imomegaqnm = imomegaqnm44;
+ }
+ else
+ {
+ fprintf( stderr,"Unsupported combination of l, m (%d, %d)\n", l, m );
+ return -1;
+ }
+ break;
+ case 5:
+ if ( l == 5 )
+ {
+ reomegaqnm = reomegaqnm55;
+ imomegaqnm = imomegaqnm55;
+ }
+ else
+ {
+ fprintf( stderr,"Unsupported combination of l, m (%d, %d)\n", l, m );
+ return -1;
+ }
+ break;
+ default:
+ fprintf( stderr,"Unsupported combination of l, m (%d, %d)\n", l, m );
+ return -1;
+ break;
+ }
+
+ spline = gsl_spline_alloc( gsl_interp_cspline, 107 );
+ acc = gsl_interp_accel_alloc();
+
+ totalMass = mass1 + mass2;
+
+ /* Call XLALSimIMREOBFinalMassSpin_re() to get mass and spin of the final black hole, locate in current file */
+ if ( XLALSimIMREOBFinalMassSpin_re(&finalMass, &finalSpin, mass1, mass2, spin1, spin2) == -1 )
+ {
+ return -1;
+ }
+#if debugOutput
+ fprintf(stderr,"finalMass = %e, finalSpin = %e\n",finalMass, finalSpin);
+#endif
+ COMPLEX16 ci = I;
+ /* Now get the QNM frequencies from interpolating the above data */
+ for ( i = 0; i < nmodes; i++ )
+ {
+ gsl_spline_init( spline, afinallist, reomegaqnm[i], 107 );
+ gsl_interp_accel_reset( acc );
+
+ modefreqs->data[i] = gsl_spline_eval( spline, finalSpin, acc );
+
+ gsl_spline_init( spline, afinallist, imomegaqnm[i], 107 );
+ gsl_interp_accel_reset( acc );
+
+ modefreqs->data[i] += ci*gsl_spline_eval( spline, finalSpin, acc );
+#if debugOutput
+ fprintf(stderr,"QNM(%d,%d,%d) = %e+i %e\n",l,m,i,
+ creal(modefreqs->data[i]),cimag(modefreqs->data[i]));
+#endif
+ /* Scale by the appropriate mass factors */
+ modefreqs->data[i] *= 1./ finalMass / (totalMass * LAL_MTSUN_SI);
+ }
+ /* Free memory and exit */
+ gsl_spline_free( spline );
+ gsl_interp_accel_free( acc );
+
+ return 0;
+}
+
+int XLALSimIMREOBFinalMassSpin_re(
+ REAL8 *finalMass, /**<< OUTPUT, the final mass (scaled by original total mass) */
+ REAL8 *finalSpin, /**<< OUTPUT, the final spin (scaled by final mass) */
+const REAL8 mass1, /**<< The mass of the 1st component of the system */
+const REAL8 mass2, /**<< The mass of the 2nd component of the system */
+const REAL8 spin1[3], /**<< The spin of the 1st object; only needed for spin waveforms */
+const REAL8 spin2[3] /**<< The spin of the 2nd object; only needed for spin waveforms */
+)
+{
+static const REAL8 root9ovr8minus1 = -0.057190958417936644;
+static const REAL8 root12 = 3.4641016151377544;
+
+/* Constants used for the spinning EOB model */
+static const REAL8 p0 = 0.04826;
+static const REAL8 p1 = 0.01559;
+static const REAL8 p2 = 0.00485;
+static const REAL8 t0 = -2.8904;
+static const REAL8 t2 = -3.5171;
+static const REAL8 t3 = 2.5763;
+static const REAL8 s4 = -0.1229;
+static const REAL8 s5 = 0.4537;
+
+REAL8 totalMass;
+REAL8 eta, eta2, eta3;
+REAL8 a1, a2, chiS, q;
+REAL8 tmpVar;
+
+/* get a local copy of the intrinsic parameters */
+totalMass = mass1 + mass2;
+eta = mass1 * mass2 / (totalMass*totalMass);
+eta2 = eta * eta;
+eta3 = eta2 * eta;
+
+
+ /* Final mass/spin comes from Eq. 8 of Tichy and Marronetti PRD78, 081501
+ and from Eqs. 1 and 3 of Barausse and Rezzolla ApJ704, L40 */
+a1 = spin1[2];
+a2 = spin2[2];
+
+chiS = 0.5 * ( a1 + a2 );
+q = mass1 / mass2;
+
+*finalMass = 1. - p0 + 2.*p1 * chiS + 4.*p2*chiS*chiS;
+*finalMass = 1. + (0.9515 - 1.0)*4.*eta - 0.013*16.*eta2*(a1+a2);
+tmpVar = ( a1 + a2 /q/q) / ( 1. + 1/q/q);
+*finalSpin = tmpVar + tmpVar * eta * (s4 * tmpVar + s5 * eta + t0 ) + eta * (2. * sqrt(3.) + t2*eta + t3*eta*eta );
+
+
+/*printf( "Final mass = %e, Final spin = %e\n", *finalMass, *finalSpin );*/
+return 0;
+}
+/**
+ * Function to calculate normalized spin of the test particle in SEOBNRv1.
+ * Eq. 5.3 of Barausse and Buonanno PRD 81, 084024 (2010).
+ */
+ int XLALSimIMRSpinEOBCalculateSigmaStar(
+ REAL8Vector *sigmaStar, /**<< OUTPUT, normalized (to total mass) spin of test particle */
+ REAL8 mass1, /**<< mass 1 */
+ REAL8 mass2, /**<< mass 2 */
+ REAL8Vector *s1, /**<< spin vector 1 */
+ REAL8Vector *s2 /**<< spin vector 2 */)
+{
+
+ UINT4 i;
+ REAL8 totalMass = mass1 + mass2;
+
+ for ( i = 0; i < 3; i++ )
+ {
+ sigmaStar->data[i] = (mass2/mass1 * s1->data[i] + mass1/mass2 * s2->data[i])/(totalMass*totalMass);
+ }
+
+ return 0;
+}
+/**
+ * Function to calculate normalized spin of the deformed-Kerr background in SEOBNRv1.
+ * Eq. 5.2 of Barausse and Buonanno PRD 81, 084024 (2010).
+ */
+ int XLALSimIMRSpinEOBCalculateSigmaKerr(
+ REAL8Vector *sigmaKerr, /**<< OUTPUT, normalized (to total mass) spin of deformed-Kerr */
+ REAL8 mass1, /**<< mass 1 */
+ REAL8 mass2, /**<< mass 2 */
+ REAL8Vector *s1, /**<< spin vector 1 */
+ REAL8Vector *s2 /**<< spin vector 2 */)
+{
+
+ UINT4 i;
+ REAL8 totalMass = mass1 + mass2;
+
+ for ( i = 0; i < 3; i++ )
+ {
+ sigmaKerr->data[i] = (s1->data[i] + s2->data[i])/(totalMass*totalMass);
+ }
+
+ return 0;
+}
+ int XLALSimIMREOBCalcSpinFacWaveformCoefficients(
+ FacWaveformCoeffs * const coeffs, /**< OUTPUT, pre-computed waveform coefficients */
+ const REAL8 m1, /**< mass 1 */
+ const REAL8 m2, /**< mass 2 */
+ const REAL8 eta, /**< symmetric mass ratio */
+ const REAL8 a, /**< Kerr spin parameter for test-particle terms */
+ const REAL8 chiS, /**< (chi1+chi2)/2 */
+ const REAL8 chiA /**< (chi1-chi2)/2 */
+ )
+{
+ REAL8 eta2 = eta*eta;
+ REAL8 eta3 = eta2 * eta;
+
+ REAL8 dM, dM2; //dM3;
+ REAL8 a2, a3;
+
+ /* Combination which appears a lot */
+ REAL8 m1Plus3eta, m1Plus3eta2, m1Plus3eta3;
+
+ dM2 = 1. - 4.*eta;
+
+ //printf( "****************************** a = %e *********************************\n", a );
+
+ /* Check that deltaM has a reasonable value */
+ if ( dM2 < 0 )
+ {
+ fprintf( stderr,"XLAL Error : eta seems to be < 0.25 - this isn't allowed!\n" );
+ return -1;
+ }
+
+ dM = sqrt( dM2 );
+ if (m1 < m2)
+ {
+ dM = -dM;
+ }
+ //dM3 = dM2 * dM;
+
+ a2 = a*a;
+ a3 = a2*a;
+
+ m1Plus3eta = - 1. + 3.*eta;
+ m1Plus3eta2 = m1Plus3eta * m1Plus3eta;
+ m1Plus3eta3 = m1Plus3eta * m1Plus3eta2;
+
+ /* Initialize all coefficients to zero */
+ /* This is important, as we will not set some if dM is zero */
+ memset( coeffs, 0, sizeof( FacWaveformCoeffs ) );
+
+
+ /* l = 2, Eqs. A8a and A8b for rho, Eq. A15a for f,
+ Eqs. 20 and 21 of DIN and Eqs. 27a and 27b of PBFRT for delta */
+
+ coeffs->delta22vh3 = 7./3.;
+ coeffs->delta22vh6 = (-4.*a)/3. + (428.*LAL_PI)/105.;
+ coeffs->delta22v8 = (20.*a)/63.;
+ coeffs->delta22vh9 = -2203./81. + (1712.*LAL_PI*LAL_PI)/315.;
+ coeffs->delta22v5 = - 24.*eta;
+
+ coeffs->rho22v2 = -43./42. + (55.*eta)/84.;
+ coeffs->rho22v3 = (-2.*(chiS + chiA*dM - chiS*eta))/3.;
+ coeffs->rho22v4 = -20555./10584. + 0.5*a2
+ - (33025.*eta)/21168. + (19583.*eta2)/42336.;
+ coeffs->rho22v5 = (-34.*a)/21.;
+ coeffs->rho22v6 = 1556919113./122245200. + (89.*a2)/252. - (48993925.*eta)/9779616.
+ - (6292061.*eta2)/3259872. + (10620745.*eta3)/39118464.
+ + (41.*eta*LAL_PI*LAL_PI)/192.;
+ coeffs->rho22v6l = - 428./105.;
+ coeffs->rho22v7 = (18733.*a)/15876. + a*a2/3.;
+ coeffs->rho22v8 = eta*(-5.6-117.6*eta) -387216563023./160190110080. + (18353.*a2)/21168. - a2*a2/8.;
+ coeffs->rho22v8l = 9202./2205.;
+ coeffs->rho22v10 = -16094530514677./533967033600.;
+ coeffs->rho22v10l = 439877./55566.;
+
+ /*printf( "v2 = %.16e, v3 = %.16e, v4 = %.16e, v5 = %.16e\n"
+ "v6 = %.16e, v6l = %.16e v7 = %.16e v8 = %.16e, v8l = %.16e v10 = %.16e v10l = %.16e\n",
+ coeffs->rho22v2, coeffs->rho22v3, coeffs->rho22v4, coeffs->rho22v5, coeffs->rho22v6,
+ coeffs->rho22v6l, coeffs->rho22v7, coeffs->rho22v8, coeffs->rho22v8l, coeffs->rho22v10,
+ coeffs->rho22v10l );*/
+
+ if ( dM2 )
+ {
+ coeffs->delta21vh3 = 2./3.;
+ coeffs->delta21vh6 = (-17.*a)/35. + (107.*LAL_PI)/105.;
+ coeffs->delta21vh7 = (3.*a2)/140.;
+ coeffs->delta21vh9 = -272./81. + (214.*LAL_PI*LAL_PI)/315.;
+ coeffs->delta21v5 = - 493. * eta /42.;
+
+ //coeffs->rho21v1 = (-3.*(chiS+chiA/dM))/(4.);
+ coeffs->rho21v1 = 0.0;
+ //coeffs->rho21v2 = -59./56 - (9.*chiAPlusChiSdM*chiAPlusChiSdM)/(32.*dM2) + (23.*eta)/84.;
+ coeffs->rho21v2 = -59./56 + (23.*eta)/84. - 9./32.*a2;
+ /*coeffs->rho21v3 = (-567.*chiA*chiA*chiA - 1701.*chiA*chiA*chiS*dM
+ + chiA*(-4708. + 1701.*chiS*chiS - 2648.*eta)*(-1. + 4.*eta)
+ + chiS* dM3 *(4708. - 567.*chiS*chiS
+ + 1816.*eta))/(2688.*dM3);*/
+ coeffs->rho21v3 = 1177./672.*a - 27./128.*a3;
+ coeffs->rho21v4 = -47009./56448.- (865.*a2)/1792. - (405.*a2*a2)/2048. - (10993.*eta)/14112.
+ + (617.*eta2)/4704.;
+ coeffs->rho21v5 = (-98635.*a)/75264. + (2031.*a*a2)/7168. - (1701.*a2*a3)/8192.;
+ coeffs->rho21v6 = 7613184941./2607897600.+ (9032393.*a2)/1806336. + (3897.*a2*a2)/16384.
+ - (15309.*a3*a3)/65536.;
+ coeffs->rho21v6l = - 107./105.;
+ coeffs->rho21v7 = (-3859374457.*a)/1159065600. - (55169.*a3)/16384.
+ + (18603.*a2*a3)/65536. - (72171.*a2*a2*a3)/262144.;
+ coeffs->rho21v7l = 107.*a/140.;
+ coeffs->rho21v8 = -1168617463883./911303737344.;
+ coeffs->rho21v8l = 6313./5880.;
+ coeffs->rho21v10 = -63735873771463./16569158860800.;
+ coeffs->rho21v10l = 5029963./5927040.;
+
+ coeffs->f21v1 = (-3.*(chiS+chiA/dM))/(2.);
+ }
+ else
+ {
+ coeffs->f21v1 = -3.*chiA/2.;
+ }
+
+ /* l = 3, Eqs. A9a - A9c for rho, Eqs. A15b and A15c for f,
+ Eqs. 22 - 24 of DIN and Eqs. 27c - 27e of PBFRT for delta */
+ if ( dM2 )
+ {
+ coeffs->delta33vh3 = 13./10.;
+ coeffs->delta33vh6 = (-81.*a)/20. + (39.*LAL_PI)/7.;
+ coeffs->delta33vh9 = -227827./3000. + (78.*LAL_PI*LAL_PI)/7.;
+ coeffs->delta33v5 = - 80897.*eta / 2430.;
+
+ coeffs->rho33v2 = -7./6. + (2.*eta)/3.;
+ //coeffs->rho33v3 = (chiS*dM*(-4. + 5.*eta) + chiA*(-4. + 19.*eta))/(6.*dM);
+ coeffs->rho33v3 = 0.0;
+ coeffs->rho33v4 = -6719./3960. + a2/2. - (1861.*eta)/990. + (149.*eta2)/330.;
+ coeffs->rho33v5 = (-4.*a)/3.;
+ coeffs->rho33v6 = 3203101567./227026800. + (5.*a2)/36.;
+ coeffs->rho33v6l = - 26./7.;
+ coeffs->rho33v7 = (5297.*a)/2970. + a*a2/3.;
+ coeffs->rho33v8 = -57566572157./8562153600.;
+ coeffs->rho33v8l = 13./3.;
+
+ coeffs->f33v3 = (chiS*dM*(-4. + 5.*eta) + chiA*(-4. + 19.*eta))/(2.*dM);
+ }
+ else
+ {
+ coeffs->f33v3 = chiA * 3./8.;
+ }
+
+ coeffs->delta32vh3 = (10. + 33.*eta)/(-15.*m1Plus3eta);
+ coeffs->delta32vh4 = 4.*a;
+ coeffs->delta32vh6 = (-136.*a)/45. + (52.*LAL_PI)/21.;
+ coeffs->delta32vh9 = -9112./405. + (208.*LAL_PI*LAL_PI)/63.;
+
+ coeffs->rho32v = (4.*chiS*eta)/(-3.*m1Plus3eta);
+ coeffs->rho32v2 = (-4.*a2*eta2)/(9.*m1Plus3eta2) + (328. - 1115.*eta
+ + 320.*eta2)/(270.*m1Plus3eta);
+ coeffs->rho32v3 = (2.*(45.*a*m1Plus3eta3
+ - a*eta*(328. - 2099.*eta + 5.*(733. + 20.*a2)*eta2
+ - 960.*eta3)))/(405.*m1Plus3eta3);
+ coeffs->rho32v4 = a2/3. + (-1444528.
+ + 8050045.*eta - 4725605.*eta2 - 20338960.*eta3
+ + 3085640.*eta2*eta2)/(1603800.*m1Plus3eta2);
+ coeffs->rho32v5 = (-2788.*a)/1215.;
+ coeffs->rho32v6 = 5849948554./940355325. + (488.*a2)/405.;
+ coeffs->rho32v6l = - 104./63.;
+ coeffs->rho32v8 = -10607269449358./3072140846775.;
+ coeffs->rho32v8l = 17056./8505.;
+
+ if ( dM2 )
+ {
+ coeffs->delta31vh3 = 13./30.;
+ coeffs->delta31vh6 = (61.*a)/20. + (13.*LAL_PI)/21.;
+ coeffs->delta31vh7 = (-24.*a2)/5.;
+ coeffs->delta31vh9 = -227827./81000. + (26.*LAL_PI*LAL_PI)/63.;
+ coeffs->delta31v5 = - 17.*eta/10.;
+
+ coeffs->rho31v2 = -13./18. - (2.*eta)/9.;
+ //coeffs->rho31v3 = (chiA*(-4. + 11.*eta) + chiS*dM*(-4. + 13.*eta))/(6.*dM);
+ coeffs->rho31v3 = 0.0;
+ coeffs->rho31v4 = 101./7128.
+ - (5.*a2)/6. - (1685.*eta)/1782. - (829.*eta2)/1782.;
+ coeffs->rho31v5 = (4.*a)/9.;
+ coeffs->rho31v6 = 11706720301./6129723600. - (49.*a2)/108.;
+ coeffs->rho31v6l = - 26./63.;
+ coeffs->rho31v7 = (-2579.*a)/5346. + a*a2/9.;
+ coeffs->rho31v8 = 2606097992581./4854741091200.;
+ coeffs->rho31v8l = 169./567.;
+
+ coeffs->f31v3 = (chiA*(-4. + 11.*eta) + chiS*dM*(-4. + 13.*eta))/(2.*dM);
+ }
+ else
+ {
+ coeffs->f31v3 = - chiA * 5./8.;
+ }
+
+ /* l = 4, Eqs. A10a - A10d for delta, Eq. A15d for f
+ Eqs. 25 - 28 of DIN and Eqs. 27f - 27i of PBFRT for delta */
+
+ coeffs->delta44vh3 = (112. + 219.*eta)/(-120.*m1Plus3eta);
+ coeffs->delta44vh6 = (-464.*a)/75. + (25136.*LAL_PI)/3465.;
+
+ coeffs->rho44v2 = (1614. - 5870.*eta + 2625.*eta2)/(1320.*m1Plus3eta);
+ coeffs->rho44v3 = (chiA*(10. - 39.*eta)*dM + chiS*(10. - 41.*eta
+ + 42.*eta2))/(15.*m1Plus3eta);
+ coeffs->rho44v4 = a2/2. + (-511573572.
+ + 2338945704.*eta - 313857376.*eta2 - 6733146000.*eta3
+ + 1252563795.*eta2*eta2)/(317116800.*m1Plus3eta2);
+ coeffs->rho44v5 = (-69.*a)/55.;
+ coeffs->rho44v6 = 16600939332793./1098809712000. + (217.*a2)/3960.;
+ coeffs->rho44v6l = - 12568./3465.;
+
+ if ( dM2 )
+ {
+ coeffs->delta43vh3 = (486. + 4961.*eta)/(810.*(1. - 2.*eta));
+ coeffs->delta43vh4 = (11.*a)/4.;
+ coeffs->delta43vh6 = 1571.*LAL_PI/385.;
+
+ //coeffs->rho43v = (5.*(chiA - chiS*dM)*eta)/(8.*dM*(-1. + 2.*eta));
+ coeffs->rho43v = 0.0;
+ coeffs->rho43v2 = (222. - 547.*eta + 160.*eta2)/(176.*(-1. + 2.*eta));
+ coeffs->rho43v4 = -6894273./7047040. + (3.*a2)/8.;
+ coeffs->rho43v5 = (-12113.*a)/6160.;
+ coeffs->rho43v6 = 1664224207351./195343948800.;
+ coeffs->rho43v6l = - 1571./770.;
+
+ coeffs->f43v = (5.*(chiA - chiS*dM)*eta)/(2.*dM*(-1. + 2.*eta));
+ }
+ else
+ {
+ coeffs->f43v = - 5.*chiA/4.;
+ }
+
+ coeffs->delta42vh3 = (7.*(1. + 6.*eta))/(-15.*m1Plus3eta);
+ coeffs->delta42vh6 = (212.*a)/75. + (6284.*LAL_PI)/3465.;
+
+ coeffs->rho42v2 = (1146. - 3530.*eta + 285.*eta2)/(1320.*m1Plus3eta);
+ coeffs->rho42v3 = (chiA*(10. - 21.*eta)*dM + chiS*(10. - 59.*eta
+ + 78.*eta2))/(15.*m1Plus3eta);
+ coeffs->rho42v4 = a2/2. + (-114859044. + 295834536.*eta + 1204388696.*eta2 - 3047981160.*eta3
+ - 379526805.*eta2*eta2)/(317116800.*m1Plus3eta2);
+ coeffs->rho42v5 = (-7.*a)/110.;
+ coeffs->rho42v6 = 848238724511./219761942400. + (2323.*a2)/3960.;
+ coeffs->rho42v6l = - 3142./3465.;
+
+ if ( dM2 )
+ {
+ coeffs->delta41vh3 = (2. + 507.*eta)/(10.*(1. - 2.*eta));
+ coeffs->delta41vh4 = (11.*a)/12.;
+ coeffs->delta41vh6 = 1571.*LAL_PI/3465.;
+
+ //coeffs->rho41v = (5.*(chiA - chiS*dM)*eta)/(8.*dM*(-1. + 2.*eta));
+ coeffs->rho41v = 0.0;
+ coeffs->rho41v2 = (602. - 1385.*eta + 288.*eta2)/(528.*(-1. + 2.*eta));
+ coeffs->rho41v4 = -7775491./21141120. + (3.*a2)/8.;
+ coeffs->rho41v5 = (-20033.*a)/55440. - (5*a*a2)/6.;
+ coeffs->rho41v6 = 1227423222031./1758095539200.;
+ coeffs->rho41v6l = - 1571./6930.;
+
+ coeffs->f41v = (5.*(chiA - chiS*dM)*eta)/(2.*dM*(-1. + 2.*eta));
+ }
+ else
+ {
+ coeffs->f41v = - 5.*chiA/4.;
+ }
+
+ /* l = 5, Eqs. A11a - A11e for rho,
+ Eq. 29 of DIN and Eqs. E1a and E1b of PBFRT for delta */
+ if ( dM2 )
+ {
+ coeffs->delta55vh3 = (96875. + 857528.*eta)/(131250.*(1 - 2*eta));
+
+ coeffs->rho55v2 = (487. - 1298.*eta + 512.*eta2)/(390.*(-1. + 2.*eta));
+ coeffs->rho55v3 = (-2.*a)/3.;
+ coeffs->rho55v4 = -3353747./2129400. + a2/2.;
+ coeffs->rho55v5 = - 241. * a / 195.;
+ }
+
+ coeffs->delta54vh3 = 8./15.;
+ coeffs->delta54vh4 = 12.*a/5.;
+
+ coeffs->rho54v2 = (-17448. + 96019.*eta - 127610.*eta2
+ + 33320.*eta3)/(13650.*(1. - 5.*eta + 5.*eta2));
+ coeffs->rho54v3 = (-2.*a)/15.;
+ coeffs->rho54v4 = -16213384./15526875. + (2.*a2)/5.;
+
+ if ( dM2 )
+ {
+ coeffs->delta53vh3 = 31./70.;
+
+ coeffs->rho53v2 = (375. - 850.*eta + 176.*eta2)/(390.*(-1. + 2.*eta));
+ coeffs->rho53v3 = (-2.*a)/3.;
+ coeffs->rho53v4 = -410833./709800. + a2/2.;
+ coeffs->rho53v5 = - 103.*a/325.;
+ }
+
+ coeffs->delta52vh3 = 4./15.;
+ coeffs->delta52vh4 = 6.*a/5.;
+
+ coeffs->rho52v2 = (-15828. + 84679.*eta - 104930.*eta2
+ + 21980.*eta3)/(13650.*(1. - 5.*eta + 5.*eta2));
+ coeffs->rho52v3 = (-2.*a)/15.;
+ coeffs->rho52v4 = -7187914./15526875. + (2.*a2)/5.;
+
+ if ( dM2 )
+ {
+ coeffs->delta51vh3 = 31./210.;
+
+ coeffs->rho51v2 = (319. - 626.*eta + 8.*eta2)/(390.*(-1. + 2.*eta));
+ coeffs->rho51v3 = (-2.*a)/3.;
+ coeffs->rho51v4 = -31877./304200. + a2/2.;
+ coeffs->rho51v5 = 139.*a/975.;
+ }
+
+ /* l = 6, Eqs. A12a - A12f for rho, Eqs. E1c and E1d of PBFRT for delta */
+
+ coeffs->delta66vh3 = 43./70.;
+
+ coeffs->rho66v2 = (-106. + 602.*eta - 861.*eta2
+ + 273.*eta3)/(84.*(1. - 5.*eta + 5.*eta2));
+ coeffs->rho66v3 = (-2.*a)/3.;
+ coeffs->rho66v4 = -1025435./659736. + a2/2.;
+
+ if ( dM2 )
+ {
+ coeffs->delta65vh3 = 10./21.;
+
+ coeffs->rho65v2 = (-185. + 838.*eta - 910.*eta2
+ + 220.*eta3)/(144.*(dM2 + 3.*eta2));
+ coeffs->rho65v3 = - 2.*a/9.;
+ }
+
+ coeffs->delta64vh3 = 43./105.;
+
+ coeffs->rho64v2 = (-86. + 462.*eta - 581.*eta2
+ + 133.*eta3)/(84.*(1. - 5.*eta + 5.*eta2));
+ coeffs->rho64v3 = (-2.*a)/3.;
+ coeffs->rho64v4 = -476887./659736. + a2/2.;
+
+ if ( dM2 )
+ {
+ coeffs->delta63vh3 = 2./7.;
+
+ coeffs->rho63v2 = (-169. + 742.*eta - 750.*eta2
+ + 156.*eta3)/(144.*(dM2 + 3.*eta2));
+ coeffs->rho63v3 = - 2.*a/9.;
+ }
+
+ coeffs->delta62vh3 = 43./210.;
+
+ coeffs->rho62v2 = (-74. + 378.*eta - 413.*eta2
+ + 49.*eta3)/(84.*(1. - 5.*eta + 5.*eta2));
+ coeffs->rho62v3 = (-2.*a)/3.;
+ coeffs->rho62v4 = -817991./3298680. + a2/2.;
+
+ if ( dM2 )
+ {
+ coeffs->delta61vh3 = 2./21.;
+
+ coeffs->rho61v2 = (-161. + 694.*eta - 670.*eta2
+ + 124.*eta3)/(144.*(dM2 + 3.*eta2));
+ coeffs->rho61v3 = - 2. * a / 9.;
+ }
+
+ /* l = 7, Eqs. A13a - A13g for rho, Eqs. E1e and E1f of PBFRT for delta */
+ if ( dM2 )
+ {
+ coeffs->delta77vh3 = 19./36.;
+
+ coeffs->rho77v2 = (-906. + 4246.*eta - 4963.*eta2
+ + 1380.*eta3)/(714.*(dM2 + 3.*eta2));
+ coeffs->rho77v3 = - 2.*a/3.;
+ }
+
+ coeffs->rho76v2 = (2144. - 16185.*eta + 37828.*eta2 - 29351.*eta3
+ + 6104.*eta2*eta2) / (1666.*(-1 + 7*eta - 14*eta2
+ + 7*eta3));
+
+ if ( dM2 )
+ {
+ coeffs->delta75vh3 = 95./252.;
+
+ coeffs->rho75v2 = (-762. + 3382.*eta - 3523.*eta2
+ + 804.*eta3)/(714.*(dM2 + 3.*eta2));
+ coeffs->rho75v3 = - 2.*a/3.;
+ }
+
+ coeffs->rho74v2 = (17756. - 131805.*eta + 298872.*eta2 - 217959.*eta3
+ + 41076.*eta2*eta2) / (14994.*(-1. + 7.*eta - 14.*eta2
+ + 7.*eta3));
+
+ if ( dM2 )
+ {
+ coeffs->delta73vh3 = 19./84.;
+
+ coeffs->rho73v2 = (-666. + 2806.*eta - 2563.*eta2
+ + 420.*eta3)/(714.*(dM2 + 3.*eta2));
+ coeffs->rho73v3 = - 2.*a/3.;
+ }
+
+ coeffs->rho72v2 = (16832. - 123489.*eta + 273924.*eta2 - 190239.*eta3
+ + 32760.*eta2*eta2) /(14994.*(-1. + 7.*eta - 14.*eta2
+ + 7.*eta3));
+
+ if ( dM2 )
+ {
+ coeffs->delta71vh3 = 19./252.;
+
+ coeffs->rho71v2 = (-618. + 2518.*eta - 2083.*eta2
+ + 228.*eta3)/(714.*(dM2 + 3.*eta2));
+ coeffs->rho71v3 = - 2.*a/3.;
+ }
+
+ /* l = 8, Eqs. A14a - A14h */
+
+ coeffs->rho88v2 = (3482. - 26778.*eta + 64659.*eta2 - 53445.*eta3
+ + 12243.*eta2*eta2) / (2736.*(-1. + 7.*eta - 14.*eta2
+ + 7.*eta3));
+
+ if ( dM2 )
+ {
+ coeffs->rho87v2 = (23478. - 154099.*eta + 309498.*eta2 - 207550.*eta3
+ + 38920*eta2*eta2) / (18240.*(-1 + 6*eta - 10*eta2
+ + 4*eta3));
+ }
+
+ coeffs->rho86v2 = (1002. - 7498.*eta + 17269.*eta2 - 13055.*eta3
+ + 2653.*eta2*eta2) / (912.*(-1. + 7.*eta - 14.*eta2
+ + 7.*eta3));
+
+ if ( dM2 )
+ {
+ coeffs->rho85v2 = (4350. - 28055.*eta + 54642.*eta2 - 34598.*eta3
+ + 6056.*eta2*eta2) / (3648.*(-1. + 6.*eta - 10.*eta2
+ + 4.*eta3));
+ }
+
+ coeffs->rho84v2 = (2666. - 19434.*eta + 42627.*eta2 - 28965.*eta3
+ + 4899.*eta2*eta2) / (2736.*(-1. + 7.*eta - 14.*eta2
+ + 7.*eta3));
+
+ if ( dM2 )
+ {
+ coeffs->rho83v2 = (20598. - 131059.*eta + 249018.*eta2 - 149950.*eta3
+ + 24520.*eta2*eta2) / (18240.*(-1. + 6.*eta - 10.*eta2
+ + 4.*eta3));
+ }
+
+ coeffs->rho82v2 = (2462. - 17598.*eta + 37119.*eta2 - 22845.*eta3
+ + 3063.*eta2*eta2) / (2736.*(-1. + 7.*eta - 14.*eta2
+ + 7.*eta3));
+
+ if ( dM2 )
+ {
+ coeffs->rho81v2 = (20022. - 126451.*eta + 236922.*eta2 - 138430.*eta3
+ + 21640.*eta2*eta2) / (18240.*(-1. + 6.*eta - 10.*eta2
+ + 4.*eta3));
+ }
+
+ /* All relevant coefficients should be set, so we return */
+
+ return 0;
+}
+
+ int XLALSimIMREOBComputeNewtonMultipolePrefixes(
+ NewtonMultipolePrefixes *prefix, /**<< OUTPUT Structure containing the coeffs */
+ const REAL8 m1, /**<< Mass of first component */
+ const REAL8 m2 /**<< Nass of second component */
+ )
+{
+
+ int l, m;
+
+ memset( prefix, 0, sizeof( NewtonMultipolePrefixes ) );
+
+ for ( l = 2; l <= 8; l++ )
+ {
+ for ( m = 1; m <= l; m++ )
+ {
+ CalculateThisMultipolePrefix( &(prefix->values[l][m]), m1, m2, l, m );
+ }
+ }
+ return 0;
+}
+/**
+ * Function to calculate the numerical prefix in the Newtonian amplitude. Eqs. 5 - 7.
+ */
+ int
+CalculateThisMultipolePrefix(
+ COMPLEX16 *prefix, /**<< OUTPUT, Prefix value */
+ const REAL8 m1, /**<< mass 1 */
+ const REAL8 m2, /**<< mass 2 */
+ int l, /**<< Mode l */
+ int m /**<< Mode m */
+ )
+{
+ COMPLEX16 n;
+ REAL8 c;
+
+ REAL8 x1, x2; /* Scaled versions of component masses */
+
+ REAL8 mult1, mult2;
+
+ REAL8 totalMass;
+ REAL8 eta;
+
+ int epsilon;
+ int sign; /* To give the sign of some additive terms */
+ COMPLEX16 ci = I;
+
+
+ //n = 0.0;
+
+ totalMass = m1 + m2;
+
+ epsilon = ( l + m ) % 2;
+
+ x1 = m1 / totalMass;
+ x2 = m2 / totalMass;
+
+ eta = m1*m2/(totalMass*totalMass);
+
+ if ( abs( m % 2 ) == 0 )
+ {
+ sign = 1;
+ }
+ else
+ {
+ sign = -1;
+ }
+ /**
+ * Eq. 7 of Damour, Iyer and Nagar 2008.
+ * For odd m, c is proportional to dM = m1-m2. In the equal-mass case, c = dM = 0.
+ * In the equal-mass unequal-spin case, however, when spins are different, the odd m term is generally not zero.
+ * In this case, c can be written as c0 * dM, while spins terms in PN expansion may take the form chiA/dM.
+ * Although the dM's cancel analytically, we can not implement c and chiA/dM with the possibility of dM -> 0.
+ * Therefore, for this case, we give numerical values of c0 for relevant modes, and c0 is calculated as
+ * c / dM in the limit of dM -> 0. Consistently, for this case, we implement chiA instead of chiA/dM
+ * in LALSimIMRSpinEOBFactorizedWaveform.c.
