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candid.py
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candid.py
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from __future__ import print_function
import numpy as np
from matplotlib import pyplot as plt
plt.ion() # interactive mode
_fitsLoaded=False
try:
from astropy.io import fits
_fitsLoaded=True
except:
try:
import pyfits as fits
_fitsLoaded=True
except:
pass
if not _fitsLoaded:
print('ERROR: astropy.io.fits or pyfits required!')
import time
import scipy.special
import scipy.interpolate
import scipy.stats
import scipy.optimize
try:
from scipy.misc import factorial
except:
from scipy.special import factorial
import random
# -- defunct ;(
#from scipy import weave
#from scipy.weave import converters
#from scipy.weave import blitz_tools
import multiprocessing
try:
# -- see https://stackoverflow.com/questions/64174552
multiprocessing.set_start_method('spawn')
except:
pass
import os
import sys
from astropy import wcs ### Alex
import matplotlib.ticker as mtick ### Alex
from matplotlib.ticker import MultipleLocator, FormatStrFormatter ### Alex
# import progressbar
import matplotlib.cm as cm
import pandas as pd ### Alex
#__version__ = '0.1 | 2014/11/25'
#__version__ = '0.2 | 2015/01/07' # big clean
#__version__ = '0.3 | 2015/01/14' # add Alex contrib and FLAG taken into account
#__version__ = '0.4 | 2015/01/30' # modified bandwidth smearing handling
#__version__ = '0.5 | 2015/02/01' # field of view, auto rmin/rmax, bootstrapping
#__version__ = '0.6 | 2015/02/10' # bug fix in smearing
#__version__ = '0.7 | 2015/02/17' # bug fix in T3 computation
#__version__ = '0.8 | 2015/02/19' # can load directories instead of single files, AMBER added, ploting V2, CP
#__version__ = '0.9 | 2015/02/25' # adding polynomial reduction (as function of wavelength) to V2 et CP
#__version__ = '0.10 | 2015/08/14' # adding LD coef and coding CP in iCP
#__version__ = '0.11 | 2015/09/03' # changing detection limits to 99% and Mag instead of %
#__version__ = '0.12 | 2015/09/17' # takes list of files; bestFit cannot be out rmin/rmax
#__version__ = '0.13 | 2015/09/30' # fixed some bugs in list on minima for
#__version__ = '0.14 | 2015/09/30' # fixed some BIG bugs in fixed diameter option
#__version__ = '0.15 | 2015/10/02' # np.nanmean instead of np.mean in _chi2func
#__version__ = '0.16 | 2015/10/22' # weave to accelerate the binary visibility!
#__version__ = '0.17 | 2015/10/24' # weave to accelerate the binary T3!
#__version__ = '0.18 | 2015/10/26' # change in injection with a simpler algorithm;
# change a bit in detectionLimit with injeciton,
# doing a UD fit now; auto smearing setting
#__version__ = '0.19 | 2015/12/26' # adding instrument selection
#__version__ = '0.20 | 2016/06/14' # adding numpy (default, slow)/weave selection, bug fixes
#__version__ = '0.21 | 2016/11/22' # some cleaning
#__version__ = '0.22 | 2017/02/23' # bug corrected in smearing computation
# __version__ = '0.22 | 2017/05/30' # adding new features, such as the choice of nsigma for the detection limit ### Alex
# __version__ = '0.22 | 2017/06/01' # adding new features, saving detection limit map in fits file ### Alex
# __version__ = '0.22 | 2017/06/26' # adding other features, print mean MJD and telescope array ### Alex
#__version__ = '0.23 | 2017/11/08' # minor bugs corrected in plots
#__version__ = '0.3.1 | 2018/02/04'# Cython acceleration
# __version__ = '0.3.1 | 2018/04/04' # Alex changes
#__version__ = '1.0 | 2018/11/08' # Converted to Python3
#__version__ = '1.0.1 | 2019/01/18'# implement curve_fit to include correlated errors
#__version__ = '1.0.2 | 2019/03/01' # many tweaks in the plots; x>0 fit only for only v2; implement history
#__version__ = '1.0.2.1 | 2021/06/16' # many new features added: saving the nsigma mam in a fits file, error ellise from the bootstrap are provided,
# possibility to plot more than 1 best detection, possibility to select a wavelength range (not in GUI yet)
#__version__ = '1.0.3 | 2020/10/27'# corrected over-estimation of smearing
