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hro.py
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# This file is part of MAGNETAR, the set of magnetic field analysis tools
#
# Copyright (C) 2013-2017 Juan Diego Soler
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.pyplot import cm
from astropy.io import fits
from astropy.convolution import convolve, convolve_fft
from astropy.convolution import Gaussian2DKernel
from astropy.stats import circstats
from scipy import ndimage
import pycircstat as circ
from tqdm import tqdm
from bvisual import *
from poltools import *
from scipy.stats import circmean
from scipy.stats import circstd
# ===================================================================================================
def roangles(Imap, Qmap, Umap, ksz=1, mask=0, mode='reflect', convention='Planck', debug=False):
# Calculates the relative orientation angle between the density structures and the magnetic field following the method
# presented in Soler, et al. ApJ 774 (2013) 128S
#
# INPUTS
# Imap - Intensity or column density map
# Qmap - Stokes Q map
# Upam - Stokes U map
# OUTPUTS
# phi - relative orientation angle between the column density and projected magnetic field.
if (mask is 0):
mask=np.ones_like(Imap)
psi=0.5*np.arctan2(Umap,Qmap)
ex=-np.sin(psi)
ey=np.cos(psi)
angleb=np.arctan2(ey,-ex)
bx=ey; by=-ex
sImap=ndimage.filters.gaussian_filter(Imap, [ksz, ksz], order=[0,0], mode=mode)
dIdx =ndimage.filters.gaussian_filter(Imap, [ksz, ksz], order=[0,1], mode=mode)
dIdy =ndimage.filters.gaussian_filter(Imap, [ksz, ksz], order=[1,0], mode=mode)
angleg=np.arctan2(dIdx,dIdy)
normgrad=np.sqrt(dIdx**2+dIdy**2)
unidIdx=dIdx/np.sqrt(dIdx**2+dIdy**2)
unidIdy=dIdy/np.sqrt(dIdx**2+dIdy**2)
cosphi=(dIdy*ey+dIdx*ex)/normgrad
sinphi=(dIdy*ex-dIdx*ey)/normgrad
#phi=np.arctan2(np.abs(dIdy*ex-dIdx*ey), dIdy*ey+dIdx*ex)
phi=np.arctan2(np.abs(sinphi), cosphi)
#phi=np.arccos(cosphi)
#phi=np.arcsin(sinphi)
bad=((dIdx**2+dIdy**2)==0.).nonzero() #np.logical_or((dIdx**2+dIdy**2)==0., (Qmap**2+Umap**2)==0.).nonzero()
phi[bad]=np.nan
bad=((Qmap**2+Umap**2)==0.).nonzero()
phi[bad]=np.nan
bad=(mask < 1.).nonzero()
phi[bad]=np.nan
# ------------------------------------------------------------------------------------
vecpitch=10
xx, yy, gx, gy = vectors(Imap, dIdx*mask, dIdy*mask, pitch=vecpitch)
xx, yy, ux, uy = vectors(Imap, bx*mask, by*mask, pitch=vecpitch)
if np.array_equal(np.shape(Imap), np.shape(mask)):
bad=(mask==0.).nonzero()
phi[bad]=np.nan
# Debugging -------------------------------------------------------------------------
if (debug):
levels=np.nanmean(Imap)+np.array([0.,1.,2.,3.,5.,7.])*np.nanstd(Imap)
fig = plt.figure(figsize=(7.0,7.0))
plt.rc('font', size=10)
ax1=plt.subplot(111)
im=ax1.imshow(np.abs(np.rad2deg(np.arctan(np.tan(phi)))), origin='lower', cmap='cividis')
ax1.quiver(xx, yy, gx, gy, units='width', color='red', pivot='middle', scale=25., headlength=0, headwidth=1, label=r'$\nabla I$')
ax1.quiver(xx, yy, ux, uy, units='width', color='black', pivot='middle', scale=25., headlength=0, headwidth=1, label=r'$B_{\perp}$')
ax1.contour(Imap, origin='lower', colors='black', levels=levels, linewidths=1.0)
cbar=fig.colorbar(im, ax=ax1, fraction=0.046, pad=0.04)
cbar.ax.set_title(r'$\phi$')
plt.legend()
plt.show()
#import pdb; pdb.set_trace()
return np.arctan(np.tan(phi))
# ===================================================================================================
def roparameterhist(phi, hsize=15, s_phi=20.):
# Calculate the relative orientation parameter $\xi$ as defined in Planck intermediate results. XXXV. A&A 586A (2016) 138P.
