MAGMA  2.3.0 Matrix Algebra for GPU and Multicore Architectures

$$C = \alpha A A^T + \beta C$$ where $$C$$ is Hermitian More...

## Functions

void magma_cherk_batched (magma_uplo_t uplo, magma_trans_t trans, magma_int_t n, magma_int_t k, float alpha, magmaFloatComplex const *const *dA_array, magma_int_t ldda, float beta, magmaFloatComplex **dC_array, magma_int_t lddc, magma_int_t batchCount, magma_queue_t queue)
CHERK performs one of the Hermitian rank k operations. More...

void magmablas_cherk_vbatched (magma_uplo_t uplo, magma_trans_t trans, magma_int_t *n, magma_int_t *k, float alpha, magmaFloatComplex const *const *dA_array, magma_int_t *ldda, float beta, magmaFloatComplex **dC_array, magma_int_t *lddc, magma_int_t batchCount, magma_queue_t queue)
CHERK performs one of the Hermitian rank k operations. More...

void magma_dsyrk_batched (magma_uplo_t uplo, magma_trans_t trans, magma_int_t n, magma_int_t k, double alpha, double const *const *dA_array, magma_int_t ldda, double beta, double **dC_array, magma_int_t lddc, magma_int_t batchCount, magma_queue_t queue)
DSYRK performs one of the symmetric rank k operations. More...

void magmablas_dsyrk_vbatched (magma_uplo_t uplo, magma_trans_t trans, magma_int_t *n, magma_int_t *k, double alpha, double const *const *dA_array, magma_int_t *ldda, double beta, double **dC_array, magma_int_t *lddc, magma_int_t batchCount, magma_queue_t queue)
DSYRK performs one of the symmetric rank k operations. More...

void magma_ssyrk_batched (magma_uplo_t uplo, magma_trans_t trans, magma_int_t n, magma_int_t k, float alpha, float const *const *dA_array, magma_int_t ldda, float beta, float **dC_array, magma_int_t lddc, magma_int_t batchCount, magma_queue_t queue)
SSYRK performs one of the symmetric rank k operations. More...

void magmablas_ssyrk_vbatched (magma_uplo_t uplo, magma_trans_t trans, magma_int_t *n, magma_int_t *k, float alpha, float const *const *dA_array, magma_int_t *ldda, float beta, float **dC_array, magma_int_t *lddc, magma_int_t batchCount, magma_queue_t queue)
SSYRK performs one of the symmetric rank k operations. More...

void magma_zherk_batched (magma_uplo_t uplo, magma_trans_t trans, magma_int_t n, magma_int_t k, double alpha, magmaDoubleComplex const *const *dA_array, magma_int_t ldda, double beta, magmaDoubleComplex **dC_array, magma_int_t lddc, magma_int_t batchCount, magma_queue_t queue)
ZHERK performs one of the Hermitian rank k operations. More...

void magmablas_zherk_batched (magma_uplo_t uplo, magma_trans_t trans, magma_int_t n, magma_int_t k, double alpha, magmaDoubleComplex const *const *dA_array, magma_int_t ldda, double beta, magmaDoubleComplex **dC_array, magma_int_t lddc, magma_int_t batchCount, magma_queue_t queue)
ZHERK performs one of the Hermitian rank k operations. More...

void magmablas_zherk_vbatched (magma_uplo_t uplo, magma_trans_t trans, magma_int_t *n, magma_int_t *k, double alpha, magmaDoubleComplex const *const *dA_array, magma_int_t *ldda, double beta, magmaDoubleComplex **dC_array, magma_int_t *lddc, magma_int_t batchCount, magma_queue_t queue)
ZHERK performs one of the Hermitian rank k operations. More...

## Detailed Description

$$C = \alpha A A^T + \beta C$$ where $$C$$ is Hermitian

## Function Documentation

 void magma_cherk_batched ( magma_uplo_t uplo, magma_trans_t trans, magma_int_t n, magma_int_t k, float alpha, magmaFloatComplex const *const * dA_array, magma_int_t ldda, float beta, magmaFloatComplex ** dC_array, magma_int_t lddc, magma_int_t batchCount, magma_queue_t queue )

CHERK performs one of the Hermitian rank k operations.