+ */
+ if ( m1 != m2 || sign == 1 )
+ {
+ // Eq.(B8) of Y Pan, et al, PRD 84, 124052 (2011)
+ c = pow( x2, l + epsilon - 1 ) + sign * pow(x1, l + epsilon - 1 );
+ }
+ else
+ {
+ switch( l )
+ {
+ case 2:
+ c = -1.0;
+ break;
+ case 3:
+ c = -1.0;
+ break;
+ case 4:
+ c = -0.5;
+ break;
+ default:
+ c = 0.0;
+ break;
+ }
+ }
+
+ /* Eqs 5 and 6. Dependent on the value of epsilon (parity), we get different n */
+ if ( epsilon == 0 )
+ {
+ // Eq.(B7a) of Y Pan et al, PRD 84, 124052 (2011)
+ n = ci * (double)m;
+
+ n = MYcpow( n, l );
+
+ mult1 = 8.0 * LAL_PI / gsl_sf_doublefact(2u*l + 1u); // 1u means unsigned int
+ mult2 = (REAL8)((l+1) * (l+2)) / (REAL8)(l * ((int)l - 1));
+ mult2 = sqrt(mult2);
+
+ n *= mult1;
+ n *= mult2;
+ }
+ else if ( epsilon == 1 )
+ {
+ // Eq.(B7b) of Y Pan et al, PRD 84, 124052 (2011)
+ n = ci * (double)m;
+ n = MYcpow( n,l );
+ n = -n;
+
+ mult1 = 16.*LAL_PI / gsl_sf_doublefact( 2u*l + 1u );
+
+ mult2 = (REAL8)( (2*l + 1) * (l+2) * (l*l - m*m) );
+ mult2 /= (REAL8)( (2*l - 1) * (l+1) * l * (l-1) );
+ mult2 = sqrt(mult2);
+
+ n *= ci * mult1;
+ n *= mult2;
+ }
+ else
+ {
+ fprintf( stderr,"Epsilon must be 0 or 1.\n");
+ return -1;
+ }
+
+ *prefix = n * eta * c;
+
+ return 0;
+}
+ int XLALSimIMRSpinEOBInitialConditions(
+ REAL8Vector *initConds, /**<< OUTPUT, Initial dynamical variables */
+ const REAL8 mass1, /**<< mass 1 */
+ const REAL8 mass2, /**<< mass 2 */
+ const REAL8 fMin, /**<< Initial frequency (given) */
+ const REAL8 e0, /**<< eccentricity at starting GW frequency (Hz) */
+ const REAL8 inc, /**<< Inclination */
+ const REAL8 spin1[], /**<< Initial spin vector 1 */
+ const REAL8 spin2[], /**<< Initial spin vector 2 */
+ SpinEOBParams *params /**<< Spin EOB parameters */
+ )
+{
+#if debugOutput
+ fprintf(stderr, "input parameters:\n");
+ fprintf( stderr,"(m1,m2)=(%.16e,%.16e)\n(fMin,inc)=(%.16e,%.16e)\n(S1x,S1y,S1z)=(%.16e,%.16e,%.16e)\n(S2x,S2y,S2z)=(%.16e,%.16e,%.16e)\n", mass1, mass2, fMin,inc,
+ spin1[0], spin1[1], spin1[2], spin2[0], spin2[1], spin2[2]);
+#endif
+
+ static const int lMax = 8;
+
+ int i;
+
+ /* Variable to keep track of whether the user requested the tortoise */
+ int tmpTortoise;
+
+ REAL8 mTotal;
+ REAL8 eta;
+ REAL8 omega, v0; /* Initial velocity and angular frequency */
+
+ REAL8 ham; /* Hamiltonian */
+
+ REAL8 LnHat[3]; /* Initial orientation of angular momentum */
+ REAL8 rHat[3]; /* Initial orientation of radial vector */
+ REAL8 vHat[3]; /* Initial orientation of velocity vector */
+ REAL8 Lhat[3]; /* Direction of relativistic ang mom */
+ REAL8 qHat[3];
+ REAL8 pHat[3];
+
+ /* q and p vectors in Cartesian and spherical coords */
+ REAL8 qCart[3], pCart[3];
+ REAL8 qSph[3], pSph[3];
+
+ /* We will need to manipulate the spin vectors */
+ /* We will use temporary vectors to do this */
+ REAL8 tmpS1[3];
+ REAL8 tmpS2[3];
+
+ REAL8Vector qCartVec, pCartVec;
+ REAL8Vector s1Vec, s2Vec;
+ REAL8Vector sKerr, sStar;
+ REAL8 sKerrData[3], sStarData[3];
+ REAL8 a = 0., chiS, chiA;
+ REAL8 chi1, chi2;
+
+ /* We will need a full values vector for calculating derivs of Hamiltonian */
+ REAL8 sphValues[12];
+ REAL8 cartValues[12];
+
+ /* Matrices for rotating to the new basis set. */
+ /* It is more convenient to calculate the ICs in a simpler basis */
+ gsl_matrix *rotMatrix = NULL;
+ gsl_matrix *invMatrix = NULL;
+ gsl_matrix *rotMatrix2 = NULL;
+ gsl_matrix *invMatrix2 = NULL;
+
+ /* Root finding stuff for finding the spherical orbit */
+ SEOBRootParams rootParams;
+ const gsl_multiroot_fsolver_type *T = gsl_multiroot_fsolver_hybrids;
+ gsl_multiroot_fsolver *rootSolver = NULL;
+
+ gsl_multiroot_function rootFunction;
+ gsl_vector *initValues = NULL;
+ gsl_vector *finalValues = NULL;
+ int gslStatus;
+ const int maxIter = 100;
+
+ memset( &rootParams, 0, sizeof( rootParams ) );
+
+ memcpy( tmpS1, spin1, sizeof(tmpS1) );
+ memcpy( tmpS2, spin2, sizeof(tmpS2) );
+
+ mTotal = mass1 + mass2;
+ eta = mass1 * mass2 / (mTotal * mTotal);
+
+ /* We compute the ICs for the non-tortoise p, and convert at the end */
+ tmpTortoise = params->tortoise;
+ params->tortoise = 0;
+
+ /* STEP 1) Rotate to LNhat0 along z-axis and N0 along x-axis frame, where LNhat0 and N0 are initial normal to
+ * orbital plane and initial orbital separation;
+ */
+
+ /* Set the initial orbital ang mom direction. Taken from STPN code */
+ LnHat[0] = sin(inc);
+ LnHat[1] = 0.;
+ LnHat[2] = cos(inc);
+
+ /* Set the radial direction - need to take care to avoid singularity if L is along z axis */
+ if ( LnHat[2] > 0.9999 )
+ {
+ rHat[0] = 1.;
+ rHat[1] = rHat[2] = 0.;
+ }
+ else
+ {
+ REAL8 theta0 = atan( - LnHat[2] / LnHat[0] ); /* theta0 is between 0 and Pi */
+ rHat[0] = sin( theta0 );
+ rHat[1] = 0;
+ rHat[2] = cos( theta0 );
+ }
+
+ /* Now we can complete the triad */
+ vHat[0] = CalculateCrossProduct( 0, LnHat, rHat );
+ vHat[1] = CalculateCrossProduct( 1, LnHat, rHat );
+ vHat[2] = CalculateCrossProduct( 2, LnHat, rHat );
+
+ NormalizeVector( vHat );
+
+ /* XXX Test code XXX */
+ /*for ( i = 0; i < 3; i++ )
+ {
+ printf ( " LnHat[%d] = %.16e, rHat[%d] = %.16e, vHat[%d] = %.16e\n", i, LnHat[i], i, rHat[i], i, vHat[i] );
+ }
+
+ printf("\n\n" );
+ for ( i = 0; i < 3; i++ )
+ {
+ printf ( " s1[%d] = %.16e, s2[%d] = %.16e\n", i, tmpS1[i], i, tmpS2[i] );
+ }*/
+
+ /* Allocate and compute the rotation matrices */
+ rotMatrix = gsl_matrix_alloc( 3, 3 );
+ invMatrix = gsl_matrix_alloc( 3, 3 );
+ if ( !rotMatrix || !invMatrix )
+ {
+ if ( rotMatrix ) gsl_matrix_free( rotMatrix );
+ if ( invMatrix ) gsl_matrix_free( invMatrix );
+ return -1;
+ }
+
+ if ( CalculateRotationMatrix( rotMatrix, invMatrix, rHat, vHat, LnHat ) == -1 )
+ {
+ gsl_matrix_free( rotMatrix );
+ gsl_matrix_free( invMatrix );
+ return -1;
+ }
+
+ /* Rotate the orbital vectors and spins */
+ ApplyRotationMatrix( rotMatrix, rHat );
+ ApplyRotationMatrix( rotMatrix, vHat );
+ ApplyRotationMatrix( rotMatrix, LnHat );
+ ApplyRotationMatrix( rotMatrix, tmpS1 );
+ ApplyRotationMatrix( rotMatrix, tmpS2 );
+
+ /* XXX Test code XXX */
+ /*printf( "\nAfter applying rotation matrix:\n\n" );
+ for ( i = 0; i < 3; i++ )
+ {
+ printf ( " LnHat[%d] = %.16e, rHat[%d] = %.16e, vHat[%d] = %.16e\n", i, LnHat[i], i, rHat[i], i, vHat[i] );
+ }
+
+ printf("\n\n" );
+ for ( i = 0; i < 3; i++ )
+ {
+ printf ( " s1[%d] = %.16e, s2[%d] = %.16e\n", i, tmpS1[i], i, tmpS2[i] );
+ }*/
+
+ /* STEP 2) After rotation in STEP 1, in spherical coordinates, phi0 and theta0 are given directly in Eq. (4.7) of PRD 74, 104005,
+ * r0, pr0, ptheta0 and pphi0 are obtained by solving Eqs. (4.8) and (4.9) of PRD 74, 104005 (using gsl_multiroot_fsolver).
+ * At this step, we find initial conditions for a spherical orbit without radiation reaction.
+ */
+
+ /* Calculate the initial velocity from the given initial frequency */
+ omega = LAL_PI * mTotal * LAL_MTSUN_SI * fMin;
+ v0 = MYcbrt( omega );
+ /* Given this, we can start to calculate the initial conditions */
+ /* for spherical coords in the new basis */
+ rootParams.omega = omega;
+ rootParams.params = params;
+
+ /* To start with, we will just assign Newtonian-ish ICs to the system */
+ rootParams.values[0] = 1./(v0*v0); /* Initial r */
+ rootParams.values[4] = v0; /* Initial p */
+ memcpy( rootParams.values+6, tmpS1, sizeof( tmpS1 ) );
+ memcpy( rootParams.values+9, tmpS2, sizeof( tmpS2 ) );
+
+ //printf( "ICs guess: r = %.16e, p = %.16e\n", rootParams.values[0], rootParams.values[4] );
+
+ /* Initialise the gsl stuff */
+ rootSolver = gsl_multiroot_fsolver_alloc( T, 3 );
+ if ( !rootSolver )
+ {
+ gsl_matrix_free( rotMatrix );
+ gsl_matrix_free( invMatrix );
+ return -1;
+ }
+
+ initValues = gsl_vector_calloc( 3 );
+ if ( !initValues )
+ {
+ gsl_multiroot_fsolver_free( rootSolver );
+ gsl_matrix_free( rotMatrix );
+ gsl_matrix_free( invMatrix );
+ return -1;
+ }
+
+ gsl_vector_set( initValues, 0, rootParams.values[0] );
+ gsl_vector_set( initValues, 1, rootParams.values[4] );
+
+ rootFunction.f = XLALFindSphericalOrbit;
+ rootFunction.n = 3;
+ rootFunction.params = &rootParams;
+
+ gsl_multiroot_fsolver_set( rootSolver, &rootFunction, initValues );
+
+ /* We are now ready to iterate to find the solution */
+ i = 0;
+
+ do
+ {
+ gslStatus = gsl_multiroot_fsolver_iterate( rootSolver ) ;
+ if ( gslStatus != GSL_SUCCESS )
+ {
+ fprintf(stderr, "Error in GSL iteration function!\n" );
+ gsl_multiroot_fsolver_free( rootSolver );
+ gsl_vector_free( initValues );
+ gsl_matrix_free( rotMatrix );
+ gsl_matrix_free( invMatrix );
+ return -1;
+ }
+
+ gslStatus = gsl_multiroot_test_residual( rootSolver->f, 1.0e-10 );
+ i++;
+ }
+ while ( gslStatus == GSL_CONTINUE && i <= maxIter );
+
+ if ( i > maxIter && gslStatus != GSL_SUCCESS )
+ {
+ gsl_multiroot_fsolver_free( rootSolver );
+ gsl_vector_free( initValues );
+ gsl_matrix_free( rotMatrix );
+ gsl_matrix_free( invMatrix );
+ return -1;
+ }
+
+ finalValues = gsl_multiroot_fsolver_root( rootSolver );
+
+ /*printf( "Spherical orbit conditions here given by the following:\n" );
+ printf( " x = %.16e, py = %.16e, pz = %.16e\n", gsl_vector_get( finalValues, 0 ),
+ gsl_vector_get( finalValues, 1 ), gsl_vector_get( finalValues, 2 ) );*/
+
+ memset( qCart, 0, sizeof(qCart) );
+ memset( pCart, 0, sizeof(pCart) );
+
+ qCart[0] = gsl_vector_get( finalValues, 0 );
+ pCart[1] = gsl_vector_get( finalValues, 1 );
+ pCart[2] = gsl_vector_get( finalValues, 2 );
+
+ /* Free the GSL root finder, since we're done with it */
+ gsl_multiroot_fsolver_free( rootSolver );
+ gsl_vector_free( initValues );
+
+ /* STEP 3) Rotate to L0 along z-axis and N0 along x-axis frame, where L0 is the initial orbital angular momentum
+ * and L0 is calculated using initial position and linear momentum obtained in STEP 2.
+ */
+
+ /* Now we can calculate the relativistic L and rotate to a new basis */
+ memcpy( qHat, qCart, sizeof(qCart) );
+ memcpy( pHat, pCart, sizeof(pCart) );
+
+ NormalizeVector( qHat );
+ NormalizeVector( pHat );
+
+ Lhat[0] = CalculateCrossProduct( 0, qHat, pHat );
+ Lhat[1] = CalculateCrossProduct( 1, qHat, pHat );
+ Lhat[2] = CalculateCrossProduct( 2, qHat, pHat );
+
+ NormalizeVector( Lhat );
+
+ rotMatrix2 = gsl_matrix_alloc( 3, 3 );
+ invMatrix2 = gsl_matrix_alloc( 3, 3 );
+
+ if ( CalculateRotationMatrix( rotMatrix2, invMatrix2, qHat, pHat, Lhat ) == -1 )
+ {
+ gsl_matrix_free( rotMatrix );
+ gsl_matrix_free( invMatrix );
+ return -1;
+ }
+
+ ApplyRotationMatrix( rotMatrix2, rHat );
+ ApplyRotationMatrix( rotMatrix2, vHat );
+ ApplyRotationMatrix( rotMatrix2, LnHat );
+ ApplyRotationMatrix( rotMatrix2, tmpS1 );
+ ApplyRotationMatrix( rotMatrix2, tmpS2 );
+ ApplyRotationMatrix( rotMatrix2, qCart );
+ ApplyRotationMatrix( rotMatrix2, pCart );
+
+ /* STEP 4) In the L0-N0 frame, we calculate (dE/dr)|sph using Eq. (4.14) of PRD 74, 104005, then initial dr/dt using Eq. (4.10) of PRD 74, 104005,
+ * and finally pr0 using Eq. (4.15) of PRD 74, 104005.
+ */
+
+ /* Now we can calculate the flux. Change to spherical co-ords */
+ CartesianToSpherical( qSph, pSph, qCart, pCart );
+ memcpy( sphValues, qSph, sizeof( qSph ) );
+ memcpy( sphValues+3, pSph, sizeof( pSph ) );
+ memcpy( sphValues+6, tmpS1, sizeof(tmpS1) );
+ memcpy( sphValues+9, tmpS2, sizeof(tmpS2) );
+
+ memcpy( cartValues, qCart, sizeof(qCart) );
+ memcpy( cartValues+3, pCart, sizeof(pCart) );
+ memcpy( cartValues+6, tmpS1, sizeof(tmpS1) );
+ memcpy( cartValues+9, tmpS2, sizeof(tmpS2) );
+
+ REAL8 dHdpphi, d2Hdr2, d2Hdrdpphi;
+ REAL8 rDot, dHdpr, flux, dEdr;
+
+ d2Hdr2 = XLALCalculateSphHamiltonianDeriv2( 0, 0, sphValues, params );
+ d2Hdrdpphi = XLALCalculateSphHamiltonianDeriv2( 0, 5, sphValues, params );
+
+ //printf( "d2Hdr2 = %.16e, d2Hdrdpphi = %.16e\n", d2Hdr2, d2Hdrdpphi );
+
+ dHdpphi = XLALSpinHcapNumDerivWRTParam( 4, cartValues, params ) / sphValues[0];
+
+ dEdr = - dHdpphi * d2Hdr2 / d2Hdrdpphi;
+
+ //printf( "d2Hdr2 = %.16e d2Hdrdpphi = %.16e dHdpphi = %.16e\n", d2Hdr2, d2Hdrdpphi, dHdpphi );
+
+ if ( d2Hdr2 != 0.0 )
+ {
+
+ /* We will need to calculate the Hamiltonian to get the flux */
+ s1Vec.length = s2Vec.length = sKerr.length = sStar.length = 3;
+ s1Vec.data = tmpS1;
+ s2Vec.data = tmpS2;
+ sKerr.data = sKerrData;
+ sStar.data = sStarData;
+
+ qCartVec.length = pCartVec.length = 3;
+ qCartVec.data = qCart;
+ pCartVec.data = pCart;
+
+ chi1 = tmpS1[0]*LnHat[0] + tmpS1[1]*LnHat[1] + tmpS1[2]*LnHat[2];
+ chi2 = tmpS2[0]*LnHat[0] + tmpS2[1]*LnHat[1] + tmpS2[2]*LnHat[2];
+
+ //printf( "magS1 = %.16e, magS2 = %.16e\n", chi1, chi2 );
+
+ chiS = 0.5 * ( chi1 / (mass1*mass1) + chi2 / (mass2*mass2) );
+ chiA = 0.5 * ( chi1 / (mass1*mass1) - chi2 / (mass2*mass2) );
+
+ XLALSimIMRSpinEOBCalculateSigmaKerr( &sKerr, mass1, mass2, &s1Vec, &s2Vec );
+ XLALSimIMRSpinEOBCalculateSigmaStar( &sStar, mass1, mass2, &s1Vec, &s2Vec );
+
+ /* The a in the flux has been set to zero, but not in the Hamiltonian */
+ a = sqrt(sKerr.data[0]*sKerr.data[0] + sKerr.data[1]*sKerr.data[1] + sKerr.data[2]*sKerr.data[2]);
+ XLALSimIMREOBCalcSpinFacWaveformCoefficients( params->eobParams->hCoeffs, mass1, mass2, eta, /*a*/0.0, chiS, chiA );
+ XLALSimIMRCalculateSpinEOBHCoeffs( params->seobCoeffs, eta, a );
+
+ ham = XLALSimIMRSpinEOBHamiltonian( eta, &qCartVec, &pCartVec, &sKerr, &sStar, params->tortoise, params->seobCoeffs );
+
+ //printf( "hamiltonian at this point is %.16e\n", ham );
+
+ /* And now, finally, the flux */
+ REAL8Vector polarDynamics;
+ REAL8 polarData[4];
+
+ polarDynamics.length = 4;
+ polarDynamics.data = polarData;
+
+ polarData[0] = qSph[0];
+ polarData[1] = 0.;
+ polarData[2] = pSph[0];
+ polarData[3] = pSph[2];
+
+ flux = XLALInspiralSpinFactorizedFlux( &polarDynamics, omega, params, ham, lMax );
+ flux = flux / eta;
+
+ rDot = - flux / dEdr;
+
+ /* We now need dHdpr - we take it that it is safely linear up to a pr of 1.0e-3 */
+ cartValues[3] = 1.0e-3;
+ dHdpr = XLALSpinHcapNumDerivWRTParam( 3, cartValues, params );
+
+
+ /*printf( "Ingredients going into prDot:\n" );
+ printf( "flux = %.16e, dEdr = %.16e, dHdpr = %.16e\n", flux, dEdr, dHdpr );*/
+
+ /* We can now calculate what pr should be taking into account the flux */
+ pSph[0] = rDot / (dHdpr / cartValues[3] );
+ }
+ else
+ {
+ /* Since d2Hdr2 has evaluated to zero, we cannot do the above. Just set pr to zero */
+ //printf( "d2Hdr2 is zero!\n" );
+ pSph[0] = 0;
+ }
+
+ /* Now we are done - convert back to cartesian coordinates ) */
+ SphericalToCartesian( qCart, pCart, qSph, pSph );
+
+ /* STEP 5) Rotate back to the original inertial frame by inverting the rotation of STEP 3 and then
+ * inverting the rotation of STEP 1.
+ */
+
+ /* Undo rotations to get back to the original basis */
+ /* Second rotation */
+ ApplyRotationMatrix( invMatrix2, rHat );
+ ApplyRotationMatrix( invMatrix2, vHat );
+ ApplyRotationMatrix( invMatrix2, LnHat );
+ ApplyRotationMatrix( invMatrix2, tmpS1 );
+ ApplyRotationMatrix( invMatrix2, tmpS2 );
+ ApplyRotationMatrix( invMatrix2, qCart );
+ ApplyRotationMatrix( invMatrix2, pCart );
+
+ /* First rotation */
+ ApplyRotationMatrix( invMatrix, rHat );
+ ApplyRotationMatrix( invMatrix, vHat );
+ ApplyRotationMatrix( invMatrix, LnHat );
+ ApplyRotationMatrix( invMatrix, tmpS1 );
+ ApplyRotationMatrix( invMatrix, tmpS2 );
+ ApplyRotationMatrix( invMatrix, qCart );
+ ApplyRotationMatrix( invMatrix, pCart );
+
+ /* If required, apply the tortoise transform */
+ if ( tmpTortoise )
+ {
+ REAL8 r = sqrt(qCart[0]*qCart[0] + qCart[1]*qCart[1] + qCart[2]*qCart[2] );
+ REAL8 deltaR = XLALSimIMRSpinEOBHamiltonianDeltaR( params->seobCoeffs, r, eta, a );
+ REAL8 deltaT = XLALSimIMRSpinEOBHamiltonianDeltaT( params->seobCoeffs, r, eta, a );
+ REAL8 csi = sqrt( deltaT * deltaR )/(r*r + a*a);
+
+ REAL8 pr = (qCart[0]*pCart[0] + qCart[1]*pCart[1] + qCart[2]*pCart[2])/r;
+
+ params->tortoise = tmpTortoise;
+#if debugOutput
+ fprintf(stderr, "Applying the tortoise to p (csi = %.26e)\n", csi );
+#endif
+ for ( i = 0; i < 3; i++ )
+ {
+ pCart[i] = pCart[i] + qCart[i] * pr * (csi - 1.) / r;
+ }
+ }
+
+ //fprintf(stderr, "DEBUG: r *= 1-e0\n");
+ qCart[0] /= 1+e0;
+ pCart[1] *= (1+e0);
+
+ /* Now copy the initial conditions back to the return vector */
+ memcpy( initConds->data, qCart, sizeof(qCart) );
+ memcpy( initConds->data+3, pCart, sizeof(pCart) );
+ memcpy( initConds->data+6, tmpS1, sizeof(tmpS1) );
+ memcpy( initConds->data+9, tmpS2, sizeof(tmpS2) );
+#if debugOutput
+ fprintf( stderr,"THE FINAL INITIAL CONDITIONS:\n");
+ fprintf( stderr,"(x,y,z)=(%.16e,%.16e,%.16e)\n(px,py,pz)=(%.16e,%.16e,%.16e)\n(S1x,S1y,S1z)=(%.16e,%.16e,%.16e)\n(S2x,S2y,S2z)=(%.16e,%.16e,%.16e)\n", initConds->data[0], initConds->data[1], initConds->data[2],
+ initConds->data[3], initConds->data[4], initConds->data[5], initConds->data[6], initConds->data[7], initConds->data[8],
+ initConds->data[9], initConds->data[10], initConds->data[11] );
+#endif
+ return 0;
+}
+
+ int
+CalculateRotationMatrix(
+ gsl_matrix *rotMatrix, /**< OUTPUT, rotation matrix */
+ gsl_matrix *rotInverse, /**< OUTPUT, rotation matrix inversed */
+ REAL8 r[], /**< position vector */
+ REAL8 v[], /**< velocity vector */
+ REAL8 L[] /**< orbital angular momentum */
+ )
+{
+
+ /** a, b, g are the angles alpha, beta and gamma */
+ /* Use a, b and g to avoid shadowing gamma and getting a warning */
+ REAL8 a, b, g;
+ REAL8 cosa, sina, cosb, sinb, cosg, sing;
+
+ /* Calculate the Euclidean Euler angles */
+
+ /* We need to avoid a singularity if L is along z axis */
+ if ( L[2] > 0.9999 )
+ {
+ a = b = g = 0.0;
+ }
+ else
+ {
+ a = atan2( L[0], -L[1] );
+ b = atan2( sqrt( L[0]*L[0] + L[1]*L[1] ), L[2] );
+ g = atan2( r[2], v[2] );
+ }
+
+ if ( ( cosa = cos( a ) ) < 1.0e-16 ) cosa = 0.0;
+ if ( ( sina = sin( a ) ) < 1.0e-16 ) sina = 0.0;
+ if ( ( cosb = cos( b ) ) < 1.0e-16 ) cosb = 0.0;
+ if ( ( sinb = sin( b ) ) < 1.0e-16 ) sinb = 0.0;
+ if ( ( cosg = cos( g ) ) < 1.0e-16 ) cosg = 0.0;
+ if ( ( sing = sin( g ) ) < 1.0e-16 ) sing = 0.0;
+
+ /** Implement the Rotation Matrix following the "x-convention"
+ * 1. rotate about the z-axis by an angle a, rotation matrix Rz(a);
+ * 2. rotate about the former x-axis (now x') by an angle b, rotation matrix Rx(b);
+ * 3. rotate about the former z-axis (now z') by an algle g, rotation matrix Rz(g);
+ */
+ /* populate the matrix */
+ gsl_matrix_set( rotMatrix, 0, 0, cosg*cosa - cosb*sina*sing );
+ gsl_matrix_set( rotMatrix, 0, 1, cosg*sina + cosb*cosa*sing );
+ gsl_matrix_set( rotMatrix, 0, 2, sing*sinb );
+ gsl_matrix_set( rotMatrix, 1, 0, -sing*cosa - cosb*sina*cosg );
+ gsl_matrix_set( rotMatrix, 1, 1, -sing*sina + cosb*cosa*cosg );
+ gsl_matrix_set( rotMatrix, 1, 2, cosg*sinb );
+ gsl_matrix_set( rotMatrix, 2, 0, sinb*sina );
+ gsl_matrix_set( rotMatrix, 2, 1, -sinb*cosa );
+ gsl_matrix_set( rotMatrix, 2, 2, cosb );
+
+ /* Now populate the transpose (which should be the inverse) */
+ gsl_matrix_transpose_memcpy( rotInverse, rotMatrix );
+
+ return 0;
+}
+
+ int
+ApplyRotationMatrix(
+ gsl_matrix *rotMatrix, /**< rotation matrix */
+ REAL8 a[] /**< OUTPUT, vector rotated */
+ )
+{
+
+ gsl_vector *tmpVec1 = gsl_vector_alloc( 3 );
+ gsl_vector *tmpVec2 = gsl_vector_calloc( 3 );
+
+ gsl_vector_set( tmpVec1, 0, a[0] );
+ gsl_vector_set( tmpVec1, 1, a[1] );
+ gsl_vector_set( tmpVec1, 2, a[2] );
+
+ gsl_blas_dgemv( CblasNoTrans, 1.0, rotMatrix, tmpVec1, 0.0, tmpVec2 );
+
+ a[0] = gsl_vector_get( tmpVec2, 0 );
+ a[1] = gsl_vector_get( tmpVec2, 1 );
+ a[2] = gsl_vector_get( tmpVec2, 2 );
+
+ gsl_vector_free( tmpVec1 );
+ gsl_vector_free( tmpVec2 );
+
+ return 0;
+}
+
+ int
+XLALFindSphericalOrbit( const gsl_vector *x, /**<< Parameters requested by gsl root finder */
+ void *params, /**<< Spin EOB parameters */
+ gsl_vector *f /**<< Function values for the given parameters */
+ )
+{
+
+ SEOBRootParams *rootParams = (SEOBRootParams *) params;
+
+ REAL8 py, pz, r, ptheta, pphi;
+
+ /* Numerical derivative of Hamiltonian wrt given value */
+ REAL8 dHdx, dHdpy, dHdpz;
+ REAL8 dHdr, dHdptheta, dHdpphi;
+
+ /* Populate the appropriate values */
+ /* In the special theta=pi/2 phi=0 case, r is x */
+ rootParams->values[0] = r = gsl_vector_get( x, 0 );
+ rootParams->values[4] = py = gsl_vector_get( x, 1 );
+ rootParams->values[5] = pz = gsl_vector_get( x, 2 );
+
+ //printf( "Values r = %.16e, py = %.16e, pz = %.16e\n", r, py, pz );
+
+ ptheta = - r * pz;
+ pphi = r * py;
+
+ /* dHdR */
+ dHdx = XLALSpinHcapNumDerivWRTParam( 0, rootParams->values, rootParams->params );
+ if ( XLAL_IS_REAL8_FAIL_NAN( dHdx ) )
+ {
+ return -1;
+ }
+ //printf( "dHdx = %.16e\n", dHdx );
+
+ /* dHdPphi (I think we can use dHdPy in this coord system) */
+ /* TODO: Check this is okay */
+ dHdpy = XLALSpinHcapNumDerivWRTParam( 4, rootParams->values, rootParams->params );
+ if ( XLAL_IS_REAL8_FAIL_NAN( dHdpy ) )
+ {
+ return -1;
+ }
+
+ /* dHdPtheta (I think we can use dHdPz in this coord system) */
+ /* TODO: Check this is okay */
+ dHdpz = XLALSpinHcapNumDerivWRTParam( 5, rootParams->values, rootParams->params );
+ if ( XLAL_IS_REAL8_FAIL_NAN( dHdpz ) )
+ {
+ return -1;
+ }
+
+ /* Now convert to spherical polars */
+ dHdr = dHdx - dHdpy * pphi / (r*r) + dHdpz * ptheta / (r*r);
+ dHdptheta = - dHdpz / r;
+ dHdpphi = dHdpy / r;
+
+ /* populate the function vector */
+ gsl_vector_set( f, 0, dHdr ); // Eq.(4.9) of PRD 74, 104005 (2006)
+ gsl_vector_set( f, 1, dHdptheta ); // Eq.(4.8) of PRD 74, 104005 (2006)
+ gsl_vector_set( f, 2, dHdpphi - rootParams->omega ); // Eq.(4.8) of PRD 74, 104005 (2006)
+
+ //printf( "Current funcvals = %.16e %.16e %.16e\n", gsl_vector_get( f, 0 ), gsl_vector_get( f, 1 ),
+ // /*gsl_vector_get( f, 2 )*/dHdpphi );
+
+ return 0;
+}
+
+ REAL8 XLALSpinHcapNumDerivWRTParam(
+ const INT4 paramIdx, /**<< Index of the parameters */
+ const REAL8 values[], /**<< Dynamical variables */
+ SpinEOBParams *funcParams /**<< EOB Parameters */
+ )
+{
+ static const REAL8 STEP_SIZE = 1.0e-3;
+
+ HcapDerivParams params; // HcapDerivParams is in Panyidatatypes.h
+
+ REAL8 result;
+
+ gsl_function F;
+ int gslStatus;
+
+ REAL8 mass1, mass2;
+
+ /* The error in a derivative as measured by GSL */
+ REAL8 absErr;
+
+ /* Set up pointers for GSL */
+ params.values = values;
+ params.params = funcParams;
+
+ F.function = &GSLSpinHamiltonianWrapper;
+ F.params = ¶ms;
+ params.varyParam = paramIdx;
+
+ mass1 = params.params->eobParams->m1;
+ mass2 = params.params->eobParams->m2;
+
+ /* Now calculate derivatives w.r.t. the required parameter */
+ if ( paramIdx >=6 && paramIdx < 9 )
+ {
+ gslStatus = gsl_deriv_central( &F, values[paramIdx],
+ STEP_SIZE*mass1*mass1, &result, &absErr );
+ }
+ else if ( paramIdx >= 9 )
+ {
+ gslStatus = gsl_deriv_central( &F, values[paramIdx],
+ STEP_SIZE*mass2*mass2, &result, &absErr );
+ }
+ else
+ {
+ gslStatus = gsl_deriv_central( &F, values[paramIdx],
+ STEP_SIZE, &result, &absErr );
+ }
+ if ( gslStatus != 0 )
+ {
+ fprintf(stderr, "XLAL Error - Failure in GSL function\n" );
+ return -1;
+ }
+
+ //printf( "Abserr = %e\n", absErr );
+
+ return result;
+}
+
+ double GSLSpinHamiltonianWrapper( double x, void *params )
+{
+ HcapDerivParams *dParams = (HcapDerivParams *)params;
+
+ EOBParams *eobParams = dParams->params->eobParams;
+
+ REAL8 tmpVec[12];
+ REAL8 sKerrData[3], sStarData[3];
+
+ /* These are the vectors which will be used in the call to the Hamiltonian */
+ REAL8Vector r, p, spin1, spin2;
+ REAL8Vector sigmaKerr, sigmaStar;
+
+ REAL8 a;
+
+ /* Use a temporary vector to avoid corrupting the main function */
+ memcpy( tmpVec, dParams->values,
+ sizeof(tmpVec) );
+
+ /* Set the relevant entry in the vector to the correct value */
+ tmpVec[dParams->varyParam] = x;
+
+ /* Set the LAL-style vectors to point to the appropriate things */
+ r.length = p.length = spin1.length = spin2.length = 3;
+ sigmaKerr.length = sigmaStar.length = 3;
+ r.data = tmpVec;
+ p.data = tmpVec+3;
+ spin1.data = tmpVec+6;
+ spin2.data = tmpVec+9;
+ sigmaKerr.data = sKerrData;
+ sigmaStar.data = sStarData;
+
+ /* Calculate various spin parameters */
+ XLALSimIMRSpinEOBCalculateSigmaKerr( &sigmaKerr, eobParams->m1, eobParams->m2, &spin1, &spin2 );
+ XLALSimIMRSpinEOBCalculateSigmaStar( &sigmaStar, eobParams->m1, eobParams->m2, &spin1, &spin2 );
+
+ a = sqrt( sigmaKerr.data[0]*sigmaKerr.data[0] + sigmaKerr.data[1]*sigmaKerr.data[1]
+ + sigmaKerr.data[2]*sigmaKerr.data[2] );
+ //printf( "a = %e\n", a );
+ //printf( "aStar = %e\n", sqrt( sigmaStar.data[0]*sigmaStar.data[0] + sigmaStar.data[1]*sigmaStar.data[1] + sigmaStar.data[2]*sigmaStar.data[2]) );
+ /*if ( isnan( a ) )
+ {
+ printf( "a is nan!!\n");
+ }*/
+ XLALSimIMRCalculateSpinEOBHCoeffs( dParams->params->seobCoeffs, eobParams->eta, a );
+
+ //printf( "Hamiltonian = %e\n", XLALSimIMRSpinEOBHamiltonian( eobParams->eta, &r, &p, &sigmaKerr, &sigmaStar, dParams->params->seobCoeffs ) );
+ return XLALSimIMRSpinEOBHamiltonian( eobParams->eta, &r, &p, &sigmaKerr, &sigmaStar, dParams->params->tortoise, dParams->params->seobCoeffs ) / eobParams->eta;
+}
+
+ int XLALSimIMRCalculateSpinEOBHCoeffs(
+ SpinEOBHCoeffs *coeffs, /**<< OUTPUT, EOB parameters including pre-computed coefficients */
+ const REAL8 eta, /**<< symmetric mass ratio */
+ const REAL8 a /**<< Normalized deformed Kerr spin */
+ )
+{
+
+ REAL8 KK, k0, k1, k2, k3, k4;
+ REAL8 m1PlusEtaKK;
+
+ /* Constants are fits taken from Eq. 37 */
+ static const REAL8 c0 = 1.4467; /* needed to get the correct self-force results */
+ static const REAL8 c1 = -1.7152360250654402;
+ static const REAL8 c2 = -3.246255899738242;
+
+ if ( !coeffs )
+ {
+ return -1;
+ }
+
+
+ coeffs->b3 = 0.;
+ coeffs->bb3 = 0.;
+ coeffs->KK = KK = c0 + c1*eta + c2*eta*eta;
+
+ m1PlusEtaKK = -1. + eta*KK;
+ /* Eqs. 5.77 - 5.81 of BB1, i.e. PRD 81, 084024 (2010) */
+ coeffs->k0 = k0 = KK*(m1PlusEtaKK - 1.);
+ coeffs->k1 = k1 = - 2.*(k0 + KK)*m1PlusEtaKK;
+ coeffs->k2 = k2 = (k1 * (k1 - 4.*m1PlusEtaKK)) / 2. - a*a*k0*m1PlusEtaKK*m1PlusEtaKK;
+ coeffs->k3 = k3 = -k1*k1*k1/3. + k1*k2 + k1*k1*m1PlusEtaKK - 2.*(k2 - m1PlusEtaKK)*m1PlusEtaKK - a*a*k1*m1PlusEtaKK*m1PlusEtaKK;
+ coeffs->k4 = k4 = (24.*k1*k1*k1*k1 - 96.*k1*k1*k2 + 48.*k2*k2 - 64.*k1*k1*k1*m1PlusEtaKK
+ + 48.*a*a*(k1*k1 - 2.*k2)*m1PlusEtaKK*m1PlusEtaKK +
+ 96.*k1*(k3 + 2.*k2*m1PlusEtaKK) - m1PlusEtaKK*(192.*k3 + m1PlusEtaKK*(-3008. + 123.*LAL_PI*LAL_PI)))/96.;
+
+ /*printf( "a = %.16e, k0 = %.16e, k1 = %.16e, k2 = %.16e, k3 = %.16e, k4 = %.16e, b3 = %.16e, bb3 = %.16e, KK = %.16e\n",
+ a, coeffs->k0, coeffs->k1, coeffs->k2, coeffs->k3, coeffs->k4, coeffs->b3, coeffs->bb3, coeffs->KK );
+ */
+ return 0;
+}
+
+
+REAL8 XLALSimIMRSpinEOBHamiltonian(
+ const REAL8 eta, /**<< Symmetric mass ratio */
+ REAL8Vector *x, /**<< Position vector */
+ REAL8Vector *p, /**<< Momentum vector (tortoise radial component pr*) */
+ REAL8Vector *sigmaKerr, /**<< Spin vector sigma_kerr */
+ REAL8Vector *sigmaStar, /**<< Spin vector sigma_star */
+ INT4 tortoise, /**<< flag to state whether the momentum is the tortoise co-ord */
+ SpinEOBHCoeffs *coeffs /**<< Structure containing various coefficients */
+ )
+{
+ REAL8 r, r2, nx, ny, nz;
+ REAL8 sKerr_x, sKerr_y, sKerr_z, a, a2;
+ REAL8 sStar_x, sStar_y, sStar_z;
+ REAL8 e3_x, e3_y, e3_z;
+ REAL8 costheta; /* Cosine of angle between Skerr and r */
+ REAL8 xi2, xi_x, xi_y, xi_z; /* Cross product of unit vectors in direction of Skerr and r */
+ REAL8 vx, vy, vz, pxir, pvr, pn, prT, pr, pf, ptheta2; /*prT is the tortoise pr */
+ REAL8 w2, rho2;
+ REAL8 u, u2, u3, u4;
+ REAL8 bulk, deltaT, deltaR, Lambda;
+ REAL8 D, qq, ww, B, w, MU, nu, BR, wr, nur, mur;
+ REAL8 wcos, nucos, mucos, ww_r, Lambda_r;
+ REAL8 logTerms, deltaU, deltaU_u, Q, deltaT_r, pn2, pp;
+ REAL8 deltaSigmaStar_x, deltaSigmaStar_y, deltaSigmaStar_z;
+ REAL8 sx, sy, sz, sxi, sv, sn, s3;
+ REAL8 H, Hns, Hs, Hss, Hreal, Hwcos, Hwr, HSOL, HSONL;
+ REAL8 m1PlusetaKK;
+
+ /* Terms which come into the 3.5PN mapping of the spins */
+ //REAL8 aaa, bbb, a13P5, a23P5, a33P5, b13P5, b23P5, b33P5;
+ REAL8 sMultiplier1, sMultiplier2;
+
+ /*Temporary p vector which we will make non-tortoise */
+ REAL8 tmpP[3];
+
+ REAL8 csi;
+
+ /* Spin gauge parameters. (YP) simplified, since both are zero. */
+ // static const double aa=0., bb=0.;
+
+ /* Calibrated coefficient in the 4.5PN spin mapping, Eq. 39 */
+ static const REAL8 d1 = -69.5;
+ static const REAL8 dheffSS = 2.75;
+
+ //printf( "In Hamiltonian:\n" );
+ //printf( "x = %.16e\t%.16e\t%.16e\n", x->data[0], x->data[1], x->data[2] );
+ //printf( "p = %.16e\t%.16e\t%.16e\n", p->data[0], p->data[1], p->data[2] );
+
+ r2 = x->data[0]*x->data[0] + x->data[1]*x->data[1] + x->data[2]*x->data[2];
+ r = sqrt(r2);
+ nx = x->data[0] / r;
+ ny = x->data[1] / r;
+ nz = x->data[2] / r;
+
+ sKerr_x = sigmaKerr->data[0];
+ sKerr_y = sigmaKerr->data[1];
+ sKerr_z = sigmaKerr->data[2];
+
+ sStar_x = sigmaStar->data[0];
+ sStar_y = sigmaStar->data[1];
+ sStar_z = sigmaStar->data[2];
+
+ a2 = sKerr_x*sKerr_x + sKerr_y*sKerr_y + sKerr_z*sKerr_z;
+ a = sqrt( a2 );
+
+ // e3 correspondes to the \hat{S}_{Kerr} in (45) of BB2, i.e., PRD 84, 104027 (2011)
+ if(a != 0.)