#__version__ = '1.0.4 | 2021/03/02' # bug with bootstraping
# __version__ = '1.0.5 | 2021/04/26' # bug in nSigma! not bad in practice
# __version__ = '1.0.5.1 | 2021/12/02' # Adding |V| as an observable
#__version__ = '1.0.6 | 2022/01/21' # tweaking default step, rmin and rmax
#__version__ = '1.0.7 | 2022/08/16' # avoid reprint in multiprocessing
__version__ = '1.0.7.1 | 2022/12/01' # Possibility to fit a region not centered on 0
# -- some general parameters:
CONFIG = {'color map':'cubehelix_r', # color map used
'chi2 scale' : 'auto', # can be log
'long exec warning': 300, # in seconds
'suptitle':False, # display over head title
'progress bar': True,
'Ncores': None, # default is to use N-1 Cores
'Nsmear': 3,
}
# -- units of the parameters
def paramUnits(s):
if 'dwavel' in s:
return 'um'
else:
if s.startswith('f_') or s.startswith('fres_'):
return '% primary'
units = {'x':'mas', 'y':'mas', 'f':'% primary', 'diam*':'mas',
'diamc':'mas', 'alpha*': 'none', 'fres':'% primary',
'bs': 'none'}
if s in units:
return units[s]
else:
return ''
def variables():
print(' | global parameters (can be updated):')
for k in CONFIG.keys():
print(" CONFIG['%s']"%k, CONFIG[k])
return
if __name__=='__main__':
print("""
========================== This is CANDID ==============================
[C]ompanion [A]nalysis and [N]on-[D]etection in [I]nterferometric [D]ata
https://github.com/amerand/CANDID
========================================================================
""")
print(' version:', __version__)
variables()
__warningDwavel = True
# -- some general functions:
def _Vud(base, diam, wavel):
"""
Complex visibility of a uniform disk for parameters:
- base in m
- diam in mas
- wavel in um
"""
x = 0.01523087098933543*diam*base/wavel
x += 1e-6*(x==0)
return 2*scipy.special.j1(x)/(x)
def _Vld(base, diam, wavel, alpha=0.36):
nu = alpha /2. + 1.
diam *= np.pi/(180*3600.*1000)
x = -1.*(np.pi*diam*base/wavel/1.e-6)**2/4.
V_ = 0
for k_ in range(50):
V_ += scipy.special.gamma(nu + 1.)/\
scipy.special.gamma(nu + 1.+k_)/\
scipy.special.gamma(k_ + 1.) *x**k_
return V_
def _VbinSlow(uv, param):
"""
Analytical complex visibility of a binary composed of a uniform
disk diameter and an unresolved source. "param" is a dictionnary
containing:
'diam*' : in mas
'alpha*' : optional LD coef for main star
'wavel' : in um
'x, y' : in mas
'f' : flux ratio in % -> takes the absolute value
'f_wl_dwl': addition flux ratio in the line at wl, width dwl
'fres' : resolved flux
'fres_wl_dwl': addition resolved flux ratio in the line at wl, width dwl
'xg', yg', 'diamg', 'fg': gaussian position, diameters and flux
"""
if 'f' in param.keys():
f = np.abs(param['f'])/100.
else:
f = 0.
for f_ in param.keys():
if f_.startswith('f_'):
wl = float(f_.split('_')[1])
dwl = float(f_.split('_')[2])
f += param[f_]*np.exp(-4*np.log(2)*(param['wavel']-wl)**2/dwl**2)/100.
if 'fres' in param.keys():
fres = param['fres']/100.0
else:
fres = 0
for f_ in param.keys():
if f_.startswith('fres_'):
wl = float(f_.split('_')[1])
dwl = float(f_.split('_')[2])
fres += param[f_]*np.exp(-4*np.log(2)*(param['wavel']-wl)**2/dwl**2)/100.
if 'fg' in param.keys():
fg = param['fg']/100.0
else:
fg = 0.
for f_ in param.keys():
if f_.startswith('fg_'):
wl = float(f_.split('_')[1])
dwl = float(f_.split('_')[2])
fg += param[f_]*np.exp(-4*np.log(2)*(param['wavel']-wl)**2/dwl**2)/100.
c = np.pi/180/3600000.*1e6
B = np.sqrt(uv[0]**2+uv[1]**2)
if 'alpha*' in param.keys() and param['alpha*']>0.0:
Vstar = _Vld(B, param['diam*'], param['wavel'], alpha=param['alpha*'])
else:
Vstar = _Vud(B, param['diam*'], param['wavel'])
if 'diamc' in param.keys():
Vcomp = _Vud(B, param['diamc'], param['wavel'])
else:
Vcomp = 1.0 + 0j # -- assumes it is unresolved.
if 'diamg' in param.keys():
Vg = np.exp(-(np.pi*c*param['diamg']*B/param['wavel'])**2/(4*np.log(2)))
if 'xg' in param.keys():
phig = 2*np.pi*c*(uv[0]*param['xg']+uv[1]*param['yg'])
phig = 0.0
else:
phig = 0.0
else:
Vg = 0.0
fg = 0.0
phig = 0.0
#dl = np.linspace(-0.5,0.5, CONFIG['Nsmear'])
if CONFIG['Nsmear']<2:
dl = np.array([0.])
