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funcs_DConeMaps_nonumba.py
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funcs_DConeMaps_nonumba.py
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import sys
import numpy as np
import scipy as sp
import os
import os.path
from scipy import ndimage
from astropy.io import fits as pf
import re
from copy import deepcopy
import time
import matplotlib as mpl
mpl.use('Agg')
import matplotlib.pyplot as plt
from pylab import *
import matplotlib.colors as colors
include_path = '/home/azuleta/common/python/include/'
sys.path.append(include_path)
from ImUtils.Resamp import gridding
from ImUtils.Cube2Im import slice0
if not sys.warnoptions:
import os, warnings
#warnings.simplefilter("default") # Change the filter in this process
warnings.simplefilter("ignore") # Change the filter in this process
#os.environ["PYTHONWARNINGS"] = "default" # Also affect subprocesses
os.environ["PYTHONWARNINGS"] = "ignore" # Also affect subprocesses
def cartesian2conicpolar(outcoords, inputshape, origin, inc=0., tanpsi=0.):
"""Coordinate transform for converting a conic polar array to Cartesian coordinates.
inputshape is a tuple containing the shape of the polar array. origin is a
tuple containing the x and y indices of where the origin should be in the
output array."""
rindex, thetaindex = outcoords
x0, y0 = origin
theta = float(thetaindex) * 2. * np.pi / float(inputshape[0])
y = rindex * np.cos(theta)
height = tanpsi * rindex
#height = -tanpsi * rindex
x = (rindex*np.sin(theta))/np.cos(inc) + \
(height - (rindex*np.sin(theta))*np.tan(inc))*np.sin(inc)
ix = -x + x0
iy = y + float(y0)
return (iy, ix)
def cartesian2polar(outcoords, inputshape, origin, inc=0.):
"""Coordinate transform for converting a polar array to Cartesian coordinates.
inputshape is a tuple containing the shape of the polar array. origin is a
tuple containing the x and y indices of where the origin should be in the
output array."""
rindex, thetaindex = outcoords
x0, y0 = origin
theta = float(thetaindex) * 2. * np.pi / float(inputshape[0] - 1.)
y = rindex * np.cos(theta)
x = rindex * np.sin(theta) * np.cos(inc)
ix = -x + x0
iy = y + float(y0)
return (iy, ix)
def conicpolar2cartesian_ellipse_reflectedazimuths(outcoords,
inputshape,
origin,
inc=0.,
tanpsi=0.):
yindex, xindex = outcoords
x0, y0 = origin
nx = inputshape[0]
ny = inputshape[1]
x = -float(xindex - x0)
y = float(yindex - y0)
tanpsi0 = tanpsi
a = ((np.tan(inc) * tanpsi0)**2 - 1.0)
b = -2. * x * np.sin(inc) * tanpsi0 / (np.cos(inc))**2
c = y**2 + (x**2 / (np.cos(inc)**2))
Delta = b**2 - 4. * a * c
rho = (-b - np.sqrt(Delta)) / (2. * a)
rindex = rho
if (rho == 0.):
costheta = 0.
else:
costheta = y / rho
theta = np.arccos(costheta)
thetaindex = (theta * float(nx) / (2. * np.pi))
return (rindex, thetaindex)
def conicpolar2cartesian_ellipse(outcoords,
inputshape,
origin,
inc=0.,
tanpsi=0.):
yindex, xindex = outcoords
x0, y0 = origin
nx = inputshape[0]
ny = inputshape[1]
x = -float(xindex - x0)
y = float(yindex - y0)
tanpsi0 = tanpsi
a = ((np.tan(inc) * tanpsi0)**2 - 1.0)
b = -2. * x * np.sin(inc) * tanpsi0 / (np.cos(inc))**2
c = y**2 + (x**2 / (np.cos(inc)**2))
Delta = b**2 - 4. * a * c
rho_m = (-b - np.sqrt(Delta)) / (2. * a)
rho_p = (-b + np.sqrt(Delta)) / (2. * a)
if (rho_p > 0.):
print("rho_p > 0", rho_p, rho_m, x, y, inc * 180. / np.pi, tanpsi,
np.arctan(tanpsi) * 180. / np.pi)
rho = rho_m
rindex = rho
if (rho == 0.):
costheta = 0.
else:
costheta = y / rho
H1 = tanpsi0 * rho
num = x - H1 * np.sin(inc)
denom = rho * ((1. / np.cos(inc)) - np.tan(inc) * np.sin(inc))
sintheta = num / denom
theta = np.arccos(costheta)
if sintheta < 0:
theta = 2. * np.pi - theta
thetaindex = (theta * (float(nx) - 1.) / (2. * np.pi))
return (rindex, thetaindex)
def polar2cartesian(outcoords, inputshape, origin, inc=0.):
yindex, xindex = outcoords
x0, y0 = origin
nx = inputshape[0]
ny = inputshape[1]
x = -float(xindex - x0)
y = float(yindex - y0)
rho = np.sqrt((x**2 / (np.cos(inc)**2)) + y**2)
rindex = rho
if (rho == 0.):
costheta = 0.