+ {
+ e3_x = sKerr_x / a;
+ e3_y = sKerr_y / a;
+ e3_z = sKerr_z / a;
+ }
+ else
+ {
+ e3_x = 0.;
+ e3_y = 0.;
+ e3_z = 1.;
+ }
+
+ // simple spherical coordinate (r,theta,phi) view to (x,y,z)
+ costheta = e3_x*nx + e3_y*ny + e3_z*nz;
+
+ //correspondes to sin^2\theta
+ xi2=1. - costheta*costheta;
+
+ // xi correspondes to the \xi in (45) of BB2, i.e., PRD 84, 104027 (2011)
+ xi_x = -e3_z*ny + e3_y*nz;
+ xi_y = e3_z*nx - e3_x*nz;
+ xi_z = -e3_y*nx + e3_x*ny;
+
+ // v correspondes to the v in (45) of BB2, i.e., PRD 84, 104027 (2011)
+ vx = -nz*xi_y + ny*xi_z;
+ vy = nz*xi_x - nx*xi_z;
+ vz = -ny*xi_x + nx*xi_y;
+
+ w2 = r2 + a2;
+ // (36) of BB2, i.e., PRD 84, 104027 (2011)
+ rho2 = r2 + a2*costheta*costheta;
+
+ u = 1./r;
+ u2 = u*u;
+ u3 = u2*u;
+ u4 = u2*u2;
+
+ //printf( "KK = %.16e\n", coeffs->KK );
+ //coeffs->KK correspondes to the K in (5.75) of BB1, i.e. PRD 81, 084024 (2010)
+ m1PlusetaKK = -1. + eta * coeffs->KK;
+ /* Eq. 5.75 of BB1, i.e. PRD 81, 084024 (2010) with assumed M=1, correspondes to the \bar{Delta}_u */
+ bulk = 1./(m1PlusetaKK*m1PlusetaKK) + (2.*u)/m1PlusetaKK + a2*u2;
+ /* Eq. 5.73 of BB1, i.e. PRD 81, 084024 (2010) */
+ //coeffs->k0...k4 corresponde to Delta0...4 of 5.73 of BB1, i.e. PRD 81, 084024 (2010)
+ logTerms = 1. + eta*coeffs->k0 + eta*log(1. + coeffs->k1*u + coeffs->k2*u2 + coeffs->k3*u3 + coeffs->k4*u4);
+ //printf( "bulk = %.16e, logTerms = %.16e\n", bulk, logTerms );
+ /* Eq. 5.73 of BB1, i.e. PRD 81, 084024 (2010), correspondes to the Delta_u */
+ deltaU = bulk*logTerms;
+ /* Eq. 5.71 of BB1, i.e. PRD 81, 084024 (2010) */
+ deltaT = r2*deltaU;
+ /* ddeltaU/du */
+ deltaU_u = 2.*(1./m1PlusetaKK + a2*u)*logTerms +
+ bulk * (eta*(coeffs->k1 + u*(2.*coeffs->k2 + u*(3.*coeffs->k3 + 4.*coeffs->k4*u))))
+ / (1. + coeffs->k1*u + coeffs->k2*u2 + coeffs->k3*u3 + coeffs->k4*u4);
+ /* ddeltaT/dr */
+ deltaT_r = 2.*r*deltaU - deltaU_u;
+ /* Eq. 5.39 of BB1, i.e. PRD 81, 084024 (2010), (35) of BB2, i.e., PRD 84, 104027 (2011) */
+ Lambda = w2*w2 - a2*deltaT*xi2;
+ /* Eq. 5.83 of BB1, i.e. PRD 81, 084024 (2010), inverse */
+ D = 1. + log(1. + 6.*eta*u2 + 2.*(26. - 3.*eta)*eta*u3);
+ /* Eq. 5.38 of BB1, i.e. PRD 81, 084024 (2010) */
+ deltaR = deltaT*D;
+ /* See Hns below, Eq. 4.34 of Damour et al. PRD 62, 084011 (2000) */
+ qq = 2.*eta*(4. - 3.*eta);
+ /* See Hns below. In Sec. II D of BB2, i.e., PRD 84, 104027 (2011),
+ * b3 and bb3 coeffs are chosen to be zero. */
+ //Eq.(5.40) of BB1, i.e. PRD 81, 084024 (2010) which is different to
+ //Eq.(37) of BB2, i.e., PRD 84, 104027 (2011)
+ ww=2.*a*r + coeffs->b3*eta*a2*a*u + coeffs->bb3*eta*a*u;
+
+ /* We need to transform the momentum to get the tortoise co-ord */
+ if ( tortoise )
+ {
+ /* Eq. 28 of Pan et al. PRD 81, 084041 (2010) */
+ // correspondes to the xi_a there
+ csi = sqrt( deltaT * deltaR )/ w2;
+ }
+ else
+ {
+ csi = 1.0;
+ }
+ //printf( "csi(miami) = %.16e\n", csi );
+
+ prT = p->data[0]*nx + p->data[1]*ny + p->data[2]*nz;
+ /* p->data is BL momentum vector; tmpP is tortoise momentum vector */
+ // Eq.(A3) of PRD 81, 084041 (2010),
+ // but it seems csi here correspondes to 1/xi_a there
+ tmpP[0] = p->data[0] - nx * prT * (csi - 1.)/csi;
+ tmpP[1] = p->data[1] - ny * prT * (csi - 1.)/csi;
+ tmpP[2] = p->data[2] - nz * prT * (csi - 1.)/csi;
+
+ pxir = (tmpP[0]*xi_x + tmpP[1]*xi_y + tmpP[2]*xi_z) * r;
+ pvr = (tmpP[0]*vx + tmpP[1]*vy + tmpP[2]*vz) * r;
+ pn = tmpP[0]*nx + tmpP[1]*ny + tmpP[2]*nz;
+
+ pr = pn;
+ pf = pxir;
+ ptheta2 = pvr * pvr / xi2;
+
+ //printf( "pr = %.16e, prT = %.16e\n", pr, prT );
+
+ //printf( " a = %.16e, r = %.16e\n", a, r );
+ //printf( "D = %.16e, ww = %.16e, rho = %.16e, Lambda = %.16e, xi = %.16e\npr = %.16e, pf = %.16e, deltaR = %.16e, deltaT = %.16e\n",
+ //D, ww, sqrt(rho2), Lambda, sqrt(xi2), pr, pf, deltaR, deltaT );
+ /* Eqs. 5.36 - 5.46 of BB1, i.e. PRD 81, 084024 (2010) */
+ /* Note that the tortoise prT appears only in the quartic term, explained in
+ * Eqs. 14 and 15 of Tarrachini et al. PRD 86, 024011 (2012) */
+ //according to the (5.45) of BB1, i.e. PRD 81, 084024 (2010)
+ //beta^\phi = ww/Lambda
+ //Q4 = prT^4/r^2*z3, z3 is in (4.34) of Damour et al. PRD 62, 084011 (2000)
+ Hns = sqrt(1. + prT*prT*prT*prT*qq*u2 + ptheta2/rho2 + pf*pf*rho2/(Lambda*xi2) + pr*pr*deltaR/rho2)
+ / sqrt(Lambda/(rho2*deltaT)) + pf*ww/Lambda;
+
+ //printf( "term 1 in Hns: %.16e\n", prT*prT*prT*prT*qq*u2 );
+ //printf( "term 2 in Hns: %.16e\n", ptheta2/rho2 );
+ //printf( "term 3 in Hns = %.16e\n", pf*pf*rho2/(Lambda*xi2) );
+ //printf( "term 4 in Hns = %.16e\n", pr*pr*deltaR/rho2 );
+ //printf( "term 5 in Hns = %.16e\n", Lambda/(rho2*deltaT) );
+ //printf( "term 6 in Hns = %.16e\n", pf*ww/Lambda );
+ /* Eqs. 5.30 - 5.33 of BB1, i.e. PRD 81, 084024 (2010) */
+ B = sqrt(deltaT);
+ w = ww/Lambda;
+ nu = 0.5 * log(deltaT*rho2/Lambda);
+ MU = 0.5 * log(rho2);
+ /* dLambda/dr */
+ Lambda_r = 4.*r*w2 - a2*deltaT_r*xi2;
+
+ //dww/dr, ww is the \tilde{\omega}_{fd} of Eq.(5.40) of BB1, i.e. PRD 81, 084024 (2010)
+ ww_r=2.*a - (a2*a*coeffs->b3*eta)*u2 - coeffs->bb3*eta*a*u2;
+ /* Eqs. 5.47a - 5.47d of BB1, i.e. PRD 81, 084024 (2010) */
+ BR = (-2.*deltaT + sqrt(deltaR)*deltaT_r)/(2.*sqrt(deltaR*deltaT));
+ wr = (-Lambda_r*ww + Lambda*ww_r)/(Lambda*Lambda);
+ nur = (r/rho2 + (w2 * (-4.*r*deltaT + w2*deltaT_r) ) / (2.*deltaT*Lambda) );
+ mur = (r/rho2 - 1./sqrt(deltaR));
+ /* Eqs. 5.47f - 5.47h of BB1, i.e. PRD 81, 084024 (2010) */
+ wcos = -2.*a2*costheta*deltaT*ww/(Lambda*Lambda);
+ nucos = a2*costheta*w2*(w2-deltaT)/(rho2*Lambda);
+ mucos = a2*costheta/rho2;
+ /* Eq. 5.52 of BB1, i.e. PRD 81, 084024 (2010), (YP) simplified */
+ //Q = 1. + pvr*pvr/(exp(2.*MU)*xi2) + exp(2.*nu)*pxir*pxir/(B*B*xi2) + pn*pn*deltaR/exp(2.*MU);
+ Q = 1. + pvr*pvr/(rho2*xi2) + deltaT*rho2/Lambda*pxir*pxir/(B*B*xi2) + pn*pn*deltaR/rho2;
+
+ pn2 = pr * pr * deltaR / rho2;
+ pp = Q - 1.;
+
+ //printf( "pn2 = %.16e, pp = %.16e\n", pn2, pp );
+ //printf( "sigmaKerr = %.16e, sigmaStar = %.16e\n", sKerr_z, sStar_z );
+ /* expanded Eq. 5.68 of BB1, i.e. PRD 81, 084024 (2010), (YP) simplified for aa=bb=0. */
+ /*
+ deltaSigmaStar_x=(- 8.*aa*(1. + 3.*pn2*r - pp*r)*sKerr_x - 8.*bb*(1. + 3.*pn2*r - pp*r)*sStar_x +
+ eta*(-8.*sKerr_x - 36.*pn2*r*sKerr_x + 3.*pp*r*sKerr_x + 14.*sStar_x - 30.*pn2*r*sStar_x + 4.*pp*r*sStar_x))/(12.*r);
+
+ deltaSigmaStar_y=(-8.*aa*(1. + 3.*pn2*r - pp*r)*sKerr_y - 8.*bb*(1. + 3.*pn2*r - pp*r)*sStar_y +
+ eta*(-8.*sKerr_y - 36.*pn2*r*sKerr_y + 3.*pp*r*sKerr_y + 14.*sStar_y - 30.*pn2*r*sStar_y + 4.*pp*r*sStar_y))/(12.*r);
+
+ deltaSigmaStar_z=(-8.*aa*(1. + 3.*pn2*r - pp*r)*sKerr_z - 8.*bb*(1. + 3.*pn2*r - pp*r)*sStar_z +
+ eta*(-8.*sKerr_z - 36.*pn2*r*sKerr_z + 3.*pp*r*sKerr_z + 14.*sStar_z - 30.*pn2*r*sStar_z + 4.*pp*r*sStar_z))/(12.*r);
+ */
+ deltaSigmaStar_x=eta*(-8.*sKerr_x - 36.*pn2*r*sKerr_x + 3.*pp*r*sKerr_x + 14.*sStar_x - 30.*pn2*r*sStar_x + 4.*pp*r*sStar_x)/(12.*r);
+
+ deltaSigmaStar_y=eta*(-8.*sKerr_y - 36.*pn2*r*sKerr_y + 3.*pp*r*sKerr_y + 14.*sStar_y - 30.*pn2*r*sStar_y + 4.*pp*r*sStar_y)/(12.*r);
+
+ deltaSigmaStar_z=eta*(-8.*sKerr_z - 36.*pn2*r*sKerr_z + 3.*pp*r*sKerr_z + 14.*sStar_z - 30.*pn2*r*sStar_z + 4.*pp*r*sStar_z)/(12.*r);
+
+
+ /* Now compute the additional 3.5PN terms. */
+ /* The following gauge parameters correspond to those given by
+ * Eqs. (69) and (70) of BB2, i.e., PRD 84, 104027 (2011) (aaa -> a0, bbb -> b0).
+ * In SEOBNRv1 model, we chose to set all of them to zero,
+ * described between Eqs. (3) and (4).
+ */
+ /*
+ aaa = -3./2.*eta;
+ bbb = -5./4.*eta;
+ a1 = eta*eta/2.;
+ a2 = -(1./8.)*eta*(-7. + 8.*eta);
+ a3 = -((9.*eta*eta)/16.);
+ b1 = 1./16.*eta*(9. + 5.*eta);
+ b2 = -(1./8.)*eta*(-17. + 5.*eta);
+ b3 = -3./8.*eta*eta;
+ */
+ /*aaa = 0.;
+ bbb = 0.;
+ a13P5 = 0.;
+ a23P5 = 0.;
+ a33P5 = 0.;
+ b13P5 = 0.;
+ b23P5 = 0.;
+ b33P5 = 0.;
+ */
+ /* Eq. 52 of BB2, i.e., PRD 84, 104027 (2011), (YP) simplified for zero gauge parameters */
+ /*
+ sMultiplier1 =-(2.*(24.*b23P5 + eta*(-353. + 27.*eta) + bbb*(56. + 60.*eta)) +
+ 2.*(24.*b13P5 - 24.*b23P5 + bbb*(14. - 66.*eta) + 103.*eta - 60.*eta*eta)*pp*
+ r + 120.*(2.*b33P5 - 3.*eta*(bbb + eta))*pn2*pn2*r*r +
+ (-48.*b13P5 + 4.*bbb*(1. + 3.*eta) + eta*(23. + 3.*eta))*pp*pp*
+ r*r + 6.*pn2*r*(16.*b13P5 + 32.*b23P5 + 24.*b33P5 - 47.*eta +
+ 54.*eta*eta + 24.*bbb*(1. + eta) +
+ (24.*b13P5 - 24.*b33P5 - 16.*eta + 21.*eta*eta + bbb*(-2. + 30.*eta))*pp*
+ r))/(72.*r*r);
+ */
+ sMultiplier1 = -(2.*eta*(-353. + 27.*eta) + 2.*(103.*eta - 60.*eta*eta)*pp*r
+ + 120.*(-3.*eta*eta)*pn2*pn2*r*r + (eta*(23. + 3.*eta))*pp*pp*r*r
+ + 6.*pn2*r*(- 47.*eta + 54.*eta*eta + (- 16.*eta + 21.*eta*eta)*pp*r))
+ / (72.*r*r);
+ /* Eq. 52 of BB2, i.e., PRD 84, 104027 (2011), (YP) simplified for zero gauge parameters */
+ /*
+ sMultiplier2 = (-16.*(6.*a23P5 + 7.*eta*(8. + 3.*eta) + aaa*(14. + 15.*eta)) +
+ 4.*(-24.*a13P5 + 24.*a23P5 - 109.*eta + 51.*eta*eta + 2.*aaa*(-7. + 33.*eta))*
+ pp*r + 30.*(-16.*a33P5 + 3.*eta*(8.*aaa + 9.*eta))*pn2*pn2*r*r +
+ (96.*a13P5 - 45.*eta - 8.*aaa*(1. + 3.*eta))*pp*pp*r*r -
+ 6.*pn2*r*(32.*a13P5 + 64.*a23P5 + 48.*a33P5 + 16.*eta + 147.*eta*eta +
+ 48.*aaa*(1. + eta) + (48.*a13P5 - 48.*a33P5 - 6.*eta + 39.*eta*eta +
+ aaa*(-4. + 60.*eta))*pp*r))/(144.*r*r);
+ */
+ sMultiplier2 = (-16.*(7.*eta*(8. + 3.*eta)) + 4.*(- 109.*eta + 51.*eta*eta)*pp*r
+ + 810.*eta*eta*pn2*pn2*r*r - 45.*eta*pp*pp*r*r
+ - 6.*pn2*r*(16.*eta + 147.*eta*eta + (- 6.*eta + 39.*eta*eta)*pp*r))
+ / (144.*r*r);
+ /* Eq. 52 of BB2, i.e., PRD 84, 104027 (2011) */
+ deltaSigmaStar_x += sMultiplier1*sigmaStar->data[0] + sMultiplier2*sigmaKerr->data[0];
+ deltaSigmaStar_y += sMultiplier1*sigmaStar->data[1] + sMultiplier2*sigmaKerr->data[1];
+ deltaSigmaStar_z += sMultiplier1*sigmaStar->data[2] + sMultiplier2*sigmaKerr->data[2];
+
+ /* And now the (calibrated) 4.5PN term */
+ deltaSigmaStar_x += d1 * eta * sigmaStar->data[0] / (r*r*r);
+ deltaSigmaStar_y += d1 * eta * sigmaStar->data[1] / (r*r*r);
+ deltaSigmaStar_z += d1 * eta * sigmaStar->data[2] / (r*r*r);
+
+ //printf( "deltaSigmaStar_x = %.16e, deltaSigmaStar_y = %.16e, deltaSigmaStar_z = %.16e\n",
+ // deltaSigmaStar_x, deltaSigmaStar_y, deltaSigmaStar_z );
+
+ sx = sStar_x + deltaSigmaStar_x;
+ sy = sStar_y + deltaSigmaStar_y;
+ sz = sStar_z + deltaSigmaStar_z;
+
+
+ sxi = sx*xi_x + sy*xi_y + sz*xi_z;
+ sv = sx*vx + sy*vy + sz*vz;
+ sn = sx*nx + sy*ny + sz*nz;
+
+ s3 = sx*e3_x + sy*e3_y + sz*e3_z;
+ /* Eq. 3.45 of BB1, i.e. PRD 81, 084024 (2010), second term */
+ Hwr = (exp(-3.*MU - nu)*sqrt(deltaR)*(exp(2.*(MU + nu))*pxir*pxir*sv - B*exp(MU + nu)*pvr*pxir*sxi +
+ B*B*xi2*(exp(2.*MU)*(sqrt(Q) + Q)*sv + pn*pvr*sn*sqrt(deltaR) - pn*pn*sv*deltaR)))/(2.*B*(1. + sqrt(Q))*sqrt(Q)*xi2);
+ /* Eq. 3.45 of BB1, i.e. PRD 81, 084024 (2010), third term */
+ Hwcos = (exp(-3.*MU - nu)*(sn*(-(exp(2.*(MU + nu))*pxir*pxir) + B*B*(pvr*pvr - exp(2.*MU)*(sqrt(Q) + Q)*xi2)) -
+ B*pn*(B*pvr*sv - exp(MU + nu)*pxir*sxi)*sqrt(deltaR)))/(2.*B*(1. + sqrt(Q))*sqrt(Q));
+ /* Eq. 3.44 of BB1, i.e. PRD 81, 084024 (2010), leading term */
+ HSOL = (exp(-MU + 2.*nu)*(-B + exp(MU + nu))*pxir*s3)/(B*B*sqrt(Q)*xi2);
+ /* Eq. 3.44 of BB1, i.e. PRD 81, 084024 (2010), next-to-leading term */
+ HSONL = (exp(-2.*MU + nu)*(-(B*exp(MU + nu)*nucos*pxir*(1. + 2.*sqrt(Q))*sn*xi2) +
+ (-(BR*exp(MU + nu)*pxir*(1. + sqrt(Q))*sv) + B*(exp(MU + nu)*nur*pxir*(1. + 2.*sqrt(Q))*sv + B*mur*pvr*sxi +
+ B*sxi*(-(mucos*pn*xi2) + sqrt(Q)*(mur*pvr - nur*pvr + (-mucos + nucos)*pn*xi2))))*sqrt(deltaR)))/(B*B*(sqrt(Q) + Q)*xi2);
+ /* Eq. 3.43 and 3.45 of BB1, i.e. PRD 81, 084024 (2010) */
+ Hs = w*s3 + Hwr*wr + Hwcos*wcos + HSOL + HSONL;
+ /* Eq. 5.70 of BB1, i.e. PRD 81, 084024 (2010), last term */
+ Hss = -0.5*u3 * (sx*sx + sy*sy + sz*sz - 3.*sn*sn);
+ /* Eq. 5.70 of BB1, i.e. PRD 81, 084024 (2010) */
+ H = Hns + Hs + Hss;
+
+ /* Add the additional calibrated term */
+ H += dheffSS * eta * (sKerr_x*sStar_x + sKerr_y*sStar_y + sKerr_z*sStar_z) / (r*r*r*r);
+
+ //printf( "Hns = %.16e, Hs = %.16e, Hss = %.16e, other = %.16e\n", Hns, Hs, Hss, dheffSS * eta * (sKerr_x*sStar_x + sKerr_y*sStar_y + sKerr_z*sStar_z) / (r*r*r*r) );
+ //printf( "H = %.16e\n", H );
+ /* Real Hamiltonian given by Eq. 2, ignoring the constant -1. */
+ /* Eq. 5.69 of BB1, i.e. PRD 81, 084024 (2010) */
+ Hreal = sqrt(1. + 2.*eta *(H - 1.));
+
+ return Hreal;
+}
+
+ int CartesianToSpherical(
+ REAL8 qSph[], /**<< OUTPUT, position vector in spherical coordinates */
+ REAL8 pSph[], /**<< OUTPUT, momentum vector in Cartesean coordinates */
+ const REAL8 qCart[], /**<< position vector in spherical coordinates */
+ const REAL8 pCart[] /**<< momentum vector in Cartesean coordinates */
+ )
+{
+
+ REAL8 r;
+ REAL8 pr, pTheta, pPhi;
+
+ REAL8 x; //, y, z;
+ REAL8 pX, pY, pZ;
+
+ x = qCart[0];
+ //y = qCart[1];
+ //z = qCart[2];
+ pX = pCart[0];
+ pY = pCart[1];
+ pZ = pCart[2];
+
+ r = x;
+ pr = pX;
+ pTheta = - r * pZ;
+ pPhi = r * pY;
+
+ /* Fill the output vectors */
+ qSph[0] = r;
+ qSph[1] = LAL_PI_2; //pi/2
+ qSph[2] = 0.0;
+ pSph[0] = pr;
+ pSph[1] = pTheta;
+ pSph[2] = pPhi;
+
+ return 0;
+}
+
+/** Tests if a value is an XLAL <tt>REAL8</tt> failure NaN. */
+ int XLALIsREAL8FailNaN(REAL8 val)
+{
+ volatile const union { LAL_INT8_C i; unsigned char s[8]; } a = { 417 }; //XLAL_REAL8_FAIL_NAN_INT } ;
+ //volatile const union { int i; unsigned char s[8]; } a = { XLAL_REAL8_FAIL_NAN_INT } ;
+ volatile union { REAL8 x; unsigned char s[8]; } b;
+ int n;
+ b.x = val;
+ for (n = 0; n < sizeof(val); ++n)
+ if (a.s[n] != b.s[n])
+ return 0;
+ return 1;
+}
+
+ REAL8 XLALCalculateSphHamiltonianDeriv2(
+ const int idx1, /**<< Derivative w.r.t. index 1 */
+ const int idx2, /**<< Derivative w.r.t. index 2 */
+ const REAL8 values[], /**<< Dynamical variables in spherical coordinates */
+ SpinEOBParams *params /**<< Spin EOB Parameters */
+ )
+{
+
+ static const REAL8 STEP_SIZE = 1.0e-5;
+
+ REAL8 result;
+ REAL8 absErr;
+
+ HcapSphDeriv2Params dParams;
+
+ gsl_function F;
+ int gslStatus;
+
+ dParams.sphValues = values;
+ dParams.varyParam1 = idx1;
+ dParams.varyParam2 = idx2;
+ dParams.params = params;
+
+ /*printf( " In second deriv function: values\n" );
+ for ( int i = 0; i < 12; i++ )
+ {
+ printf( "%.16e ", values[i] );
+ }
+ printf( "\n" );
+*/
+ F.function = GSLSpinHamiltonianDerivWrapper;
+ F.params = &dParams;
+
+ /* GSL seemed to give weird answers - try my own code */
+ /*result = GSLSpinHamiltonianDerivWrapper( values[idx1] + STEP_SIZE, &dParams )
+ - GSLSpinHamiltonianDerivWrapper( values[idx1] - STEP_SIZE, &dParams );
+ printf( "%.16e - %.16e / 2h\n", GSLSpinHamiltonianDerivWrapper( values[idx1] + STEP_SIZE, &dParams ), GSLSpinHamiltonianDerivWrapper( values[idx1] - STEP_SIZE, &dParams ) );
+
+ result = result / ( 2.*STEP_SIZE );
+*/
+
+ gslStatus = gsl_deriv_central( &F, values[idx1],
+ STEP_SIZE, &result, &absErr );
+
+ if ( gslStatus != GSL_SUCCESS )
+ {
+ fprintf(stderr, "XLAL Error %d - Failure in GSL function\n", gslStatus );
+ return -1;
+ }
+
+ //printf( "Second deriv abs err = %.16e\n", absErr );
+
+ //printf( "RESULT = %.16e\n", result );
+ return result;
+}
+
+ double GSLSpinHamiltonianDerivWrapper( double x, /**<< Derivative at x */
+ void *params /**<< Function parameters */)
+{
+
+ HcapSphDeriv2Params *dParams = (HcapSphDeriv2Params *) params;
+
+ REAL8 sphValues[12];
+ REAL8 cartValues[12];
+
+ REAL8 dHdr, dHdx, dHdpy, dHdpz;
+ REAL8 r, ptheta, pphi;
+
+ memcpy( sphValues, dParams->sphValues, sizeof( sphValues ) );
+ sphValues[dParams->varyParam1] = x;
+
+ SphericalToCartesian( cartValues, cartValues+3, sphValues, sphValues+3 );
+ memcpy( cartValues+6, sphValues+6, 6*sizeof(REAL8) );
+
+ r = sphValues[0];
+ ptheta = sphValues[4];
+ pphi = sphValues[5];
+
+ /* Return the appropriate derivative according to varyParam2 */
+ switch ( dParams->varyParam2 )
+ {
+ case 0:
+ /* dHdr */
+ dHdx = XLALSpinHcapNumDerivWRTParam( 0, cartValues, dParams->params );
+ dHdpy = XLALSpinHcapNumDerivWRTParam( 4, cartValues, dParams->params );
+ dHdpz = XLALSpinHcapNumDerivWRTParam( 5, cartValues, dParams->params );
+
+ dHdr = dHdx - dHdpy * pphi / (r*r) + dHdpz * ptheta / (r*r);
+ //printf( "dHdr = %.16e\n", dHdr );
+ return dHdr;
+
+ break;
+ case 4:
+ /* dHdptheta */
+ dHdpz = XLALSpinHcapNumDerivWRTParam( 5, cartValues, dParams->params );
+ return - dHdpz / r;
+ break;
+ case 5:
+ /* dHdpphi */
+ dHdpy = XLALSpinHcapNumDerivWRTParam( 4, cartValues, dParams->params );
+ return dHdpy / r;
+ break;
+ default:
+ fprintf( stderr,"This option is not supported in the second derivative function!\n" );
+ return -1;
+ break;
+ }
+}
+
+ int SphericalToCartesian(
+ REAL8 qCart[], /**<< OUTPUT, position vector in Cartesean coordinates */
+ REAL8 pCart[], /**<< OUTPUT, momentum vector in Cartesean coordinates */
+ const REAL8 qSph[], /**<< position vector in spherical coordinates */
+ const REAL8 pSph[] /**<< momentum vector in spherical coordinates */
+ )
+{
+
+ REAL8 r;
+ REAL8 pr, pTheta, pPhi;
+
+ REAL8 x, y, z;
+ REAL8 pX, pY, pZ;
+
+ r = qSph[0];
+ pr = pSph[0];
+ pTheta = pSph[1];
+ pPhi = pSph[2];
+
+ x = r;
+ y = 0.0;
+ z = 0.0;
+
+ pX = pr;
+ pY = pPhi / r;
+ pZ = - pTheta / r;
+
+ /* Copy these values to the output vectors */
+ qCart[0] = x;
+ qCart[1] = y;
+ qCart[2] = z;
+ pCart[0] = pX;
+ pCart[1] = pY;
+ pCart[2] = pZ;
+
+ return 0;
+}
+
+ REAL8 XLALInspiralSpinFactorizedFlux(
+ REAL8Vector *values, /**< dynamical variables */
+ const REAL8 omega, /**< orbital frequency */
+ SpinEOBParams *ak, /**< physical parameters */
+ const REAL8 H, /**< real Hamiltonian */
+ const int lMax /**< upper limit of the summation over l */
+ )
+
+{
+
+ REAL8 flux = 0.0;
+ REAL8 v;
+ REAL8 omegaSq;
+ COMPLEX16 hLM;
+ int l, m;
+
+ EOBNonQCCoeffs nqcCoeffs;
+
+
+ if ( lMax < 2 )
+ {
+ return -1;
+ }
+
+ /* Omegs is the derivative of phi */
+ omegaSq = omega*omega;
+
+ v = MYcbrt( omega );
+// printf( "v = %.16e\n", v );
+ for ( l = 2; l <= lMax; l++ )
+ {
+ for ( m = 1; m <= l; m++ )
+ {
+
+ if ( XLALSimIMRSpinEOBGetSpinFactorizedWaveform( &hLM, values, v, H, l, m, ak )
+ == -1 )
+ {
+ fprintf(stderr,"Error!(%d)", XLAL_EFUNC );
+ }
+ /* For the 2,2 mode, we apply NQC correction to the flux */
+ if ( l == 2 && m == 2 )
+ {
+ COMPLEX16 hNQC;
+ XLALSimIMRGetEOBCalibratedSpinNQC( &nqcCoeffs, l, m, ak->eobParams->eta, ak->a );
+ XLALSimIMREOBNonQCCorrection( &hNQC, values, omega, &nqcCoeffs );
+ /* Eq. 16 */
+ hLM *= hNQC;
+ }
+ // printf( "l = %d, m = %d, mag(hLM) = %.17e\n", l, m, XLALCOMPLEX16Abs2( hLM ) );
+ /* Eq. 13, Eq.(12) of PRD 84, 124052 (2011)*/
+ flux += (REAL8)(m * m) * omegaSq * ( creal(hLM)*creal(hLM) + cimag(hLM)*cimag(hLM));
+ }
+ }
+ return flux * LAL_1_PI / 8.0;
+}
+
+// The resummed factorized waveform was proposed by first time in
+// Eq.(1) of PRD 79, 064004 (2009)
+ int XLALSimIMRSpinEOBGetSpinFactorizedWaveform(
+ COMPLEX16 * hlm, /**< OUTPUT, hlm waveforms */
+ REAL8Vector * values, /**< dyanmical variables */
+ const REAL8 v, /**< velocity */
+ const REAL8 Hreal, /**< real Hamiltonian */
+ const int l, /**< l mode index */
+ const int m, /**< m mode index */
+ SpinEOBParams * params /**< Spin EOB parameters */
+ )
+{
+ /* Status of function calls */
+ int status;
+ int i;
+
+ REAL8 eta;
+ REAL8 r, pp, Omega, v2, vh, vh3, k, hathatk, eulerlogxabs; //pr
+ REAL8 Slm, deltalm, rholm, rholmPwrl;
+ REAL8 auxflm = 0.0;
+ COMPLEX16 Tlm;
+ COMPLEX16 hNewton;
+ gsl_sf_result lnr1, arg1, z2;
+
+ /* Non-Keplerian velocity */
+ REAL8 vPhi, vPhi2;
+
+ /* Pre-computed coefficients */
+ FacWaveformCoeffs *hCoeffs = params->eobParams->hCoeffs;
+ COMPLEX16 ci = I;
+
+ if ( abs(m) > (int) l )
+ {
+ return -1;
+ }
+ if ( m == 0 )
+ {
+ return -1;
+ }
+
+ eta = params->eobParams->eta;
+
+ /* Check our eta was sensible */
+ if ( eta > 0.25 )
+ {
+ fprintf(stderr,"XLAL Error: Eta seems to be > 0.25 - this isn't allowed!\n" );
+ return -1;
+ }
+ /*else if ( eta == 0.25 && m % 2 )
+ {
+ // If m is odd and dM = 0, hLM will be zero
+ memset( hlm, 0, sizeof( COMPLEX16 ) );
+ return XLAL_SUCCESS;
+ }*/
+
+ r = values->data[0];
+ //pr = values->data[2];
+ pp = values->data[3];
+
+ v2 = v * v;
+ Omega = v2 * v;
+ vh3 = Hreal * Omega;
+ vh = MYcbrt(vh3);
+ eulerlogxabs = LAL_GAMMA + log( 2.0 * (REAL8)m * v );
+
+ /* Calculate the non-Keplerian velocity */
+ if ( params->alignedSpins )
+ {
+ vPhi = XLALSimIMRSpinAlignedEOBNonKeplerCoeff( values->data, params );
+
+ if ( XLAL_IS_REAL8_FAIL_NAN( vPhi ) )
+ {
+ return -1;
+ }
+
+ vPhi = r * MYcbrt(vPhi);
+ vPhi *= Omega;
+ vPhi2 = vPhi*vPhi;
+ }
+ else
+ {
+ vPhi = v;
+ vPhi2 = v2;
+ }
+
+ /* Calculate the newtonian multipole, 1st term in Eq. 17, given by Eq. A1 */
+ status = XLALSimIMRSpinEOBCalculateNewtonianMultipole( &hNewton, vPhi2, r,
+ values->data[1], (UINT4)l, m, params->eobParams );
+ if ( status == -1 )
+ {
+ return -1;
+ }
+
+ /* Calculate the source term, 2nd term in Eq. 17, given by Eq. A5 */
+ // Eq.(20) of PRD 84, 124052
+ if ( ( (l+m)%2 ) == 0)
+ {
+ Slm = (Hreal*Hreal - 1.)/(2.*eta) + 1.;
+ }
+ else
+ {
+ Slm = v * pp;
+ }
+ //printf( "Hreal = %e, Slm = %e, eta = %e\n", Hreal, Slm, eta );
+
+ /* Calculate the Tail term, 3rd term in Eq. 17, given by Eq. A6 */
+ k = m * Omega;
+ hathatk = Hreal * k;
+ status = gsl_sf_lngamma_complex_e( l+1.0, -2.0*hathatk, &lnr1, &arg1 );
+ if (status != GSL_SUCCESS)
+ {
+ fprintf(stderr,"XLAL Error -: Error in GSL function\n" );
+ return -1;
+ }
+ status = gsl_sf_fact_e( l, &z2 );
+ if ( status != GSL_SUCCESS)
+ {
+ fprintf(stderr,"XLAL Error - : Error in GSL function\n" );
+ return -1;
+ }
+
+
+ Tlm = cexp( ( lnr1.val + LAL_PI * hathatk ) + ci * (
+ arg1.val + 2.0 * hathatk * log(4.0*k/sqrt(LAL_E)) ) );
+ Tlm /= z2.val;
+
+
+ /* Calculate the residue phase and amplitude terms */
+ /* deltalm is the 4th term in Eq. 17, delta 22 given by Eq. A15, others */
+ /* rholm is the 5th term in Eq. 17, given by Eqs. A8 - A14 */
+ /* auxflm is a special part of the 5th term in Eq. 17, given by Eq. A15 */
+ /* Actual values of the coefficients are defined in the next function of this file */
+ switch( l )
+ {
+ case 2:
+ switch( abs(m) )
+ {
+ case 2:
+ deltalm = vh3*(hCoeffs->delta22vh3 + vh3*(hCoeffs->delta22vh6
+ + vh*vh*(hCoeffs->delta22vh9*vh)))
+ + hCoeffs->delta22v5 *v*v2*v2 + hCoeffs->delta22v8 *v2*v2*v2*v2;
+ rholm = 1. + v2*(hCoeffs->rho22v2 + v*(hCoeffs->rho22v3
+ + v*(hCoeffs->rho22v4
+ + v*(hCoeffs->rho22v5 + v*(hCoeffs->rho22v6
+ + hCoeffs->rho22v6l*eulerlogxabs + v*(hCoeffs->rho22v7
+ + v*(hCoeffs->rho22v8 + hCoeffs->rho22v8l*eulerlogxabs
+ + (hCoeffs->rho22v10 + hCoeffs->rho22v10l * eulerlogxabs)*v2)))))));
+ break;
+ case 1:
+ {
+ deltalm = vh3*(hCoeffs->delta21vh3 + vh3*(hCoeffs->delta21vh6
+ + vh*(hCoeffs->delta21vh7 + (hCoeffs->delta21vh9)*vh*vh)))
+ + hCoeffs->delta21v5*v*v2*v2 + hCoeffs->delta21v7*v2*v2*v2*v;
+ rholm = 1. + v*(hCoeffs->rho21v1
+ + v*( hCoeffs->rho21v2 + v*(hCoeffs->rho21v3 + v*(hCoeffs->rho21v4
+ + v*(hCoeffs->rho21v5 + v*(hCoeffs->rho21v6 + hCoeffs->rho21v6l*eulerlogxabs
+ + v*(hCoeffs->rho21v7 + hCoeffs->rho21v7l * eulerlogxabs
+ + v*(hCoeffs->rho21v8 + hCoeffs->rho21v8l * eulerlogxabs
+ + (hCoeffs->rho21v10 + hCoeffs->rho21v10l * eulerlogxabs)*v2))))))));
+ auxflm = v*hCoeffs->f21v1;
+ }
+ break;
+ default:
+ break;
+ }
+ break;
+ case 3:
+ switch (m)
+ {
+ case 3:
+ deltalm = vh3*(hCoeffs->delta33vh3 + vh3*(hCoeffs->delta33vh6 + hCoeffs->delta33vh9*vh3))
+ + hCoeffs->delta33v5*v*v2*v2 + hCoeffs->delta33v7*v2*v2*v2*v;
+ rholm = 1. + v2*(hCoeffs->rho33v2 + v*(hCoeffs->rho33v3 + v*(hCoeffs->rho33v4
+ + v*(hCoeffs->rho33v5 + v*(hCoeffs->rho33v6 + hCoeffs->rho33v6l*eulerlogxabs
+ + v*(hCoeffs->rho33v7 + (hCoeffs->rho33v8 + hCoeffs->rho33v8l*eulerlogxabs)*v))))));
+ auxflm = v*v2*hCoeffs->f33v3;
+ break;
+ case 2:
+ deltalm = vh3*(hCoeffs->delta32vh3 + vh*(hCoeffs->delta32vh4 + vh*vh*(hCoeffs->delta32vh6
+ + hCoeffs->delta32vh9*vh3)));
+ rholm = 1. + v*(hCoeffs->rho32v