Tr = np.array([1.0])
elif CONFIG['Nsmear']==3:
# -- original implementation, with top-hat transmission (slow and a little innacurate)
dl = np.linspace(-0.5, 0.5, CONFIG['Nsmear'])
Tr = np.ones(CONFIG['Nsmear'])
else: # -- gaussian
tsigma = 1/2.355 # FWHM of 1
#tsigma /= 0.57282 # FWH Maximum -> FWH Flux,
# -- takes most of the Gaussian transmission
dl = np.linspace(-0.8, 0.8, CONFIG['Nsmear'])
Tr = np.exp(-dl**2/(2*tsigma**2))
Tr /= np.sum(Tr)
if np.isscalar(param['wavel'] ):
wl = param['wavel']+dl*param['dwavel']
phi = 2*np.pi*c*(uv[0][:,None]*param['x']+uv[1][:,None]*param['y'])/wl[None,:]
tmp = f*Vcomp[:,None]*np.exp(-1j*phi)
if np.isscalar(phig):
phig = phig/wl[None,:] +0.*uv[0][:,None]
tmp += fg*Vg*np.exp(-1j*phig)
else:
phig = phig[:,None]/wl[None,:]
tmp += fg*Vg[:,None]*np.exp(-1j*phig)
tmp *= Tr[None,:]
# -- compute smearing
res = (Vstar + tmp.sum(axis=1))/(1.0 + f + fres + fg)
else:
# -- assumes u, v, and wavel are 2D
wl = param['wavel'][:,:,None] + dl[None,None,:]*param['dwavel']
phi = 2*np.pi*c*(uv[0][:,:,None]*param['x']+uv[1][:,:,None]*param['y'])/wl
if not np.isscalar(Vcomp):
Vcomp = Vcomp[:,:,None]
tmp = f*Vcomp*np.exp(-1j*phi)
if not np.isscalar(phig):
phig = phig[:,:,None]/wl
if not np.isscalar(fg):
fg = fg[:,:,None]/(1+0*wl)
if not np.isscalar(Vg):
Vg = Vg[:,:,None]/(1+0*wl)
tmp += fg*Vg*np.exp(-1j*phig)
tmp *= Tr[None,None,:]
# -- mean to compute smearing
res = (Vstar + tmp.sum(axis=2))/(1.0 + f + fres + fg)
return res
try:
# -- Using Cython visibility function
import cyvis_
def _VbinCy(uv, p):
N = np.size(uv[0])
if not 'diam*' in p.keys():
diam = 0.0
else:
diam = p['diam*']*1.0 # copy
if not 'diamc' in p.keys():
diamc = 0.0
else:
diamc = p['diamc']*1.0 # copy
if not 'fres' in p.keys():
fres = 0.0
else:
fres = p['fres']*1.0 # copy
if isinstance(p['wavel'], float):
wavel = np.ones(N)*p['wavel']
else:
wavel = p['wavel'].flatten()
if not 'dwavel' in p.keys():
dwavel = 0.0
else:
dwavel = p['dwavel']*1.0 # copy
if isinstance(dwavel, float):
dwavel = np.ones(N)*p['dwavel']
else:
dwavel = p['wavel'].flatten()
Vr = np.ones(np.size(uv[0]), dtype=np.double)
Vi = np.zeros(np.size(uv[0]), dtype=np.double)
cyvis.cyVbin(len(Vr), Vr, Vi, uv[0].flatten(), uv[1].flatten(),
wavel, dwavel, CONFIG['Nsmear'],
p['x'], p['y'], min(p['f'], 105), fres, ### Alex
diam, diamc)
return np.reshape(Vr+1j*Vi, uv[0].shape)
_Vbin = _VbinCy
if __name__=='__main__':
print('Using Cython visibilities computation (Faster than Numpy)') ### Alex
except:
# -- Using Numpy visibility function
_Vbin = _VbinSlow
if __name__=='__main__':
print('Using Numpy visibilities computation (Slower than Cython)')
def _V2binSlow(uv, param):
"""
