import numpy as np
from astropy import constants as const
from breads.utils import get_spline_model, pixgauss2d
from breads.utils import get_spline_model
[docs]
def hc_splinefm(nonlin_paras, cubeobj, planet_f=None, transmission=None, star_spectrum=None,boxw=1, psfw=1.2,nodes=20,
badpixfraction=0.75,loc=None,fix_parameters=None):
"""
For high-contrast companions (planet + speckles).
Generate forward model fitting the continuum with a spline. No high pass filter or continuum normalization here.
The spline are defined with a linear model. Each spaxel (if applicable) is independently modeled which means the
number of linear parameters increases as N_nodes*boxw^2+1.
Args:
nonlin_paras: Non-linear parameters of the model, which are the radial velocity and the position (if loc is not
defined) of the planet in the FOV.
[rv,y,x] for 3d cubes (e.g. OSIRIS)
[rv,y] for 2d (e.g. KPIC, y being fiber)
[rv] for 1d spectra
cubeobj: Data object.
Must inherit breads.instruments.instrument.Instrument.
planet_f: Planet atmospheric model spectrum as an interp1d object. Wavelength in microns.
transmission: Transmission spectrum (tellurics and instrumental).
np.ndarray of size the number of wavelength bins.
star_spectrum: Stellar spectrum to be continuum renormalized to fit the speckle noise at each location. It is
(for now) assumed to be the same everywhere which is not compatible with a field dependent wavelength solution.
np.ndarray of size the number of wavelength bins.
boxw: size of the stamp to be extracted and modeled around the (x,y) location of the planet.
Must be odd. Default is 1.
psfw: Width (sigma) of the 2d gaussian used to model the planet PSF. This won't matter if boxw=1 however.
nodes: If int, number of nodes equally distributed. If list, custom locations of nodes [x1,x2,..].
To model discontinous functions, use a list of list [[x1,...],[xn,...]].
badpixfraction: Max fraction of bad pixels in data.
loc: Deprecated, Use fix_parameters.
(x,y) position of the planet for spectral cubes, or fiber position (y position) for 2d data.
When loc is not None, the x,y non-linear parameters should not be given.
fix_parameters: List. Use to fix the value of some non-linear parameters. The values equal to None are being
fitted for, other elements will be fixed to the value specified.
Returns:
d: Data as a 1d vector with bad pixels removed (no nans)
M: Linear model as a matrix of shape (Nd,Np) with bad pixels removed (no nans). Nd is the size of the data
vector and Np = N_nodes*boxw^2+1 is the number of linear parameters.
s: Noise vector (standard deviation) as a 1d vector matching d.
"""
if transmission is None:
transmission = np.ones(cubeobj.data.shape[0])
# import matplotlib.pyplot as plt
# plt.plot(star_spectrum)
# plt.show()
if fix_parameters is not None:
_nonlin_paras = np.array(fix_parameters)
_nonlin_paras[np.where(np.array(fix_parameters)==None)] = nonlin_paras
else:
_nonlin_paras = nonlin_paras
# Handle the different data dimensions
# Convert everything to 3D cubes (wv,y,x) for the followying
if len(cubeobj.data.shape)==1:
data = cubeobj.data[:,None,None]
noise = cubeobj.noise[:,None,None]
bad_pixels = cubeobj.bad_pixels[:,None,None]
elif len(cubeobj.data.shape)==2:
data = cubeobj.data[:,:,None]
noise = cubeobj.noise[:,:,None]
bad_pixels = cubeobj.bad_pixels[:,:,None]
elif len(cubeobj.data.shape)==3:
data = cubeobj.data
noise = cubeobj.noise
bad_pixels = cubeobj.bad_pixels
if cubeobj.refpos is None:
refpos = [0,0]
else:
refpos = cubeobj.refpos
rv = _nonlin_paras[0]
# Defining the position of companion
# If loc is not defined, then the x,y position is assume to be a non linear parameter.
if np.size(loc) ==2:
x,y = loc
elif np.size(loc) ==1 and loc is not None:
x,y = 0,loc
elif loc is None:
if len(cubeobj.data.shape)==1:
x,y = 0,0
elif len(cubeobj.data.shape)==2:
x,y = 0,_nonlin_paras[1]
elif len(cubeobj.data.shape)==3:
x,y = _nonlin_paras[2],_nonlin_paras[1]
nz, ny, nx = data.shape
if len(cubeobj.wavelengths.shape)==1:
wvs = cubeobj.wavelengths[:,None,None]
elif len(cubeobj.wavelengths.shape)==2:
wvs = cubeobj.wavelengths[:,:,None]
elif len(cubeobj.wavelengths.shape)==3:
wvs = cubeobj.wavelengths
_, nywv, nxwv = wvs.shape
if boxw % 2 == 0:
raise ValueError("boxw, the width of stamp around the planet, must be odd in splinefm().")
if boxw > ny or boxw > nx:
raise ValueError("boxw cannot be bigger than the data in splinefm().")
