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plotmap.py
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#!/usr/bin/python
#Mattieu de Villiers mattieu@ska.ac.za 10 May 2010
import sys
import commands
import optparse
import pickle
import numpy
import matplotlib
import matplotlib.pyplot as plt
import matplotlib.mlab as mlab
# ================================ Helper functions ================================
def ensurepathformat(outputpath):
if len(outputpath):
if outputpath[-1]!='/':
outputpath+='/'
return outputpath
#loads pointing information
def LoadPointingInfo(outputpath):
tmplog=commands.getstatusoutput('ls %spointinginfo' % (outputpath))
if (tmplog[0]):
return []
results=open('%spointinginfo' % (outputpath), 'rb')
RA=pickle.load(results)
DEC=pickle.load(results)
RAoffset=pickle.load(results)
DECoffset=pickle.load(results)
AZ=pickle.load(results)
EL=pickle.load(results)
CHI=pickle.load(results)
LST=pickle.load(results)
starttime=pickle.load(results)
stoptime=pickle.load(results)
utstarttime=pickle.load(results)
utstoptime=pickle.load(results)
freq=pickle.load(results)
nant=pickle.load(results)
results.close()
return RA,DEC,RAoffset,DECoffset,AZ,EL,CHI,LST,starttime,stoptime,utstarttime,utstoptime,freq,nant
#loads leakages and IQUV results
def readresults(outputpath):
results=open('%sresults' % (outputpath), 'rb')
leakageX=pickle.load(results)
leakageY=pickle.load(results)
peakIQUV=pickle.load(results)
noiseIQUV=pickle.load(results)
convergeFail=pickle.load(results)
nactiveAntennas=pickle.load(results)
npointings=len(leakageX)
nfreq=len(leakageX[0])
nant=len(leakageX[0][0])
validant=[];
maxleakant=[];
avgabsleakant=[];
for iant in range(nant):
fleakageX=numpy.array(range(nfreq),dtype='complex')
fleakageY=numpy.array(range(nfreq),dtype='complex')
firstfinitepiece=-1
for ifreq in range(nfreq):
fleakageX[ifreq]=leakageX[0][ifreq][iant];
fleakageY[ifreq]=leakageY[0][ifreq][iant];
if ((firstfinitepiece<0)&(numpy.isfinite(fleakageX[ifreq]))&(numpy.isfinite(fleakageY[ifreq]))&(~((fleakageX[ifreq]==0.0)&(fleakageY[ifreq]==0.0)))):
firstfinitepiece=ifreq
if (firstfinitepiece<0):
continue
validant.append(iant+1)
maxleakant.append(max([max(abs(fleakageX)),max(abs(fleakageY))]))
avgabsleakant.append(numpy.mean([numpy.mean(abs(fleakageX)),numpy.mean(abs(fleakageY))]))
print "Valid antennas: ",validant
print "Max abs leakage:",maxleakant
print "Mean abs leakage:",avgabsleakant
if len(maxleakant):
print "Max abs leakage:",max(maxleakant)
else:
print "Max abs leakage: inf"
print "Mean abs leakage:",numpy.mean(avgabsleakant)
npointingswithfailures=0
npieceswithfailures=[]
for point in range(npointings):
if (numpy.sum(convergeFail[point])>0):
npieceswithfailures.append(numpy.sum(numpy.array(convergeFail[point])>0))
print "Number of pointings with calibration failures: %d" %(len(npieceswithfailures))
if (len(npieceswithfailures)==0):
print "Maximum pieces per pointing failed: %d" % (0)
print "Total pieces failed: %d" % (0)
else:
print "Maximum pieces per pointing failed: %d" % (numpy.max(npieceswithfailures))
print "Total pieces failed: %d" % (numpy.sum(npieceswithfailures))
return leakageX, leakageY, peakIQUV, noiseIQUV, convergeFail, nactiveAntennas, validant
def plotPattern(title, az, el, E, plt, useSinCoords=False, addLines=True, levels=None):
"""Plot beam pattern as filled contour plot in dBs.
The beam pattern should be real-valued, but may contain negative parts.
These are indicated by dashed contours. This function can therefore plot
generic single-dish Stokes parameters. To plot voltage patterns, let E be
the squared magnitude of the pattern.
Parameters
----------
title : string
Figure title
az : real array, shape (numPixels)
Vector of azimuth coordinates, in degrees
el : real array, shape (numPixels)
Vector of elevation coordinates, in degrees
E : real array, shape (numPixels, numPixels)
Beam pattern (in units of power) as a function of (az, el)
useSinCoords : bool
True if coordinates should be converted to sine values
addLines : bool, optional
True if contour lines should be added to plot
levels : sequence of floats, optional
Contour levels to plot, in dB below the peak beam response (default
is -60 dB to 0 dB in 3 dB steps, i.e. ``np.linspace(-60., 0., 21)``)
"""
np=numpy
# Crude corner cutouts to indicate region outside spherical projection
quadrant = np.linspace(0.0, np.pi / 2.0, 401)
corner_az = np.concatenate([np.cos(quadrant), [1.0, 1.0]])
corner_el = np.concatenate([np.sin(quadrant), [1.0, 0.0]])
if not useSinCoords:
corner_az, corner_el = 90.0 * corner_az, 90.0 * corner_el
if useSinCoords:
x, y = np.sin(az * np.pi / 180.0), np.sin(el * np.pi / 180.0)
else:
x, y = az, el
if levels is None:
# levels = np.linspace(-60.0, 0.0, 21)
levels = np.linspace(-40.0, 0.0, 17)
# levels = np.linspace(-40.0, -10.0, 16)
# Transpose the data for plotting purposes, so that rows of E correspond to y and columns of E correspond to x
E = E.transpose()
E_dB = 10.0 * np.log10(np.abs(E))
# Remove -infs (keep above lowest contour level to prevent white patches in contourf)
E_dB[E_dB < levels.min() + 0.01] = levels.min() + 0.01
# Also keep below highest contour level for the same reason
E_dB[E_dB > levels.max() - 0.01] = levels.max() - 0.01
cset = plt.contourf(x, y, E_dB, levels)
matplotlib.rc('contour', negative_linestyle='solid')
if addLines:
# Positive beam patterns are straightforward
if E.min() >= 0.0:
plt.contour(x, y, E_dB, levels, colors='k', linewidths=0.5)
else:
# Indicate positive parts with solid contours
E_dB_pos = E_dB.copy()
E_dB_pos[E < 0.0] = levels.min() + 0.01
plt.contour(x, y, E_dB_pos, levels, colors='k', linewidths=0.5)
# Indicate negative parts with dashed contours
E_dB_neg = E_dB.copy()
E_dB_neg[E > 0.0] = levels.min() + 0.01
matplotlib.rc('contour', negative_linestyle='dashed')
plt.contour(x, y, E_dB_neg, levels, colors='k', linewidths=0.5)
if useSinCoords:
plt.xlabel(r'sin $\theta$ sin $\phi$')
plt.ylabel(r'sin $\theta$ cos $\phi$')
else:
plt.xlabel('az (deg)')
plt.ylabel('el (deg)')
for ticklabel in plt.xticks()[1] + plt.yticks()[1]:
ticklabel.set_size('small')
plt.title(title)
plt.axis('image')
plt.fill(corner_az, corner_el, facecolor='w')
plt.fill(-corner_az, corner_el, facecolor='w')
