?getrf2

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 4/28/2026

Version

Public

?getrf2

Computes LU factorization using partial pivoting with row interchanges.

Syntax

lapack_intLAPACKE_sgetrf2 ( intmatrix_layout , lapack_intm , lapack_intn , float*a , lapack_intlda , lapack_int*ipiv );

lapack_intLAPACKE_dgetrf2 ( intmatrix_layout , lapack_intm , lapack_intn , double*a , lapack_intlda , lapack_int*ipiv );

lapack_intLAPACKE_cgetrf2 ( intmatrix_layout , lapack_intm , lapack_intn , lapack_complex_float*a , lapack_intlda , lapack_int*ipiv );

lapack_intLAPACKE_zgetrf2 ( intmatrix_layout , lapack_intm , lapack_intn , lapack_complex_double*a , lapack_intlda , lapack_int*ipiv );

Include Files

mkl.h

Description

?getrf2 computes an LU factorization of a general m -by- n matrix A using partial pivoting with row interchanges.

The factorization has the form

\(A = PLU\)

where \(P\) is a permutation matrix, \(L\) is lower triangular with unit diagonal elements (lower trapezoidal if m > n ), and \(U\) is upper triangular (upper trapezoidal if m < n ).

This is the recursive version of the algorithm. It divides the matrix into four submatrices:

\[A = \begin{pmatrix} A_{11} & A_{12} \\ A_{21} & A_{22} \end{pmatrix}\]

where \(A_{11}\) is n1 by n1 and \(A_{22}\) is n2 by n2 with n1 = min(m,n), and n2 = n-n1 .

The subroutine calls itself to factor \(\begin{pmatrix} A_{11} \\ A_{21} \end{pmatrix}\), do the swaps on \(\begin{pmatrix} A_{12} \\ A_{22} \end{pmatrix}\), solve A12 , update \(A_{22}\) , then it calls itself to factor \(A_{22}\) and do the swaps on \(A_{21}\) .

Input Parameters

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

m

The number of rows of the matrix A. m >= 0.

n

The number of columns of the matrix A. n >= 0.

a

REAL for sgetrf2 DOUBLE PRECISION for dgetrf2 COMPLEX for cgetrf2 DOUBLE COMPLEX for zgetrf2

Array, size lda * n .

On entry, the m -by- n matrix to be factored.

lda

The leading dimension of the array a . lda >= max(1, m ).

Output Parameters

a: On exit, the factors L and U from the factorization A = P * L * U ; the unit diagonal elements of L are not stored.

ipiv

Array, size (min(m,n)).

The pivot indices; for 1 <= i <= min( m , n ), row i of the matrix was interchanged with row ipiv[i-1] .

Return Values

This function returns a value info .

= 0: successful exit
< 0: if info = - i , the i -th argument had an illegal value.
> 0: if info = i , \(U_{ii}\) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations.

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?getrf2

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values