# remove pixels that are bad in the transmission or the star spectrum
bad_pixels[np.where(np.isnan(star_spectrum*transmission))[0],:,:] = np.nan
# Extract stamp data cube cropping at the edges
w = int((boxw - 1) // 2)
_paddata =np.pad(data,[(0,0),(w,w),(w,w)],mode="constant",constant_values = np.nan)
_padnoise =np.pad(noise,[(0,0),(w,w),(w,w)],mode="constant",constant_values = np.nan)
_padbad_pixels =np.pad(bad_pixels,[(0,0),(w,w),(w,w)],mode="constant",constant_values = np.nan)
k, l = int(np.round(refpos[1] + y)), int(np.round(refpos[0] + x))
dx,dy = x-l+refpos[0],y-k+refpos[1]
padk,padl = k+w,l+w
# high pass filter the data
cube_stamp = _paddata[:, padk-w:padk+w+1, padl-w:padl+w+1]
badpix_stamp = _padbad_pixels[:, padk-w:padk+w+1, padl-w:padl+w+1]
badpixs = np.ravel(badpix_stamp)
d = np.ravel(cube_stamp)
s = np.ravel(_padnoise[:, padk-w:padk+w+1, padl-w:padl+w+1])
badpixs[np.where(s==0)] = np.nan
# manage all the different cases to define the position of the spline nodes
if type(nodes) is int:
N_nodes = nodes
x_knots = np.linspace(np.min(wvs), np.max(wvs), N_nodes, endpoint=True).tolist()
elif type(nodes) is list or type(nodes) is np.ndarray :
x_knots = nodes
if type(nodes[0]) is list or type(nodes[0]) is np.ndarray :
N_nodes = np.sum([np.size(n) for n in nodes])
else:
N_nodes = np.size(nodes)
else:
raise ValueError("Unknown format for nodes.")
fitback = False
if fitback:
N_linpara = boxw * boxw * N_nodes +1 + 3*boxw**2
else:
N_linpara = boxw * boxw * N_nodes +1
where_finite = np.where(np.isfinite(badpixs))
if np.size(where_finite[0]) <= (1-badpixfraction) * np.size(badpixs) or \
padk > ny+2*w-1 or padk < 0 or padl > nx+2*w-1 or padl < 0:
# don't bother to do a fit if there are too many bad pixels
return np.array([]), np.array([]).reshape(0,N_linpara), np.array([])
else:
# Get the linear model (ie the matrix) for the spline
M_speckles = np.zeros((nz, boxw, boxw, boxw, boxw, N_nodes))
for _k in range(boxw):
for _l in range(boxw):
lwvs = wvs[:,np.clip(k-w+_k,0,nywv-1),np.clip(l-w+_l,0,nxwv-1)]
M_spline = get_spline_model(x_knots, lwvs, spline_degree=3)
M_speckles[:, _k, _l, _k, _l, :] = M_spline * star_spectrum[:, None]
M_speckles = np.reshape(M_speckles, (nz, boxw, boxw, boxw * boxw * N_nodes))
if fitback:
M_background = np.zeros((nz, boxw, boxw, boxw, boxw,3))
for _k in range(boxw):
for _l in range(boxw):
lwvs = wvs[:,np.clip(k-w+_k,0,nywv-1),np.clip(l-w+_l,0,nxwv-1)]
M_background[:, _k, _l, _k, _l, 0] = 1
M_background[:, _k, _l, _k, _l, 1] = lwvs
M_background[:, _k, _l, _k, _l, 2] = lwvs**2
M_background = np.reshape(M_background, (nz, boxw, boxw, 3*boxw**2))
psfs = np.zeros((nz, boxw, boxw))
# Technically allows super sampled PSF to account for a true 2d gaussian integration of the area of a pixel.
# But this is disabled for now with hdfactor=1.
hdfactor = 1#5
xhdgrid, yhdgrid = np.meshgrid(np.arange(hdfactor * (boxw)).astype(float) / hdfactor,
np.arange(hdfactor * (boxw)).astype(float) / hdfactor)
psfs += pixgauss2d([1., w+dx, w+dy, psfw, 0.], (boxw, boxw), xhdgrid=xhdgrid, yhdgrid=yhdgrid)[None, :, :]
psfs = psfs / np.nansum(psfs, axis=(1, 2))[:, None, None]
# flux ratio normalization
star_flux = np.nanmean(star_spectrum) * np.size(star_spectrum)
scaled_psfs = np.zeros((nz,boxw,boxw))+np.nan
for _k in range(boxw):
for _l in range(boxw):
lwvs = wvs[:,np.clip(k-w+_k,0,nywv-1),np.clip(l-w+_l,0,nxwv-1)]
# The planet spectrum model is RV shifted and multiplied by the tranmission
planet_spec = transmission * planet_f(lwvs * (1 - (rv - cubeobj.bary_RV) / const.c.to('km/s').value))
scaled_psfs[:,_k,_l] = psfs[:, _k,_l] * planet_spec
planet_flux = np.size(scaled_psfs) * np.nanmean(scaled_psfs)
scaled_psfs = scaled_psfs / planet_flux * star_flux
# print(np.nansum(scaled_psfs))
# combine planet model with speckle model
if fitback:
M = np.concatenate([scaled_psfs[:, :, :, None], M_speckles,M_background], axis=3)
else:
M = np.concatenate([scaled_psfs[:, :, :, None], M_speckles], axis=3)
# Ravel data dimension
M = np.reshape(M, (nz * boxw * boxw, N_linpara))
# Get rid of bad pixels
sr = s[where_finite]
dr = d[where_finite]
Mr = M[where_finite[0], :]
return dr, Mr, sr