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

or

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

where alpha and beta are real scalars, C is an n by n Hermitian matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.

## Parameters

Parameters
 [in] uplo magma_uplo_t. On entry, uplo specifies whether the upper or lower triangular part of the array C is to be referenced as follows:

uplo = MagmaUpper Only the upper triangular part of C is to be referenced.

uplo = MagmaLower Only the lower triangular part of C is to be referenced.

Parameters
 [in] trans magma_trans_t. On entry, trans specifies the operation to be performed as follows:

trans = MagmaNoTrans C := alpha*A*A**H + beta*C.

trans = MagmaConjTrans C := alpha*A**H*A + beta*C.

Parameters
 [in] n INTEGER. On entry, specifies the order of the matrix C. N must be at least zero. [in] k INTEGER. On entry with trans = MagmaNoTrans, k specifies the number of columns of the matrix A, and on entry with trans = MagmaConjTrans, k specifies the number of rows of the matrix A. K must be at least zero. [in] alpha REAL On entry, ALPHA specifies the scalar alpha. [in] dA_array Array of pointers, dimension (batchCount). Each is a COMPLEX A array of DIMENSION ( ldda, ka ), where ka is k when trans = MagmaNoTrans, and is n otherwise. Before entry with trans = MagmaNoTrans, the leading m by k part of the array A must contain the matrix A, otherwise the leading k by m part of the array A must contain the matrix A. [in] ldda INTEGER. On entry, ldda specifies the first dimension of each array A as declared in the calling (sub) program. When trans = MagmaNoTrans then ldda must be at least max( 1, n ), otherwise ldda must be at least max( 1, k ). [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_array Array of pointers, dimension (batchCount). Each is a COMPLEX array C of DIMENSION ( lddc, n ). Before entry with uplo = MagmaUpper, the leading n by n upper triangular part of the array C must contain the upper triangular part of the Hermitian matrix and the strictly lower triangular part of C is not referenced. On exit, the upper triangular part of the array C is overwritten by the upper triangular part of the updated matrix. Before entry with uplo = MagmaLower, the leading n by n lower triangular part of the array C must contain the lower triangular part of the Hermitian matrix and the strictly upper triangular part of C is not referenced. On exit, the lower triangular part of the array C is overwritten by the lower triangular part of the updated matrix. Note that the imaginary parts of the diagonal elements need not be set, they are assumed to be zero, and on exit they are set to zero. [in] lddc INTEGER. On entry, lddc specifies the first dimension of each array C as declared in the calling (sub) program. lddc must be at least max( 1, m ). [in] batchCount INTEGER The number of matrices to operate on. [in] queue magma_queue_t Queue to execute in.
 void magmablas_cherk_vbatched ( magma_uplo_t uplo, magma_trans_t trans, magma_int_t * n, magma_int_t * k, float alpha, magmaFloatComplex const *const * dA_array, magma_int_t * ldda, float beta, magmaFloatComplex ** dC_array, magma_int_t * lddc, magma_int_t batchCount, magma_queue_t queue )

CHERK performs one of the Hermitian rank k operations.

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

or

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

where alpha and beta are real scalars, C is an n by n Hermitian matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.

## Parameters

Parameters
 [in] uplo magma_uplo_t. On entry, uplo specifies whether the upper or lower triangular part of the array C is to be referenced as follows:

uplo = MagmaUpper Only the upper triangular part of C is to be referenced.

uplo = MagmaLower Only the lower triangular part of C is to be referenced.

Parameters
 [in] trans magma_trans_t. On entry, trans specifies the operation to be performed as follows:

trans = MagmaNoTrans C := alpha*A*A**H + beta*C.

trans = MagmaConjTrans C := alpha*A**H*A + beta*C.

