gemseo / post / core

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robustness_quantifier module

Quantification of robustness of the optimum to variables perturbations.

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

Bases: object

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)

Bases: StrEnum

The approximation types.

BFGS = 'BFGS'

LEAST_SQUARES = 'LEAST_SQUARES'

SR1 = 'SR1'

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

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)

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:

• expect (Sized) – The expected value of the inputs.

• cov – The covariance matrix of the inputs.

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)

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)

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)

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:

• expect (Sized) – The expected value of the inputs.

• cov – The covariance matrix of the inputs.

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)

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.