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Commit c9f32128 authored by Daniel Brown's avatar Daniel Brown
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adding in more ROMHOM computation and weighting file generations as well as... 

adding in more ROMHOM computation and weighting file generations as well as some knm computations utilities. Adding more functions in beam parameter object for plotting parameters
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pykat/testing/test.py 100644 → 100755
+ 1
− 1
View file @ c9f32128
......@@ -47,7 +47,7 @@ def run_kat_file(item):
#try:
start = time.time()
out,err = utils.runcmd([FINESSE_EXE, "--noheader", kat], cwd=SUITE_PATH)
out,err = utils.runcmd(["nice", "--18", FINESSE_EXE, "--noheader", kat], cwd=SUITE_PATH)
runtime = time.time()-start
OUT_FILE = os.path.join(SUITE_PATH,basename + ".out")
......
pykat/utilities/greedypoints/matched20.txt 0 → 100644
+ 99
− 0
View file @ c9f32128
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pykat/utilities/greedypoints/mismatched10.txt 0 → 100644
+ 237
− 0
View file @ c9f32128
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pykat/utilities/greedypoints/mismatched20.txt 0 → 100644
+ 249
− 0
View file @ c9f32128
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0.001000 0.001000 2206.896552 413.793103 1 4
0.002333 0.001000 689.655172 137.931034 2 7
0.001000 0.003667 3172.413793 551.724138 3 8
0.001000 0.003667 137.931034 3862.068966 19 19
0.001000 0.001000 1241.379310 275.862069 1 10
0.001000 0.011667 1931.034483 3448.275862 1 17
0.001000 0.001000 413.793103 1655.172414 1 7
0.006333 0.001000 3724.137931 137.931034 13 18
0.001000 0.001000 275.862069 1793.103448 2 3
0.001000 0.001000 3586.206897 689.655172 1 3
0.001000 0.003667 137.931034 3862.068966 6 11
0.001000 0.001000 1655.172414 413.793103 1 1
0.010333 0.005000 1793.103448 0.000000 19 20
0.001000 0.001000 1241.379310 2896.551724 3 9
0.001000 0.003667 275.862069 1103.448276 3 9
0.001000 0.001000 551.724138 2344.827586 1 1
0.001000 0.001000 137.931034 689.655172 2 3
0.001000 0.001000 413.793103 137.931034 1 20
0.002333 0.001000 413.793103 137.931034 1 2
0.001000 0.001000 1793.103448 275.862069 1 3
0.001000 0.001000 3034.482759 1103.448276 0 1
0.001000 0.001000 137.931034 413.793103 11 15
0.001000 0.001000 275.862069 827.586207 2 3
0.002333 0.010333 2068.965517 4000.000000 5 19
0.002333 0.001000 827.586207 275.862069 1 6
0.001000 0.001000 137.931034 689.655172 5 5
0.001000 0.001000 689.655172 137.931034 1 10
0.013000 0.001000 3448.275862 137.931034 16 17
0.001000 0.002333 551.724138 1793.103448 1 3
0.011667 0.006333 0.000000 0.000000 1 15
0.001000 0.003667 137.931034 3586.206897 17 18
0.001000 0.005000 3034.482759 1793.103448 1 20
0.005000 0.001000 2482.758621 827.586207 1 1
0.005000 0.001000 965.517241 3310.344828 14 15
0.010333 0.005000 0.000000 0.000000 1 13
0.005000 0.001000 827.586207 137.931034 7 9
0.001000 0.003667 0.000000 0.000000 17 17
0.001000 0.002333 137.931034 275.862069 2 3
0.001000 0.006333 137.931034 827.586207 10 11
0.001000 0.001000 413.793103 137.931034 1 7
0.001000 0.001000 1931.034483 551.724138 1 1
0.001000 0.006333 275.862069 1103.448276 1 9
0.005000 0.001000 1241.379310 137.931034 3 8
0.001000 0.001000 275.862069 137.931034 3 10
0.001000 0.001000 1379.310345 413.793103 1 1
0.001000 0.001000 137.931034 413.793103 13 13
0.005000 0.001000 1241.379310 137.931034 3 11
0.001000 0.006333 3448.275862 1931.034483 1 20
0.001000 0.001000 965.517241 0.000000 0 2
0.003667 0.001000 1241.379310 275.862069 1 6
0.001000 0.003667 137.931034 3724.137931 8 9
0.013000 0.003667 1241.379310 0.000000 15 17
0.002333 0.010333 689.655172 3862.068966 3 3