else:
costheta = y / rho
# theta=np.arccos(costheta)
theta = np.arctan2((-x / np.cos(inc)), y)
if (theta < 0):
theta = theta + 2. * np.pi
thetaindex = (theta * (float(nx) - 1.) / (2. * np.pi))
return (rindex, thetaindex)
def carttoconicpolar(im, inc, tanpsi):
(ny, nx) = im.shape
(i0, j0) = (((float(nx) + 1.) / 2.) - 1., ((float(ny) + 1.) / 2.) - 1.)
im_polar = sp.ndimage.geometric_transform(im,
cartesian2conicpolar,
order=1,
output_shape=(im.shape[0],
im.shape[1]),
extra_keywords={
'inputshape': im.shape,
'inc': inc,
'tanpsi': tanpsi,
'origin': (i0, j0)
})
return im_polar
def carttopolar(im, inc):
(ny, nx) = im.shape
(i0, j0) = (((float(nx) + 1.) / 2.) - 1., ((float(ny) + 1.) / 2.) - 1.)
im_polar = sp.ndimage.geometric_transform(im,
cartesian2polar,
order=1,
output_shape=(im.shape[0],
im.shape[1]),
extra_keywords={
'inputshape': im.shape,
'inc': inc,
'origin': (i0, j0)
})
return im_polar
def conicpolartocart(im_polar, inc, tanpsi):
(ny, nx) = im_polar.shape
(i0, j0) = (((float(nx) + 1.) / 2.) - 1., ((float(ny) + 1.) / 2.) - 1.)
im_cart = sp.ndimage.geometric_transform(im_polar,
conicpolar2cartesian_ellipse,
order=1,
output_shape=(im_polar.shape[0],
im_polar.shape[1]),
extra_keywords={
'inputshape': im_polar.shape,
'inc': inc,
'tanpsi': tanpsi,
'origin': (i0, j0)
})
im_cart = np.nan_to_num(im_cart)
return im_cart
def polartocart(im_polar, inc):
(ny, nx) = im_polar.shape
(i0, j0) = (((float(nx) + 1.) / 2.) - 1., ((float(ny) + 1.) / 2.) - 1.)
im_cart = sp.ndimage.geometric_transform(im_polar,
polar2cartesian,
order=1,
output_shape=(im_polar.shape[0],
im_polar.shape[1]),
extra_keywords={
'inputshape': im_polar.shape,
'inc': inc,
'origin': (i0, j0)
})
im_cart = np.nan_to_num(im_cart)
return im_cart
def exec_prep_files(M):
filename_source = M.filename_source
workdir = M.workdir
DumpAllFitsFiles = M.DumpAllFitsFiles
if (not re.search(r"\/$", workdir)):
workdir += '/'
M.workdir = workdir
print("added trailing back slash to outputdir")
inbasename = os.path.basename(filename_source)
filename_fullim = re.sub('.fits', '_fullim.fits', inbasename)
filename_fullim = workdir + filename_fullim
if (M.DoErrorMap):
inbasenameerr = os.path.basename(M.filename_errormap)
filename_fullimerr = re.sub('.fits', '_fullim.fits', inbasenameerr)
filename_fullimerr = workdir + filename_fullimerr
filename_fullimw = re.sub('.fits', '_fullimw.fits', inbasenameerr)
filename_fullimw = workdir + filename_fullimw
if (M.Verbose): #
print("BUILDING WORKDIR AND GENERATING CENTERED IMAGE")
hdu = pf.open(filename_source)
hdr0 = hdu[0].header
if (hdr0['NAXIS'] > 2):
if (M.Verbose): #
print("running cube2im")
hdu = slice0(filename_source, False)
im1 = hdu[0].data
im1 = im1 * M.unitscale
print("applied unit scale factor:", M.unitscale)
hdr1 = hdu[0].header
typicalerror = M.typicalerror
if (M.InjectNoise):
print("INJECTING NOISE")
im1 = im1 + np.random.normal(
loc=0.0, scale=typicalerror, size=im1.shape)
if (DumpAllFitsFiles):
pf.writeto(filename_fullim, im1, hdr1, overwrite=True)
hdu[0].data = im1
hduw = False
if (M.DoErrorMap):
hduerr = pf.open(M.filename_errormap)
hdrerr = hduerr[0].header
if (hdrerr['NAXIS'] > 2):
hduerr = slice0(M.filename_errormap, False)
imerr1 = hduerr[0].data
imerr1 = imerr1 * M.unitscale
#typicalerror=np.median(imerr1)
#imerr1[np.where(imerr1 < (typicalerror/3.))] = typicalerror
#imerr1[np.where(imerr1 > (100.*typicalerror))] = 1E20
hdrerr1 = hduerr[0].header
imw0 = 1. / imerr1**2
imw0 = np.nan_to_num(imw0)
imw0[np.where(np.fabs(imw0) > 1E10)] = 0.
