?getrf_batch

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?getrf_batch_strided

Computes the LU factorization of a group of general m-by-n matrices that are stored at a constant stride from each other in a contiguous block of memory.

Syntax

call sgetrf_batch_strided(m, n, A, lda, stride_a, ipiv, stride_ipiv, batch_size, info)

call dgetrf_batch_strided(m, n, A, lda, stride_a, ipiv, stride_ipiv, batch_size, info)

call cgetrf_batch_strided(m, n, A, lda, stride_a, ipiv, stride_ipiv, batch_size, info)

call zgetrf_batch_strided(m, n, A, lda, stride_a, ipiv, stride_ipiv, batch_size, info)

Include Files

mkl.fi

Description

The ?getrf_batch_strided routines are similar to the ?getrf counterparts, but instead compute the LU factorization for a group of general m-by-n matrices.

All matrices have the same parameters (matrix size, leading dimension) and are stored at constant stride_a from each other in a contiguous block of memory. Their respective pivot arrays associated with each of the LU-factored A_i matrices are stored at constant stride_ipiv from each other. The operation is defined as

for i = 0 … batch_size-1
	A_i is a matrix at offset i * stride_a from A
	ipiv_i is an array at offset i * stride_ipiv from ipiv
	A_i :=  P_i * L_i* U_i
end for

where P_i is a permutation matrix, L_i is lower triangular with unit diagonal elements (lower trapezoidal if m> n) and U_i is upper triangular (upper trapezoidal if m< n). The routine uses partial pivoting, with row interchanges.

Input Parameters

m

INTEGER. The number of rows in the A matrices: m ≥ 0.

n

INTEGER. The number of columns in the A matrices: n ≥ 0.

A

REAL for sgetrf_batch_strided

DOUBLE PRECISION for dgetrf_batch_strided

COMPLEX for cgetrf_batch_strided

DOUBLE COMPLEX for zgetrf_batch_strided

The A array of size at least stride_a * batch_size holding the A_i matrices.

lda

INTEGER. Specifies the leading dimension of the A_i matrices; lda ≥ max(1,m).

stride_a

INTEGER.

Stride between two consecutive A_i matrices; stride_a ≥ lda * n.

stride_ipiv

INTEGER.

Stride between two consecutive pivot arrays; stride_ipiv ≥ min(m, n).

batch_size

INTEGER.

Number of A_i matrices to be factorized. Must be at least 0.

Output Parameters

A

Array holding the LU-factored A_i matrices. Each matrix is overwritten by their respective L_i and U_i factors. The unit diagonal elements of L are not stored.

ipiv

INTEGER

Array of size at least stride_ipiv * batch_size holding the pivot array associated with each of the LU-factored A_i matrices. The pivot array ipiv_i contains the pivot indices associated with matrix A_i; for 1 ≤ j ≤ min(m,n), row j was interchanged with row ipiv_i(j).

info

INTEGER.

Array of size at least batch_size, which reports the factorization status for each matrix.

If info(i) = 0, the execution is successful for A_i.

If info(i) = -j, the j-th parameter had an illegal value for A_i.

If info(i) = j, the j-th diagonal element of U_i is 0. The factorization has been completed, but U_i is exactly singular. Division by 0 will occur if you use the factor U_i for solving a system of linear equations.

After calling this routine with m=n, you can call the following:

?getrs_batch_strided

to solve systems of linear equations of the form with the group of LU-factored matrices.

Related Information

See ?getrf_batch, which computes the LU factorization for a group of general m-by-n matrices that are allocated at a constant stride from each other in the same contiguous block of memory.

Parent topic: Matrix Factorization: LAPACK Computational Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?getrf_batch_strided