cblas_?trsm

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 6/30/2025

Version

Public

cblas_?trsm_oop

Solves a triangular matrix equation and adds the result to another scaled matrix.

Syntax

void cblas_strsm_oop (
    const CBLAS_LAYOUT layout, const CBLAS_SIDE side, const CBLAS_UPLO uplo,
    const CBLAS_TRANSPOSE transa, const CBLAS_DIAG diag, const MKL_INT m,
    const MKL_INT n, const float alpha, const float *a, const MKL_INT lda,
    const float *b, const MKL_INT ldb, const float beta, float *c,
    const MKL_INT ldc);

void cblas_dtrsm_oop (
    const CBLAS_LAYOUT layout, const CBLAS_SIDE side, const CBLAS_UPLO uplo,
    const CBLAS_TRANSPOSE transa, const CBLAS_DIAG diag, const MKL_INT m,
    const MKL_INT n, const double alpha, const double *a, const MKL_INT lda,
    const double *b, const MKL_INT ldb, const double beta, double *c,
    const MKL_INT ldc);

void cblas_ctrsm_oop (
    const CBLAS_LAYOUT layout, const CBLAS_SIDE side,
    const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE transa,
    const CBLAS_DIAG diag, const MKL_INT m, const MKL_INT n,
    const void* alpha, const void *a, const MKL_INT lda, const void *b,
    const MKL_INT ldb, const void* beta, void *c, const MKL_INT ldc);

void cblas_ztrsm_oop (
    const CBLAS_LAYOUT layout, const CBLAS_SIDE side,
    const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE transa,
    const CBLAS_DIAG diag, const MKL_INT m, const MKL_INT n,
    const void* alpha, const void *a, const MKL_INT lda, const void *b,
    const MKL_INT ldb, const void* beta, void *c, const MKL_INT ldc);

Include Files

mkl.h

Description

The cblas_?trsm_oop routines perform a triangular matrix solve followed by a scaled matrix addition.

For a left-side solve, the routine solves

op(A)*X=alpha*B

for x and then computes

C := X + beta*C

For a right-side solve, the routine solves

X*op(A)=alpha*B

followed by the same-scaled addition

C := X + beta*C

where:

alpha and beta are scalars.
A is a unit or non-unit upper or lower triangular matrix.
B is an m-by-n matrix.
C is an m-by-n matrix.
op(A) is one of op(A) = A, op(A) = A', or op(A) = conjg(A').

Input Parameters

layout

Specifies whether two-dimensional array storage is row-major (CblasRowMajor) or column-major (CblasColMajor).

side

Specifies whether op(A) appears on the left or right of B in the triangular solve.

If side = CblasLeft, then we solve op(A)*X = alpha*B before performing C := X + beta*C.

If side = CblasRight, then we solve X*op(A) = alpha*B before performing C := X + beta*C.

uplo

Specifies whether the matrix A is upper or lower triangular.

If uplo = CblasUpper, then the matrix is upper triangular.

If uplo = CblasLower, then the matrix is lower triangular.

transa

Specifies the form of op(A) used in the triangular solve.

If transa=CblasNoTrans, then op(A) = A.

If transa=CblasTrans, then op(A) = A'.

If transa=CblasConjTrans, then op(A) = conjg(A').

diag

Specifies whether the matrix A is unit triangular.

If diag = CblasUnit then the matrix is unit triangular.

If diag = CblasNonUnit, then the matrix is not unit triangular.

m

Specifies the number of rows of matrix B. The value of m must be at least zero.

n

Specifies the number of columns of matrix B. The value of n must be at least zero.

alpha

Specifies the scalar alpha.

a

Array of size lda*k, where k is m when side = CblasLeft and k is n when side = CblasRight.

Before entry with uplo = CblasUpper, the leading k by k upper triangular part of the array a must contain the upper triangular matrix and the strictly lower triangular part of a is not referenced.

Before entry with uplo = CblasLower the lower triangular part of the array a must contain the lower triangular matrix and the strictly upper triangular part of a is not referenced.

When diag = CblasUnit, the diagonal elements of a are not referenced either, but are assumed to be unity.

lda

Specifies the leading dimension of a. When side = CblasLeft, then lda must be at least max(1, m). When side = CblasRight, then lda must be at least max(1, n).

b

For layout = CblasColMajor, array of size ldb*n. Before entry, the leading m-by-n part of the array b must contain the matrix B.

For layout = CblasRowMajor, array of size ldb*m. Before entry, the leading n-by-m part of the array b must contain the matrix B.

ldb

Specifies the leading dimension of b. When layout = CblasColMajor, ldb must be at least max(1, m); otherwise, ldb must be at least max(1, n).

beta

Specifies the scalar beta.

c

For layout = CblasColMajor, array of size ldc*n. Before entry, the leading m-by-n part of the array c must contain the matrix C.

For layout = CblasRowMajor, array of size ldc*m. Before entry, the leading n-by-m part of the array c must contain the matrix C.

ldc

Specifies the leading dimension of c. When layout = CblasColMajor, ldc must be at least max(1, m); otherwise, ldc must be at least max(1, n).

Output Parameters

c: Output matrix overwritten by the operation.

Parent topic: BLAS Level 3 Routines

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