+ + v*(hCoeffs->rho32v2 + v*(hCoeffs->rho32v3 + v*(hCoeffs->rho32v4 + v*(hCoeffs->rho32v5
+ + v*(hCoeffs->rho32v6 + hCoeffs->rho32v6l*eulerlogxabs
+ + (hCoeffs->rho32v8 + hCoeffs->rho32v8l*eulerlogxabs)*v2))))));
+ break;
+ case 1:
+ deltalm = vh3*(hCoeffs->delta31vh3 + vh3*(hCoeffs->delta31vh6
+ + vh*(hCoeffs->delta31vh7 + hCoeffs->delta31vh9*vh*vh)))
+ + hCoeffs->delta31v5*v*v2*v2;
+ rholm = 1. + v2*(hCoeffs->rho31v2 + v*(hCoeffs->rho31v3 + v*(hCoeffs->rho31v4
+ + v*(hCoeffs->rho31v5 + v*(hCoeffs->rho31v6 + hCoeffs->rho31v6l*eulerlogxabs
+ + v*(hCoeffs->rho31v7 + (hCoeffs->rho31v8 + hCoeffs->rho31v8l*eulerlogxabs)*v))))));
+ auxflm = v*v2*hCoeffs->f31v3;
+ break;
+ default:
+ break;
+ }
+ break;
+ case 4:
+ switch (m)
+ {
+ case 4:
+
+ deltalm = vh3*(hCoeffs->delta44vh3 + hCoeffs->delta44vh6 *vh3)
+ + hCoeffs->delta44v5*v2*v2*v;
+ rholm = 1. + v2*(hCoeffs->rho44v2
+ + v*( hCoeffs->rho44v3 + v*(hCoeffs->rho44v4
+ + v*(hCoeffs->rho44v5 + (hCoeffs->rho44v6
+ + hCoeffs->rho44v6l*eulerlogxabs)*v))));
+ break;
+ case 3:
+ deltalm = vh3*(hCoeffs->delta43vh3 + vh*(hCoeffs->delta43vh4
+ + hCoeffs->delta43vh6*vh*vh));
+ rholm = 1. + v*(hCoeffs->rho43v
+ + v*(hCoeffs->rho43v2
+ + v2*(hCoeffs->rho43v4 + v*(hCoeffs->rho43v5
+ + (hCoeffs->rho43v6 + hCoeffs->rho43v6l*eulerlogxabs)*v))));
+ auxflm = v*hCoeffs->f43v;
+ break;
+ case 2:
+ deltalm = vh3*(hCoeffs->delta42vh3 + hCoeffs->delta42vh6*vh3);
+ rholm = 1. + v2*(hCoeffs->rho42v2
+ + v*(hCoeffs->rho42v3 + v*(hCoeffs->rho42v4 + v*(hCoeffs->rho42v5
+ + (hCoeffs->rho42v6 + hCoeffs->rho42v6l*eulerlogxabs)*v))));
+ break;
+ case 1:
+ deltalm = vh3*(hCoeffs->delta41vh3 + vh*(hCoeffs->delta41vh4
+ + hCoeffs->delta41vh6*vh*vh));
+ rholm = 1. + v*(hCoeffs->rho41v
+ + v*(hCoeffs->rho41v2
+ + v2*(hCoeffs->rho41v4 + v*(hCoeffs->rho41v5
+ + (hCoeffs->rho41v6 + hCoeffs->rho41v6l*eulerlogxabs)*v))));
+ auxflm = v*hCoeffs->f41v;
+ break;
+ default:
+ break;
+ }
+ break;
+ case 5:
+ switch (m)
+ {
+ case 5:
+ deltalm = hCoeffs->delta55vh3*vh3 + hCoeffs->delta55v5*v2*v2*v;
+ rholm = 1. + v2*( hCoeffs->rho55v2
+ + v*(hCoeffs->rho55v3 + v*(hCoeffs->rho55v4
+ + v*(hCoeffs->rho55v5 + hCoeffs->rho55v6*v))));
+ break;
+ case 4:
+ deltalm = vh3*(hCoeffs->delta54vh3 + hCoeffs->delta54vh4*vh);
+ rholm = 1. + v2*(hCoeffs->rho54v2 + v*(hCoeffs->rho54v3
+ + hCoeffs->rho54v4*v));
+ break;
+ case 3:
+ deltalm = hCoeffs->delta53vh3 * vh3;
+ rholm = 1. + v2*(hCoeffs->rho53v2
+ + v*(hCoeffs->rho53v3 + v*(hCoeffs->rho53v4 + hCoeffs->rho53v5*v)));
+ break;
+ case 2:
+ deltalm = vh3*(hCoeffs->delta52vh3 + hCoeffs->delta52vh4*vh);
+ rholm = 1. + v2*(hCoeffs->rho52v2 + v*(hCoeffs->rho52v3
+ + hCoeffs->rho52v4*v));
+ break;
+ case 1:
+ deltalm = hCoeffs->delta51vh3 * vh3;
+ rholm = 1. + v2*(hCoeffs->rho51v2
+ + v*(hCoeffs->rho51v3 + v*(hCoeffs->rho51v4 + hCoeffs->rho51v5*v)));
+ break;
+ default:
+ break;
+ }
+ break;
+ case 6:
+ switch (m)
+ {
+ case 6:
+ deltalm = hCoeffs->delta66vh3*vh3;
+ rholm = 1. + v2*(hCoeffs->rho66v2 + v*(hCoeffs->rho66v3
+ + hCoeffs->rho66v4*v));
+ break;
+ case 5:
+ deltalm = hCoeffs->delta65vh3*vh3;
+ rholm = 1. + v2*(hCoeffs->rho65v2 + hCoeffs->rho65v3*v);
+ break;
+ case 4:
+ deltalm = hCoeffs->delta64vh3 * vh3;
+ rholm = 1. + v2*(hCoeffs->rho64v2 + v*(hCoeffs->rho64v3
+ + hCoeffs->rho64v4*v));
+ break;
+ case 3:
+ deltalm = hCoeffs->delta63vh3 * vh3;
+ rholm = 1. + v2*(hCoeffs->rho63v2 + hCoeffs->rho63v3*v);
+ break;
+ case 2:
+ deltalm = hCoeffs->delta62vh3 * vh3;
+ rholm = 1. + v2*(hCoeffs->rho62v2 + v*(hCoeffs->rho62v3
+ + hCoeffs->rho62v4 * v));
+ break;
+ case 1:
+ deltalm = hCoeffs->delta61vh3 * vh3;
+ rholm = 1. + v2*(hCoeffs->rho61v2 + hCoeffs->rho61v3*v);
+ break;
+ default:
+ break;
+ }
+ break;
+ case 7:
+ switch (m)
+ {
+ case 7:
+ deltalm = hCoeffs->delta77vh3 * vh3;
+ rholm = 1. + v2*(hCoeffs->rho77v2 + hCoeffs->rho77v3 * v);
+ break;
+ case 6:
+ deltalm = 0.0;
+ rholm = 1. + hCoeffs->rho76v2 * v2;
+ break;
+ case 5:
+ deltalm = hCoeffs->delta75vh3 * vh3;
+ rholm = 1. + v2*(hCoeffs->rho75v2 + hCoeffs->rho75v3*v);
+ break;
+ case 4:
+ deltalm = 0.0;
+ rholm = 1. + hCoeffs->rho74v2 * v2;
+ break;
+ case 3:
+ deltalm = hCoeffs->delta73vh3 *vh3;
+ rholm = 1. + v2*(hCoeffs->rho73v2 + hCoeffs->rho73v3 * v);
+ break;
+ case 2:
+ deltalm = 0.0;
+ rholm = 1. + hCoeffs->rho72v2 * v2;
+ break;
+ case 1:
+ deltalm = hCoeffs->delta71vh3 * vh3;
+ rholm = 1. + v2*(hCoeffs->rho71v2 +hCoeffs->rho71v3 * v);
+ break;
+ default:
+ break;
+ }
+ break;
+ case 8:
+ switch (m)
+ {
+ case 8:
+ deltalm = 0.0;
+ rholm = 1. + hCoeffs->rho88v2 * v2;
+ break;
+ case 7:
+ deltalm = 0.0;
+ rholm = 1. + hCoeffs->rho87v2 * v2;
+ break;
+ case 6:
+ deltalm = 0.0;
+ rholm = 1. + hCoeffs->rho86v2 * v2;
+ break;
+ case 5:
+ deltalm = 0.0;
+ rholm = 1. + hCoeffs->rho85v2 * v2;
+ break;
+ case 4:
+ deltalm = 0.0;
+ rholm = 1. + hCoeffs->rho84v2 * v2;
+ break;
+ case 3:
+ deltalm = 0.0;
+ rholm = 1. + hCoeffs->rho83v2 * v2;
+ break;
+ case 2:
+ deltalm = 0.0;
+ rholm = 1. + hCoeffs->rho82v2 * v2;
+ break;
+ case 1:
+ deltalm = 0.0;
+ rholm = 1. + hCoeffs->rho81v2 * v2;
+ break;
+ default:
+ break;
+ }
+ break;
+ default:
+ break;
+ }
+
+ /* Raise rholm to the lth power */
+ rholmPwrl = 1.0;
+ i = l;
+ while ( i-- )
+ {
+ rholmPwrl *= rholm;
+ }
+ /* In the equal-mass odd m case, there is no contribution from nonspin terms,
+ * and the only contribution comes from the auxflm term that is proportional to chiA (asymmetric spins).
+ * In this case, we must ignore the nonspin terms directly, since the leading term defined by
+ * CalculateThisMultipolePrefix in LALSimIMREOBNewtonianMultipole.c is not zero (see comments there).
+ */
+ if (eta == 0.25 && m % 2)
+ {
+ rholmPwrl = auxflm;
+ }
+ else
+ {
+ rholmPwrl += auxflm;
+ }
+
+ /*if (r > 8.5)
+ {
+ printf("YP::dynamics variables in waveform: %i, %i, %e, %e\n",l,m,r,pp);
+ printf( "rholm^l = %.16e, Tlm = %.16e + i %.16e, \nSlm = %.16e, hNewton = %.16e + i %.16e, delta = %.16e\n", rholmPwrl, Tlm.re, Tlm.im, Slm, hNewton.re, hNewton.im, deltalm );}*/
+ /* Put all factors in Eq. 17 together, Eq.(14) of PRD 84, 124052 (2011) */
+
+ *hlm = Tlm * cexp(ci * deltalm) * Slm * rholmPwrl;
+ //printf("multiplied factor (l=%i,m=%i) = %e\n",l,m,abs(*hlm));
+ *hlm *= hNewton;
+ /*if (r > 8.5)
+ {
+ printf("YP::FullWave: %.16e,%.16e, %.16e\n",hlm->re,hlm->im,sqrt(hlm->re*hlm->re+hlm->im*hlm->im));
+ }*/
+ return 0;
+}
+
+// Eq.(16) of Y. Pan et al, PRD 84, 124052 (2011)
+ int
+XLALSimIMRSpinEOBCalculateNewtonianMultipole(
+ COMPLEX16 *multipole, /**<< OUTPUT, Newtonian multipole */
+ REAL8 x, /**<< Dimensionless parameter \f$\equiv v^2\f$ */
+ REAL8 r, /**<< Orbital separation (units of total mass M */
+ REAL8 phi, /**<< Orbital phase (in radians) */
+ UINT4 l, /**<< Mode l */
+ int m, /**<< Mode m */
+ EOBParams *params /**<< Pre-computed coefficients, parameters, etc. */
+ )
+{
+ int xlalStatus;
+
+ COMPLEX16 y;
+
+ int epsilon = (l + m) % 2;
+
+ y = 0.0;
+
+ /* Calculate the necessary Ylm */
+ xlalStatus = XLALScalarSphHarmThetaPiBy2( &y, l - epsilon, - m, phi );
+ if (xlalStatus != -1 )
+ {
+ }
+ // a little different to the factor V^l_\Phi in Eq.(16) of Y Pan et al, PRD 84, 124052 (2011)
+ // Eq.(1) and (4) of PRD 79, 064004 (2009)
+ *multipole = params->prefixes->values[l][m] * pow( x, (REAL8)(l+epsilon)/2.0) ;
+ *multipole *= y;
+
+ return 0;
+}
+
+ int
+XLALScalarSphHarmThetaPiBy2(
+ COMPLEX16 *y, /**<< OUTPUT, Ylm(pi/2,phi) */
+ int l, /**<< Mode l */
+ int m, /**<< Mode m */
+ REAL8 phi /**<< Orbital phase (in radians) */
+ )
+{
+
+ REAL8 legendre;
+ int absM = abs( m );
+
+ if ( l < 0 || absM > (INT4) l )
+ {
+ }
+
+ /* For some reason GSL will not take negative m */
+ /* We will have to use the relation between sph harmonics of +ve and -ve m */
+ legendre = XLALAssociatedLegendreXIsZero( l, absM );
+ if ( XLAL_IS_REAL8_FAIL_NAN( legendre ))
+ {
+ }
+
+ /* Compute the values for the spherical harmonic */
+ *y = legendre * cos(m * phi);
+ *y += I * legendre * sin(m * phi);
+
+ /* If m is negative, perform some jiggery-pokery */
+ if ( m < 0 && absM % 2 == 1 )
+ {
+ *y *= -1.0;
+ }
+
+ return 0;
+}
+
+/**
+ * Function to calculate associated Legendre function used by the spherical harmonics function
+ */
+ REAL8
+XLALAssociatedLegendreXIsZero( const int l,
+ const int m )
+{
+
+ REAL8 legendre;
+
+ if ( l < 0 )
+ {
+ }
+
+ if ( m < 0 || m > l )
+ {
+ }
+
+ /* we will switch on the values of m and n */
+ switch ( l )
+ {
+ case 1:
+ switch ( m )
+ {
+ case 1:
+ legendre = - 1.;
+ break;
+ default:
+ break;
+ }
+ break;
+ case 2:
+ switch ( m )
+ {
+ case 2:
+ legendre = 3.;
+ break;
+ case 1:
+ legendre = 0.;
+ break;
+ default:
+ break;
+ }
+ break;
+ case 3:
+ switch ( m )
+ {
+ case 3:
+ legendre = -15.;
+ break;
+ case 2:
+ legendre = 0.;
+ break;
+ case 1:
+ legendre = 1.5;
+ break;
+ default:
+ break;
+ }
+ break;
+ case 4:
+ switch ( m )
+ {
+ case 4:
+ legendre = 105.;
+ break;
+ case 3:
+ legendre = 0.;
+ break;
+ case 2:
+ legendre = - 7.5;
+ break;
+ case 1:
+ legendre = 0;
+ break;
+ default:
+ break;
+ }
+ break;
+ case 5:
+ switch ( m )
+ {
+ case 5:
+ legendre = - 945.;
+ break;
+ case 4:
+ legendre = 0.;
+ break;
+ case 3:
+ legendre = 52.5;
+ break;
+ case 2:
+ legendre = 0;
+ break;
+ case 1:
+ legendre = - 1.875;
+ break;
+ default:
+ break;
+ }
+ break;
+ case 6:
+ switch ( m )
+ {
+ case 6:
+ legendre = 10395.;
+ break;
+ case 5:
+ legendre = 0.;
+ break;
+ case 4:
+ legendre = - 472.5;
+ break;
+ case 3:
+ legendre = 0;
+ break;
+ case 2:
+ legendre = 13.125;
+ break;
+ case 1:
+ legendre = 0;
+ break;
+ default:
+ break;
+ }
+ break;
+ case 7:
+ switch ( m )
+ {
+ case 7:
+ legendre = - 135135.;
+ break;
+ case 6:
+ legendre = 0.;
+ break;
+ case 5:
+ legendre = 5197.5;
+ break;
+ case 4:
+ legendre = 0.;
+ break;
+ case 3:
+ legendre = - 118.125;
+ break;
+ case 2:
+ legendre = 0.;
+ break;
+ case 1:
+ legendre = 2.1875;
+ break;
+ default:
+ break;
+ }
+ break;
+ case 8:
+ switch ( m )
+ {
+ case 8:
+ legendre = 2027025.;
+ break;
+ case 7:
+ legendre = 0.;
+ break;
+ case 6:
+ legendre = - 67567.5;
+ break;
+ case 5:
+ legendre = 0.;
+ break;
+ case 4:
+ legendre = 1299.375;
+ break;
+ case 3:
+ legendre = 0.;
+ break;
+ case 2:
+ legendre = - 19.6875;
+ break;
+ case 1:
+ legendre = 0.;
+ break;
+ default:
+ break;
+ }
+ break;
+ default:
+ fprintf( stderr,"Unsupported (l, m): %d, %d\n", l, m );
+ }
+
+ legendre *= sqrt( (REAL8)(2*l+1)*gsl_sf_fact( l-m ) / (4.*LAL_PI*gsl_sf_fact(l+m)));
+
+ return legendre;
+}
+
+ REAL8 XLALSimIMRSpinEOBHamiltonianDeltaR(
+ SpinEOBHCoeffs *coeffs, /**<< Pre-computed coefficients which appear in the function */
+ const REAL8 r, /**<< Current orbital radius (in units of total mass) */
+ const REAL8 eta, /**<< Symmetric mass ratio */
+ const REAL8 a /**<< Normalized deformed Kerr spin */
+ )
+{
+
+
+ REAL8 u2, u3;
+ REAL8 D;
+ REAL8 deltaT; /* The potential function, not a time interval... */
+ REAL8 deltaR;
+
+ u2 = 1./(r*r);
+ u3 = u2 / r;
+
+ D = 1. + log(1. + 6.*eta*u2 + 2.*(26. - 3.*eta)*eta*u3);
+
+ deltaT = XLALSimIMRSpinEOBHamiltonianDeltaT( coeffs, r, eta, a );
+
+ deltaR = deltaT*D;
+ return deltaR;
+}
+
+ REAL8 XLALSimIMRSpinEOBHamiltonianDeltaT(
+ SpinEOBHCoeffs *coeffs, /**<< Pre-computed coefficients which appear in the function */
+ const REAL8 r, /**<< Current orbital radius (in units of total mass) */
+ const REAL8 eta, /**<< Symmetric mass ratio */
+ const REAL8 a /**<< Normalized deformed Kerr spin */
+ )
+
+{
+
+ REAL8 a2;
+ REAL8 u, u2, u3, u4;
+ REAL8 m1PlusetaKK;
+
+ REAL8 bulk;
+ REAL8 logTerms;
+ REAL8 deltaU;
+ REAL8 deltaT;
+
+ u = 1./r;
+ u2 = u*u;
+ u3 = u2*u;
+ u4 = u2*u2;
+
+ a2 = a*a;
+
+ m1PlusetaKK = -1. + eta * coeffs->KK;
+
+ bulk = 1./(m1PlusetaKK*m1PlusetaKK) + (2.*u)/m1PlusetaKK + a2*u2;
+
+ logTerms = 1. + eta*coeffs->k0 + eta*log(1. + coeffs->k1*u + coeffs->k2*u2 + coeffs->k3*u3 + coeffs->k4*u4);
+ //printf( "bulk = %.16e, logTerms = %.16e\n", bulk, logTerms );
+ deltaU = bulk*logTerms;
+
+ deltaT = r*r*deltaU;
+
+ return deltaT;
+}
+
+/* ark4GSLIntegrator is in Panyidatatypes.h */
+ark4GSLIntegrator *XLALAdaptiveRungeKutta4Init( int dim,
+ int (* dydt) (double t, const double y[], double dydt[], void * params), /* These are XLAL functions! */
+ int (* stop) (double t, const double y[], double dydt[], void * params),
+ double eps_abs, double eps_rel
+ )
+{
+ ark4GSLIntegrator *integrator;
+
+ /* allocate our custom integrator structure */
+ if (!(integrator = (ark4GSLIntegrator *) calloc(1, sizeof(ark4GSLIntegrator))))
+ {
+ }
+
+ /* allocate the GSL ODE components */
+ integrator->step = gsl_odeiv_step_alloc(gsl_odeiv_step_rkf45,dim) ;
+ integrator->control = gsl_odeiv_control_y_new(eps_abs,eps_rel);
+ integrator->evolve = gsl_odeiv_evolve_alloc(dim);
+
+ /* allocate the GSL system (functions, etc.) */
+ integrator->sys = (gsl_odeiv_system *)calloc(1, sizeof(gsl_odeiv_system));
+
+ /* if something failed to be allocated, bail out */
+ if ( !(integrator->step) || !(integrator->control) || !(integrator->evolve) || !(integrator->sys) )
+ {
+ XLALAdaptiveRungeKutta4Free(integrator);
+ }
+
+ integrator->dydt = dydt;
+ integrator->stop = stop;
+
+ integrator->sys->function = dydt;
+ integrator->sys->jacobian = NULL;
+ integrator->sys->dimension = dim;
+ integrator->sys->params = NULL;
+
+ integrator->retries = 6;
+ integrator->stopontestonly = 0;
+
+ return integrator;
+}
+
+void XLALAdaptiveRungeKutta4Free( ark4GSLIntegrator *integrator )
+{
+ if (!integrator) return;
+
+ if (integrator->evolve) gsl_odeiv_evolve_free(integrator->evolve);
+ if (integrator->control) gsl_odeiv_control_free(integrator->control);
+ if (integrator->step) gsl_odeiv_step_free(integrator->step);
+
+ LALFree( integrator->sys );
+ LALFree( integrator );
+
+ return;
+}
+
+ int XLALSpinAlignedHcapDerivative(
+ double t, /**< UNUSED */
+ const REAL8 values[], /**< dynamical varables, r, phi, pr, pphi */
+ REAL8 dvalues[], /**< time derivative of dynamical variables */
+ void *funcParams /**< EOB parameters */
+ )
+{
+ //printf("%.8f %.8f %.8f %.8f\n",values[0],values[1],values[2],values[3]);
+ //exit(0);
+
+ static const REAL8 STEP_SIZE = 1.0e-4;
+
+ static const INT4 lMax = 8;
+
+ HcapDerivParams params;
+
+ /* Since we take numerical derivatives wrt dynamical variables */
+ /* but we want them wrt time, we use this temporary vector in */
+ /* the conversion */
+ REAL8 tmpDValues[6];
+
+ /* Cartesian values for calculating the Hamiltonian */
+ REAL8 cartValues[6];
+
+ REAL8 H; //Hamiltonian
+ REAL8 flux;
+
+ gsl_function F;
+ INT4 gslStatus;
+
+ UINT4 i;
+
+ REAL8Vector rVec, pVec;
+ REAL8 rData[3], pData[3];
+
+ /* We need r, phi, pr, pPhi to calculate the flux */
+ REAL8 r;
+ REAL8Vector polarDynamics;
+ REAL8 polData[4];
+
+ REAL8 mass1, mass2, eta;
+
+ /* Spins */
+ REAL8Vector *sKerr = NULL;
+ REAL8Vector *sStar = NULL;
+ REAL8Vector *Spin1 = NULL;
+ REAL8Vector *Spin2 = NULL;
+
+ REAL8 a;
+
+ REAL8 omega;
+
+ /* EOB potential functions */
+ REAL8 DeltaT, DeltaR;
+ REAL8 csi;
+
+ /* The error in a derivative as measured by GSL */
+ REAL8 absErr;
+
+ /* Set up pointers for GSL */
+ params.values = cartValues;
+ params.params = (SpinEOBParams *)funcParams;
+
+ sKerr = params.params->sigmaKerr;
+ sStar = params.params->sigmaStar;
+
+ Spin1 = params.params->Spin1;
+ Spin2 = params.params->Spin2;
+
+ F.function = &GSLSpinAlignedHamiltonianWrapper;
+ F.params = ¶ms;
+
+ mass1 = params.params->eobParams->m1;
+ mass2 = params.params->eobParams->m2;
+ eta = params.params->eobParams->eta;
+
+ r = values[0];
+
+ /* Since this is spin aligned, I make the assumption */
+ /* that the spin vector is along the z-axis. */
+ a = sKerr->data[2];
+
+ /* Calculate the potential functions and the tortoise coordinate factor csi,
+ given by Eq. 28 of Pan et al. PRD 81, 084041 (2010) */
+ DeltaT = XLALSimIMRSpinEOBHamiltonianDeltaT( params.params->seobCoeffs, r, eta, a );
+ DeltaR = XLALSimIMRSpinEOBHamiltonianDeltaR( params.params->seobCoeffs, r, eta, a );
+ csi = sqrt( DeltaT * DeltaR ) / (r*r + a*a);
+ //printf( "csi in derivatives function = %.16e\n", csi );
+
+ /* Populate the Cartesian values vector, using polar coordinate values */
+ /* We can assume phi is zero wlog */
+ memset( cartValues, 0, sizeof( cartValues ) );
+ cartValues[0] = values[0];
+ cartValues[3] = values[2];
+ cartValues[4] = values[3] / values[0];
+
+ /* Now calculate derivatives w.r.t. each Cartesian variable */
+ for ( i = 0; i < 6; i++ )
+ {
+ params.varyParam = i;
+ gslStatus = gsl_deriv_central( &F, cartValues[i],
+ STEP_SIZE, &tmpDValues[i], &absErr );
+
+ if ( gslStatus != GSL_SUCCESS )
+ {
+ fprintf( stderr,"XLAL Error : Failure in GSL function\n" );
+ }
+ }
+
+ /* Calculate the Cartesian vectors rVec and pVec */
+ polarDynamics.length = 4;
+ polarDynamics.data = polData;
+
+ memcpy( polData, values, sizeof( polData ) );
+
+ rVec.length = pVec.length = 3;
+ rVec.data = rData;
+ pVec.data = pData;
+
+ memset( rData, 0, sizeof(rData) );
+ memset( pData, 0, sizeof(pData) );
+
+ rData[0] = values[0];
+ pData[0] = values[2];
+ pData[1] = values[3] / values[0];
+ /* Calculate Hamiltonian using Cartesian vectors rVec and pVec */
+ H = XLALSimIMRSpinEOBHamiltonian( eta, &rVec, &pVec, sKerr, sStar, params.params->tortoise, params.params->seobCoeffs );
+
+ //printf( "csi = %.16e, ham = %.16e ( tortoise = %d)\n", csi, H, params.params->tortoise );
+ //exit(1);
+ //printf( "Hamiltonian = %e\n", H );
+ H = H * (mass1 + mass2);
+
+ //printf( "Cartesian derivatives:\n%.16e %.16e %.16e %.16e %.16e %.16e\n",
+ // dx/dt, dy/dt, dz/dt, dpx/dt, dpy/dt, dpz/dt
+ // tmpDValues[3], tmpDValues[4], tmpDValues[5], -tmpDValues[0], -tmpDValues[1], -tmpDValues[2] );
+ // r, phi, pr, pphi
+ // values[0], values[1], values[2], values[3]
+
+ /* Now calculate omega, and hence the flux */
+ omega = tmpDValues[4] / r;
+
+ /* Now we can calculate the final (spherical) derivatives */
+ /* csi is needed because we use the tortoise co-ordinate */
+ /* Right hand side of Eqs. 10a - 10d of Pan et al. PRD 84, 124052 (2011) */
+ dvalues[0] = csi * tmpDValues[3];
+ dvalues[1] = omega;
+
+ // Eq.(6.12) of PRD 54, 4813 (1996)
+ REAL8 m=mass1+mass2;
+ REAL8 v = MYcbrt( omega );
+ REAL8 rd = dvalues[0];
+#if 0
+ //compare to Wenbiao IJMPD
+ flux = 0; // works for mass ratio 1:1000
+#elif 0
+ // does not work for mass ratio 1:1000
+ flux = XLALInspiralSpinFactorizedFlux( &polarDynamics, omega, params.params, H/m, lMax );
+#elif 0
+ //works for mass ratio 1:1000
+ flux = 8./15*eta*eta*pow(m/r,4)*(
+ (12*v*v-11*rd*rd) // (6.13a) of PRD 54, 4813 (1996); (3.25a) of PRD 52, 821 (1995)
+ +((785-852*eta)*pow(v,4)-2*(1487-1392*eta)*v*v*rd*rd
+ +3*(687-620*eta)*pow(rd,4)-160*(17-eta)*m/r*v*v
+ +8*(367-15*eta)*m/r*rd*rd+16*(1-4*eta)*pow(m/r,2))/28 // (6.13b) of PRD 54, 4813 (1996); (3.25b) of PRD 52, 821 (1995)
+ +(18*(1692-5497*eta+4430*eta*eta)*pow(v,6)-54*(1719-10278*eta+6292*eta*eta)*pow(v,4)*rd*rd
+ +54*(2018-15207*eta+7572*eta*eta)*v*v*pow(rd,4)-18*(2501-20234*eta+8404*eta*eta)*pow(rd,6)
+ -12*(33510-60971*eta+14290*eta*eta)*m/r*pow(rd,4)-36*(4446-5237*eta+1393*eta*eta)*m/r*pow(v,4)
+ +108*(4987-8513*eta+2165*eta*eta)*m/r*rd*rd*v*v-3*(106319+9798*eta+5376*eta*eta)*m/r*m/r*rd*rd
+ +(281473+81828*eta+4368*eta*eta)*m/r*m/r*v*v-24*(253-1026*eta+56*eta*eta)*pow(m/r,3))/756 // (6.13d) of PRD 54, 4813 (1996)
+ );
+#elif 0 // SEOBNREv2, this flux does not work for almost equal mass cases
+ //works for mass ratio 1:1000
+ flux = EOBPNflux(mass1/(mass1+mass2),mass2/(mass1+mass2),Spin1->data[0],Spin1->data[1],Spin1->data[2],
+ Spin2->data[0],Spin2->data[1],Spin2->data[2],
+ cartValues[0], cartValues[1], cartValues[2],
+ dvalues[0],dvalues[1]*r,0);
+#elif 0 // SEOBNREv1
+ //compare flux
+
+ double fluxwoQNC;
+ flux = EOBPNflux(mass1/(mass1+mass2),mass2/(mass1+mass2),
+ Spin1->data[0],Spin1->data[1],Spin1->data[2],
+ Spin2->data[0],Spin2->data[1],Spin2->data[2],
+ cartValues[0], cartValues[1], cartValues[2],
+ dvalues[0],dvalues[1]*r,0,
+ &fluxwoQNC);
+ //flux = EOBPNflux(1.,1.,
+ // 0.1,0.1,0.1,
+ // 0.1,0.1,0.1,
+ // 0.5,0.5,0.5,
+ // 0.5,0.5,0.5,
+ // &fluxwoQNC);
+#endif
+
+#if 0
+ static FILE *out = 0;
+ if(!out) out= fopen( "compareflux.dat", "w" );
+ fprintf( out, "%.16e %.16e %.16e ", t, fluxwoQNC, flux);
+#endif
+ //
+ /* Note: in this special coordinate setting, namely y = z = 0, dpr/dt = dpx/dt + dy/dt * py/r, where py = pphi/r */
+ dvalues[2] = - tmpDValues[0] + tmpDValues[4] * values[3] / (r*r);
+ dvalues[2] = dvalues[2] * csi;
+ dvalues[3] = 0;
+ flux = XLALInspiralSpinFactorizedFlux_elip(&polarDynamics, values, dvalues, omega, params.params, H/m, lMax);
+#if 0
+ fprintf( out, "%.16e\n", flux);
+#endif
+
+ // because Eq.(8) of PRD 85, 024046 (2012)
+ // compared to Eq.(23) of PRD 81, 084041 (2010), factor 1/eta is added
+ flux = flux / eta;
+
+ //printf( "Flux in derivatives function = %.16e\n", flux );
+
+ //printf("%.8f %.8f %.8f %.8f %.8f %.8f\n",polData[0],polData[1],polData[2],polData[3],omega,H/m);
+ //printf("%.8f %.8f\n",values[3],flux);
+ //exit(0);
+
+ /* Note: in this special coordinate setting, namely y = z = 0, dpr/dt = dpx/dt + dy/dt * py/r, where py = pphi/r */
+ dvalues[2] = - tmpDValues[0] + tmpDValues[4] * values[3] / (r*r);
+ dvalues[2] = dvalues[2] * csi - ( values[2] / values[3] ) * flux / omega;
+ dvalues[3] = - flux / omega;
+
+ //printf("Values:\n%.16e %.16e %.16e %.16e\n", values[0], values[1], values[2], values[3] );
+
+ //printf("Derivatives:\n%.16e %.16e %.16e %.16e\n", dvalues[0], dvalues[1], dvalues[2], dvalues[3] );
+
+ /*if ( isnan( dvalues[0] ) || isnan( dvalues[1] ) || isnan( dvalues[2] ) || isnan( dvalues[3] ) )
+ {
+ //printf( "Deriv is nan: %e %e %e %e\n", dvalues[0], dvalues[1], dvalues[2], dvalues[3] );
+ return 1;
+ }*/
+
+ return 0;
+}
+
+ double GSLSpinAlignedHamiltonianWrapper( double x, void *params )
+{
+ HcapDerivParams *dParams = (HcapDerivParams *)params;
+
+ EOBParams *eobParams = dParams->params->eobParams;
+
+ REAL8 tmpVec[6];
+
+ /* These are the vectors which will be used in the call to the Hamiltonian */
+ REAL8Vector r, p;
+ REAL8Vector *sigmaKerr = dParams->params->sigmaKerr;
+ REAL8Vector *sigmaStar = dParams->params->sigmaStar;
+
+ /* Use a temporary vector to avoid corrupting the main function */
+ memcpy( tmpVec, dParams->values,
+ sizeof(tmpVec) );
+
+ /* Set the relevant entry in the vector to the correct value */
+ tmpVec[dParams->varyParam] = x;
+
+ /* Set the LAL-style vectors to point to the appropriate things */
+ r.length = p.length = 3;
+ r.data = tmpVec;
+ p.data = tmpVec+3;
+
+ return XLALSimIMRSpinEOBHamiltonian( eobParams->eta, &r, &p, sigmaKerr, sigmaStar, dParams->params->tortoise, dParams->params->seobCoeffs ) / eobParams->eta;
+}
+
+ int
+XLALEOBSpinAlignedStopCondition(double t, /**< UNUSED */
+ const double values[], /**< dynamical variable values */
+ double dvalues[], /**< dynamical variable time derivative values */
+ void *funcParams /**< physical parameters */
+ )
+{
+
+ REAL8 omega, r;
+ SpinEOBParams *params = (SpinEOBParams *)funcParams;
+
+ r = values[0];
+ omega = dvalues[1];
+
+ if ( r < 6. && omega < params->eobParams->omega )
+ {
+ return 1;
+ }
+
+ params->eobParams->omega = omega;
+ return 0;
+}
+
+int XLALAdaptiveRungeKutta4( ark4GSLIntegrator *integrator,
+ void *params,
+ REAL8 *yinit,
+ REAL8 tinit, REAL8 tend, REAL8 deltat,
+ REAL8Array **yout
+ )
+{
+ int status; /* used throughout */
+
+ /* needed for the integration */
+ size_t dim, bufferlength, cnt, retries;
+ REAL8 t, tnew, h0;
+ REAL8Array *buffers = NULL;
+ REAL8 *temp = NULL, *y, *y0, *dydt_in, *dydt_in0, *dydt_out, *yerr; /* aliases */
+
+ /* needed for the final interpolation */
+ gsl_spline *interp = NULL;
+ gsl_interp_accel *accel = NULL;
+ int outputlen = 0;
+ REAL8Array *output = NULL;
+ REAL8 *times, *vector; /* aliases */
+
+ /* allocate the buffers!