uv = (u,v) where u,v a are ndarray
param MUST contain:
- diam*, x, y: in mas
- f: in %
- wavel: in um
optional:
- diamc: in mas
- dwavel: in um
- fres: fully resolved flux, in fraction of primary flux
"""
if 'f' in param.keys():
param['f'] = min(np.abs(param['f']),105) ### Alex
return np.abs(_Vbin(uv, param))**2
def _T3binSlow(uv, param):
"""
uv = (u1,v1, u2, v2) where u1,v1, u2,v2 a are ndarray
param MUST contain:
- diam*, x, y: in mas
- f: in %
- wavel: in um
optional:
- diamc: in mas
- dwavel: in um
- fres: unresolved flux, in fraction of primary flux
"""
if 'f' in param.keys():
param['f'] = min(np.abs(param['f']),105) ### Alex
return _Vbin((uv[0], uv[1]), param)*\
_Vbin((uv[2], uv[3]), param)*\
np.conj(_Vbin((uv[0]+uv[2], uv[1]+uv[3]), param))
def _approxVUD(x='x', maxM=8):
"""
bases on polynomial approx of Bessel's J1
"""
n = 1
cm = lambda m: 2**(n+2*m-1)*factorial(m)*factorial(n+m)
return ['%s%s/%.1f'%(' -' if (-1)**m < 0 else ' +',
'*'.join(x*(n+2*m-1)) if (n+2*m-1)>0 else '1',
cm(m)) for m in range(maxM+1)]
# -- set the approximation for UD visibility
_VUDX = ''.join(_approxVUD('X', maxM=7)).strip()
_VUDX =_VUDX[3:]
#print(_VUDX)
_VUDXeval = eval('lambda X:'+_VUDX)
if False: # -- check approximation
print(_VUDX)
plt.close('all')
plt.subplot(211)
x = np.linspace(1e-6, 7, 500)
plt.plot(x, 2*scipy.special.j1(x)/x, '-r', label='Bessel')
plt.plot(x, _VUDXeval(x), '-b', label='approximation')
plt.plot(x, 0*x, linestyle='dashed')
plt.ylim(-0.3,1)
plt.ylabel('visibility')
plt.subplot(212)
plt.plot(x, 100*(2*scipy.special.j1(x)/x-_VUDXeval(x))/(
scipy.special.j1(x)/x+_VUDXeval(x)/2.), '-k')
plt.ylabel('rel. err. %')
plt.xlabel(r'$\pi$ B $\theta$ / $\lambda$')
plt.ylim(-1,1)
plt.legend()
def _V2binFast(uv, param):
"""
using weave
uv = (u,v) where u,v a are ndarray
param MUST contain:
- diam*, x, y: in mas
- f: in %
- wavel: in um
optional:
- diamc: in mas
- dwavel: in um
- fres: fully resolved flux, in fraction of primary flux
"""
u, v = uv
B = np.sqrt(u**2+v**2)
s = u.shape
u, v = u.flatten(), v.flatten()
NU = len(u)
vr, vi, v2 = np.zeros(NU), np.zeros(NU), np.zeros(NU)
diam = np.abs(float(param['diam*']))
wavel = param['wavel']
if isinstance(wavel, np.ndarray):
wavel = wavel.flatten()
else:
wavel = np.ones(NU)*wavel
if 'x' in param.keys():
x = param['x']*1.0
else:
x = 0.0
if 'y' in param.keys():
y = param['y']*1.0
else:
y = 0.0
if 'f' in param.keys():
f = np.abs(param['f'])*1.0
else:
f = 0.0
if 'diamc' in param.keys():
diamc = np.abs(param['diamc'])*1.0
else:
diamc = 0.0
if 'dwavel' in param.keys():
dwavel = param['dwavel']*1.0
else:
dwavel = 0.0
if __warningDwavel and dwavel==0:
print(' >>> WARNING: no spectral bandwidth provided!')
