single precision
[Level-3 BLAS]

Functions

magma_int_t magma_strsm_m (magma_int_t ngpu, magma_side_t side, magma_uplo_t uplo, magma_trans_t transa, magma_diag_t diag, magma_int_t m, magma_int_t n, float alpha, float *A, magma_int_t lda, float *B, magma_int_t ldb)
 STRSM solves one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B, where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of.
void magma_sgemm (magma_trans_t transA, magma_trans_t transB, magma_int_t m, magma_int_t n, magma_int_t k, float alpha, magmaFloat_const_ptr dA, magma_int_t ldda, magmaFloat_const_ptr dB, magma_int_t lddb, float beta, magmaFloat_ptr dC, magma_int_t lddc)
 Perform matrix-matrix product, $ C = \alpha op(A) op(B) + \beta C $.
void magma_ssymm (magma_side_t side, magma_uplo_t uplo, magma_int_t m, magma_int_t n, float alpha, magmaFloat_const_ptr dA, magma_int_t ldda, magmaFloat_const_ptr dB, magma_int_t lddb, float beta, magmaFloat_ptr dC, magma_int_t lddc)
 Perform symmetric matrix-matrix product.
void magma_ssyrk (magma_uplo_t uplo, magma_trans_t trans, magma_int_t n, magma_int_t k, float alpha, magmaFloat_const_ptr dA, magma_int_t ldda, float beta, magmaFloat_ptr dC, magma_int_t lddc)
 Perform symmetric rank-k update.
void magma_ssyr2k (magma_uplo_t uplo, magma_trans_t trans, magma_int_t n, magma_int_t k, float alpha, magmaFloat_const_ptr dA, magma_int_t ldda, magmaFloat_const_ptr dB, magma_int_t lddb, float beta, magmaFloat_ptr dC, magma_int_t lddc)
 Perform symmetric rank-2k update.
void magma_strmm (magma_side_t side, magma_uplo_t uplo, magma_trans_t trans, magma_diag_t diag, magma_int_t m, magma_int_t n, float alpha, magmaFloat_const_ptr dA, magma_int_t ldda, magmaFloat_ptr dB, magma_int_t lddb)
 Perform triangular matrix-matrix product.
void magma_strsm (magma_side_t side, magma_uplo_t uplo, magma_trans_t trans, magma_diag_t diag, magma_int_t m, magma_int_t n, float alpha, magmaFloat_const_ptr dA, magma_int_t ldda, magmaFloat_ptr dB, magma_int_t lddb)
 Solve triangular matrix-matrix system (multiple right-hand sides).
void magmablas_sgemm_batched (magma_trans_t transA, magma_trans_t transB, magma_int_t m, magma_int_t n, magma_int_t k, float alpha, float const *const *dA_array, magma_int_t ldda, float const *const *dB_array, magma_int_t lddb, float beta, float **dC_array, magma_int_t lddc, magma_int_t batchCount, magma_queue_t queue)
 SGEMM performs one of the matrix-matrix operations.
void magmablas_sgemm (magma_trans_t transA, magma_trans_t transB, magma_int_t m, magma_int_t n, magma_int_t k, float alpha, magmaFloat_const_ptr dA, magma_int_t ldda, magmaFloat_const_ptr dB, magma_int_t lddb, float beta, magmaFloat_ptr dC, magma_int_t lddc)
 SGEMM performs one of the matrix-matrix operations.
void magmablas_sgemm_batched_lg (magma_trans_t transA, magma_trans_t transB, magma_int_t m, magma_int_t n, magma_int_t k, float alpha, float const *const *dA_array, magma_int_t ldda, float const *const *dB_array, magma_int_t lddb, float beta, float **dC_array, magma_int_t lddc, magma_int_t batchCount, magma_queue_t queue)
 SGEMM performs one of the matrix-matrix operations.
void magmablas_sgemm_batched_k32 (magma_trans_t transA, magma_trans_t transB, magma_int_t m, magma_int_t n, magma_int_t k, float alpha, float const *const *dA_array, magma_int_t ldda, float const *const *dB_array, magma_int_t lddb, float beta, float **dC_array, magma_int_t lddc, magma_int_t batchCount, magma_queue_t queue)
 SGEMM performs one of the matrix-matrix operations.
void magmablas_sgemm_reduce (magma_int_t m, magma_int_t n, magma_int_t k, float alpha, magmaFloat_const_ptr dA, magma_int_t ldda, magmaFloat_const_ptr dB, magma_int_t lddb, float beta, magmaFloat_ptr dC, magma_int_t lddc)
 SGEMM_REDUCE performs one of the matrix-matrix operations.
void magmablas_sgemm_tesla (magma_trans_t transA, magma_trans_t transB, magma_int_t m, magma_int_t n, magma_int_t k, float alpha, const float *A, magma_int_t lda, const float *B, magma_int_t ldb, float beta, float *C, magma_int_t ldc)
 SGEMM performs one of the matrix-matrix operations.
__global__ void sgemm_kernel_N_N_64_16_16_16_4 (float *__restrict__ C, const float *__restrict__ A, const float *__restrict__ B, int m, int n, int k, int lda, int ldb, int ldc, float alpha, float beta)
 Purpose: -------- This routine computes C = alpha * A*B + beta * C.
__global__ void sgemm_kernel_N_N_64_16_16_16_4_special (float *__restrict__ C, const float *__restrict__ A, const float *__restrict__ B, int m, int n, int k, int lda, int ldb, int ldc, float alpha, float beta)
 Purpose: -------- This routine computes C = alpha * A*B + beta * C.
__global__ void sgemm_kernel_N_T_64_16_4_16_4 (float *__restrict__ C, const float *__restrict__ A, const float *__restrict__ B, int m, int n, int k, int lda, int ldb, int ldc, float alpha, float beta)
 Purpose: -------- This routine computes C = alpha * A*B^T + beta * C.
__global__ void sgemm_kernel_T_N_32_32_8_8_8 (float *__restrict__ C, const float *__restrict__ A, const float *__restrict__ B, int m, int n, int k, int lda, int ldb, int ldc, float alpha, float beta)
 Purpose: -------- This routine computes C = alpha * A^T*B + beta * C.
__global__ void sgemm_kernel_T_T_64_16_16_16_4 (float *__restrict__ C, const float *__restrict__ A, const float *__restrict__ B, int m, int n, int k, int lda, int ldb, int ldc, float alpha, float beta)
 Purpose: -------- This routine computes C = alpha * A^T*B^T + beta * C.
__global__ void sgemm_kernel_T_T_64_16_16_16_4_special (float *__restrict__ C, const float *__restrict__ A, const float *__restrict__ B, int m, int n, int k, int lda, int ldb, int ldc, float alpha, float beta)
 Purpose: -------- This routine computes C = alpha * A^T*B^T + beta * C.
void magmablas_ssyr2k_mgpu2 (magma_uplo_t uplo, magma_trans_t trans, magma_int_t n, magma_int_t k, float alpha, magmaFloat_ptr dA[], magma_int_t ldda, magma_int_t a_offset, 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 ngpu, magma_int_t nb, magma_queue_t queues[][20], magma_int_t nqueue)
 SSYR2K performs one of the symmetric rank 2k operations.
void magmablas_ssyr2k_mgpu_spec (magma_uplo_t uplo, magma_trans_t trans, magma_int_t n, magma_int_t k, float alpha, magmaFloat_ptr dA[], magma_int_t ldda, magma_int_t a_offset, 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 ngpu, magma_int_t nb, magma_queue_t queues[][20], magma_int_t nqueue)
 SSYR2K performs one of the symmetric rank 2k operations.
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.
void magmablas_ssyrk_batched_lg (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.
void magmablas_ssyrk_batched_k32 (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.
void magmablas_strsm_outofplace (magma_side_t side, magma_uplo_t uplo, magma_trans_t transA, magma_diag_t diag, magma_int_t m, magma_int_t n, float alpha, magmaFloat_const_ptr dA, magma_int_t ldda, magmaFloat_ptr dB, magma_int_t lddb, magma_int_t flag, magmaFloat_ptr d_dinvA, magmaFloat_ptr dX)
 strsm_outofplace solves one of the matrix equations on gpu
void magmablas_strsm_work (magma_side_t side, magma_uplo_t uplo, magma_trans_t transA, magma_diag_t diag, magma_int_t m, magma_int_t n, float alpha, magmaFloat_const_ptr dA, magma_int_t ldda, magmaFloat_ptr dB, magma_int_t lddb, magma_int_t flag, magmaFloat_ptr d_dinvA, magmaFloat_ptr dX)
void magmablas_strsm (magma_side_t side, magma_uplo_t uplo, magma_trans_t transA, magma_diag_t diag, magma_int_t m, magma_int_t n, float alpha, magmaFloat_const_ptr dA, magma_int_t ldda, magmaFloat_ptr dB, magma_int_t lddb)
void magmablas_strsm_outofplace_batched (magma_side_t side, magma_uplo_t uplo, magma_trans_t transA, magma_diag_t diag, magma_int_t flag, magma_int_t m, magma_int_t n, float alpha, float **dA_array, magma_int_t ldda, float **dB_array, magma_int_t lddb, float **dX_array, magma_int_t lddx, float **dinvA_array, magma_int_t dinvA_length, float **dA_displ, float **dB_displ, float **dX_displ, float **dinvA_displ, magma_int_t resetozero, magma_int_t batchCount, magma_queue_t queue)
 strsm_work solves one of the matrix equations on gpu
void magmablas_strsm_work_batched (magma_side_t side, magma_uplo_t uplo, magma_trans_t transA, magma_diag_t diag, magma_int_t flag, magma_int_t m, magma_int_t n, float alpha, float **dA_array, magma_int_t ldda, float **dB_array, magma_int_t lddb, float **dX_array, magma_int_t lddx, float **dinvA_array, magma_int_t dinvA_length, float **dA_displ, float **dB_displ, float **dX_displ, float **dinvA_displ, magma_int_t resetozero, magma_int_t batchCount, magma_queue_t queue)
void magmablas_strsm_batched (magma_side_t side, magma_uplo_t uplo, magma_trans_t transA, magma_diag_t diag, magma_int_t m, magma_int_t n, float alpha, float **dA_array, magma_int_t ldda, float **dB_array, magma_int_t lddb, magma_int_t batchCount, magma_queue_t queue)
void magmablas_strtri_diag_q (magma_uplo_t uplo, magma_diag_t diag, magma_int_t n, magmaFloat_const_ptr dA, magma_int_t ldda, magmaFloat_ptr d_dinvA, magma_queue_t queue)
 Inverts the NB x NB diagonal blocks of a triangular matrix.
void magmablas_strtri_diag (magma_uplo_t uplo, magma_diag_t diag, magma_int_t n, magmaFloat_const_ptr dA, magma_int_t ldda, magmaFloat_ptr d_dinvA)
void magmablas_strtri_diag_batched (magma_uplo_t uplo, magma_diag_t diag, magma_int_t n, float const *const *dA_array, magma_int_t ldda, float **dinvA_array, magma_int_t resetozero, magma_int_t batchCount, magma_queue_t queue)
 Inverts the NB x NB diagonal blocks of a triangular matrix.