+ note: REAL8Array has a field dimLength (UINT4Vector) with dimensions, and a field data that points to a single memory block;
+ dimLength itself has fields length and data */
+ dim = integrator->sys->dimension;
+ bufferlength = (int)((tend - tinit)/deltat) + 2; /* allow for the initial value and possibly a final semi-step */
+ buffers = XLALCreateREAL8ArrayL(2,dim+1,bufferlength); /* 2-dimensional array, (dim+1) x bufferlength */
+ temp = (REAL8 *)calloc(6*dim,sizeof(REAL8));
+
+ if (!buffers || !temp) {
+ status = XLAL_ENOMEM;
+ goto bail_out;
+ }
+
+ y = temp; y0 = temp + dim; dydt_in = temp + 2*dim; dydt_in0 = temp + 3*dim; dydt_out = temp + 4*dim; yerr = temp + 5*dim; /* aliases */
+
+ /* set up to get started */
+ integrator->sys->params = params;
+
+ integrator->returncode = 0;
+
+ cnt = 0;
+ retries = integrator->retries;
+
+ t = tinit; h0 = deltat;
+ memcpy(y,yinit,dim*sizeof(REAL8));
+
+ /* store the first data point */
+ buffers->data[0] = t;
+ unsigned int i;
+ for(i=1;i<=dim;i++) buffers->data[i*bufferlength] = y[i-1];
+ /* compute derivatives at the initial time (dydt_in), bail out if impossible */
+ if ((status = integrator->dydt(t,y,dydt_in,params)) != GSL_SUCCESS) {
+ integrator->returncode = status;
+ goto bail_out;
+ }
+
+ /* note: for speed, this replaces the single CALLGSL wrapper applied before each GSL call */
+ //XLAL_BEGINGSL;
+ while(1)
+ {
+
+ if (!integrator->stopontestonly && t >= tend)
+ {
+ break;
+ }
+
+ if (integrator->stop)
+ {
+ if ((status = integrator->stop(t,y,dydt_in,params)) != GSL_SUCCESS)
+ {
+ integrator->returncode = status;
+ break;
+ }
+// printf("\r\nr,phi,pr,pt=%.4f %.4f %.8f %.8f\n",y[0],y[1],y[2],y[3]);
+ }
+
+ /* ready to try stepping! */
+ try_step:
+
+ /* if we would be stepping beyond the final time, stop there instead... */
+ if (!integrator->stopontestonly && t + h0 > tend)
+ h0 = tend - t;
+
+ memcpy(y0 ,y, dim*sizeof(REAL8)); /* save y to y0, dydt_in to dydt_in0 */
+ memcpy(dydt_in0,dydt_in,dim*sizeof(REAL8));
+
+ /* call the GSL stepper function */
+ status = gsl_odeiv_step_apply(integrator->step,t,h0,y,yerr,dydt_in,dydt_out,integrator->sys);
+ /* note: If the user-supplied functions defined in the system dydt return a status other than GSL_SUCCESS,
+ the step will be aborted. In this case, the elements of y will be restored to their pre-step values,
+ and the error code from the user-supplied function will be returned. */
+
+ /* did the stepper report a derivative-evaluation error? */
+ if (status != GSL_SUCCESS) {
+ if (retries--) {
+ h0 = h0 / 10.0; /* if we have singularity retries left, reduce the timestep and try again */
+ goto try_step;
+ } else {
+ integrator->returncode = status;
+ break; /* otherwise exit the loop */
+ }
+ } else {
+ retries = integrator->retries; /* we stepped successfully, reset the singularity retries */
+ }
+
+ tnew = t + h0;
+
+ /* call the GSL error-checking function */
+ status = gsl_odeiv_control_hadjust(integrator->control,integrator->step,y,yerr,dydt_out,&h0);
+
+ /* did the error-checker reduce the stepsize?
+ note: other possible return codes are GSL_ODEIV_HADJ_INC if it was increased,
+ GSL_ODEIV_HADJ_NIL if it was unchanged */
+ if (status == GSL_ODEIV_HADJ_DEC) {
+ memcpy(y, y0, dim*sizeof(REAL8)); /* if so, undo the step, and try again */
+ memcpy(dydt_in,dydt_in0,dim*sizeof(REAL8));
+ goto try_step;
+ }
+
+ /* update the current time and input derivatives */
+ t = tnew;
+ memcpy(dydt_in,dydt_out,dim*sizeof(REAL8));
+ cnt++;
+
+ /* check if interpolation buffers need to be extended */
+ if (cnt >= bufferlength) {
+ REAL8Array *rebuffers;
+
+ /* sadly, we cannot use ResizeREAL8Array, because it would only work if we extended the first array dimension,
+ so we need to copy everything over and switch the buffers. Oh well. */
+ if (!(rebuffers = XLALCreateREAL8ArrayL(2,dim+1,2*bufferlength))) {
+ status = XLAL_ENOMEM; /* ouch, that hurt */
+ goto bail_out;
+ } else {
+ for(i=0;i<=dim;i++) memcpy(&rebuffers->data[i*2*bufferlength],&buffers->data[i*bufferlength],cnt*sizeof(REAL8));
+ XLALDestroyREAL8Array(buffers); buffers = rebuffers;
+ bufferlength *= 2;
+ }
+ }
+
+ /* copy time and state into interpolation buffers */
+ buffers->data[cnt] = t;
+ for(i=1;i<=dim;i++)
+ buffers->data[i*bufferlength + cnt] = y[i-1]; /* y does not have time */
+
+ }
+ //XLAL_ENDGSL;
+
+ /* copy the final state into yinit */
+
+ memcpy(yinit,y,dim*sizeof(REAL8));
+
+ /* if we have completed at least one step, allocate the GSL interpolation object and the output array */
+ if (cnt == 0) goto bail_out;
+
+ //XLAL_CALLGSL( interp = gsl_spline_alloc(gsl_interp_cspline,cnt+1) );
+ interp = gsl_spline_alloc(gsl_interp_cspline,cnt+1);
+ //XLAL_CALLGSL( accel = gsl_interp_accel_alloc() );
+ accel = gsl_interp_accel_alloc();
+
+ outputlen = (int)(t / deltat) + 1;
+ output = XLALCreateREAL8ArrayL(2,dim+1,outputlen);
+
+ if (!interp || !accel || !output) {
+ status = XLAL_ENOMEM; /* ouch again, ran out of memory */
+ if (output) XLALDestroyREAL8Array(output);
+ outputlen = 0;
+ goto bail_out;
+ }
+
+ /* make an array of times */
+ times = output->data;
+ unsigned int j;
+ for(j=0;j<outputlen;j++) times[j] = tinit + deltat * j;
+
+ /* interpolate! */
+ //XLAL_BEGINGSL;
+ for(i=1;i<=dim;i++) {
+ gsl_spline_init(interp,&buffers->data[0],&buffers->data[bufferlength*i],cnt+1);
+
+ vector = output->data + outputlen*i;
+ for(j=0;j<outputlen;j++) {
+ gsl_spline_eval_e(interp,times[j],accel, &(vector[j]));
+ }
+ }
+ //XLAL_ENDGSL;
+
+ /* deallocate stuff and return */
+ bail_out:
+
+ if (buffers) XLALDestroyREAL8Array(buffers); /* let's be careful, although all these checks may not be needed */
+ if (temp) LALFree(temp);
+
+ if (interp) gsl_spline_free(interp);
+ //if (interp) XLAL_CALLGSL( gsl_spline_free(interp) );
+ if (accel) gsl_interp_accel_free(accel);
+// if (accel) XLAL_CALLGSL( gsl_interp_accel_free(accel) );
+
+ if (status == XLAL_ENOMEM)
+ //XLAL_ERROR(XLAL_ENOMEM); /* TO DO: will this return? */
+ fprintf(stderr,"Error!");
+
+ *yout = output;
+ return outputlen; /* TO DO: check XLAL error reporting conventions */
+}
+
+
+int XLALSpinAlignedHiSRStopCondition(double t, /**< UNUSED */
+ const double values[], /**< dynamical variable values */
+ double dvalues[], /**< dynamical variable time derivative values */
+ void *funcParams /**< physical parameters */
+ )
+{
+ SpinEOBParams *params = (SpinEOBParams *)funcParams;
+ REAL8 K, eta;
+ eta = params->eobParams->eta;
+ K = 1.4467 - 1.7152360250654402 * eta - 3.246255899738242 * eta * eta;
+
+ //if ( values[0] <= (1.+sqrt(1-params->a * params->a))*(1.-K*eta) + 0.3 || isnan( dvalues[3] ) || isnan (dvalues[2]) || isnan (dvalues[1]) || isnan (dvalues[0]) )
+ if ( values[0] <= (1.+sqrt(1-params->a * params->a))*(1.-K*eta) + 0.3 )
+ {
+ return 1;
+ }
+ return GSL_SUCCESS;
+}
+
+/**
+ * Function to calculate the value of omega for the spin-aligned EOB waveform.
+ * Can NOT be used in precessing cases. This omega is defined as \f$\dot{y}/r\f$ by setting \f$y=0\f$.
+ * The function calculates omega = v/r, by first converting (r,phi,pr,pphi) to Cartesian coordinates
+ * in which rVec={r,0,0} and pVec={0,pphi/r,0}, i.e. the effective-test-particle is positioned at x=r,
+ * and its velocity along y-axis. Then it computes omega, which is now given by dydt/r = (dH/dp_y)/r.
+ */
+ REAL8
+XLALSimIMRSpinAlignedEOBCalcOmega(
+ const REAL8 values[], /**<< Dynamical variables */
+ SpinEOBParams *funcParams /**<< EOB parameters */
+ )
+{
+ static const REAL8 STEP_SIZE = 1.0e-4;
+
+ HcapDerivParams params;
+
+ /* Cartesian values for calculating the Hamiltonian */
+ REAL8 cartValues[6];
+
+ gsl_function F;
+ INT4 gslStatus;
+
+ REAL8 omega;
+ REAL8 r;
+
+ /* The error in a derivative as measured by GSL */
+ REAL8 absErr;
+
+ /* Set up pointers for GSL */
+ params.values = cartValues;
+ params.params = funcParams;
+
+ F.function = &GSLSpinAlignedHamiltonianWrapper;
+ F.params = ¶ms;
+
+ /* Populate the Cartesian values vector */
+ /* We can assume phi is zero wlog */
+ memset( cartValues, 0, sizeof( cartValues ) );
+ cartValues[0] = r = values[0];
+ cartValues[3] = values[2];
+ cartValues[4] = values[3] / values[0];
+
+ /* Now calculate omega. In the chosen co-ordinate system, */
+ /* we need dH/dpy to calculate this, i.e. varyParam = 4 */
+ params.varyParam = 4;
+ gslStatus = gsl_deriv_central( &F, cartValues[4],
+ STEP_SIZE, &omega, &absErr );
+
+ if ( gslStatus != GSL_SUCCESS )
+ {
+ fprintf(stderr, "XLAL Error - : Failure in GSL function\n" );
+ }
+
+ omega = omega / r;
+
+ return omega;
+}
+ REAL8
+XMYSimIMRSpinAlignedEOBCalcOmega(
+ const REAL8 values[], /**<< Dynamical variables */
+ SpinEOBParams *funcParams /**<< EOB parameters */
+ )
+{
+ static const REAL8 STEP_SIZE = 1.0e-4;
+
+ HcapDerivParams params;
+
+ /* Cartesian values for calculating the Hamiltonian */
+ REAL8 cartValues[6];
+
+ gsl_function F;
+ INT4 gslStatus;
+
+ REAL8 omega;
+ REAL8 r;
+
+ /* The error in a derivative as measured by GSL */
+ REAL8 absErr;
+
+ /* Set up pointers for GSL */
+ params.values = cartValues;
+ params.params = funcParams;
+
+ F.function = &GSLSpinAlignedHamiltonianWrapper;
+ F.params = ¶ms;
+
+ /* Populate the Cartesian values vector */
+ /* We can assume phi is zero wlog */
+ memset( cartValues, 0, sizeof( cartValues ) );
+ cartValues[0] = r = values[0];
+ cartValues[3] = values[2];
+ cartValues[4] = values[3] / values[0];
+
+ /* Now calculate omega. In the chosen co-ordinate system, */
+ /* we need dH/dpy to calculate this, i.e. varyParam = 4 */
+ params.varyParam = 4;
+ gslStatus = gsl_deriv_central( &F, cartValues[4],
+ STEP_SIZE, &omega, &absErr );
+
+ if ( gslStatus != GSL_SUCCESS )
+ {
+ fprintf( stderr,"XLAL Error - : Failure in GSL function\n" );
+ }
+
+ /* Now calculate omega. In the chosen co-ordinate system, */
+ /* we need dH/dpx to calculate this, i.e. varyParam = 3 */
+ const REAL8 gamma=1;
+ REAL8 vx;
+ params.varyParam = 3;
+ gslStatus = gsl_deriv_central( &F, cartValues[3],
+ STEP_SIZE, &vx, &absErr );
+
+ if ( gslStatus != GSL_SUCCESS )
+ {
+ fprintf( stderr,"XLAL Error - : Failure in GSL function\n" );
+ }
+ //printf("factor = %f, vx = %f, px = %f\n",pow(omega/(omega+vx),gamma),vx,cartValues[3]);
+ omega *=pow(omega/(omega+vx),gamma);
+
+ omega = omega / r;
+
+ return omega;
+}
+
+/** Adds a double to a GPS time. */
+LIGOTimeGPS * XLALGPSAdd( LIGOTimeGPS *epoch, REAL8 dt )
+{
+ LIGOTimeGPS dt_gps;
+ if(!XLALGPSSetREAL8(&dt_gps, dt))
+ fprintf(stderr,"error!");
+ return XLALGPSAddGPS(epoch, &dt_gps);
+}
+
+
+/** Sets GPS time given GPS seconds as a REAL8. */
+LIGOTimeGPS * XLALGPSSetREAL8( LIGOTimeGPS *epoch, REAL8 t )
+{
+ INT4 gpssec = (INT4)floor(t);
+ INT4 gpsnan = (INT4)floor((t - gpssec) * XLAL_BILLION_REAL8 + 0.5);
+ /* if(isnan(t)) {
+ printf("%s(): NaN", __func__);
+ }*/
+ if(fabs(t) > 0x7fffffff) {
+ fprintf(stderr,"(): overflow %g", t);
+ }
+ /* use XLALGPSSet() to normalize the nanoseconds */
+ return XLALGPSSet(epoch, gpssec, gpsnan);
+}
+
+/** Adds two GPS times. */
+LIGOTimeGPS * XLALGPSAddGPS( LIGOTimeGPS *epoch, const LIGOTimeGPS *dt )
+{
+ return XLALINT8NSToGPS( epoch, XLALGPSToINT8NS( epoch ) + XLALGPSToINT8NS( dt ) );
+}
+
+/** Sets GPS time given GPS integer seconds and residual nanoseconds. */
+LIGOTimeGPS * XLALGPSSet( LIGOTimeGPS *epoch, INT4 gpssec, INT8 gpsnan )
+{
+ //return XLALINT8NSToGPS( epoch, XLAL_BILLION_INT8 * gpssec + gpsnan );
+ return XLALINT8NSToGPS( epoch, 1e9 * gpssec + gpsnan );
+}
+
+/** Converts nano seconds stored as an INT8 to GPS time. */
+LIGOTimeGPS * XLALINT8NSToGPS( LIGOTimeGPS *epoch, INT8 ns )
+{
+// epoch->gpsSeconds = (int)(ns / XLAL_BILLION_INT8);
+// epoch->gpsNanoSeconds =(int)( ns % XLAL_BILLION_INT8);
+ epoch->gpsSeconds = (int)(ns / 1e9);
+ epoch->gpsNanoSeconds =(int)( ns % 1000000000);
+ return epoch;
+}
+
+/** Converts GPS time to nano seconds stored as an INT8. */
+INT8 XLALGPSToINT8NS( const LIGOTimeGPS *epoch )
+{
+ //return XLAL_BILLION_INT8 * epoch->gpsSeconds + epoch->gpsNanoSeconds;
+ return 1e9 * epoch->gpsSeconds + epoch->gpsNanoSeconds;
+}
+
+
+ int XLALSimIMRGetEOBCalibratedSpinNQC( EOBNonQCCoeffs *coeffs,
+ INT4 l,
+ INT4 m,
+ REAL8 eta,
+ REAL8 a )
+{
+ const unsigned int nsqdim = 100;
+ const unsigned int qdim = 50;
+ const unsigned int adim = 69;
+ UINT4 i;
+ /* REAL8 eta2 = eta*eta;*/
+ REAL8 a3slist[qdim], a4list[qdim], a5list[qdim];
+
+ memset( coeffs, 0, sizeof( *coeffs ) );
+ const double nsetalist[100] = {0.0025, 0.005, 0.0075, 0.01, 0.0125, 0.015, 0.0175, 0.02, 0.0225, 0.025, 0.0275, 0.03, 0.0325, 0.035, 0.0375, 0.04, 0.0425, 0.045, 0.0475, 0.05, 0.0525, 0.055, 0.0575, 0.06, 0.0625, 0.065, 0.0675, 0.07, 0.0725, 0.075, 0.0775, 0.08, 0.0825, 0.085, 0.0875, 0.09, 0.0925, 0.095, 0.0975, 0.1, 0.1025, 0.105, 0.1075, 0.11, 0.1125, 0.115, 0.1175, 0.12, 0.1225, 0.125, 0.1275, 0.13, 0.1325, 0.135, 0.1375, 0.14, 0.1425, 0.145, 0.1475, 0.15, 0.1525, 0.155, 0.1575, 0.16, 0.1625, 0.165, 0.1675, 0.17, 0.1725, 0.175, 0.1775, 0.18, 0.1825, 0.185, 0.1875, 0.19, 0.1925, 0.195, 0.1975, 0.2, 0.2025, 0.205, 0.2075, 0.21, 0.2125, 0.215, 0.2175, 0.22, 0.2225, 0.225, 0.2275, 0.23, 0.2325, 0.235, 0.2375, 0.24, 0.2425, 0.245, 0.2475, 0.25};
+ const double etalist[50] = {0.005, 0.01, 0.015, 0.02, 0.025, 0.03, 0.035, 0.04, 0.045, 0.05, 0.055, 0.06, 0.065, 0.07, 0.075, 0.08, 0.085, 0.09, 0.095, 0.1, 0.105, 0.11, 0.115, 0.12, 0.125, 0.13, 0.135, 0.14, 0.145, 0.15, 0.155, 0.16, 0.165, 0.17, 0.175, 0.18, 0.185, 0.19, 0.195, 0.2, 0.205, 0.21, 0.215, 0.22, 0.225, 0.23, 0.235, 0.24, 0.245, 0.25};
+ const double alist[69] = {-1., -0.975, -0.95, -0.925, -0.9, -0.875, -0.85, -0.825, -0.8, -0.775, -0.75, -0.725, -0.7, -0.675, -0.65, -0.625, -0.6, -0.575, -0.55, -0.525, -0.5, -0.475, -0.45, -0.425, -0.4, -0.375, -0.35, -0.325, -0.3, -0.275, -0.25, -0.225, -0.2, -0.175, -0.15, -0.125, -0.1, -0.075, -0.05, -0.025, 0., 0.025, 0.05, 0.075, 0.1, 0.125, 0.15, 0.175, 0.2, 0.225, 0.25, 0.275, 0.3, 0.325, 0.35, 0.375, 0.4, 0.425, 0.45, 0.475, 0.5, 0.525, 0.55, 0.575, 0.6, 0.625, 0.65, 0.675, 0.7};
+
+ const double a1list[100] = {-21.648106754277453, -20.47585498319721, -19.530321799953853, -18.760004570030972, -18.079213572570588, -17.419521042795658, -16.859312290615286, -16.28756533894047, -15.772560753656803, -15.303367029222859, -14.847798623544204, -14.404050939670224, -13.976897526988164, -13.578815297784823, -13.200763216702892, -12.841976980076495, -12.501692284239752, -12.179144825526786, -11.865421415437213, -11.561721630442458, -11.267369305715642, -10.980678895252732, -10.699964853049693, -10.42829543384451, -10.167524207712544, -9.914674799750443, -9.669372681081281, -9.43124332282813, -9.199912196114067, -8.97500477206216, -8.756146521795488, -8.542962916437121, -8.335079427110134, -8.130867290476582, -7.9313984345769715, -7.736518055359128, -7.545988962963793, -7.35957396753171, -7.177035879203623, -6.998068318971551, -6.8224288840577945, -6.649961333309703, -6.480441962265538, -6.313647066463564, -6.149352941442041, -5.9873358827392344, -5.827372185893404, -5.669238146442815, -5.512513869477759, -5.347444298469859, -5.183197664196798, -5.019955297249104, -4.857898528217308, -4.697208687691938, -4.538067106263523, -4.380655114522592, -4.225154043059675, -4.071745222465302, -3.9206099833299994, -3.771929656244297, -3.6258855717987246, -3.4826590605838113, -3.342431453190086, -3.2053840802080775, -3.0798495456033685, -2.957143501994997, -2.837141996613968, -2.7197210766912865, -2.6047567894579564, -2.4921251821449832, -2.381702301983373, -2.273364196204128, -2.1669869120382543, -2.0624464967167566, -1.9596189974706397, -1.8495581080328225, -1.7409749049276515, -1.6340876818580403, -1.5291147325269023, -1.4262743506371505, -1.3257848298916983, -1.2278644639934593, -1.1327315466453465, -1.0406043715502744, -0.9517012324111543, -0.8662404229309005, -0.7844402368124264, -0.7065189677586451, -0.6326949094724702, -0.5631863556568149, -0.4982116000145925, -0.4379889362487165, -0.3827366580621, -0.3326730591576565, -0.28801643323829923, -0.24898507400694198, -0.21579727516649713, -0.18867133041987855, -0.1678255334699995, -0.15347817801977337};
+
+ const double a2list[100] = {178.73204288078207, 167.7345170263427, 158.85457776976878, 151.63702661020528, 145.25886103554546, 139.08071349079492, 133.85300186061994, 128.49833153024582, 123.69581397508206, 119.34304449990263, 115.1225036726121, 111.02138715464824, 107.08437843884623, 103.42908442981195, 99.96941370234742, 96.69762600347904, 93.6059810802332, 90.68673867963636, 87.86042720725196, 85.13659365364732, 82.50827361644501, 79.95961751850369, 77.47477578268207, 75.08044751075573, 72.79299640785891, 70.58542621544011, 68.45392194344085, 66.39466860180258, 64.40385120046682, 62.47765474937501, 60.61226425846867, 58.80386473768926, 57.04864119697828, 55.32723154023535, 53.65375061411054, 52.0271070701423, 50.44518833065014, 48.905881817953585, 47.407074954372156, 45.94482445612376, 44.51687981462722, 43.123270309615144, 41.76224017946817, 40.43203366256695, 39.13089499729211, 37.85706842202429, 36.60879817514412, 35.384328495032264, 34.180608559988464, 32.932965816541305, 31.701640999519693, 30.48755199799916, 29.291616701055233, 28.11475299776345, 26.95787877719934, 25.821911928438432, 24.70777034055626, 23.616371902628366, 22.54863450373026, 21.50547603293748, 20.487814379325563, 19.496567431970035, 18.53265307994643, 17.596989212330282, 16.733055464585682, 15.895477726977264, 15.083579856295431, 14.296685709330593, 13.53411914287315, 12.795204013713512, 12.079264178642092, 11.385623494449275, 10.71360581792548, 10.06253500586111, 9.431734915046569, 8.755551062926262, 8.098379005319565, 7.462063310457031, 6.848448546569211, 6.259379281886656, 5.69670008463992, 5.162255523059555, 4.657890165376111, 4.1854485798201475, 3.7467753346222055, 3.3437149980128416, 2.978112138222609, 2.651811323482059, 2.366657122021744, 2.124494102072216, 1.9271668318640272, 1.77651987962773, 1.674397813593876, 1.6226452019930173, 1.6231066130557064, 1.6776266150124943, 1.7880497760939342, 1.956220664530578, 2.1839838485529777, 2.4731838963916855};
+
+ const double a3list[100] = {-198.6684740510964, -185.71560983427335, -175.26102024642407, -166.7798147654891, -159.28986302859136, -152.03810090459336, -145.91734205946045, -139.6355596843493, -134.01653939524905, -128.93945143613453, -124.02034829337536, -119.24645127356649, -114.67037356959001, -110.43118685036107, -106.4264567068743, -102.6466423946065, -99.08220316903453, -95.72359828563523, -92.4798228915885, -89.36096908139594, -86.35837723133453, -83.45329697039512, -80.62697792756852, -77.90968987612793, -75.32016588735331, -72.82709457524146, -70.42579806564999, -68.11159848443651, -65.87981795745866, -63.72577861057402, -61.64480256964021, -59.63221196051487, -57.683328909055604, -55.7731074201788, -53.92035933426217, -52.12397499502319, -50.38150684315194, -48.69050731933857, -47.04852886427319, -45.45070004394427, -43.89439067703587, -42.37998904664536, -40.90552002179141, -39.46900847149271, -38.068479264767944, -36.70195727063581, -35.36746735811498, -34.063034396224154, -32.78536874375959, -31.468633548362497, -30.173781283368523, -28.901550623295833, -27.652680242662605, -26.427908815987003, -25.227975017787198, -24.053617522581362, -22.905575004887663, -21.78458613922428, -20.691389600109368, -19.6267240620611, -18.59132819959765, -17.585940687237187, -16.61130019949788, -15.668145410897901, -14.794309398041404, -13.950185357101319, -13.135122694543167, -12.348470816832473, -11.589579130434757, -10.857797041815543, -10.152473957440362, -9.47295928377472, -8.818602427284151, -8.188752794434174, -7.582759791690314, -6.932160232642741, -6.304213548518645, -5.700899806714059, -5.124199074625014, -4.576091419647542, -4.0585569091776765, -3.573575610611449, -3.123127591344892, -2.709192918774041, -2.3337516602949204, -1.9987838833035663, -1.706269655196011, -1.458189043368287, -1.2565221152164259, -1.1032489381364605, -1.0003495795244224, -0.9498041067763443, -0.953592587288258, -1.0136950884561957, -1.1320916776761898, -1.31076242234427, -1.5516873898564725, -1.8568466476088277, -2.2282202629973678, -2.667788303418125};
+
+ const double b1list[100] = {-0.5693500504085347, -0.576434151837257, -0.5827940588889807, -0.5875005969333106, -0.5915255507494274, -0.5970658827548452, -0.6057016775611604, -0.6053160995270499, -0.6070988602490128, -0.6110941958474475, -0.6140262971912503, -0.6172989788502661, -0.6206089494421659, -0.6234488672149939, -0.6258813681301192, -0.6277498501118401, -0.628897711084455, -0.6291683489722621, -0.6308371388180571, -0.6331613723912005, -0.6359581432020665, -0.6393457874435003, -0.6434426413083475, -0.6478966252652467, -0.6524003236766366, -0.6571425380351175, -0.6620695856777987, -0.6671277839417898, -0.6722634501642004, -0.6774229016821397, -0.6825524558327174, -0.6875984299530429, -0.6925071413802255, -0.6961049747777461, -0.6996298196832709, -0.7032241904115, -0.7069570372346382, -0.7108973104248908, -0.7151139602544623, -0.720064149835206, -0.7258460785616149, -0.7320745022572427, -0.7387427060855165, -0.7458439752098636, -0.7533715947937112, -0.7613188500004865, -0.7696790259936167, -0.778445407936529, -0.7876035918776259, -0.7967733093076456, -0.8063159350249182, -0.8162406283658405, -0.8265565486668099, -0.8372728552642233, -0.8483987074944775, -0.8599432646939698, -0.871915686199097, -0.884325131346256, -0.8971807594718443, -0.9104917299122585, -0.9242672020038958, -0.938516335083153, -0.9532482884864274, -0.9684722215501159, -0.9837886712042127, -0.9996512322126136, -1.0160843677317775, -1.0331125409181625, -1.0507602149282274, -1.0690518529184303, -1.08801191804523, -1.1076648734650847, -1.1280351823344532, -1.1491473078097938, -1.171025713047565, -1.1939017528688474, -1.2175927015073384, -1.2421149961497486, -1.2674850739827876, -1.2937193721931661, -1.320834327967594, -1.3488463784927816, -1.377771960955439, -1.4076275125422764, -1.4384294704400042, -1.4701942718353325, -1.5029383539149717, -1.5366781538656316, -1.5714301088740226, -1.6072106561268549, -1.6440362328108387, -1.6819232761126843, -1.7208882232191016, -1.7609475113168012, -1.802117577592493, -1.8444148592328868, -1.8878557934246936, -1.9324568173546235, -1.9782343682093864, -2.0252048831756926};
+
+ const double b2list[100] = {1.6514745488753086, 1.6733593678301482, 1.687838328174986, 1.7031979370575185, 1.712831020475929, 1.7266279186283089, 1.7581796869631672, 1.7499867318965905, 1.7518398412177276, 1.7634468469918447, 1.770740685014047, 1.779639998248617, 1.788893228893931, 1.7964389585725973, 1.8024779675983216, 1.8063408969988246, 1.8073583878018264, 1.8048610810350476, 1.8077536017385523, 1.8130592620946404, 1.8200051503317694, 1.8290042591854243, 1.8404695813910905, 1.8531136802761718, 1.8658884601302625, 1.8795206835759333, 1.8938451458175296, 1.908696642059398, 1.923909967505884, 1.9393199173613336, 1.9547612868300928, 1.9700688711165077, 1.9850774654249244, 1.9960816492286722, 2.0069990026439246, 2.0182845185376195, 2.0301606467081585, 2.042849836953944, 2.056574539073377, 2.0726094682881886, 2.0912563552368337, 2.111506538675078, 2.1333773752936596, 2.1568862217833127, 2.1820504348347747, 2.208887371138781, 2.2374143873860683, 2.2676488402673725, 2.299578947658098, 2.3318064402049257, 2.3657435940219895, 2.4014679228653333, 2.439056940491002, 2.478588160655038, 2.520139097113486, 2.56378726362239, 2.609610173937794, 2.657685341815741, 2.708090281012276, 2.760902505283443, 2.8161995283852854, 2.874058864073847, 2.9345580261051722, 2.9977745282353045, 3.0615596376827443, 3.128412230361185, 3.1984931979224718, 3.271963432018449, 3.3489838243009618, 3.429715266421855, 3.5143186500329735, 3.602954866786163, 3.6957848083332676, 3.792969366326133, 3.894669432416603, 4.002044979667201, 4.114256382857298, 4.23142577617022, 4.353675293789295, 4.48112706989785, 4.613903238679211, 4.752125934316707, 4.895917290993665, 5.04539944289341, 5.200694524199272, 5.361924669094577, 5.529212011762653, 5.702678686386827, 5.882446827150425, 6.068638568236777, 6.261376043829206, 6.460781388111044, 6.666976735265615, 6.880084219476247, 7.100225974926268, 7.327524135799001, 7.5621008362777795, 7.804078210545929, 8.053578392786775, 8.310723517183646};
