Uncertainty Quantification (labtoolbox.uncertainty)#

Uncertainty quantification utilities for LabToolbox.

This package exposes methods for uncertainty propagation and several uncertainty modeling strategies.

labtoolbox.uncertainty.montecarlo(func, values, errs, N=10000, seed=None)[source]#

Estimate the propagated uncertainty on a function of N variables using Monte Carlo simulation.

Parameters:

  • func (callable) – The function to evaluate. Must accept the same number of arguments as the length of values.

  • values (array-like) – Central values of the input variables. Must be of the same length as errs.

  • errs (array-like) – Standard deviations (1-sigma uncertainties) of the input variables.

  • N (int, optional) – Number of Monte Carlo samples to generate. Default is 1e4.

  • seed (int or None, optional) – Seed for the random number generator, for reproducibility. Default is None.

Returns:

  • mean (float) – Mean value of the function evaluated over the sampled inputs.

  • std (float) – Standard deviation (uncertainty) of the function output.

Notes

  • The input variables are sampled as independent normal distributions with given means and standard deviations.

  • Correlations between input variables are not taken into account.

Example

>>> def f(x, y): return x * y
>>> montecarlo(f, [2.0, 3.0], [0.1, 0.2])
(6.00..., 0.42...)
labtoolbox.uncertainty.numerical(f, x_val, x_err, params=())[source]#

Uncertainty propagation via numerical derivatives.

Parameters:

  • f (callable) – Function f(x1, …, xn; a1, …, am) that returns an array of shape (N,).

  • x_val (list of np.ndarray) – List of input arrays x1,…, xn, each with shape (N,).

  • x_err (list of np.ndarray) – List of uncertainty arrays corresponding to each x_i, shape (N,).

  • params (tuple, optional) – Tuple of constant parameters (a1, …, am) to be passed to the function.

Returns:

  • f_val (np.ndarray) – Central values of the function, shape (N,).

  • f_err (np.ndarray) – Propagated uncertainty, shape (N,).

labtoolbox.uncertainty.propagate(func, x_val, x_err, params=None, method='Monte_Carlo', MC_sample_size=10000)[source]#

Propagates uncertainty from i_nput arrays to a generic function using the uncertainty_class library.

Parameters:

  • func (callable) – The base function, in the form f(x, a) where: - x is a vector of variables. - a is a vector of parameters (optional).

  • x_val (list of numpy.array) – List containing the i_nput variable arrays [x1, x2, …, xn]. Each entry can be: - a scalar, - a numpy array of values (same length across all xi).

  • x_err (list or numpy.array) – List of uncertainties for each variable (scalars or arrays), or a full covariance matrix.

  • params (list or numpy.array, optional) – List or array of constant parameters [a1, a2, …, am].

  • method (str, optional) – The uncertainty propagation method (‘Delta’ or ‘Monte_Carlo’).

  • MC_sample_size (int, optional) – Sample size for the Monte Carlo method.

Returns:

  • f_values (numpy.ndarray) – Values of the function calculated at each point j.

  • f_err (numpy.ndarray) – Propagated uncertainties on the output function for each point j.

  • confidence_bands (tuple of numpy.ndarray) – Lower and upper confidence bands for each point j.