if 'fres' in param.keys():
fres = param['fres']*1.0
else:
fres = 0.0
Nsmear = CONFIG['Nsmear']
print('#'*12, f, diam, '#'*12)
code = u"""
int i, j;
float vis, X, pi, phi, visc, wl, t_vr, t_vi, c;
pi = 3.1415926535;
c = 0.004848136;
f /= 100.0; /* flux ratio given in % */
if (f>1){
f = 1.0;
}
fres /= 100.0; /* flux ratio given in % */
phi = 0.0;
/* -- companion visibility, default is unresoved (V=1) */
visc = 1.0;
vis = 1.0;
for (i=0; i<NU; i++){
/* -- primary star of V_UD */
phi = -2*pi*c*(u[i]*x + v[i]*y);
if (Nsmear<2){
if (diam>0){
X = pi*c*B[i]*diam/wavel[i];
vis = VUDX;
}
if (diamc>0) {
X = pi*c*B[i]*diamc/wavel[i];
visc = VUDX;
}
vr[i] = vis/(1.0+f+fres) + f * visc * cos( phi/wavel[i] ) / (1.0 + f + fres);
vi[i] = f * visc * sin( phi/wavel[i] ) / (1.0 + f + fres);
v2[i] = vr[i]*vr[i] + vi[i]*vi[i];
} else {
for (j=0;j<Nsmear;j++) {
wl = wavel[i]+(-0.5 + j/(Nsmear-1.0))*dwavel;
if (diam>0){
X = pi*c*B[i]*diam/wl;
vis = VUDX;
}
if (diamc>0) {
X = pi*c*B[i]*diamc/wl;
visc = VUDX;
}
t_vr = (vis + f * visc * cos(phi/wl) ) / (1.0 + f + fres);
t_vi = (0.0 + f * visc * sin(phi/wl) ) / (1.0 + f + fres);
vr[i] += t_vr / Nsmear;
vi[i] += t_vi / Nsmear;
v2[i] += (t_vr*t_vr + t_vi*t_vi) / Nsmear;
}
}
}""".replace('VUDX', _VUDX)
err = weave.inline(code, ['u','v','NU','diam','x','y','f','diamc','B',
'wavel','dwavel','vr','vi', 'v2', 'Nsmear','fres'],
compiler = 'gcc', verbose=0, #extra_compile_args=['-O3'],
type_converters = converters.blitz,
#headers=['<algorithm>', '<limits>']
)
v2 = v2.reshape(s)
return v2
def _T3binFast(uv, param):
"""
using weave
uv = (u1,v1, u2, v2) where u1,v1, u2,v2 a are ndarray
param MUST contain:
- diam*, x, y: in mas
- f: in %
- wavel: in um
optional:
- diamc: in mas
- dwavel: in um
- fres: unresolved flux, in fraction of primary flux
"""
u1, v1, u2, v2 = uv
s = u1.shape
u1, v1 = u1.flatten(), v1.flatten()
u2, v2 = u2.flatten(), v2.flatten()
NU = len(u1)
t3r, t3i = np.zeros(NU), np.zeros(NU)
diam = np.abs(float(param['diam*']))
wavel = param['wavel']
if isinstance(wavel, np.ndarray):
wavel = wavel.flatten()
else:
wavel = np.ones(NU)*wavel
if 'x' in param.keys():
x = float(param['x'])
else:
x = 0.0
if 'y' in param.keys():
y = float(param['y'])
else:
y = 0.0
if 'f' in param.keys():
f = float(np.abs(param['f']))
#f = min(f, 1.0)
else:
f = 0.0
if 'diamc' in param.keys():
diamc = np.abs(float(param['diamc']))
else:
diamc = 0.0
if 'dwavel' in param.keys():
dwavel = float(param['dwavel'])
else:
dwavel = 0.0
if __warningDwavel and dwavel==0:
print(' >>> WARNING: no spectral bandwidth provided!')
if 'fres' in param.keys():
fres = float(param['fres'])
else:
fres = 0.0
Nsmear = CONFIG['Nsmear']
code = u"""int i, j;
/* -- first baseline */
double B1, vis1, phi1, visc1, vr1, vi1;
/* -- second baseline */
double B2, vis2, phi2, visc2, vr2, vi2;
/* -- third baseline */
double u12, v12;
double B12, vis12, phi12, visc12, vr12, vi12;
double X, pi, wl, c;
pi = 3.1415926535;
c = 0.004848136;
f /= 100.; /* flux ratio given in % */
if (f>1) {f = 1.0;}
fres /= 100.; /* flux ratio given in % */
phi1 = 0.0;
phi2 = 0.0;
phi12 = 0.0;
vis1 = 1.0;
vis2 = 1.0;
vis12 = 1.0;
