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Commit 338b40b1 authored by Daniel Brown's avatar Daniel Brown
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adding bayerhelms knm calculator, fixing bits with maps and romhom

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pykat/__init__.py
+ 1
− 0
View file @ 338b40b1
......@@ -5,3 +5,4 @@ import components
import detectors
import commands
from pykat.utilities.optics.gaussian_beams import beam_param
pykat/utilities/knm.py
+ 225
− 97
View file @ 338b40b1
......@@ -2,12 +2,14 @@ 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 time
import maps
import os.path
import numpy as np
import pykat
import collections
import math
import cmath
from romhom import u_star_u
from progressbar import ProgressBar, ETA, Percentage, Bar
......@@ -34,7 +36,7 @@ def makeCouplingMatrix(max_order):
return np.array(M)
def riemann_HG_knm(x, y, mode_in, mode_out, q1, q2, q1y=None, q2y=None, Axy=None, cache=None):
def riemann_HG_knm(x, y, mode_in, mode_out, q1, q2, q1y=None, q2y=None, Axy=None, cache=None, delta=(0,0)):
if Axy == None:
Axy == np.ones((len(x), len(y)))
......@@ -55,7 +57,7 @@ def riemann_HG_knm(x, y, mode_in, mode_out, q1, q2, q1y=None, q2y=None, Axy=None
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])
U1 = Hg_in.Unm(x,y)
U1 = Hg_in.Unm(x+delta[0], y+delta[1])
U2 = Hg_out.Unm(x,y).conjugate()
return dx * dy * np.einsum('ij,ij', Axy, U1*U2)
......@@ -69,8 +71,7 @@ def riemann_HG_knm(x, y, mode_in, mode_out, q1, q2, q1y=None, q2y=None, Axy=None
def __gen_riemann_knm_cache(x, y, couplings, q1, q2, q1y=None, q2y=None):
def __gen_riemann_knm_cache(x, y, couplings, q1, q2, q1y=None, q2y=None, delta=(0,0)):
if q1y == None:
q1y = q1
......@@ -89,20 +90,24 @@ def __gen_riemann_knm_cache(x, y, couplings, q1, q2, q1y=None, q2y=None):
strx = "u1[%i,%i]" % (mode_in[0], mode_out[0])
stry = "u2[%i,%i]" % (mode_in[1], mode_out[1])
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])
#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])
if strx not in cache:
cache[strx] = Hg_in.Un(x) * Hg_out.Un(x).conjugate()
cache[strx] = u_star_u(q1.z, q2.z, q1.w0, q2.w0, mode_in[0], mode_out[0], x, x+delta[0])
#Hg_in.Un(x) * Hg_out.Un(x).conjugate()
if stry not in cache:
cache[stry] = Hg_in.Um(y) * Hg_out.Um(y).conjugate()
cache[stry] = u_star_u(q1y.z, q2y.z, q1y.w0, q2y.w0, mode_in[1], mode_out[1], y, y+delta[1])
#Hg_in.Um(y) * Hg_out.Um(y).conjugate()
except StopIteration:
break
return cache
def __gen_ROM_HG_knm_cache(weights, couplings, q1, q2, q1y=None, q2y=None):
if q1y == None:
......@@ -142,6 +147,8 @@ def __gen_ROM_HG_knm_cache(weights, couplings, q1, q2, q1y=None, q2y=None):
return cache
def ROM_HG_knm(weights, mode_in, mode_out, q1, q2, q1y=None, q2y=None, cache=None):
if q1y == None:
q1y = q1
......@@ -157,10 +164,6 @@ def ROM_HG_knm(weights, mode_in, mode_out, q1, q2, q1y=None, q2y=None, cache=Non
npr = mode_in[1]
mpr = mode_out[1]
foundSymmetry = np.all(weights.EI["ym"].nodes == weights.EI["xm"].nodes) and np.all(weights.EI["xp"].nodes == -weights.EI["xm"].nodes) and np.all(weights.EI["yp"].nodes == -weights.EI["ym"].nodes)
if foundSymmetry:
if cache == None:
u_x_nodes = u_star_u(q1.z, q2.z, q1.w0, q2.w0, n, m, weights.EI["xm"].nodes)
u_y_nodes = u_star_u(q1y.z, q2y.z, q1y.w0, q2y.w0, npr, mpr, weights.EI["ym"].nodes)
......@@ -211,28 +214,104 @@ def ROM_HG_knm(weights, mode_in, mode_out, q1, q2, q1y=None, q2y=None, cache=Non
else:
k_ROQ = np.einsum('ij,ij', u_xy_nodes, w_ij_Q2Q4) + np.einsum('ij,ij', -u_xy_nodes, w_ij_Q1Q3)
else:
