MAGMA  2.7.1
Matrix Algebra for GPU and Multicore Architectures
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Functions
herk: Hermitian rank k update
Level 3: matrix-matrix operations, O(n^3) work

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

Functions

void magma_cherk (magma_uplo_t uplo, magma_trans_t trans, magma_int_t n, magma_int_t k, float alpha, magmaFloatComplex_const_ptr dA, magma_int_t ldda, float beta, magmaFloatComplex_ptr dC, magma_int_t lddc, magma_queue_t queue)
 Perform Hermitian rank-k update. More...
 
void magma_zherk (magma_uplo_t uplo, magma_trans_t trans, magma_int_t n, magma_int_t k, double alpha, magmaDoubleComplex_const_ptr dA, magma_int_t ldda, double beta, magmaDoubleComplex_ptr dC, magma_int_t lddc, magma_queue_t queue)
 Perform Hermitian rank-k update. More...
 
void magma_cherk_mgpu (magma_int_t ngpu, magma_uplo_t uplo, magma_trans_t trans, magma_int_t nb, magma_int_t n, magma_int_t k, float alpha, magmaFloatComplex_ptr dB[], magma_int_t lddb, magma_int_t b_offset, float beta, magmaFloatComplex_ptr dC[], magma_int_t lddc, magma_int_t c_offset, magma_int_t nqueue, magma_queue_t queues[][10])
 This cherk_mgpu is internal routine used by cpotrf_mgpu_right. More...
 
void magmablas_cherk_small_reduce (magma_uplo_t uplo, magma_trans_t trans, magma_int_t n, magma_int_t k, float alpha, magmaFloatComplex *dA, magma_int_t ldda, float beta, magmaFloatComplex *dC, magma_int_t lddc, magma_int_t nthread_blocks, magma_queue_t queue)
 CHERK performs one of the Hermitian rank k operations. More...
 
void magma_dsyrk_mgpu (magma_int_t ngpu, magma_uplo_t uplo, magma_trans_t trans, magma_int_t nb, magma_int_t n, magma_int_t k, double alpha, magmaDouble_ptr dB[], magma_int_t lddb, magma_int_t b_offset, double beta, magmaDouble_ptr dC[], magma_int_t lddc, magma_int_t c_offset, magma_int_t nqueue, magma_queue_t queues[][10])
 This dsyrk_mgpu is internal routine used by dpotrf_mgpu_right. More...
 
void magmablas_dsyrk_small_reduce (magma_uplo_t uplo, magma_trans_t trans, magma_int_t n, magma_int_t k, double alpha, double *dA, magma_int_t ldda, double beta, double *dC, magma_int_t lddc, magma_int_t nthread_blocks, magma_queue_t queue)
 DSYRK performs one of the symmetric rank k operations. More...
 
void magma_ssyrk_mgpu (magma_int_t ngpu, magma_uplo_t uplo, magma_trans_t trans, magma_int_t nb, magma_int_t n, magma_int_t k, float alpha, magmaFloat_ptr dB[], magma_int_t lddb, magma_int_t b_offset, float beta, magmaFloat_ptr dC[], magma_int_t lddc, magma_int_t c_offset, magma_int_t nqueue, magma_queue_t queues[][10])
 This ssyrk_mgpu is internal routine used by spotrf_mgpu_right. More...
 
void magmablas_ssyrk_small_reduce (magma_uplo_t uplo, magma_trans_t trans, magma_int_t n, magma_int_t k, float alpha, float *dA, magma_int_t ldda, float beta, float *dC, magma_int_t lddc, magma_int_t nthread_blocks, magma_queue_t queue)
 SSYRK performs one of the symmetric rank k operations. More...
 
void magma_zherk_mgpu (magma_int_t ngpu, magma_uplo_t uplo, magma_trans_t trans, magma_int_t nb, magma_int_t n, magma_int_t k, double alpha, magmaDoubleComplex_ptr dB[], magma_int_t lddb, magma_int_t b_offset, double beta, magmaDoubleComplex_ptr dC[], magma_int_t lddc, magma_int_t c_offset, magma_int_t nqueue, magma_queue_t queues[][10])
 This zherk_mgpu is internal routine used by zpotrf_mgpu_right. More...
 