/* -- companion visibility, default is unresoved (V=1) */
visc1 = 1.0;
visc2 = 1.0;
visc12 = 1.0;
for (i=0; i<NU; i++){
/* -- baselines for each u,v coordinates */
B1 = sqrt(u1[i]*u1[i] + v1[i]*v1[i]);
B2 = sqrt(u2[i]*u2[i] + v2[i]*v2[i]);
u12 = u1[i] + u2[i];
v12 = v1[i] + v2[i];
B12 = sqrt(u12*u12 + v12*v12);
phi1 = -2*pi*0.004848136*(u1[i] * x + v1[i] * y);
phi2 = -2*pi*0.004848136*(u2[i] * x + v2[i] * y);
phi12 = -2*pi*0.004848136*( u12 * x + v12 * y);
if (Nsmear<2) { /* -- monochromatic */
if (diam>0) {
/* -- approximation of V_UD */
X = pi*c*B1*diam/wavel[i];
vis1 = VUDX;
X = pi*c*B2*diam/wavel[i];
vis2 = VUDX;
X = pi*c*B12*diam/wavel[i];
vis12 = VUDX;
}
if (diamc>0) {
/* -- approximation of V_UD */
X = pi*c*B1*diamc/wavel[i];
visc1 = VUDX;
X = pi*c*B2*diamc/wavel[i];
visc2 = VUDX;
X = pi*c*B12*diamc/wavel[i];
visc12 = VUDX;
}
/* -- binary visibilities: */
vr1 = (vis1 + f*cos(phi1/wavel[i])) / (1.0 + f + fres);
vi1 = f*sin(phi1/wavel[i]) / (1.0 + f + fres);
vr2 = (vis2 + f*cos(phi2/wavel[i])) / (1.0 + f + fres);
vi2 = f*sin(phi2/wavel[i]) / (1.0 + f + fres);
vr12 = (vis12 + f*cos(phi12/wavel[i])) / (1.0 + f + fres);
vi12 = f*sin(phi12/wavel[i]) / (1.0 + f + fres);
/* -- T3 = V1 * V2 * conj(V12) */
t3r[i] = vr1*(vr2*vr12 + vi2*vi12);
t3r[i] += vi1*(vr2*vi12 - vi2*vr12);
t3i[i] = vr1*(vi2*vr12 - vr2*vi12);
t3i[i] += vi1*(vr2*vr12 + vi2*vi12);
} else { /* -- smeared */
vr1 = 0.0;
vi1 = 0.0;
vr2 = 0.0;
vi2 = 0.0;
vr12 = 0.0;
vi12 = 0.0;
for (j=0; j<Nsmear; j++) {
/* -- wavelength in bin: */
wl = wavel[i] + (-0.5 + j/(Nsmear-1.0)) * dwavel;
if (diam>0) {
/* -- approximation of V_UD */
X = pi*c*B1*diam/wl;
vis1 = VUDX;
X = pi*c*B2*diam/wl;
vis2 = VUDX;
X = pi*c*B12*diam/wl;
vis12 = VUDX;
}
if (diamc>0) {
/* -- approximation of V_UD */
X = pi*c*B1*diamc/wl;
visc1 = VUDX;
X = pi*c*B2*diamc/wl;
visc2 = VUDX;
X = pi*c*B12*diamc/wl;
visc12 = VUDX;
}
/* == smear in T3 ======================= */
/* -- binary visibilities: */
vr1 = (vis1 + f*cos(phi1/wl)) / (1.0 + f + fres);
vi1 = f*sin(phi1/wl) / (1.0 + f + fres);
vr2 = (vis2 + f*cos(phi2/wl)) / (1.0 + f + fres);
vi2 = f*sin(phi2/wl) / (1.0 + f + fres);
vr12 = (vis12 + f*cos(phi12/wl)) / (1.0 + f + fres);
vi12 = f*sin(phi12/wl) / (1.0 + f + fres);
/* -- T3 = V1 * V2 * conj(V12) */
t3r[i] += vr1*(vr2*vr12 + vi2*vi12)/Nsmear;
t3r[i] += vi1*(vr2*vi12 - vi2*vr12)/Nsmear;
t3i[i] += vr1*(vi2*vr12 - vr2*vi12)/Nsmear;
t3i[i] += vi1*(vr2*vr12 + vi2*vi12)/Nsmear;
}
}
}""".replace('VUDX', _VUDX)
err = weave.inline(code, ['u1','v1','u2','v2','NU','diam','x','y', 'fres',
'f','diamc','wavel','dwavel','t3r','t3i','Nsmear'],
#type_factories = blitz_type_factories,
compiler = 'gcc', verbose=0)
res = t3r + 1j*t3i
res = res.reshape(s)
return res
def _NsmearForCPaccuracy(errCP, B, sep, wavel, dwavel, f):
"""
- errCP in degrees
- B in meters
- sep in mas
- wavel, dwavel in um
- f in percent
"""
R = wavel/dwavel
mod = (B/100.*sep/10./wavel)**2/(R/20.)**2*f/2.
return min(np.ceil((mod/errCP)**(2/3.)), 2)
_N_modelObservables = 0
def _modelObservables(obs, param, flattened=True):
"""
model observables contained in "obs".
param -> see _Vbin
--> will force the contrast ratio to be positive!