Function Documentation

void magma_sgemm ( magma_trans_t  transA,
magma_trans_t  transB,
magma_int_t  m,
magma_int_t  n,
magma_int_t  k,
float  alpha,
magmaFloat_const_ptr  dA,
magma_int_t  ldda,
magmaFloat_const_ptr  dB,
magma_int_t  lddb,
float  beta,
magmaFloat_ptr  dC,
magma_int_t  lddc 
)

Perform matrix-matrix product, $ C = \alpha op(A) op(B) + \beta C $.

Parameters:
[in] transA Operation op(A) to perform on matrix A.
[in] transB Operation op(B) to perform on matrix B.
[in] m Number of rows of C and op(A). m >= 0.
[in] n Number of columns of C and op(B). n >= 0.
[in] k Number of columns of op(A) and rows of op(B). k >= 0.
[in] alpha Scalar $ \alpha $
[in] dA REAL array on GPU device. If transA == MagmaNoTrans, the m-by-k matrix A of dimension (ldda,k), ldda >= max(1,m);
otherwise, the k-by-m matrix A of dimension (ldda,m), ldda >= max(1,k).
[in] ldda Leading dimension of dA.
[in] dB REAL array on GPU device. If transB == MagmaNoTrans, the k-by-n matrix B of dimension (lddb,n), lddb >= max(1,k);
otherwise, the n-by-k matrix B of dimension (lddb,k), lddb >= max(1,n).
[in] lddb Leading dimension of dB.
[in] beta Scalar $ \beta $
[in,out] dC REAL array on GPU device. The m-by-n matrix C of dimension (lddc,n), lddc >= max(1,m).
[in] lddc Leading dimension of dC.
void magma_ssymm ( magma_side_t  side,
magma_uplo_t  uplo,
magma_int_t  m,
magma_int_t  n,
float  alpha,
magmaFloat_const_ptr  dA,
magma_int_t  ldda,
magmaFloat_const_ptr  dB,
magma_int_t  lddb,
float  beta,
magmaFloat_ptr  dC,
magma_int_t  lddc 
)

Perform symmetric matrix-matrix product.

