Source code for special.chi

#! /usr/bin/env python

"""
Function defining the goodness of fit.
"""

__author__ = 'Valentin Christiaens'
__all__ = ['goodness_of_fit',
           'gof_scal']

import numpy as np
from matplotlib import pyplot as plt
from .config import figsize
from .model_resampling import resample_model
from .utils_spec import extinction

[docs]def goodness_of_fit(lbda_obs, spec_obs, err_obs, lbda_mod, spec_mod, dlbda_obs=None, instru_corr=None, instru_fwhm=None, instru_idx=None, filter_reader=None, plot=False, outfile=None): """ Function to estimate the goodness of fit indicator defined as in Olofsson et al. 2016 (Eq. 8). In addition, if a spectral correlation matrix is provided, it is used to take into account the correlated noise between spectral channels (see Greco & Brandt 2016). The goodness of fit indicator is identical to a chi square when all points are obtained from the same instrument (no additional weighting). Parameters ---------- lbda_obs : numpy 1d ndarray or list Wavelength of observed spectrum. If several instruments, should be ordered per instrument, not necessarily as monotonically increasing wavelength. Hereafter, n_ch = len(lbda_obs). spec_obs : numpy 1d ndarray or list Observed spectrum for each value of lbda_obs. err_obs : numpy 1d/2d ndarray or list Uncertainties on the observed spectrum. If 2d array, should be [2,n_ch] where the first (resp. second) column corresponds to lower (upper) uncertainty, and n_ch is the length of lbda_obs and spec_obs. lbda_mod : numpy 1d ndarray or list Wavelength of tested model. Should have a wider wavelength extent than the observed spectrum. spec_mod : numpy 1d ndarray Model spectrum. It does not require the same wavelength sampling as the observed spectrum. If higher spectral resolution, it will be convolved with the instrumental spectral psf (if instru_fwhm is provided) and then binned to the same sampling. If lower spectral resolution, a linear interpolation is performed to infer the value at the observed spectrum wavelength sampling. dlbda_obs: numpy 1d ndarray or list, optional Spectral channel width for the observed spectrum. It should be provided IF one wants to weigh each point based on the spectral resolution of the respective instruments (as in Olofsson et al. 2016). instru_corr : numpy 2d ndarray or list, optional Spectral correlation throughout post-processed images in which the spectrum is measured. It is specific to the combination of instrument, algorithm and radial separation of the companion from the central star. Can be computed using distances.spectral_correlation(). In case of a spectrum obtained with different instruments, build it with distances.combine_corrs(). If not provided, it will consider the uncertainties in each spectral channels are independent. See Greco & Brandt (2017) for details. instru_fwhm : float or list, optional The instrumental spectral fwhm provided in nm. This is used to convolve the model spectrum. If several instruments are used, provide a list of instru_fwhm values, one for each instrument whose spectral resolution is coarser than the model - including broad band filter FWHM if relevant. instru_idx: numpy 1d array, optional 1d array containing an index representing each instrument used to obtain the spectrum, label them from 0 to n_instru. Zero for points that don't correspond to any instru_fwhm provided above, and i in [1,n_instru] for points associated to instru_fwhm[i-1]. This parameter must be provided if the spectrum consists of points obtained with different instruments. filter_reader: python routine, optional External routine that reads a filter file and returns a 2D numpy array, where the first column corresponds to wavelengths, and the second contains transmission values. Important: if not provided, but strings are detected in instru_fwhm, the default format assumed for the files: - first row containing header - starting from 2nd row: 1st column: WL in mu, 