pystra.integration.rho_integral#

rho_integral(rho0, margi, margj, Z1, Z2, X1, X2, WIP, detJ)[source]#

Evaluate the Nataf correlation integral for a trial rho_0.

Computes the physical-space correlation that results from a standard-normal-space correlation of rho0, by numerically integrating the bivariate standard normal density weighted by the normalised marginal values.

Parameters:

  • rho0 (float) – Trial correlation in standard-normal space.

  • margi (Distribution) – Marginal distributions of the two random variables.

  • margj (Distribution) – Marginal distributions of the two random variables.

  • Z1 (ndarray) – Meshgrid arrays of standard-normal integration coordinates.

  • Z2 (ndarray) – Meshgrid arrays of standard-normal integration coordinates.

  • X1 (ndarray) – Corresponding physical-space values via the marginal transformations.

  • X2 (ndarray) – Corresponding physical-space values via the marginal transformations.

  • WIP (ndarray) – Outer product of quadrature weights.

  • detJ (float) – Jacobian determinant of the coordinate mapping from [-zmax, zmax] to [-1, 1].

Returns:

The resulting physical-space correlation coefficient.

Return type:

float