Parameters
 [in] n Array of integers, size (batchCount + 1). On entry, each INTEGER N specifies the order of the corresponding matrix C. N must be at least zero. The last element of the array is used internally by the routine. [in] k Array of integers, size (batchCount + 1). On entry with trans = MagmaNoTrans, each INTEGER K specifies the number of columns of the corresponding matrix A, and on entry with trans = MagmaConjTrans, K specifies the number of rows of the corresponding matrix A. K must be at least zero. The last element of the array is used internally by the routine. [in] alpha REAL On entry, ALPHA specifies the scalar alpha. [in] dA_array Array of pointers, size (batchCount). Each is a COMPLEX array of DIMENSION ( LDDA, Ka ), where Ka is K when trans = MagmaNoTrans, and is N otherwise. Before entry with trans = MagmaNoTrans, the leading N by K part of the corresponding array A must contain the matrix A, otherwise the leading K by N part of the corresponding array must contain the matrix A. [in] ldda Array of integers, size (batchCount + 1). On entry, each INTEGER LDDA specifies the first dimension of the corresponding matrix A as declared in the calling (sub) program. When trans = MagmaNoTrans then LDDA must be at least max( 1, N ), otherwise ldda must be at least max( 1, K ). The last element of the array is used internally by the routine. [in] beta REAL. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then dC need not be set on input. [in,out] dC_array Array of pointers, size (batchCount). Each is a COMPLEX array of DIMENSION ( LDDC, N ). Before entry with uplo = MagmaUpper, the leading N by N upper triangular part of the corresponding array C must contain the upper triangular part of the corresponding Hermitian matrix and the strictly lower triangular part of C is not referenced. On exit, the upper triangular part of the array C is overwritten by the upper triangular part of the updated matrix. Before entry with uplo = MagmaLower, the leading N by N lower triangular part of the corresponding array C must contain the lower triangular part of the corresponding Hermitian matrix and the strictly upper triangular part of C is not referenced. On exit, the lower triangular part of the array C is overwritten by the lower triangular part of the updated matrix. Note that the imaginary parts of the diagonal elements need not be set, they are assumed to be zero, and on exit they are set to zero. [in] lddc Array of integers, size (batchCount + 1). On entry, each INTEGER LDDC specifies the first dimension of the corresponding matrix C as declared in the calling (sub) program. LDDC must be at least max( 1, M ). [in] batchCount INTEGER The number of matrices to operate on. [in] queue magma_queue_t Queue to execute in.
 void magma_dsyrk_batched ( magma_uplo_t uplo, magma_trans_t trans, magma_int_t n, magma_int_t k, double alpha, double const *const * dA_array, magma_int_t ldda, double beta, double ** dC_array, magma_int_t lddc, magma_int_t batchCount, magma_queue_t queue )

DSYRK performs one of the symmetric rank k operations.

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

or

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

where alpha and beta are real scalars, C is an n by n symmetric matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.

## Parameters

Parameters
 [in] uplo magma_uplo_t. On entry, uplo specifies whether the upper or lower triangular part of the array C is to be referenced as follows:

uplo = MagmaUpper Only the upper triangular part of C is to be referenced.

uplo = MagmaLower Only the lower triangular part of C is to be referenced.

Parameters
 [in] trans magma_trans_t. On entry, trans specifies the operation to be performed as follows:

trans = MagmaNoTrans C := alpha*A*A**H + beta*C.

trans = MagmaConjTrans C := alpha*A**H*A + beta*C.

