mkl_?trsm_compact

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/31/2023

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mkl_?trsm_compact

Solves a triangular matrix equation for a set of general, m x n matrices that have been stored in Compact format.

Syntax

mkl_strsm_compact (MKL_LAYOUT layout, MKL_SIDE side, MKL_UPLO uplo, MKL_TRANSPOSE transa, MKL_DIAG diag, MKL_INT m, MKL_INT n, float alpha, const float *ap, MKL_INT a_stride, float *bp, MKL_INT b_stide, MKL_COMPACT_PACK format, MKL_INT nm);

mkl_dtrsm_compact (MKL_LAYOUT layout, MKL_SIDE side, MKL_UPLO uplo, MKL_TRANSPOSE transa, MKL_DIAG diag, MKL_INT m, MKL_INT n, double alpha, const double*ap, MKL_INT a_stride, double *bp, MKL_INT b_stride, MKL_COMPACT_PACK format, MKL_INT nm);

mkl_ctrsm_compact (MKL_LAYOUT layout, MKL_SIDE side, MKL_UPLO uplo, MKL_TRANSPOSE transa, MKL_DIAG diag, MKL_INT m, MKL_INT n, mkl_compact_complex_float *alpha, const float *ap, MKL_INT a_stride, float *bp, MKL_INT b_stride, MKL_COMPACT_PACK format, MKL_INT nm);

mkl_ztrsm_compact (MKL_LAYOUT layout, MKL_SIDE side, MKL_UPLO uplo, MKL_TRANSPOSE transa, MKL_DIAG diag, MKL_INT m, MKL_INT n, mkl_compact_complex_double *alpha, const double *ap, MKL_INT a_stride, double *bp, MKL_INT b_stride, MKL_COMPACT_PACK format, MKL_INT nm);

Description

The routine solves one of the following matrix equations for a group of nm matrices:

op(A_c)*X_c = alpha*B_c,

X_c*op(A_c) = alpha*B_c

where:

alpha is a scalar, X_c and B_c are m-by-n matrices that have been stored in compact format, and A_c is a m-by-m unit, or non-unit, upper or lower triangular matrix that has been stored in compact format.

op(A_c) is one of op(A_c) = A_c, or op(A_c) = A_c^T, or op(A_c) = A_c^H,

B_c is overwritten by the solution matrix X_c.

Input Parameters

layout

Specifies whether two-dimensional array storage is row-major (MKL_ROW_MAJOR) or column-major (MKL_COL_MAJOR).

side

Specifies whether op(A_c) appears on the left or right of X_c in the equation:

if side = MKL_LEFT, then op(A_c)*X_c = alpha*B_c, if side = MKL_RIGHT, then X_c*op(A_c) = alpha*B_c

uplo

Specifies whether matrix A_c is upper or lower triangular.

If uplo = MKL_UPPER, A_c is upper triangular.

If uplo = MKL_LOWER, A_c is lower triangular.

transa

Specifies the operation:

If transa=MKL_NOTRANS, then op(A_c) = A_c;

If transa=MKL_TRANS, then op(A_c) = A_c^T;

If transa=MKL_CONJTRANS, then op(A_c) = A_c^H ;

diag

Specifies whether the matrix A_c is unit triangular:

If diag=MKL_UNIT, then the matrix is unit triangular;

if diag=MKL_NONUNIT, then the matrix is not unit triangular.

m

The number of rows of B_c and the number of rows and columns of A_c when side=MKL_LEFT; m >= 0.

n

The number of columns of B_c and the number of rows and columns of A_c when side=MKL_RIGHT; n >= 0.

alpha

Specifies the scalar alpha. When alpha is zero, then ap is not referenced and bp need not be set before entry.

ap

Array, size ldap*k*nm, where k is m when side= MKL_LEFTand n when side = MKL_RIGHT. ap points to the beginning of nm A_c matrices stored in compact format. When uplo = MKL_UPPER, A_c is assumed to be an upper triangular matrix and the lower triangular part of A_c is not referenced. With uplo = MKL_LOWER, A_c is assumed to be a lower triangular matrix and the upper triangular part of A_c is not referenced. With diag = MKL_UNIT, the diagonal elements of A_c are not referenced either, but are assumed to be unity.

ldap

Column stride (column-major layout) or row stride (row-major layout) of A_c.

When side=MKL_LEFT, ldap must be at least max (1,m).

When side=MKL_RIGHT, ldap must be at least max (1,n).

bp

Array, size ldbp*n*nm when layout = MKL_COL_MAJOR; size ldbp*m*nm when layout = MKL_ROW_MAJOR. Before entry, bp points to the beginning of nm B_c matrices stored in compact format.

ldbp

Column stride (column-major layout) or row stride (row-major layout) of B_c.

layout = MKL_COL_MAJOR	ldbp must be at least max (1,m).
layout = MKL_ROW_MAJOR	*ldbp must be at least max (1,n).

format

Specifies the format of the compact matrices. See <Compact Format> or mkl_get_format_compact for details.

nm

Total number of matrices stored in Compact format; nm >= 0.

NOTE:

The values of ldap and ldbp used in mkl_?trsm_compact must be consistent with the values used in mkl_?get_size_compact, mkl_?gepack_compact, and mkl_?geunpack_compact.

Output Parameters

bp: On exit, B_c is overwritten by the solution matrix X_c. bp points to the beginning of nm such X_c matrices.

Parent topic: Compact BLAS and LAPACK Functions

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Developer Reference for Intel® oneAPI Math Kernel Library for C

mkl_?trsm_compact