Observations are entered as:
obs = [('|v|;ins', u, v, wavel, ...),
('v2;ins', u, v, wavel, ...),
('cp;ins', u1, v1, u2, v2, wavel, ...),
('t3;ins', u1, v1, u2, v2, wavel, ...)]
each tuple can be longer, the '...' part will be ignored
units: u,v in m; wavel in um
width of the wavelength channels in param:
- a global "dwavel" is defined, the width of the pixels
- "dwavel;ins" average value per intrument
for CP and T3, the third u,v coordinate is computed as u1+u2, v1+v2
"""
global CONFIG, _N_modelObservables
#c = np.pi/180/3600000.*1e6
res = [0.0 for o in obs]
# -- copy parameters:
tmp = {k:param[k] for k in param.keys()}
tmp['f'] = np.abs(tmp['f'])
for i, o in enumerate(obs):
if 'dwavel' in param.keys():
dwavel = param['dwavel']
elif 'dwavel;'+o[0].split(';')[1] in param.keys():
dwavel = param['dwavel;'+o[0].split(';')[1]]
else:
dwavel = 0.0
# -- remove dwavel(s)
tmp = {k:tmp[k] for k in param.keys() if not k.startswith('dwavel')}
if o[0].split(';')[0]=='v2':
tmp['wavel'] = o[3]
tmp['dwavel'] = dwavel
res[i] = _V2binSlow([o[1], o[2]], tmp)
elif o[0].split(';')[0]=='|v|':
tmp['wavel'] = o[3]
tmp['dwavel'] = dwavel
res[i] = np.abs(_VbinSlow([o[1], o[2]], tmp))
elif o[0].split(';')[0].startswith('v2_'): # polynomial fit
p = int(o[0].split(';')[0].split('_')[1])
n = int(o[0].split(';')[0].split('_')[2])
# -- wl range based on min, mean, max
_wl = np.linspace(o[-4][0], o[-4][2], 2*n+2)
_v2 = []
for _l in _wl:
tmp['wavel']=_l
_v2.append(_V2binFast([o[1], o[2]], tmp))
_v2 = np.array(_v2)
res[i] = np.array([np.polyfit(_wl-o[-4][1], _v2[:,j], n)[n-p]
for j in range(_v2.shape[1])])
elif o[0].split(';')[0]=='cp' or o[0].split(';')[0]=='t3' or\
o[0].split(';')[0]=='icp' or o[0].split(';')[0]=='scp' or\
o[0].split(';')[0]=='ccp':
tmp['wavel'] = o[5]
tmp['dwavel'] = dwavel
t3 = _T3binSlow((o[1], o[2], o[3], o[4]), tmp)
if o[0].split(';')[0]=='cp':
res[i] = np.angle(t3)
elif o[0].split(';')[0]=='scp':
res[i] = np.sin(np.angle(t3))
elif o[0].split(';')[0]=='ccp':
res[i] = np.cos(np.angle(t3))
elif o[0].split(';')[0]=='icp':
# -- icp is complex t3 normalized, i.e exp(i*CP)
res[i] = t3/np.absolute(t3)
elif o[0].split(';')[0]=='t3':
res[i] = np.absolute(t3)
elif o[0].split(';')[0].startswith('cp_'): # polynomial fit
p = int(o[0].split(';')[0].split('_')[1])
n = int(o[0].split(';')[0].split('_')[2])
# -- wl range based on min, mean, max
_wl = np.linspace(o[-4][0], o[-4][2], 2*n+2)
# -- remove pix width
tmp.pop('dwavel')
_cp = []
for _l in _wl:
tmp['wavel']=_l
_cp.append(np.angle(_T3binFast((o[1], o[2], o[3], o[4]), tmp)))
_cp = np.array(_cp)
res[i] = np.array([np.polyfit(_wl-o[-4][1], _cp[:,j], n)[n-p] for j in range(_cp.shape[1])])
else:
print('ERROR: unreckognized observable:', o[0])
if not flattened:
return res
res2 = np.array([])
for r in res:
res2 = np.append(res2, r.flatten())
_N_modelObservables += 1
return res2
def _nSigmas(chi2r_TEST, chi2r_TRUE, NDOF):
"""
- chi2r_TEST is the hypothesis we test
- chi2r_TRUE is what we think is what described best the data
- NDOF: numer of degres of freedom
chi2r_TRUE <= chi2r_TEST
returns the nSigma detection
"""
q = scipy.stats.chi2.cdf(NDOF*chi2r_TEST/chi2r_TRUE, NDOF)
p = 1.0-q
nsigma = np.sqrt(scipy.stats.chi2.ppf(1-p, 1))
if isinstance(nsigma, np.ndarray):
nsigma[p<1e-15] = np.sqrt(scipy.stats.chi2.ppf(1-1e-15, 1))
elif p<1e-15:
nsigma = np.sqrt(scipy.stats.chi2.ppf(1-1e-15, 1))
return nsigma
def _injectCompanionData(data, delta, param):
"""
Inject analytically a companion defined as 'param' in the 'data' using
'delta'. 'delta' contains the corresponding V2 for T3 and CP first order
calculations.
