MAGMA  2.3.0 Matrix Algebra for GPU and Multicore Architectures
hemm: Hermitian matrix multiply

$$C = \alpha A B + \beta C$$ or $$C = \alpha B A + \beta C$$ where $$A$$ is Hermitian More...

## Functions

void magma_chemm (magma_side_t side, magma_uplo_t uplo, magma_int_t m, magma_int_t n, magmaFloatComplex alpha, magmaFloatComplex_const_ptr dA, magma_int_t ldda, magmaFloatComplex_const_ptr dB, magma_int_t lddb, magmaFloatComplex beta, magmaFloatComplex_ptr dC, magma_int_t lddc, magma_queue_t queue)
Perform Hermitian matrix-matrix product. More...

void magma_zhemm (magma_side_t side, magma_uplo_t uplo, magma_int_t m, magma_int_t n, magmaDoubleComplex alpha, magmaDoubleComplex_const_ptr dA, magma_int_t ldda, magmaDoubleComplex_const_ptr dB, magma_int_t lddb, magmaDoubleComplex beta, magmaDoubleComplex_ptr dC, magma_int_t lddc, magma_queue_t queue)
Perform Hermitian matrix-matrix product. More...

void magmablas_chemm_mgpu (magma_side_t side, magma_uplo_t uplo, magma_int_t m, magma_int_t n, magmaFloatComplex alpha, magmaFloatComplex_ptr dA[], magma_int_t ldda, magma_int_t offset, magmaFloatComplex_ptr dB[], magma_int_t lddb, magmaFloatComplex beta, magmaFloatComplex_ptr dC[], magma_int_t lddc, magmaFloatComplex_ptr dwork[], magma_int_t dworksiz, magma_int_t ngpu, magma_int_t nb, magma_queue_t queues[][20], magma_int_t nqueue, magma_event_t events[][MagmaMaxGPUs *MagmaMaxGPUs+10], magma_int_t nevents, magma_int_t gnode[MagmaMaxGPUs][MagmaMaxGPUs+2], magma_int_t ncmplx)
CHEMM performs one of the matrix-matrix operations. More...

void magmablas_dsymm_mgpu (magma_side_t side, magma_uplo_t uplo, magma_int_t m, magma_int_t n, double alpha, magmaDouble_ptr dA[], magma_int_t ldda, magma_int_t offset, magmaDouble_ptr dB[], magma_int_t lddb, double beta, magmaDouble_ptr dC[], magma_int_t lddc, magmaDouble_ptr dwork[], magma_int_t dworksiz, magma_int_t ngpu, magma_int_t nb, magma_queue_t queues[][20], magma_int_t nqueue, magma_event_t events[][MagmaMaxGPUs *MagmaMaxGPUs+10], magma_int_t nevents, magma_int_t gnode[MagmaMaxGPUs][MagmaMaxGPUs+2], magma_int_t ncmplx)
DSYMM performs one of the matrix-matrix operations. More...

void magmablas_ssymm_mgpu (magma_side_t side, magma_uplo_t uplo, magma_int_t m, magma_int_t n, float alpha, magmaFloat_ptr dA[], magma_int_t ldda, magma_int_t offset, magmaFloat_ptr dB[], magma_int_t lddb, float beta, magmaFloat_ptr dC[], magma_int_t lddc, magmaFloat_ptr dwork[], magma_int_t dworksiz, magma_int_t ngpu, magma_int_t nb, magma_queue_t queues[][20], magma_int_t nqueue, magma_event_t events[][MagmaMaxGPUs *MagmaMaxGPUs+10], magma_int_t nevents, magma_int_t gnode[MagmaMaxGPUs][MagmaMaxGPUs+2], magma_int_t ncmplx)
SSYMM performs one of the matrix-matrix operations. More...

