pinv Interface

public interface pinv

Pseudo-inverse of a matrix (Specification)

Summary

This interface provides methods for computing the Moore-Penrose pseudo-inverse of a matrix. The pseudo-inverse $A^{+}$ is a generalization of the matrix inverse, computed for square, singular, or rectangular matrices. It is defined such that it satisfies the conditions: - $A \cdot A^{+} \cdot A = A$ - $A^{+} \cdot A \cdot A^{+} = A^{+}$ - $(A \cdot A^{+})^T = A \cdot A^{+}$ - $(A^{+} \cdot A)^T = A^{+} \cdot A$

Description

This function interface provides methods that return the Moore-Penrose pseudo-inverse of a matrix.
Supported data types include real and complex. The pseudo-inverse $A^{+}$ is returned as a function result. The computation is based on the singular value decomposition (SVD). An optional relative tolerance rtol is provided to control the inclusion of singular values during inversion. Singular values below $\text{rtol} \cdot \sigma_{\max}$ are treated as zero, where $\sigma_{\max}$ is the largest singular value. If rtol is not provided, a default threshold is applied.

Exceptions are raised in case of computational errors or invalid input, and trigger an error stop if the state flag err is not provided.

Functions