#
# INPUTS
# phi - vector with the reference values for the histogram
# s_phi - range for the definitions of parallel (0 < phi < s_phi and 180-s_phi < phi < 180) or
# perpendicular (90-s_phi < phi < 90+s_phi)
# OUTPUTS
# xi - relative orientation parameter
hist, bin_edges = np.histogram((180/np.pi)*phi, bins=hsize, range=(-90.,90.))
bin_centre=0.5*(bin_edges[0:np.size(bin_edges)-1]+bin_edges[1:np.size(bin_edges)])
perp=(np.abs(bin_centre) > 90.-s_phi).nonzero()
para=(np.abs(bin_centre) < s_phi).nonzero()
xi=float(np.mean(hist[para])-np.mean(hist[perp]))/float(np.mean(hist[para])+np.mean(hist[perp]))
s_xi=2.*np.sqrt((np.mean(hist[para])*np.std(hist[perp]))**2+(np.mean(hist[perp])*np.std(hist[para]))**2)/(np.mean(hist[para])+np.mean(hist[perp]))**2
return xi, s_xi
# ===================================================================================================
def roparameter(phi, hist, s_phi=20.):
# Calculate the relative orientation parameter $\xi$ as defined in Planck intermediate results. XXXV. A&A 586A (2016) 138P.
#
# INPUTS
# phi - vector with the reference values for the histogram
# hist - histogram of relative orientations
# s_phi - range for the definitions of parallel (0 < phi < s_phi and 180-s_phi < phi < 180) or
# perpendicular (90-s_phi < phi < 90+s_phi)
# OUTPUTS
# xi - relative orientation parameter
perp=(np.abs(phi) > 90.-s_phi).nonzero()
para=(np.abs(phi) < s_phi).nonzero()
xi=float(np.mean(hist[para])-np.mean(hist[perp]))/float(np.mean(hist[para])+np.mean(hist[perp]))
s_xi=2.*np.sqrt((np.mean(hist[para])*np.std(hist[perp]))**2+(np.mean(hist[perp])*np.std(hist[para]))**2)/(np.mean(hist[para])+np.mean(hist[perp]))**2
return xi, s_xi
# ===================================================================================================
def projRS(angles, w=None):
# Calculate the projected Rayleight statistics as defined in Jow, et al. MNRAS (2018) in press.
#
# INPUTS
# phi - relative orientation angles defined between -pi/2 and pi/2
# w -
# OUTPUTS
# psr - projected Rayleigh statistic
# s_prs -
if w is None:
w = np.ones_like(angles)
assert w.shape == angles.shape, "Dimensions of phi and wgts must match"
circX=np.sum(w*np.cos(angles))/np.sum(w)
circY=np.sum(w*np.sin(angles))/np.sum(w)
mrl=np.sqrt(circX**2+circY**2)
Zx=np.sum(w*np.cos(angles))/np.sqrt(np.sum(w)/2.)
temp=np.sum(np.cos(angles)*np.cos(angles))
s_Zx=np.sqrt((2.*temp-Zx*Zx)/np.size(angles))
Zy=np.sum(w*np.sin(angles))/np.sqrt(np.sum(w)/2.)
temp=np.sum(np.sin(angles)*np.sin(angles))
s_Zy=np.sqrt((2.*temp-Zy*Zy)/np.size(angles))
#x=np.sum(w*np.cos(angles))/np.sum(w)
#y=np.sum(w*np.sin(angles))/np.sum(w)
#mrl=circ.descriptive.resultant_vector_length(angles, w=w)
#s_mrl=np.sqrt(np.sum(w*(np.cos(angles)-x)**2)+np.sum(w*(np.sin(angles)-y)**2))/np.sqrt(np.sum(w))
meanphi=np.arctan2(circY,circX)
#s_meanphi=np.sqrt(circ.descriptive.var(angles, w=w))
s_meanphi=np.sqrt(Zx*Zx*s_Zy*s_Zy+Zy*Zy*s_Zx*s_Zx)/(Zx**2+Zy**2)
# using astropy
#meanphi[i]=circstats.circmean(angles, weights=w[good])
#s_meanphi=np.sqrt(circstats.circvar(angles, weights=w))
return {'Zx': Zx, 's_Zx': s_Zx, 'Zy': Zy, 's_Zy': Zy, 'meanphi': meanphi, 's_meanphi': s_meanphi, 'r': mrl}
# ===================================================================================================
def hroLITE(Imap, Qmap, Umap, steps=10, hsize=15, minI=None, mask=0, ksz=1, showplots=False, w=None, convention='Planck', outh=[0,4,9], savefig=False, prefix='', segmap=None, debug=False):