if (M.Verbose):
print("fullim weights: max", np.max(imw0), " min ", np.min(imw0))
imerr = np.sqrt(1. / imw0)
imerr = np.nan_to_num(imerr)
imerr[np.where(np.fabs(imw0) < 1E-30)] = 1E20
typicalerror = np.median(imerr)
if (M.Verbose):
print("resamp errors: max", np.max(imerr), " min ", np.min(imerr))
print("typicalerror= ", typicalerror, " vs", M.typicalerror)
if (DumpAllFitsFiles):
pf.writeto(filename_fullimw, imw0, hdrerr1, overwrite=True)
hduw = pf.PrimaryHDU()
hduw.data = imw0
hduw.header = hdrerr1
M.Hdu = hdu
M.Hduw = hduw
return
def exec_grid_4center(M):
workdir = M.workdir
RA = M.RA
DEC = M.DEC
x_center = M.x_center
y_center = M.y_center
fieldscale = M.fieldscale # shrink radial field of view of polar maps by this factor
hdu = M.Hdu
hduw = M.Hduw
filename_source = M.filename_source
inbasename = os.path.basename(filename_source)
filename_fullim = re.sub('.fits', '_fullim.fits', inbasename)
filename_fullim = workdir + filename_fullim
fileout_centered = re.sub('fullim.fits', 'centered.fits', filename_fullim)
if (M.DoErrorMap):
inbasenameerr = os.path.basename(M.filename_errormap)
filename_fullimerr = re.sub('.fits', '_fullim.fits', inbasenameerr)
filename_fullimerr = workdir + filename_fullimerr
filename_fullimw = re.sub('.fits', '_fullimw.fits', inbasenameerr)
filename_fullimw = workdir + filename_fullimw
fileout_centerederr = re.sub('fullim.fits', 'centered.fits',
filename_fullimerr)
fileout_centeredw = re.sub('fullim.fits', 'wcentered.fits',
filename_fullimerr)
hdr1 = hdu[0].header
if (not (isinstance(y_center, bool))):
if (not isinstance(RA, float)):
RA = hdr1['CRVAL1']
DEC = hdr1['CRVAL2']
if (M.Verbose):
print("using center of coords CRVAL1 CRVAL2")
#RA=RA+(np.sin(x_center*np.pi/180.)*y_center/3600.)/np.cos(DEC*np.pi/180.)
RA = RA + ((x_center / 3600.) / np.cos(DEC * np.pi / 180.))
#DEC=DEC+np.cos(x_center*np.pi/180.)*y_center/3600.
DEC = DEC + ((y_center / 3600.) * np.pi / 180.)
if (M.Verbose):
print("RA =", RA)
print("DEC =", DEC)
nx = int(hdr1['NAXIS1'] / (M.pixscale_factor * M.fieldscale))
ny = nx
if ((nx % 2) == 0):
nx = nx + 1
ny = ny + 1
hdr2 = deepcopy(hdr1)
hdr2['NAXIS1'] = nx
hdr2['NAXIS2'] = ny
hdr2['CRPIX1'] = (nx + 1) / 2
hdr2['CRPIX2'] = (ny + 1) / 2
hdr2['CRVAL1'] = RA
hdr2['CRVAL2'] = DEC
hdr2['CDELT1'] = M.pixscale_factor * hdr2['CDELT1']
hdr2['CDELT2'] = M.pixscale_factor * hdr2['CDELT2']
resamp = gridding(hdu, hdr2, fullWCS=False)
resamp = np.nan_to_num(resamp)
if (M.DumpAllFitsFiles):
fileout_centered = re.sub('fullim.fits', 'centered.fits',
filename_fullim)
pf.writeto(fileout_centered, resamp, hdr2, overwrite=True)
hducentered = pf.PrimaryHDU()
hducentered.data = resamp
hducentered.header = hdr2
hduwcentered = False
if (M.DoErrorMap):
resampw = gridding(hduw, hdr2, fullWCS=False)
resampw = np.nan_to_num(resampw)
resampw[np.where(resampw < 0.)] = 0.