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

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 REAL array on GPU device. If side == MagmaLeft, the m-by-m symmetric matrix A of dimension (ldda,m), ldda >= max(1,m);
otherwise, the n-by-n symmetric matrix A of dimension (ldda,n), ldda >= max(1,n).
[in] ldda Leading dimension of dA.
[in] dB REAL 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 REAL array on GPU device. The m-by-n matrix C of dimension (lddc,n), lddc >= max(1,m).
[in] lddc Leading dimension of dC.
void magma_ssyr2k ( magma_uplo_t  uplo,
magma_trans_t  trans,
magma_int_t  n,
magma_int_t  k,
float  alpha,
magmaFloat_const_ptr  dA,
magma_int_t  ldda,
magmaFloat_const_ptr  dB,
magma_int_t  lddb,
float  beta,
magmaFloat_ptr  dC,
magma_int_t  lddc 
)

Perform symmetric rank-2k update.

$ C = \alpha A B^T + \alpha B A^T \beta C $ (trans == MagmaNoTrans), or
$ C = \alpha A^T B + \alpha B^T A \beta C $ (trans == MagmaTrans),
where $ C $ is symmetric.

Parameters:
[in] uplo Whether the upper or lower triangle of C is referenced.
[in] trans Operation to perform on A and B.
[in] n Number of rows and columns of C. n >= 0.
[in] k Number of columns of A and B (for MagmaNoTrans) or rows of A and B (for MagmaTrans). k >= 0.
[in] alpha Scalar $ \alpha $
[in] dA REAL 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] ldda Leading dimension of dA.
[in] dB REAL array on GPU device. If trans == MagmaNoTrans, the n-by-k matrix B of dimension (lddb,k), lddb >= max(1,n);
otherwise, the k-by-n matrix B of dimension (lddb,n), lddb >= max(1,k).
[in] lddb Leading dimension of dB.
[in] beta Scalar $ \beta $
[in,out] dC REAL array on GPU device. The n-by-n symmetric matrix C of dimension (lddc,n), lddc >= max(1,n).
[in] lddc Leading dimension of dC.
void magma_ssyrk ( magma_uplo_t  uplo,
magma_trans_t  trans,
magma_int_t  n,
magma_int_t  k,
float  alpha,
magmaFloat_const_ptr  dA,
magma_int_t  ldda,
float  beta,
magmaFloat_ptr  dC,
magma_int_t  lddc 
)

Perform symmetric rank-k update.

$ C = \alpha A A^T + \beta C $ (trans == MagmaNoTrans), or
$ C = \alpha A^T A + \beta C $ (trans == MagmaTrans),
where $ C $ is symmetric.

Parameters:
[in] uplo Whether the upper or lower triangle of C is referenced.
[in] trans Operation to perform on A.
[in] n Number of rows and columns of C. n >= 0.
[in] k Number of columns of A (for MagmaNoTrans) or rows of A (for MagmaTrans). k >= 0.
[in] alpha Scalar $ \alpha $
[in] dA REAL 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] ldda Leading dimension of dA.
[in] beta Scalar $ \beta $
[in,out] dC REAL array on GPU device. The n-by-n symmetric matrix C of dimension (lddc,n), lddc >= max(1,n).
[in] lddc Leading dimension of dC.
void magma_strmm ( magma_side_t  side,
magma_uplo_t  uplo,
magma_trans_t  trans,
magma_diag_t  diag,
magma_int_t  m,
magma_int_t  n,
float  alpha,
magmaFloat_const_ptr  dA,
magma_int_t  ldda,
magmaFloat_ptr  dB,
magma_int_t  lddb 
)

Perform triangular matrix-matrix product.

$ B = \alpha op(A) B $ (side == MagmaLeft), or
$ B = \alpha B op(A) $ (side == MagmaRight),
where $ A $ is triangular.

Parameters:
[in] side Whether A is on the left or right.
[in] uplo Whether A is upper or lower triangular.
[in] trans Operation to perform on A.
[in] diag Whether the diagonal of A is assumed to be unit or non-unit.
[in] m Number of rows of B. m >= 0.
[in] n Number of columns of B. n >= 0.
[in] alpha Scalar $ \alpha $
[in] dA REAL array on GPU device. If side == MagmaLeft, the n-by-n triangular matrix A of dimension (ldda,n), ldda >= max(1,n);
otherwise, the m-by-m triangular matrix A of dimension (ldda,m), ldda >= max(1,m).
[in] ldda Leading dimension of dA.
[in] dB REAL array on GPU device. The m-by-n matrix B of dimension (lddb,n), lddb >= max(1,m).
[in] lddb Leading dimension of dB.
void magma_strsm ( magma_side_t  side,
magma_uplo_t  uplo,
magma_trans_t  trans,
magma_diag_t  diag,
magma_int_t  m,
magma_int_t  n,
float  alpha,
magmaFloat_const_ptr  dA,
magma_int_t  ldda,
magmaFloat_ptr  dB,
magma_int_t  lddb 
)

Solve triangular matrix-matrix system (multiple right-hand sides).

$ op(A) X = \alpha B $ (side == MagmaLeft), or
$ X op(A) = \alpha B $ (side == MagmaRight),
where $ A $ is triangular.

Parameters:
[in] side Whether A is on the left or right.
[in] uplo Whether A is upper or lower triangular.
[in] trans Operation to perform on A.
[in] diag Whether the diagonal of A is assumed to be unit or non-unit.
[in] m Number of rows of B. m >= 0.
[in] n Number of columns of B. n >= 0.
[in] alpha Scalar $ \alpha $
[in] dA REAL array on GPU device. If side == MagmaLeft, the m-by-m triangular matrix A of dimension (ldda,m), ldda >= max(1,m);
otherwise, the n-by-n triangular matrix A of dimension (ldda,n), ldda >= max(1,n).
[in] ldda Leading dimension of dA.
[in,out] dB REAL array on GPU device. On entry, m-by-n matrix B of dimension (lddb,n), lddb >= max(1,m). On exit, overwritten with the solution matrix X.
[in] lddb Leading dimension of dB.
magma_int_t magma_strsm_m ( magma_int_t  ngpu,
magma_side_t  side,
magma_uplo_t  uplo,
magma_trans_t  transa,
magma_diag_t  diag,
magma_int_t  m,
magma_int_t  n,
float  alpha,
float *  A,
magma_int_t  lda,
float *  B,
magma_int_t  ldb 
)

STRSM solves one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B, where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of.

op( A ) = A or op( A ) = A**T or op( A ) = A**H.

