Intel® oneAPI Math Kernel Library Developer Reference - Fortran
Computes the LU factorization for 1 or more groups of general m-by-n matrices.
call sgetrf_batch(m_array, n_array, A_array, lda_array, ipiv_array, group_size, group_count, info_array)
call dgetrf_batch(m_array, n_array, A_array, lda_array, ipiv_array, group_size, group_count, info_array)
call cgetrf_batch(m_array, n_array, A_array, lda_array, ipiv_array, group_size, group_count, info_array)
call zgetrf_batch(m_array, n_array, A_array, lda_array, ipiv_array, group_size, group_count, info_array)
mkl.fi
The ?getrf_batch routines are similar to the ?getrf counterparts, but instead compute the LU factorization for a group of general m-by-n 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
mg ng and ldag in m_array(g), n_array(g) and lda_array(g)
for j = 1 … group_size(g)
Ai, ipivi in A_array(i), ipiv_array(i)
Ai := Pi * Li * Ui
i = i + 1
end for
end for
where Pi is a permutation matrix, Li is lower triangular with unit diagonal elements (lower trapezoidal if mg> ng) and Ui is upper triangular (upper trapezoidal if mg< ng). These routines use partial pivoting, with row interchanges.
Ai represents matrices stored at the addresses pointed to by A_array. The dimensions of each matrix is mg-by-ng, where mg and ng are the g-th elements of m_array and n_array, respectively. Similarly, ipivi represents the pivot arrays stored at addresses pointed to by ipiv_array, where the size of the pivoting arrays is min(mg, ng).
The number of entries in A_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 ?getrf for a detailed description of the LU factorization of general matrices.
INTEGER. Array of size group_count. For the group g, mg = m_array(g) specifies the number of rows of the matrices Ai in group g.
The value of each element of m_array must be at least zero.
INTEGER. Array of size group_count. For the group g, ng = n_array(g) specifies the number of columns of the matrices Ai in group g.
The value of each element of n_array must be at least zero.
INTEGER*8 for Intel® 64 architecture
INTEGER*4 for IA-32 architecture
Array, size total_batch_count, of pointers to arrays used to store Ai matrices.
INTEGER. Array of size group_count. For group g, ldag = lda_array(g) specifies the leading dimension of the matricies Ai in group g, as declared in the calling (sub)program.
The value of ldag must be at least max(1, mg).
INTEGER.
Specifies the number of groups. Must be at least 0.
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 array, overwritten by the total_batch_count LU-factored matrices. Each matrix Ai is overwritten by Li and Ui. The unit diagonal elements of Li are not stored.
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 Ai matrices.
INTEGER.
Array of size total_batch_count, which reports the factorization status for each matrix.
If info(i) = 0, the execution is successful for Ai.
If info(i) = -j, the j-th parameter had an illegal value for Ai.
If info(i) = j, the j-th diagonal element of Ui is 0. The factorization has been completed, but Ui is exactly singular. Division by 0 will occur if you use the factor Ui for solving a system of linear equations.
Refer to ?getrf_batch_strided , 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.