pystra.model.LimitState#

class LimitState(expression=None)[source]#

Bases: object

The Limit State function definition class.

The limit state function can be defined in two main ways:

1. Numerical differentiation (FFD): the limit state function need only return its value at a set of evaluation points, X. In this form, the function can be either:

  1. A python lambda object;

  2. A python function object.

2. Using the Direct Differentiation Method (DDM): the limit state function is a python function object return both its value and gradient vector at each of the evaluation points.

Note in both cases that each parameter (i.e. function argument) may be passed as a vector, depending on the algorithm being called.

Where a function returns a gradient vector, it is only utilized when DDM is specified.

Argument matching: the function is called as expression(**kwargs) where each keyword argument is a variable name from the StochasticModel. Arguments may therefore be declared explicitly (def lsf(X1, X2, X3): ...) or collected with **kwargs for a dimension-agnostic definition:

def lsf(**kwargs):
    return sum(v**2 for v in kwargs.values())

Methods

compute_lsf

Call the user-defined limit state function.

evaluate_ddm

Evaluate the LSF using direct differentiation (user-supplied gradient).

evaluate_ffd

Evaluate the LSF and approximate the gradient by forward finite difference.

evaluate_lsf

Evaluate the limit state function and (optionally) its gradient.

evaluate_nogradient

Evaluate the LSF without computing gradients (used for MCS).

getExpression

setExpression

expression#

Expression of the limit-state function

evaluate_lsf(x, stochastic_model, analysis_options, diff_mode=None)[source]#

Evaluate the limit state function and (optionally) its gradient.

Dispatches to the appropriate evaluation strategy based on the differentiation mode: no gradient ("no"), forward finite difference ("ffd"), or direct differentiation ("ddm").

Parameters:

  • x (ndarray) – Evaluation points, shape (nrv, nx) where nrv is the number of random variables and nx the number of points.

  • stochastic_model (StochasticModel) – The probabilistic model.

  • analysis_options (AnalysisOptions) – Algorithm settings (differentiation mode, block size, etc.).

  • diff_mode (str or None, optional) – Override the differentiation mode. If a string is passed (any value), gradient computation is suppressed ("no").

Returns:

  • G (ndarray) – Limit state function values, shape (1, nx).

  • grad_G (ndarray) – Gradient matrix, shape (nrv, nx). Zero when no gradient is computed.

evaluate_nogradient(x)[source]#

Evaluate the LSF without computing gradients (used for MCS).

evaluate_ffd(x)[source]#

Evaluate the LSF and approximate the gradient by forward finite difference.

evaluate_ddm(x)[source]#

Evaluate the LSF using direct differentiation (user-supplied gradient).

compute_lsf(x, ddm=False)[source]#

Call the user-defined limit state function.

Builds a keyword-argument dictionary mapping variable names to their column vectors in x, then calls self.expression(**kwargs).

Parameters:

  • x (ndarray) – Evaluation points, shape (nrv, nc).

  • ddm (bool, optional) – If True, expects the expression to return both the function value and a gradient vector.

Returns:

  • G (ndarray) – Function value(s).

  • gradient (ndarray or int) – Gradient vector (if ddm) or 0.