+
+ const double a3stab[50][69] = {
+{1298.87913, 1261.29637, 1227.72908, 1197.25947, 1168.96973, 1141.94207, 1115.2587, 1088.00181, 1059.25362, 1022.90618, 985.307903, 947.617046, 910.991876, 881.346609, 853.181173, 825.751447, 798.313312, 767.87765, 736.843339, 705.36426, 673.594293, 642.125047, 610.497581, 578.690684, 546.683144, 514.497622, 482.051486, 449.305976, 416.222332, 382.495195, 348.459044, 314.181759, 279.731222, 245.411071, 210.959123, 176.348956, 141.554145, 106.628243, 71.43286, 35.9095836, 0., -36.1519021, -72.887899, -110.347365, -148.669675, -186.733245, -226.44279, -268.442067, -313.374835, -358.91977, -409.871742, -468.06054, -535.315953, -602.768787, -687.227409, -794.8012, -931.599543, -1073.78457, -1269.39181, -1536.50955, -1893.22609, -2326.65745, -2947.80866, -3741.68954, -4974.29064, -6365.10282, -9538.63496, -15643.1414, -25826.8766},
+{1196.32002, 1167.06104, 1137.27475, 1107.12301, 1076.76769, 1046.37066, 1016.09379, 986.098937, 956.547978, 928.8469, 901.415801, 873.918898, 846.020409, 814.568078, 783.16919, 752.614552, 723.694973, 702.877684, 683.006503, 662.601671, 640.183429, 607.718815, 572.902552, 536.876163, 500.78117, 469.351999, 438.700105, 408.529845, 378.545579, 347.703945, 316.75611, 285.705522, 254.555628, 223.39562, 192.108901, 160.664621, 129.031928, 97.2453174, 65.1824526, 32.7863434, 0., -33.0547348, -66.6852171, -101.01997, -136.187517, -170.971669, -207.383546, -246.089556, -287.756108, -330.313665, -378.258958, -433.352771, -497.35589, -562.191692, -643.393334, -746.656564, -877.67713, -1013.79966, -1200.41146, -1454.54875, -1793.24772, -2204.40576, -2792.4755, -3542.23306, -4707.36116, -6024.93464, -9029.55323, -14806.4354, -24440.7998},
+{1111.34089, 1088.04208, 1061.93086, 1033.65502, 1003.86233, 973.200551, 942.317471, 911.86086, 882.478492, 858.393797, 835.248631, 812.260507, 788.646935, 759.48951, 729.796029, 700.438372, 672.288418, 651.387883, 631.370875, 611.041341, 589.203225, 559.502697, 527.964588, 495.455951, 462.843844, 433.627925, 404.989603, 376.74289, 348.701797, 320.308767, 291.898012, 263.432172, 234.873889, 206.130982, 177.242843, 148.194039, 118.969142, 89.6533759, 60.0903922, 30.2244979, 0., -30.4005164, -61.3663335, -93.0484555, -125.597886, -157.893074, -191.866601, -228.178495, -267.488782, -307.871972, -353.607815, -406.390546, -467.914398, -530.2754, -608.605274, -708.437534, -835.305696, -967.651586, -1148.93709, -1395.53239, -1723.80769, -2122.58454, -2690.87904, -3414.09589, -4533.73512, -5812.62405, -8672.18555, -14119.1936, -23160.4223},
+{1039.53251, 1020.2822, 997.603313, 972.198968, 944.772298, 916.02643, 886.664491, 857.389611, 828.904917, 804.925294, 781.93741, 759.439688, 736.930555, 712.636669, 687.836926, 662.538457, 636.748394, 609.788544, 582.625489, 555.540492, 528.814811, 504.169828, 479.870634, 455.622441, 431.13046, 404.996091, 378.469884, 351.698574, 324.8289, 298.520437, 272.201947, 245.815032, 219.301294, 192.43116, 165.385874, 138.17551, 110.810137, 83.4601202, 55.9111218, 28.1090968, 0., -28.1232207, -56.8004007, -86.2243824, -116.588008, -146.981092, -179.140716, -213.700934, -251.2958, -290.060701, -334.127824, -385.130693, -444.702827, -504.716717, -580.471327, -677.504592, -801.354447, -931.385611, -1109.77852, -1352.54038, -1675.67843, -2068.96254, -2627.11195, -3337.00139, -4427.97475, -5693.23265, -8428.0796, -13552.2941, -21985.6547},
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+{65.4719479, 57.4208681, 51.1223649, 46.3288876, 42.792886, 40.2668095, 38.5031077, 37.2542302, 36.2726266, 34.6627386, 33.0842266, 31.5487434, 30.0679416, 28.9024083, 27.7152878, 26.4186592, 24.9246012, 22.6910859, 20.2659417, 17.7428902, 15.2156527, 12.9020086, 10.7219986, 8.71972156, 6.93927587, 5.70709501, 4.6720087, 3.76518156, 2.9177782, 1.89110459, 0.854127432, -0.194045212, -1.25430528, -2.72905117, -4.05706578, -5.07863845, -5.63405853, -4.49776766, -3.002242, -1.41410996, 0., -0.232086191, -0.689233061, -1.15585079, -1.41634954, -0.326326355, 1.02947019, 2.49510466, 3.91464163, 6.02483426, 7.41998307, 7.58707717, 6.01310568, 4.25526237, -1.09775015, -11.3870246, -27.9536538, -30.037432, -49.9212697, -97.7867791, -183.815572, -309.038656, -511.089458, -801.715921, -1230.32357, -1857.50504, -2661.44699, -3640.93761, -4794.76507},
+{60.4371914, 52.8944439, 47.0061111, 42.5344545, 39.2417357, 36.8902165, 35.2421584, 34.0598231, 33.1054723, 31.4888045, 29.8856696, 28.3193545, 26.8131459, 25.6686144, 24.5194497, 23.2776252, 21.8551143, 19.7300162, 17.4217281, 15.0157733, 12.5976748, 10.34573, 8.215578, 6.25563199, 4.51430532, 3.33212144, 2.34853948, 1.49512871, 0.703458391, -0.282898639, -1.26917813, -2.24861224, -3.21443316, -4.5363881, -5.68058815, -6.48965946, -6.80622818, -5.41661253, -3.64226975, -1.74834914, 0., 0.144274795, 0.0900209157, 0.0494304766, 0.23469559, 1.80159795, 3.64130425, 5.58857079, 7.47815384, 9.93910759, 11.6941713, 12.260382, 11.1547768, 9.8495151, 5.12446293, -4.2853914, -19.6450596, -22.6973878, -42.0384195, -86.7420329, -165.882106, -281.689148, -463.767142, -721.985092, -1095.87966, -1636.34431, -2319.17767, -3138.9521, -4090.23996},
+{54.4780137, 48.4428385, 43.6791707, 39.9986734, 37.21301, 35.1338437, 33.5728378, 32.3416556, 31.2519604, 29.5621783, 27.8585046, 26.1738973, 24.5413145, 23.2625116, 21.9941304, 20.6616102, 19.1903901, 17.1513851, 14.9663681, 12.7025882, 10.427294, 8.26356395, 6.20048559, 4.282976, 2.55595225, 1.31323844, 0.251281779, -0.684563488, -1.54894311, -2.57958539, -3.57482051, -4.51606121, -5.38472022, -6.45481104, -7.29810532, -7.77897552, -7.76179404, -6.16045051, -4.16999329, -2.03498794, 0., 0.606819966, 1.05792541, 1.54218478, 2.24846652, 4.24757601, 6.49367, 8.82284217, 11.0711862, 13.6883341, 15.6514259, 16.5511399, 15.9781543, 15.634255, 12.1545697, 4.28533388, -9.22721724, -13.6309911, -32.5879525, -73.754209, -144.785868, -247.984626, -407.069825, -631.311504, -949.22515, -1399.94534, -1960.88484, -2624.88686, -3384.79461},
+{48.7227738, 44.6398442, 41.3066454, 38.604258, 36.4137625, 34.6162396, 33.0927698, 31.7244338, 30.3923122, 28.5817329, 26.7278303, 24.8699861, 23.0475818, 21.5306864, 20.0357196, 18.509788, 16.8999986, 14.9106943, 12.8288514, 10.6986821, 8.56439891, 6.48920575, 4.49072666, 2.60557732, 0.870373416, -0.504197236, -1.72521994, -2.82570787, -3.83867419, -4.96010825, -5.99485657, -6.91074186, -7.67558681, -8.43282424, -8.90442271, -8.98796086, -8.58101735, -6.79594598, -4.62964023, -2.2937687, 0., 1.13083567, 2.15989592, 3.23917679, 4.5206743, 6.91731822, 9.51579733, 12.1637342, 14.7087513, 17.3991688, 19.5216327, 20.7634863, 20.8120732, 21.7274658, 19.8751872, 13.9934892, 2.82062372, -2.85138016, -21.1595584, -58.1871699, -120.017474, -208.348795, -342.419193, -531.534524, -793.157935, -1154.12298, -1595.62429, -2110.26622, -2690.65314},
+{44.2998304, 42.0592533, 40.0536373, 38.233922, 36.5510472, 34.9559528, 33.3995785, 31.832864, 30.2067492, 28.2463412, 26.2187454, 24.1652348, 22.1270823, 20.3197254, 18.5406064, 16.7613322, 14.9535099, 12.9634457, 10.9381676, 8.89940251, 6.86887778, 4.85635082, 2.90030642, 1.02725964, -0.73627446, -2.27482884, -3.6864212, -4.98011725, -6.16498272, -7.38561978, -8.46134313, -9.34700391, -9.99745327, -10.418932, -10.4943457, -10.1579897, -9.34415937, -7.38976337, -5.06543819, -2.54443376, 0., 1.69160825, 3.34134796, 5.05717119, 6.94702998, 9.71653493, 12.6369161, 15.5770622, 18.4058619, 21.1982666, 23.5346769, 25.2015565, 25.9853686, 28.2471315, 28.1689322, 24.5074123, 16.0192136, 9.6283068, -7.34292715, -39.4047781, -91.0675361, -163.20536, -271.236932, -424.493521, -630.475917, -904.692043, -1232.45178, -1606.61452, -2020.03966},
+{31.3611692, 33.4138344, 34.6123875, 35.0543707, 34.837326, 34.0587958, 32.8163219, 31.2074467, 29.3297123, 27.404283, 25.3556298, 23.2318459, 21.0810247, 19.0533799, 17.0540359, 15.0902378, 13.1692306, 11.3600238, 9.58339213, 7.82187479, 6.05801097, 4.17746025, 2.29839333, 0.442101287, -1.37012481, -3.08825048, -4.73122545, -6.289256, -7.75254846, -9.29802506, -10.6544898, -11.7374626, -12.4624633, -12.5589911, -12.202995, -11.3844033, -10.0931443, -7.98083331, -5.51103668, -2.80900778, 0., 2.33855583, 4.71445469, 7.18331415, 9.80075179, 13.1193625, 16.4989955, 19.7964776, 22.8686353, 25.1976694, 27.1648828, 28.7769525, 30.0405554, 34.3745852, 37.0086155, 36.5844368, 31.7438393, 24.3660043, 8.56037482, -18.326215, -58.9469312, -111.659095, -192.003407, -312.956989, -466.821193, -649.230038, -863.162643, -1109.76185, -1390.17051},
+{37.107078, 37.9494898, 38.1475584, 37.7748672, 36.9049999, 35.61154, 33.9680713, 32.0481773, 29.9254415, 27.7748251, 25.5279832, 23.2179484, 20.8777534, 18.5825868, 16.3064628, 14.0655515, 11.8760232, 9.83055734, 7.83821112, 5.88455095, 3.9551433, 1.96138975, -0.00731245436, -1.93573091, -3.80863323, -5.6288923, -7.35592834, -8.96726683, -10.4404333, -11.8918334, -13.1045604, -14.0005876, -14.5018883, -14.3327386, -13.6918882, -12.5803894, -10.9992944, -8.70169555, -6.03578926, -3.10181195, 0., 2.87088123, 5.82853593, 8.89213931, 12.0808666, 15.681342, 19.3383122, 22.9639726, 26.4705188, 29.5587418, 32.4368037, 35.1014621, 37.5494744, 42.4526156, 46.0626187, 47.3062344, 45.1102132, 39.9921181, 28.651562, 9.37897069, -19.5352305, -57.2665312, -113.12676, -196.55736, -298.235907, -413.117734, -537.811019, -668.510728, -801.411827},
+{54.2496337, 50.3266662, 46.8385324, 43.7179324, 40.8975662, 38.3101336, 35.8883348, 33.5648695, 31.2724379, 28.7494751, 26.2006517, 23.6363737, 21.0670471, 18.525831, 15.9912767, 13.4646886, 10.9473713, 8.38916945, 5.86343143, 3.39204573, 0.99690084, -1.26416265, -3.41958917, -5.46187108, -7.3835007, -9.22601578, -10.9132451, -12.4180629, -13.7133433, -14.8183369, -15.6409909, -16.1356292, -16.2565754, -15.8913591, -15.0878157, -13.8269866, -12.089913, -9.575889, -6.66040207, -3.43719234, 0., 3.32808289, 6.77440878, 10.3369783, 14.0137919, 17.7915291, 21.6840401, 25.6938539, 29.8234995, 34.4683192, 39.0809036, 43.5066565, 47.5909816, 52.0892308, 55.5728806, 57.5233557, 57.4220807, 57.0603078, 52.6857029, 42.8557596, 26.1279713, 0.306807571, -33.7911656, -77.5102898, -128.97305, -194.828091, -250.841278, -280.499173, -267.288336},
+{45.9632263, 43.5948047, 41.2944117, 39.0497927, 36.8486933, 34.6788586, 32.5280343, 30.3839656, 28.2343979, 26.0514214, 23.8446989, 21.6082379, 19.3360459, 16.9792869, 14.5919492, 12.1851779, 9.7701179, 7.3618403, 4.9659933, 2.59215129, 0.249888704, -2.11170034, -4.39836902, -6.57635081, -8.61187918, -10.3777734, -11.9710468, -13.3952985, -14.6541278, -15.978402, -17.0535448, -17.792248, -18.1072036, -17.711688, -16.7975747, -15.3573219, -13.3833878, -10.6397615, -7.43875759, -3.86422188, 0., 3.91966746, 8.02148764, 12.2817728, 16.6768352, 21.1786397, 25.7695849, 30.427722, 35.1311022, 39.788373, 44.4747508, 49.1960481, 53.9580778, 59.5390344, 64.8633958, 69.6280218, 73.5297724, 77.145323, 78.9397916, 78.2581119, 74.4452177, 65.9571768, 54.8055203, 38.1237308, 26.1576508, 25.2296282, 44.2436292, 91.4582154, 175.131949},
+{51.3870855, 48.6794894, 46.1831565, 43.8403542, 41.59335, 39.3844114, 37.155806, 34.8498012, 32.4086645, 29.4555478, 26.3794804, 23.2503763, 20.1381492, 17.3421612, 14.6110986, 11.9230958, 9.25628726, 6.47079096, 3.70996456, 0.999149184, -1.63631406, -4.15046897, -6.54683554, -8.80831871, -10.9178234, -12.8574803, -14.6112782, -16.1624317, -17.4941555, -18.7345028, -19.6639141, -20.2076685, -20.2910453, -19.6603376, -18.491405, -16.7811208, -14.5263586, -11.5733769, -8.12991022, -4.25307808, 0., 4.55743405, 9.3827832, 14.4248361, 19.6323815, 24.7770149, 30.0555953, 35.4877886, 41.0932604, 46.9053614, 52.9245989, 59.1651649, 65.6412515, 72.5154609, 79.5942109, 86.8323292, 94.184644, 100.942288, 107.989262, 115.545873, 123.832425, 131.321797, 143.476579, 160.747982, 191.051251, 237.852606, 314.950336, 433.559716, 604.896017},
+{52.5791609, 52.189412, 50.9809292, 49.0755733, 46.5952055, 43.6616866, 40.3968776, 36.9226396, 33.3608334, 30.1281937, 26.9337584, 23.7814391, 20.6751474, 17.664573, 14.689538, 11.7356427, 8.78848729, 5.69032192, 2.6274371, -0.357226835, -3.22072955, -5.77288536, -8.1768974, -10.4487235, -12.6043213, -14.8262476, -16.8972218, -18.766562, -20.3835865, -21.7939441, -22.8120902, -23.348811, -23.3148923, -22.3006067, -20.6654593, -18.4484415, -15.6885449, -12.4879459, -8.79717705, -4.62995592, 0., 5.28008011, 10.9150172, 16.810651, 22.8728212, 28.6611796, 34.566229, 40.6322844, 46.9036604, 53.1753873, 59.8407787, 67.0438633, 74.92867, 83.7004277, 93.417485, 104.199391, 116.165694, 127.53876, 141.094195, 157.710418, 178.265852, 202.213911, 234.708038, 276.259409, 335.688216, 421.713219, 535.1499, 678.789558, 855.423494}
+};
+
+ const double a4tab[50][69] = {
+{-4795.25483, -4657.11547, -4533.57386, -4420.99082, -4315.72713, -4214.14359, -4112.601, -4007.46016, -3895.08186, -3749.86323, -3598.9142, -3447.38103, -3300.40998, -3183.58631, -3073.44169, -2966.94678, -2861.07226, -2743.59299, -2624.35375, -2504.00351, -2383.19127, -2264.35938, -2145.64608, -2026.98299, -1908.30176, -1789.65691, -1670.80798, -1551.63744, -1432.02772, -1310.85768, -1189.41483, -1067.98309, -946.846341, -827.165104, -707.996037, -589.272406, -470.927472, -353.153181, -235.520643, -117.859652, 0., 117.602012, 235.993705, 355.595891, 476.829381, 595.994952, 719.281464, 848.757742, 986.492612, 1125.29678, 1280.20043, 1456.97565, 1661.39451, 1865.75367, 2122.69078, 2451.36808, 2870.9478, 3306.89371, 3909.54591, 4735.54605, 5841.53576, 7186.8075, 9120.05042, 11591.8611, 15444.2924, 19758.4141, 29767.7712, 49167.7902, 81653.8973},
+{-4386.2486, -4276.4998, -4166.87176, -4057.27842, -3947.63375, -3837.85169, -3727.8462, -3617.53124, -3506.82077, -3396.24985, -3284.86287, -3172.32536, -3058.30283, -2934.12142, -2811.12175, -2692.30507, -2580.67265, -2501.29049, -2426.26919, -2349.78411, -2266.0106, -2143.26267, -2011.92156, -1876.50719, -1741.53944, -1625.69861, -1513.68005, -1404.33951, -1296.53273, -1186.17111, -1076.23248, -966.750311, -857.758075, -749.581249, -641.844515, -534.46455, -427.358033, -320.645434, -213.958122, -107.131257, 0., 107.056887, 214.965285, 324.107473, 434.865731, 543.216635, 655.710448, 774.491733, 901.705051, 1031.01986, 1176.44587, 1343.51767, 1537.76987, 1733.97589, 1980.73599, 2295.88922, 2697.27467, 3113.77504, 3687.76832, 4472.67611, 5521.92004, 6796.91537, 8627.10278, 10961.4315, 14608.3709, 18698.1916, 28214.4395, 46677.342, 77607.1262},
+{-4089.70007, -3999.83272, -3900.40845, -3793.52861, -3681.29454, -3565.8076, -3449.16915, -3333.48054, -3220.84311, -3124.77905, -3031.40055, -2938.24064, -2842.83236, -2728.08787, -2612.00939, -2497.97828, -2389.37592, -2309.8317, -2234.37973, -2158.30216, -2076.88115, -1964.99854, -1846.4969, -1724.8185, -1603.40559, -1496.11382, -1391.80673, -1289.76124, -1189.25426, -1088.05749, -987.55515, -887.626246, -788.149784, -688.774549, -589.701849, -490.902776, -392.348421, -294.336138, -196.38025, -98.321342, 0., 97.9874303, 196.858427, 297.074709, 399.097994, 499.259521, 603.803679, 714.844378, 834.49553, 956.8933, 1095.32044, 1255.08195, 1441.48285, 1629.7946, 1867.36916, 2171.52496, 2559.58043, 2963.77126, 3520.53168, 4281.21321, 5297.16736, 6532.52802, 8300.29955, 10550.9045, 14057.1258, 18028.6165, 27105.1878, 44569.1112, 73702.6582},
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+{-226.724899, -212.764992, -200.613432, -190.033165, -180.787138, -172.638298, -165.34959, -158.683961, -152.404358, -145.81283, -139.317579, -132.865911, -126.40513, -119.900384, -113.273999, -106.466146, -99.4169927, -91.5262098, -83.4906648, -75.4667261, -67.6107623, -60.4573783, -53.6334118, -47.1439369, -40.9940276, -35.2433287, -29.8205152, -24.7088327, -19.8915271, -15.2693682, -10.9410679, -6.92286233, -3.23098758, 0.61081133, 3.89681083, 6.41377843, 7.9484816, 6.40498557, 4.20584103, 1.89089637, 0., 1.36847131, 3.32249934, 5.4837441, 7.4738656, 7.10299269, 6.52892902, 6.09794707, 6.15631933, 4.78894311, 5.50801613, 9.56436095, 18.2088001, 19.6826667, 33.4500685, 65.965624, 123.683951, 138.560516, 221.348751, 408.302935, 735.677349, 1179.71831, 1956.70398, 3138.69873, 4942.56472, 7595.34243, 11138.5612, 15660.1283, 21247.9508},
+{-236.84171, -211.295632, -190.740811, -174.495373, -161.877439, -152.205134, -144.796581, -138.969903, -134.043225, -127.670992, -121.500477, -115.515274, -109.698978, -104.443078, -99.1601186, -93.6705368, -87.7947709, -80.3881138, -72.6222059, -64.7035429, -56.8386203, -49.4919717, -42.5088397, -35.9925048, -30.0462478, -25.3821555, -21.2511794, -17.5130774, -14.0276074, -10.327812, -6.73085042, -3.2271669, 0.192794552, 4.54191817, 8.42510028, 11.4505655, 13.2265385, 10.5952775, 7.03736001, 3.26739713, 0., 1.10351971, 2.87733143, 4.77455029, 6.24829142, 4.25773493, 1.74750499, -0.831709239, -3.02921862, -7.34619724, -9.19934742, -6.95723472, 1.01157529, 6.82986723, 25.4411853, 62.2804239, 122.782477, 135.652615, 213.747207, 393.192996, 710.116727, 1156.14026, 1900.90499, 2996.52076, 4644.78844, 7069.78957, 10256.7919, 14250.7667, 19096.6851},
+{-232.280967, -202.805662, -179.493136, -161.488734, -147.937801, -137.985681, -130.77772, -125.459263, -121.175653, -114.86966, -108.770235, -102.903752, -97.2965875, -92.6305548, -88.0144139, -83.2123638, -77.9886036, -70.9785561, -63.5267075, -55.8487674, -48.1604456, -40.8346679, -33.8670415, -27.4103897, -21.6175357, -17.5081853, -14.0215263, -10.963629, -8.14056397, -4.8928611, -1.67834712, 1.51069153, 4.68196843, 9.02829042, 12.8982405, 15.8254948, 17.3437298, 13.841766, 9.25607751, 4.37828269, 0., 0.430831866, 1.53721913, 2.70358662, 3.31435919, -0.0847916974, -4.13518649, -8.31689902, -12.1100031, -18.0667268, -21.3661281, -20.2594189, -12.9978114, -5.65089228, 14.4758508, 52.2585556, 112.57336, 127.359326, 203.604497, 375.359842, 676.676327, 1108.31316, 1804.19659, 2804.49135, 4284.70754, 6449.15256, 9251.59936, 12708.4545, 16836.1246},
+{-217.723575, -189.98152, -168.069873, -151.165799, -138.446465, -129.089038, -122.270683, -117.168567, -112.959856, -106.589909, -100.360423, -94.3412868, -88.602391, -83.9929754, -79.4918381, -74.8571281, -69.8469946, -63.1281994, -55.9868336, -48.6176009, -41.2152054, -34.0498118, -27.2104788, -20.8617257, -15.168072, -11.1893742, -7.83668007, -4.91637443, -2.23484203, 0.921668114, 4.01858121, 7.04145819, 9.97586002, 13.921929, 17.3048121, 19.6642379, 20.5399346, 16.3430655, 10.9933504, 5.28194367, 0., -0.573489477, -0.530341535, -0.4745363, -1.0100539, -5.63864982, -10.9074187, -16.2612305, -21.1449552, -27.7808742, -31.7254815, -31.3126825, -24.8763827, -18.1852808, 0.835428433, 36.825757, 94.4257167, 113.608134, 189.54708, 352.749442, 633.722106, 1037.49814, 1671.00588, 2568.45021, 3871.51835, 5752.88672, 8153.79254, 11073.3328, 14510.6046},
+{-197.850438, -175.509646, -157.670492, -143.67912, -132.881674, -124.624299, -118.253141, -113.114343, -108.55405, -102.012813, -95.5046078, -89.1378169, -83.0208222, -78.0605024, -73.2473444, -68.3703316, -63.2184475, -56.6677061, -49.7852481, -42.7252446, -35.6418668, -28.701748, -22.0416126, -15.8106468, -10.1580371, -5.99367853, -2.40176533, 0.772799518, 3.68511306, 7.00195942, 10.1620738, 13.1158783, 15.8137953, 19.0748347, 21.6333959, 23.0924661, 23.0550322, 18.2977904, 12.3805353, 6.03677068, 0., -1.83334156, -3.15785451, -4.50520788, -6.40707065, -12.1179021, -18.3574648, -24.5683118, -30.1929959, -36.8968677, -41.0105633, -41.0875167, -35.6811617, -31.1989674, -15.1987182, 16.907766, 69.7086655, 94.3265236, 170.201412, 323.307766, 579.620021, 944.956329, 1505.75997, 2294.23711, 3414.41715, 5000.44737, 6994.1804, 9385.54253, 12164.4601},
+{-177.34246, -162.076478, -149.494462, -139.181246, -130.721668, -123.700563, -117.702768, -112.313118, -107.11645, -100.319447, -93.4363589, -86.6032825, -79.9563146, -74.3632984, -68.935886, -63.5174757, -57.9514658, -51.4277386, -44.704615, -37.8868996, -31.0793971, -24.3548212, -17.8629043, -11.7212873, -6.04761157, -1.48905451, 2.57809353, 6.24800591, 9.61485598, 13.2341966, 16.5542697, 19.4846971, 21.9351002, 24.3390085, 25.8725726, 26.2358508, 25.1289017, 19.9045551, 13.5489893, 6.70115434, 0., -3.27262161, -6.17782377, -9.13381751, -12.5588139, -19.2366111, -26.2735981, -33.1417511, -39.3130462, -45.8229357, -49.9545293, -50.5544126, -46.4691713, -45.1176209, -33.3452256, -6.56967931, 39.791324, 69.4419812, 144.193951, 284.980784, 512.73603, 831.948853, 1312.88596, 1987.69175, 2922.60026, 4211.28985, 5803.57192, 7685.22462, 9842.0261},
+{-160.880546, -152.368455, -144.741251, -137.82473, -131.444689, -125.426926, -119.597237, -113.78142, -107.805271, -100.690886, -93.3892444, -86.0476237, -78.8133015, -72.4315259, -66.2124162, -60.0640621, -53.8945533, -47.2389595, -40.5275983, -33.8177671, -27.1667634, -20.5733762, -14.1768151, -8.05778129, -2.29697582, 2.75654163, 7.39777206, 11.6533579, 15.5499414, 19.5045633, 22.9973084, 25.8986598, 28.0791008, 29.5664513, 30.0109229, 29.2200637, 27.0014222, 21.3619739, 14.6300691, 7.33348529, 0., -4.81522689, -9.42275327, -14.1057546, -19.1474064, -26.7088395, -34.4440918, -41.8851566, -48.5640273, -54.9673069, -59.290535, -60.683861, -58.2974344, -60.3669104, -53.3227302, -32.6808411, 6.04281005, 38.8819919, 110.151155, 235.714466, 431.436092, 699.736845, 1096.81095, 1654.65389, 2405.26399, 3404.86948, 4612.77606, 6012.52008, 7587.63786},
+{-117.464876, -123.918365, -127.492752, -128.518553, -127.326281, -124.246452, -119.609581, -113.746181, -106.986767, -100.040866, -92.7083752, -85.1682045, -77.5992633, -70.6372629, -63.8215906, -57.1484355, -50.6139865, -44.2722108, -38.038408, -31.8856556, -25.7870314, -19.5202853, -13.3319539, -7.27324596, -1.3953703, 4.18790751, 9.51295815, 14.5535955, 19.2836336, 24.2243411, 28.5830951, 32.1147276, 34.5740706, 35.1779179, 34.4343549, 32.3134286, 28.7851863, 22.7771943, 15.718973, 7.99756168, 0., -6.61155838, -13.2352339, -19.9940327, -27.010961, -35.9903708, -44.8413841, -53.054469, -60.1200932, -64.6781795, -67.4099591, -68.1461179, -66.7173418, -74.5060328, -75.1704745, -63.9206668, -35.9666093, 0.717528466, 68.7915847, 178.151228, 338.692126, 545.47663, 852.90036, 1304.26458, 1880.44809, 2572.04849, 3393.21069, 4352.19278, 5457.25286},
+{-136.527966, -139.159539, -139.607421, -138.121857, -134.953088, -130.351358, -124.566911, -117.849989, -110.450837, -102.93602, -95.112929, -87.1052792, -79.0367843, -71.261443, -63.5805711, -56.0257688, -48.6286365, -41.5501343, -34.6407587, -27.880366, -21.2488126, -14.5876696, -8.07039264, -1.7321522, 4.3918813, 10.3326244, 15.962385, 21.2195577, 26.0425374, 30.7830152, 34.8007711, 37.8688812, 39.7604217, 39.674461, 38.1876865, 35.3027776, 31.0224139, 24.5660901, 17.0329442, 8.73892973, 0., -8.04750415, -16.2361718, -24.5782045, -33.0858038, -42.6581978, -52.0657511, -60.9658549, -69.0159002, -75.50637, -80.6083267, -84.1259248, -85.8633187, -94.7693226, -97.845567, -91.2383424, -71.0939391, -40.7141918, 13.7723711, 99.0816769, 221.929653, 380.179382, 607.105325, 934.522007, 1336.34321, 1800.19873, 2316.75508, 2875.91963, 3467.59973},