Parameters
 [in] n INTEGER. On entry, specifies the order of the matrix C. N must be at least zero. [in] k INTEGER. On entry with trans = MagmaNoTrans, k specifies the number of columns of the matrix A, and on entry with trans = MagmaConjTrans, k specifies the number of rows of the matrix A. K must be at least zero. [in] alpha DOUBLE PRECISION On entry, ALPHA specifies the scalar alpha. [in] dA_array Array of pointers, dimension (batchCount). Each is a DOUBLE PRECISION A array of DIMENSION ( ldda, ka ), where ka is k when trans = MagmaNoTrans, and is n otherwise. Before entry with trans = MagmaNoTrans, the leading m by k part of the array A must contain the matrix A, otherwise the leading k by m part of the array A must contain the matrix A. [in] ldda INTEGER. On entry, ldda specifies the first dimension of each array A as declared in the calling (sub) program. When trans = MagmaNoTrans then ldda must be at least max( 1, n ), otherwise ldda must be at least max( 1, k ). [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_array Array of pointers, dimension (batchCount). Each is a DOUBLE PRECISION array C of DIMENSION ( lddc, n ). Before entry with uplo = MagmaUpper, the leading n by n upper triangular part of the array C must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of C is not referenced. On exit, the upper triangular part of the array C is overwritten by the upper triangular part of the updated matrix. Before entry with uplo = MagmaLower, the leading n by n lower triangular part of the array C must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of C is not referenced. On exit, the lower triangular part of the array C is overwritten by the lower triangular part of the updated matrix. Note that the imaginary parts of the diagonal elements need not be set, they are assumed to be zero, and on exit they are set to zero. [in] lddc INTEGER. On entry, lddc specifies the first dimension of each array C as declared in the calling (sub) program. lddc must be at least max( 1, m ). [in] batchCount INTEGER The number of matrices to operate on. [in] queue magma_queue_t Queue to execute in.
 void magmablas_dsyrk_vbatched ( magma_uplo_t uplo, magma_trans_t trans, magma_int_t * n, magma_int_t * k, double alpha, double const *const * dA_array, magma_int_t * ldda, double beta, double ** dC_array, magma_int_t * lddc, magma_int_t batchCount, magma_queue_t queue )

DSYRK performs one of the symmetric rank k operations.

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

or

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

where alpha and beta are real scalars, C is an n by n symmetric matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.

## Parameters

Parameters
 [in] uplo magma_uplo_t. On entry, uplo specifies whether the upper or lower triangular part of the array C is to be referenced as follows:

uplo = MagmaUpper Only the upper triangular part of C is to be referenced.

uplo = MagmaLower Only the lower triangular part of C is to be referenced.

Parameters
 [in] trans magma_trans_t. On entry, trans specifies the operation to be performed as follows:

trans = MagmaNoTrans C := alpha*A*A**H + beta*C.

trans = MagmaConjTrans C := alpha*A**H*A + beta*C.

Parameters
 [in] n Array of integers, size (batchCount + 1). On entry, each INTEGER N specifies the order of the corresponding matrix C. N must be at least zero. The last element of the array is used internally by the routine. [in] k Array of integers, size (batchCount + 1). On entry with trans = MagmaNoTrans, each INTEGER K specifies the number of columns of the corresponding matrix A, and on entry with trans = MagmaConjTrans, K specifies the number of rows of the corresponding matrix A. K must be at least zero. The last element of the array is used internally by the routine. [in] alpha DOUBLE PRECISION On entry, ALPHA specifies the scalar alpha. [in] dA_array Array of pointers, size (batchCount). Each is a DOUBLE PRECISION array of DIMENSION ( LDDA, Ka ), where Ka is K when trans = MagmaNoTrans, and is N otherwise. Before entry with trans = MagmaNoTrans, the leading N by K part of the corresponding array A must contain the matrix A, otherwise the leading K by N part of the corresponding array must contain the matrix A. [in] ldda Array of integers, size (batchCount + 1). On entry, each INTEGER LDDA specifies the first dimension of the corresponding matrix A as declared in the calling (sub) program. When trans = MagmaNoTrans then LDDA must be at least max( 1, N ), otherwise ldda must be at least max( 1, K ). The last element of the array is used internally by the routine. [in] beta DOUBLE PRECISION. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then dC need not be set on input. [in,out] dC_array Array of pointers, size (batchCount). Each is a DOUBLE PRECISION array of DIMENSION ( LDDC, N ). Before entry with uplo = MagmaUpper, the leading N by N upper triangular part of the corresponding array C must contain the upper triangular part of the corresponding symmetric matrix and the strictly lower triangular part of C is not referenced. On exit, the upper triangular part of the array C is overwritten by the upper triangular part of the updated matrix. Before entry with uplo = MagmaLower, the leading N by N lower triangular part of the corresponding array C must contain the lower triangular part of the corresponding symmetric matrix and the strictly upper triangular part of C is not referenced. On exit, the lower triangular part of the array C is overwritten by the lower triangular part of the updated matrix. Note that the imaginary parts of the diagonal elements need not be set, they are assumed to be zero, and on exit they are set to zero. [in] lddc Array of integers, size (batchCount + 1). On entry, each INTEGER LDDC specifies the first dimension of the corresponding matrix C as declared in the calling (sub) program. LDDC must be at least max( 1, M ). [in] batchCount INTEGER The number of matrices to operate on. [in] queue magma_queue_t Queue to execute in.
 void magma_ssyrk_batched ( magma_uplo_t uplo, magma_trans_t trans, magma_int_t n, magma_int_t k, float alpha, float const *const * dA_array, magma_int_t ldda, float beta, float ** dC_array, magma_int_t lddc, magma_int_t batchCount, magma_queue_t queue )