plt.fill(-corner_az, -corner_el, facecolor='w')
plt.fill(corner_az, -corner_el, facecolor='w')
return cset
def getrefpointing(outputpath):
for ind in range((len(outputpath)-1),1,-1):
if (outputpath[ind]=='p'):
if ((outputpath[ind+2]=='T')|(outputpath[ind+2]=='f')|(outputpath[ind+2]=='E')):
return int(outputpath[ind+1:ind+2])
elif ((outputpath[ind+3]=='T')|(outputpath[ind+3]=='f')|(outputpath[ind+3]=='E')):
return int(outputpath[ind+1:ind+3])
return 0
#Casey's rotate to convert dra,ddec to az,el
def rotate(RAoffset,DECoffset,PARANG):
ANG=PARANG*numpy.pi/180.0
xx=-RAoffset*numpy.cos(ANG)+DECoffset*numpy.sin(ANG)
yy=RAoffset*numpy.sin(ANG)+DECoffset*numpy.cos(ANG)
return xx,yy
#period=360 or 2*pi
#unwrapped=(angle+0.5*period) % period -0.5*period
#calculate epsilon, zetas at x,y
#def solve(x,y,I_true,Q_true,U_true,V_true,I_harpoon,Q_harpoon,U_harpoon,V_harpoon,xx,yy,chi):
#assumes xx,yy in units of fraction of half power point
def solvezetaepsilon(x,y,I,Q,U,V,I_harpoon,Q_harpoon,U_harpoon,V_harpoon,xx,yy,chi,maxextent,sigma):
ndata=len(chi)
w=numpy.exp(-0.5*((xx-x)**2+(yy-y)**2)/(sigma)**2)
m=[w[c]*numpy.array([I_harpoon[c],Q_harpoon[c],U_harpoon[c],V_harpoon[c]]) for c in range(ndata)]
m=numpy.array(m).reshape(4*ndata,1)
X=[ w[c]*numpy.array(
[[I,Q*numpy.cos(2.0*chi[c])+U*numpy.sin(2.0*chi[c]),0,U*numpy.cos(2.0*chi[c])-Q*numpy.sin(2.0*chi[c]),0,0,-V],
[Q,I*numpy.cos(2.0*chi[c]),U,-I*numpy.sin(2.0*chi[c]),-V*numpy.sin(2.0*chi[c]),-V*numpy.cos(2.0*chi[c]),0],
[U,I*numpy.sin(2.0*chi[c]),-Q,I*numpy.cos(2.0*chi[c]),V*numpy.cos(2.0*chi[c]),-V*numpy.sin(2.0*chi[c]),0],
[V,0,0,0,Q*numpy.sin(2.0*chi[c])-U*numpy.cos(2.0*chi[c]),Q*numpy.cos(2.0*chi[c])+U*numpy.sin(2.0*chi[c]),-I]]) for c in range(ndata)]
X=numpy.array(X).reshape(4*ndata,7);
# [I_harpoon;Q_harpoon;U_harpoon;V_harpoon]=
# [[I,Q*cos(2*chi)+U*sin(2*chi),0,U*cos(2*chi)-Q*sin(2*chi),0,0,-V],
# [Q,I*cos(2*chi),U,-I*sin(2*chi),-V*sin(2*chi),-V*cos(2*chi),0],
# [U,I*sin(2*chi),-Q,I*cos(2*chi),V*cos(2*chi),-V*sin(2*chi),0],
# [V,0,0,0,Q*sin(2*chi)-U*cos(2*chi),Q*cos(2*chi)+U*sin(2*chi),-I]]
# [1/2*epsilon_pp+1;
# 1/2*epsilon_np;
# 1/2*zeta_np;
# 1/2*zeta_pp;
# 1/2*epsilon_nn*j;
# 1/2*zeta_pn*j;
# 1/2*zeta_nn*j]
# m=X*u
# u_best=pinv(X)*m
# W*m=W*X*u;
# u_best=pinv(W*X)*W*m
#gathering weighting terms based on position
#if matrix W use
#epsilon_zeta=numpy.dot(numpy.linalg.pinv(numpy.dot(W,X)),numpy.dot(W,m))
#if vector w, use
#epsilon_zeta=numpy.dot(numpy.linalg.pinv((w*X.transpose()).transpose()),(w*m))
epsilon_zeta=numpy.dot(numpy.linalg.pinv(X),m)
# epsilon_zeta[0]=epsilon_zeta[0]-1
return numpy.array(epsilon_zeta).reshape(7,)
#fits epsilon zeta to smooth surface of form a[0]*x^2+a[1]*x+a[2]*x*y+a[3]*y+a[4]*y^2+a[5]
#then evaluate epsilon zetas at given location
def solvefitzetaepsilon(x,y,I,Q,U,V,I_harpoon,Q_harpoon,U_harpoon,V_harpoon,xx,yy,chi,maxextent,sigma):
ndata=len(chi)
w=numpy.exp(-0.5*(numpy.sqrt((xx-x)**2+(yy-y)**2))/(sigma)**2)
m=[w[c]*numpy.array([I_harpoon[c],Q_harpoon[c],U_harpoon[c],V_harpoon[c]]) for c in range(ndata)]
m=numpy.array(m).reshape(4*ndata,1)
range06=numpy.array(range(0,6))
X=numpy.zeros([4*ndata,7*ndata])
XY=numpy.zeros([7*ndata,6*7])
for c in range(ndata):
X[4*c][(7*c):(7*c+7)]=w[c]*numpy.array([I,Q*numpy.cos(2.0*chi[c])+U*numpy.sin(2.0*chi[c]),0,U*numpy.cos(2.0*chi[c])-Q*numpy.sin(2.0*chi[c]),0,0,-V])
X[4*c+1][(7*c):(7*c+7)]=w[c]*numpy.array([Q,I*numpy.cos(2.0*chi[c]),U,-I*numpy.sin(2.0*chi[c]),-V*numpy.sin(2.0*chi[c]),-V*numpy.cos(2.0*chi[c]),0])
X[4*c+2][(7*c):(7*c+7)]=w[c]*numpy.array([U,I*numpy.sin(2.0*chi[c]),-Q,I*numpy.cos(2.0*chi[c]),V*numpy.cos(2.0*chi[c]),-V*numpy.sin(2.0*chi[c]),0])
X[4*c+3][(7*c):(7*c+7)]=w[c]*numpy.array([V,0,0,0,Q*numpy.sin(2.0*chi[c])-U*numpy.cos(2.0*chi[c]),Q*numpy.cos(2.0*chi[c])+U*numpy.sin(2.0*chi[c]),-I])
XY[7*c+0][6*0+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*epp+1
XY[7*c+1][6*1+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*enp
XY[7*c+2][6*2+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*znp
XY[7*c+3][6*3+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*zpp
XY[7*c+4][6*4+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*ennj
XY[7*c+5][6*5+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*zpnj
XY[7*c+6][6*6+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*znnj
X=numpy.array(X)
XY=numpy.array(XY)
# W*m=W*X*XY*A
# m=X*XY*A
# A=pinv(X*XY)*m
#a[0]*x^2+a[1]*x+a[2]*x*y+a[3]*y+a[4]*y^2+a[5]
#A=numpy.zeros(6*7)
#A=[a0epp,a1epp,a2epp,a3epp,a4epp,a5epp, a0enp,a1enp,a2enp,a3enp,a4enp,a5enp, a0ezp,a1ezp,a2ezp,a3ezp,a4ezp,a5ezp,...]'
A=numpy.dot(numpy.linalg.pinv(numpy.dot(X,XY)),m)
#now evaluate A at x,y
thisXY=numpy.zeros([7,6*7])
thisXY[0][6*0+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*epp+1
thisXY[1][6*1+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*enp
thisXY[2][6*2+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*znp
thisXY[3][6*3+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*zpp
thisXY[4][6*4+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*ennj
thisXY[5][6*5+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*zpnj
thisXY[6][6*6+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*znnj
epsilon_zeta=numpy.dot(thisXY,A)
# [I_harpoon;Q_harpoon;U_harpoon;V_harpoon]=
# [[I,Q*cos(2*chi)+U*sin(2*chi),0,U*cos(2*chi)-Q*sin(2*chi),0,0,-V],
# [Q,I*cos(2*chi),U,-I*sin(2*chi),-V*sin(2*chi),-V*cos(2*chi),0],
# [U,I*sin(2*chi),-Q,I*cos(2*chi),V*cos(2*chi),-V*sin(2*chi),0],
# [V,0,0,0,Q*sin(2*chi)-U*cos(2*chi),Q*cos(2*chi)+U*sin(2*chi),-I]]
# [1/2*epsilon_pp+1;
# 1/2*epsilon_np;
# 1/2*zeta_np;
# 1/2*zeta_pp;
# 1/2*epsilon_nn*j;
# 1/2*zeta_pn*j;
# 1/2*zeta_nn*j]
#becomes
#mIQUV[4*ndata,1]
#[I_harpoon;Q_harpoon;U_harpoon;V_harpoon]
#[I_harpoon;Q_harpoon;U_harpoon;V_harpoon]
#[I_harpoon;Q_harpoon;U_harpoon;V_harpoon]
#=
#X[4(iquv)*ndata,7(epsilonzeta)]
#[[I,Q*cos(2*chi)+U*sin(2*chi),0,U*cos(2*chi)-Q*sin(2*chi),0,0,-V],
# [Q,I*cos(2*chi),U,-I*sin(2*chi),-V*sin(2*chi),-V*cos(2*chi),0],
# [U,I*sin(2*chi),-Q,I*cos(2*chi),V*cos(2*chi),-V*sin(2*chi),0],
# [V,0,0,0,Q*sin(2*chi)-U*cos(2*chi),Q*cos(2*chi)+U*sin(2*chi),-I]]
#[[I,Q*cos(2*chi)+U*sin(2*chi),0,U*cos(2*chi)-Q*sin(2*chi),0,0,-V],