if (M.Verbose): #
print("resamp weights: max", np.max(resampw), " min ",
np.min(resampw))
resamperr = np.sqrt(1. / resampw)
if (M.DumpAllFitsFiles):
fileout_centeredw = re.sub('fullim.fits', 'wcentered.fits',
filename_fullimerr)
pf.writeto(fileout_centeredw, resampw, hdr2, overwrite=True)
fileout_centerederr = re.sub('fullim.fits', 'centered.fits',
filename_fullimerr)
pf.writeto(fileout_centerederr, resamperr, hdr2, overwrite=True)
hduwcentered = pf.PrimaryHDU()
hduwcentered.data = resampw
hduwcentered.header = hdr2
M.Ncorr = (np.pi / (4. * np.log(2))) * M.bmaj * M.bmin / (hdr2['CDELT2'] *
3600.)**2
M.Hducentered = hducentered
M.Hduwcentered = hduwcentered
def exec_conicpolar_expansions(M):
filename_source = M.filename_source
workdir = M.workdir
inc = M.inc
tanpsi = M.tanpsi
PlotRadialProfile = M.PlotRadialProfile
a_min = M.a_min
a_max = M.a_max
typicalerror = M.typicalerror
DumpAllFitsFiles = M.DumpAllFitsFiles
DoDCone = M.DoDCone
DoAccr = M.DoAccr
DoMerid = M.DoMerid
RestrictAvToRadialDomain = M.RestrictAvToRadialDomain # set to True is faster but may lead to discontinuities in region averages.
DoFarSideOnly = M.DoFarSideOnly
hdu = M.Hducentered
hduw = M.Hduwcentered
#typicalerror=ExpectedError
#cosi=np.cos(inc*np.pi/ 180.)
inbasename = os.path.basename(filename_source)
filename_fullim = re.sub('.fits', '_fullim.fits', inbasename)
filename_fullim = workdir + filename_fullim
if (M.DoErrorMap):
inbasenameerr = os.path.basename(M.filename_errormap)
filename_fullimerr = re.sub('.fits', '_fullim.fits', inbasenameerr)
filename_fullimerr = workdir + filename_fullimerr
filename_fullimw = re.sub('.fits', '_fullimw.fits', inbasenameerr)
filename_fullimw = workdir + filename_fullimw
resamp = hdu.data
hdr2 = hdu.header
nx = hdr2['NAXIS1']
ny = hdr2['NAXIS2']
if M.Verbose:
print("M.Ncorr = ", M.Ncorr)
if (M.DoErrorMap):
resampw = hduw.data
if (M.InheritMumap):
if (M.mumap is None):
mumap = np.ones(resamp.shape)
else:
mumap = M.mumap
else:
mumap = np.ones(resamp.shape)
rotangle = M.PA
im1rot = ndimage.rotate(resamp, rotangle, reshape=False)
hdr3 = deepcopy(hdr2)
im3 = np.double(im1rot)
if (DumpAllFitsFiles):
fileout_rotated = re.sub('fullim.fits', 'rotated.fits',
filename_fullim)
pf.writeto(fileout_rotated, im1rot, hdr2, overwrite=True)
if (M.DoErrorMap):
if (np.any(resampw < 0.)):
print("min / max:", np.min(resampw), np.max(resampw))
sys.exit("negative sky weights!!!!")
im1rotw = ndimage.rotate(resampw, rotangle, reshape=False, order=0)
im3w = np.double(im1rotw)
if (DumpAllFitsFiles):
fileout_rotatedw = re.sub('fullim.fits', 'wrotated.fits',
filename_fullimerr)
pf.writeto(fileout_rotatedw, im1rotw, hdr2, overwrite=True)
if (np.any(im1rotw < 0.)):
print("min / max:", np.min(im1rotw), np.max(im1rotw))
sys.exit("negative rot sky weights!!!!")
# #####################################################################
# take conic polar transforms
if (M.Verbose):
print("CARTESIAN2CONICPOLAR TRANSFORM START")
print("using inc ", inc * np.pi / 180., " tanpsi ", tanpsi)
im_polar = carttoconicpolar(im3, inc, tanpsi)
if (DoDCone):
mumap_polarpos = carttoconicpolar(mumap, inc, tanpsi)
nphis, nrs = im_polar.shape
if ((nphis != nx) or (nrs != ny)):
sys.exit("bug")
hdupolar = pf.PrimaryHDU()
hdupolar.data = im_polar
hdrpolar = hdupolar.header
hdrpolar['CRPIX1'] = 1
hdrpolar['CRVAL1'] = 0.
hdrpolar['CDELT1'] = 2. * np.pi / nphis
hdrpolar['CRPIX2'] = 1
hdrpolar['CRVAL2'] = 0.
