file data/profile_theory.py

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Source code #

#!/usr/bin/env python
"""
Profile a chi-squared in a data file with a fractional theory error
===================================================================

python profile_theory.py <file> <frac-error> <min> <max> <log-normal>

prints (parameter, profiled chi-squared) from a file containing
(parameter, chi-squared).
"""

import sys
import numpy as np
from scipy.interpolate import interp1d
from scipy.optimize import minimize_scalar
from scipy.stats import norm, lognorm


def profile(file_name, frac_error=0.1, min_=0., max_=1., log_normal=True):
    """
    Profile a chi-squared in a data file with a fractional theory error

    Args:
        file_name (str): Data file with columns (parameter, chi-squared).
        frac_error (float, optional): Fractional theory error on the parameter.
        min_ (float, optional): Minimum value of parameter.
        max_ (float, optional): Maximum value of parameter.
        log_normal (bool, optional): Whether to use log-normal or normal error.

    Returns:
        list(tuples): List of (parameter, profiled chi-squared)
    """
    # Unpack data
    param, chi_squared_ = np.loadtxt(file_name, unpack=True)

    # Interpolate chi-squared function
    chi_squared = interp1d(param, chi_squared_,
        kind='linear', bounds_error=False, fill_value="extrapolate")

    # Make penalty for true prediction
    def penalty(x, mu):
        if log_normal:
            sigma = np.log(1. + frac_error)
            mode = np.exp(np.log(mu) - sigma**2)
            dist = lognorm(sigma, scale=mu)
        else:
            sigma = frac_error * mu
            mode = mu
            dist = norm(mu, sigma)
        return -2. * (dist.logpdf(x) - dist.logpdf(mode))

    # Make functions for profile
    objective = lambda x, mu: chi_squared(x) + penalty(x, mu)
    def profiled(mu):
        if mu == 0.:
            return chi_squared(0.)
        else:
            return minimize_scalar(objective, bounds=[min_, max_],
                method="Bounded", options={'xatol': 1E-20, 'maxiter': 1000}, args=(mu)).fun

    # Profile
    return [(p, profiled(p)) for p in param]

if __name__ == "__main__":

    try:
        FILE_NAME = sys.argv[1]
    except IndexError:
        raise RuntimeError(__doc__)

    ARGS = map(float, sys.argv[2:])

    for p, c in profile(FILE_NAME, *ARGS):
        print p, c

Updated on 2022-08-03 at 12:57:57 +0000