# [Q,I*cos(2*chi),U,-I*sin(2*chi),-V*sin(2*chi),-V*cos(2*chi),0],
# [U,I*sin(2*chi),-Q,I*cos(2*chi),V*cos(2*chi),-V*sin(2*chi),0],
# [V,0,0,0,Q*sin(2*chi)-U*cos(2*chi),Q*cos(2*chi)+U*sin(2*chi),-I]]
#[[I,Q*cos(2*chi)+U*sin(2*chi),0,U*cos(2*chi)-Q*sin(2*chi),0,0,-V],
# [Q,I*cos(2*chi),U,-I*sin(2*chi),-V*sin(2*chi),-V*cos(2*chi),0],
# [U,I*sin(2*chi),-Q,I*cos(2*chi),V*cos(2*chi),-V*sin(2*chi),0],
# [V,0,0,0,Q*sin(2*chi)-U*cos(2*chi),Q*cos(2*chi)+U*sin(2*chi),-I]]
#
#a[0]*x^2+a[1]*x+a[2]*x*y+a[3]*y+a[4]*y^2+a[5]
#[xx x xy y yy 1] [a0_epp,a0_enp,a0_znp,a0_zpp,a0_enn,a0_zpn,a0_znn]
#[xx x xy y yy 1]*[a1_epp,a1_enp,a1_znp,a1_zpp,a1_enn,a1_zpn,a1_znn]
#[xx x xy y yy 1] [a2_epp,a2_enp,a2_znp,a2_zpp,a2_enn,a2_zpn,a2_znn]
#[xx x xy y yy 1] [a3_epp,a3_enp,a3_znp,a3_zpp,a3_enn,a3_zpn,a3_znn]
#xxyy[4*ndata,6]*A[6,7] gives [4*ndata,7] which is [zeta epsilon values at each data point]
# m=X*u
# u_best=pinv(X)*m
# W*m=W*X*u;
# u_best=pinv(W*X)*W*m
#gathering weighting terms based on position
#if matrix W use
#epsilon_zeta=numpy.dot(numpy.linalg.pinv(numpy.dot(W,X)),numpy.dot(W,m))
#if vector w, use
#epsilon_zeta=numpy.dot(numpy.linalg.pinv((w*X.transpose()).transpose()),(w*m))
# epsilon_zeta=numpy.dot(numpy.linalg.pinv(X),m)
return numpy.array(epsilon_zeta).reshape(7,)
#
#fits epsilon zeta to smooth surface of form a[0]*x^2+a[1]*x+a[2]*x*y+a[3]*y+a[4]*y^2+a[5]
#then evaluate epsilon zetas at given location
def solvefitlinearzetaepsilon(x,y,I,Q,U,V,I_harpoon,Q_harpoon,U_harpoon,V_harpoon,xx,yy,chi,maxextent,sigma):
ndata=len(chi)
w=numpy.exp(-0.5*(numpy.sqrt((xx-x)**2+(yy-y)**2))/(sigma)**2)
m=[w[c]*numpy.array([I_harpoon[c],Q_harpoon[c],U_harpoon[c],V_harpoon[c]]) for c in range(ndata)]
m=numpy.array(m).reshape(4*ndata,1)
range03=numpy.array(range(0,3))
X=numpy.zeros([4*ndata,7*ndata])
XY=numpy.zeros([7*ndata,3*7])
for c in range(ndata):
X[4*c][(7*c):(7*c+7)]=w[c]*numpy.array([I,Q*numpy.cos(2.0*chi[c])+U*numpy.sin(2.0*chi[c]),0,U*numpy.cos(2.0*chi[c])-Q*numpy.sin(2.0*chi[c]),0,0,-V])
X[4*c+1][(7*c):(7*c+7)]=w[c]*numpy.array([Q,I*numpy.cos(2.0*chi[c]),U,-I*numpy.sin(2.0*chi[c]),-V*numpy.sin(2.0*chi[c]),-V*numpy.cos(2.0*chi[c]),0])
X[4*c+2][(7*c):(7*c+7)]=w[c]*numpy.array([U,I*numpy.sin(2.0*chi[c]),-Q,I*numpy.cos(2.0*chi[c]),V*numpy.cos(2.0*chi[c]),-V*numpy.sin(2.0*chi[c]),0])
X[4*c+3][(7*c):(7*c+7)]=w[c]*numpy.array([V,0,0,0,Q*numpy.sin(2.0*chi[c])-U*numpy.cos(2.0*chi[c]),Q*numpy.cos(2.0*chi[c])+U*numpy.sin(2.0*chi[c]),-I])
XY[7*c+0][3*0+range03]=[xx[c], yy[c], 1]#1/2*epp+1
XY[7*c+1][3*1+range03]=[xx[c], yy[c], 1]#1/2*enp
XY[7*c+2][3*2+range03]=[xx[c], yy[c], 1]#1/2*znp
XY[7*c+3][3*3+range03]=[xx[c], yy[c], 1]#1/2*zpp
XY[7*c+4][3*4+range03]=[xx[c], yy[c], 1]#1/2*ennj
XY[7*c+5][3*5+range03]=[xx[c], yy[c], 1]#1/2*zpnj
XY[7*c+6][3*6+range03]=[xx[c], yy[c], 1]#1/2*znnj
X=numpy.array(X)
XY=numpy.array(XY)
# W*m=W*X*XY*A
# m=X*XY*A
# A=pinv(X*XY)*m
#a[0]*x^2+a[1]*x+a[2]*x*y+a[3]*y+a[4]*y^2+a[5]
#A=numpy.zeros(3*7)
#A=[a0epp,a1epp,a2epp, a0enp,a1enp,a2enp, a0ezp,a1ezp,a2ezp, ...]'
A=numpy.dot(numpy.linalg.pinv(numpy.dot(X,XY)),m)
#now evaluate A at x,y
thisXY=numpy.zeros([7,3*7])
thisXY[0][3*0+range03]=[x,y, 1]#1/2*epp+1
thisXY[1][3*1+range03]=[x,y, 1]#1/2*enp
thisXY[2][3*2+range03]=[x,y, 1]#1/2*znp
thisXY[3][3*3+range03]=[x,y, 1]#1/2*zpp
thisXY[4][3*4+range03]=[x,y, 1]#1/2*ennj
thisXY[5][3*5+range03]=[x,y, 1]#1/2*zpnj
thisXY[6][3*6+range03]=[x,y, 1]#1/2*znnj
epsilon_zeta=numpy.dot(thisXY,A)
return numpy.array(epsilon_zeta).reshape(7,)
#
#fits epsilon zeta to smooth surface of form a[0]*x^2+a[1]*x+a[2]*x*y+a[3]*y+a[4]*y^2+a[5]
#except e_nn and z_pn are modeled as planes only!
#then evaluate epsilon zetas at given location
def solvefitlesszetaepsilon(x,y,I,Q,U,V,I_harpoon,Q_harpoon,U_harpoon,V_harpoon,xx,yy,chi,maxextent,sigma):
ndata=len(chi)
w=numpy.exp(-0.5*(numpy.sqrt((xx-x)**2+(yy-y)**2))/(sigma)**2)
m=[w[c]*numpy.array([I_harpoon[c],Q_harpoon[c],U_harpoon[c],V_harpoon[c]]) for c in range(ndata)]
m=numpy.array(m).reshape(4*ndata,1)
range06=numpy.array(range(0,6))
range03=numpy.array(range(0,3))
X=numpy.zeros([4*ndata,7*ndata])
XY=numpy.zeros([7*ndata,6*7-2*3])
for c in range(ndata):
X[4*c][(7*c):(7*c+7)]=w[c]*numpy.array([I,Q*numpy.cos(2.0*chi[c])+U*numpy.sin(2.0*chi[c]),0,U*numpy.cos(2.0*chi[c])-Q*numpy.sin(2.0*chi[c]),0,0,-V])
X[4*c+1][(7*c):(7*c+7)]=w[c]*numpy.array([Q,I*numpy.cos(2.0*chi[c]),U,-I*numpy.sin(2.0*chi[c]),-V*numpy.sin(2.0*chi[c]),-V*numpy.cos(2.0*chi[c]),0])
X[4*c+2][(7*c):(7*c+7)]=w[c]*numpy.array([U,I*numpy.sin(2.0*chi[c]),-Q,I*numpy.cos(2.0*chi[c]),V*numpy.cos(2.0*chi[c]),-V*numpy.sin(2.0*chi[c]),0])
X[4*c+3][(7*c):(7*c+7)]=w[c]*numpy.array([V,0,0,0,Q*numpy.sin(2.0*chi[c])-U*numpy.cos(2.0*chi[c]),Q*numpy.cos(2.0*chi[c])+U*numpy.sin(2.0*chi[c]),-I])
XY[7*c+0][6*0+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*epp+1
XY[7*c+1][6*1+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*enp
XY[7*c+2][6*2+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*znp
XY[7*c+3][6*3+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*zpp
XY[7*c+4][6*4+range03]=[xx[c], yy[c], 1]#1/2*ennj***
XY[7*c+5][6*5-3+range03]=[xx[c], yy[c], 1]#1/2*zpnj***
XY[7*c+6][6*6-6+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*znnj
X=numpy.array(X)
XY=numpy.array(XY)
# W*m=W*X*XY*A
# m=X*XY*A
# A=pinv(X*XY)*m
#a[0]*x^2+a[1]*x+a[2]*x*y+a[3]*y+a[4]*y^2+a[5]
#A=numpy.zeros(6*7)
#A=[a0epp,a1epp,a2epp,a3epp,a4epp,a5epp, a0enp,a1enp,a2enp,a3enp,a4enp,a5enp, a0ezp,a1ezp,a2ezp,a3ezp,a4ezp,a5ezp,...]'
A=numpy.dot(numpy.linalg.pinv(numpy.dot(X,XY)),m)
#now evaluate A at x,y
thisXY=numpy.zeros([7,6*7-2*3])
thisXY[0][6*0+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*epp+1
thisXY[1][6*1+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*enp
thisXY[2][6*2+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*znp
thisXY[3][6*3+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*zpp
thisXY[4][6*4+range03]=[x, y, 1]#1/2*ennj***
thisXY[5][6*5-3+range03]=[x, y, 1]#1/2*zpnj***
thisXY[6][6*6-6+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*znnj
epsilon_zeta=numpy.dot(thisXY,A)
return numpy.array(epsilon_zeta).reshape(7,)
#
#fits epsilon zeta to smooth surface of form a[0]*x^2+a[1]*x+a[2]*x*y+a[3]*y+a[4]*y^2+a[5]
#except e_nn and z_pn are modeled as planes only!