void magmablas_zherk_small_reduce (magma_uplo_t uplo, magma_trans_t trans, magma_int_t n, magma_int_t k, double alpha, magmaDoubleComplex *dA, magma_int_t ldda, double beta, magmaDoubleComplex *dC, magma_int_t lddc, magma_int_t nthread_blocks, 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 ( magma_uplo_t  uplo,
magma_trans_t  trans,
magma_int_t  n,
magma_int_t  k,
float  alpha,
magmaFloatComplex_const_ptr  dA,
magma_int_t  ldda,
float  beta,
magmaFloatComplex_ptr  dC,
magma_int_t  lddc,
magma_queue_t  queue 
)

Perform Hermitian rank-k update.

\( C = \alpha A A^H + \beta C \) (trans == MagmaNoTrans), or
\( C = \alpha A^H A + \beta C \) (trans == MagmaConjTrans),
where \( C \) is Hermitian.

Parameters
[in]uploWhether the upper or lower triangle of C is referenced.
[in]transOperation to perform on A.
[in]nNumber of rows and columns of C. n >= 0.
[in]kNumber of columns of A (for MagmaNoTrans) or rows of A (for MagmaConjTrans). k >= 0.
[in]alphaScalar \( \alpha \)
[in]dACOMPLEX array on GPU device. If trans == MagmaNoTrans, the n-by-k matrix A of dimension (ldda,k), ldda >= max(1,n);
otherwise, the k-by-n matrix A of dimension (ldda,n), ldda >= max(1,k).
[in]lddaLeading dimension of dA.
[in]betaScalar \( \beta \)
[in,out]dCCOMPLEX array on GPU device. The n-by-n Hermitian matrix C of dimension (lddc,n), lddc >= max(1,n).
[in]lddcLeading dimension of dC.
[in]queuemagma_queue_t Queue to execute in.
void magma_zherk ( magma_uplo_t  uplo,
magma_trans_t  trans,
magma_int_t  n,
magma_int_t  k,
double  alpha,
magmaDoubleComplex_const_ptr  dA,
magma_int_t  ldda,
double  beta,
magmaDoubleComplex_ptr  dC,
magma_int_t  lddc,
magma_queue_t  queue 
)

Perform Hermitian rank-k update.

\( C = \alpha A A^H + \beta C \) (trans == MagmaNoTrans), or
\( C = \alpha A^H A + \beta C \) (trans == MagmaConjTrans),
where \( C \) is Hermitian.

Parameters
[in]uploWhether the upper or lower triangle of C is referenced.
[in]transOperation to perform on A.
[in]nNumber of rows and columns of C. n >= 0.
[in]kNumber of columns of A (for MagmaNoTrans) or rows of A (for MagmaConjTrans). k >= 0.
[in]alphaScalar \( \alpha \)
[in]dACOMPLEX_16 array on GPU device. If trans == MagmaNoTrans, the n-by-k matrix A of dimension (ldda,k), ldda >= max(1,n);
otherwise, the k-by-n matrix A of dimension (ldda,n), ldda >= max(1,k).
[in]lddaLeading dimension of dA.
[in]betaScalar \( \beta \)
[in,out]dCCOMPLEX_16 array on GPU device. The n-by-n Hermitian matrix C of dimension (lddc,n), lddc >= max(1,n).
[in]lddcLeading dimension of dC.
[in]queuemagma_queue_t Queue to execute in.
void magma_cherk_mgpu ( magma_int_t  ngpu,
magma_uplo_t  uplo,
magma_trans_t  trans,
magma_int_t  nb,
magma_int_t  n,
magma_int_t  k,
float  alpha,
magmaFloatComplex_ptr  dB[],
magma_int_t  lddb,
magma_int_t  b_offset,
float  beta,
magmaFloatComplex_ptr  dC[],
magma_int_t  lddc,
magma_int_t  c_offset,
magma_int_t  nqueue,
magma_queue_t  queues[][10] 
)

This cherk_mgpu is internal routine used by cpotrf_mgpu_right.

