Example and Test of Predefined Parametric Functions of Time

Function Documentation

param_time_fun

Example Source Code

import numpy
import scipy
from curvefit.core.functions import *


eps99 = 99.0 * numpy.finfo(float).eps
sqrt_eps = numpy.sqrt(numpy.finfo(float).eps)
quad_eps = numpy.sqrt(sqrt_eps)
d_tolerance = 1e-6


def eval_expit(t, alpha, beta, p):
    return p / (1.0 + numpy.exp(- alpha * (t - beta)))


def eval_gaussian_cdf(t, alpha, beta, p):
    z = alpha * (t - beta)
    return p * (1.0 + scipy.special.erf(z)) / 2.0


# test values for t, alpha, beta, p
t = numpy.array([5.0, 10.0])
beta = numpy.array([30.0, 20.0])
alpha = 2.0 / beta
p = numpy.array([0.1, 0.2])
params = numpy.vstack((alpha, beta, p))

# check gaussian_cdf
value = gaussian_cdf(t, params)
check = eval_gaussian_cdf(t, alpha, beta, p)
rel_error = value / check - 1.0
assert all(abs(rel_error) < eps99)

# check ln_gaussian_cdf
value = ln_gaussian_cdf(t, params)
check = numpy.log(check)
rel_error = value / check - 1.0
assert all(abs(rel_error) < eps99)

# check gaussian_pdf
step = sqrt_eps * beta
value = gaussian_pdf(t, params)
check_m = eval_gaussian_cdf(t - step, alpha, beta, p)
check_p = eval_gaussian_cdf(t + step, alpha, beta, p)
check = (check_p - check_m) / (2.0 * step)
rel_error = value / check - 1.0
assert all(abs(rel_error) < d_tolerance)

# check ln_gaussian_pdf
value = ln_gaussian_pdf(t, params)
check = numpy.log(check)
rel_error = value / check - 1.0
assert all(abs(rel_error) < d_tolerance)

# check_dgaussian_pdf
step = quad_eps * beta
value = dgaussian_pdf(t, params)
check_m = eval_gaussian_cdf(t - step, alpha, beta, p)
check_0 = eval_gaussian_cdf(t, alpha, beta, p)
check_p = eval_gaussian_cdf(t + step, alpha, beta, p)
check = (check_p - 2.0 * check_0 + check_m) / step ** 2
rel_error = value / check - 1.0
assert all(abs(rel_error) < d_tolerance)

print('param_time_fun.py: OK')