SSYRK performs one of the symmetric rank k operations.

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

or

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

where alpha and beta are real scalars, C is an n by n symmetric matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.

## Parameters

Parameters
 [in] uplo magma_uplo_t. On entry, uplo specifies whether the upper or lower triangular part of the array C is to be referenced as follows:

uplo = MagmaUpper Only the upper triangular part of C is to be referenced.

uplo = MagmaLower Only the lower triangular part of C is to be referenced.

Parameters
 [in] trans magma_trans_t. On entry, trans specifies the operation to be performed as follows:

trans = MagmaNoTrans C := alpha*A*A**H + beta*C.

trans = MagmaConjTrans C := alpha*A**H*A + beta*C.

Parameters
 [in] n INTEGER. On entry, specifies the order of the matrix C. N must be at least zero. [in] k INTEGER. On entry with trans = MagmaNoTrans, k specifies the number of columns of the matrix A, and on entry with trans = MagmaConjTrans, k specifies the number of rows of the matrix A. K must be at least zero. [in] alpha REAL On entry, ALPHA specifies the scalar alpha. [in] dA_array Array of pointers, dimension (batchCount). Each is a REAL A array of DIMENSION ( ldda, ka ), where ka is k when trans = MagmaNoTrans, and is n otherwise. Before entry with trans = MagmaNoTrans, the leading m by k part of the array A must contain the matrix A, otherwise the leading k by m part of the array A must contain the matrix A. [in] ldda INTEGER. On entry, ldda specifies the first dimension of each array A as declared in the calling (sub) program. When trans = MagmaNoTrans then ldda must be at least max( 1, n ), otherwise ldda must be at least max( 1, k ). [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_array Array of pointers, dimension (batchCount). Each is a REAL array C of DIMENSION ( lddc, n ). Before entry with uplo = MagmaUpper, the leading n by n upper triangular part of the array C must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of C is not referenced. On exit, the upper triangular part of the array C is overwritten by the upper triangular part of the updated matrix. Before entry with uplo = MagmaLower, the leading n by n lower triangular part of the array C must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of C is not referenced. On exit, the lower triangular part of the array C is overwritten by the lower triangular part of the updated matrix. Note that the imaginary parts of the diagonal elements need not be set, they are assumed to be zero, and on exit they are set to zero. [in] lddc INTEGER. On entry, lddc specifies the first dimension of each array C as declared in the calling (sub) program. lddc must be at least max( 1, m ). [in] batchCount INTEGER The number of matrices to operate on. [in] queue magma_queue_t Queue to execute in.
 void magmablas_ssyrk_vbatched ( magma_uplo_t uplo, magma_trans_t trans, magma_int_t * n, magma_int_t * k, float alpha, float const *const * dA_array, magma_int_t * ldda, float beta, float ** dC_array, magma_int_t * lddc, magma_int_t batchCount, magma_queue_t queue )

SSYRK performs one of the symmetric rank k operations.

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

or

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

where alpha and beta are real scalars, C is an n by n symmetric matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.

## Parameters

Parameters
 [in] uplo magma_uplo_t. On entry, uplo specifies whether the upper or lower triangular part of the array C is to be referenced as follows:

uplo = MagmaUpper Only the upper triangular part of C is to be referenced.

uplo = MagmaLower Only the lower triangular part of C is to be referenced.