2nd column: transmission Note: files should all have the same format and wavelength units. plot : bool, optional Whether to plot the outfile : string, optional Path+filename for the plot to be saved if provided. Returns ------- chi_sq : float Goodness of fit indicator. """ lbda_obs = np.array(lbda_obs) spec_obs = np.array(spec_obs) err_obs = np.array(err_obs) lbda_mod = np.array(lbda_mod) spec_mod = np.array(spec_mod) if lbda_obs.ndim != 1 or spec_obs.ndim != 1: raise TypeError('Observed lbda and spec must be lists or 1d arrays') if lbda_obs.shape[0] != spec_obs.shape[0]: raise TypeError('Obs lbda and spec need same shape') if lbda_obs.shape[0] != err_obs.shape[-1]: raise TypeError('Obs lbda and err need same shape') if lbda_mod.ndim != 1 or spec_mod.ndim != 1: raise TypeError('The input model lbda/spec must be lists or 1d arrays') else: if lbda_mod.shape != spec_mod.shape: raise TypeError('The input model lbda and spec need same shape') if dlbda_obs is not None: if isinstance(dlbda_obs, list): dlbda_obs = np.array(dlbda_obs) if lbda_obs.shape != dlbda_obs.shape: raise TypeError('The input lbda_obs and dlbda_obs need same shape') n_ch = lbda_obs.shape[0] # interpolate OR convolve+bin model spectrum if not same sampling if len(lbda_obs) != len(lbda_mod): _,spec_mod_fin = resample_model(lbda_obs, lbda_mod, spec_mod, dlbda_obs, instru_fwhm, instru_idx, filter_reader) elif not np.allclose(lbda_obs, lbda_mod): _,spec_mod_fin = resample_model(lbda_obs, lbda_mod, spec_mod, dlbda_obs, instru_fwhm, instru_idx, filter_reader) else: spec_mod_fin = spec_mod # compute covariance matrix if err_obs.ndim == 2: err_obs = (np.absolute(err_obs[0])+np.absolute(err_obs[1]))/2. if instru_corr is None: instru_corr = np.diag(np.ones(n_ch)) cov = np.ones_like(instru_corr) for ii in range(n_ch): for jj in range(n_ch): cov[ii,jj] = instru_corr[ii,jj]*err_obs[ii]*err_obs[jj] # replace potential NaN values nnan_idx = np.where(np.isfinite(spec_mod_fin)) if len(nnan_idx[0])>0: cov_crop = [] for i in range(len(lbda_obs)): if i in nnan_idx[0]: tmp = cov[i] cov_crop.append(tmp[nnan_idx]) cov = np.array(cov_crop) spec_obs = spec_obs[nnan_idx] spec_mod_fin = spec_mod_fin[nnan_idx] dlbda_obs = dlbda_obs[nnan_idx] lbda_obs = lbda_obs[nnan_idx] delta = spec_obs-spec_mod_fin wi = np.ones_like(dlbda_obs) if dlbda_obs is not None: if np.sum(np.power((dlbda_obs[1:]/lbda_obs[1:])-(dlbda_obs[:-1]/lbda_obs[:-1]),2))!=0: # normalize weights for their sum to be equal to the number of points wi = np.sqrt(((dlbda_obs/lbda_obs)/np.sum(dlbda_obs/lbda_obs))*dlbda_obs.shape[0]) chi_sq = np.linalg.multi_dot((wi*delta,np.linalg.inv(cov),wi*delta)) if plot: _, ax = plt.subplots(figsize=figsize) ax.plot(lbda_obs, lbda_obs*spec_obs, 'o', alpha=0.6, color='#1f77b4', label="Measured spectrum") ax.plot(lbda_obs, lbda_mod*spec_mod, '-', alpha=0.4, color='#1f77b4', label="Model") plt.xlabel('Wavelength') plt.ylabel(r'Flux density ($\lambda F_{\lambda}$)') plt.xlim(xmin=0.9*lbda_obs[0], xmax=1.1*lbda_obs[-1]) plt.minorticks_on() plt.legend(fancybox=True, framealpha=0.5, fontsize=12, loc='best') plt.grid(which='major', alpha=0.2) if outfile: plt.savefig(outfile, bbox_inches='tight') plt.show() return chi_sq
[docs]def gof_scal(params, lbda_obs, spec_obs, err_obs, lbda_tmp, spec_mod, dlbda_obs, instru_corr, instru_fwhm, instru_idx, filter_reader, ext_range): """ Wrapper for the goodness of fit routine to search for best template library fitting spectrum. The only difference with `goodness_of_fit` is the "params" argument. Parameters ---------- params: tuple Tuple of 1 or 2 elements: scaling factor and (optionally) differential optical extinction $\Delta A_V$ ($\Delta A_V$ can be negative if template spectra are not dereddened). lbda_obs : numpy 1d ndarray or list Wavelength of observed spectrum. If several instruments, should be ordered per instrument, not necessarily as monotonically increasing wavelength. Hereafter, n_ch = len(lbda_obs). spec_obs : numpy 1d ndarray or list Observed spectrum for each value of lbda_obs. err_obs : numpy 1d/2d ndarray or list Uncertainties on the observed spectrum. If 2d array, should be [2,n_ch] where the first (resp. second) column corresponds to lower (upper) uncertainty, and n_ch is the length of lbda_obs and spec_obs. lbda_tmp : numpy 1d ndarray or list Wavelength of tested template or model. Should have a wider wavelength extent than the observed spectrum. spec_mod : numpy 1d ndarray Model spectrum. It does not require the same wavelength sampling as the observed spectrum. If higher spectral resolution, it will be convolved with the instrumental spectral psf (if instru_fwhm is provided) and then binned to the same sampling. If lower spectral resolution, a linear interpolation is performed to infer the value at the observed spectrum wavelength sampling. dlbda_obs: numpy 1d ndarray or list, optional Spectral channel width for the observed spectrum. It should be provided IF one wants to weigh each point based on the spectral resolution of the respective instruments (as in Olofsson et al. 2016). instru_corr : numpy 2d ndarray or list, optional Spectral correlation throughout post-processed images in which the spectrum is measured. It is specific to the combination of instrument, algorithm and radial separation of the companion from the central star. Can be computed using distances.spectral_correlation(). In case of a spectrum obtained with different instruments, build it with distances.combine_corrs(). If not provided, it will consider the uncertainties in each spectral channels are independent. See Greco & Brandt (2017) for details. instru_fwhm : float or list, optional The instrumental spectral fwhm provided in nm. This is used to convolve the model spectrum. If several instruments are used, provide a list of instru_fwhm values, one for each instrument whose spectral resolution is coarser than the model - including broad band filter FWHM if relevant. instru_idx: numpy 1d array, optional 1d array containing an index representing each instrument used to obtain the spectrum, label them from 0 to n_instru. Zero for points that don't correspond to any instru_fwhm provided above, and i in [1,n_instru] for points associated to instru_fwhm[i-1]. This parameter must be provided if the spectrum consists of points obtained with different instruments. filter_reader: python routine, optional External routine that reads a filter file and returns a 2D numpy array, where the first column corresponds to wavelengths, and the second contains transmission values. Important: if not provided, but strings are detected in instru_fwhm, the default format assumed for the files: - first row containing header - starting from 2nd row: 1st column: WL in mu, 2nd column: transmission Note: files should all have the same format and wavelength units. ext_range: tuple or None, opt If None: differential extinction is not to be considered as a free parameter. Elif a tuple of 3 floats is provided, differential extinction will be considered, with the floats as lower limit, upper limit and step of the grid search. Note: if simplex search, the range is still used to set a chi of np.inf outside of the range. Returns ------- chi_sq : float Goodness of fit indicator. """ tmp_spec = spec_mod*params[0] if len(params) == 2: if ext_range is None: raise TypeError("ext_range should be a tuple of 3 elements") else: if params[1]<ext_range[0] or params[1]>ext_range[1]: return np.inf AV=params[1] thr = ext_range[-1] if abs(AV) < thr: AV = 0 Albdas = extinction(lbda_tmp,abs(AV)) extinc_fac = np.power(10.,-Albdas/2.5) if AV>0: tmp_spec *= extinc_fac elif AV<0: tmp_spec /= extinc_fac elif len(params) > 2: raise TypeError("params tuple should have length 1 or 2") return goodness_of_fit(lbda_obs, spec_obs, err_obs, lbda_tmp, tmp_spec, dlbda_obs=dlbda_obs, instru_corr=instru_corr, instru_fwhm=instru_fwhm, instru_idx=instru_idx, filter_reader=filter_reader)