# If there is no symmetry about the axes then each quadrant is different
u_xm_nodes = u_star_u(q1.z, q2.z, q1.w0, q2.w0, n, m, weights.EI["xm"].nodes)
u_xp_nodes = u_star_u(q1.z, q2.z, q1.w0, q2.w0, n, m, weights.EI["xp"].nodes)
u_ym_nodes = u_star_u(q1y.z, q2y.z, q1y.w0, q2y.w0, npr, mpr, weights.EI["ym"].nodes)
u_yp_nodes = u_star_u(q1y.z, q2y.z, q1y.w0, q2y.w0, npr, mpr, weights.EI["yp"].nodes)
u_xy_Q1 = np.outer(u_xm_nodes, u_yp_nodes)
u_xy_Q2 = np.outer(u_xp_nodes, u_yp_nodes)
u_xy_Q3 = np.outer(u_xp_nodes, u_ym_nodes)
u_xy_Q4 = np.outer(u_xm_nodes, u_ym_nodes)
k_ROQ = np.einsum('ij,ij', u_xy_Q1, weights.w_ij_Q1)
k_ROQ += np.einsum('ij,ij', u_xy_Q2, weights.w_ij_Q2)
k_ROQ += np.einsum('ij,ij', u_xy_Q3, weights.w_ij_Q3)
k_ROQ += np.einsum('ij,ij', u_xy_Q4, weights.w_ij_Q4)
return k_ROQ
__fac_cache = []
def fac(n):
global __fac_cache
return __fac_cache[n]
#return math.factorial(int(n))
def m_1_pow(n):
if n % 2 == 0:
return 1
else:
return -1
def __Ss(u, _u, F, _F, d=0):
r = 0
for s in range(0, min(u,_u)+1):
r += m_1_pow(s) * _F ** (u-s) * _F ** (_u-s) / (fac(2*s+d)*fac(u-s)*fac(_u-s))
return r
def knmHG(couplings, q1, q2, surface_map=None, q1y=None, q2y=None, method="riemann", verbose=True):
def __S(m, _m, X, _X, F, _F, d=0):
if m % 2 == 1:
lim1 = (m-1)/2
else:
lim1 = m/2
if _m % 2 == 1:
lim2 = (_m-1)/2
else:
lim2 = _m/2
r = 0
for u in range(0, lim1+1):
for _u in range(0, lim2+1):
r += m_1_pow(u) * _X**(m-2*u) * X**(_m-2*_u) / ( fac(m-2*u)*fac(_m-2*_u) ) * __Ss(u, _u, F, _F, d=d)
return r
def __bayerhelms_kn(n, _n, q1, q2, gamma=0.0):
K0 = (q1.zr - q2.zr)/q2.zr
K2 = (q1.z - q2.z)/q2.zr
K = (K0 + 1j*K2)/2.0
Ktilde = abs(K / (1+K))
if gamma != 0:
a = q2.zr * math.sin(gamma) / (cmath.sqrt(1+K.conjugate()) * q2.w0)
_X = - a * (q2.z/q2.zr - 1j)
X = - a * (q2.z/q2.zr + 1j*(1+2*K.conjugate()))
Ex = cmath.exp(-_X*X / 2.0)
else:
_X = 0.0
X = 0.0
Ex = 1.0
_F = K / (2.0 * (1.0+K0))
F = K.conjugate() / 2.0
Sg = __S(n, _n, X, _X, F, _F)
if n > 0 and _n > 0:
Su = __S(n-1, _n-1, X, _X, F, _F, 1)
else:
Su = 0
b = m_1_pow(_n) * cmath.sqrt(fac(n) * fac(_n) * (1.0 + K.real)**(n+0.5) * (1.0 + K.conjugate()) ** (-(n+_n+1)))
return b * Ex * (Sg - Su)
def bayerhelms_HG_knm(mode_in, mode_out, q1, q2, q1y=None, q2y=None, gamma=(0,0)):
if q1y == None:
q1y = q1
if q2y == None:
q2y = q2
# x modes
n = mode_in[0]
_n = mode_out[0]
# y modes
m = mode_in[1]
_m = mode_out[1]
return __bayerhelms_kn(n,_n, q1, q2, 2*gamma[0]) * __bayerhelms_kn(m, _m, q1y, q2y, 2*gamma[1])
def knmHG(couplings, q1, q2, surface_map=None, q1y=None, q2y=None, method="riemann", verbose=False, profile=False, gamma=(0,0), delta=(0,0)):
if q1y == None:
q1y = q1
......@@ -248,6 +327,18 @@ def knmHG(couplings, q1, q2, surface_map=None, q1y=None, q2y=None, method="riema
if int(a) - a != 0:
raise BasePyKatException("Iterator should be product of 4, each element of coupling array should be [n,m,n',m']")
maxtem = 0
c = couplings.flatten()
for i in range(0, c.size/2):
maxtem = max(sum(c[i*2:(i*2+2)]), maxtem)
global __fac_cache
for n in range(0, maxtem+1):
__fac_cache.append(math.factorial(n))
if surface_map != None:
Axy = surface_map.z_xy(q1.wavelength)
x = surface_map.x
......@@ -259,6 +350,9 @@ def knmHG(couplings, q1, q2, surface_map=None, q1y=None, q2y=None, method="riema
i = 0
if profile:
t0 = time.time()
if method == "romhom":
if surface_map == None:
raise BasePyKatException("Using 'romhom' method requires a surface map to be specified")
......@@ -268,32 +362,44 @@ def knmHG(couplings, q1, q2, surface_map=None, q1y=None, q2y=None, method="riema
if weights == None:
raise BasePyKatException("The ROM weights need to be generated for this map before use.")