void magmablas_zhemm_mgpu (magma_side_t side, magma_uplo_t uplo, magma_int_t m, magma_int_t n, magmaDoubleComplex alpha, magmaDoubleComplex_ptr dA[], magma_int_t ldda, magma_int_t offset, magmaDoubleComplex_ptr dB[], magma_int_t lddb, magmaDoubleComplex beta, magmaDoubleComplex_ptr dC[], magma_int_t lddc, magmaDoubleComplex_ptr dwork[], magma_int_t dworksiz, magma_int_t ngpu, magma_int_t nb, magma_queue_t queues[][20], magma_int_t nqueue, magma_event_t events[][MagmaMaxGPUs *MagmaMaxGPUs+10], magma_int_t nevents, magma_int_t gnode[MagmaMaxGPUs][MagmaMaxGPUs+2], magma_int_t ncmplx)
ZHEMM performs one of the matrix-matrix operations. More...

## Detailed Description

$$C = \alpha A B + \beta C$$ or $$C = \alpha B A + \beta C$$ where $$A$$ is Hermitian

## Function Documentation

 void magma_chemm ( magma_side_t side, magma_uplo_t uplo, magma_int_t m, magma_int_t n, magmaFloatComplex alpha, magmaFloatComplex_const_ptr dA, magma_int_t ldda, magmaFloatComplex_const_ptr dB, magma_int_t lddb, magmaFloatComplex beta, magmaFloatComplex_ptr dC, magma_int_t lddc, magma_queue_t queue )

Perform Hermitian matrix-matrix product.

$$C = \alpha A B + \beta C$$ (side == MagmaLeft), or
$$C = \alpha B A + \beta C$$ (side == MagmaRight),
where $$A$$ is Hermitian.

Parameters
 [in] side Whether A is on the left or right. [in] uplo Whether the upper or lower triangle of A is referenced. [in] m Number of rows of C. m >= 0. [in] n Number of columns of C. n >= 0. [in] alpha Scalar $$\alpha$$ [in] dA COMPLEX array on GPU device. If side == MagmaLeft, the m-by-m Hermitian matrix A of dimension (ldda,m), ldda >= max(1,m); otherwise, the n-by-n Hermitian matrix A of dimension (ldda,n), ldda >= max(1,n). [in] ldda Leading dimension of dA. [in] dB COMPLEX array on GPU device. The m-by-n matrix B of dimension (lddb,n), lddb >= max(1,m). [in] lddb Leading dimension of dB. [in] beta Scalar $$\beta$$ [in,out] dC COMPLEX array on GPU device. The m-by-n matrix C of dimension (lddc,n), lddc >= max(1,m). [in] lddc Leading dimension of dC. [in] queue magma_queue_t Queue to execute in.
 void magma_zhemm ( magma_side_t side, magma_uplo_t uplo, magma_int_t m, magma_int_t n, magmaDoubleComplex alpha, magmaDoubleComplex_const_ptr dA, magma_int_t ldda, magmaDoubleComplex_const_ptr dB, magma_int_t lddb, magmaDoubleComplex beta, magmaDoubleComplex_ptr dC, magma_int_t lddc, magma_queue_t queue )

Perform Hermitian matrix-matrix product.

$$C = \alpha A B + \beta C$$ (side == MagmaLeft), or
$$C = \alpha B A + \beta C$$ (side == MagmaRight),
where $$A$$ is Hermitian.

Parameters
 [in] side Whether A is on the left or right. [in] uplo Whether the upper or lower triangle of A is referenced. [in] m Number of rows of C. m >= 0. [in] n Number of columns of C. n >= 0. [in] alpha Scalar $$\alpha$$ [in] dA COMPLEX_16 array on GPU device. If side == MagmaLeft, the m-by-m Hermitian matrix A of dimension (ldda,m), ldda >= max(1,m); otherwise, the n-by-n Hermitian matrix A of dimension (ldda,n), ldda >= max(1,n). [in] ldda Leading dimension of dA. [in] dB COMPLEX_16 array on GPU device. The m-by-n matrix B of dimension (lddb,n), lddb >= max(1,m). [in] lddb Leading dimension of dB. [in] beta Scalar $$\beta$$ [in,out] dC COMPLEX_16 array on GPU device. The m-by-n matrix C of dimension (lddc,n), lddc >= max(1,m). [in] lddc Leading dimension of dC. [in] queue magma_queue_t Queue to execute in.
 void magmablas_chemm_mgpu ( magma_side_t side, magma_uplo_t uplo, magma_int_t m, magma_int_t n, magmaFloatComplex alpha, magmaFloatComplex_ptr dA[], magma_int_t ldda, magma_int_t offset, magmaFloatComplex_ptr dB[], magma_int_t lddb, magmaFloatComplex beta, magmaFloatComplex_ptr dC[], magma_int_t lddc, magmaFloatComplex_ptr dwork[], magma_int_t dworksiz, magma_int_t ngpu, magma_int_t nb, magma_queue_t queues[][20], magma_int_t nqueue, magma_event_t events[][MagmaMaxGPUs *MagmaMaxGPUs+10], magma_int_t nevents, magma_int_t gnode[MagmaMaxGPUs][MagmaMaxGPUs+2], magma_int_t ncmplx )