It has specific assumption on the block diagonal.

void magmablas_cherk_small_reduce ( magma_uplo_t  uplo,
magma_trans_t  trans,
magma_int_t  n,
magma_int_t  k,
float  alpha,
magmaFloatComplex *  dA,
magma_int_t  ldda,
float  beta,
magmaFloatComplex *  dC,
magma_int_t  lddc,
magma_int_t  nthread_blocks,
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.

This is a special routine that supports n up to 32 only. It assumes that k is very large so that the computation of the small matrix C is distributed across many thread blocks. The number of thread blocks can be defined by the user through the interface. However, the kernel can work with a maximum of ceil(k / n) thread blocks. Extra thread blocks, if any, are ignored by the kernel. Reduction across thread blocks is performed using atomics.

Parameters

Parameters
[in]uplomagma_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]transmagma_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]nINTEGER. On entry, specifies the order of the matrix C. N must be at least zero, and at most 32.
[in]kINTEGER. 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]alphaREAL On entry, ALPHA specifies the scalar alpha.
[in]dAA COMPLEX array 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 array A must contain the matrix A, otherwise the leading k by n part of the array A must contain the matrix A.
[in]lddaINTEGER. On entry, ldda specifies the first dimension of 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]betaREAL. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then C need not be set on input.
[in,out]dCA COMPLEX array 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]lddcINTEGER. On entry, lddc specifies the first dimension of C as declared in the calling (sub) program. lddc must be at least max( 1, n ).
[in]nthread_blocksINTEGER The number of thread blocks used to update C.
[in]queuemagma_queue_t Queue to execute in.
void magma_dsyrk_mgpu ( magma_int_t  ngpu,
magma_uplo_t  uplo,
magma_trans_t  trans,
magma_int_t  nb,
magma_int_t  n,
magma_int_t  k,
double  alpha,
magmaDouble_ptr  dB[],
magma_int_t  lddb,
magma_int_t  b_offset,
double  beta,
magmaDouble_ptr  dC[],
magma_int_t  lddc,
magma_int_t  c_offset,
magma_int_t  nqueue,
magma_queue_t  queues[][10] 
)

This dsyrk_mgpu is internal routine used by dpotrf_mgpu_right.

It has specific assumption on the block diagonal.

void magmablas_dsyrk_small_reduce ( magma_uplo_t  uplo,
magma_trans_t  trans,
magma_int_t  n,
magma_int_t  k,
double  alpha,
double *  dA,
magma_int_t  ldda,
double  beta,
double *  dC,
magma_int_t  lddc,
magma_int_t  nthread_blocks,
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.

This is a special routine that supports n up to 32 only. It assumes that k is very large so that the computation of the small matrix C is distributed across many thread blocks. The number of thread blocks can be defined by the user through the interface. However, the kernel can work with a maximum of ceil(k / n) thread blocks. Extra thread blocks, if any, are ignored by the kernel. Reduction across thread blocks is performed using atomics.

Parameters

Parameters
[in]uplomagma_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]transmagma_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]nINTEGER. On entry, specifies the order of the matrix C. N must be at least zero, and at most 32.
[in]kINTEGER. 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]alphaDOUBLE PRECISION On entry, ALPHA specifies the scalar alpha.
[in]dAA DOUBLE PRECISION array 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 array A must contain the matrix A, otherwise the leading k by n part of the array A must contain the matrix A.
[in]lddaINTEGER. On entry, ldda specifies the first dimension of 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]betaDOUBLE PRECISION. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then C need not be set on input.
[in,out]dCA DOUBLE PRECISION array 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]lddcINTEGER. On entry, lddc specifies the first dimension of C as declared in the calling (sub) program. lddc must be at least max( 1, n ).
[in]nthread_blocksINTEGER The number of thread blocks used to update C.
[in]queuemagma_queue_t Queue to execute in.
void magma_ssyrk_mgpu ( magma_int_t  ngpu,
magma_uplo_t  uplo,
magma_trans_t  trans,
magma_int_t  nb,
magma_int_t  n,
magma_int_t  k,
float  alpha,
magmaFloat_ptr  dB[],
magma_int_t  lddb,
magma_int_t  b_offset,
float  beta,
magmaFloat_ptr  dC[],
magma_int_t  lddc,
magma_int_t  c_offset,
magma_int_t  nqueue,
magma_queue_t  queues[][10] 
)

This ssyrk_mgpu is internal routine used by spotrf_mgpu_right.