if verbose: print "Computing caches"
cache = __gen_ROM_HG_knm_cache(weights, couplings, q1=q1, q2=q2, q1y=q1y, q2y=q2y)
elif method == "riemann":
if verbose: print "Computing caches"
cache = __gen_riemann_knm_cache(x, y, couplings, q1, q2, q1y=None, q2y=None)
if surface_map == None:
raise BasePyKatException("Using 'riemann' method requires a surface map to be specified")
cache = __gen_riemann_knm_cache(x, y, couplings, q1, q2, q1y=None, q2y=None, delta=delta)
else:
cache = None
weights = None
if profile:
cache_time = time.time() - t0
Ktime = np.zeros((couplings.size/4,), dtype=np.float64)
if verbose:
p = ProgressBar(maxval=couplings.size, widgets=["Knm (%s): " % method, Percentage(), Bar(), ETA()])
while not it.finished:
try:
if profile:
t0 = time.time()
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, cache=cache)
K[i] = riemann_HG_knm(x, y, mode_in, mode_out, q1=q1, q2=q2, q1y=q1y, q2y=q2y, Axy=Axy, cache=cache, delta=delta)
elif method == "romhom":
K[i] = ROM_HG_knm(weights, mode_in, mode_out, q1=q1, q2=q2, q1y=q1y, q2y=q2y, cache=cache)
elif method == "bayerhelms":
K[i] = bayerhelms_HG_knm(mode_in, mode_out, q1=q1, q2=q2, q1y=q1y, q2y=q2y, gamma=gamma)
else:
raise BasePyKatException("method value '%s' not accepted" % method)
if profile:
Ktime[i] = time.time() - t0
i +=1
if verbose:
......@@ -303,19 +409,41 @@ def knmHG(couplings, q1, q2, surface_map=None, q1y=None, q2y=None, method="riema
except StopIteration:
break
if profile:
return K.reshape(couplings.shape[:-1]), Ktime.reshape(couplings.shape[:-1]), cache_time
else:
return K.reshape(couplings.shape[:-1])
def plot_knm_matrix(couplings, knm):
import pylab as plt
fig = plt.figure()
ax = fig.add_subplot(111)
cax = ax.imshow(knm, interpolation='nearest')
fig.colorbar(cax)
numrows, numcols = knm.shape
c = couplings[:, 0, :2]
c_ = []
for d in c:
c_.append("%i,%i"%(d[0], d[1]))
ax.set_xticklabels(c_)
ax.set_yticklabels(c_)
def format_coord(x, y):
col = int(x+0.5)
row = int(y+0.5)
if col>=0 and col<numcols and row>=0 and row<numrows:
z = knm[row,col]
return 'x=%s, y=%s, z=%1.4f' % (c_[col], c_[row], z)
else:
return 'x=%1.4f, y=%1.4f'%(x, y)
ax.format_coord = format_coord
plt.show()
pykat/utilities/maps.py
+ 3
− 10
View file @ 338b40b1
......@@ -65,25 +65,18 @@ class surfacemap(object):
raise BasePyKatException("Map type needs handling")
def generateROMWeights(self, isModeMatched=True):
xp = self.x[self.x>0]
yp = self.y[self.y>0]
def generateROMWeights(self, isModeMatched=True, verbose=False):
xm = self.x[self.x<0]
ym = self.y[self.y<0]
EI = {}
if len(xm) > 0: EI["xm"] = makeEmpiricalInterpolant(makeReducedBasis(xm, isModeMatched=isModeMatched))
if len(xp) > 0: EI["xp"] = makeEmpiricalInterpolant(makeReducedBasis(xp, isModeMatched=isModeMatched))
if len(ym) > 0: EI["ym"] = makeEmpiricalInterpolant(makeReducedBasis(ym, isModeMatched=isModeMatched))
if len(yp) > 0: EI["yp"] = makeEmpiricalInterpolant(makeReducedBasis(yp, isModeMatched=isModeMatched))
#if len(x0) > 0: EI["x0"] = makeEmpiricalInterpolant(makeReducedBasis(x0, isModeMatched=isModeMatched))
#if len(y0) > 0: EI["y0"] = makeEmpiricalInterpolant(makeReducedBasis(y0, isModeMatched=isModeMatched))
EI["limits"] = EI["xm"].limits
self._rom_weights = makeWeights(self, EI)
self._rom_weights = makeWeights(self, EI, verbose=verbose)
return self.ROMWeights, EI
......@@ -129,7 +122,7 @@ class tiltmap(surfacemap):
xx, yy = np.meshgrid(self.x, self.y)
self.data = xx * self.tilt[0] + yy * self.tilt[1]
self.data = xx * self.tilt[1] + yy * self.tilt[0]
......