hdrpolar['CDELT2'] = (hdr3['CDELT2'])
hdupolar.header = hdrpolar
fileout_polar = re.sub('fullim.fits', 'polar.fits', filename_fullim)
if (DumpAllFitsFiles):
hdupolar.writeto(fileout_polar, overwrite=True)
if (M.DoErrorMap):
im_polarw = carttoconicpolar(im3w, inc, tanpsi)
nphis, nrs = im_polarw.shape
hdupolarw = pf.PrimaryHDU()
hdupolarw.data = im_polarw
hdupolarw.header = hdrpolar
fileout_polarw = re.sub('fullim.fits', 'wpolar.fits',
filename_fullimerr)
if (DumpAllFitsFiles):
hdupolarw.writeto(fileout_polarw, overwrite=True)
else:
im_polarw = np.ones(im_polar.shape) / typicalerror**2
######################################################################
# take azimuthal averages on polar maps
weights = im_polarw.copy()
im_Npolcorr = np.ones(im_polarw.shape)
if (np.any(weights < 0.)):
print("min / max:", np.min(weights), np.max(weights))
sys.exit("negative polarweights!!")
im_polar_av = np.copy(im_polar)
rrs = 3600. * (np.arange(hdrpolar['NAXIS2']) - hdrpolar['CRPIX2'] +
1.0) * hdrpolar['CDELT2'] + hdrpolar['CRVAL2']
phis = (180. / np.pi) * (
(np.arange(hdrpolar['NAXIS1']) - hdrpolar['CRPIX1'] + 1.0) *
hdrpolar['CDELT1'] + hdrpolar['CRVAL1'])
phis_rad = np.double(
((np.arange(hdrpolar['NAXIS1']) - hdrpolar['CRPIX1'] + 1.0) *
hdrpolar['CDELT1'] + hdrpolar['CRVAL1']))
KepAmps = np.double(np.zeros(len(rrs)))
sKepAmps = np.double(np.zeros(len(rrs)))
AccrAmps = np.double(np.zeros(len(rrs)))
sAccrAmps = np.double(np.zeros(len(rrs)))
MeridAmps = np.double(np.zeros(len(rrs)))
sMeridAmps = np.double(np.zeros(len(rrs)))
vsysts = np.zeros(hdrpolar['NAXIS2'])
if (a_min > 0):
ia_min = np.argmin(np.abs(rrs - a_min))
if (a_max > 0):
ia_max = np.argmin(np.abs(rrs - a_max))
if (M.ComputeSystVelo):
if (M.DoErrorMap):
for irrs in range(len(rrs)):
v0_vec = im_polar[irrs, :]
w_vec = im_polarw[irrs, :]
av_v0 = np.sum(w_vec * v0_vec) / np.sum(w_vec)
av_cosphi = np.sum(w_vec * np.cos(phis_rad)) / np.sum(w_vec)
KepAmp = np.sum(
(v0_vec - av_v0) * w_vec *
np.cos(phis_rad)) / np.sum(w_vec *
(np.cos(phis_rad))**2 - w_vec *
np.cos(phis_rad) * av_cosphi)
vsysts[irrs] = np.sum(
w_vec *
(v0_vec - KepAmp * np.cos(phis_rad))) / np.sum(w_vec)
else:
for irrs in range(len(rrs)):
v0_vec = im_polar[irrs, :]
KepAmp = np.sum(
(v0_vec - np.average(v0_vec)) * np.cos(phis_rad)) / np.sum(
(np.cos(phis_rad))**2 -
np.cos(phis_rad) * np.average(np.cos(phis_rad)))
vsysts[irrs] = np.average(v0_vec - KepAmp * np.cos(phis_rad))
vsyst = np.asscalar(np.median(vsysts[ia_min:ia_max]))
sigma_vsyst = np.asscalar(np.std(vsysts[ia_min:ia_max]))
print("vsyst calculated = ", vsyst, "+-", sigma_vsyst)
M.vsyst = vsyst
M.sigma_vsyst = sigma_vsyst
else:
vsyst = M.vsyst
if (M.Verbose):
print("vsyst from M = ", vsyst)
for irrs in range(len(rrs)):
KepAmps[irrs] = 0.
sKepAmps[irrs] = 0.
AccrAmps[irrs] = 0.
sAccrAmps[irrs] = 0.
MeridAmps[irrs] = 0.
sMeridAmps[irrs] = 0.
im_polar_av[irrs, :] = 0.
if (((irrs < ia_min) or (irrs > ia_max)) and RestrictAvToRadialDomain):
continue
v0_vec = im_polar[irrs, :] - vsyst
if (M.DoErrorMap):
w_vec = weights[irrs, :]
else:
w_vec = np.ones(len(v0_vec)) / typicalerror**2
mask = (w_vec < 1E-10)
w_vec_nozeros = w_vec
w_vec_nozeros[mask] = 1E-10
err_vec = (1.0 / np.sqrt(w_vec_nozeros))
err_vec[mask] = 1E20 # np.inf
w_vec[mask] = 0.
