?getri

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/22/2024

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?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, ldan)) contains the factorization of the matrix `A`, as returned by ?getrf: `A = PL*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.

Parent topic: Matrix Inversion: LAPACK Computational Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?getri

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

Application Notes

See Also