?getrs_batch

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?getrs_batch_strided

Solves a group of systems of linear equations, each with an LU-factored square coefficient matrix and multiple right hand sides.

Syntax

call sgetrs_batch_strided ( trans , n , nrhs , A , lda , stride_a , ipiv , stride_ipiv , b , ldb , stride_b , batch_size , info )

call dgetrs_batch_strided ( trans , n , nrhs , A , lda , stride_a , ipiv , stride_ipiv , b , ldb , stride_b , batch_size , info )

call cgetrs_batch_strided ( trans , n , nrhs , A , lda , stride_a , ipiv , stride_ipiv , b , ldb , stride_b , batch_size , info )

call zgetrs_batch_strided ( trans , n , nrhs , A , lda , stride_a , ipiv , stride_ipiv , b , ldb , stride_b , batch_size , info )

Include Files

mkl.fi

Description

The ?getrs_batch_strided routines are similar to the ?getrs counterparts, but instead solve a group of systems of linear equations. Before calling this routine, you must call ?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.) to compute the LU factorization of the square coefficient matrix of each linear system.

All coefficient matrices, A_i have the same parameters (matrix size, leading dimension) and are stored at constant stride_a from each other. Similarly, all right-hand-side matrices, B_i , have the same parameters and are stored at constant stride_b from each other. The respective pivot array 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}, B_{i} are matrices at offset i * stride_a, i * stride_b from A and B
    ipiv_{i} is an array at offset i * stride_ipiv from ipiv

    Solve the system
    * A_{i} * x_{i}   = B_{i}  , if trans='N'
    * X^T_{i} * x_{i} = B_{i}  , if trans='T'
    * X^H_{i} * x_{i} = B_{i}  , if trans='C' (for complex matrices)
end for

Input Parameters

trans

CHARACTER*1 . Must be ‘N’, ‘T’, or ‘C’.

Indicates the form of the systems of linear equations:

If trans = ‘N’, \(A_i X_i = B_i\) is solved for \(X_i\) .

If trans = ‘T’, \(A_i X_i^T = B_i\) is solved for \(X_i\) .

If trans = ‘C’, \(A_i X_i^H = B_i\) is solved for \(X_i\) .

n

INTEGER . The order fo the A_i matrices; n ≥ 0.

nrhs

INTEGER . The number of right hand sides in each linear system of equations ( nrhs ≥ 0).

A, B: REAL for sgetrs_batch_strided DOUBLE PRECISION for dgetrs_batch_strided COMPLEX for cgetrs_batch_strided DOUBLE COMPLEX for zgetrs_batch_strided The A array of size at least stride_a * batch_size holding the LU-factorized A_i matrices resulting from the call to ?getrf_batch_strided . The B array of size at least stride_b * batch_size holding the B_i matrices, whose columns are the right -hand sides for each linear system of equations.

lda

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

ldb

INTEGER . Specifies the leading dimension of the B_i matrices; ldb ≥ max(1, n ).

stride_a: INTEGER . Stride between two consecutive A_i matrices; stride_a ≥ lda * n .
stride_b: INTEGER . Stride between two consecutive B_i matrices; stride_b ≥ ldb * nrhs .
ipiv: INTEGER . Array of size at least stride_ipiv * batch_size holding the pivoting indices for each LU-factorized matrix A_i .
stride_ipiv: INTEGER . Stride between two consecutive pivot arrays; stride_ipiv ≥ n ).
batch_size: INTEGER . Number of linear systems to be solved; batch_size ≥ 0.

Output Parameters

B: Array is overwritten by the solution matrices X_i .

info

INTEGER .

Array of size at least batch_size , which reports the status for each linear system solve.
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 .

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