#then evaluate epsilon zetas at given location
def solvefitevenlesszetaepsilon(x,y,I,Q,U,V,I_harpoon,Q_harpoon,U_harpoon,V_harpoon,xx,yy,chi,maxextent,sigma):
ndata=len(chi)
w=numpy.exp(-0.5*(numpy.sqrt((xx-x)**2+(yy-y)**2))/(sigma)**2)
m=[w[c]*numpy.array([I_harpoon[c],Q_harpoon[c],U_harpoon[c],V_harpoon[c]]) for c in range(ndata)]
m=numpy.array(m).reshape(4*ndata,1)
range06=numpy.array(range(0,6))
range03=numpy.array(range(0,3))
X=numpy.zeros([4*ndata,7*ndata])
XY=numpy.zeros([7*ndata,6*7-2*5])
for c in range(ndata):
X[4*c][(7*c):(7*c+7)]=w[c]*numpy.array([I,Q*numpy.cos(2.0*chi[c])+U*numpy.sin(2.0*chi[c]),0,U*numpy.cos(2.0*chi[c])-Q*numpy.sin(2.0*chi[c]),0,0,-V])
X[4*c+1][(7*c):(7*c+7)]=w[c]*numpy.array([Q,I*numpy.cos(2.0*chi[c]),U,-I*numpy.sin(2.0*chi[c]),-V*numpy.sin(2.0*chi[c]),-V*numpy.cos(2.0*chi[c]),0])
X[4*c+2][(7*c):(7*c+7)]=w[c]*numpy.array([U,I*numpy.sin(2.0*chi[c]),-Q,I*numpy.cos(2.0*chi[c]),V*numpy.cos(2.0*chi[c]),-V*numpy.sin(2.0*chi[c]),0])
X[4*c+3][(7*c):(7*c+7)]=w[c]*numpy.array([V,0,0,0,Q*numpy.sin(2.0*chi[c])-U*numpy.cos(2.0*chi[c]),Q*numpy.cos(2.0*chi[c])+U*numpy.sin(2.0*chi[c]),-I])
XY[7*c+0][6*0+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*epp+1
XY[7*c+1][6*1+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*enp
XY[7*c+2][6*2+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*znp
XY[7*c+3][6*3+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*zpp
XY[7*c+4][6*4]=1#1/2*ennj***
XY[7*c+5][6*5-5]=1#1/2*zpnj***
XY[7*c+6][6*6-10+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*znnj
X=numpy.array(X)
XY=numpy.array(XY)
# W*m=W*X*XY*A
# m=X*XY*A
# A=pinv(X*XY)*m
#a[0]*x^2+a[1]*x+a[2]*x*y+a[3]*y+a[4]*y^2+a[5]
#A=numpy.zeros(6*7)
#A=[a0epp,a1epp,a2epp,a3epp,a4epp,a5epp, a0enp,a1enp,a2enp,a3enp,a4enp,a5enp, a0ezp,a1ezp,a2ezp,a3ezp,a4ezp,a5ezp,...]'
A=numpy.dot(numpy.linalg.pinv(numpy.dot(X,XY)),m)
#now evaluate A at x,y
thisXY=numpy.zeros([7,6*7-2*5])
thisXY[0][6*0+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*epp+1
thisXY[1][6*1+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*enp
thisXY[2][6*2+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*znp
thisXY[3][6*3+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*zpp
thisXY[4][6*4]=1#1/2*ennj***
thisXY[5][6*5-5]=1#1/2*zpnj***
thisXY[6][6*6-10+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*znnj
epsilon_zeta=numpy.dot(thisXY,A)
return numpy.array(epsilon_zeta).reshape(7,)
#
def solvefitevenevenlesszetaepsilon(x,y,I,Q,U,V,I_harpoon,Q_harpoon,U_harpoon,V_harpoon,xx,yy,chi,maxextent,sigma):
ndata=len(chi)
w=numpy.exp(-0.5*(numpy.sqrt((xx-x)**2+(yy-y)**2))/(sigma)**2)
m=[w[c]*numpy.array([I_harpoon[c],Q_harpoon[c],U_harpoon[c],V_harpoon[c]]) for c in range(ndata)]
m=numpy.array(m).reshape(4*ndata,1)
range06=numpy.array(range(0,6))
range03=numpy.array(range(0,3))
X=numpy.zeros([4*ndata,7*ndata])
XY=numpy.zeros([7*ndata,6*7-3*5])
for c in range(ndata):
X[4*c][(7*c):(7*c+7)]=w[c]*numpy.array([I,Q*numpy.cos(2.0*chi[c])+U*numpy.sin(2.0*chi[c]),0,U*numpy.cos(2.0*chi[c])-Q*numpy.sin(2.0*chi[c]),0,0,-V])
X[4*c+1][(7*c):(7*c+7)]=w[c]*numpy.array([Q,I*numpy.cos(2.0*chi[c]),U,-I*numpy.sin(2.0*chi[c]),-V*numpy.sin(2.0*chi[c]),-V*numpy.cos(2.0*chi[c]),0])
X[4*c+2][(7*c):(7*c+7)]=w[c]*numpy.array([U,I*numpy.sin(2.0*chi[c]),-Q,I*numpy.cos(2.0*chi[c]),V*numpy.cos(2.0*chi[c]),-V*numpy.sin(2.0*chi[c]),0])
X[4*c+3][(7*c):(7*c+7)]=w[c]*numpy.array([V,0,0,0,Q*numpy.sin(2.0*chi[c])-U*numpy.cos(2.0*chi[c]),Q*numpy.cos(2.0*chi[c])+U*numpy.sin(2.0*chi[c]),-I])
XY[7*c+0][6*0+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*epp+1
XY[7*c+1][6*1+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*enp
XY[7*c+2][6*2]=1#1/2*znp
XY[7*c+3][6*3-5+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*zpp
XY[7*c+4][6*4-5]=1#1/2*ennj***
XY[7*c+5][6*5-10]=1#1/2*zpnj***
XY[7*c+6][6*6-15+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*znnj
X=numpy.array(X)
XY=numpy.array(XY)
# W*m=W*X*XY*A
# m=X*XY*A
# A=pinv(X*XY)*m
#a[0]*x^2+a[1]*x+a[2]*x*y+a[3]*y+a[4]*y^2+a[5]
#A=numpy.zeros(6*7)
#A=[a0epp,a1epp,a2epp,a3epp,a4epp,a5epp, a0enp,a1enp,a2enp,a3enp,a4enp,a5enp, a0ezp,a1ezp,a2ezp,a3ezp,a4ezp,a5ezp,...]'
A=numpy.dot(numpy.linalg.pinv(numpy.dot(X,XY)),m)
#now evaluate A at x,y
thisXY=numpy.zeros([7,6*7-3*5])
thisXY[0][6*0+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*epp+1
thisXY[1][6*1+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*enp
thisXY[2][6*2]=1#1/2*znp
thisXY[3][6*3-5+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*zpp
thisXY[4][6*4-5]=1#1/2*ennj***
thisXY[5][6*5-10]=1#1/2*zpnj***
thisXY[6][6*6-15+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*znnj
epsilon_zeta=numpy.dot(thisXY,A)
return numpy.array(epsilon_zeta).reshape(7,)
#
def solvefitevenevenlesslinzetaepsilon(x,y,I,Q,U,V,I_harpoon,Q_harpoon,U_harpoon,V_harpoon,xx,yy,chi,maxextent,sigma):
ndata=len(chi)
w=numpy.exp(-0.5*(numpy.sqrt((xx-x)**2+(yy-y)**2))/(sigma)**2)
m=[w[c]*numpy.array([I_harpoon[c],Q_harpoon[c],U_harpoon[c],V_harpoon[c]]) for c in range(ndata)]
m=numpy.array(m).reshape(4*ndata,1)
range06=numpy.array(range(0,6))
range03=numpy.array(range(0,3))
X=numpy.zeros([4*ndata,7*ndata])
XY=numpy.zeros([7*ndata,6*7-3*5-3])
for c in range(ndata):
X[4*c][(7*c):(7*c+7)]=w[c]*numpy.array([I,Q*numpy.cos(2.0*chi[c])+U*numpy.sin(2.0*chi[c]),0,U*numpy.cos(2.0*chi[c])-Q*numpy.sin(2.0*chi[c]),0,0,-V])
X[4*c+1][(7*c):(7*c+7)]=w[c]*numpy.array([Q,I*numpy.cos(2.0*chi[c]),U,-I*numpy.sin(2.0*chi[c]),-V*numpy.sin(2.0*chi[c]),-V*numpy.cos(2.0*chi[c]),0])
X[4*c+2][(7*c):(7*c+7)]=w[c]*numpy.array([U,I*numpy.sin(2.0*chi[c]),-Q,I*numpy.cos(2.0*chi[c]),V*numpy.cos(2.0*chi[c]),-V*numpy.sin(2.0*chi[c]),0])
X[4*c+3][(7*c):(7*c+7)]=w[c]*numpy.array([V,0,0,0,Q*numpy.sin(2.0*chi[c])-U*numpy.cos(2.0*chi[c]),Q*numpy.cos(2.0*chi[c])+U*numpy.sin(2.0*chi[c]),-I])
XY[7*c+0][6*0+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*epp+1
XY[7*c+1][6*1+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*enp
XY[7*c+2][6*2]=1#1/2*znp
XY[7*c+3][6*3-5+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*zpp
XY[7*c+4][6*4-5]=1#1/2*ennj***
XY[7*c+5][6*5-10]=1#1/2*zpnj***
XY[7*c+6][6*6-15+range03]=[xx[c], yy[c], 1]#1/2*znnj
X=numpy.array(X)
XY=numpy.array(XY)
# W*m=W*X*XY*A
# m=X*XY*A
# A=pinv(X*XY)*m
#a[0]*x^2+a[1]*x+a[2]*x*y+a[3]*y+a[4]*y^2+a[5]
#A=numpy.zeros(6*7)
#A=[a0epp,a1epp,a2epp,a3epp,a4epp,a5epp, a0enp,a1enp,a2enp,a3enp,a4enp,a5enp, a0ezp,a1ezp,a2ezp,a3ezp,a4ezp,a5ezp,...]'