# Calculates the relative orientation angle between the density structures and the magnetic field.
# INPUTS
# Imap - Intensity or column density map
# Qmap - Stokes Q map
# Umap - Stokes U map
# mask -
sz=np.shape(Imap)
if w is None:
w=np.ones_like(Imap)
assert w.shape == Imap.shape, "Dimensions of Imap and w must match"
# Calculation of relative orientation angles
phi=roangles(Imap, Qmap, Umap, mask=mask, ksz=ksz, convention=convention, debug=debug)
if segmap is None:
stepmap=Imap.copy()
else:
assert Imap.shape == segmap.shape, "Dimensions of Imap and segmap must match"
stepmap=segmap.copy()
if np.array_equal(np.shape(Imap), np.shape(mask)):
bad=np.isnan(Imap).nonzero()
mask[bad]=0.
bad=np.isnan(stepmap).nonzero()
mask[bad]=0.
else:
mask=np.ones_like(Imap)
bad=np.isnan(Imap).nonzero()
mask[bad]=0.
bad=np.isnan(stepmap).nonzero()
mask[bad]=0.
if minI is None:
minI=np.nanmin(stepmap)
bad=(stepmap <= minI).nonzero()
mask[bad]=0.
bad=np.isnan(phi).nonzero()
mask[bad]=0.
good=(mask > 0.).nonzero()
bad=(mask < 1.).nonzero()
stepmap[bad]=np.nan
hist, bin_edges = np.histogram(stepmap[good], bins=int(0.75*np.size(Imap)))
bin_centre=0.5*(bin_edges[0:np.size(bin_edges)-1]+bin_edges[1:np.size(bin_edges)])
chist=np.cumsum(hist)
pitch=np.max(chist)/float(steps)
hsteps=pitch*np.arange(0,steps+1,1)
Isteps=np.zeros(steps+1)
for i in range(0,steps):
good=np.logical_and(chist>hsteps[i], chist<=hsteps[i+1]).nonzero()
Isteps[i]=np.min(bin_centre[good])
Isteps[np.size(Isteps)-1]=np.nanmax(stepmap)
# Preparing output of the HRO
hros=np.zeros([steps,hsize])
s_hros=np.zeros([steps,hsize])
Smap=np.nan*Imap
xi=np.zeros(steps)
s_xi=np.zeros(steps)
Zx=np.zeros(steps)
Zy=np.zeros(steps)
s_Zx=np.zeros(steps)
s_Zy=np.zeros(steps)
meanphi=np.zeros(steps)
s_meanphi=np.zeros(steps)
mrl=np.zeros(steps)
cdens=np.zeros(steps)
for i in range(0, np.size(Isteps)-1):
#import pdb; pdb.set_trace()
temp=stepmap.copy()
temp[np.isnan(temp).nonzero()]=Isteps[i]
temp[(mask > 1.).nonzero()]=Isteps[i]
good=np.logical_and(temp > Isteps[i], temp <= Isteps[i+1]).nonzero()
#good=np.logical_and(segmap > Isteps[i], segmap <= Isteps[i+1]).nonzero()
print(np.size(good))
hist, bin_edges = np.histogram((180/np.pi)*phi[good], bins=hsize, range=(-90.,90.))