Parameters
 [in] trans magma_trans_t. On entry, trans specifies the operation to be performed as follows:

trans = MagmaNoTrans C := alpha*A*A**H + beta*C.

trans = MagmaConjTrans C := alpha*A**H*A + beta*C.

Parameters
 [in] n Array of integers, size (batchCount + 1). On entry, each INTEGER N specifies the order of the corresponding matrix C. N must be at least zero. The last element of the array is used internally by the routine. [in] k Array of integers, size (batchCount + 1). On entry with trans = MagmaNoTrans, each INTEGER K specifies the number of columns of the corresponding matrix A, and on entry with trans = MagmaConjTrans, K specifies the number of rows of the corresponding matrix A. K must be at least zero. The last element of the array is used internally by the routine. [in] alpha REAL On entry, ALPHA specifies the scalar alpha. [in] dA_array Array of pointers, size (batchCount). Each is a REAL array of DIMENSION ( LDDA, Ka ), where Ka is K when trans = MagmaNoTrans, and is N otherwise. Before entry with trans = MagmaNoTrans, the leading N by K part of the corresponding array A must contain the matrix A, otherwise the leading K by N part of the corresponding array must contain the matrix A. [in] ldda Array of integers, size (batchCount + 1). On entry, each INTEGER LDDA specifies the first dimension of the corresponding matrix A as declared in the calling (sub) program. When trans = MagmaNoTrans then LDDA must be at least max( 1, N ), otherwise ldda must be at least max( 1, K ). The last element of the array is used internally by the routine. [in] beta REAL. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then dC need not be set on input. [in,out] dC_array Array of pointers, size (batchCount). Each is a REAL array of DIMENSION ( LDDC, N ). Before entry with uplo = MagmaUpper, the leading N by N upper triangular part of the corresponding array C must contain the upper triangular part of the corresponding symmetric matrix and the strictly lower triangular part of C is not referenced. On exit, the upper triangular part of the array C is overwritten by the upper triangular part of the updated matrix. Before entry with uplo = MagmaLower, the leading N by N lower triangular part of the corresponding array C must contain the lower triangular part of the corresponding symmetric matrix and the strictly upper triangular part of C is not referenced. On exit, the lower triangular part of the array C is overwritten by the lower triangular part of the updated matrix. Note that the imaginary parts of the diagonal elements need not be set, they are assumed to be zero, and on exit they are set to zero. [in] lddc Array of integers, size (batchCount + 1). On entry, each INTEGER LDDC specifies the first dimension of the corresponding matrix C as declared in the calling (sub) program. LDDC must be at least max( 1, M ). [in] batchCount INTEGER The number of matrices to operate on. [in] queue magma_queue_t Queue to execute in.
 void magma_zherk_batched ( magma_uplo_t uplo, magma_trans_t trans, magma_int_t n, magma_int_t k, double alpha, magmaDoubleComplex const *const * dA_array, magma_int_t ldda, double beta, magmaDoubleComplex ** dC_array, magma_int_t lddc, magma_int_t batchCount, magma_queue_t queue )

ZHERK performs one of the Hermitian rank k operations.

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

or

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

where alpha and beta are real scalars, C is an n by n Hermitian matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.

## Parameters

Parameters
 [in] uplo magma_uplo_t. On entry, uplo specifies whether the upper or lower triangular part of the array C is to be referenced as follows:

uplo = MagmaUpper Only the upper triangular part of C is to be referenced.

uplo = MagmaLower Only the lower triangular part of C is to be referenced.

Parameters
 [in] trans magma_trans_t. On entry, trans specifies the operation to be performed as follows:

trans = MagmaNoTrans C := alpha*A*A**H + beta*C.

trans = MagmaConjTrans C := alpha*A**H*A + beta*C.