The matrix X is overwritten on B.

Parameters:
[in] ngpu INTEGER Number of GPUs to use. ngpu > 0.
[in] side magma_side_t. On entry, SIDE specifies whether op( A ) appears on the left or right of X as follows:

  • = MagmaLeft: op( A )*X = alpha*B.
  • = MagmaRight: X*op( A ) = alpha*B.
[in] uplo magma_uplo_t. On entry, UPLO specifies whether the matrix A is an upper or lower triangular matrix as follows:

  • = MagmaUpper: A is an upper triangular matrix.
  • = MagmaLower: A is a lower triangular matrix.
[in] transa magma_trans_t. On entry, TRANSA specifies the form of op( A ) to be used in the matrix multiplication as follows:

  • = MagmaNoTrans: op( A ) = A.
  • = MagmaTrans: op( A ) = A**T.
  • = MagmaConjTrans: op( A ) = A**H.
[in] diag magma_diag_t. On entry, DIAG specifies whether or not A is unit triangular as follows:

  • = MagmaUnit: A is assumed to be unit triangular.
  • = MagmaNonUnit: A is not assumed to be unit triangular.
[in] m INTEGER. On entry, M specifies the number of rows of B. M must be at least zero.
[in] n INTEGER. On entry, N specifies the number of columns of B. N must be at least zero.
[in] alpha REAL. On entry, ALPHA specifies the scalar alpha. When alpha is zero then A is not referenced and B need not be set before entry.
[in] A REAL array of DIMENSION ( LDA, k ), where k is m when SIDE = MagmaLeft and is n when SIDE = MagmaRight. Before entry with UPLO = MagmaUpper, the leading k by k upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. Before entry with UPLO = MagmaLower, the leading k by k lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. Note that when DIAG = MagmaUnit, the diagonal elements of A are not referenced either, but are assumed to be unity.
[in] lda INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When SIDE = MagmaLeft then LDA >= max( 1, m ), when SIDE = MagmaRight then LDA >= max( 1, n ).
[in,out] B REAL array of DIMENSION ( LDB, n ). Before entry, the leading m by n part of the array B must contain the right-hand side matrix B, and on exit is overwritten by the solution matrix X.
[in] ldb INTEGER. On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. LDB must be at least max( 1, m ).
void magmablas_sgemm ( magma_trans_t  transA,
magma_trans_t  transB,
magma_int_t  m,
magma_int_t  n,
magma_int_t  k,
float  alpha,
magmaFloat_const_ptr  dA,
magma_int_t  ldda,
magmaFloat_const_ptr  dB,
magma_int_t  lddb,
float  beta,
magmaFloat_ptr  dC,
magma_int_t  lddc 
)

SGEMM performs one of the matrix-matrix operations.

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

where op( X ) is one of

op( X ) = X or op( X ) = X**T or op( X ) = X**H,

alpha and beta are scalars, and A, B and C are matrices, with op( A ) an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.

Parameters ----------

Parameters:
[in] transA CHARACTER*1. On entry, transA specifies the form of op( A ) to be used in the matrix multiplication as follows:

  • = 'N': op( A ) = A.
  • = 'T': op( A ) = A**T.
  • = 'C': op( A ) = A**H.
[in] transB CHARACTER*1. On entry, transB specifies the form of op( B ) to be used in the matrix multiplication as follows:

  • = 'N': op( B ) = B.
  • = 'T': op( B ) = B**T.
  • = 'C': op( B ) = B**H.
[in] m INTEGER. On entry, M specifies the number of rows of the matrix op( dA ) and of the matrix dC. M must be at least zero.
[in] n INTEGER. On entry, N specifies the number of columns of the matrix op( dB ) and the number of columns of the matrix dC. N must be at least zero.
[in] k INTEGER. On entry, K specifies the number of columns of the matrix op( dA ) and the number of rows of the matrix op( dB ). K must be at least zero.
[in] alpha REAL On entry, ALPHA specifies the scalar alpha.
[in] dA REAL array of DIMENSION ( LDA, ka ), where ka is k when transA = MagmaNoTrans, and is m otherwise. Before entry with transA = MagmaNoTrans, the leading m by k part of the array dA must contain the matrix dA, otherwise the leading k by m part of the array dA must contain the matrix dA.
[in] ldda INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When transA = MagmaNoTrans then LDA must be at least max( 1, m ), otherwise LDA must be at least max( 1, k ).
[in] dB REAL array of DIMENSION ( LDB, kb ), where kb is n when transB = MagmaNoTrans, and is k otherwise. Before entry with transB = MagmaNoTrans, the leading k by n part of the array dB must contain the matrix dB, otherwise the leading n by k part of the array dB must contain the matrix dB.
[in] lddb INTEGER. On entry, LDB specifies the first dimension of dB as declared in the calling (sub) program. When transB = MagmaNoTrans then LDB must be at least max( 1, k ), otherwise LDB must be at least max( 1, n ).
[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 REAL array of DIMENSION ( LDC, n ). Before entry, the leading m by n part of the array dC must contain the matrix dC, except when beta is zero, in which case dC need not be set on entry. On exit, the array dC is overwritten by the m by n matrix ( alpha*op( dA )*op( dB ) + beta*dC ).
[in] lddc INTEGER. On entry, LDC specifies the first dimension of dC as declared in the calling (sub) program. LDC must be at least max( 1, m ).
void magmablas_sgemm_batched ( magma_trans_t  transA,
magma_trans_t  transB,
magma_int_t  m,
magma_int_t  n,
magma_int_t  k,
float  alpha,
float const *const *  dA_array,
magma_int_t  ldda,
float const *const *  dB_array,
magma_int_t  lddb,
float  beta,
float **  dC_array,
magma_int_t  lddc,
magma_int_t  batchCount,
magma_queue_t  queue 
)

SGEMM performs one of the matrix-matrix operations.