A=numpy.dot(numpy.linalg.pinv(numpy.dot(X,XY)),m)
#now evaluate A at x,y
thisXY=numpy.zeros([7,6*7-3*5-3])
thisXY[0][6*0+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*epp+1
thisXY[1][6*1+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*enp
thisXY[2][6*2]=1#1/2*znp
thisXY[3][6*3-5+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*zpp
thisXY[4][6*4-5]=1#1/2*ennj***
thisXY[5][6*5-10]=1#1/2*zpnj***
thisXY[6][6*6-15+range03]=[x, y, 1]#1/2*znnj
epsilon_zeta=numpy.dot(thisXY,A)
return numpy.array(epsilon_zeta).reshape(7,)
#
def solvefitleastzetaepsilon(x,y,I,Q,U,V,I_harpoon,Q_harpoon,U_harpoon,V_harpoon,xx,yy,chi,maxextent,sigma):
ndata=len(chi)
w=numpy.exp(-0.5*(numpy.sqrt((xx-x)**2+(yy-y)**2))/(sigma)**2)
m=[w[c]*numpy.array([I_harpoon[c],Q_harpoon[c],U_harpoon[c],V_harpoon[c]]) for c in range(ndata)]
m=numpy.array(m).reshape(4*ndata,1)
range06=numpy.array(range(0,6))
range03=numpy.array(range(0,3))
X=numpy.zeros([4*ndata,7*ndata])
XY=numpy.zeros([7*ndata,6*7-4*5])
for c in range(ndata):
X[4*c][(7*c):(7*c+7)]=w[c]*numpy.array([I,Q*numpy.cos(2.0*chi[c])+U*numpy.sin(2.0*chi[c]),0,U*numpy.cos(2.0*chi[c])-Q*numpy.sin(2.0*chi[c]),0,0,-V])
X[4*c+1][(7*c):(7*c+7)]=w[c]*numpy.array([Q,I*numpy.cos(2.0*chi[c]),U,-I*numpy.sin(2.0*chi[c]),-V*numpy.sin(2.0*chi[c]),-V*numpy.cos(2.0*chi[c]),0])
X[4*c+2][(7*c):(7*c+7)]=w[c]*numpy.array([U,I*numpy.sin(2.0*chi[c]),-Q,I*numpy.cos(2.0*chi[c]),V*numpy.cos(2.0*chi[c]),-V*numpy.sin(2.0*chi[c]),0])
X[4*c+3][(7*c):(7*c+7)]=w[c]*numpy.array([V,0,0,0,Q*numpy.sin(2.0*chi[c])-U*numpy.cos(2.0*chi[c]),Q*numpy.cos(2.0*chi[c])+U*numpy.sin(2.0*chi[c]),-I])
XY[7*c+0][6*0+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*epp+1
XY[7*c+1][6*1+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*enp
XY[7*c+2][6*2]=1#1/2*znp
XY[7*c+3][6*3-5+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*zpp
XY[7*c+4][6*4-5]=1#1/2*ennj***
XY[7*c+5][6*5-10]=1#1/2*zpnj***
XY[7*c+6][6*6-15]=1#1/2*znnj
X=numpy.array(X)
XY=numpy.array(XY)
# W*m=W*X*XY*A
# m=X*XY*A
# A=pinv(X*XY)*m
#a[0]*x^2+a[1]*x+a[2]*x*y+a[3]*y+a[4]*y^2+a[5]
#A=numpy.zeros(6*7)
#A=[a0epp,a1epp,a2epp,a3epp,a4epp,a5epp, a0enp,a1enp,a2enp,a3enp,a4enp,a5enp, a0ezp,a1ezp,a2ezp,a3ezp,a4ezp,a5ezp,...]'
A=numpy.dot(numpy.linalg.pinv(numpy.dot(X,XY)),m)
#now evaluate A at x,y
thisXY=numpy.zeros([7,6*7-4*5])
thisXY[0][6*0+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*epp+1
thisXY[1][6*1+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*enp
thisXY[2][6*2]=1#1/2*znp
thisXY[3][6*3-5+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*zpp
thisXY[4][6*4-5]=1#1/2*ennj***
thisXY[5][6*5-10]=1#1/2*zpnj***
thisXY[6][6*6-15]=1#1/2*znnj
epsilon_zeta=numpy.dot(thisXY,A)
return numpy.array(epsilon_zeta).reshape(7,)
#
def solvefitconstantzetaepsilon(x,y,I,Q,U,V,I_harpoon,Q_harpoon,U_harpoon,V_harpoon,xx,yy,chi,maxextent,sigma):
ndata=len(chi)
w=numpy.exp(-0.5*(numpy.sqrt((xx-x)**2+(yy-y)**2))/(sigma)**2)
m=[w[c]*numpy.array([I_harpoon[c],Q_harpoon[c],U_harpoon[c],V_harpoon[c]]) for c in range(ndata)]
m=numpy.array(m).reshape(4*ndata,1)
range06=numpy.array(range(0,6))
X=numpy.zeros([4*ndata,7*ndata])
XY=numpy.zeros([7*ndata,6+6])
for c in range(ndata):
X[4*c][(7*c):(7*c+7)]=w[c]*numpy.array([I,Q*numpy.cos(2.0*chi[c])+U*numpy.sin(2.0*chi[c]),0,U*numpy.cos(2.0*chi[c])-Q*numpy.sin(2.0*chi[c]),0,0,-V])
X[4*c+1][(7*c):(7*c+7)]=w[c]*numpy.array([Q,I*numpy.cos(2.0*chi[c]),U,-I*numpy.sin(2.0*chi[c]),-V*numpy.sin(2.0*chi[c]),-V*numpy.cos(2.0*chi[c]),0])
X[4*c+2][(7*c):(7*c+7)]=w[c]*numpy.array([U,I*numpy.sin(2.0*chi[c]),-Q,I*numpy.cos(2.0*chi[c]),V*numpy.cos(2.0*chi[c]),-V*numpy.sin(2.0*chi[c]),0])
X[4*c+3][(7*c):(7*c+7)]=w[c]*numpy.array([V,0,0,0,Q*numpy.sin(2.0*chi[c])-U*numpy.cos(2.0*chi[c]),Q*numpy.cos(2.0*chi[c])+U*numpy.sin(2.0*chi[c]),-I])
XY[7*c+0][6*0+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*epp+1
XY[7*c+1][6+0]=1#1/2*enp
XY[7*c+2][6+1]=1#1/2*znp
XY[7*c+3][6+2]=1#1/2*zpp
XY[7*c+4][6+3]=1#1/2*ennj***
XY[7*c+5][6+4]=1#1/2*zpnj***
XY[7*c+6][6+5]=1#1/2*znnj
X=numpy.array(X)
XY=numpy.array(XY)
# W*m=W*X*XY*A
# m=X*XY*A
# A=pinv(X*XY)*m
#a[0]*x^2+a[1]*x+a[2]*x*y+a[3]*y+a[4]*y^2+a[5]
#A=numpy.zeros(6*7)
#A=[a0epp,a1epp,a2epp,a3epp,a4epp,a5epp, a0enp,a1enp,a2enp,a3enp,a4enp,a5enp, a0ezp,a1ezp,a2ezp,a3ezp,a4ezp,a5ezp,...]'
