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| #!/usr/bin/env python3 | ||
| # -*- coding: utf-8 -*- | ||
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| """hyperparam_transforms.py -- This module contains parameter transformations that are | ||
| used in the stochastic SFH prior. | ||
| These are taken from the implementation of | ||
| https://ui.adsabs.harvard.edu/abs/2024ApJ...961...53I/abstract given in | ||
| https://github.com/kartheikiyer/GP-SFH | ||
| They can be used as ``"depends_on"`` entries in parameter specifications. | ||
| """ | ||
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| import numpy as np | ||
| from astropy.cosmology import FlatLambdaCDM | ||
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| __all__ = ["get_sfr_covar", "sfr_covar_to_sfr_ratio_covar"] | ||
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| # -------------------------------------- | ||
| # --- Functions/transforms for stochastic SFH prior --- | ||
| # -------------------------------------- | ||
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| # Creating a base class that simplifies a lot of things. | ||
| # The way this is set up, you can pass a kernel as an argument | ||
| # to compute the covariance matrix and draw samples from it. | ||
| class simple_GP_sfh(): | ||
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| """ | ||
| A class that creates and holds information about a specific | ||
| kernel, and can generate samples from it. | ||
| From https://github.com/kartheikiyer/GP-SFH | ||
| Attributes | ||
| ---------- | ||
| tarr: fiducial time array used to draw samples | ||
| kernel: accepts an input function as an argument, | ||
| of the format: | ||
| def kernel_function(delta_t, **kwargs): | ||
| ... function interior ... | ||
| return kernel_val[array of len(delta_t)] | ||
| Methods | ||
| ------- | ||
| get_covariance_matrix | ||
| [although this has double for loops for maximum flexibility | ||
| with generic kernel functions, it only has to be computed once, | ||
| which makes drawing random samples super fast once it's computed.] | ||
| sample_kernel | ||
| plot_samples | ||
| plot_kernel | ||
| [to-do] condition on data | ||
| """ | ||
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| def __init__(self, sp = 'none', cosmo = FlatLambdaCDM(H0=70, Om0=0.3), zval = 0.1): | ||
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| self.kernel = [] | ||
| self.covariance_matrix = [] | ||
| self.zval = zval | ||
| self.sp = sp | ||
| self.cosmo = cosmo | ||
| self.get_t_univ() | ||
| self.get_tarr() | ||
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| def get_t_univ(self): | ||
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| self.t_univ = self.cosmo.age(self.zval).value | ||
| return | ||
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| def get_tarr(self, n_tarr = 1000): | ||
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| self.get_t_univ() | ||
| if n_tarr > 1: | ||
| self.tarr = np.linspace(0,self.t_univ, n_tarr) | ||
| elif n_tarr < 1: | ||
| self.tarr = np.arange(0,self.t_univ, n_tarr) | ||
| else: | ||
| raise('Undefined n_tarr: expected int or float.') | ||
| return | ||
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| def get_covariance_matrix(self, show_prog = True, **kwargs): | ||
| """ | ||
| Evaluate covariance matrix with a particular kernel | ||
| """ | ||
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| cov_matrix = np.zeros((len(self.tarr),len(self.tarr))) | ||
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| if show_prog == True: | ||
| iterrange = range(len(cov_matrix)) | ||
| else: | ||
| iterrange = range(len(cov_matrix)) | ||
| for i in iterrange: | ||
| for j in range(len(cov_matrix)): | ||
| cov_matrix[i,j] = self.kernel(self.tarr[i] - self.tarr[j], **kwargs) | ||
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| return cov_matrix | ||
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| def extended_regulator_model_kernel_paramlist(delta_t, kernel_params, base_e_to_10 = False): | ||
| """ | ||
| A basic implementation of the regulator model kernel, with five parameters: | ||
| kernel_params = [sigma, tau_eq, tau_in, sigma_gmc, tau_gmc] | ||
| sigma: \sigma, the amount of overall variance | ||
| tau_eq: equilibrium timescale | ||
| tau_x: inflow correlation timescale (includes 2pi factor) | ||
| sigma_gmc: gmc variability | ||
| tau_l: cloud lifetime | ||
| from https://github.com/kartheikiyer/GP-SFH | ||
| """ | ||
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| sigma, tau_eq, tau_in, sigma_gmc, tau_gmc = kernel_params | ||
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| if base_e_to_10 == True: | ||
| # in TCF20, this is defined in base e, so convert to base 10 | ||
| sigma = sigma*np.log10(np.e) | ||
| sigma_gmc = sigma_gmc*np.log10(np.e) | ||
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| tau = np.abs(delta_t) | ||
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| if tau_in == tau_eq: | ||
| c_reg = sigma**2 * (1 + tau/tau_eq) * (np.exp(-tau/tau_eq)) | ||
| else: | ||
| c_reg = sigma**2 / (tau_in - tau_eq) * (tau_in*np.exp(-tau/tau_in) - tau_eq*np.exp(-tau/tau_eq)) | ||
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| c_gmc = sigma_gmc**2 * np.exp(-tau/tau_gmc) | ||
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| kernel_val = (c_reg + c_gmc) | ||
| return kernel_val | ||
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| def get_sfr_covar(psd_params, agebins=[], **extras): | ||
| """Caluclates SFR covariance matrix for a given set of PSD parameters and agebins | ||
| PSD parameters must be in the order: [sigma_reg, tau_eq, tau_in, sigma_dyn, tau_dyn] | ||
| from https://github.com/kartheikiyer/GP-SFH | ||
| Returns | ||
| ------- | ||
| covar_matrix: (Nbins, Nbins)-dim array of covariance values for SFR | ||
| """ | ||
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| bincenters = np.array([np.mean(agebins[i]) for i in range(len(agebins))]) | ||
| bincenters = (10**bincenters)/1e9 | ||
| case1 = simple_GP_sfh() | ||
| case1.tarr = bincenters | ||
| case1.kernel = extended_regulator_model_kernel_paramlist | ||
| covar_matrix = case1.get_covariance_matrix(kernel_params = psd_params, show_prog=False) | ||
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| return covar_matrix | ||
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| def sfr_covar_to_sfr_ratio_covar(covar_matrix): | ||
| """Caluclates log SFR ratio covariance matrix from SFR covariance matrix | ||
| from https://github.com/kartheikiyer/GP-SFH | ||
| Returns | ||
| ------- | ||
| sfr_ratio_covar: (Nbins-1, Nbins-1)-dim array of covariance values for log SFR | ||
| """ | ||
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| dim = covar_matrix.shape[0] | ||
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| sfr_ratio_covar = [] | ||
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| for i in range(dim-1): | ||
| row = [] | ||
| for j in range(dim-1): | ||
| cov = covar_matrix[i][j] - covar_matrix[i+1][j] - covar_matrix[i][j+1] + covar_matrix[i+1][j+1] | ||
| row.append(cov) | ||
| sfr_ratio_covar.append(row) | ||
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| return np.array(sfr_ratio_covar) |
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