CHEMM performs one of the matrix-matrix operations.

C := alpha*A*B + beta*C,


or C := alpha*B*A + beta*C,

where alpha and beta are scalars, A is a Hermitian matrix, and B and C are m by n matrices.

Parameters
 [in] side magma_side_t On entry, SIDE specifies whether the Hermitian matrix A appears on the left or right in the operation as follows:

SIDE = MagmaLeft C := alpha*A*B + beta*C,

SIDE = MagmaRight C := alpha*B*A + beta*C.

Currently, only MagmaLeft is implemented ***

Parameters
 [in] uplo magma_uplo_t On entry, UPLO specifies whether the upper or lower triangular part of the Hermitian matrix A is to be referenced as follows:

UPLO = MagmaUpper Only the upper triangular part of the Hermitian matrix is to be referenced.

UPLO = MagmaLower Only the lower triangular part of the Hermitian matrix is to be referenced.

Currently, only MagmaLower is implemented ***

Parameters
 [in] m INTEGER On entry, M specifies the number of rows of the matrix dC. M >= 0. [in] n INTEGER On entry, N specifies the number of columns of the matrix dC. N >= 0. [in] alpha COMPLEX On entry, ALPHA specifies the scalar alpha. [in] dA COMPLEX array of DIMENSION ( LDDA, ka ), where ka is m when SIDE = MagmaLower and is n otherwise. Before entry with SIDE = MagmaLeft, the m by m part of the array A must contain the Hermitian matrix, such that when UPLO = MagmaUpper, the leading m by m upper triangular part of the array A must contain the upper triangular part of the Hermitian matrix and the strictly lower triangular part of A is not referenced, and when UPLO = MagmaLower, the leading m by m lower triangular part of the array A must contain the lower triangular part of the Hermitian matrix and the strictly upper triangular part of A is not referenced. Before entry with SIDE = MagmaRight, the n by n part of the array A must contain the Hermitian matrix, such that when UPLO = MagmaUpper, the leading n by n upper triangular part of the array A must contain the upper triangular part of the Hermitian matrix and the strictly lower triangular part of A is not referenced, and when UPLO = MagmaLower, the leading n by n lower triangular part of the array A must contain the lower triangular part of the Hermitian matrix and the strictly upper triangular part of A is not referenced. Note that the imaginary parts of the diagonal elements need not be set, they are assumed to be zero. [in] ldda INTEGER On entry, LDDA specifies the first dimension of A as declared in the calling (sub) program. When SIDE = MagmaLower then LDDA >= max( 1, m ), otherwise LDDA >= max( 1, n ). [in] dB COMPLEX array of DIMENSION ( LDDB, n ). Before entry, the leading m by n part of the array B must contain the matrix B. [in] lddb INTEGER On entry, LDDB specifies the first dimension of B as declared in the calling (sub) program. LDDB >= max( 1, m ). [in] beta COMPLEX On entry, BETA specifies the scalar beta. When BETA is supplied as zero then C need not be set on input. [in,out] dC COMPLEX array of DIMENSION ( LDDC, n ). Before entry, the leading m by n part of the array C must contain the matrix C, except when beta is zero, in which case C need not be set on entry. On exit, the array C is overwritten by the m by n updated matrix. [in] lddc INTEGER On entry, LDDC specifies the first dimension of C as declared in the calling (sub) program. LDDC >= max( 1, m ).
 void magmablas_dsymm_mgpu ( magma_side_t side, magma_uplo_t uplo, magma_int_t m, magma_int_t n, double alpha, magmaDouble_ptr dA[], magma_int_t ldda, magma_int_t offset, magmaDouble_ptr dB[], magma_int_t lddb, double beta, magmaDouble_ptr dC[], magma_int_t lddc, magmaDouble_ptr dwork[], magma_int_t dworksiz, magma_int_t ngpu, magma_int_t nb, magma_queue_t queues[][20], magma_int_t nqueue, magma_event_t events[][MagmaMaxGPUs *MagmaMaxGPUs+10], magma_int_t nevents, magma_int_t gnode[MagmaMaxGPUs][MagmaMaxGPUs+2], magma_int_t ncmplx )

