?getri

Computes the inverse of an LU-factored general matrix.

Syntax

lapack_int LAPACKE_sgetri (int matrix_layout , lapack_int n , float * a , lapack_int lda , const lapack_int * ipiv );

lapack_int LAPACKE_dgetri (int matrix_layout , lapack_int n , double * a , lapack_int lda , const lapack_int * ipiv );

lapack_int LAPACKE_cgetri (int matrix_layout , lapack_int n , lapack_complex_float * a , lapack_int lda , const lapack_int * ipiv );

lapack_int LAPACKE_zgetri (int matrix_layout , lapack_int n , lapack_complex_double * a , lapack_int lda , const lapack_int * ipiv );

Include Files

  • mkl.h

Description

The routine computes the inverse inv(A) of a general matrix A. Before calling this routine, call ?getrf to factorize A.

Input Parameters

matrix_layout

Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).

n

The order of the matrix A; n 0.

a

Array a(size max(1, lda*n)) contains the factorization of the matrix A, as returned by ?getrf: A = P*L*U. The second dimension of a must be at least max(1,n).

lda

The leading dimension of a; lda max(1, n).

ipiv

Array, size at least max(1, n).

The ipiv array, as returned by ?getrf.

Output Parameters

a

Overwritten by the n-by-n matrix inv(A).

Return Values

This function returns a value info.

If info = 0, the execution is successful.

If info = -i, parameter i had an illegal value.

If info = i, the i-th diagonal element of the factor U is zero, U is singular, and the inversion could not be completed.

Application Notes

The computed inverse X satisfies the following error bound:

|XA - I|  c(n)ε|X|P|L||U|,

where c(n) is a modest linear function of n; ε is the machine precision; I denotes the identity matrix; P, L, and U are the factors of the matrix factorization A = P*L*U.

The total number of floating-point operations is approximately (4/3)n3 for real flavors and (16/3)n3 for complex flavors.

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