0.001000 0.001000 413.793103 1379.310345 1 1
0.001000 0.005000 137.931034 551.724138 16 16
0.001000 0.001000 413.793103 1931.034483 0 1
0.003667 0.001000 551.724138 137.931034 8 9
0.001000 0.001000 137.931034 413.793103 9 16
0.013000 0.001000 3724.137931 137.931034 17 19
0.001000 0.001000 2206.896552 413.793103 0 3
0.005000 0.001000 137.931034 0.000000 19 19
0.005000 0.001000 1241.379310 965.517241 1 10
0.001000 0.007667 137.931034 965.517241 7 8
0.001000 0.007667 827.586207 2068.965517 3 20
0.001000 0.001000 137.931034 275.862069 8 9
0.002333 0.001000 0.000000 0.000000 19 20
0.001000 0.001000 275.862069 137.931034 3 7
0.001000 0.003667 275.862069 1103.448276 8 9
0.001000 0.010333 137.931034 1241.379310 10 12
0.001000 0.001000 137.931034 689.655172 11 12
0.001000 0.001000 275.862069 137.931034 1 2
0.001000 0.005000 275.862069 1103.448276 3 14
0.002333 0.001000 2206.896552 689.655172 8 9
0.003667 0.001000 0.000000 0.000000 14 19
0.005000 0.005000 0.000000 0.000000 8 18
0.005000 0.001000 1793.103448 275.862069 2 5
0.001000 0.003667 137.931034 3448.275862 15 19
0.001000 0.001000 689.655172 137.931034 1 16
0.001000 0.001000 137.931034 413.793103 18 19
0.002333 0.001000 1241.379310 137.931034 9 13
0.001000 0.001000 413.793103 3724.137931 3 3
0.011667 0.002333 965.517241 0.000000 19 20
0.001000 0.001000 965.517241 275.862069 1 2
0.001000 0.001000 3724.137931 137.931034 1 20
0.001000 0.002333 137.931034 275.862069 7 13
0.001000 0.001000 137.931034 413.793103 8 8
0.006333 0.005000 0.000000 0.000000 8 20
0.001000 0.001000 965.517241 137.931034 1 4
0.011667 0.001000 3586.206897 137.931034 7 17
0.002333 0.001000 413.793103 137.931034 2 19
0.003667 0.001000 827.586207 2068.965517 3 20
0.001000 0.001000 275.862069 1793.103448 7 9
0.001000 0.001000 137.931034 689.655172 8 8
0.001000 0.001000 137.931034 1241.379310 4 5
0.001000 0.002333 137.931034 275.862069 9 20
0.002333 0.001000 0.000000 0.000000 13 19
0.002333 0.001000 0.000000 0.000000 2 18
0.011667 0.001000 3724.137931 137.931034 18 18
0.005000 0.006333 0.000000 0.000000 18 19
0.003667 0.001000 551.724138 137.931034 8 12
0.001000 0.003667 137.931034 551.724138 10 19
0.010333 0.001000 3448.275862 413.793103 2 13
0.005000 0.005000 0.000000 0.000000 11 18
0.001000 0.003667 137.931034 551.724138 9 14
0.002333 0.001000 275.862069 137.931034 7 18
0.001000 0.007667 137.931034 3586.206897 17 17
0.003667 0.001000 413.793103 137.931034 16 18
0.009000 0.005000 0.000000 0.000000 20 20
0.001000 0.003667 137.931034 275.862069 5 15
0.001000 0.002333 275.862069 827.586207 2 16
0.007667 0.002333 4000.000000 137.931034 11 19
0.001000 0.007667 137.931034 965.517241 13 19
0.003667 0.007667 137.931034 3586.206897 19 19
0.003667 0.001000 413.793103 137.931034 13 18
0.002333 0.007667 0.000000 0.000000 19 20
0.010333 0.007667 3586.206897 1793.103448 3 18
0.001000 0.002333 137.931034 413.793103 13 20
0.001000 0.003667 137.931034 413.793103 5 19
0.001000 0.001000 275.862069 137.931034 9 16
0.001000 0.011667 137.931034 0.000000 1 20
0.002333 0.003667 0.000000 0.000000 14 18
0.009000 0.003667 0.000000 137.931034 9 20
0.001000 0.010333 137.931034 3724.137931 18 19
0.002333 0.001000 0.000000 0.000000 13 18
0.003667 0.002333 0.000000 0.000000 19 20
0.001000 0.001000 137.931034 413.793103 14 16
0.011667 0.003667 0.000000 137.931034 19 20
0.010333 0.001000 3172.413793 551.724138 3 10
0.002333 0.013000 137.931034 0.000000 16 20
0.009000 0.001000 0.000000 137.931034 19 20
0.001000 0.001000 137.931034 275.862069 13 16
0.013000 0.002333 0.000000 137.931034 18 18
0.003667 0.002333 0.000000 0.000000 18 19
0.002333 0.013000 137.931034 0.000000 11 17
0.003667 0.001000 551.724138 137.931034 5 8
0.001000 0.001000 275.862069 137.931034 1 16
