pystra.integration.zi_and_xi#

zi_and_xi(margi, margj, zmax, nIP)[source]#

Set up the 2-D quadrature grid for the Nataf correlation integral.

Computes the meshgrid arrays of standard-normal coordinates (Z1, Z2), their physical-space counterparts (X1, X2), the outer-product weight matrix, and the Jacobian determinant for the coordinate mapping.

Parameters:

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

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

  • zmax (float) – Truncation limit for the integration domain ([-zmax, zmax] on each axis).

  • nIP (int) – Number of Gauss-Legendre integration points per axis.

Returns:

  • Z1, Z2 (ndarray) – Meshgrid arrays of standard-normal coordinates, each of shape (nIP, nIP).

  • X1, X2 (ndarray) – Physical-space values corresponding to Z1 and Z2.

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

  • detJ (float) – Jacobian determinant of the affine coordinate mapping.