data and delta have same length
"""
global CONFIG
bi = _modelObservables(data, param, flattened=False)
ud = param.copy(); ud['f'] = 0.0
ud = _modelObservables(data, ud, flattened=False)
for i,d in enumerate(data):
d[-2] += np.sign(param['f'])*(bi[i]-ud[i])
return data
return res
def _generateFitData(chi2Data, observables, instruments):
"""
filter only the meaningful observables
returns:
- measurements, flattened
- errors, flattened
- uv = B flattened if V2
uv = max baseline flattened if CP or T3
- type, flattened
- wl, flattened
"""
_meas, _errs, _wl, _uv, _type = np.array([]), np.array([]), np.array([]), [], []
for c in chi2Data:
if c[0].split(';')[0] in observables and \
c[0].split(';')[1] in instruments:
_type.extend([c[0]]*len(c[-2].flatten()))
_meas = np.append(_meas, c[-2].flatten())
_errs = np.append(_errs, c[-1].flatten())
_wl = np.append(_wl, c[-4].flatten())
if c[0].split(';')[0] == 'v2':
_uv = np.append(_uv, np.sqrt(c[1].flatten()**2+c[2].flatten()**2)/c[3].flatten())
elif c[0].split(';')[0] == '|v|':
_uv = np.append(_uv, np.sqrt(c[1].flatten()**2+c[2].flatten()**2)/c[3].flatten())
elif c[0].split(';')[0].startswith('v2_'):
_uv = np.append(_uv, np.sqrt(c[1].flatten()**2+c[2].flatten()**2)/c[3][1])
elif c[0].split(';')[0] == 't3' or c[0].split(';')[0] == 'cp' or\
c[0].split(';')[0] == 'icp' or c[0].split(';')[0] == 'scp' or c[0].split(';')[0] == 'ccp':
tmp = np.maximum(np.sqrt(c[1].flatten()**2+c[2].flatten()**2)/c[5].flatten(),
np.sqrt(c[3].flatten()**2+c[4].flatten()**2)/c[5].flatten())
tmp = np.maximum(tmp, np.sqrt((c[1]+c[3]).flatten()**2+(c[2]+c[4]).flatten()**2)/c[5].flatten() )
_uv = np.append(_uv, tmp)
_errs += _errs==0. # remove bad point in a dirty way
return _meas, _errs, _uv, np.array(_type), _wl
_N_fitFunc = 0
def _fitFunc(param, chi2Data, observables, instruments, fitAlso=[], doNotFit=[]):
"""
fit the data in "chi2data" (only "observables") using starting parameters
returns a dpfit dictionnary
"""
global _N_fitFunc
# -- extract meaningfull data
_meas, _errs, _uv, _types, _wl = _generateFitData(chi2Data, observables,
instruments)
# -- guess what needs to be fitted
fitOnly=[]
if param['f']!=0:
fitOnly.extend(['x', 'y', 'f'])
if 'v2' in observables or 'v' in observables or 't3' in observables:
for k in ['diam*', 'diamc', 'fres']:
if k in param.keys():
fitOnly.append(k)
if not fitAlso is None:
fitOnly.extend(fitAlso)
fitOnly = list(set(fitOnly))
for f in doNotFit:
if f in fitOnly:
fitOnly.remove(f)
# -- does the actual fit
res = _dpfit_leastsqFit(_modelObservables,
list(filter(lambda c: c[0].split(';')[0] in observables and
c[0].split(';')[1] in instruments,
chi2Data)),
param, _meas, _errs, fitOnly = fitOnly)
# -- _k used in some callbacks
if '_k' in param.keys():
res['_k'] = param['_k']
# -- diam* and f can only be positive
if 'diam*' in res['best'].keys():
res['best']['diam*'] = np.abs(res['best']['diam*'])
if 'f' in res['best'].keys():
res['best']['f'] = np.abs(res['best']['f'])
_N_fitFunc += 1
return res
def _chi2Func(param, chi2Data, observables, instruments):
"""
Returns the chi2r comparing model of parameters "param" and data "chi2Data", only
considering "observables" (such as v2, cp, t3)
"""
_meas, _errs, _uv, _types, _wl = _generateFitData(chi2Data, observables, instruments)
res = (_meas-_modelObservables(list(filter(lambda c: c[0].split(';')[0] in observables and
c[0].split(';')[1] in instruments, chi2Data)), param))
res = np.nan_to_num(res) # FLAG == TRUE are nans in the data
res[np.iscomplex(res)] = np.abs(res[np.iscomplex(res)])
res = np.abs(res)**2/_errs**2
res = np.nanmean(res)
if '_i' in param.keys() and '_j' in param.keys():
return param['_i'], param['_j'], res
else:
#print('test:', res)
return res
def _detectLimit(param, chi2Data, observables, instruments, delta=None, method='Gallenne', n_Sigma=3): ### Alex