sensitivities

Methods for linear and stochastic sensitivities analysis and error propagation.

Install

You can install the sensitivities module using pip:

pip install sensitivities

Usage

sensitivities.stochastic

The sensitivities.stochastic module provides functionality for stochastic sensitivities analysis. It allows you to stochastically sample input parameters from various distributions and evaluate the sensitivities of a function to those inputs. Available distributions are

• Gaussian (given mean and standard deviation)
• Uniform (between lower and upper bound)
• Discrete (multiple discrete options)

Example for stochastic sampling:

from sensitivities.stochastic import sample, Gaussian, Uniform, Discrete, seed
import matplotlib.pyplot as plt

def my_function(a, b, c=0, d=0):
    return a + b + c + d

samples = sample(
    my_function,
    [Gaussian(10, 0.05), Discrete([1, 2])],
    {"c": Uniform(-0.4, 0.4), "d": -10},
    n=100000,
)

plt.hist(samples, 100)
plt.show()

sensitivities.linear

This module contains the propagate_errors function for linear propagation of errors for a given function based on the principle of differentials. It makes use of the scipy function approx_fprime to calculate the partial derivatives of the given function. The propagated error is calculated by taking the square root of the sum of squares of the product of the partial derivatives and the uncertainties.

Here is a simple usage example:

from sensitivities.linear import propagate_errors

def my_function(x, y):
    return [x ** 2, y]

print(propagate_errors(my_function, errors=[0.1, 0.2], x0=[1, 1]))

This will output:

np.array([0.2, 0.2])