It has specific assumption on the block diagonal.

void magmablas_ssyrk_small_reduce ( magma_uplo_t  uplo,
magma_trans_t  trans,
magma_int_t  n,
magma_int_t  k,
float  alpha,
float *  dA,
magma_int_t  ldda,
float  beta,
float *  dC,
magma_int_t  lddc,
magma_int_t  nthread_blocks,
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.

This is a special routine that supports n up to 32 only. It assumes that k is very large so that the computation of the small matrix C is distributed across many thread blocks. The number of thread blocks can be defined by the user through the interface. However, the kernel can work with a maximum of ceil(k / n) thread blocks. Extra thread blocks, if any, are ignored by the kernel. Reduction across thread blocks is performed using atomics.

Parameters

Parameters
[in]uplomagma_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]transmagma_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]nINTEGER. On entry, specifies the order of the matrix C. N must be at least zero, and at most 32.
[in]kINTEGER. 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]alphaREAL On entry, ALPHA specifies the scalar alpha.
[in]dAA REAL array 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 array A must contain the matrix A, otherwise the leading k by n part of the array A must contain the matrix A.
[in]lddaINTEGER. On entry, ldda specifies the first dimension of 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]betaREAL. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then C need not be set on input.
[in,out]dCA REAL array 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]lddcINTEGER. On entry, lddc specifies the first dimension of C as declared in the calling (sub) program. lddc must be at least max( 1, n ).
[in]nthread_blocksINTEGER The number of thread blocks used to update C.
[in]queuemagma_queue_t Queue to execute in.
void magma_zherk_mgpu ( magma_int_t  ngpu,
magma_uplo_t  uplo,
magma_trans_t  trans,
magma_int_t  nb,
magma_int_t  n,
magma_int_t  k,
double  alpha,
magmaDoubleComplex_ptr  dB[],
magma_int_t  lddb,
magma_int_t  b_offset,
double  beta,
magmaDoubleComplex_ptr  dC[],
magma_int_t  lddc,
magma_int_t  c_offset,
magma_int_t  nqueue,
magma_queue_t  queues[][10] 
)

This zherk_mgpu is internal routine used by zpotrf_mgpu_right.

It has specific assumption on the block diagonal.

void magmablas_zherk_small_reduce ( magma_uplo_t  uplo,
magma_trans_t  trans,
magma_int_t  n,
magma_int_t  k,
double  alpha,
magmaDoubleComplex *  dA,
magma_int_t  ldda,
double  beta,
magmaDoubleComplex *  dC,
magma_int_t  lddc,
magma_int_t  nthread_blocks,
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.

This is a special routine that supports n up to 32 only. It assumes that k is very large so that the computation of the small matrix C is distributed across many thread blocks. The number of thread blocks can be defined by the user through the interface. However, the kernel can work with a maximum of ceil(k / n) thread blocks. Extra thread blocks, if any, are ignored by the kernel. Reduction across thread blocks is performed using atomics.

Parameters

Parameters
[in]uplomagma_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]transmagma_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]nINTEGER. On entry, specifies the order of the matrix C. N must be at least zero, and at most 32.
[in]kINTEGER. 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]alphaDOUBLE PRECISION On entry, ALPHA specifies the scalar alpha.
[in]dAA COMPLEX_16 array 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 array A must contain the matrix A, otherwise the leading k by n part of the array A must contain the matrix A.
[in]lddaINTEGER. On entry, ldda specifies the first dimension of 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]betaDOUBLE PRECISION. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then C need not be set on input.
[in,out]dCA COMPLEX_16 array 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]lddcINTEGER. On entry, lddc specifies the first dimension of C as declared in the calling (sub) program. lddc must be at least max( 1, n ).
[in]nthread_blocksINTEGER The number of thread blocks used to update C.
[in]queuemagma_queue_t Queue to execute in.