import numpy as np
from PyAstronomy import pyasl
from astropy import constants as const
from scipy.interpolate import interp1d
from breads.utils import get_spline_model, pixgauss2d
[docs]
def iso_atmgrid_splinefm(nonlin_paras, cubeobj, atm_grid=None, atm_grid_wvs=None, transmission=None,boxw=1, psfw=1.2,nodes=20,badpixfraction=0.75,loc=None,fix_parameters=None):
"""
For characterization of isolated objects, so no speckle.
Generate forward model fitting the continuum with a spline. No high pass filter or continuum normalization here.
Fitting for a grid of atmospheric models.
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 first the parameters defining the atmopsheric grid
(atm_grid). The following parameters are the spin (vsini), the radial velocity, and the position (if loc is
not defined) of the planet in the FOV.
[atm paras ....,vsini,rv,y,x] for 3d cubes (e.g. OSIRIS)
[atm paras ....,vsini,rv,y] for 2d (e.g. KPIC, y being fiber)
[atm paras ....,vsini,rv] for 1d spectra
cubeobj: Data object.
Must inherit breads.instruments.instrument.Instrument.
atm_grid: Planet atmospheric model grid as a scipy.interpolate.RegularGridInterpolator object. Make sure the
wavelength coverage of the grid is just right and not too big as it will slow down the spin broadening.
atm_grid_wvs: Wavelength sampling on which atm_grid is defined. Wavelength needs to be uniformly sampled.
transmission: Transmission spectrum (tellurics and instrumental).
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 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
Natmparas = len(atm_grid.values.shape)-1
atm_paras = [p for p in _nonlin_paras[0:Natmparas]]
other_nonlin_paras = _nonlin_paras[Natmparas::]
# 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
vsini,rv = other_nonlin_paras[0:2]
# 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,other_nonlin_paras[2]
elif len(cubeobj.data.shape)==3:
x,y = other_nonlin_paras[3],other_nonlin_paras[2]
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(transmission))[0],:,:] = np.nan
# Extract stamp data cube cropping at the edges
w = int((boxw - 1) // 2)
# right, left = np.min([l+w+1,nx]), np.max([l-w,0])
# top, bottom = np.min([k+w+1,ny]), np.max([k-w,0])
_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 = N_nodes + 3*boxw**2
else:
N_linpara = N_nodes
where_finite = np.where(np.isfinite(badpixs))
if np.size(where_finite[0]) <= (1-badpixfraction) * np.size(badpixs) or vsini < 0 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:
planet_model = atm_grid(atm_paras)[0]
if np.sum(np.isnan(planet_model)) >= 1 or np.sum(planet_model)==0 or np.size(atm_grid_wvs) != np.size(planet_model):
return np.array([]), np.array([]).reshape(0,N_linpara), np.array([])
else:
if vsini != 0:
spinbroad_model = pyasl.fastRotBroad(atm_grid_wvs, planet_model, 0.1, vsini)
else:
spinbroad_model = planet_model
planet_f = interp1d(atm_grid_wvs,spinbroad_model, bounds_error=False, fill_value=0)
lwvs = wvs[:,np.clip(k-2*w,0,nywv-1),np.clip(l-2*w,0,nxwv-1)]
# Get the linear model (ie the matrix) for the spline
M_spline = get_spline_model(x_knots, lwvs, spline_degree=3)
if fitback:
M_background = np.zeros((nz, boxw, boxw, boxw, boxw,3))
for m in range(boxw):
for n in range(boxw):
lwvs = wvs[:,np.clip(k-2*w+m,0,nywv-1),np.clip(l-2*w+m,0,nxwv-1)]
M_background[:, m, n, m, n, 0] = 1
M_background[:, m, n, m, n, 1] = lwvs
M_background[:, m, n, m, n, 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(np.float) / hdfactor,
np.arange(hdfactor * (boxw)).astype(np.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]
# The planet spectrum model is RV shifted and multiplied by the tranmission
# planet_spec = transmission * planet_f(wvs * (1 - (rv - cubeobj.bary_RV) / const.c.to('km/s').value))
# Go from a 1d spectrum to the 3D scaled PSF
scaled_psfs = np.zeros((nz,boxw,boxw,N_nodes))+np.nan
for _k in range(boxw):
for _l in range(boxw):
lwvs = wvs[:,np.clip(k-2*w+_k,0,nywv-1),np.clip(l-2*w+_l,0,nxwv-1)]
planet_spec = transmission * planet_f(lwvs * (1 - (rv - cubeobj.bary_RV) / const.c.to('km/s').value))
scaled_psfs[:,_k,_l,:] = psfs[:, _k,_l,None] * M_spline * planet_spec[:,None]
# combine planet model with speckle model
if fitback:
M = np.concatenate([scaled_psfs[:, :, :, None],M_background], axis=3)
else:
M = np.concatenate([scaled_psfs[:, :, :, None]], 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