0.001000 0.003667 137.931034 413.793103 10 19
0.013000 0.002333 137.931034 137.931034 15 20
0.001000 0.001000 0.000000 0.000000 17 20
0.005000 0.006333 0.000000 0.000000 20 20
0.002333 0.001000 275.862069 137.931034 15 18
0.001000 0.002333 137.931034 275.862069 11 18
0.001000 0.002333 137.931034 413.793103 3 18
0.001000 0.013000 137.931034 4000.000000 19 20
0.003667 0.005000 0.000000 0.000000 19 20
0.013000 0.002333 0.000000 137.931034 20 20
0.005000 0.006333 137.931034 0.000000 19 20
0.005000 0.001000 413.793103 137.931034 18 18
0.011667 0.002333 4000.000000 137.931034 19 19
0.002333 0.002333 0.000000 0.000000 19 20
0.003667 0.010333 137.931034 0.000000 20 20
0.001000 0.002333 137.931034 275.862069 19 20
0.007667 0.003667 0.000000 137.931034 19 20
0.002333 0.007667 137.931034 4000.000000 20 20
0.002333 0.002333 0.000000 0.000000 16 19
0.002333 0.001000 275.862069 137.931034 18 20
0.003667 0.003667 0.000000 0.000000 20 20
0.003667 0.001000 413.793103 137.931034 20 20
0.001000 0.003667 137.931034 413.793103 18 20
0.001000 0.001000 0.000000 0.000000 20 20
0.005000 0.005000 0.000000 137.931034 20 20
0.002333 0.013000 137.931034 0.000000 20 20
0.013000 0.001000 4000.000000 137.931034 20 20
0.001000 0.011667 137.931034 1517.241379 13 14
0.002333 0.002333 0.000000 0.000000 20 20
0.001000 0.001000 413.793103 1241.379310 11 12
0.010333 0.003667 0.000000 137.931034 20 20
0.005000 0.005000 0.000000 0.000000 20 20
0.006333 0.001000 965.517241 137.931034 9 12
0.002333 0.001000 0.000000 0.000000 20 20
0.003667 0.007667 137.931034 0.000000 20 20
0.002333 0.013000 137.931034 4000.000000 20 20
0.003667 0.003667 0.000000 0.000000 18 20
0.013000 0.002333 4000.000000 137.931034 20 20
0.002333 0.003667 0.000000 0.000000 20 20
0.006333 0.003667 0.000000 137.931034 20 20
0.001000 0.013000 137.931034 2896.551724 20 20
0.011667 0.001000 3724.137931 137.931034 3 14
0.005000 0.005000 137.931034 0.000000 20 20
0.002333 0.003667 0.000000 0.000000 9 14
0.002333 0.002333 0.000000 0.000000 18 19
0.011667 0.002333 0.000000 137.931034 20 20
0.002333 0.011667 137.931034 0.000000 20 20
0.003667 0.005000 0.000000 0.000000 20 20
0.001000 0.001000 137.931034 689.655172 18 20
0.001000 0.001000 0.000000 0.000000 19 20
0.009000 0.003667 0.000000 137.931034 20 20
0.002333 0.013000 137.931034 137.931034 20 20
0.013000 0.001000 0.000000 137.931034 20 20
0.003667 0.006333 137.931034 0.000000 20 20
0.001000 0.013000 137.931034 3586.206897 20 20
0.013000 0.001000 3586.206897 137.931034 20 20
0.005000 0.002333 0.000000 0.000000 20 20
0.003667 0.009000 137.931034 0.000000 20 20
0.002333 0.001000 0.000000 0.000000 14 20
0.002333 0.001000 551.724138 137.931034 5 18
pykat/utilities/hermite.py 0 → 100644
+ 69
− 0
View file @ c9f32128
import numpy as np
def hermite(n, x):
if n == 0:
return 1.0
elif n == 1:
return (2.0 * x)
elif n == 2:
return (4.0 * x * x - 2.0)
elif n == 3:
return (8.0 * x * x * x - 12.0 * x)
elif n == 4:
x_sq = x * x
return (16.0 * x_sq*x_sq - 48.0 * x_sq + 12.0)
elif n == 5:
x_sq = x * x
x_cb = x * x_sq
return (32.0 * x_cb * x_sq - 160.0 * x_cb + 120.0 * x)
elif n == 6:
x_sq = x * x
x_four = x_sq * x_sq
return (64.0 * x_four*x_sq - 480.0 * x_four + 720.0 * x_sq - 120.0)
elif n == 7:
x_sq = x*x
x_cb = x_sq*x
x_four = x_cb*x
return (128.0 * x_cb*x_four - 1344.0 * x_cb*x_sq + 3360.0 * x_cb - 1680.0 * x)
elif n == 8:
x_sq = x*x
x_four = x_sq*x_sq
x_six = x_four*x_sq
return (256.0 * x_four*x_four - 3584.0 * x_six + 13440.0 * x_four - 13440.0 * x_sq + 1680.0)
elif n == 9:
x_sq = x*x
x_cb = x_sq*x
x_four = x_cb*x
return (512.0 * x_cb*x_cb*x_cb - 9216.0 * x_four*x_cb + 48384.0 * x_cb*x_sq - 80640.0 * x_cb + 30240.0 * x)
elif n == 10:
x_sq = x*x
x_cb = x_sq*x
