?getri_oop

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?getri_oop_batch

Computes the inverses for 1 or more groups of LU factored, n-by-n matrices.

Syntax

call sgetri_oop_batch(n_array, A_array, lda_array, ipiv_array, Ainv_array, ldainv_array, group_count, group_size, info_array)

call dgetri_oop_batch(n_array, A_array, lda_array, ipiv_array, Ainv_array, ldainv_array, group_count, group_size, info_array)

call cgetri_oop_batch(n_array, A_array, lda_array, ipiv_array, Ainv_array, ldainv_array, group_count, group_size, info_array)

call zgetri_oop_batch(n_array, A_array, lda_array, ipiv_array, Ainv_array, ldainv_array, group_count, group_size, info_array)

Include Files

mkl.fi

Description

The ?getri_oop_batch routines are similar to the ?getri counterparts, but instead compute the inverses for groups of n-by-n LU factored matrices, processing one or more groups at once. Each group contains matrices with the same parameters.

The operation is defined as

i = 1
for g = 1 … group_count
    n_g and lda_g in n_array(g) and lda_array(g)
    for j = 1 … group_size(g)
	A_i, Ainv_i, ipiv_i in A_array(i), Ainv_array(i), ipiv_array(i)
	Ainv_i :=  inv(P_i * L_i* U_i)
	i = i + 1
    end for
end for

where P_i is a permutation matrix, L_i is lower triangular with unit diagonal elements and U_i is upper triangular. These routines use partial pivoting, with row interchanges.

A_i and Ainv_i represents matrices stored at the addresses pointed to by A_array and Ainv_array. The dimensions of each matrix is n_g-by-n_g, where n_g is the g-th elements of n_array. Similarly, ipiv_i represents the pivot arrays stored at addresses pointed to by ipiv_array, where the size of the pivoting arrays is n_g.

The number of entries in A_array, Ainv_array and ipiv_array is total_batch_count, which is equal to the sum of all the entries in the array group_size.

Refer to ?getri for a detailed description of the inversion of LU factorized matrices.

Input Parameters

n_array

INTEGER. Array of size group_count. For the group g, n_g = n_array(g) specifies the order of the matrices A_i in group g.

The value of each element of n_array must be at least zero.

A_array

INTEGER*8 for Intel^® 64 architecture

INTEGER*4 for IA-32 architecture

Array, size total_batch_count, of pointers to the A_i matrices.

lda_array

INTEGER. Array of size group_count. For group g, lda_g = lda_array(g) specifies the leading dimension of the matricies A_i in group g, as declared in the calling (sub)program.

The value of lda_g must be at least max(1, n_g).

ipiv_array

INTEGER*8 for Intel^® 64 architecture

INTEGER*4 for IA-32 architecture

Array, size total_batch_count, of pointers to the pivot arrays associated with the LU-factored A_i matrices, as returned by ?getrf_batch.

group_count

INTEGER.

Specifies the number of groups. Must be at least 0.

group_size

INTEGER.

Array of size group_count. The element group_size(g) specifies the number of matrices in group g. Each element in group_size must be at least 0.

Output Parameters

Ainv_array

INTEGER*8 for Intel^® 64 architecture

INTEGER*4 for IA-32 architecture

Array, size total_batch_count, of pointers to the Ainv_i matrices.

Each matrix is overwritten by the n_g-by-n_g matrix inv(A_i).

ldainv_array

INTEGER.

Array of size group_count. For group g, ldainv_g = ldainv_array(g) specifies the leading dimension of the matrices Ainv_i in group g.

The value of ldainv_g must be at least max(1, n_g).

info_array

INTEGER.

Array of size total_batch_count, which reports the inversion 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 the factor U_i is 0, U_i is singular, and the inversion could not be completed.

Related Information

Refer to ?getri_oop_batch_strided , which computes inverses for a group of n-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

?getri_oop_batch