DSYMM performs one of the matrix-matrix operations.

C := alpha*A*B + beta*C,


or C := alpha*B*A + beta*C,

where alpha and beta are scalars, A is a symmetric matrix, and B and C are m by n matrices.

Parameters
 [in] side magma_side_t On entry, SIDE specifies whether the symmetric matrix A appears on the left or right in the operation as follows:

SIDE = MagmaLeft C := alpha*A*B + beta*C,

SIDE = MagmaRight C := alpha*B*A + beta*C.

Currently, only MagmaLeft is implemented ***

Parameters
 [in] uplo magma_uplo_t On entry, UPLO specifies whether the upper or lower triangular part of the symmetric matrix A is to be referenced as follows:

UPLO = MagmaUpper Only the upper triangular part of the symmetric matrix is to be referenced.

UPLO = MagmaLower Only the lower triangular part of the symmetric matrix is to be referenced.

Currently, only MagmaLower is implemented ***

Parameters
 [in] m INTEGER On entry, M specifies the number of rows of the matrix dC. M >= 0. [in] n INTEGER On entry, N specifies the number of columns of the matrix dC. N >= 0. [in] alpha DOUBLE PRECISION On entry, ALPHA specifies the scalar alpha. [in] dA DOUBLE PRECISION array of DIMENSION ( LDDA, ka ), where ka is m when SIDE = MagmaLower and is n otherwise. Before entry with SIDE = MagmaLeft, the m by m part of the array A must contain the symmetric matrix, such that when UPLO = MagmaUpper, the leading m by m upper triangular part of the array A must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of A is not referenced, and when UPLO = MagmaLower, the leading m by m lower triangular part of the array A must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of A is not referenced. Before entry with SIDE = MagmaRight, the n by n part of the array A must contain the symmetric matrix, such that when UPLO = MagmaUpper, the leading n by n upper triangular part of the array A must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of A is not referenced, and when UPLO = MagmaLower, the leading n by n lower triangular part of the array A must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of A is not referenced. Note that the imaginary parts of the diagonal elements need not be set, they are assumed to be zero. [in] ldda INTEGER On entry, LDDA specifies the first dimension of A as declared in the calling (sub) program. When SIDE = MagmaLower then LDDA >= max( 1, m ), otherwise LDDA >= max( 1, n ). [in] dB DOUBLE PRECISION array of DIMENSION ( LDDB, n ). Before entry, the leading m by n part of the array B must contain the matrix B. [in] lddb INTEGER On entry, LDDB specifies the first dimension of B as declared in the calling (sub) program. LDDB >= max( 1, m ). [in] beta DOUBLE PRECISION On entry, BETA specifies the scalar beta. When BETA is supplied as zero then C need not be set on input. [in,out] dC DOUBLE PRECISION array of DIMENSION ( LDDC, n ). Before entry, the leading m by n part of the array C must contain the matrix C, except when beta is zero, in which case C need not be set on entry. On exit, the array C is overwritten by the m by n updated matrix. [in] lddc INTEGER On entry, LDDC specifies the first dimension of C as declared in the calling (sub) program. LDDC >= max( 1, m ).
 void magmablas_ssymm_mgpu ( magma_side_t side, magma_uplo_t uplo, magma_int_t m, magma_int_t n, float alpha, magmaFloat_ptr dA[], magma_int_t ldda, magma_int_t offset, magmaFloat_ptr dB[], magma_int_t lddb, float beta, magmaFloat_ptr dC[], magma_int_t lddc, magmaFloat_ptr dwork[], magma_int_t dworksiz, magma_int_t ngpu, magma_int_t nb, magma_queue_t queues[][20], magma_int_t nqueue, magma_event_t events[][MagmaMaxGPUs *MagmaMaxGPUs+10], magma_int_t nevents, magma_int_t gnode[MagmaMaxGPUs][MagmaMaxGPUs+2], magma_int_t ncmplx )