x_four = x_cb*x
x_five = x_four * x
return (1024.0 * x_five*x_five - 23040.0 * x_four*x_four + 161280.0 * x_cb*x_cb - 403200.0 * x_four + 302400.0 * x_sq - 30240.0)
else :
return (2 * x * hermite(n - 1, x) - 2 * (n - 1) * hermite(n - 2, x))
pykat/utilities/knm.py 0 → 100644
+ 83
− 0
View file @ c9f32128
from itertools import combinations_with_replacement as combinations
from pykat.utilities.optics.gaussian_beams import beam_param, HG_beam
from pykat.exceptions import BasePyKatException
import maps
import os.path
import numpy as np
import pykat
import collections
import math
def makeCouplingMatrix(max_order):
pass
def riemann_HG_knm(x, y, mode_in, mode_out, q1, q2, q1y=None, q2y=None, Axy=None):
if Axy == None:
Axy == np.ones((len(x), len(y)))
if q1y == None:
q1y = q1
if q2y == None:
q2y = q2
if len(mode_in) != 2 or len(mode_out) != 2:
raise BasePyKatException("Both mode in and out should be a container with modes [n m]")
Hg_in = HG_beam(qx=q1, qy=q1y, n=mode_in[0], m=mode_in[1])
Hg_out = HG_beam(qx=q2, qy=q2y, n=mode_out[0], m=mode_out[1])
dx = abs(x[1] - x[0])
dy = abs(y[1] - y[0])
U1 = Hg_in.Unm(x,y)
U2 = Hg_out.Unm(x,y).conjugate()
return dx * dy * np.einsum('ij,ij', Axy, U1*U2)
def ROM_HG_knm(m, mode_in, mode_out, q1, q2, q1y=None, q2y=None):
pass
def knmHG(couplings, surface_map, q1, q2, q1y=None, q2y=None, method="riemann"):
couplings = np.array(couplings)
a = couplings.size / 4.0
if int(a) - a != 0:
raise BasePyKatException("Iterator should be product of 4, each element of coupling array should be [n,m,n',m']")
if "phase" in surface_map.type:
Axy = np.exp(2j * 2 * math.pi / q1.wavelength * surface_map.data * surface_map.scaling)
x = surface_map.x
y = surface_map.y
K = np.zeros((couplings.size/4,), dtype=np.complex128)
it = np.nditer(couplings, flags=['refs_ok','f_index'])
i = 0
while not it.finished:
try:
mode_in = [int(it.next()), int(it.next())]
mode_out = [int(it.next()), int(it.next())]
if method == "riemann":
K[i] = riemann_HG_knm(x, y, mode_in, mode_out, q1=q1, q2=q2, q1y=q1y, q2y=q2y, Axy=Axy)
else:
raise BasePyKatException("method value not accepted")
i +=1
except StopIteration:
break
return K.reshape(couplings.shape[:-1])
\ No newline at end of file
pykat/utilities/maps.py
+ 24
− 5
View file @ c9f32128
from pykat.utilities.romhom import makeReducedBasis, makeEmpiricalInterpolant, makeWeights
import numpy
class surfacemap:
def __init__(self, name, maptype, size, center, step_size, scaling, data=None):
......@@ -11,6 +11,7 @@ class surfacemap:
self.step_size = step_size
self.scaling = scaling
self.data = data
self._rom_weights = None
def write_map(self, filename):
with open(filename,'w') as mapfile:
......@@ -31,16 +32,32 @@ class surfacemap:
@property
def x(self):
return self.step_size[0] * (numpy.array(range(0, self.data.shape[0]))- self.center[0])
return self.step_size[0] * (numpy.array(range(1, self.data.shape[0]+1)) - self.center[0])
@property
def y(self):
return self.step_size[1] * (numpy.array(range(0, self.data.shape[1]))- self.center[1])
return self.step_size[1] * (numpy.array(range(1, self.data.shape[1]+1))- self.center[1])
@property
def offset(self):
return numpy.array(self.step_size)*(self.center - numpy.array(self.size)/2)
@property
def ROMWeights(self):
return self._rom_weights
def generateROMWeights(self):
b = makeReducedBasis(self.x[0:(len(self.x)/2)], offset=self.offset)
EI = makeEmpiricalInterpolant(b)
self._rom_weights = makeWeights(self, EI)
return self.ROMWeights
def plot(self, show=True, clabel=None):
import pylab
# 100 factor for scaling to cm
xrange = 100*self.x
yrange = 100*self.y
......@@ -61,6 +78,8 @@ class surfacemap:
return fig
def read_map(filename):
with open(filename, 'r') as f:
......