A=numpy.dot(numpy.linalg.pinv(numpy.dot(X,XY)),m)
#now evaluate A at x,y
thisXY=numpy.zeros([7,6+6])
thisXY[0][6*0+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*epp+1
thisXY[1][6+0]=1#1/2*enp
thisXY[2][6+1]=1#1/2*znp
thisXY[3][6+2]=1#1/2*zpp
thisXY[4][6+3]=1#1/2*ennj***
thisXY[5][6+4]=1#1/2*zpnj***
thisXY[6][6+5]=1#1/2*znnj
epsilon_zeta=numpy.dot(thisXY,A)
return numpy.array(epsilon_zeta).reshape(7,)
#given measured IQUV values, parallactic angle and epsilon_zeta terms, calculate the true (estimated) IQUV values
#epsilon_zeta=[1/2*epsilon_pp+1;
# 1/2*epsilon_np;
# 1/2*zeta_np;
# 1/2*zeta_pp;
# 1/2*epsilon_nn*j;
# 1/2*zeta_pn*j;
# 1/2*zeta_nn*j]
#solves the equation:
#[I..harpoon;Q..harpoon;U..harpoon;V..harpoon]=
#[1/2*e.pp+1,1/2*(-z.pp*sin(2*chi)+e.np*cos(2*chi)),1/2*(z.pp*cos(2*chi)+e.np*sin(2*chi)),-1/2*z.nn*j;
#1/2*(-z.pp*sin(2*chi)+e.np*cos(2*chi)),1/2*e.pp+1,1/2*z.np,1/2*(-z.pn*cos(2*chi)-e.nn*sin(2*chi))*j;
#1/2*(z.pp*cos(2*chi)+e.np*sin(2*chi)),-1/2*z.np,1/2*e.pp+1,1/2*(-z.pn*sin(2*chi)+e.nn*cos(2*chi))*j;
#-1/2*z.nn*j,1/2*(z.pn*cos(2*chi)+e.nn*sin(2*chi))*j,1/2*(z.pn*sin(2*chi)-e.nn*cos(2*chi))*j,1/2*e.pp+1]
#*[I;Q;U;V]
def estimatetrueIQUV(I_harpoon,Q_harpoon,U_harpoon,V_harpoon,epsilon_zeta,chi):
[he_pp1,he_np,hz_np,hz_pp,he_nnj,hz_pnj,hz_nnj]=epsilon_zeta
#[1/2*e.pp+1,1/2*(-z.pp*sin(2*chi)+e.np*cos(2*chi)),1/2*(z.pp*cos(2*chi)+e.np*sin(2*chi)),-1/2*z.nn*j;
#1/2*(-z.pp*sin(2*chi)+e.np*cos(2*chi)),1/2*e.pp+1,1/2*z.np,1/2*(-z.pn*cos(2*chi)-e.nn*sin(2*chi))*j;
#1/2*(z.pp*cos(2*chi)+e.np*sin(2*chi)),-1/2*z.np,1/2*e.pp+1,1/2*(-z.pn*sin(2*chi)+e.nn*cos(2*chi))*j;
#-1/2*z.nn*j,1/2*(z.pn*cos(2*chi)+e.nn*sin(2*chi))*j,1/2*(z.pn*sin(2*chi)-e.nn*cos(2*chi))*j,1/2*e.pp+1]
EZ=numpy.array([[he_pp1,-hz_pp*numpy.sin(2.0*chi)+he_np*numpy.cos(2.0*chi),hz_pp*numpy.cos(2.0*chi)+he_np*numpy.sin(2.0*chi),-hz_nnj],
[-hz_pp*numpy.sin(2.0*chi)+he_np*numpy.cos(2.0*chi),he_pp1,hz_np,-hz_pnj*numpy.cos(2.0*chi)-he_nnj*numpy.sin(2.0*chi)],
[hz_pp*numpy.cos(2.0*chi)+he_np*numpy.sin(2.0*chi),-hz_np,he_pp1,-hz_pnj*numpy.sin(2.0*chi)+he_nnj*numpy.cos(2.0*chi)],
[-hz_nnj,hz_pnj*numpy.cos(2.0*chi)+he_nnj*numpy.sin(2.0*chi),hz_pnj*numpy.sin(2.0*chi)-he_nnj*numpy.cos(2.0*chi),he_pp1]])
IQUV_harpoon=numpy.array([I_harpoon,Q_harpoon,U_harpoon,V_harpoon]).reshape(4,1)
IQUVestimated=numpy.dot(numpy.linalg.pinv(EZ),IQUV_harpoon)
return IQUVestimated
def solvezetaepsilon6(x,y,I,Q,U,V,I_harpoon,Q_harpoon,U_harpoon,V_harpoon,xx,yy,chi,maxextent,sigma):
ndata=len(chi)
w=numpy.exp(-0.5*((xx-x)**2+(yy-y)**2)/(sigma)**2)
w_for_epp1=numpy.exp(-0.5*((xx-x)**2+(yy-y)**2)/(0.1)**2)
# epp1=(I_harpoon[c]*I-Q_harpoon[c]*Q-U_harpoon[c]*U-V_harpoon[c]*V)/(I**2-Q**2-U**2-V**2)
wepp1=[w_for_epp1[c]*numpy.array((I_harpoon[c]*I-Q_harpoon[c]*Q-U_harpoon[c]*U-V_harpoon[c]*V)/(I**2-Q**2-U**2-V**2)) for c in range(ndata)]
smoothepp1=numpy.sum(wepp1)/numpy.sum(w_for_epp1)
m=[w[c]*numpy.array([I_harpoon[c]-I*(I_harpoon[c]*I-Q_harpoon[c]*Q-U_harpoon[c]*U-V_harpoon[c]*V)/(I**2-Q**2-U**2-V**2),Q_harpoon[c]-Q*(I_harpoon[c]*I-Q_harpoon[c]*Q-U_harpoon[c]*U-V_harpoon[c]*V)/(I**2-Q**2-U**2-V**2),U_harpoon[c]-U*(I_harpoon[c]*I-Q_harpoon[c]*Q-U_harpoon[c]*U-V_harpoon[c]*V)/(I**2-Q**2-U**2-V**2),V_harpoon[c]-V*(I_harpoon[c]*I-Q_harpoon[c]*Q-U_harpoon[c]*U-V_harpoon[c]*V)/(I**2-Q**2-U**2-V**2)]) for c in range(ndata)]
m=numpy.array(m).reshape(4*ndata,1)
X=[ w[c]*numpy.array(
[[Q*numpy.cos(2.0*chi[c])+U*numpy.sin(2.0*chi[c]),0,U*numpy.cos(2.0*chi[c])-Q*numpy.sin(2.0*chi[c]),0,0,-V],
[I*numpy.cos(2.0*chi[c]),U,-I*numpy.sin(2.0*chi[c]),-V*numpy.sin(2.0*chi[c]),-V*numpy.cos(2.0*chi[c]),0],
[I*numpy.sin(2.0*chi[c]),-Q,I*numpy.cos(2.0*chi[c]),V*numpy.cos(2.0*chi[c]),-V*numpy.sin(2.0*chi[c]),0],
[0,0,0,Q*numpy.sin(2.0*chi[c])-U*numpy.cos(2.0*chi[c]),Q*numpy.cos(2.0*chi[c])+U*numpy.sin(2.0*chi[c]),-I]]) for c in range(ndata)]
X=numpy.array(X).reshape(4*ndata,6);
# [I_harpoon;Q_harpoon;U_harpoon;V_harpoon]=
# [[I,Q*cos(2*chi)+U*sin(2*chi),0,U*cos(2*chi)-Q*sin(2*chi),0,0,-V],
# [Q,I*cos(2*chi),U,-I*sin(2*chi),-V*sin(2*chi),-V*cos(2*chi),0],
# [U,I*sin(2*chi),-Q,I*cos(2*chi),V*cos(2*chi),-V*sin(2*chi),0],
# [V,0,0,0,Q*sin(2*chi)-U*cos(2*chi),Q*cos(2*chi)+U*sin(2*chi),-I]]
# [1/2*epsilon_pp+1;
# 1/2*epsilon_np;
# 1/2*zeta_np;
# 1/2*zeta_pp;
# 1/2*epsilon_nn*j;
# 1/2*zeta_pn*j;
# 1/2*zeta_nn*j]
# m=X*u
# u_best=pinv(X)*m
# W*m=W*X*u;
# u_best=pinv(W*X)*W*m
#gathering weighting terms based on position
#if matrix W use
#epsilon_zeta=numpy.dot(numpy.linalg.pinv(numpy.dot(W,X)),numpy.dot(W,m))
#if vector w, use
#epsilon_zeta=numpy.dot(numpy.linalg.pinv((w*X.transpose()).transpose()),(w*m))
# epsilon_zeta=[1 numpy.dot(numpy.linalg.pinv(X),m)
epsilon_zeta=range(7)
# epsilon_zeta[0]=smoothepp1-1.0
epsilon_zeta[0]=smoothepp1
epsilon_zeta[1:]=numpy.dot(numpy.linalg.pinv(X),m)
return numpy.array(epsilon_zeta)
#
#fits epsilon zeta to smooth surface of form a[0]*x^2+a[1]*x+a[2]*x*y+a[3]*y+a[4]*y^2+a[5]
#except e_nn and z_pn are modeled as planes only!