bin_centre=0.5*(bin_edges[0:np.size(bin_edges)-1]+bin_edges[1:np.size(bin_edges)])
hros[i,:]=hist
cdens[i]=np.mean([Isteps[i],Isteps[i+1]])
Smap[good]=Isteps[i]
TEMPxi, TEMPs_xi = roparameter(bin_centre, hist)
xi[i]=TEMPxi
s_xi[i]=TEMPs_xi
outprojRS = projRS(2.*phi[good], w=w[good])
Zx[i]=outprojRS['Zx']
Zy[i]=outprojRS['Zy']
s_Zx[i]=outprojRS['s_Zx']
s_Zy[i]=outprojRS['s_Zy']
meanphi[i]=0.5*circmean(2.*phi[good], low=-np.pi, high=np.pi) #0.5*outprojRS['meanphi']
s_meanphi[i]=circstd(phi[good], low=0, high=np.pi/2.) #0.5*outprojRS['s_meanphi']
mrl[i]=outprojRS['r']
return {'csteps': Isteps, 'xi': xi, 's_xi': s_xi, 'Zx': Zx, 's_Zx': s_Zx, 'Zy': Zy, 's_Zy': s_Zy, 'meanphi': meanphi, 's_meanphi': s_meanphi, 'asteps': bin_centre, 'hros': hros, 's_hros': s_hros, 'mrl': mrl, 'Smap': Smap, 'Amap': phi}
# ==================================================================================================
def hro(Imap, Qmap, Umap, steps=10, hsize=15, minI=0., mask=0, ksz=1, w=None, convention='Planck', sigmaQQ=None, sigmaUU=None, mcflag=None, nruns=10, errorbar=None, segmap=None, debug=False):
#if (convention=='Planck'):
# Qmap0=Qmap
# Umap0=Umap
#else:
# Qmap0=Qmap
# Umap0=-1.*Umap
if np.logical_or(np.logical_and(sigmaQQ is None, sigmaUU is None), mcflag):
output0 = hroLITE(Imap, Qmap, Umap, steps=steps, hsize=hsize, minI=minI, mask=mask, ksz=ksz, w=w, convention=convention, segmap=segmap, debug=debug)
isteps=output0['csteps']
asteps=output0['asteps']
hros=output0['hros']
shros=output0['s_hros']
zeta=output0['xi'] #roms[0]
Zx =output0['Zx'] #roms[1]
Zy =output0['Zy']
mphi=output0['meanphi'] #roms[2]
s_zeta=output0['s_xi'] #sroms[0]
s_Zx =output0['s_Zx'] #sroms[1]
s_Zy =output0['s_Zy']
s_mphi=output0['s_meanphi'] #sroms[2]
Amap=output0['Amap']
else:
assert Qmap.shape == sigmaQQ.shape, "Dimensions of Qmap and sigmaQQ must match"
assert Umap.shape == sigmaUU.shape, "Dimensions of Umap and sigmaUU must match"
hrosvec=np.zeros([nruns,steps,hsize])
zetavecMC=np.zeros([nruns,steps])
ZxvecMC=np.zeros([nruns,steps])
ZyvecMC=np.zeros([nruns,steps])
mphivecMC=np.zeros([nruns,steps])
mrlMC=np.zeros([nruns,steps])
s_zetavecMC=np.zeros([nruns,steps])
s_ZxvecMC=np.zeros([nruns,steps])
s_ZyvecMC=np.zeros([nruns,steps])
s_mphivecMC=np.zeros([nruns,steps])
s_mrlMC=np.zeros([nruns,steps])
Acube=np.zeros([nruns,Qmap.shape[0],Qmap.shape[1]])
pbar = tqdm(total=nruns)
for i in range(0,nruns):
QmapR=np.random.normal(loc=Qmap, scale=sigmaQQ)
UmapR=np.random.normal(loc=Umap, scale=sigmaUU)
hrooutput= hroLITE(Imap, QmapR, UmapR, steps=steps, hsize=hsize, minI=minI, mask=mask, ksz=ksz, w=w, convention=convention, segmap=segmap, debug=False)
zetavecMC[i,:]=hrooutput['xi']
ZxvecMC[i,:] =hrooutput['Zx']
ZyvecMC[i,:] =hrooutput['Zy']
mphivecMC[i,:]=hrooutput['meanphi']
mrlMC[i,:]=hrooutput['mrl']
s_zetavecMC[i,:]=hrooutput['s_xi']
s_ZxvecMC[i,:] =hrooutput['s_Zx']
s_ZyvecMC[i,:] =hrooutput['s_Zy']
s_mphivecMC[i,:]=hrooutput['s_meanphi']
hrosvec[i,:,:]=hrooutput['hros']
Acube[i,:,:]=hrooutput['Amap']
pbar.update()
pbar.close()
zeta=zetavecMC.mean(axis=0)
Zx=ZxvecMC.mean(axis=0)
Zy=ZyvecMC.mean(axis=0)
meanphi=circstats.circmean(mphivecMC, axis=0)
mrl=mrlMC.mean(axis=0)
Amap=circstats.circmean(Acube, axis=0)
if (errorbar=='MC'):
s_zeta=s_zetavecMC.std(axis=0)
s_Zx=s_ZxvecMC.std(axis=0)
s_Zy=s_ZyvecMC.std(axis=0)
s_meanphi=circ.descriptive.mean(s_mphivecMC, axis=0)
else:
s_zeta=hrooutput['s_xi'] #np.max([s_zetavecMC.std(axis=0),hrooutput['s_xi']], axis=0)
s_Zx=hrooutput['s_Zx'] #np.max([s_prsvecMC.std(axis=0),hrooutput['s_prs']], axis=0)
s_Zy=hrooutput['s_Zy']
s_meanphi=hrooutput['s_meanphi'] #np.max([circ.descriptive.mean(s_mphivecMC, axis=0),hrooutput['s_meanphi']], axis=0)
s_mrl=mrlMC.std(axis=0)
csteps=hrooutput['csteps']
asteps=hrooutput['asteps']
Smap=hrooutput['Smap']
outhros=hrosvec.mean(axis=0)
s_outhros=hrosvec.std(axis=0)
return {'csteps': csteps, 'xi': zeta, 's_xi': s_zeta, 'Zx': Zx, 's_Zx': s_Zx, 'Zy': Zy, 's_Zy': s_Zy, 'meanphi': meanphi, 's_meanphi': s_meanphi, 'asteps': asteps, 'hros': outhros, 's_hros': s_outhros, 'mrl': mrl, 's_mrl': s_mrl, 'Smap': Smap, 'Amap': Amap}
# ===================================================================================================
def hroplts(csteps, roms, sroms, asteps, hros, s_hros, saveplots=False, prefix='', outh=None):
bin_centres= 0.5*(csteps[0:np.size(csteps)-1]+csteps[1:np.size(csteps)])
nhist=np.size(bin_centres)
if outh is None:
outh=[0, int(nhist/2.), nhist-1]
if outh=='all':
outh=np.arange(nhist)
color=iter(cm.rainbow(np.linspace(0, 1, np.size(outh))))
fig = plt.figure(figsize=(4.0, 4.0), dpi=150)
plt.rc('font', size=8)
for i in range(0, np.size(outh)):
c=next(color)
#labeltext="%.2f"%Isteps[outh[i]] + r' < $N_{\rm H}/$cm$^{-2}$ < ' + "%.2f"%Isteps[outh[i]+1]
labeltext=str(np.round(csteps[outh[i]],2)) + r' < $N_{\rm H}/$cm$^{-2}$ < ' + str(np.round(csteps[outh[i]+1],2))
plt.plot(asteps, hros[outh[i],:], '-', linewidth=2, c=c, label=labeltext) #drawstyle
plt.errorbar(asteps, hros[outh[i],:], yerr=s_hros[0], c=c)
plt.xlabel(r'$\phi$')
plt.ylabel('Histogram density')
plt.legend()
if (saveplots):
plt.savefig(prefix+'_HROs.png', bbox_inches='tight')
plt.close()
else:
plt.show()
# --------------------------------------------------------------
fig = plt.figure(figsize=(4.0, 2.5), dpi=150)
plt.rc('font', size=8)
#plt.xlim(csteps[0],csteps[np.size(csteps)-1])
#plt.plot(bin_centres, roms[0], linewidth=0.5, c='orange', marker='.')
plt.errorbar(bin_centres, roms[0], yerr=sroms[0], c='orange')
plt.axhline(y=0., c='k', ls='--')
plt.xlabel(r'log$_{10}$ ($N_{\rm H}/$cm$^{-2}$)')
plt.ylabel(r'$\zeta$')
if (saveplots):
plt.savefig(prefix+'_zeta.png', bbox_inches='tight')
plt.close()
else:
plt.show()
# --------------------------------------------------------------
fig = plt.figure(figsize=(4.0, 2.5), dpi=150)
plt.rc('font', size=8)
#plt.xlim(csteps[0],csteps[np.size(csteps)-1])
#plt.plot(bin_centres, roms[1], linewidth=0.5, c='cyan', marker='.')
plt.errorbar(bin_centres, roms[1], yerr=sroms[1], c='cyan')
plt.axhline(y=0., c='k', ls='--')
plt.xlabel(r'log$_{10}$ ($N_{\rm H}/$cm$^{-2}$)')
plt.ylabel(r'$V$')
if (saveplots):
plt.savefig(prefix+'_PRS.png', bbox_inches='tight')
plt.close()
else:
plt.show()
# --------------------------------------------------------------
fig = plt.figure(figsize=(4.0, 2.5), dpi=150)
plt.rc('font', size=8)
#plt.xlim(csteps[0],csteps[np.size(csteps)-1])
#plt.plot(bin_centres, (180./np.pi)*np.abs(roms[2]), linewidth=0.5, c='magenta', marker='.')
plt.errorbar(bin_centres, (180./np.pi)*np.abs(roms[2]), yerr=(180./np.pi)*sroms[2], c='magenta')
plt.axhline(y=0., c='k', ls='--')
plt.axhline(y=90., c='k', ls='--')
plt.xlabel(r'log$_{10}$ ($N_{\rm H}/$cm$^{-2}$)')
plt.ylabel(r'$\phi$')
if (saveplots):
plt.savefig(prefix+'_meanphi.png', bbox_inches='tight')
plt.close()
else:
plt.show()