pykat/utilities/optics/gaussian_beams.py
+ 91
− 15
View file @ c9f32128
......@@ -81,7 +81,57 @@ class gauss_param(object):
@property
def w(self):
return abs(self.__q)*math.sqrt(self.__lambda / (self.__nr * math.pi * self.__q.imag))
#return self.w0 * math.sqrt(1 + (self.__q.real/self.__q.imag)**2)
def w(self, z=None, wavelength=None, nr=None, w0=None):
if z == None:
z = self.z
else:
z = np.array(z)
if wavelength == None:
wavelength = self.wavelength
else:
wavelength = np.array(wavelength)
if nr == None:
nr = self.nr
else:
nr = np.array(nr)
if w0 == None:
w0 = self.w0
else:
w0 = np.array(w0)
q = z + 1j * math.pi * w0 **2 / wavelength
return np.abs(q)*np.sqrt(wavelength / (nr * math.pi * q.imag))
def gouy(self, z=None, wavelength=None, nr=None, w0=None):
if z == None:
z = self.z
else:
z = np.array(z)
if wavelength == None:
wavelength = self.wavelength
else:
wavelength = np.array(wavelength)
if nr == None:
nr = self.nr
else:
nr = np.array(nr)
if w0 == None:
w0 = self.w0
else:
w0 = np.array(w0)
q = z + 1j * math.pi * w0 **2 / wavelength
return np.arctan2(q.real, q.imag)
@property
def w0(self):
......@@ -94,6 +144,31 @@ class gauss_param(object):
else:
return float("inf")
def Rc(self, z=None, wavelength=None, nr=None, w0=None):
if z == None:
z = self.z
else:
z = np.array(z)
if wavelength == None:
wavelength = self.wavelength
else:
wavelength = np.array(wavelength)
if nr == None:
nr = self.nr
else:
nr = np.array(nr)
if w0 == None:
w0 = self.w0
else:
w0 = np.array(w0)
q = z + 1j * math.pi * w0 **2 / wavelength
return q.real * (1+ (q.imag/q.real)**2)
def conjugate(self):
return beam_param(self.__lambda, self.__nr, self.__q.conjugate())
......@@ -145,6 +220,9 @@ class gauss_param(object):
return beam_param(self.__lambda, self.__nr, -self.__q)
def __eq__(self, q):
if q == None:
return False
return complex(q) == self.__q
@property
......@@ -161,26 +239,24 @@ class gauss_param(object):
def reverse(self):
self.__q = -1.0 * self.__q.real + 1j * self.__q.imag
class beam_param(gauss_param):
pass
class HG_beam(object):
def __init__(self, qx, qy=None, n=0, m=0):
self._qx = copy.deepcopy(qx)
self._2pi_qrt = math.pow(2.0/math.pi, 0.25)
if qy.__class__ == beam_param:
if qy == None:
self._qy = copy.deepcopy(qx)
else:
self._qy = copy.deepcopy(qy)
self._n = n
self._m = m
self._hn = hermite(n)
self._hm = hermite(m)
self._n = int(n)
self._m = int(m)
self._hn = hermite(self._n)
self._hm = hermite(self._m)
self._calc_constants()
@property
......@@ -238,12 +314,12 @@ class HG_beam(object):
def _calc_constants(self):
self.__xpre_const = math.pow(2.0/math.pi, 0.25)
self.__xpre_const *= math.sqrt(1.0/(2**self._n * math.factorial(self._n)))
self.__xpre_const *= math.sqrt(1.0/(self._qx.w*2**self._n * math.factorial(self._n)))
self.__xpre_const *= cmath.sqrt(1j*self._qx.imag / self._qx.q)
self.__xpre_const *= ((1j*self._qx.imag * self._qx.q.conjugate())/(-1j*self._qx.imag * self._qx.q)) ** ( self._n/2.0)
self.__ypre_const = math.pow(2.0/math.pi, 0.25)
self.__ypre_const *= math.sqrt(1.0/(2**self._m * math.factorial(self._m)))
self.__ypre_const *= math.sqrt(1.0/(self._qy.w*2**self._m * math.factorial(self._m)))
self.__ypre_const *= cmath.sqrt(1j*self._qy.imag / self._qy.q)
self.__ypre_const *= ((1j*self._qy.imag * self._qy.q.conjugate())/(-1j*self._qy.imag * self._qy.q)) **(self._m/2.0)
......@@ -263,7 +339,9 @@ class HG_beam(object):
return self.__ypre_const * self._hm(self.__sqrt2_wyz * y) * np.exp(-0.5j * self.__ky * y*y * self.__invqy)
def Unm(self, x, y):
return self.Un(x) * self.Um(y)
_un = self.Un(x)
_um = self.Um(y)
return np.outer(_un, _um)
def plot(self, ndx=100, ndy=100, xscale=4, yscale=4):
import pylab
......@@ -274,9 +352,7 @@ class HG_beam(object):
dx = xrange[1]-xrange[0]
dy = yrange[1]-yrange[0]
xx, yy = np.meshgrid(xrange,yrange)
data = self.Unm(xx, yy)
data = self.Unm(xrange,yrange)
fig = pylab.figure()
axes = pylab.imshow(np.abs(data), aspect=dx/dy, extent=[min(xrange),max(xrange),min(yrange),max(yrange)])
......
pykat/utilities/romhom.py 0 → 100644
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import maps
import os.path
import numpy as np
import pykat
import collections
from itertools import combinations_with_replacement as combinations
from pykat.utilities.optics.gaussian_beams import beam_param, HG_beam
from scipy.linalg import inv
from math import factorial
from hermite import *
import math
EmpiricalInterpolant = collections.namedtuple('EmpiricalInterpolant', 'B nodes node_indices limits x')
ReducedBasis = collections.namedtuple('ReducedBasis', 'RB limits x')
ROMLimits = collections.namedtuple('ROMLimits', 'zmin zmax w0min w0max max_order')
class ROMWeights:
def __init__(self, w_ij_Q1, w_ij_Q2, w_ij_Q3, w_ij_Q4, limits):
self.w_ij_Q1 = w_ij_Q1
self.w_ij_Q2 = w_ij_Q2
self.w_ij_Q3 = w_ij_Q3
self.w_ij_Q4 = w_ij_Q4
self.limits = limits
def writeToFile(self, filename):
f = open(filename, 'w+')
f.write(repr(self.limits) + "\n")
f.write(repr(self.w_ij_Q1.shape) + "\n")
for v in self.w_ij_Q1.flatten():
f.write("%s " % repr(complex(v))[1:-1])
f.write("\n")
f.write(repr(self.w_ij_Q2.shape) + "\n")
for v in self.w_ij_Q2.flatten():
f.write("%s " % repr(complex(v))[1:-1])
f.write("\n")
f.write(repr(self.w_ij_Q3.shape) + "\n")
for v in self.w_ij_Q3.flatten():
f.write("%s " % repr(complex(v))[1:-1])
f.write("\n")
f.write(repr(self.w_ij_Q4.shape) + "\n")
for v in self.w_ij_Q4.flatten():
f.write("%s " % repr(complex(v))[1:-1])
f.write("\n")
f.close()
def combs(a, r):
"""
Return successive r-length combinations of elements in the array a.