#then evaluate epsilon zetas at given location
def solve6fitlesszetaepsilon(x,y,I,Q,U,V,I_harpoon,Q_harpoon,U_harpoon,V_harpoon,xx,yy,chi,maxextent,sigma):
ndata=len(chi)
w=numpy.exp(-0.5*(numpy.sqrt((xx-x)**2+(yy-y)**2))/(sigma)**2)
w_for_epp1=numpy.exp(-0.5*((xx-x)**2+(yy-y)**2)/(0.00001)**2)
# epp1=(I_harpoon[c]*I-Q_harpoon[c]*Q-U_harpoon[c]*U-V_harpoon[c]*V)/(I**2-Q**2-U**2-V**2)
wepp1=[w_for_epp1[c]*numpy.array((I_harpoon[c]*I-Q_harpoon[c]*Q-U_harpoon[c]*U-V_harpoon[c]*V)/(I**2-Q**2-U**2-V**2)) for c in range(ndata)]
smoothepp1=numpy.sum(wepp1)/numpy.sum(w_for_epp1)
m=[w[c]*numpy.array([I_harpoon[c]-I*(I_harpoon[c]*I-Q_harpoon[c]*Q-U_harpoon[c]*U-V_harpoon[c]*V)/(I**2-Q**2-U**2-V**2),Q_harpoon[c]-Q*(I_harpoon[c]*I-Q_harpoon[c]*Q-U_harpoon[c]*U-V_harpoon[c]*V)/(I**2-Q**2-U**2-V**2),U_harpoon[c]-U*(I_harpoon[c]*I-Q_harpoon[c]*Q-U_harpoon[c]*U-V_harpoon[c]*V)/(I**2-Q**2-U**2-V**2),V_harpoon[c]-V*(I_harpoon[c]*I-Q_harpoon[c]*Q-U_harpoon[c]*U-V_harpoon[c]*V)/(I**2-Q**2-U**2-V**2)]) for c in range(ndata)]
m=numpy.array(m).reshape(4*ndata,1)
range06=numpy.array(range(0,6))
range03=numpy.array(range(0,3))
X=numpy.zeros([4*ndata,6*ndata])
XY=numpy.zeros([6*ndata,6*6-2*3])
for c in range(ndata):
X[4*c][(6*c):(6*c+6)]=w[c]*numpy.array([Q*numpy.cos(2.0*chi[c])+U*numpy.sin(2.0*chi[c]),0,U*numpy.cos(2.0*chi[c])-Q*numpy.sin(2.0*chi[c]),0,0,-V])
X[4*c+1][(6*c):(6*c+6)]=w[c]*numpy.array([I*numpy.cos(2.0*chi[c]),U,-I*numpy.sin(2.0*chi[c]),-V*numpy.sin(2.0*chi[c]),-V*numpy.cos(2.0*chi[c]),0])
X[4*c+2][(6*c):(6*c+6)]=w[c]*numpy.array([I*numpy.sin(2.0*chi[c]),-Q,I*numpy.cos(2.0*chi[c]),V*numpy.cos(2.0*chi[c]),-V*numpy.sin(2.0*chi[c]),0])
X[4*c+3][(6*c):(6*c+6)]=w[c]*numpy.array([0,0,0,Q*numpy.sin(2.0*chi[c])-U*numpy.cos(2.0*chi[c]),Q*numpy.cos(2.0*chi[c])+U*numpy.sin(2.0*chi[c]),-I])
XY[6*c+0][6*0+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*enp
XY[6*c+1][6*1+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*znp
XY[6*c+2][6*2+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*zpp
XY[6*c+3][6*3+range03]=[xx[c], yy[c], 1]#1/2*ennj***
XY[6*c+4][6*4-3+range03]=[xx[c], yy[c], 1]#1/2*zpnj***
XY[6*c+5][6*5-6+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*znnj
X=numpy.array(X)
XY=numpy.array(XY)
# W*m=W*X*XY*A
# m=X*XY*A
# A=pinv(X*XY)*m
#a[0]*x^2+a[1]*x+a[2]*x*y+a[3]*y+a[4]*y^2+a[5]
#A=numpy.zeros(6*7)
#A=[a0epp,a1epp,a2epp,a3epp,a4epp,a5epp, a0enp,a1enp,a2enp,a3enp,a4enp,a5enp, a0ezp,a1ezp,a2ezp,a3ezp,a4ezp,a5ezp,...]'
A=numpy.dot(numpy.linalg.pinv(numpy.dot(X,XY)),m)
#now evaluate A at x,y
thisXY=numpy.zeros([6,6*6-2*3])
thisXY[0][6*0+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*enp
thisXY[1][6*1+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*znp
thisXY[2][6*2+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*zpp
thisXY[3][6*3+range03]=[x, y, 1]#1/2*ennj***
thisXY[4][6*4-3+range03]=[x, y, 1]#1/2*zpnj***
thisXY[5][6*5-6+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*znnj
epsilon_zeta=range(7)
epsilon_zeta[0]=smoothepp1
epsilon_zeta[1:]=numpy.dot(thisXY,A)
return numpy.array(epsilon_zeta).reshape(7,)
#fits epsilon zeta to smooth surface of form a[0]*x^2+a[1]*x+a[2]*x*y+a[3]*y+a[4]*y^2+a[5]
#except e_nn and z_pn are modeled as planes only!
#then evaluate epsilon zetas at given location
def solve6fitevenlesszetaepsilon(x,y,I,Q,U,V,I_harpoon,Q_harpoon,U_harpoon,V_harpoon,xx,yy,chi,maxextent,sigma):
ndata=len(chi)
w=numpy.exp(-0.5*(numpy.sqrt((xx-x)**2+(yy-y)**2))/(sigma)**2)
w_for_epp1=numpy.exp(-0.5*((xx-x)**2+(yy-y)**2)/(0.00001)**2)
# epp1=(I_harpoon[c]*I-Q_harpoon[c]*Q-U_harpoon[c]*U-V_harpoon[c]*V)/(I**2-Q**2-U**2-V**2)
wepp1=[w_for_epp1[c]*numpy.array((I_harpoon[c]*I-Q_harpoon[c]*Q-U_harpoon[c]*U-V_harpoon[c]*V)/(I**2-Q**2-U**2-V**2)) for c in range(ndata)]
smoothepp1=numpy.sum(wepp1)/numpy.sum(w_for_epp1)
m=[w[c]*numpy.array([I_harpoon[c]-I*(I_harpoon[c]*I-Q_harpoon[c]*Q-U_harpoon[c]*U-V_harpoon[c]*V)/(I**2-Q**2-U**2-V**2),Q_harpoon[c]-Q*(I_harpoon[c]*I-Q_harpoon[c]*Q-U_harpoon[c]*U-V_harpoon[c]*V)/(I**2-Q**2-U**2-V**2),U_harpoon[c]-U*(I_harpoon[c]*I-Q_harpoon[c]*Q-U_harpoon[c]*U-V_harpoon[c]*V)/(I**2-Q**2-U**2-V**2),V_harpoon[c]-V*(I_harpoon[c]*I-Q_harpoon[c]*Q-U_harpoon[c]*U-V_harpoon[c]*V)/(I**2-Q**2-U**2-V**2)]) for c in range(ndata)]
m=numpy.array(m).reshape(4*ndata,1)
range06=numpy.array(range(0,6))
range03=numpy.array(range(0,3))
X=numpy.zeros([4*ndata,6*ndata])
XY=numpy.zeros([6*ndata,6*6-2*5])
for c in range(ndata):
X[4*c][(6*c):(6*c+6)]=w[c]*numpy.array([Q*numpy.cos(2.0*chi[c])+U*numpy.sin(2.0*chi[c]),0,U*numpy.cos(2.0*chi[c])-Q*numpy.sin(2.0*chi[c]),0,0,-V])
X[4*c+1][(6*c):(6*c+6)]=w[c]*numpy.array([I*numpy.cos(2.0*chi[c]),U,-I*numpy.sin(2.0*chi[c]),-V*numpy.sin(2.0*chi[c]),-V*numpy.cos(2.0*chi[c]),0])
X[4*c+2][(6*c):(6*c+6)]=w[c]*numpy.array([I*numpy.sin(2.0*chi[c]),-Q,I*numpy.cos(2.0*chi[c]),V*numpy.cos(2.0*chi[c]),-V*numpy.sin(2.0*chi[c]),0])
X[4*c+3][(6*c):(6*c+6)]=w[c]*numpy.array([0,0,0,Q*numpy.sin(2.0*chi[c])-U*numpy.cos(2.0*chi[c]),Q*numpy.cos(2.0*chi[c])+U*numpy.sin(2.0*chi[c]),-I])
XY[6*c+0][6*0+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*enp
XY[6*c+1][6*1+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*znp
XY[6*c+2][6*2+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*zpp
XY[6*c+3][6*3]=1#1/2*ennj***
XY[6*c+4][6*4-5]=1#1/2*zpnj***
XY[6*c+5][6*5-10+range06]=[xx[c]**2, xx[c], xx[c]*yy[c], yy[c], yy[c]**2, 1]#1/2*znnj
X=numpy.array(X)
XY=numpy.array(XY)
# W*m=W*X*XY*A
# m=X*XY*A
# A=pinv(X*XY)*m
#a[0]*x^2+a[1]*x+a[2]*x*y+a[3]*y+a[4]*y^2+a[5]
#A=numpy.zeros(6*7)
#A=[a0epp,a1epp,a2epp,a3epp,a4epp,a5epp, a0enp,a1enp,a2enp,a3enp,a4enp,a5enp, a0ezp,a1ezp,a2ezp,a3ezp,a4ezp,a5ezp,...]'