Parameters
 [in] n INTEGER. On entry, specifies the order of the matrix C. N must be at least zero. [in] k INTEGER. On entry with trans = MagmaNoTrans, k specifies the number of columns of the matrix A, and on entry with trans = MagmaConjTrans, k specifies the number of rows of the matrix A. K must be at least zero. [in] alpha DOUBLE PRECISION On entry, ALPHA specifies the scalar alpha. [in] dA_array Array of pointers, dimension (batchCount). Each is a COMPLEX_16 A array of DIMENSION ( ldda, ka ), where ka is k when trans = MagmaNoTrans, and is n otherwise. Before entry with trans = MagmaNoTrans, the leading m by k part of the array A must contain the matrix A, otherwise the leading k by m part of the array A must contain the matrix A. [in] ldda INTEGER. On entry, ldda specifies the first dimension of each array A as declared in the calling (sub) program. When trans = MagmaNoTrans then ldda must be at least max( 1, n ), otherwise ldda must be at least max( 1, k ). [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_array Array of pointers, dimension (batchCount). Each is a COMPLEX_16 array C of DIMENSION ( lddc, n ). Before entry with uplo = MagmaUpper, the leading n by n upper triangular part of the array C must contain the upper triangular part of the Hermitian matrix and the strictly lower triangular part of C is not referenced. On exit, the upper triangular part of the array C is overwritten by the upper triangular part of the updated matrix. Before entry with uplo = MagmaLower, the leading n by n lower triangular part of the array C must contain the lower triangular part of the Hermitian matrix and the strictly upper triangular part of C is not referenced. On exit, the lower triangular part of the array C is overwritten by the lower triangular part of the updated matrix. Note that the imaginary parts of the diagonal elements need not be set, they are assumed to be zero, and on exit they are set to zero. [in] lddc INTEGER. On entry, lddc specifies the first dimension of each array C as declared in the calling (sub) program. lddc must be at least max( 1, m ). [in] batchCount INTEGER The number of matrices to operate on. [in] queue magma_queue_t Queue to execute in.
 void magmablas_zherk_batched ( magma_uplo_t uplo, magma_trans_t trans, magma_int_t n, magma_int_t k, double alpha, magmaDoubleComplex const *const * dA_array, magma_int_t ldda, double beta, magmaDoubleComplex ** dC_array, magma_int_t lddc, magma_int_t batchCount, magma_queue_t queue )

ZHERK performs one of the Hermitian rank k operations.

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

or

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

where alpha and beta are real scalars, C is an n by n Hermitian matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.

## Parameters

Parameters
 [in] uplo magma_uplo_t. On entry, uplo specifies whether the upper or lower triangular part of the array C is to be referenced as follows:

uplo = MagmaUpper Only the upper triangular part of C is to be referenced.

uplo = MagmaLower Only the lower triangular part of C is to be referenced.

Parameters
 [in] trans magma_trans_t. On entry, trans specifies the operation to be performed as follows:

trans = MagmaNoTrans, C := alpha*A*A**H + beta*C.

trans = MagmaConjTrans, C := alpha*A**H*A + beta*C.

Parameters
 [in] n INTEGER. On entry, specifies the order of the matrix C. N must be at least zero. [in] k INTEGER. On entry with trans = MagmaNoTrans, k specifies the number of columns of the matrix A, and on entry with trans = MagmaConjTrans, k specifies the number of rows of the matrix A. K must be at least zero. [in] alpha DOUBLE PRECISION On entry, ALPHA specifies the scalar alpha. [in] dA_array Array of pointers, dimension (batchCount). Each is a COMPLEX_16 array A of DIMENSION ( ldda, ka ), where ka is k when trans = MagmaNoTrans, and is n otherwise. Before entry with trans = MagmaNoTrans, the leading m by k part of the array A must contain the matrix A, otherwise the leading k by m part of the array A must contain the matrix A. [in] ldda INTEGER. On entry, ldda specifies the first dimension of each array A as declared in the calling (sub) program. When trans = MagmaNoTrans then ldda must be at least max( 1, n ), otherwise ldda must be at least max( 1, k ). [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_array Array of pointers, dimension (batchCount). Each is a COMPLEX_16 array C of DIMENSION ( lddc, n ). Before entry with uplo = MagmaUpper, the leading n by n upper triangular part of the array C must contain the upper triangular part of the Hermitian matrix and the strictly lower triangular part of C is not referenced. On exit, the upper triangular part of the array C is overwritten by the upper triangular part of the updated matrix. Before entry with uplo = MagmaLower, the leading n by n lower triangular part of the array C must contain the lower triangular part of the Hermitian matrix and the strictly upper triangular part of C is not referenced. On exit, the lower triangular part of the array C is overwritten by the lower triangular part of the updated matrix. Note that the imaginary parts of the diagonal elements need not be set, they are assumed to be zero, and on exit they are set to zero. [in] lddc INTEGER. On entry, lddc specifies the first dimension of each array C as declared in the calling (sub) program. lddc must be at least max( 1, m ). [in] batchCount INTEGER The number of matrices to operate on. [in] queue magma_queue_t Queue to execute in.
 void magmablas_zherk_vbatched ( magma_uplo_t uplo, magma_trans_t trans, magma_int_t * n, magma_int_t * k, double alpha, magmaDoubleComplex const *const * dA_array, magma_int_t * ldda, double beta, magmaDoubleComplex ** dC_array, magma_int_t * lddc, magma_int_t batchCount, magma_queue_t queue )

