?getrf2

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

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:

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

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

m

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

n

INTEGER. 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

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