Should produce the same output as array(list(combinations(a, r))), but
faster.
"""
a = np.asarray(a)
dt = np.dtype([('', a.dtype)]*r)
b = np.fromiter(combinations(a, r), dt)
return b.view(a.dtype).reshape(-1, r)
def project_onto_basis(integration_weights, e, h, projections, proj_coefficients, idx):
for j in range(len(h)):
proj_coefficients[idx][j] = np.vdot(integration_weights* e[idx], h[j])
projections[j] += proj_coefficients[idx][j]*e[idx]
return projections
def B_matrix(invV, e):
return np.inner(invV.T, e[0:(invV.shape[0])].T)
def emp_interp(B_matrix, func, indices):
# B : RB matrix
assert B_matrix.shape[0] == len(indices)
interpolant = np.inner(func[indices].T, B_matrix.T)
return interpolant
def w(w0, im_q, re_q):
return w0 * np.sqrt( 1 + (re_q / im_q)**2. )
def u(re_q1, w0_1, n1, x):
im_q1 = np.pi*w0_1**2 / 1064e-9
q_z1 = re_q1 + 1j*im_q1
A_n1 = (2./np.pi)**(1./4.) * (1./((2.**n1)*factorial(n1)*w0_1))**(1./2.) * (im_q1 / q_z1)**(1./2.) * ( im_q1*q_z1.conjugate() / (-im_q1*q_z1) )**(n1/2.)
wz1 = w(w0_1, im_q1, re_q1)
return A_n1 * hermite(n1, np.sqrt(2.)*x / wz1) * np.exp(-1j*(2*math.pi/(1064e-9))* x**2 /(2.*q_z1))
def u_star_u(re_q1, re_q2, w0_1, w0_2, n1, n2, x):
return u(re_q1, w0_1, n1, x) * u(re_q2, w0_2, n2, x).conjugate()
def makeReducedBasis(x, offset=np.array([0,0]), isModeMatched=True, tolerance = 1e-12, sigma = 1):
if isModeMatched:
greedypts = 'matched20.txt'
else:
greedypts = 'mismatched20.txt'
greedyfile = os.path.join(pykat.__path__[0],'utilities','greedypoints',greedypts)
limits = np.loadtxt(greedyfile, usecols=(1,))[:5]
romlimits = ROMLimits(w0min=limits[0], w0max=limits[1], zmin=limits[2], zmax=limits[3], max_order=limits[4])
w_min = limits[0]
w_max = limits[1]
re_q_min = limits[2]
re_q_max = limits[3]
max_order = int(limits[4])
indices = range(0, max_order+1)
nm_pairs = combs(indices, 2)
dx = x[1] - x[0]
params = np.loadtxt(greedyfile, skiprows=5)
TS_size = len(params) # training space of TS_size number of waveforms
#### allocate memory for training space ####
TS = np.zeros(TS_size*len(x), dtype = complex).reshape(TS_size, len(x)) # store training space in TS_size X len(x) array
IDx = 0 #TS index
for i in range(len(params)):
q1 = beam_param(w0=params[i][0], z=params[i][2])
if isModeMatched:
q2 = q1
n = int(params[i][2])
m = int(params[i][3])
w0_1 = params[i][0]
w0_2 = w0_1
re_q1 = params[i][1]
re_q2 = re_q1
else:
q2 = beam_param(w0=params[i][1], z=params[i][3])
n = int(params[i][4])
m = int(params[i][5])
TS[IDx] = u_star_u(re_q1, re_q2, w0_1, w0_2, n, m, x)
# normalize
norm = np.sqrt(abs(np.vdot(dx * TS[IDx], TS[IDx])))
if norm != 0:
TS[IDx] /= norm
IDx += 1
else:
np.delete(TS, IDx)
#### Begin greedy: see Field et al. arXiv:1308.3565v2 ####
tolerance = 1e-12 # set maximum RB projection error
sigma = 1 # projection error at 0th iteration
RB_matrix = [TS[0]] # seed greedy algorithm (arbitrary)
proj_coefficients = np.zeros(TS_size*TS_size, dtype = complex).reshape(TS_size, TS_size)
projections = np.zeros(TS_size*len(x), dtype = complex).reshape(TS_size, len(x))
iter = 0
while sigma > tolerance:
#for k in range(TS_size-1):