thisradius = rrs[irrs] #arcsec
# cosi=np.cos(M.inc)
#Nind=2.*np.pi*thisradius * np.fabs(cosi) /(M.bmaj) # aprox number of beams at each radius
Nind = 2. * np.pi * thisradius / (
M.bmaj) # aprox number of beams at each radius
Nsum = len(w_vec)
Npolcorr = Nsum / Nind
#print("irrs ",irrs,Nsum, Nind, Npolcorr)
if Npolcorr < 1:
Npolcorr = 1.
im_Npolcorr[irrs, :] = Npolcorr
if ((np.sum(w_vec) == 0.)
or (np.sum(w_vec * (np.cos(phis_rad))**2)**2 == 0.)):
KepAmp = 0.
sKepAmp = 1E20
AccrAmp = 0.
sAccrAmp = 1E20
MeridAmp = 0.
sMeridAmp = 1E20
else:
if (M.InheritMumap):
mumap_vec = mumap_polarpos[irrs, :]
if (DoAccr):
sys.exit("Not yet programmed DoAccr with mumap")
else:
KepAmp = np.sum(w_vec * v0_vec * mumap_vec *
np.cos(phis_rad)) / np.sum(
w_vec * mumap_vec *
(np.cos(phis_rad))**2)
AccrAmp = 0.
else:
Cramer = True
if (DoMerid and Cramer):
if (np.any(phis_rad < 0.)):
sys.exit("negative phis_rad")
maskphis = (phis_rad >= 0.)
if DoFarSideOnly:
maskphis = ((phis_rad > 0.) & (phis_rad < np.pi))
subw_vec = w_vec[maskphis]
subv0_vec = v0_vec[maskphis]
subphis_rad = phis_rad[maskphis]
sinphis = np.sin(subphis_rad)
cosphis = np.cos(subphis_rad)
a_1 = np.sum(subw_vec * cosphis**2)
b_1 = np.sum(subw_vec * sinphis * cosphis)
c_1 = np.sum(subw_vec * cosphis)
d_1 = np.sum(subw_vec * cosphis * subv0_vec)
vard_1 = np.sum(subw_vec * cosphis**2)
a_2 = b_1
b_2 = np.sum(subw_vec * sinphis**2)
c_2 = np.sum(subw_vec * sinphis)
d_2 = np.sum(subw_vec * sinphis * subv0_vec)
vard_2 = np.sum(subw_vec * sinphis**2)
a_3 = c_1
b_3 = c_2
c_3 = np.sum(subw_vec)
d_3 = np.sum(subw_vec * subv0_vec)
vard_3 = np.sum(subw_vec)
detM = a_1 * (b_2 * c_3 - b_3 * c_2) - b_1 * (
a_2 * c_3 - a_3 * c_2) + c_1 * (a_2 * b_3 - a_3 * b_2)
if (detM == 0.):
#print("singular matrix")
continue
A = (d_1 * (b_2 * c_3 - b_3 * c_2) + d_2 *
(c_1 * b_3 - b_1 * c_3) + d_3 *
(b_1 * c_2 - c_1 * b_2)) / detM
sigmaA = np.sqrt(vard_1 *
(b_2 * c_3 - b_3 * c_2)**2 + vard_2 *
(c_1 * b_3 - b_1 * c_3)**2 + vard_3 *
(b_1 * c_2 - c_1 * b_2)**2) / detM
B = (d_1 * (a_3 * c_2 - a_2 * c_3) + d_2 *
(a_1 * c_3 - c_1 * a_3) + d_3 *
(c_1 * a_2 - a_1 * c_2)) / detM
#Bcheck = (a_1 * ( d_2 *c_3 - d_3 * c_2) - d_1 * (a_2 * c_3 - a_3 * c_2) + c_1 * (a_2 * d_3 - a_3 * d_2)) /detM
sigmaB = np.sqrt(vard_1 *
(a_3 * c_2 - a_2 * c_3)**2 + vard_2 *
(a_1 * c_3 - c_1 * a_3)**2 + vard_3 *
(c_1 * a_2 - a_1 * c_2)**2) / detM
C = (d_1 * (a_2 * b_3 - a_3 * b_2) + d_2 *
(b_1 * a_3 - a_1 * b_3) + d_3 *
(a_1 * b_2 - b_1 * a_2)) / detM
sigmaC = np.sqrt(vard_1 *
(a_2 * b_3 - a_3 * b_2)**2 + vard_2 *
(b_1 * a_3 - a_1 * b_3)**2 + vard_3 *
(a_1 * b_2 - b_1 * a_2)**2) / detM
#if (np.fabs((Bcheck-B)/B) > 1E-8) :
# print("A ",A," C" ,C)
# print("B ",B,"Bcheck",Bcheck)
# sys.exit("check algebra ")
KepAmp = A
sKepAmp = sigmaA
AccrAmp = B
sAccrAmp = sigmaB
MeridAmp = C
sMeridAmp = sigmaC
sAccrAmp *= np.sqrt(Npolcorr)
sKepAmp *= np.sqrt(Npolcorr)
sMeridAmp *= np.sqrt(Npolcorr)
elif (DoMerid):
sum_w = np.sum(w_vec)
sum_wv0 = np.sum(w_vec * v0_vec)
sum_wsinphi = np.sum(w_vec * np.sin(phis_rad))
sum_wcosphi = np.sum(w_vec * np.cos(phis_rad))
