gemseo / post / core

robustness_quantifier module¶

Quantification of robustness of the optimum to variables perturbations.

class gemseo.post.core.robustness_quantifier.RobustnessQuantifier(history, approximation_method=Approximation.SR1)[source]

classdocs.

Parameters:

history – An approximation history.
approximation_method (Approximation) –
The approximation method for the Hessian.

By default it is set to “SR1”.

class Approximation(value)[source]

Bases: StrEnum

The approximation types.

compute_approximation(funcname, first_iter=0, last_iter=None, b0_mat=None, at_most_niter=None, func_index=None)[source]

Build the BFGS approximation for the Hessian.

Parameters:

funcname (str) – The name of the function.
first_iter (int) –
The index of the first iteration.

By default it is set to 0.
last_iter (int | None) – The last iteration of the history to be considered. If None, consider all the iterations.
b0_mat – The Hessian matrix at the first iteration.
at_most_niter (int | None) – The maximum number of iterations to be considered. If None, consider all the iterations.
func_index – The component of the function.

Returns:

An approximation of the Hessian matrix.

compute_expected_value(expect, cov)[source]

Compute the expected value of the output.

Equal to \(0.5\mathbb{E}[e^TBe]\) where \(e\) is the expected values and \(B\) the covariance matrix.

Parameters:

Returns:

The expected value of the output.

Raises:

ValueError – When expectation and covariance matrices have inconsistent shapes or when the Hessian approximation is missing.

compute_function_approximation(x_vars)[source]

Compute a second order approximation of the function.

Parameters:: x_vars – The point on which the approximation is evaluated.
Returns:: A second order approximation of the function.
Return type:: float

compute_gradient_approximation(x_vars)[source]

Computes a first order approximation of the gradient based on the hessian.

Parameters:: x_vars – The point on which the approximation is evaluated.

compute_variance(expect, cov)[source]

Compute the variance of the output.

Equal to \(0.5\mathbb{E}[e^TBe]\) where \(e\) is the expected values and \(B\) the covariance matrix.

Parameters:

Returns:

The variance of the output.

Raises:

ValueError – When expectation and covariance matrices have inconsistent shapes or when the Hessian approximation is missing.

montecarlo_average_var(mean, cov, n_samples=100000, func=None)[source]

Computes the variance and expected value using Monte Carlo approach.

Parameters:

mean (Sized) – The mean value.
cov – The covariance matrix.
n_samples (int) –
The number of samples for the distribution.

By default it is set to 100000.
func – If None, the compute_function_approximation function, otherwise a user function.