General

This routine computes the in-place inverse of a general fully-populated (invertible) matrix \(A\) as

\[A^{-1} = U^{-1} L^{-1} P,\]

where \(PA=LU\) is the result of LU factorization with partial pivoting. The algorithm essentially factors \(A\), inverts \(U\) in place, solves against \(L\) one block column at a time, and then applies the row pivots in reverse order to the columns of the result.

Python API

Inverse(A)

C++ API

void Inverse(Matrix<F> &A)
void Inverse(AbstractDistMatrix<F> &A)

C API

Single-precision

ElError ElInverse_s(ElMatrix_s A)
ElError ElInverseDist_s(ElDistMatrix_s A)

Double-precision

ElError ElInverse_d(ElMatrix_d A)
ElError ElInverseDist_d(ElDistMatrix_d A)

Single-precision complex

ElError ElInverse_c(ElMatrix_c A)
ElError ElInverseDist_c(ElDistMatrix_c A)

Double-precision complex

ElError ElInverse_z(ElMatrix_z A)
ElError ElInverseDist_z(ElDistMatrix_z A)