sinphis = np.sin(phis_rad)
cosphis = np.cos(phis_rad)
subA_num = (np.sum(w_vec * sinphis**2 -
w_vec * sinphis * sum_wsinphi / sum_w) /
np.sum(w_vec * sinphis * cosphis -
w_vec * cosphis * sum_wsinphi / sum_w))
A_num = (
np.sum(v0_vec * w_vec * sinphis -
w_vec * sinphis * sum_wv0 / sum_w) -
subA_num * np.sum(v0_vec * w_vec * cosphis -
w_vec * cosphis * sum_wv0 / sum_w))
subA_denom1_num1 = np.sum(w_vec * cosphis**2 - w_vec *
cosphis * sum_wcosphi / sum_w)
subA_denom1_denom1 = np.sum(w_vec * cosphis * sinphis -
w_vec * cosphis * sum_wsinphi /
sum_w)
A_denom = (np.sum((w_vec * sinphis * cosphis -
w_vec * sinphis * sum_wcosphi / sum_w) -
(w_vec * sinphis**2 -
w_vec * sinphis * sum_wsinphi / sum_w) *
subA_denom1_num1 / subA_denom1_denom1))
A = A_num / A_denom
varA_num = np.sum(
sinphis**2 * w_vec +
w_vec**2 * sinphis**2 / sum_w) + subA_num**2 * np.sum(
cosphis**2 * w_vec + w_vec**2 * cosphis**2 / sum_w)
sigma_A = np.sqrt(varA_num / A_denom**2)
B_denom = np.sum(w_vec * cosphis * sinphis -
w_vec * cosphis * sum_wsinphi / sum_w)
subB_num = np.sum(w_vec * cosphis**2 -
w_vec * cosphis * sum_wcosphi / sum_w)
B = ((np.sum(v0_vec * w_vec * cosphis - w_vec * cosphis *
sum_wv0 / sum_w) - A * subB_num) / B_denom)
varB = (np.sum(w_vec * cosphis**2 +
w_vec**2 * cosphis**2 / sum_w) +
sigma_A**2 * subB_num**2) / B_denom**2
sigma_B = np.sqrt(varB)
C_denom = sum_w * abs(np.cos(M.inc))
C = np.sum(w_vec *
(v0_vec - A * cosphis - B * sinphis)) / C_denom
varC = np.sum(w_vec**2 *
(err_vec**2 + sigma_A**2 * cosphis**2 +
sigma_B**2 + sinphis**2)) / C_denom**2
sigma_C = np.sqrt(varC)
KepAmp = A
sKepAmp = sigma_A
AccrAmp = B
sAccrAmp = sigma_B
MeridAmp = C
sMeridAmp = sigma_C
sAccrAmp *= np.sqrt(Npolcorr)
sKepAmp *= np.sqrt(Npolcorr)
sMeridAmp *= np.sqrt(Npolcorr)
elif (DoAccr):
subsum1 = np.sum(
w_vec * v0_vec * np.cos(phis_rad)) / np.sum(
w_vec * (np.cos(phis_rad))**2)
varsubsum1 = np.sum(
(np.sqrt(w_vec) * np.cos(phis_rad)) /
np.sum(w_vec * (np.cos(phis_rad))**2)**2)
numerator = np.sum(w_vec * np.sin(phis_rad) *
(v0_vec - np.cos(phis_rad) * subsum1))
#dum1=w_vec**2 * np.sin(phis_rad)**2
##if ((~np.isfinite(varsubsum1)).any()):
## print("varsubsum1 bad values")
#dum2=np.cos(phis_rad)**2 * varsubsum1
#dum3=((err_vec)**2 + dum2)
#varnumerator=np.sum(dum1*dum3)
varnumerator = np.sum(
w_vec**2 * np.sin(phis_rad)**2 *
((err_vec)**2 + np.cos(phis_rad)**2 * varsubsum1))
subsum2 = np.sum(
w_vec * np.sin(phis_rad) * np.cos(phis_rad)) / np.sum(
w_vec * (np.cos(phis_rad))**2)
denom = np.sum(w_vec * ((np.sin(phis_rad))**2 - subsum2))
AccrAmp = numerator / denom
sAccrAmp = np.sqrt(varnumerator) / denom
KepAmp = np.sum(
w_vec * (v0_vec - AccrAmp * np.sin(phis_rad)) *
np.cos(phis_rad)) / np.sum(w_vec *
(np.cos(phis_rad))**2)
sKdenom = np.sum(w_vec * (np.cos(phis_rad))**2)
varKnum = np.sum(
w_vec**2 *
(err_vec**2 + sAccrAmp**2 * np.sin(phis_rad)**2) *
np.cos(phis_rad)**2)
sKnum = np.sqrt(varKnum)
sKepAmp = sKnum / sKdenom
#print("sKepAmp>",rrs[irrs],KepAmp, varKnum, sKnum,sKdenom, sKepAmp, sAccrAmp)
sAccrAmp *= np.sqrt(Npolcorr)
sKepAmp *= np.sqrt(Npolcorr)
MeridAmp = 0.