ZHERK performs one of the Hermitian rank k operations.

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

or

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

where alpha and beta are real scalars, C is an n by n Hermitian matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.

## Parameters

Parameters
 [in] uplo magma_uplo_t. On entry, uplo specifies whether the upper or lower triangular part of the array C is to be referenced as follows:

uplo = MagmaUpper Only the upper triangular part of C is to be referenced.

uplo = MagmaLower Only the lower triangular part of C is to be referenced.

Parameters
 [in] trans magma_trans_t. On entry, trans specifies the operation to be performed as follows:

trans = MagmaNoTrans C := alpha*A*A**H + beta*C.

trans = MagmaConjTrans C := alpha*A**H*A + beta*C.

Parameters
 [in] n Array of integers, size (batchCount + 1). On entry, each INTEGER N specifies the order of the corresponding matrix C. N must be at least zero. The last element of the array is used internally by the routine. [in] k Array of integers, size (batchCount + 1). On entry with trans = MagmaNoTrans, each INTEGER K specifies the number of columns of the corresponding matrix A, and on entry with trans = MagmaConjTrans, K specifies the number of rows of the corresponding matrix A. K must be at least zero. The last element of the array is used internally by the routine. [in] alpha DOUBLE PRECISION On entry, ALPHA specifies the scalar alpha. [in] dA_array Array of pointers, size (batchCount). Each is a COMPLEX_16 array of DIMENSION ( LDDA, Ka ), where Ka is K when trans = MagmaNoTrans, and is N otherwise. Before entry with trans = MagmaNoTrans, the leading N by K part of the corresponding array A must contain the matrix A, otherwise the leading K by N part of the corresponding array must contain the matrix A. [in] ldda Array of integers, size (batchCount + 1). On entry, each INTEGER LDDA specifies the first dimension of the corresponding matrix A as declared in the calling (sub) program. When trans = MagmaNoTrans then LDDA must be at least max( 1, N ), otherwise ldda must be at least max( 1, K ). The last element of the array is used internally by the routine. [in] beta DOUBLE PRECISION. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then dC need not be set on input. [in,out] dC_array Array of pointers, size (batchCount). Each is a COMPLEX_16 array of DIMENSION ( LDDC, N ). Before entry with uplo = MagmaUpper, the leading N by N upper triangular part of the corresponding array C must contain the upper triangular part of the corresponding Hermitian matrix and the strictly lower triangular part of C is not referenced. On exit, the upper triangular part of the array C is overwritten by the upper triangular part of the updated matrix. Before entry with uplo = MagmaLower, the leading N by N lower triangular part of the corresponding array C must contain the lower triangular part of the corresponding Hermitian matrix and the strictly upper triangular part of C is not referenced. On exit, the lower triangular part of the array C is overwritten by the lower triangular part of the updated matrix. Note that the imaginary parts of the diagonal elements need not be set, they are assumed to be zero, and on exit they are set to zero. [in] lddc Array of integers, size (batchCount + 1). On entry, each INTEGER LDDC specifies the first dimension of the corresponding matrix C as declared in the calling (sub) program. LDDC must be at least max( 1, M ). [in] batchCount INTEGER The number of matrices to operate on. [in] queue magma_queue_t Queue to execute in.