SSYMM performs one of the matrix-matrix operations.

C := alpha*A*B + beta*C,


or C := alpha*B*A + beta*C,

where alpha and beta are scalars, A is a symmetric matrix, and B and C are m by n matrices.

Parameters
 [in] side magma_side_t On entry, SIDE specifies whether the symmetric matrix A appears on the left or right in the operation as follows:

SIDE = MagmaLeft C := alpha*A*B + beta*C,

SIDE = MagmaRight C := alpha*B*A + beta*C.

Currently, only MagmaLeft is implemented ***

Parameters
 [in] uplo magma_uplo_t On entry, UPLO specifies whether the upper or lower triangular part of the symmetric matrix A is to be referenced as follows:

UPLO = MagmaUpper Only the upper triangular part of the symmetric matrix is to be referenced.

UPLO = MagmaLower Only the lower triangular part of the symmetric matrix is to be referenced.

Currently, only MagmaLower is implemented ***

Parameters
 [in] m INTEGER On entry, M specifies the number of rows of the matrix dC. M >= 0. [in] n INTEGER On entry, N specifies the number of columns of the matrix dC. N >= 0. [in] alpha REAL On entry, ALPHA specifies the scalar alpha. [in] dA REAL array of DIMENSION ( LDDA, ka ), where ka is m when SIDE = MagmaLower and is n otherwise. Before entry with SIDE = MagmaLeft, the m by m part of the array A must contain the symmetric matrix, such that when UPLO = MagmaUpper, the leading m by m upper triangular part of the array A must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of A is not referenced, and when UPLO = MagmaLower, the leading m by m lower triangular part of the array A must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of A is not referenced. Before entry with SIDE = MagmaRight, the n by n part of the array A must contain the symmetric matrix, such that when UPLO = MagmaUpper, the leading n by n upper triangular part of the array A must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of A is not referenced, and when UPLO = MagmaLower, the leading n by n lower triangular part of the array A must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of A is not referenced. Note that the imaginary parts of the diagonal elements need not be set, they are assumed to be zero. [in] ldda INTEGER On entry, LDDA specifies the first dimension of A as declared in the calling (sub) program. When SIDE = MagmaLower then LDDA >= max( 1, m ), otherwise LDDA >= max( 1, n ). [in] dB REAL array of DIMENSION ( LDDB, n ). Before entry, the leading m by n part of the array B must contain the matrix B. [in] lddb INTEGER On entry, LDDB specifies the first dimension of B as declared in the calling (sub) program. LDDB >= max( 1, m ). [in] beta REAL On entry, BETA specifies the scalar beta. When BETA is supplied as zero then C need not be set on input. [in,out] dC REAL array of DIMENSION ( LDDC, n ). Before entry, the leading m by n part of the array C must contain the matrix C, except when beta is zero, in which case C need not be set on entry. On exit, the array C is overwritten by the m by n updated matrix. [in] lddc INTEGER On entry, LDDC specifies the first dimension of C as declared in the calling (sub) program. LDDC >= max( 1, m ).
 void magmablas_zhemm_mgpu ( magma_side_t side, magma_uplo_t uplo, magma_int_t m, magma_int_t n, magmaDoubleComplex alpha, magmaDoubleComplex_ptr dA[], magma_int_t ldda, magma_int_t offset, magmaDoubleComplex_ptr dB[], magma_int_t lddb, magmaDoubleComplex beta, magmaDoubleComplex_ptr dC[], magma_int_t lddc, magmaDoubleComplex_ptr dwork[], magma_int_t dworksiz, magma_int_t ngpu, magma_int_t nb, magma_queue_t queues[][20], magma_int_t nqueue, magma_event_t events[][MagmaMaxGPUs *MagmaMaxGPUs+10], magma_int_t nevents, magma_int_t gnode[MagmaMaxGPUs][MagmaMaxGPUs+2], magma_int_t ncmplx )