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

where op( X ) is one of

op( X ) = X or op( X ) = X**T or op( X ) = X**H,

alpha and beta are scalars, and A, B and C are matrices, with op( A ) an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.

Parameters ----------

Parameters:
[in] transA CHARACTER*1. On entry, transA specifies the form of op( A ) to be used in the matrix multiplication as follows:

  • = 'N': op( A ) = A.
  • = 'T': op( A ) = A**T.
  • = 'C': op( A ) = A**H.
[in] transB CHARACTER*1. On entry, transB specifies the form of op( B ) to be used in the matrix multiplication as follows:

  • = 'N': op( B ) = B.
  • = 'T': op( B ) = B**T.
  • = 'C': op( B ) = B**H.
[in] m INTEGER. On entry, M specifies the number of rows of the matrix op( dA ) and of the matrix dC. M must be at least zero.
[in] n INTEGER. On entry, N specifies the number of columns of the matrix op( dB ) and the number of columns of the matrix dC. N must be at least zero.
[in] k INTEGER. On entry, K specifies the number of columns of the matrix op( dA ) and the number of rows of the matrix op( dB ). K must be at least zero.
[in] alpha REAL On entry, ALPHA specifies the scalar alpha.
[in] dA REAL array of DIMENSION ( LDA, ka ), where ka is k when transA = MagmaNoTrans, and is m otherwise. Before entry with transA = MagmaNoTrans, the leading m by k part of the array dA must contain the matrix dA, otherwise the leading k by m part of the array dA must contain the matrix dA.
[in] ldda INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When transA = MagmaNoTrans then LDA must be at least max( 1, m ), otherwise LDA must be at least max( 1, k ).
[in] dB REAL array of DIMENSION ( LDB, kb ), where kb is n when transB = MagmaNoTrans, and is k otherwise. Before entry with transB = MagmaNoTrans, the leading k by n part of the array dB must contain the matrix dB, otherwise the leading n by k part of the array dB must contain the matrix dB.
[in] lddb INTEGER. On entry, LDB specifies the first dimension of dB as declared in the calling (sub) program. When transB = MagmaNoTrans then LDB must be at least max( 1, k ), otherwise LDB must be at least max( 1, n ).
[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 REAL array of DIMENSION ( LDC, n ). Before entry, the leading m by n part of the array dC must contain the matrix dC, except when beta is zero, in which case dC need not be set on entry. On exit, the array dC is overwritten by the m by n matrix ( alpha*op( dA )*op( dB ) + beta*dC ).
[in] lddc INTEGER. On entry, LDC specifies the first dimension of dC as declared in the calling (sub) program. LDC must be at least max( 1, m ).
void magmablas_sgemm_batched_k32 ( magma_trans_t  transA,
magma_trans_t  transB,
magma_int_t  m,
magma_int_t  n,
magma_int_t  k,
float  alpha,
float const *const *  dA_array,
magma_int_t  ldda,
float const *const *  dB_array,
magma_int_t  lddb,
float  beta,
float **  dC_array,
magma_int_t  lddc,
magma_int_t  batchCount,
magma_queue_t  queue 
)

SGEMM performs one of the matrix-matrix operations.

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

where op( X ) is one of

op( X ) = X or op( X ) = X**T or op( X ) = X**H,

alpha and beta are scalars, and A, B and C are matrices, with op( A ) an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.

Parameters ----------

Parameters:
[in] transA CHARACTER*1. On entry, transA specifies the form of op( A ) to be used in the matrix multiplication as follows:

  • = 'N': op( A ) = A.
  • = 'T': op( A ) = A**T.
  • = 'C': op( A ) = A**H.
[in] transB CHARACTER*1. On entry, transB specifies the form of op( B ) to be used in the matrix multiplication as follows:

  • = 'N': op( B ) = B.
  • = 'T': op( B ) = B**T.
  • = 'C': op( B ) = B**H.
[in] m INTEGER. On entry, M specifies the number of rows of the matrix op( dA ) and of the matrix dC. M must be at least zero.
[in] n INTEGER. On entry, N specifies the number of columns of the matrix op( dB ) and the number of columns of the matrix dC. N must be at least zero.
[in] k INTEGER. On entry, K specifies the number of columns of the matrix op( dA ) and the number of rows of the matrix op( dB ). K must be at least zero.
[in] alpha REAL On entry, ALPHA specifies the scalar alpha.
[in] dA REAL array of DIMENSION ( LDA, ka ), where ka is k when transA = MagmaNoTrans, and is m otherwise. Before entry with transA = MagmaNoTrans, the leading m by k part of the array dA must contain the matrix dA, otherwise the leading k by m part of the array dA must contain the matrix dA.
[in] ldda INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When transA = MagmaNoTrans then LDA must be at least max( 1, m ), otherwise LDA must be at least max( 1, k ).
[in] dB REAL array of DIMENSION ( LDB, kb ), where kb is n when transB = MagmaNoTrans, and is k otherwise. Before entry with transB = MagmaNoTrans, the leading k by n part of the array dB must contain the matrix dB, otherwise the leading n by k part of the array dB must contain the matrix dB.
[in] lddb INTEGER. On entry, LDB specifies the first dimension of dB as declared in the calling (sub) program. When transB = MagmaNoTrans then LDB must be at least max( 1, k ), otherwise LDB must be at least max( 1, n ).
[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 REAL array of DIMENSION ( LDC, n ). Before entry, the leading m by n part of the array dC must contain the matrix dC, except when beta is zero, in which case dC need not be set on entry. On exit, the array dC is overwritten by the m by n matrix ( alpha*op( dA )*op( dB ) + beta*dC ).
[in] lddc INTEGER. On entry, LDC specifies the first dimension of dC as declared in the calling (sub) program. LDC must be at least max( 1, m ).
void magmablas_sgemm_batched_lg ( magma_trans_t  transA,
magma_trans_t  transB,
magma_int_t  m,
magma_int_t  n,
magma_int_t  k,
float  alpha,
float const *const *  dA_array,
magma_int_t  ldda,
float const *const *  dB_array,
magma_int_t  lddb,
float  beta,
float **  dC_array,
magma_int_t  lddc,
magma_int_t  batchCount,
magma_queue_t  queue 
)

SGEMM performs one of the matrix-matrix operations.

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

where op( X ) is one of

op( X ) = X or op( X ) = X**T or op( X ) = X**H,

alpha and beta are scalars, and A, B and C are matrices, with op( A ) an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.