pykat/utilities/romhom.py
+ 23
− 27
View file @ 338b40b1
import math
import maps
import os.path
import pykat
import collections
......@@ -109,8 +108,11 @@ def u(re_q1, w0_1, n1, x):
return A_n1 * hermite(n1, np.sqrt(2.)*x / wz1) * np.exp(np.array(-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 u_star_u(re_q1, re_q2, w0_1, w0_2, n1, n2, x, x2=None):
if x2 == None:
x2 = x
return u(re_q1, w0_1, n1, x) * u(re_q2, w0_2, n2, x2).conjugate()
def makeReducedBasis(x, isModeMatched=True, tolerance = 1e-12, sigma = 1):
......@@ -150,14 +152,13 @@ def makeReducedBasis(x, isModeMatched=True, tolerance = 1e-12, sigma = 1):
IDx = 0 #TS index
for i in range(len(params)):
q1 = beam_param(w0=float(params[i][0]), z=float(params[i][2]))
if isModeMatched:
q1 = beam_param(w0=float(params[i][0]), z=float(params[i][1]))
q2 = q1
n = int(params[i][2])
m = int(params[i][3])
else:
q1 = beam_param(w0=float(params[i][0]), z=float(params[i][2]))
q2 = beam_param(w0=float(params[i][1]), z=float(params[i][3]))
n = int(params[i][4])
m = int(params[i][5])
......@@ -180,10 +181,6 @@ def makeReducedBasis(x, isModeMatched=True, tolerance = 1e-12, sigma = 1):
#### 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)
......@@ -196,6 +193,7 @@ def makeReducedBasis(x, isModeMatched=True, tolerance = 1e-12, sigma = 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)
......@@ -208,6 +206,7 @@ def makeReducedBasis(x, isModeMatched=True, tolerance = 1e-12, sigma = 1):
iter += 1
return ReducedBasis(RB=np.array(RB_matrix), limits=romlimits, x=x)
def makeEmpiricalInterpolant(RB):
......@@ -282,17 +281,14 @@ def makeWeights(smap, EI, verbose=True):
dy = full_y[1] - full_y[0]
if verbose:
count = len(EI["xm"].B) * len(EI["yp"].B)
count += len(EI["xp"].B) * len(EI["yp"].B)
count += len(EI["xp"].B) * len(EI["ym"].B)
count += len(EI["xm"].B) * len(EI["ym"].B)
count = 4*len(EI["xm"].B) * len(EI["ym"].B)
p = ProgressBar(maxval=count, widgets=["Computing weights: ", Percentage(), Bar(), ETA()])
n = 0
# make integration weights
Bx = EI["xm"].B
By = EI["yp"].B
By = EI["ym"].B[:,::-1]
w_ij_Q1 = np.zeros((len(Bx),len(By)), dtype = complex)
for i in range(len(Bx)):
......@@ -304,8 +300,8 @@ def makeWeights(smap, EI, verbose=True):
p.update(n)
n+=1
Bx = EI["xp"].B
By = EI["yp"].B
Bx = EI["xm"].B[:,::-1]
By = EI["ym"].B[:,::-1]
w_ij_Q2 = np.zeros((len(Bx),len(By)), dtype = complex)
for i in range(len(Bx)):
......@@ -317,7 +313,7 @@ def makeWeights(smap, EI, verbose=True):
p.update(n)
n+=1
Bx = EI["xp"].B
Bx = EI["xm"].B[:,::-1]
By = EI["ym"].B
w_ij_Q3 = np.zeros((len(Bx),len(By)), dtype = complex)
......
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