sMeridAmp = 1E20
else:
denom = np.sum(w_vec * (np.cos(phis_rad))**2)
numerator = np.sum(w_vec * v0_vec * np.cos(phis_rad))
KepAmp = numerator / denom
sdenom = np.sqrt(np.sum(w_vec * (np.cos(phis_rad))**2))
sKepAmp = 1. / sdenom
#print( "bmaj = ",M.bmaj, " thisradius ",thisradius, " inc ", M.inc ,"Nind ",Nind," Ncorr ",Ncorr, " \n")
sKepAmp *= np.sqrt(Npolcorr)
AccrAmp = 0.
sAccrAmp = 1E20
MeridAmp = 0.
sMeridAmp = 1E20
# else:
# v0_vec=im_polar[irrs,:]-vsyst
# KepAmp = np.sum(v0_vec * np.cos(phis_rad)) / np.sum((np.cos(phis_rad))**2)
if (M.Verbose and (KepAmp < 0.) and (irrs == int(len(rrs) / 4.))):
print("KepAmp negative, wrong PA: KepAmp=", KepAmp, " PA: ", M.PA,
" inc", M.inc * np.pi / 180., "deg tanpsi", tanpsi)
print((np.array(zip(v0_vec, np.cos(phis_rad)))))
KepAmps[irrs] = KepAmp
sKepAmps[irrs] = sKepAmp
AccrAmps[irrs] = AccrAmp
sAccrAmps[irrs] = sAccrAmp
MeridAmps[irrs] = MeridAmp
sMeridAmps[irrs] = sMeridAmp
if (DoMerid):
# v0_vec_av = KepAmp * np.cos(phis_rad) + AccrAmp * np.sin(phis_rad) * MeridAmp*np.cos(M.inc)
v0_vec_av = KepAmp * np.cos(phis_rad) + AccrAmp * np.sin(
phis_rad) + MeridAmp
im_polar_av[irrs, :] = v0_vec_av + vsyst
elif (DoAccr):
v0_vec_av = KepAmp * np.cos(phis_rad) + AccrAmp * np.sin(phis_rad)
im_polar_av[irrs, :] = v0_vec_av + vsyst
else:
v0_vec_av = KepAmp * np.cos(phis_rad)
im_polar_av[irrs, :] = v0_vec_av + vsyst
# SIGNS CALIBRATED ON THE RT TRIALS WIGGLERT
# beware when flipping across the sky as observer sees the cone with psi < 0, with z<0, where a wind would have v_z < 0 in disk coordinates.
# /strelka_ssd/simon/wiggleRT/
sini = np.sin(M.inc)
cosi = np.cos(M.inc)
if (np.fabs(M.inc) > (np.pi / 2.)):
# this fabs to report values for the upper side z>0 of the disk even when retrograde
# cosi=np.fabs(np.cos(M.inc))
# best not to do change the results, and instead take care when reporting in RotOrient
cosi = np.cos(M.inc)
v_Phi_prof = KepAmps / sini
sv_Phi_prof = sKepAmps / np.fabs(sini)
v_Phi_prof = np.nan_to_num(v_Phi_prof)
sv_Phi_prof = np.nan_to_num(sv_Phi_prof)
v_R_prof = AccrAmps / sini
sv_R_prof = sAccrAmps / np.fabs(sini)
v_R_prof = np.nan_to_num(v_R_prof)
sv_R_prof = np.nan_to_num(sv_R_prof)
v_z_prof = -MeridAmps / cosi
sv_z_prof = sMeridAmps / np.fabs(cosi)
v_z_prof = np.nan_to_num(v_z_prof)
sv_z_prof = np.nan_to_num(sv_z_prof)
######################################################################
# now compute chi2 in polar coords
if (DoDCone):
imazim_far = conicpolartocart(im_polar_av, inc, -tanpsi)
im_polar_av_far_near = carttoconicpolar(imazim_far, inc, tanpsi)
for irrs in range(len(rrs)):
v0_vec = im_polar[irrs, :] - vsyst
v0_vec_m = im_polar_av[irrs, :] - vsyst
v0_vec_FN_m = im_polar_av_far_near[irrs, :] - vsyst
if (M.DoErrorMap):