# go through training set and find worst projection error
projections = project_onto_basis(dx, RB_matrix, TS, projections, proj_coefficients, iter)
residual = TS - projections
projection_errors = [np.vdot(dx* residual[i], residual[i]) for i in range(len(residual))]
sigma = abs(max(projection_errors))
index = np.argmax(projection_errors)
#Gram-Schmidt to get the next basis and normalize
next_basis = TS[index] - projections[index]
next_basis /= np.sqrt(abs(np.vdot(dx* next_basis, next_basis)))
RB_matrix.append(next_basis)
iter += 1
return ReducedBasis(RB=np.array(RB_matrix), limits=romlimits, x=x)
def makeEmpiricalInterpolant(RB):
e_x = RB.RB
x = RB.x
node_indices = []
x_nodes = []
V = np.zeros((len(e_x), len(e_x)), dtype = complex)
# seed EIM algorithm
node_indices.append( int(np.argmax( np.abs(e_x[0]) )))
x_nodes.append(x[node_indices])
for i in range(1, len(e_x)):
#build empirical interpolant for e_iter
for j in range(len(node_indices)):
for k in range(len(node_indices)):
V[k][j] = e_x[j][node_indices[k]]
invV = inv(V[0:len(node_indices), 0:len(node_indices)])
B = B_matrix(invV, e_x)
interpolant = emp_interp(B, e_x[i], node_indices)
res = interpolant - e_x[i]
index = int(np.argmax(np.abs(res)))
node_indices.append(index)
x_nodes.append( x[index] )
# make B matrix with all the indices
for j in range(len(node_indices)):
for k in range(len(node_indices)):
V[k][j] = e_x[j][node_indices[k]]
invV = inv(V[0:len(node_indices), 0:len(node_indices)])
B = B_matrix(invV, e_x)
return EmpiricalInterpolant(B=np.array(B), nodes=np.array(x_nodes), node_indices=np.array(node_indices), limits=RB.limits, x=RB.x)
def makeWeights(smap, EI):
# get full A_xy
A_xy = smap.data
hx = len(smap.x)/2
hy = len(smap.y)/2
fx = hx*2
fy = hy*2
# get A_xy in the four quadrants of the x-y plane
A_xy_Q1 = A_xy[0:hx][0:hy, hy:fy]
A_xy_Q2 = A_xy[hx:fx][0:hy, hy:fy]
A_xy_Q3 = A_xy[hx:fx][0:hy, 0:hy]
A_xy_Q4 = A_xy[0:hx][0:hy, 0:hy]
full_x = smap.x
full_y = smap.y
dx = full_x[1] - full_x[0]
dy = full_y[1] - full_y[0]
B = EI.B
nodes_nv = EI.nodes
nodes_pv = - EI.nodes
# make integration weights
w_ij_Q1 = np.zeros((len(B), len(B)), dtype = complex)
w_ij_Q2 = np.zeros((len(B), len(B)), dtype = complex)
w_ij_Q3 = np.zeros((len(B), len(B)), dtype = complex)
w_ij_Q4 = np.zeros((len(B), len(B)), dtype = complex)
for i in range(len(B)):
for j in range(len(B)):
B_ij_Q1 = np.outer(B[i], B[j][::-1])
w_ij_Q1[i][j] = dx*dy*np.einsum('ij,ij', B_ij_Q1, A_xy_Q1)
B_ij_Q2 = np.outer(B[i][::-1], B[j][::-1])
w_ij_Q2[i][j] = dx*dy*np.einsum('ij,ij', B_ij_Q2, A_xy_Q2)
B_ij_Q3 = np.outer(B[i][::-1], B[j])
w_ij_Q3[i][j] = dx*dy*np.einsum('ij,ij', B_ij_Q3, A_xy_Q3)
B_ij_Q4 = np.outer(B[i], B[j])
w_ij_Q4[i][j] = dx*dy*np.einsum('ij,ij', B_ij_Q4, A_xy_Q4)
return ROMWeights(w_ij_Q1=w_ij_Q1, w_ij_Q2=w_ij_Q2, w_ij_Q3=w_ij_Q3, w_ij_Q4=w_ij_Q4, limits=EI.limits)
def ROMKnm(W, max_order, q1, q2, q1y=None, q2y=None):
if q1y == None:
q1y = q1
if q2y == None:
q2y = q2
# get symmetric and anti-symmetric w_ij's
w_ij_Q1Q3 = W.w_ij_Q1 + W.w_ij_Q3
w_ij_Q2Q4 = W.w_ij_Q2 + W.w_ij_Q4
w_ij_Q1Q2 = W.w_ij_Q1 + W.w_ij_Q2
w_ij_Q1Q4 = W.w_ij_Q1 + W.w_ij_Q4
w_ij_Q2Q3 = W.w_ij_Q2 + W.w_ij_Q3
w_ij_Q3Q4 = W.w_ij_Q3 + W.w_ij_Q4
w_ij_Q1Q2Q3Q4 = W.w_ij_Q1 + W.w_ij_Q3 + W.w_ij_Q2 + W.w_ij_Q4