Parameters ----------

Parameters:
[in] transA CHARACTER*1. On entry, transA specifies the form of op( A ) to be used in the matrix multiplication as follows:

  • = 'N': op( A ) = A.
  • = 'T': op( A ) = A**T.
  • = 'C': op( A ) = A**H.
[in] transB CHARACTER*1. On entry, transB specifies the form of op( B ) to be used in the matrix multiplication as follows:

  • = 'N': op( B ) = B.
  • = 'T': op( B ) = B**T.
  • = 'C': op( B ) = B**H.
[in] m INTEGER. On entry, M specifies the number of rows of the matrix op( dA ) and of the matrix dC. M must be at least zero.
[in] n INTEGER. On entry, N specifies the number of columns of the matrix op( dB ) and the number of columns of the matrix dC. N must be at least zero.
[in] k INTEGER. On entry, K specifies the number of columns of the matrix op( dA ) and the number of rows of the matrix op( dB ). K must be at least zero.
[in] alpha REAL On entry, ALPHA specifies the scalar alpha.
[in] dA REAL array of DIMENSION ( LDA, ka ), where ka is k when transA = MagmaNoTrans, and is m otherwise. Before entry with transA = MagmaNoTrans, the leading m by k part of the array dA must contain the matrix dA, otherwise the leading k by m part of the array dA must contain the matrix dA.
[in] ldda INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When transA = MagmaNoTrans then LDA must be at least max( 1, m ), otherwise LDA must be at least max( 1, k ).
[in] dB REAL array of DIMENSION ( LDB, kb ), where kb is n when transB = MagmaNoTrans, and is k otherwise. Before entry with transB = MagmaNoTrans, the leading k by n part of the array dB must contain the matrix dB, otherwise the leading n by k part of the array dB must contain the matrix dB.
[in] lddb INTEGER. On entry, LDB specifies the first dimension of dB as declared in the calling (sub) program. When transB = MagmaNoTrans then LDB must be at least max( 1, k ), otherwise LDB must be at least max( 1, n ).
[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 REAL array of DIMENSION ( LDC, n ). Before entry, the leading m by n part of the array dC must contain the matrix dC, except when beta is zero, in which case dC need not be set on entry. On exit, the array dC is overwritten by the m by n matrix ( alpha*op( dA )*op( dB ) + beta*dC ).
[in] lddc INTEGER. On entry, LDC specifies the first dimension of dC as declared in the calling (sub) program. LDC must be at least max( 1, m ).
void magmablas_sgemm_reduce ( magma_int_t  m,
magma_int_t  n,
magma_int_t  k,
float  alpha,
magmaFloat_const_ptr  dA,
magma_int_t  ldda,
magmaFloat_const_ptr  dB,
magma_int_t  lddb,
float  beta,
magmaFloat_ptr  dC,
magma_int_t  lddc 
)

SGEMM_REDUCE performs one of the matrix-matrix operations.

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

where alpha and beta are scalars, and A, B and C are matrices, with A a k-by-m matrix, B a k-by-n matrix, and C an m-by-n matrix.

This routine is tuned for m, n << k. Typically, m and n are expected to be less than 128.

void magmablas_sgemm_tesla ( magma_trans_t  transA,
magma_trans_t  transB,
magma_int_t  m,
magma_int_t  n,
magma_int_t  k,
float  alpha,
const float *  A,
magma_int_t  lda,
const float *  B,
magma_int_t  ldb,
float  beta,
float *  C,
magma_int_t  ldc 
)

SGEMM performs one of the matrix-matrix operations.

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

where op( X ) is one of

op( X ) = X or op( X ) = X**T,

alpha and beta are scalars, and A, B and C are matrices, with op( A ) an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.

Parameters ----------

Parameters:
[in] transA magma_trans_t. On entry, transA specifies the form of op( A ) to be used in the matrix multiplication as follows:

  • = MagmaNoTrans: op( A ) = A.
  • = MagmaTrans: op( A ) = A**T.
  • = MagmaConjTrans: op( A ) = A**T.
[in] transB magma_trans_t. On entry, transB specifies the form of op( B ) to be used in the matrix multiplication as follows:

  • = MagmaNoTrans: op( B ) = B.
  • = MagmaTrans: op( B ) = B**T.
  • = MagmaConjTrans: op( B ) = B**T.
[in] m INTEGER. On entry, M specifies the number of rows of the matrix op( A ) and of the matrix C. M must be at least zero.
[in] n INTEGER. On entry, N specifies the number of columns of the matrix op( B ) and the number of columns of the matrix C. N must be at least zero.
[in] k INTEGER. On entry, K specifies the number of columns of the matrix op( A ) and the number of rows of the matrix op( B ). K must be at least zero.
[in] alpha REAL. On entry, ALPHA specifies the scalar alpha.
[in] A REAL array of DIMENSION ( LDA, ka ), where ka is k when transA = MagmaNoTrans, and is m otherwise. Before entry with transA = 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] lda INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When transA = MagmaNoTrans then LDA must be at least max( 1, m ), otherwise LDA must be at least max( 1, k ).
[in] B REAL array of DIMENSION ( LDB, kb ), where kb is n when transB = MagmaNoTrans, and is k otherwise. Before entry with transB = MagmaNoTrans, the leading k by n part of the array B must contain the matrix B, otherwise the leading n by k part of the array B must contain the matrix B.
[in] ldb INTEGER. On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. When transB = MagmaNoTrans then LDB must be at least max( 1, k ), otherwise LDB must be at least max( 1, n ).
[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] C REAL array of DIMENSION ( LDC, 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 matrix ( alpha*op( A )*op( B ) + beta*C ).
[in] ldc INTEGER. On entry, LDC specifies the first dimension of C as declared in the calling (sub) program. LDC must be at least max( 1, m ).
void magmablas_ssyr2k_mgpu2 ( magma_uplo_t  uplo,
magma_trans_t  trans,
magma_int_t  n,
magma_int_t  k,
float  alpha,
magmaFloat_ptr  dA[],
magma_int_t  ldda,
magma_int_t  a_offset,
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  ngpu,
magma_int_t  nb,
magma_queue_t  queues[][20],
magma_int_t  nqueue 
)

SSYR2K performs one of the symmetric rank 2k operations.

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

or

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

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

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:

  • = MagmaUpper: Only the upper triangular part of C is to be referenced.
  • = MagmaLower: Only the lower triangular part of C is to be referenced.

current only Lower case is implemented.