A=numpy.dot(numpy.linalg.pinv(numpy.dot(X,XY)),m)
#now evaluate A at x,y
thisXY=numpy.zeros([6,6*6-2*5])
thisXY[0][6*0+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*enp
thisXY[1][6*1+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*znp
thisXY[2][6*2+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*zpp
thisXY[3][6*3]=1#1/2*ennj***
thisXY[4][6*4-5]=1#1/2*zpnj***
thisXY[5][6*5-10+range06]=[x**2, x, x*y, y, y**2, 1]#1/2*znnj
epsilon_zeta=range(7)
epsilon_zeta[0]=smoothepp1
epsilon_zeta[1:]=numpy.dot(thisXY,A)
return numpy.array(epsilon_zeta).reshape(7,)
#
def solve6fitconstantzetaepsilon(x,y,I,Q,U,V,I_harpoon,Q_harpoon,U_harpoon,V_harpoon,xx,yy,chi,maxextent,sigma):
ndata=len(chi)
w=numpy.exp(-0.5*(numpy.sqrt((xx-x)**2+(yy-y)**2))/(sigma)**2)
w_for_epp1=numpy.exp(-0.5*((xx-x)**2+(yy-y)**2)/(0.00001)**2)
# epp1=(I_harpoon[c]*I-Q_harpoon[c]*Q-U_harpoon[c]*U-V_harpoon[c]*V)/(I**2-Q**2-U**2-V**2)
wepp1=[w_for_epp1[c]*numpy.array((I_harpoon[c]*I-Q_harpoon[c]*Q-U_harpoon[c]*U-V_harpoon[c]*V)/(I**2-Q**2-U**2-V**2)) for c in range(ndata)]
smoothepp1=numpy.sum(wepp1)/numpy.sum(w_for_epp1)
m=[w[c]*numpy.array([I_harpoon[c]-I*(I_harpoon[c]*I-Q_harpoon[c]*Q-U_harpoon[c]*U-V_harpoon[c]*V)/(I**2-Q**2-U**2-V**2),Q_harpoon[c]-Q*(I_harpoon[c]*I-Q_harpoon[c]*Q-U_harpoon[c]*U-V_harpoon[c]*V)/(I**2-Q**2-U**2-V**2),U_harpoon[c]-U*(I_harpoon[c]*I-Q_harpoon[c]*Q-U_harpoon[c]*U-V_harpoon[c]*V)/(I**2-Q**2-U**2-V**2),V_harpoon[c]-V*(I_harpoon[c]*I-Q_harpoon[c]*Q-U_harpoon[c]*U-V_harpoon[c]*V)/(I**2-Q**2-U**2-V**2)]) for c in range(ndata)]
m=numpy.array(m).reshape(4*ndata,1)
X=numpy.zeros([4*ndata,6*ndata])
XY=numpy.zeros([6*ndata,6])
for c in range(ndata):
X[4*c][(6*c):(6*c+6)]=w[c]*numpy.array([Q*numpy.cos(2.0*chi[c])+U*numpy.sin(2.0*chi[c]),0,U*numpy.cos(2.0*chi[c])-Q*numpy.sin(2.0*chi[c]),0,0,-V])
X[4*c+1][(6*c):(6*c+6)]=w[c]*numpy.array([I*numpy.cos(2.0*chi[c]),U,-I*numpy.sin(2.0*chi[c]),-V*numpy.sin(2.0*chi[c]),-V*numpy.cos(2.0*chi[c]),0])
X[4*c+2][(6*c):(6*c+6)]=w[c]*numpy.array([I*numpy.sin(2.0*chi[c]),-Q,I*numpy.cos(2.0*chi[c]),V*numpy.cos(2.0*chi[c]),-V*numpy.sin(2.0*chi[c]),0])
X[4*c+3][(6*c):(6*c+6)]=w[c]*numpy.array([0,0,0,Q*numpy.sin(2.0*chi[c])-U*numpy.cos(2.0*chi[c]),Q*numpy.cos(2.0*chi[c])+U*numpy.sin(2.0*chi[c]),-I])
XY[6*c+0][0]=1#1/2*enp
XY[6*c+1][1]=1#1/2*znp
XY[6*c+2][2]=1#1/2*zpp
XY[6*c+3][3]=1#1/2*ennj***
XY[6*c+4][4]=1#1/2*zpnj***
XY[6*c+5][5]=1#1/2*znnj
X=numpy.array(X)
XY=numpy.array(XY)
# W*m=W*X*XY*A
# m=X*XY*A
# A=pinv(X*XY)*m
#a[0]*x^2+a[1]*x+a[2]*x*y+a[3]*y+a[4]*y^2+a[5]
#A=numpy.zeros(6*7)
#A=[a0epp,a1epp,a2epp,a3epp,a4epp,a5epp, a0enp,a1enp,a2enp,a3enp,a4enp,a5enp, a0ezp,a1ezp,a2ezp,a3ezp,a4ezp,a5ezp,...]'
A=numpy.dot(numpy.linalg.pinv(numpy.dot(X,XY)),m)
#now evaluate A at x,y
thisXY=numpy.zeros([6,6])
thisXY[0][0]=1#1/2*enp
thisXY[1][1]=1#1/2*znp
thisXY[2][2]=1#1/2*zpp
thisXY[3][3]=1#1/2*ennj***
thisXY[4][4]=1#1/2*zpnj***
thisXY[5][5]=1#1/2*znnj
epsilon_zeta=range(7)
epsilon_zeta[0]=smoothepp1
epsilon_zeta[1:]=numpy.dot(thisXY,A)
return numpy.array(epsilon_zeta).reshape(7,)
#[0.5*e.pp+1,0.5*e.np,0.5*z.pp,-0.5*z.nn*j;
#0.5*e.np,0.5*e.pp+1,0.5*z.np,-0.5*z.pn*j;
#0.5*z.pp,-0.5*z.np,0.5*e.pp+1,0.5*e.nn*j;
#-0.5*z.nn*j,0.5*z.pn*j,-0.5*e.nn*j,0.5*e.pp+1]
#[[0,1,3,-6],[1,0,2,-5],[3,-2,0,4],[-6,5,-4,0]]
def plotMueller(title,epsilonzeta,maxextent):
labels=['1/2*e.pp+1','1/2*e.np','1/2*z.np','1/2*z.pp','1/2*e.nn*j','1/2*z.pn*j','1/2*z.nn*j']
mapping=[[0,1,3,-6],[1,0,2,-5],[3,-2,0,4],[-6,5,-4,0]]
names=['I','Q','U','V']
az=numpy.linspace(-maxextent,maxextent,len(epsilonzeta[0][0]))
el=numpy.linspace(-maxextent,maxextent,len(epsilonzeta[0][0]))
fig=plt.figure(1,dpi=100)
plt.clf()
plt.title('%s' % (outputpath[:-1]))
cset=0
vmin_=numpy.min(numpy.min(numpy.min(epsilonzeta)))
vmax_=numpy.max(numpy.max(numpy.max(epsilonzeta)))
for irow in range(4):
for icol in range(4):
a = plt.subplot(4, 4, icol+irow*4+1)
# a.set(xlabel='', xticks=[])
# a.set_ylabel('I', rotation='horizontal')
iez=numpy.abs(mapping[irow][icol])
sg=1
if (mapping[irow][icol]<0):
iez=-mapping[irow][icol]
sg=-1
else:
iez=mapping[irow][icol]
cset=plotPattern('', az, el, (sg*epsilonzeta[iez]), plt)
# plt.imshow((sg*epsilonzeta[iez]).transpose(),extent=[-maxextent,maxextent,-maxextent,maxextent],vmin=vmin_,vmax=vmax_,origin='lower')
if (irow==3):
a.set_xlabel(names[icol], rotation='horizontal')
else:
a.set(xlabel='', xticks=[])
if (icol==0):
a.set_ylabel(names[irow], rotation='horizontal')
else:
a.set(ylabel='', yticks=[])
plt.gcf().text(0.5, 0.95, '%s Beam Mueller matrix %s' % (outputpath[:-1],title), ha='center', size='x-large')
plt.subplots_adjust(left=0.1, right=0.9, bottom=0.1, top=0.9, wspace=0.05, hspace=0.05)
if (cset):
plt.colorbar(cset, cax=plt.axes([0.9, 0.1, 0.02, 0.8]), format='%d')
plt.gcf().text(0.96, 0.5, 'dB')
fig.set_size_inches((10.24, 7.68))
plt.savefig('%smueller%s.eps'%(outputpath,title))
plt.clf()
def mygriddata(xx,yy,zz,xgrid,ygrid):
if 1:
org=mlab.find((xx==0.0) & (yy==0.0))
norg=len(org)
if (norg):
corg=mlab.find(((xx!=0.0) | (yy!=0.0)))
ndata=len(xx)
nz=range(ndata-norg+1);
nx=range(ndata-norg+1);
ny=range(ndata-norg+1);
nz[0]=zz[org].mean()
nx[0]=0
ny[0]=0
nz[1:]=zz[corg]
nx[1:]=xx[corg]
ny[1:]=yy[corg]
return mlab.griddata(nx,ny,nz,xgrid,ygrid)
# return mlab.griddata(xx+0.000001*numpy.random.rand(len(xx)),yy+0.000001*numpy.random.rand(len(xx)),zz,xgrid,ygrid)
return mlab.griddata(xx,yy,zz,xgrid,ygrid)
#using equations that determines az,el,parang from RA,DEC,LAT,LST
#calculate the az el coordinate of a pointing at particular time WRT where pointing 0 would be at that time
def getRelAZEL(RA,DEC,RAoffset,DECoffset,AZ,EL,CHI,LST):
pointingRA=RAoffset/numpy.cos(DEC*numpy.pi/180.0)*24.0/(60.0*60.0*360.0)+RA
pointingDEC=DECoffset/(60.0*60.0)+DEC
print 'pointingRA',pointingRA