num_fields = int((max_order + 1) * (max_order + 2) / 2);
K_ROQ = np.array((num_fields, num_fields))
for i in range(len(nm_pairs)):
for j in range(len(nm_pairs)):
# full quadrature
n = nm_pairs[i][0]
m = nm_pairs[i][1]
npr = nm_pairs[j][0]
mpr = nm_pairs[j][1]
u_xy = np.outer(u_star_u(re_q1, re_q2, w0_1, w0_2, n, m, full_x), u_star_u(re_q1, re_q2, w0_1, w0_2, npr, mpr, full_x))
k = dx*dy*np.einsum('ij,ij', u_xy, A_xy)
# ROQ
if nm_pairs[i][0] % 2 == 0 and nm_pairs[i][1] % 2 == 0 and nm_pairs[j][0] % 2 == 0 and nm_pairs[j][1] % 2 == 0:
u_xy_nodes = np.outer(u_star_u(re_q1, re_q2, w0_1, w0_2, n, m, nodes_nv), u_star_u(re_q1, re_q2, w0_1, w0_2, npr, mpr, nodes_nv))
k_ROQ = np.einsum('ij,ij', u_xy_nodes, w_ij_Q1Q2Q3Q4)
elif nm_pairs[i][0] % 2 == 1 and nm_pairs[i][1] % 2 == 1 and nm_pairs[j][0] % 2 == 1 and nm_pairs[j][1] % 2 == 1:
u_xy_nodes = np.outer(u_star_u(re_q1, re_q2, w0_1, w0_2, n, m, nodes_nv), u_star_u(re_q1, re_q2, w0_1, w0_2, npr, mpr, nodes_nv))
k_ROQ = np.einsum('ij,ij', u_xy_nodes, w_ij_Q1Q2Q3Q4)
elif nm_pairs[i][0] % 2 == 0 and nm_pairs[i][1] % 2 == 0 and nm_pairs[j][0] % 2 == 1 and nm_pairs[j][1] % 2 == 1:
u_xy_nodes = np.outer(u_star_u(re_q1, re_q2, w0_1, w0_2, n, m, nodes_nv), u_star_u(re_q1, re_q2, w0_1, w0_2, npr, mpr, nodes_nv))
k_ROQ = np.einsum('ij,ij', u_xy_nodes, w_ij_Q1Q2Q3Q4)
elif nm_pairs[i][0] % 2 == 1 and nm_pairs[i][1] % 2 == 1 and nm_pairs[j][0] % 2 == 0 and nm_pairs[j][1] % 2 == 0:
u_xy_nodes = np.outer(u_star_u(re_q1, re_q2, w0_1, w0_2, n, m, nodes_nv), u_star_u(re_q1, re_q2, w0_1, w0_2, npr, mpr, nodes_nv))
k_ROQ = np.einsum('ij,ij', u_xy_nodes, w_ij_Q1Q2Q3Q4)
elif nm_pairs[i][0] % 2 == 0 and nm_pairs[i][1] % 2 == 1 or nm_pairs[i][0] % 2 == 1 and nm_pairs[i][1] % 2 == 0:
u_x_nodes = u_star_u(re_q1, re_q2, w0_1, w0_2, n,m, nodes_nv)
u_y_nodes = u_star_u(re_q1, re_q2, w0_1, w0_2, npr, mpr, nodes_nv)
if nm_pairs[j][0] % 2 == 0 and nm_pairs[j][1] % 2 == 0 or nm_pairs[j][0] % 2 == 1 and nm_pairs[j][1] % 2 == 1:
u_xy_nodes_Q1Q4 = np.outer(u_x_nodes, u_y_nodes)
u_xy_nodes_Q2Q3 = - u_xy_nodes_Q1Q4
k_ROQ = np.einsum('ij,ij', u_xy_nodes_Q1Q4, w_ij_Q1Q4) + np.einsum('ij,ij', u_xy_nodes_Q2Q3, w_ij_Q2Q3)
else:
u_xy_nodes_Q2Q4 = np.outer(u_x_nodes, u_y_nodes)
u_xy_nodes_Q1Q3 = - u_xy_nodes_Q2Q4
k_ROQ = np.einsum('ij,ij', u_xy_nodes_Q2Q4, w_ij_Q2Q4) + np.einsum('ij,ij', u_xy_nodes_Q1Q3, w_ij_Q1Q3)
elif nm_pairs[j][0] % 2 == 0 and nm_pairs[j][1] % 2 == 1 or nm_pairs[j][0] % 2 == 1 and nm_pairs[j][1] % 2 == 0:
u_x_nodes = u_star_u(re_q1, re_q2, w0_1, w0_2, n, m, nodes_nv)
u_y_nodes = u_star_u(re_q1, re_q2, w0_1, w0_2, npr, mpr, nodes_nv)
if nm_pairs[i][0] % 2 == 0 and nm_pairs[i][1] % 2 == 0 or nm_pairs[i][0] % 2 == 1 and nm_pairs[i][1] % 2 == 1:
u_xy_nodes_Q3Q4 = np.outer(u_x_nodes, u_y_nodes)
u_xy_nodes_Q1Q2 = - u_xy_nodes_Q3Q4
k_ROQ = np.einsum('ij,ij', u_xy_nodes_Q3Q4, w_ij_Q3Q4) + np.einsum('ij,ij', u_xy_nodes_Q1Q2, w_ij_Q1Q2)
else:
u_xy_nodes_Q2Q4 = np.outer(u_x_nodes, u_y_nodes)
u_xy_nodes_Q1Q3 = - u_xy_nodes_Q2Q4
k_ROQ = np.einsum('ij,ij', u_xy_nodes_Q2Q4, w_ij_Q2Q4) + np.einsum('ij,ij', u_xy_nodes_Q1Q3, w_ij_Q1Q3)
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