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

  • = MagmaNoTrans: C := alpha*A*B**H + conj( alpha )*B*A**H + beta*C.
  • = MagmaTrans: C := alpha*A**H*B + conj( alpha )*B**H*A + beta*C.

current only NoTrans case is implemented.

Parameters:
[in] n INTEGER. On entry, N 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 matrices A and B, and on entry with TRANS = MagmaTrans, K specifies the number of rows of the matrices A and B. K must be at least zero.
[in] alpha REAL. On entry, ALPHA specifies the scalar alpha.
[in] dA REAL array of DIMENSION ( LDA, 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.

[TODO: describe distribution: duplicated on all GPUs.]

Parameters:
[in] ldda INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When TRANS = MagmaNoTrans then LDA must be at least max( 1, n ), otherwise LDA must be at least max( 1, k ).
[in] a_offset INTEGER Row offset to start sub-matrix of dA. Uses dA(a_offset:a_offset+n, :). 0 <= a_offset < ldda.
[in] dB REAL array of DIMENSION ( LDB, kb ), where kb is k when TRANS = MagmaNoTrans, and is n otherwise. Before entry with TRANS = MagmaNoTrans, the leading n by k part of the array B must contain the matrix B, otherwise the leading k by n part of the array B must contain the matrix B.

[TODO: describe distribution: duplicated on all GPUs.]

Parameters:
[in] lddb INTEGER. On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. When TRANS = MagmaNoTrans then LDB must be at least max( 1, n ), otherwise LDB must be at least max( 1, k ).
[in] b_offset INTEGER Row offset to start sub-matrix of dB. Uses dB(b_offset:b_offset+n, :). 0 <= b_offset < lddb.
[in] beta REAL. On entry, BETA specifies the scalar beta.
[in,out] dC REAL array of DIMENSION ( LDC, 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. [TODO: verify]

[TODO: describe distribution: 1D column block-cyclic across GPUs.]

Parameters:
[in] lddc INTEGER. On entry, LDC specifies the first dimension of C as declared in the calling (sub) program. LDC must be at least max( 1, n ).
[in] c_offset INTEGER. Row and column offset to start sub-matrix of dC. Uses dC(c_offset:c_offset+n, c_offset:c_offset+n). 0 <= c_offset < lddc.
[in] ngpu INTEGER. Number of GPUs over which matrix C is distributed.
[in] nb INTEGER. Block size used for distribution of C.
[in] queues array of CUDA queues, of dimension NGPU by 20. Streams to use for running multiple GEMMs in parallel. Only up to NSTREAM queues are used on each GPU.
[in] nqueue INTEGER. Number of queues to use on each device
void magmablas_ssyr2k_mgpu_spec ( magma_uplo_t  uplo,
magma_trans_t  trans,
magma_int_t  n,
magma_int_t  k,
float  alpha,
magmaFloat_ptr  dA[],
magma_int_t  ldda,
magma_int_t  a_offset,
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  ngpu,
magma_int_t  nb,
magma_queue_t  queues[][20],
magma_int_t  nqueue 
)

SSYR2K performs one of the symmetric rank 2k operations.

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

or

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

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

This version assumes C has been symmetrized, so both upper and lower are stored, and it maintains the symmetry, doing twice the operations.

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:

  • = MagmaUpper: Only the upper triangular part of C is to be referenced.
  • = MagmaLower: Only the lower triangular part of C is to be referenced.

current only Lower case is implemented.

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

  • = MagmaNoTrans: C := alpha*A*B**H + conj( alpha )*B*A**H + beta*C.
  • = MagmaTrans: C := alpha*A**H*B + conj( alpha )*B**H*A + beta*C.

current only NoTrans case is implemented.

Parameters:
[in] n INTEGER. On entry, N 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 matrices A and B, and on entry with TRANS = MagmaTrans, K specifies the number of rows of the matrices A and B. K must be at least zero.
[in] alpha REAL. On entry, ALPHA specifies the scalar alpha.
[in] dA REAL array of DIMENSION ( LDA, 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.

[TODO: describe distribution: duplicated on all GPUs.]

Parameters:
[in] ldda INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When TRANS = MagmaNoTrans then LDA must be at least max( 1, n ), otherwise LDA must be at least max( 1, k ).
[in] a_offset INTEGER Row offset to start sub-matrix of dA. Uses dA(a_offset:a_offset+n, :). 0 <= a_offset < ldda.
[in] dB REAL array of DIMENSION ( LDB, kb ), where kb is k when TRANS = MagmaNoTrans, and is n otherwise. Before entry with TRANS = MagmaNoTrans, the leading n by k part of the array B must contain the matrix B, otherwise the leading k by n part of the array B must contain the matrix B.

[TODO: describe distribution: duplicated on all GPUs.]

Parameters:
[in] lddb INTEGER. On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. When TRANS = MagmaNoTrans then LDB must be at least max( 1, n ), otherwise LDB must be at least max( 1, k ).
[in] b_offset INTEGER Row offset to start sub-matrix of dB. Uses dB(b_offset:b_offset+n, :). 0 <= b_offset < lddb.
[in] beta REAL. On entry, BETA specifies the scalar beta.
[in,out] dC REAL array of DIMENSION ( LDC, 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. [TODO: verify]

[TODO: describe distribution: 1D column block-cyclic across GPUs.]

Parameters:
[in] lddc INTEGER. On entry, LDC specifies the first dimension of C as declared in the calling (sub) program. LDC must be at least max( 1, n ).
[in] c_offset INTEGER. Row and column offset to start sub-matrix of dC. Uses dC(c_offset:c_offset+n, c_offset:c_offset+n). 0 <= c_offset < lddc.
[in] ngpu INTEGER. Number of GPUs over which matrix C is distributed.
[in] nb INTEGER. Block size used for distribution of C.
[in] queues array of CUDA queues, of dimension NGPU by 20. Streams to use for running multiple GEMMs in parallel. Only up to NSTREAM queues are used on each GPU.
[in] nqueue INTEGER. Number of queues to use on each device
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.

Parameters ----------

Parameters:
[in] uplo CHARACTER*1. On entry, uplo specifies whether the upper or lower triangular part of the array C is to be referenced as follows:

uplo = 'U' or 'u' Only the upper triangular part of C is to be referenced.

uplo = 'L' or 'l' Only the lower triangular part of C is to be referenced.

