MAGMA
2.3.0
Matrix Algebra for GPU and Multicore Architectures

\( C = \alpha A A^T + \beta C \) where \( C \) is symmetric More...
Functions  
void  magmablas_csyrk_batched (magma_uplo_t uplo, magma_trans_t trans, magma_int_t n, magma_int_t k, magmaFloatComplex alpha, magmaFloatComplex const *const *dA_array, magma_int_t ldda, magmaFloatComplex 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_csyrk_vbatched (magma_uplo_t uplo, magma_trans_t trans, magma_int_t *n, magma_int_t *k, magmaFloatComplex alpha, magmaFloatComplex const *const *dA_array, magma_int_t *ldda, magmaFloatComplex beta, magmaFloatComplex **dC_array, magma_int_t *lddc, magma_int_t batchCount, magma_queue_t queue) 
CSYRK performs one of the symmetric rank k operations. More...  
void  magmablas_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_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_zsyrk_batched (magma_uplo_t uplo, magma_trans_t trans, magma_int_t n, magma_int_t k, magmaDoubleComplex alpha, magmaDoubleComplex const *const *dA_array, magma_int_t ldda, magmaDoubleComplex beta, magmaDoubleComplex **dC_array, magma_int_t lddc, magma_int_t batchCount, magma_queue_t queue) 
ZSYRK performs one of the symmetric rank k operations. More...  
void  magmablas_zsyrk_vbatched (magma_uplo_t uplo, magma_trans_t trans, magma_int_t *n, magma_int_t *k, magmaDoubleComplex alpha, magmaDoubleComplex const *const *dA_array, magma_int_t *ldda, magmaDoubleComplex beta, magmaDoubleComplex **dC_array, magma_int_t *lddc, magma_int_t batchCount, magma_queue_t queue) 
ZSYRK performs one of the symmetric rank k operations. More...  
\( C = \alpha A A^T + \beta C \) where \( C \) is symmetric
void magmablas_csyrk_batched  (  magma_uplo_t  uplo, 
magma_trans_t  trans,  
magma_int_t  n,  
magma_int_t  k,  
magmaFloatComplex  alpha,  
magmaFloatComplex const *const *  dA_array,  
magma_int_t  ldda,  
magmaFloatComplex  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.
[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.
[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.
[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 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  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_csyrk_vbatched  (  magma_uplo_t  uplo, 
magma_trans_t  trans,  
magma_int_t *  n,  
magma_int_t *  k,  
magmaFloatComplex  alpha,  
magmaFloatComplex const *const *  dA_array,  
magma_int_t *  ldda,  
magmaFloatComplex  beta,  
magmaFloatComplex **  dC_array,  
magma_int_t *  lddc,  
magma_int_t  batchCount,  
magma_queue_t  queue  
) 
CSYRK performs one of the symmetric rank k operations.
C := alpha*A*A**T + beta*C,
or
C := alpha*A**T*A + beta*C,
where alpha and beta are 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.
[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.
[in]  trans  magma_trans_t. On entry, trans specifies the operation to be performed as follows: 
trans = MagmaNoTrans C := alpha*A*A**T + beta*C.
trans = MagmaConjTrans C := alpha*A**T*A + beta*C.
[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  COMPLEX. 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  COMPLEX. 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 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 magmablas_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.
[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.
[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 = MagmaTrans C := alpha*A**H*A + beta*C.
[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 = MagmaTrans, 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 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 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_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.
[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.
[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 = MagmaTrans C := alpha*A**H*A + beta*C.
[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 = MagmaTrans, 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 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  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_zsyrk_batched  (  magma_uplo_t  uplo, 
magma_trans_t  trans,  
magma_int_t  n,  
magma_int_t  k,  
magmaDoubleComplex  alpha,  
magmaDoubleComplex const *const *  dA_array,  
magma_int_t  ldda,  
magmaDoubleComplex  beta,  
magmaDoubleComplex **  dC_array,  
magma_int_t  lddc,  
magma_int_t  batchCount,  
magma_queue_t  queue  
) 
ZSYRK performs one of the symmetric rank k operations.
C := alpha*A*A**T + beta*C,
or
C := alpha*A**T*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.
[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.
[in]  trans  magma_trans_t. On entry, trans specifies the operation to be performed as follows: 
trans = MagmaNoTrans C := alpha*A*A**T + beta*C.
trans = MagmaTrans C := alpha*A**T*A + beta*C.
[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 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_zsyrk_vbatched  (  magma_uplo_t  uplo, 
magma_trans_t  trans,  
magma_int_t *  n,  
magma_int_t *  k,  
magmaDoubleComplex  alpha,  
magmaDoubleComplex const *const *  dA_array,  
magma_int_t *  ldda,  
magmaDoubleComplex  beta,  
magmaDoubleComplex **  dC_array,  
magma_int_t *  lddc,  
magma_int_t  batchCount,  
magma_queue_t  queue  
) 
ZSYRK performs one of the symmetric rank k operations.
C := alpha*A*A**T + beta*C,
or
C := alpha*A**T*A + beta*C,
where alpha and beta are 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.
[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.
[in]  trans  magma_trans_t. On entry, trans specifies the operation to be performed as follows: 
trans = MagmaNoTrans C := alpha*A*A**T + beta*C.
trans = MagmaConjTrans C := alpha*A**T*A + beta*C.
[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  COMPLEX_16. 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  COMPLEX_16. 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 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. 