ZHEMM performs one of the matrix-matrix operations.

C := alpha*A*B + beta*C,


or C := alpha*B*A + beta*C,

where alpha and beta are scalars, A is a Hermitian matrix, and B and C are m by n matrices.

Parameters
 [in] side magma_side_t On entry, SIDE specifies whether the Hermitian matrix A appears on the left or right in the operation as follows:

SIDE = MagmaLeft C := alpha*A*B + beta*C,

SIDE = MagmaRight C := alpha*B*A + beta*C.

Currently, only MagmaLeft is implemented ***

Parameters
 [in] uplo magma_uplo_t On entry, UPLO specifies whether the upper or lower triangular part of the Hermitian matrix A is to be referenced as follows:

UPLO = MagmaUpper Only the upper triangular part of the Hermitian matrix is to be referenced.

UPLO = MagmaLower Only the lower triangular part of the Hermitian matrix is to be referenced.

Currently, only MagmaLower is implemented ***

Parameters
 [in] m INTEGER On entry, M specifies the number of rows of the matrix dC. M >= 0. [in] n INTEGER On entry, N specifies the number of columns of the matrix dC. N >= 0. [in] alpha COMPLEX*16 On entry, ALPHA specifies the scalar alpha. [in] dA COMPLEX*16 array of DIMENSION ( LDDA, ka ), where ka is m when SIDE = MagmaLower and is n otherwise. Before entry with SIDE = MagmaLeft, the m by m part of the array A must contain the Hermitian matrix, such that when UPLO = MagmaUpper, the leading m by m upper triangular part of the array A must contain the upper triangular part of the Hermitian matrix and the strictly lower triangular part of A is not referenced, and when UPLO = MagmaLower, the leading m by m lower triangular part of the array A must contain the lower triangular part of the Hermitian matrix and the strictly upper triangular part of A is not referenced. Before entry with SIDE = MagmaRight, the n by n part of the array A must contain the Hermitian matrix, such that when UPLO = MagmaUpper, the leading n by n upper triangular part of the array A must contain the upper triangular part of the Hermitian matrix and the strictly lower triangular part of A is not referenced, and when UPLO = MagmaLower, the leading n by n lower triangular part of the array A must contain the lower triangular part of the Hermitian matrix and the strictly upper triangular part of A is not referenced. Note that the imaginary parts of the diagonal elements need not be set, they are assumed to be zero. [in] ldda INTEGER On entry, LDDA specifies the first dimension of A as declared in the calling (sub) program. When SIDE = MagmaLower then LDDA >= max( 1, m ), otherwise LDDA >= max( 1, n ). [in] dB COMPLEX*16 array of DIMENSION ( LDDB, n ). Before entry, the leading m by n part of the array B must contain the matrix B. [in] lddb INTEGER On entry, LDDB specifies the first dimension of B as declared in the calling (sub) program. LDDB >= max( 1, m ). [in] beta COMPLEX*16 On entry, BETA specifies the scalar beta. When BETA is supplied as zero then C need not be set on input. [in,out] dC COMPLEX*16 array of DIMENSION ( LDDC, n ). Before entry, the leading m by n part of the array C must contain the matrix C, except when beta is zero, in which case C need not be set on entry. On exit, the array C is overwritten by the m by n updated matrix. [in] lddc INTEGER On entry, LDDC specifies the first dimension of C as declared in the calling (sub) program. LDDC >= max( 1, m ).