cblas_?gemmt

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/31/2023

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cblas_?gemmt

Computes a matrix-matrix product with general matrices but updates only the upper or lower triangular part of the result matrix.

Syntax

void cblas_sgemmt (const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE transa, const CBLAS_TRANSPOSE transb, const MKL_INT n, const MKL_INT k, 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_dgemmt (const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE transa, const CBLAS_TRANSPOSE transb, const MKL_INT n, const MKL_INT k, 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_cgemmt (const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE transa, const CBLAS_TRANSPOSE transb, const MKL_INT n, const MKL_INT k, 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_zgemmt (const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE transa, const CBLAS_TRANSPOSE transb, const MKL_INT n, const MKL_INT k, 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 ?gemmt routines compute a scalar-matrix-matrix product with general matrices and add the result to the upper or lower part of a scalar-matrix product. These routines are similar to the ?gemm routines, but they only access and update a triangular part of the square result matrix (see Application Notes below).

The operation is defined as

C := alpha*op(A)*op(B) + beta*C,

where:

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

alpha and beta are scalars,

A, B and C are matrices:

op(A) is an n-by-k matrix,

op(B) is a k-by-n matrix,

C is an n-by-n upper or lower triangular matrix.

Input Parameters

Layout

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

uplo

Specifies whether the upper or lower triangular part of the array c is used. If uplo = 'CblasUpper', then the upper triangular part of the array c is used. If uplo = 'CblasLower', then the lower triangular part of the array c is used.

transa

Specifies the form of op(A) used in the matrix multiplication:

if transa = 'CblasNoTrans', then op(A) = A;

if transa = 'CblasTrans', then op(A) = A^T;

if transa = 'CblasConjTrans', then op(A) = A^H.

transb

Specifies the form of op(B) used in the matrix multiplication:

if transb = 'CblasNoTrans', then op(B) = B;

if transb = 'CblasTrans', then op(B) = B^T;

if transb = 'CblasConjTrans', then op(B) = B^H.

n

Specifies the order of the matrix C. The value of n must be at least zero.

k

Specifies the number of columns of the matrix op(A) and the number of rows of the matrix op(B). The value of k must be at least zero.

alpha

Specifies the scalar alpha.

a

	transa=`'CblasNoTrans'`	transa=`'CblasTrans' or 'CblasConjTrans'`
`Layout`=`'CblasColMajor'`	Array, size lda * `k`. Before entry, the leading n-by-k part of the array a must contain the matrix `A`.	Array, size lda * `n`. Before entry, the leading k-by-n part of the array a must contain the matrix `A`.
`Layout`=`'CblasRowMajor'`	Array, size lda * `n`. Before entry, the leading k-by-n part of the array a must contain the matrix `A`.	Array, size lda * `k`. Before entry, the leading n-by-k part of the array a must contain the matrix `A`.

lda

Specifies the leading dimension of a as declared in the calling (sub)program.

	transa=`'CblasNoTrans'`	transa=`'CblasTrans' or 'CblasConjTrans'`
`Layout`=`'CblasColMajor'`	lda must be at least max(1, n).	lda must be at least max(1, k).
`Layout`=`'CblasRowMajor'`	lda must be at least max(1, k).	lda must be at least max(1, n).

b

	transb=`'CblasNoTrans'`	transb=`'CblasTrans' or 'CblasConjTrans'`
`Layout`=`'CblasColMajor'`	Array, size ldb * `n`. Before entry, the leading k-by-n part of the array b must contain the matrix `B`.	Array, size ldb * `k`. Before entry, the leading n-by-k part of the array b must contain the matrix `B`.
`Layout`=`'CblasRowMajor'`	Array, size ldb * `k`. Before entry, the leading n-by-k part of the array b must contain the matrix `B`.	Array, size ldb * `n`. Before entry, the leading k-by-n part of the array b must contain the matrix `B`.

ldb

Specifies the leading dimension of b as declared in the calling (sub)program.

	transb=`'CblasNoTrans'`	transb=`'CblasTrans' or 'CblasConjTrans'`
`Layout`=`'CblasColMajor'`	ldb must be at least max(1, k).	ldb must be at least max(1, n).
`Layout`=`'CblasRowMajor'`	ldb must be at least max(1, n).	ldb must be at least max(1, k).

beta

Specifies the scalar beta. When beta is equal to zero, then c need not be set on input.

c

Array, size ldc by n.

When beta is equal to zero, c need not be set on input.

uplo = `'CblasUpper'`	uplo = `'CblasLower'`
The leading n-by-n upper triangular part of the array c must contain the upper triangular part of the matrix `C` and the strictly lower triangular part of c is not referenced.	The leading n-by-n lower triangular part of the array c must contain the lower triangular part of the matrix `C` and the strictly upper triangular part of c is not referenced.

ldc

Specifies the leading dimension of c as declared in the calling (sub)program. The value of ldc must be at least max(1, n).

Output Parameters

c	When uplo = `'CblasUpper'`, the upper triangular part of the array c is overwritten by the upper triangular part of the updated matrix. When uplo = `'CblasLower'`, the lower triangular part of the array c is overwritten by the lower triangular part of the updated matrix.

Application Notes

These routines only access and update the upper or lower triangular part of the result matrix. This can be useful when the result is known to be symmetric; for example, when computing a product of the form C := alpha*B*S*B^T + beta*C , where S and C are symmetric matrices and B is a general matrix. In this case, first compute A := B*S (which can be done using the corresponding ?symm routine), then compute C := alpha*A*B^T + beta*C using the ?gemmt routine.

Parent topic: BLAS-like Extensions

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Developer Reference for Intel® oneAPI Math Kernel Library for C

cblas_?gemmt