?getri

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 10/15/2026

Version

Public

?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 (Computes the LU factorization of a general m-by-n matrix.) 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: Specifies the order of the matrix A . The value of n must be at least zero.

a , work

Arrays: a(lda,*) , work(*) .

a(lda,*) contains the factorization of the matrix A , as returned by ?getrf (Computes the LU factorization of a general m-by-n matrix.) : A = P*L*U .

work(*) is a workspace array of dimension at least max(1,lwork) .

a

Array a (size max(1, lda * n )) contains the factorization of the matrix A , as returned by GUID-A02DB70F-9704-42A4-9071-D409D783D911.xml#GUID-A02DB70F-9704-42A4-9071-D409D783D911 : 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 (Computes the LU factorization of a general m-by-n matrix.) .

lwork

The size of the work array; lwork ≥ n .

If lwork = -1 , then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued by xerbla .

Output Parameters

a

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

work(1)

If info = 0 , on exit work(1) contains the minimum value of lwork required for optimum performance. Use this lwork for subsequent runs.

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.

LAPACK 95 Interface Notes

There exist FORTRAN 77 and FORTRAN 95 interfaces for this routine. See the Intel® oneMKL Fortran Developer Reference for details.

Application Notes

The computed inverse \(X\) satisfies the following error bound:

\[|XA - I| \leq c(n)\varepsilon|X|P|L||U|,\]

where c(n) is a modest linear function of n ; \(\varepsilon\) 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 \((4/3)n^{3}\) for real flavors and \((16/3)n^{3}\) for complex flavors.

NOTE:

Matrix Storage Schemes

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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

LAPACK 95 Interface Notes

Application Notes