?getrf2

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 10/15/2026

Version

Public

?getrf2

Computes LU factorization using partial pivoting with row interchanges.

Syntax

call sgetrf2(m, n, a, lda, ipiv, info)
call dgetrf2(m, n, a, lda, ipiv, info)
call cgetrf2(m, n, a, lda, ipiv, info)
call zgetrf2(m, n, a, lda, ipiv, info)

Include Files

mkl.fi

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:

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

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

m: INTEGER. The number of rows in the matrix A. The value of m must be at least zero.

n: INTEGER. The number of columns in the matrix A. The value of n must be at least zero.

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

INTEGER. 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

INTEGER. 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) .

info

INTEGER.

= 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.

Return Values

No return value, info is an Output Parameter.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?getrf2

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values