+{-194.664249, -181.230941, -169.302868, -158.648225, -149.035212, -140.232023, -132.006856, -124.127907, -116.363375, -107.812862, -99.1805959, -90.502209, -81.8133354, -73.2086007, -64.6410495, -56.1227188, -47.6656453, -39.1592333, -30.7872051, -22.6106505, -14.6906592, -7.17655082, -0.00589349249, 6.79551487, 13.2018764, 19.3079585, 24.9191718, 29.9614923, 34.3608958, 38.1894679, 41.1686312, 43.1659177, 44.0488595, 43.4935761, 41.6355773, 38.4189602, 33.7878219, 26.7947351, 18.6319311, 9.6001171, 0., -9.24386883, -18.7041645, -28.3297179, -38.0693597, -47.9114983, -57.7495558, -67.516532, -77.1454268, -88.0404396, -98.0748906, -106.593299, -112.940186, -120.019097, -122.191915, -117.379548, -103.502907, -87.2876613, -54.3280535, 0.976913021, 84.2282345, 202.753802, 356.973927, 552.751261, 786.612743, 1083.52895, 1364.03162, 1574.7622, 1662.36213},
+{-175.36164, -166.624748, -158.159801, -149.925768, -141.881618, -133.986319, -126.198841, -118.478152, -110.783222, -103.030633, -95.2386948, -87.3833331, -79.440472, -71.2174429, -62.9261997, -54.6101037, -46.3125163, -38.121428, -30.017719, -22.0268988, -14.1744769, -6.30376836, 1.30464509, 8.55237609, 15.3410373, 21.2894899, 26.6951987, 31.5728771, 35.9372383, 40.4691856, 44.2507664, 47.0302182, 48.5557784, 48.0057096, 45.9262139, 42.2935185, 37.0838506, 29.5326914, 20.6533127, 10.7182403, 0., -10.8380537, -22.0705555, -33.5813111, -45.2541263, -57.0379543, -68.7253946, -80.1741938, -91.2420989, -101.801961, -111.69038, -120.759063, -128.859713, -138.865711, -146.398417, -150.100866, -148.616093, -144.359406, -130.692659, -104.749978, -63.6654913, -2.1174713, 75.3923952, 179.345261, 277.973065, 352.592929, 374.43045, 317.234105, 154.752373},
+{-191.788584, -182.390037, -173.740918, -165.639879, -157.885566, -150.276631, -142.611723, -134.68949, -126.308584, -116.144987, -105.569081, -94.8285798, -84.1712001, -74.6575672, -65.3973217, -56.3130147, -47.3271972, -37.9729249, -28.7180425, -19.6408993, -10.8198446, -2.39999017, 5.63378214, 13.2298281, 20.3365033, 26.8791912, 32.8384087, 38.1717007, 42.8366119, 47.2220462, 50.6816452, 53.00041, 53.9633413, 52.8498506, 50.1527642, 45.859319, 39.9567519, 31.9102235, 22.4378773, 11.7357803, 0., -12.5765892, -25.7934503, -39.453239, -53.3586108, -66.8576235, -80.38937, -93.9383452, -107.489044, -121.262378, -134.911858, -148.327413, -161.398972, -174.938597, -187.545228, -198.739941, -208.043809, -213.510736, -216.715838, -217.767058, -216.77234, -208.338342, -209.076867, -219.416934, -264.909434, -355.793203, -538.433422, -850.163683, -1328.31758},
+{-198.71236, -197.308699, -193.101836, -186.510063, -177.951671, -167.844951, -156.608195, -144.659693, -132.417739, -121.285996, -110.303233, -99.4935919, -88.8812147, -78.707498, -68.6924271, -58.7732421, -48.8871829, -38.459504, -28.1442253, -18.0833812, -8.41900594, 0.229792022, 8.38888204, 16.1070594, 23.4331194, 30.88596, 37.8562326, 44.2046916, 49.7920911, 54.7738453, 58.5981843, 61.0079983, 61.7461775, 59.6423142, 55.7179154, 50.0811906, 42.840349, 34.2000096, 24.1334081, 12.7101898, 0., -14.5670711, -30.0260009, -46.0513217, -62.3175661, -77.5333094, -92.7254243, -107.954826, -123.28243, -138.151262, -153.487283, -169.598565, -186.793178, -205.872273, -226.45361, -248.648032, -272.566377, -292.582224, -316.83858, -347.741193, -387.695808, -434.404278, -504.384028, -598.974796, -746.35905, -974.171705, -1285.39517, -1689.17496, -2194.65663}
+};
+
+ const double a5tab[50][69] = {
+{4296.48547, 4145.14906, 4028.39347, 3938.25617, 3866.77463, 3805.98633, 3747.92872, 3684.63929, 3608.15549, 3470.8602, 3320.30733, 3164.39619, 3011.02609, 2895.53131, 2787.40219, 2683.56406, 2580.94224, 2467.08826, 2352.05074, 2236.50453, 2121.12447, 2008.42576, 1896.50673, 1785.30605, 1674.76241, 1564.89358, 1455.52754, 1346.57134, 1237.93205, 1128.57981, 1019.73336, 911.67453, 804.685139, 699.870801, 596.360042, 494.10517, 393.058497, 293.389367, 194.746242, 96.9946212, 0., -95.8821865, -191.472354, -287.100981, -383.098545, -476.415091, -572.113704, -671.877035, -777.387735, -883.098866, -1000.81451, -1135.10914, -1290.55726, -1445.5122, -1641.25806, -1892.85779, -2215.37433, -2550.46591, -3015.96209, -3656.28769, -4515.86756, -5562.5241, -7070.48939, -8999.14401, -12015.737, -15367.8837, -23273.8659, -38709.2987, -64649.7973},
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+{177.272638, 176.171898, 172.67048, 167.127495, 159.902055, 151.353269, 141.840249, 131.722107, 121.357952, 111.932907, 102.649669, 93.5369434, 84.6234388, 76.1690857, 67.8788777, 59.6890322, 51.5357667, 42.9013283, 34.3574928, 26.0220658, 18.0128529, 10.8353733, 4.06463329, -2.336647, -8.40574756, -14.5091726, -20.223288, -25.4536843, -30.1059515, -34.3111544, -37.6592191, -39.965546, -41.0455356, -40.0655795, -37.7496906, -34.1728732, -29.4101313, -23.5468726, -16.6435361, -8.77096437, 0., 10.1187145, 20.7860564, 31.7231031, 42.6509319, 52.6140477, 62.2807294, 71.6426832, 80.6916156, 89.0636486, 97.2483064, 105.379529, 113.591258, 122.654121, 131.810694, 140.94024, 149.922024, 154.37936, 160.149841, 168.815111, 181.956813, 197.339586, 227.99609, 274.768336, 359.778501, 504.715443, 711.721124, 987.824231, 1340.05345}
+};
+
+ /* Stuff for interpolating the NQC data */
+ gsl_spline *spline = NULL;
+ gsl_interp_accel *acc = NULL;
+ /* Interpolate the spin NQC data in 2-D parameter space -- spin and mass ratio */
+ /* First, interpolate in spin dimension for all mass ratios */
+ spline = gsl_spline_alloc( gsl_interp_cspline, adim );
+ acc = gsl_interp_accel_alloc();
+ for (i = 0; i < qdim; i++)
+ {
+ gsl_spline_init( spline, alist, a3stab[i], adim );
+ gsl_interp_accel_reset( acc );
+ a3slist[i] = gsl_spline_eval( spline, a/(1.0-2.0*eta), acc );
+ gsl_spline_init( spline, alist, a4tab[i], adim );
+ gsl_interp_accel_reset( acc );
+ a4list[i] = gsl_spline_eval( spline, a/(1.0-2.0*eta), acc );
+ gsl_spline_init( spline, alist, a5tab[i], adim );
+ gsl_interp_accel_reset( acc );
+ a5list[i] = gsl_spline_eval( spline, a/(1.0-2.0*eta), acc );
+//printf("%.15f\n",a3slist[i]);
+ }
+//printf("%.15f\n",a);
+ gsl_spline_free(spline);
+ gsl_interp_accel_free(acc);
+ /* Second, interpolate in mass ratio dimension */
+ spline = gsl_spline_alloc( gsl_interp_cspline, qdim );
+ acc = gsl_interp_accel_alloc();
+ gsl_spline_init( spline, etalist, a3slist, qdim );
+ gsl_interp_accel_reset( acc );
+ coeffs->a3S = gsl_spline_eval( spline, eta, acc );
+ gsl_spline_init( spline, etalist, a4list, qdim );
+ gsl_interp_accel_reset( acc );
+ coeffs->a4 = gsl_spline_eval( spline, eta, acc );
+ gsl_spline_init( spline, etalist, a5list, qdim );
+ gsl_interp_accel_reset( acc );
+ coeffs->a5 = gsl_spline_eval( spline, eta, acc );
+ gsl_spline_free(spline);
+ gsl_interp_accel_free(acc);
+
+ /* Interpolate nonspin NQC data in the mass ratio dimension */
+ spline = gsl_spline_alloc( gsl_interp_cspline, nsqdim );
+ acc = gsl_interp_accel_alloc();
+ gsl_spline_init( spline, nsetalist, a1list, nsqdim );
+ gsl_interp_accel_reset( acc );
+ coeffs->a1 = gsl_spline_eval( spline, eta, acc );
+ gsl_spline_init( spline, nsetalist, a2list, nsqdim );
+ gsl_interp_accel_reset( acc );
+ coeffs->a2 = gsl_spline_eval( spline, eta, acc );
+ gsl_spline_init( spline, nsetalist, a3list, nsqdim );
+ gsl_interp_accel_reset( acc );
+ coeffs->a3 = gsl_spline_eval( spline, eta, acc );
+ gsl_spline_init( spline, nsetalist, b1list, nsqdim );
+ gsl_interp_accel_reset( acc );
+ coeffs->b1 = gsl_spline_eval( spline, eta, acc );
+ gsl_spline_init( spline, nsetalist, b2list, nsqdim );
+ gsl_interp_accel_reset( acc );
+ coeffs->b2 = gsl_spline_eval( spline, eta, acc );
+ gsl_spline_free(spline);
+ gsl_interp_accel_free(acc);
+ /* Andrea and I have different sign conventions, so I need to put a minus sign in front */
+ coeffs->b1 = - coeffs->b1;
+ coeffs->b2 = - coeffs->b2;
+ /*coeffs->a1 = -6.292993135543338;
+ coeffs->a2 = 40.26795686019975;
+ coeffs->a3 = -39.29214347590138;
+ coeffs->a3S= 226.3844538692294;
+ coeffs->a4 = -747.9690610155075;
+ coeffs->a5 = 623.9090070111784;
+ coeffs->b1 = 0.7467610798775989;
+ coeffs->b2 = -2.159938635119833;
+ */
+ /* Obsolete polynomial fitting of nonspin NQC coefficients a1, a2, a3, b1 and b2 */
+ /*
+ coeffs->a1 = -12.67955358602124 + 75.41927959573084 * eta - 106.15933052937714 * eta2;
+ coeffs->a2 = 101.45522216901628 - 757.3158549733314 * eta + 1473.314771676588 * eta2;
+ coeffs->a3 = -107.6647834845902 + 857.6219519536213 * eta - 1776.2776804623143 * eta2;
+ // Andrea and I have different sign conventions, so I need to put a minus sign in front
+ coeffs->b1 = - (-1.464129495621165 + 12.81732978488213 * eta - 60.09957767247623 * eta2);
+ coeffs->b2 = - ( 7.477426352542122 - 85.26122117590637 * eta + 353.3251639728075 * eta2);
+ */
+
+ return XLAL_SUCCESS;
+
+}
+
+
+ int XLALSimIMRSpinEOBCalculateNQCCoefficients(
+ REAL8Vector *amplitude, /**<< Waveform amplitude, func of time */
+ REAL8Vector *phase, /**<< Waveform phase(rad), func of time */
+ REAL8Vector *rVec, /**<< Position-vector, function of time */
+ REAL8Vector *prVec, /**<< Momentum vector, function of time */
+ REAL8Vector *orbOmegaVec, /**<< Orbital frequency, func of time */
+ INT4 l, /**<< Mode index l */
+ INT4 m, /**<< Mode index m */
+ REAL8 timePeak, /**<< Time of peak orbital frequency */
+ REAL8 deltaT, /**<< Sampling interval */
+ REAL8 eta, /**<< Symmetric mass ratio */
+ REAL8 a, /**<< Normalized spin of deformed-Kerr */
+ EOBNonQCCoeffs *coeffs /**<< OUTPUT, NQC coefficients */)
+{
+
+ /* For gsl permutation stuff */
+
+ int signum;
+
+ REAL8Vector *timeVec = NULL;
+
+ /* Vectors which are used in the computation of the NQC coefficients */
+ REAL8Vector *q3 = NULL, *q4 = NULL, *q5 = NULL;
+ REAL8Vector *p3 = NULL, *p4 = NULL;
+
+ REAL8Vector *qNS = NULL, *pNS = NULL;
+
+ /* Since the vectors we actually want are q etc * A, we will have to generate them here */
+ REAL8Vector *q3LM = NULL;
+ REAL8Vector *q4LM = NULL;
+ REAL8Vector *q5LM = NULL;
+ REAL8Vector *qNSLM = NULL;
+
+ REAL8 amp, aDot, aDDot;
+ REAL8 omega, omegaDot;
+
+ REAL8 qNSLMPeak, qNSLMDot, qNSLMDDot;
+ REAL8 pNSLMDot, pNSLMDDot;
+
+ REAL8 nra, nraDDot;
+ REAL8 nromega, nromegaDot;
+
+ REAL8 nrDeltaT, nrTimePeak;
+
+ /* Stuff for finding numerical derivatives */
+ gsl_spline *spline = NULL;
+ gsl_interp_accel *acc = NULL;
+
+ /* Matrix stuff for calculating coefficients */
+ gsl_matrix *qMatrix = NULL, *pMatrix = NULL;
+ gsl_vector *aCoeff = NULL, *bCoeff = NULL;
+
+ gsl_vector *amps = NULL, *omegaVec = NULL;
+
+ gsl_permutation *perm1 = NULL, *perm2 = NULL;
+
+ memset( coeffs, 0, sizeof( EOBNonQCCoeffs ) );
+
+ /* Populate the time vector */
+ /* It is okay to assume initial t = 0 */
+ timeVec = XLALCreateREAL8Vector( rVec->length );
+ q3 = XLALCreateREAL8Vector( rVec->length );
+ q4 = XLALCreateREAL8Vector( rVec->length );
+ q5 = XLALCreateREAL8Vector( rVec->length );
+ p3 = XLALCreateREAL8Vector( rVec->length );
+ p4 = XLALCreateREAL8Vector( rVec->length );
+ qNS = XLALCreateREAL8Vector( rVec->length );
+ pNS = XLALCreateREAL8Vector( rVec->length );
+ q3LM = XLALCreateREAL8Vector( rVec->length );
+ q4LM = XLALCreateREAL8Vector( rVec->length );
+ q5LM = XLALCreateREAL8Vector( rVec->length );
+ qNSLM = XLALCreateREAL8Vector( rVec->length );
+
+ if ( !timeVec || !q3 || !q4 || !q5 || !p3 || !p4 || !qNS || !pNS || !q3LM
+ || !q4LM || !q5LM || !qNSLM )
+ {
+ XLALDestroyREAL8Vector( timeVec );
+ XLALDestroyREAL8Vector( q3 );
+ XLALDestroyREAL8Vector( q4 );
+ XLALDestroyREAL8Vector( q5 );
+ XLALDestroyREAL8Vector( p3 );
+ XLALDestroyREAL8Vector( p4 );
+ XLALDestroyREAL8Vector( qNS );
+ XLALDestroyREAL8Vector( pNS );
+ XLALDestroyREAL8Vector( q3LM );
+ XLALDestroyREAL8Vector( q4LM );
+ XLALDestroyREAL8Vector( q5LM );
+ XLALDestroyREAL8Vector( qNSLM );
+ fprintf(stderr,"Error(%d)",XLAL_EFUNC );
+ }
+
+ /* We need the calibrated non-spinning NQC coefficients */
+ if ( XLALSimIMRGetEOBCalibratedSpinNQC( coeffs, l, m, eta, a ) == XLAL_FAILURE )
+ {
+ XLALDestroyREAL8Vector( timeVec );
+ XLALDestroyREAL8Vector( q3 );
+ XLALDestroyREAL8Vector( q4 );
+ XLALDestroyREAL8Vector( q5 );
+ XLALDestroyREAL8Vector( p3 );
+ XLALDestroyREAL8Vector( p4 );
+ XLALDestroyREAL8Vector( qNS );
+ XLALDestroyREAL8Vector( pNS );
+ XLALDestroyREAL8Vector( q3LM );
+ XLALDestroyREAL8Vector( q4LM );
+ XLALDestroyREAL8Vector( q5LM );
+ XLALDestroyREAL8Vector( qNSLM );
+ fprintf(stderr,"Error(%d)",XLAL_EFUNC );
+ }
+
+ /* Populate vectors as necessary. Eqs. 14 - 17 of the LIGO DCC document T1100433v2 */
+ unsigned int i;
+ for ( i = 0; i < timeVec->length; i++ )
+ {
+
+ REAL8 rootR = sqrt(rVec->data[i]);
+ REAL8 rOmega = rVec->data[i] * orbOmegaVec->data[i];
+
+ /* We don't need these as vectors as their coefficients are calibrated */
+ REAL8 q1, q2, p1, p2;
+
+ timeVec->data[i] = i * deltaT;
+ q1 = prVec->data[i]*prVec->data[i] / (rOmega*rOmega);
+ q2 = q1 / rVec->data[i];
+ q3->data[i] = q2 / rootR;
+ q4->data[i] = q2 / rVec->data[i];
+ q5->data[i] = q3->data[i] / rVec->data[i];
+
+ p1 = prVec->data[i] / rOmega;
+ p2 = p1 * prVec->data[i] * prVec->data[i];
+ p3->data[i] = p2 / rootR;
+ p4->data[i] = p2 / rVec->data[i];
+
+ qNS->data[i] = coeffs->a1 * q1 + coeffs->a2 * q2 + coeffs->a3 * q3->data[i];
+ pNS->data[i] = coeffs->b1 * p1 + coeffs->b2 * p2;
+ q3LM->data[i] = q3->data[i] * amplitude->data[i];
+ q4LM->data[i] = q4->data[i] * amplitude->data[i];
+ q5LM->data[i] = q5->data[i] * amplitude->data[i];
+
+ qNSLM->data[i] = qNS->data[i] * amplitude->data[i];
+ }
+
+ /* Allocate all the memory we need */
+ //XLAL_CALLGSL(
+ /* a stuff */
+ qMatrix = gsl_matrix_alloc( 3, 3 );
+ aCoeff = gsl_vector_alloc( 3 );
+ amps = gsl_vector_alloc( 3 );
+ perm1 = gsl_permutation_alloc( 3 );
+
+ /* b stuff */
+ pMatrix = gsl_matrix_alloc( 2, 2 );
+ bCoeff = gsl_vector_alloc( 2 );
+ omegaVec = gsl_vector_alloc( 2 );
+ perm2 = gsl_permutation_alloc( 2 );
+ //);
+
+ if ( !qMatrix || !aCoeff || !amps || !pMatrix || !bCoeff || !omegaVec )
+ {
+ XLALDestroyREAL8Vector( timeVec );
+ XLALDestroyREAL8Vector( q3 );
+ XLALDestroyREAL8Vector( q4 );
+ XLALDestroyREAL8Vector( q5 );
+ XLALDestroyREAL8Vector( p3 );
+ XLALDestroyREAL8Vector( p4 );
+ XLALDestroyREAL8Vector( qNS );
+ XLALDestroyREAL8Vector( pNS );
+ XLALDestroyREAL8Vector( q3LM );
+ XLALDestroyREAL8Vector( q4LM );
+ XLALDestroyREAL8Vector( q5LM );
+ XLALDestroyREAL8Vector( qNSLM );
+ fprintf(stderr,"Error(%d)",XLAL_EFUNC );
+ }
+
+ /* The time we want to take as the peak time depends on l and m */
+ /* Calculate the adjustment we need to make here */
+ nrDeltaT = XLALSimIMREOBGetNRSpinPeakDeltaT( l, m, eta, a );
+#if debugOutput
+ fprintf(stderr, "DEBUG:nrDeltaT=%f\n", nrDeltaT);
+#endif
+ if ( XLAL_IS_REAL8_FAIL_NAN( nrDeltaT ) )
+ {
+ XLALDestroyREAL8Vector( timeVec );
+ XLALDestroyREAL8Vector( q3 );
+ XLALDestroyREAL8Vector( q4 );
+ XLALDestroyREAL8Vector( q5 );
+ XLALDestroyREAL8Vector( p3 );
+ XLALDestroyREAL8Vector( p4 );
+ XLALDestroyREAL8Vector( qNS );
+ XLALDestroyREAL8Vector( pNS );
+ XLALDestroyREAL8Vector( q3LM );
+ XLALDestroyREAL8Vector( q4LM );
+ XLALDestroyREAL8Vector( q5LM );
+ XLALDestroyREAL8Vector( qNSLM );
+ fprintf(stderr,"Error(%d)",XLAL_EFUNC );
+ }
+
+ /* nrDeltaT defined in XLALSimIMREOBGetNRSpinPeakDeltaT is a minus sign different from Eq. (33) of Taracchini et al.
+ * Therefore, the plus sign in Eq. (21) of Taracchini et al and Eq. (18) of DCC document T1100433v2 is
+ * changed to a minus sign here.
+ */
+ nrTimePeak = timePeak - nrDeltaT;
+#if debugOutput
+ fprintf(stderr, "DEBUG:nrTimePeak=%f\n", nrTimePeak);
+#endif
+ /* We are now in a position to use the interp stuff to calculate the derivatives we need */
+ /* We will start with the quantities used in the calculation of the a coefficients */
+ spline = gsl_spline_alloc( gsl_interp_cspline, amplitude->length );
+ acc = gsl_interp_accel_alloc();
+
+ /* Populate the Q matrix in Eq. 18 of the LIGO DCC document T1100433v2 */
+ /* Q3 */
+ gsl_spline_init( spline, timeVec->data, q3LM->data, q3LM->length );
+ gsl_matrix_set( qMatrix, 0, 0, gsl_spline_eval( spline, nrTimePeak, acc ) );
+ gsl_matrix_set( qMatrix, 1, 0, gsl_spline_eval_deriv( spline, nrTimePeak, acc ) );
+ gsl_matrix_set( qMatrix, 2, 0, gsl_spline_eval_deriv2( spline, nrTimePeak, acc ) );
+
+ /* Q4 */
+ gsl_spline_init( spline, timeVec->data, q4LM->data, q4LM->length );
+ gsl_interp_accel_reset( acc );
+ gsl_matrix_set( qMatrix, 0, 1, gsl_spline_eval( spline, nrTimePeak, acc ) );
+ gsl_matrix_set( qMatrix, 1, 1, gsl_spline_eval_deriv( spline, nrTimePeak, acc ) );
+ gsl_matrix_set( qMatrix, 2, 1, gsl_spline_eval_deriv2( spline, nrTimePeak, acc ) );
+
+ /* Q5 */
+ gsl_spline_init( spline, timeVec->data, q5LM->data, q5LM->length );
+ gsl_interp_accel_reset( acc );
+ gsl_matrix_set( qMatrix, 0, 2, gsl_spline_eval( spline, nrTimePeak, acc ) );
+ gsl_matrix_set( qMatrix, 1, 2, gsl_spline_eval_deriv( spline, nrTimePeak, acc ) );
+ gsl_matrix_set( qMatrix, 2, 2, gsl_spline_eval_deriv2( spline, nrTimePeak, acc ) );
+
+ /* Populate the r.h.s vector of Eq. 18 of the LIGO DCC document T1100433v2 */
+ /* Amplitude */
+ gsl_spline_init( spline, timeVec->data, amplitude->data, amplitude->length );
+ gsl_interp_accel_reset( acc );
+ amp = gsl_spline_eval( spline, nrTimePeak, acc );
+ aDot = gsl_spline_eval_deriv( spline, nrTimePeak, acc );
+ aDDot = gsl_spline_eval_deriv2( spline, nrTimePeak, acc );
+
+ /* qNSLM */
+ gsl_spline_init( spline, timeVec->data, qNSLM->data, qNSLM->length );
+ gsl_interp_accel_reset( acc );
+ qNSLMPeak = gsl_spline_eval( spline, nrTimePeak, acc );
+ qNSLMDot = gsl_spline_eval_deriv( spline, nrTimePeak, acc );
+ qNSLMDDot = gsl_spline_eval_deriv2( spline, nrTimePeak, acc );
+
+ nra = GetNRSpinPeakAmplitude( l, m, eta, a );
+ nraDDot = - GetNRSpinPeakADDot( l, m, eta, a );
+
+ if ( XLAL_IS_REAL8_FAIL_NAN( nra ) || XLAL_IS_REAL8_FAIL_NAN( nraDDot ) )
+ {
+ XLALDestroyREAL8Vector( timeVec );
+ XLALDestroyREAL8Vector( q3 );
+ XLALDestroyREAL8Vector( q4 );
+ XLALDestroyREAL8Vector( q5 );
+ XLALDestroyREAL8Vector( p3 );
+ XLALDestroyREAL8Vector( p4 );
+ XLALDestroyREAL8Vector( qNS );
+ XLALDestroyREAL8Vector( pNS );
+ XLALDestroyREAL8Vector( q3LM );
+ XLALDestroyREAL8Vector( q4LM );
+ XLALDestroyREAL8Vector( q5LM );
+ XLALDestroyREAL8Vector( qNSLM );
+ fprintf(stderr,"Error(%d)",XLAL_EFUNC );
+ }
+
+ gsl_vector_set( amps, 0, nra - amp - qNSLMPeak );
+ gsl_vector_set( amps, 1, - aDot - qNSLMDot );
+ gsl_vector_set( amps, 2, nraDDot - aDDot - qNSLMDDot );
+
+ /* We have now set up all the stuff to calculate the a coefficients */
+ /* So let us do it! */
+ gsl_linalg_LU_decomp( qMatrix, perm1, &signum );
+ gsl_linalg_LU_solve( qMatrix, perm1, amps, aCoeff );
+
+ /* Now we (should) have calculated the a values. Now we can do the b values */
+
+ /* Populate the P matrix in Eq. 18 of the LIGO DCC document T1100433v2 */
+ /* P3 */
+ gsl_spline_init( spline, timeVec->data, p3->data, p3->length );
+ gsl_interp_accel_reset( acc );
+ gsl_matrix_set( pMatrix, 0, 0, - gsl_spline_eval_deriv( spline, nrTimePeak, acc ) );
+ gsl_matrix_set( pMatrix, 1, 0, - gsl_spline_eval_deriv2( spline, nrTimePeak, acc ) );
+
+ /* P4 */
+ gsl_spline_init( spline, timeVec->data, p4->data, p4->length );
+ gsl_interp_accel_reset( acc );
+ gsl_matrix_set( pMatrix, 0, 1, - gsl_spline_eval_deriv( spline, nrTimePeak, acc ) );
+ gsl_matrix_set( pMatrix, 1, 1, - gsl_spline_eval_deriv2( spline, nrTimePeak, acc ) );
+
+ /* Populate the r.h.s vector of Eq. 18 of the LIGO DCC document T1100433v2 */
+ /* Phase */
+ gsl_spline_init( spline, timeVec->data, phase->data, phase->length );
+ gsl_interp_accel_reset( acc );
+ omega = gsl_spline_eval_deriv( spline, nrTimePeak, acc );
+ omegaDot = gsl_spline_eval_deriv2( spline, nrTimePeak, acc );
+
+ /* pNSLM */
+ gsl_spline_init( spline, timeVec->data, pNS->data, pNS->length );
+ gsl_interp_accel_reset( acc );
+ pNSLMDot = gsl_spline_eval_deriv( spline, nrTimePeak, acc );
+ pNSLMDDot = gsl_spline_eval_deriv2( spline, nrTimePeak, acc );
+
+ /* Since the phase can be decreasing, we need to take care not to have a -ve frequency */
+ if ( omega * omegaDot > 0.0 )
+ {
+ omega = fabs( omega );
+ omegaDot = fabs( omegaDot );
+ }
+ else
+ {
+ omega = fabs( omega );
+ omegaDot = - fabs( omegaDot );
+ }
+
+ //nromega = GetNRPeakOmega( l, m, eta );
+ //nromegaDot = GetNRPeakOmegaDot( l, m, eta );
+ nromega = GetNRSpinPeakOmega( l, m, eta, a );
+ nromegaDot = GetNRSpinPeakOmegaDot( l, m, eta, a );
+
+ //printf("NR inputs: %.16e, %.16e, %.16e, %.16e\n",nra,nraDDot,nromega,nromegaDot);
+
+ if ( XLAL_IS_REAL8_FAIL_NAN( nromega ) || XLAL_IS_REAL8_FAIL_NAN( nromegaDot ) )
+ {
+ XLALDestroyREAL8Vector( timeVec );
+ XLALDestroyREAL8Vector( q3 );
+ XLALDestroyREAL8Vector( q4 );
+ XLALDestroyREAL8Vector( q5 );
+ XLALDestroyREAL8Vector( p3 );
+ XLALDestroyREAL8Vector( p4 );
+ XLALDestroyREAL8Vector( qNS );
+ XLALDestroyREAL8Vector( pNS );
+ XLALDestroyREAL8Vector( q3LM );
+ XLALDestroyREAL8Vector( q4LM );
+ XLALDestroyREAL8Vector( q5LM );
+ XLALDestroyREAL8Vector( qNSLM );
+ fprintf(stderr,"Error(%d)",XLAL_EFUNC );
+ }
+
+ gsl_vector_set( omegaVec, 0, nromega - omega + pNSLMDot );
+ gsl_vector_set( omegaVec, 1, nromegaDot - omegaDot + pNSLMDDot );
+
+ /*printf( "P MATRIX\n" );
+ for (unsigned int i = 0; i < 2; i++ )
+ {
+ for (unsigned int j = 0; j < 2; j++ )
+ {
+ printf( "%.12e\t", gsl_matrix_get( pMatrix, i, j ));
+ }
+ printf( "= %.12e\n", gsl_vector_get( omegaVec, i ) );
+ }*/
+
+ /* And now solve for the b coefficients */
+ gsl_linalg_LU_decomp( pMatrix, perm2, &signum );
+ gsl_linalg_LU_solve( pMatrix, perm2, omegaVec, bCoeff );
+
+ /* We can now populate the coefficients structure */
+/* coeffs->a3S = gsl_vector_get( aCoeff, 0 );
+ coeffs->a4 = gsl_vector_get( aCoeff, 1 );
+ coeffs->a5 = gsl_vector_get( aCoeff, 2 );*/
+ coeffs->b3 = gsl_vector_get( bCoeff, 0 );
+ coeffs->b4 = gsl_vector_get( bCoeff, 1 );
+
+ /*printf( "NQC coefficients:\n" );
+ printf( "a1 = %.16e, a2 = %.16e, a3 = %.16e, a3s = %.16e, a4 = %.16e, a5 = %.16e\n",
+ coeffs->a1, coeffs->a2, coeffs->a3, coeffs->a3S, coeffs->a4, coeffs->a5 );
+
+ printf( "b1 = %.16e, b2 = %.16e, b3 = %.16e, b4 = %.16e\n",
+ coeffs->b1, coeffs->b2, coeffs->b3, coeffs->b4 );*/
+
+ /* Free memory and exit */
+ gsl_matrix_free( qMatrix );
+ gsl_vector_free( amps );
+ gsl_vector_free( aCoeff );
+ gsl_permutation_free( perm1 );
+
+ gsl_matrix_free( pMatrix );
+ gsl_vector_free( omegaVec );
+ gsl_vector_free( bCoeff );
+ gsl_permutation_free( perm2 );
+
+ gsl_spline_free( spline );
+ gsl_interp_accel_free( acc );
+
+ XLALDestroyREAL8Vector( timeVec );
+ XLALDestroyREAL8Vector( q3 );
+ XLALDestroyREAL8Vector( q4 );
+ XLALDestroyREAL8Vector( q5 );
+ XLALDestroyREAL8Vector( p3 );
+ XLALDestroyREAL8Vector( p4 );
+ XLALDestroyREAL8Vector( qNS );
+ XLALDestroyREAL8Vector( pNS );
+ XLALDestroyREAL8Vector( q3LM );
+ XLALDestroyREAL8Vector( q4LM );
+ XLALDestroyREAL8Vector( q5LM );
+ XLALDestroyREAL8Vector( qNSLM );
+
+ return XLAL_SUCCESS;
+}
+
+ int XLALSimIMREOBNonQCCorrection(
+ COMPLEX16 *nqc, /**<< OUTPUT, The NQC correction */
+ REAL8Vector *values, /**<< Dynamics r, phi, pr, pphi */
+ const REAL8 omega, /**<< Angular frequency */
+ EOBNonQCCoeffs *coeffs /**<< NQC coefficients */
+ )
+
+{
+
+ REAL8 rOmega, rOmegaSq;
+ REAL8 r, p, sqrtR;
+
+ REAL8 mag, phase;
+
+
+ r = values->data[0];
+ p = values->data[2];
+
+ sqrtR = sqrt(r);
+
+ rOmega = r * omega;
+ rOmegaSq = rOmega*rOmega;
+
+ /* In EOBNRv2, coeffs->a3S, coeffs->a4 and coeffs->a5 are set to zero */
+ /* through XLALSimIMREOBGetCalibratedNQCCoeffs() */
+ /* and XLALSimIMREOBCalculateNQCCoefficients() */
+ mag = 1. + (p*p / rOmegaSq) * ( coeffs->a1
+ + coeffs->a2 / r + ( coeffs->a3 + coeffs->a3S) / (r*sqrtR)
+ + coeffs->a4 / (r*r) + coeffs->a5 / (r*r*sqrtR));
+
+ phase = coeffs->b1 * p / rOmega + p*p*p/rOmega * ( coeffs->b2
+ + coeffs->b3 / sqrtR + coeffs->b4 / r );
+
+ *nqc = mag * cos(phase);
+ *nqc += I * mag * sin(phase);
+
+ return XLAL_SUCCESS;
+
+}
+/**
+ * Function which calculates the value of the waveform, plus its
+ * first and second derivatives, for the points which will be required
+ * in the hybrid comb attachment of the ringdown.
+ */
+ INT4 XLALGenerateHybridWaveDerivatives (
+ REAL8Vector *rwave, /**<< OUTPUT, values of the waveform at comb points */
+ REAL8Vector *dwave, /**<< OUTPUT, 1st deriv of the waveform at comb points */
+ REAL8Vector *ddwave, /**<< OUTPUT, 2nd deriv of the waveform at comb points */
+ REAL8Vector *timeVec, /**<< Vector containing the time */
+ REAL8Vector *wave, /**<< Last part of inspiral waveform */
+ REAL8Vector *matchrange, /**<< Times which determine the size of the comb */
+ REAL8 dt, /**<< Sample time step */
+ REAL8 mass1, /**<< First component mass (in Solar masses) */
+ REAL8 mass2 /**<< Second component mass (in Solar masses) */
+ )
+{
+
+ /* XLAL error handling */
+ INT4 errcode = XLAL_SUCCESS;
+
+ /* For checking GSL return codes */
+ INT4 gslStatus;
+
+ UINT4 j;
+ UINT4 vecLength;
+ REAL8 m;
+ double *y;
+ double ry, dy, dy2;
+ double rt;
+ double *tlist;
+ gsl_interp_accel *acc;
+ gsl_spline *spline;
+
+ /* Total mass in geometric units */
+ m = (mass1 + mass2) * LAL_MTSUN_SI;
+
+ tlist = (double *) malloc(6 * sizeof(double));
+ rt = (matchrange->data[1] - matchrange->data[0]) / 5.;
+ tlist[0] = matchrange->data[0];
+ tlist[1] = tlist[0] + rt;
+ tlist[2] = tlist[1] + rt;
+ tlist[3] = tlist[2] + rt;
+ tlist[4] = tlist[3] + rt;
+ tlist[5] = matchrange->data[1];
+
+ /* Set the length of the interpolation vectors */
+ vecLength = (UINT4)( m * matchrange->data[2] / dt ) + 1;
+
+ /* Getting interpolation and derivatives of the waveform using gsl spline routine */
+ /* Initiate arrays and supporting variables for gsl */
+ y = (double *) malloc(vecLength * sizeof(double));
+
+ if ( !y )
+ {
+ fprintf(stderr,"Error!(%d)" ,XLAL_ENOMEM );
+ }
+
+ for (j = 0; j < vecLength; ++j)
+ {
+ y[j] = wave->data[j];
+ }
+
+
+ //XLAL_CALLGSL( acc = (gsl_interp_accel*) gsl_interp_accel_alloc() );
+ acc = (gsl_interp_accel*) gsl_interp_accel_alloc();
+ //XLAL_CALLGSL( spline = (gsl_spline*) gsl_spline_alloc(gsl_interp_cspline, vecLength) );
+ spline = (gsl_spline*) gsl_spline_alloc(gsl_interp_cspline, vecLength);
+ if ( !acc || !spline )
+ {
+ if ( acc ) gsl_interp_accel_free(acc);
+ if ( spline ) gsl_spline_free(spline);
+ LALFree( y );
+ fprintf(stderr,"Error!(%d)" ,XLAL_ENOMEM );
+ }
+
+ /* Gall gsl spline interpolation */
+ gslStatus = gsl_spline_init(spline, timeVec->data, y, vecLength);
+ if ( gslStatus != GSL_SUCCESS )
+ {
+ gsl_spline_free(spline);
+ gsl_interp_accel_free(acc);
+ LALFree( y );
+
+ fprintf(stderr,"Error!(%d)" ,XLAL_EFUNC );
+ }
+
+ /* Getting first and second order time derivatives from gsl interpolations */
+ for (j = 0; j < 6; ++j)
+ {
+ gslStatus = gsl_spline_eval_e( spline, tlist[j], acc, &ry );
+ if ( gslStatus == GSL_SUCCESS )
+ {
+ gslStatus = gsl_spline_eval_deriv_e(spline, tlist[j], acc, &dy );
+ gslStatus = gsl_spline_eval_deriv2_e(spline, tlist[j], acc, &dy2 );
+ }
+ if (gslStatus != GSL_SUCCESS )
+ {
+ gsl_spline_free(spline);
+ gsl_interp_accel_free(acc);
+ LALFree( y );
+ fprintf(stderr,"Error!(%d)" ,XLAL_EFUNC );
+ }
+ rwave->data[j] = (REAL8)(ry);
+ dwave->data[j] = (REAL8)(dy/m);
+ ddwave->data[j] = (REAL8)(dy2/m/m);
+
+ }
+
+ /* Free gsl variables */
+ gsl_spline_free(spline);
+ gsl_interp_accel_free(acc);
+ LALFree( tlist );
+ LALFree(y);
+
+ return errcode;
+}
+
+
+/**
+ * Computes the (s)Y(l,m) spin-weighted spherical harmonic.
+ *
+ * From somewhere ....
+ *
+ * See also:
+ * Implements Equations (II.9)-(II.13) of
+ * D. A. Brown, S. Fairhurst, B. Krishnan, R. A. Mercer, R. K. Kopparapu,
+ * L. Santamaria, and J. T. Whelan,
+ * "Data formats for numerical relativity waves",
+ * arXiv:0709.0093v1 (2007).
+ *
+ * Currently only supports s=-2, l=2,3,4,5,6,7,8 modes.
+ */
+COMPLEX16 XLALSpinWeightedSphericalHarmonic(
+ REAL8 theta, /**< polar angle (rad) */
+ REAL8 phi, /**< azimuthal angle (rad) */
+ int s, /**< spin weight */
+ int l, /**< mode number l */
+ int m /**< mode number m */
+ )
+{
+ REAL8 fac;
+ COMPLEX16 ans;
+
+ /* sanity checks ... */
+ if ( l < abs(s) )
+ {
+ fprintf(stderr,"XLAL Error - : Invalid mode s=%d, l=%d, m=%d - require |s| <= l\n", s, l, m );
+ //XLAL_ERROR_VAL(0, XLAL_EINVAL);
+ }
+ if ( l < abs(m) )
+ {
+ fprintf(stderr,"XLAL Error -: Invalid mode s=%d, l=%d, m=%d - require |m| <= l\n", s, l, m );
+ //XLAL_ERROR_VAL(0, XLAL_EINVAL);
+ }
+
+ if ( s == -2 )
+ {
+ if ( l == 2 )
+ {
+ switch ( m )
+ {
+ case -2:
+ fac = sqrt( 5.0 / ( 64.0 * LAL_PI ) ) * ( 1.0 - cos( theta ))*( 1.0 - cos( theta ));
+ break;
+ case -1:
+ fac = sqrt( 5.0 / ( 16.0 * LAL_PI ) ) * sin( theta )*( 1.0 - cos( theta ));
+ break;
+
+ case 0:
+ fac = sqrt( 15.0 / ( 32.0 * LAL_PI ) ) * sin( theta )*sin( theta );
+ break;
+
+ case 1:
+ fac = sqrt( 5.0 / ( 16.0 * LAL_PI ) ) * sin( theta )*( 1.0 + cos( theta ));
+ break;
+
+ case 2:
+ fac = sqrt( 5.0 / ( 64.0 * LAL_PI ) ) * ( 1.0 + cos( theta ))*( 1.0 + cos( theta ));
+ break;
+ default:
+ fprintf(stderr,"XLAL Error -: Invalid mode s=%d, l=%d, m=%d - require |m| <= l\n", s, l, m );
+ //XLAL_ERROR_VAL(0, XLAL_EINVAL);
+ break;
+ } /* switch (m) */
+ } /* l==2*/
+ else if ( l == 3 )
+ {
+ switch ( m )
+ {
+ case -3:
+ fac = sqrt(21.0/(2.0*LAL_PI))*cos(theta/2.0)*pow(sin(theta/2.0),5.0);
+ break;
+ case -2:
+ fac = sqrt(7.0/(4.0*LAL_PI))*(2.0 + 3.0*cos(theta))*pow(sin(theta/2.0),4.0);
+ break;
+ case -1:
+ fac = sqrt(35.0/(2.0*LAL_PI))*(sin(theta) + 4.0*sin(2.0*theta) - 3.0*sin(3.0*theta))/32.0;
+ break;
+ case 0:
+ fac = (sqrt(105.0/(2.0*LAL_PI))*cos(theta)*pow(sin(theta),2.0))/4.0;
+ break;
+ case 1:
+ fac = -sqrt(35.0/(2.0*LAL_PI))*(sin(theta) - 4.0*sin(2.0*theta) - 3.0*sin(3.0*theta))/32.0;
+ break;
+
+ case 2:
+ fac = sqrt(7.0/LAL_PI)*pow(cos(theta/2.0),4.0)*(-2.0 + 3.0*cos(theta))/2.0;
+ break;
+
+ case 3:
+ fac = -sqrt(21.0/(2.0*LAL_PI))*pow(cos(theta/2.0),5.0)*sin(theta/2.0);
+ break;
+
+ default:
+ fprintf(stderr,"XLAL Error -: Invalid mode s=%d, l=%d, m=%d - require |m| <= l\n", s, l, m );
+ //XLAL_ERROR_VAL(0, XLAL_EINVAL);
+ break;
+ }
+ } /* l==3 */
+ else if ( l == 4 )
+ {
+ switch ( m )
+ {
+ case -4:
+ fac = 3.0*sqrt(7.0/LAL_PI)*pow(cos(theta/2.0),2.0)*pow(sin(theta/2.0),6.0);
+ break;
+ case -3:
+ fac = 3.0*sqrt(7.0/(2.0*LAL_PI))*cos(theta/2.0)*(1.0 + 2.0*cos(theta))*pow(sin(theta/2.0),5.0);
+ break;
+
+ case -2:
+ fac = (3.0*(9.0 + 14.0*cos(theta) + 7.0*cos(2.0*theta))*pow(sin(theta/2.0),4.0))/(4.0*sqrt(LAL_PI));
+ break;
+ case -1:
+ fac = (3.0*(3.0*sin(theta) + 2.0*sin(2.0*theta) + 7.0*sin(3.0*theta) - 7.0*sin(4.0*theta)))/(32.0*sqrt(2.0*LAL_PI));
+ break;
+ case 0:
+ fac = (3.0*sqrt(5.0/(2.0*LAL_PI))*(5.0 + 7.0*cos(2.0*theta))*pow(sin(theta),2.0))/16.0;
+ break;
+ case 1:
+ fac = (3.0*(3.0*sin(theta) - 2.0*sin(2.0*theta) + 7.0*sin(3.0*theta) + 7.0*sin(4.0*theta)))/(32.0*sqrt(2.0*LAL_PI));
+ break;
+ case 2:
+ fac = (3.0*pow(cos(theta/2.0),4.0)*(9.0 - 14.0*cos(theta) + 7.0*cos(2.0*theta)))/(4.0*sqrt(LAL_PI));
+ break;
+ case 3:
+ fac = -3.0*sqrt(7.0/(2.0*LAL_PI))*pow(cos(theta/2.0),5.0)*(-1.0 + 2.0*cos(theta))*sin(theta/2.0);
+ break;
+ case 4:
+ fac = 3.0*sqrt(7.0/LAL_PI)*pow(cos(theta/2.0),6.0)*pow(sin(theta/2.0),2.0);
+ break;
+ default:
+ fprintf(stderr,"XLAL Error -: Invalid mode s=%d, l=%d, m=%d - require |m| <= l\n", s, l, m );
+ // XLAL_ERROR_VAL(0, XLAL_EINVAL);
+ break;
+ }
+ } /* l==4 */
+ else if ( l == 5 )
+ {
+ switch ( m )
+ {
+ case -5:
+ fac = sqrt(330.0/LAL_PI)*pow(cos(theta/2.0),3.0)*pow(sin(theta/2.0),7.0);
+ break;
+ case -4:
+ fac = sqrt(33.0/LAL_PI)*pow(cos(theta/2.0),2.0)*(2.0 + 5.0*cos(theta))*pow(sin(theta/2.0),6.0);
+ break;
+ case -3:
+ fac = (sqrt(33.0/(2.0*LAL_PI))*cos(theta/2.0)*(17.0 + 24.0*cos(theta) + 15.0*cos(2.0*theta))*pow(sin(theta/2.0),5.0))/4.0;
+ break;
+ case -2:
+ fac = (sqrt(11.0/LAL_PI)*(32.0 + 57.0*cos(theta) + 36.0*cos(2.0*theta) + 15.0*cos(3.0*theta))*pow(sin(theta/2.0),4.0))/8.0;
+ break;
+ case -1:
+ fac = (sqrt(77.0/LAL_PI)*(2.0*sin(theta) + 8.0*sin(2.0*theta) + 3.0*sin(3.0*theta) + 12.0*sin(4.0*theta) - 15.0*sin(5.0*theta)))/256.0;
+ break;
+ case 0:
+ fac = (sqrt(1155.0/(2.0*LAL_PI))*(5.0*cos(theta) + 3.0*cos(3.0*theta))*pow(sin(theta),2.0))/32.0;
+ break;
+ case 1:
+ fac = sqrt(77.0/LAL_PI)*(-2.0*sin(theta) + 8.0*sin(2.0*theta) - 3.0*sin(3.0*theta) + 12.0*sin(4.0*theta) + 15.0*sin(5.0*theta))/256.0;
+ break;
+ case 2:
+ fac = sqrt(11.0/LAL_PI)*pow(cos(theta/2.0),4.0)*(-32.0 + 57.0*cos(theta) - 36.0*cos(2.0*theta) + 15.0*cos(3.0*theta))/8.0;
+ break;
+ case 3:
+ fac = -sqrt(33.0/(2.0*LAL_PI))*pow(cos(theta/2.0),5.0)*(17.0 - 24.0*cos(theta) + 15.0*cos(2.0*theta))*sin(theta/2.0)/4.0;
+ break;
+ case 4:
+ fac = sqrt(33.0/LAL_PI)*pow(cos(theta/2.0),6.0)*(-2.0 + 5.0*cos(theta))*pow(sin(theta/2.0),2.0);
+ break;
+ case 5:
+ fac = -sqrt(330.0/LAL_PI)*pow(cos(theta/2.0),7.0)*pow(sin(theta/2.0),3.0);
+ break;
+ default:
+ fprintf(stderr,"XLAL Error - nvalid mode s=%d, l=%d, m=%d - require |m| <= l\n", s, l, m );
+ //XLAL_ERROR_VAL(0, XLAL_EINVAL);
+ break;
+ }
+ } /* l==5 */
+ else if ( l == 6 )
+ {
+ switch ( m )
+ {
+ case -6:
+ fac = (3.*sqrt(715./LAL_PI)*pow(cos(theta/2.0),4)*pow(sin(theta/2.0),8))/2.0;
+ break;
+ case -5:
+ fac = (sqrt(2145./LAL_PI)*pow(cos(theta/2.0),3)*(1. + 3.*cos(theta))*pow(sin(theta/2.0),7))/2.0;
+ break;
+ case -4:
+ fac = (sqrt(195./(2.0*LAL_PI))*pow(cos(theta/2.0),2)*(35. + 44.*cos(theta)
+ + 33.*cos(2.*theta))*pow(sin(theta/2.0),6))/8.0;
+ break;
+ case -3:
+ fac = (3.*sqrt(13./LAL_PI)*cos(theta/2.0)*(98. + 185.*cos(theta) + 110.*cos(2*theta)
+ + 55.*cos(3.*theta))*pow(sin(theta/2.0),5))/32.0;
+ break;
+ case -2:
+ fac = (sqrt(13./LAL_PI)*(1709. + 3096.*cos(theta) + 2340.*cos(2.*theta) + 1320.*cos(3.*theta)
+ + 495.*cos(4.*theta))*pow(sin(theta/2.0),4))/256.0;
+ break;
+ case -1:
+ fac = (sqrt(65./(2.0*LAL_PI))*cos(theta/2.0)*(161. + 252.*cos(theta) + 252.*cos(2.*theta)
+ + 132.*cos(3.*theta) + 99.*cos(4.*theta))*pow(sin(theta/2.0),3))/64.0;
+ break;
+ case 0:
+ fac = (sqrt(1365./LAL_PI)*(35. + 60.*cos(2.*theta) + 33.*cos(4.*theta))*pow(sin(theta),2))/512.0;
+ break;
+ case 1:
+ fac = (sqrt(65./(2.0*LAL_PI))*pow(cos(theta/2.0),3)*(161. - 252.*cos(theta) + 252.*cos(2.*theta)
+ - 132.*cos(3.*theta) + 99.*cos(4.*theta))*sin(theta/2.0))/64.0;
+ break;
+ case 2:
+ fac = (sqrt(13./LAL_PI)*pow(cos(theta/2.0),4)*(1709. - 3096.*cos(theta) + 2340.*cos(2.*theta)
+ - 1320*cos(3*theta) + 495*cos(4*theta)))/256.0;
+ break;
+ case 3:
+ fac = (-3.*sqrt(13./LAL_PI)*pow(cos(theta/2.0),5)*(-98. + 185.*cos(theta) - 110.*cos(2*theta)
+ + 55.*cos(3.*theta))*sin(theta/2.0))/32.0;
+ break;
+ case 4:
+ fac = (sqrt(195./(2.0*LAL_PI))*pow(cos(theta/2.0),6)*(35. - 44.*cos(theta)
+ + 33.*cos(2*theta))*pow(sin(theta/2.0),2))/8.0;
+ break;
+ case 5:
+ fac = -(sqrt(2145./LAL_PI)*pow(cos(theta/2.0),7)*(-1. + 3.*cos(theta))*pow(sin(theta/2.0),3))/2.0;
+ break;
+ case 6:
+ fac = (3.*sqrt(715./LAL_PI)*pow(cos(theta/2.0),8)*pow(sin(theta/2.0),4))/2.0;
+ break;
+ default:
+ fprintf(stderr,"XLAL Error : Invalid mode s=%d, l=%d, m=%d - require |m| <= l\n", s, l, m );
+ //XLAL_ERROR_VAL(0, XLAL_EINVAL);
+ break;
+ }
+ } /* l==6 */
+ else if ( l == 7 )
+ {
+ switch ( m )
+ {
+ case -7:
+ fac = sqrt(15015./(2.0*LAL_PI))*pow(cos(theta/2.0),5)*pow(sin(theta/2.0),9);
+ break;
+ case -6:
+ fac = (sqrt(2145./LAL_PI)*pow(cos(theta/2.0),4)*(2. + 7.*cos(theta))*pow(sin(theta/2.0),8))/2.0;
+ break;
+ case -5:
+ fac = (sqrt(165./(2.0*LAL_PI))*pow(cos(theta/2.0),3)*(93. + 104.*cos(theta)
+ + 91.*cos(2.*theta))*pow(sin(theta/2.0),7))/8.0;
+ break;
+ case -4:
+ fac = (sqrt(165./(2.0*LAL_PI))*pow(cos(theta/2.0),2)*(140. + 285.*cos(theta)
+ + 156.*cos(2.*theta) + 91.*cos(3.*theta))*pow(sin(theta/2.0),6))/16.0;
+ break;
+ case -3:
+ fac = (sqrt(15./(2.0*LAL_PI))*cos(theta/2.0)*(3115. + 5456.*cos(theta) + 4268.*cos(2.*theta)
+ + 2288.*cos(3.*theta) + 1001.*cos(4.*theta))*pow(sin(theta/2.0),5))/128.0;
+ break;
+ case -2:
+ fac = (sqrt(15./LAL_PI)*(5220. + 9810.*cos(theta) + 7920.*cos(2.*theta) + 5445.*cos(3.*theta)
+ + 2860.*cos(4.*theta) + 1001.*cos(5.*theta))*pow(sin(theta/2.0),4))/512.0;
+ break;
+ case -1:
+ fac = (3.*sqrt(5./(2.0*LAL_PI))*cos(theta/2.0)*(1890. + 4130.*cos(theta) + 3080.*cos(2.*theta)
+ + 2805.*cos(3.*theta) + 1430.*cos(4.*theta) + 1001.*cos(5*theta))*pow(sin(theta/2.0),3))/512.0;
+ break;
+ case 0:
+ fac = (3.*sqrt(35./LAL_PI)*cos(theta)*(109. + 132.*cos(2.*theta)
+ + 143.*cos(4.*theta))*pow(sin(theta),2))/512.0;
+ break;
+ case 1:
+ fac = (3.*sqrt(5./(2.0*LAL_PI))*pow(cos(theta/2.0),3)*(-1890. + 4130.*cos(theta) - 3080.*cos(2.*theta)
+ + 2805.*cos(3.*theta) - 1430.*cos(4.*theta) + 1001.*cos(5.*theta))*sin(theta/2.0))/512.0;
+ break;
+ case 2:
+ fac = (sqrt(15./LAL_PI)*pow(cos(theta/2.0),4)*(-5220. + 9810.*cos(theta) - 7920.*cos(2.*theta)
+ + 5445.*cos(3.*theta) - 2860.*cos(4.*theta) + 1001.*cos(5.*theta)))/512.0;
+ break;
+ case 3:
+ fac = -(sqrt(15./(2.0*LAL_PI))*pow(cos(theta/2.0),5)*(3115. - 5456.*cos(theta) + 4268.*cos(2.*theta)
+ - 2288.*cos(3.*theta) + 1001.*cos(4.*theta))*sin(theta/2.0))/128.0;
+ break;
+ case 4:
+ fac = (sqrt(165./(2.0*LAL_PI))*pow(cos(theta/2.0),6)*(-140. + 285.*cos(theta) - 156.*cos(2*theta)
+ + 91.*cos(3.*theta))*pow(sin(theta/2.0),2))/16.0;
+ break;
+ case 5:
+ fac = -(sqrt(165./(2.0*LAL_PI))*pow(cos(theta/2.0),7)*(93. - 104.*cos(theta)
+ + 91.*cos(2.*theta))*pow(sin(theta/2.0),3))/8.0;
+ break;
+ case 6:
+ fac = (sqrt(2145./LAL_PI)*pow(cos(theta/2.0),8)*(-2. + 7.*cos(theta))*pow(sin(theta/2.0),4))/2.0;
+ break;
+ case 7:
+ fac = -(sqrt(15015./(2.0*LAL_PI))*pow(cos(theta/2.0),9)*pow(sin(theta/2.0),5));
+ break;
+ default:
+ fprintf(stderr,"XLAL Error : Invalid mode s=%d, l=%d, m=%d - require |m| <= l\n", s, l, m );
+ //XLAL_ERROR_VAL(0, XLAL_EINVAL);
+ break;
+ }
+ } /* l==7 */
+ else if ( l == 8 )
+ {
+ switch ( m )
+ {
+ case -8:
+ fac = sqrt(34034./LAL_PI)*pow(cos(theta/2.0),6)*pow(sin(theta/2.0),10);
+ break;
+ case -7:
+ fac = sqrt(17017./(2.0*LAL_PI))*pow(cos(theta/2.0),5)*(1. + 4.*cos(theta))*pow(sin(theta/2.0),9);
+ break;
+ case -6:
+ fac = sqrt(255255./LAL_PI)*pow(cos(theta/2.0),4)*(1. + 2.*cos(theta))
+ *sin(LAL_PI/4.0 - theta/2.0)*sin(LAL_PI/4.0 + theta/2.0)*pow(sin(theta/2.0),8);
+ break;
+ case -5:
+ fac = (sqrt(12155./(2.0*LAL_PI))*pow(cos(theta/2.0),3)*(19. + 42.*cos(theta)
+ + 21.*cos(2.*theta) + 14.*cos(3.*theta))*pow(sin(theta/2.0),7))/8.0;
+ break;
+ case -4:
+ fac = (sqrt(935./(2.0*LAL_PI))*pow(cos(theta/2.0),2)*(265. + 442.*cos(theta) + 364.*cos(2.*theta)
+ + 182.*cos(3.*theta) + 91.*cos(4.*theta))*pow(sin(theta/2.0),6))/32.0;
+ break;
+ case -3:
+ fac = (sqrt(561./(2.0*LAL_PI))*cos(theta/2.0)*(869. + 1660.*cos(theta) + 1300.*cos(2.*theta)
+ + 910.*cos(3.*theta) + 455.*cos(4.*theta) + 182.*cos(5.*theta))*pow(sin(theta/2.0),5))/128.0;
+ break;
+ case -2:
+ fac = (sqrt(17./LAL_PI)*(7626. + 14454.*cos(theta) + 12375.*cos(2.*theta) + 9295.*cos(3.*theta)
+ + 6006.*cos(4.*theta) + 3003.*cos(5.*theta) + 1001.*cos(6.*theta))*pow(sin(theta/2.0),4))/512.0;
+ break;
+ case -1:
+ fac = (sqrt(595./(2.0*LAL_PI))*cos(theta/2.0)*(798. + 1386.*cos(theta) + 1386.*cos(2.*theta)
+ + 1001.*cos(3.*theta) + 858.*cos(4.*theta) + 429.*cos(5.*theta) + 286.*cos(6.*theta))*pow(sin(theta/2.0),3))/512.0;
+ break;
+ case 0:
+ fac = (3.*sqrt(595./LAL_PI)*(210. + 385.*cos(2.*theta) + 286.*cos(4.*theta)
+ + 143.*cos(6.*theta))*pow(sin(theta),2))/4096.0;
+ break;
+ case 1:
+ fac = (sqrt(595./(2.0*LAL_PI))*pow(cos(theta/2.0),3)*(798. - 1386.*cos(theta) + 1386.*cos(2.*theta)
+ - 1001.*cos(3.*theta) + 858.*cos(4.*theta) - 429.*cos(5.*theta) + 286.*cos(6.*theta))*sin(theta/2.0))/512.0;
+ break;
+ case 2:
+ fac = (sqrt(17./LAL_PI)*pow(cos(theta/2.0),4)*(7626. - 14454.*cos(theta) + 12375.*cos(2.*theta)
+ - 9295.*cos(3.*theta) + 6006.*cos(4.*theta) - 3003.*cos(5.*theta) + 1001.*cos(6.*theta)))/512.0;
+ break;
+ case 3:
+ fac = -(sqrt(561./(2.0*LAL_PI))*pow(cos(theta/2.0),5)*(-869. + 1660.*cos(theta) - 1300.*cos(2.*theta)
+ + 910.*cos(3.*theta) - 455.*cos(4.*theta) + 182.*cos(5.*theta))*sin(theta/2.0))/128.0;
+ break;
+ case 4:
+ fac = (sqrt(935./(2.0*LAL_PI))*pow(cos(theta/2.0),6)*(265. - 442.*cos(theta) + 364.*cos(2.*theta)
+ - 182.*cos(3.*theta) + 91.*cos(4.*theta))*pow(sin(theta/2.0),2))/32.0;
+ break;
+ case 5:
+ fac = -(sqrt(12155./(2.0*LAL_PI))*pow(cos(theta/2.0),7)*(-19. + 42.*cos(theta) - 21.*cos(2.*theta)
+ + 14.*cos(3.*theta))*pow(sin(theta/2.0),3))/8.0;
+ break;
+ case 6:
+ fac = sqrt(255255./LAL_PI)*pow(cos(theta/2.0),8)*(-1. + 2.*cos(theta))*sin(LAL_PI/4.0 - theta/2.0)
+ *sin(LAL_PI/4.0 + theta/2.0)*pow(sin(theta/2.0),4);
+ break;
+ case 7:
+ fac = -(sqrt(17017./(2.0*LAL_PI))*pow(cos(theta/2.0),9)*(-1. + 4.*cos(theta))*pow(sin(theta/2.0),5));
+ break;
+ case 8:
+ fac = sqrt(34034./LAL_PI)*pow(cos(theta/2.0),10)*pow(sin(theta/2.0),6);
+ break;
+ default:
+ fprintf(stderr,"XLAL Error -: Invalid mode s=%d, l=%d, m=%d - require |m| <= l\n", s, l, m );
+ //XLAL_ERROR_VAL(0, XLAL_EINVAL);
+ break;
+ }
+ } /* l==8 */
+ else
+ {
+ fprintf(stderr,"XLAL Error -: Unsupported mode l=%d (only l in [2,8] implemented)\n", l);
+ //XLAL_ERROR_VAL(0, XLAL_EINVAL);
+ }
+ }
+ else
+ {
+ fprintf(stderr,"XLAL Error -: Unsupported mode s=%d (only s=-2 implemented)\n", s);
+ //XLAL_ERROR_VAL(0, XLAL_EINVAL);
+ }
+ if (m)
+
+ ans = CX16polar(1.0, m*phi) * fac;
+ else
+ ans = fac;
+ return ans;
+}
+/**
+ * Function to calculate the non-Keplerian coefficient for the spin-aligned EOB model.
+ * radius \f$r\f$ times the cuberoot of the returned number is \f$r_\Omega\f$ defined in Eq. A2.
+ * i.e. the function returns \f$(r_{\Omega} / r)^3\f$.
+ */
+ REAL8
+XLALSimIMRSpinAlignedEOBNonKeplerCoeff(
+ const REAL8 values[], /**<< Dynamical variables */
+ SpinEOBParams *funcParams /**<< EOB parameters */
+ )
+{
+
+ REAL8 omegaCirc;
+
+ REAL8 tmpValues[4];
+
+ REAL8 r3;
+
+ /* We need to find the values of omega assuming pr = 0 */
+ memcpy( tmpValues, values, sizeof(tmpValues) );
+ tmpValues[2] = 0.0;
+
+ omegaCirc = XLALSimIMRSpinAlignedEOBCalcOmega( tmpValues, funcParams );
+ if ( XLAL_IS_REAL8_FAIL_NAN( omegaCirc ) )
+ {
+ fprintf(stderr,"Error(%d)", XLAL_EFUNC );
+ }
+
+ r3 = values[0]*values[0]*values[0];
+
+ return 1.0/(omegaCirc*omegaCirc*r3);
+}
+
+REAL8 GetNRSpinPeakAmplitude( INT4 l, INT4 m, REAL8 eta, REAL8 a )
+{
+ /* Fit for HOMs missing */
+ return 1.3547468629743946*eta + 0.9187885481024214*eta*eta;
+}
+
+REAL8 GetNRSpinPeakADDot( INT4 l, INT4 m, REAL8 eta, REAL8 a )
+{
+ /* Fit for HOMs missing */
+ return eta*(-0.0024971911410897156 + (-0.006128515435641139 + 0.01732656*a/(2.0-4.0*eta))*eta);
+}
+
+COMPLEX16 XLALCOMPLEX16Rect (REAL8 x, REAL8 y)
+{
+ COMPLEX16 z = x + I*y;
+ //do {(&z)->re=(x); (&z)->im=(y);} while(0);
+
+ return z;
+}
+
+double MYlog2(double x)
+{
+ return log(x)/log(2.0);
+}
+double MYcbrt(double x)
+{
+ return pow(x,1.0/3.0);
+}
+
+double carg (COMPLEX16 z)
+{
+ double x = creal(z);
+ double y = cimag(z);
+
+ if (x == 0.0 && y == 0.0)
+ {
+ return 0;
+ }
+
+ return atan2 (y, x);
+}
+COMPLEX16 cexp (COMPLEX16 a)
+{
+ double rho = exp(creal(a));
+ double theta = cimag(a);
+
+ COMPLEX16 z = rho * cos (theta)+I*rho * sin (theta);
+ return z;
+}
+
+COMPLEX16 CX16polar(double r,double phi)
+{
+ double re,im;
+ re = r*cos(phi);
+ im = r*sin(phi);
+
+
+ COMPLEX16 z=re+I*im;
+
+ return z;
+}
+
+COMPLEX16 MYcpow(COMPLEX16 a,UINT4 n)
+{
+ COMPLEX16 z1 = 1;
+ UINT4 i;
+ for(i = 0;i < n;i++)
+ {
+ z1 = z1*a;
+ }
+
+ return z1;
+}
+
+double cabs(COMPLEX16 z)
+{
+ double a = creal(z);
+ double b = cimag(z);
+
+ return sqrt(a*a+b*b);
+}
+REAL8 CalculateCrossProduct( const int i, const REAL8 a[], const REAL8 b[] )
+{
+ return a[(i+1)%3]*b[(i+2)%3] - a[(i+2)%3]*b[(i+1)%3];
+}
+int
+NormalizeVector( REAL8 a[] )
+{
+ REAL8 norm = sqrt( a[0]*a[0] + a[1]*a[1] + a[2]*a[2] );
+
+ a[0] /= norm;
+ a[1] /= norm;
+ a[2] /= norm;
+
+ return 0;
+}
+#if 1
+REAL8 XLALSimIMREOBGetNRSpinPeakDeltaT(
+ INT4 l, /**<< Mode l */
+ INT4 m, /**<< Mode m */
+ REAL8 eta, /**<< Symmetric mass ratio */
+ REAL8 a /**<< Dimensionless spin */
+ )
+{
+
+ switch ( l )
+ {
+ case 2:
+ switch ( m )
+ {
+ case 2:
+ /* DeltaT22 defined here is a minus sign different from Eq. (33) of Taracchini et al. */
+ if ( a <= 0.0 )
+ {
+ return 2.5;
+ }
+ else
+ {
+ return (2.5 + 1.77*a*a*a*a/(0.43655*0.43655*0.43655*0.43655)/(1.0-2.0*eta)/(1.0-2.0*eta)/(1.0-2.0*eta)/(1.0-2.0*eta));
+ }
+ break;
+ default:
+ fprintf(stderr,"Error(%d)", XLAL_EINVAL );
+ }
+ break;
+ default:
+ fprintf(stderr,"Error(%d)", XLAL_EINVAL );
+ }
+
+ /* We should never get here, but I expect a compiler whinge without it... */
+ fprintf( stderr,"XLAL Error - We should never get here!!\n" );
+ fprintf(stderr,"Error(%d)", XLAL_EINVAL );
+ return 0;
+}
+REAL8 GetNRSpinPeakOmega( INT4 l, INT4 m, REAL8 eta, REAL8 a )
+{
+ /* Fit for HOMs missing */
+ return 0.27581190323955274 + 0.19347381066059993*eta
+ - 0.08898338208573725*log(1.0 - a/(1.0-2.0*eta))
+ + eta*eta*(1.78832*(0.2690779744133912 + a/(2.0-4.0*eta))*(1.2056469070395925
+ + a/(2.0-4.0*eta)) + 1.423734113371796*log(1.0 - a/(1.0-2.0*eta)));
+}
+#else
+REAL8 XLALSimIMREOBGetNRSpinPeakDeltaT(
+ int l, /**<< Mode l */
+ int m, /**<< Mode m */
+ REAL8 eta, /**<< Symmetric mass ratio */
+ REAL8 a /**<< Dimensionless spin */
+ )
+{
+
+ switch ( l )
+ {
+ case 2:
+ switch ( m )
+ {
+ case 2:
+ /* DeltaT22 defined here is a minus sign different from Eq. (33) of Taracchini et al. */
+ if ( a <= 0.0 )
+ {
+ return 2.5;
+ }
+ else
+ {
+ return (2.5 + 1.77*a*a*a*a/(0.43655*0.43655*0.43655*0.43655)/(1.0-2.0*eta)/(1.0-2.0*eta)/(1.0-2.0*eta)/(1.0-2.0*eta));
+ }
+ break;
+ default:
+ fprintf(stderr,"Error(%d)", XLAL_EINVAL );
+ }
+ break;
+ default:
+ fprintf(stderr,"Error(%d)", XLAL_EINVAL );
+ }
+
+ /* We should never get here, but I expect a compiler whinge without it... */
+ fprintf( stderr,"XLAL Error - We should never get here!!\n" );
+ fprintf(stderr,"Error(%d)", XLAL_EINVAL );
+ return 0;
+}
+REAL8 GetNRSpinPeakOmega( int l, int m, REAL8 eta, REAL8 a )
+{
+ /* Fit for HOMs missing */
+ return 0.27581190323955274 + 0.19347381066059993*eta
+ - 0.08898338208573725*log(1.0 - a/(1.0-2.0*eta))
+ + eta*eta*(1.78832*(0.2690779744133912 + a/(2.0-4.0*eta))*(1.2056469070395925
+ + a/(2.0-4.0*eta)) + 1.423734113371796*log(1.0 - a/(1.0-2.0*eta)));
+}
+#endif
+REAL8 GetNRSpinPeakOmegaDot( INT4 l, INT4 m, REAL8 eta, REAL8 a )
+{
+ /* Fit for HOMs missing */
+ return 0.006075014646800278 + 0.012040017219351778*eta
+ + (0.0007353536801336875 + 0.0015592659912461832*a/(1.0-2.0*eta))*log(1.0-a/(1.0-2.0*eta))
+ + eta*eta*(0.03575969677378844 + (-0.011765658882139 - 0.02494825585993893*a/(1.0-2.0*eta))
+ * log(1.0 - a/(1.0-2.0*eta)));
+}
diff --git a/SEOBNREv1/readme.txt b/SEOBNREv1/readme.txt
new file mode 100755
index 0000000..437f8fd
--- /dev/null
+++ b/SEOBNREv1/readme.txt
@@ -0,0 +1,11 @@
+1. compile
+gcc DIY_SEOBNRE_main.c LALSimSEOBNRE_DIY.c -lgsl -lgslcblas -o SEOBNRE
+
+mpicc DIY_SEOBNRE_main.c LALSimSEOBNRE_DIY.c -lgsl -lgslcblas -o SEOBNRE -I/share/home/zjcao/Lib/usr/local/include/ -L/share/home/zjcao/Lib/usr/local/lib -lm
+
+2. example
+export LD_LIBRARY_PATH=/share/home/zjcao/Lib/usr/local/lib
+
+SEOBNRE --m1 10 --m2 10 --f-min 20.304334346643405 --e0 0.5
+
+These parameters are for LIGO detector which is inherited from SEOBNR code. The above setting corresponds to fM = 0.002.
--
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