Parameters:
[in] trans CHARACTER*1. On entry, trans specifies the operation to be performed as follows:

trans = 'N' or 'n' C := alpha*A*A**H + beta*C.

trans = 'C' or 'c' 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 = 'N' or 'n', k specifies the number of columns of the matrix A, and on entry with trans = 'C' or 'c', 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 REAL 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 dA must contain the matrix dA, otherwise the leading k by m part of the array dA must contain the matrix dA.
[in] ldda INTEGER. 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] 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 REAL array of DIMENSION ( lddc, n ). Before entry with uplo = 'U' or 'u', 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 = 'L' or 'l', 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 dC as declared in the calling (sub) program. lddc must be at least max( 1, m ).
void magmablas_ssyrk_batched_k32 ( 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 CHARACTER*1. On entry, uplo specifies whether the upper or lower triangular part of the array C is to be referenced as follows:

uplo = 'U' or 'u' Only the upper triangular part of C is to be referenced.

uplo = 'L' or 'l' Only the lower triangular part of C is to be referenced.

Parameters:
[in] trans CHARACTER*1. On entry, trans specifies the operation to be performed as follows:

trans = 'N' or 'n' C := alpha*A*A**H + beta*C.

trans = 'C' or 'c' 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 = 'N' or 'n', k specifies the number of columns of the matrix A, and on entry with trans = 'C' or 'c', 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 REAL 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 dA must contain the matrix dA, otherwise the leading k by m part of the array dA must contain the matrix dA.
[in] ldda INTEGER. 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] 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 REAL array of DIMENSION ( lddc, n ). Before entry with uplo = 'U' or 'u', 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 = 'L' or 'l', 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 dC as declared in the calling (sub) program. lddc must be at least max( 1, m ).
void magmablas_ssyrk_batched_lg ( 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 CHARACTER*1. On entry, uplo specifies whether the upper or lower triangular part of the array C is to be referenced as follows:

uplo = 'U' or 'u' Only the upper triangular part of C is to be referenced.

uplo = 'L' or 'l' Only the lower triangular part of C is to be referenced.

Parameters:
[in] trans CHARACTER*1. On entry, trans specifies the operation to be performed as follows:

trans = 'N' or 'n' C := alpha*A*A**H + beta*C.

trans = 'C' or 'c' 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 = 'N' or 'n', k specifies the number of columns of the matrix A, and on entry with trans = 'C' or 'c', 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 REAL 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 dA must contain the matrix dA, otherwise the leading k by m part of the array dA must contain the matrix dA.
[in] ldda INTEGER. 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] 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 REAL array of DIMENSION ( lddc, n ). Before entry with uplo = 'U' or 'u', 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 = 'L' or 'l', 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 dC as declared in the calling (sub) program. lddc must be at least max( 1, m ).
void magmablas_strsm ( magma_side_t  side,
magma_uplo_t  uplo,
magma_trans_t  transA,
magma_diag_t  diag,
magma_int_t  m,
magma_int_t  n,
float  alpha,
magmaFloat_const_ptr  dA,
magma_int_t  ldda,
magmaFloat_ptr  dB,
magma_int_t  lddb 
)
void magmablas_strsm_batched ( magma_side_t  side,
magma_uplo_t  uplo,
magma_trans_t  transA,
magma_diag_t  diag,
magma_int_t  m,
magma_int_t  n,
float  alpha,
float **  dA_array,
magma_int_t  ldda,
float **  dB_array,
magma_int_t  lddb,
magma_int_t  batchCount,
magma_queue_t  queue 
)
void magmablas_strsm_outofplace ( magma_side_t  side,
magma_uplo_t  uplo,
magma_trans_t  transA,
magma_diag_t  diag,
magma_int_t  m,
magma_int_t  n,
float  alpha,
magmaFloat_const_ptr  dA,
magma_int_t  ldda,
magmaFloat_ptr  dB,
magma_int_t  lddb,
magma_int_t  flag,
magmaFloat_ptr  d_dinvA,
magmaFloat_ptr  dX 
)

strsm_outofplace solves one of the matrix equations on gpu

op(A)*X = alpha*B, or X*op(A) = alpha*B,

where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower triangular matrix and op(A) is one of

op(A) = A, or op(A) = A^T, or op(A) = A^H.

The matrix X is output.

This is an asynchronous version of magmablas_strsm with flag, d_dinvA and dX workspaces as arguments.

Parameters:
[in] side magma_side_t. On entry, side specifies whether op(A) appears on the left or right of X as follows:

  • = MagmaLeft: op(A)*X = alpha*B.
  • = MagmaRight: X*op(A) = alpha*B.
[in] uplo magma_uplo_t. On entry, uplo specifies whether the matrix A is an upper or lower triangular matrix as follows:

  • = MagmaUpper: A is an upper triangular matrix.
  • = MagmaLower: A is a lower triangular matrix.
[in] transA magma_trans_t. On entry, transA specifies the form of op(A) to be used in the matrix multiplication as follows:

  • = MagmaNoTrans: op(A) = A.
  • = MagmaTrans: op(A) = A^T.
  • = MagmaConjTrans: op(A) = A^H.
[in] diag magma_diag_t. On entry, diag specifies whether or not A is unit triangular as follows:

  • = MagmaUnit: A is assumed to be unit triangular.
  • = MagmaNonUnit: A is not assumed to be unit triangular.
[in] m INTEGER. On entry, m specifies the number of rows of B. m >= 0.
[in] n INTEGER. On entry, n specifies the number of columns of B. n >= 0.
[in] alpha REAL. On entry, alpha specifies the scalar alpha. When alpha is zero then A is not referenced and B need not be set before entry.
[in] dA REAL array of dimension ( ldda, k ), where k is m when side = MagmaLeft and is n when side = MagmaRight. Before entry with uplo = MagmaUpper, the leading k by k upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. Before entry with uplo = MagmaLower, the leading k by k lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. Note that when diag = MagmaUnit, the diagonal elements of A are not referenced either, but are assumed to be unity.
[in] ldda INTEGER. On entry, ldda specifies the first dimension of A. When side = MagmaLeft, ldda >= max( 1, m ), when side = MagmaRight, 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 right-hand side matrix B.
[in] lddb INTEGER. On entry, lddb specifies the first dimension of B. lddb >= max( 1, m ).
[in] flag BOOLEAN. If flag is true, invert diagonal blocks. If flag is false, assume diagonal blocks (stored in d_dinvA) are already inverted.
d_dinvA (workspace) on device. If side == MagmaLeft, d_dinvA must be of size >= ceil(m/NB)*NB*NB, If side == MagmaRight, d_dinvA must be of size >= ceil(n/NB)*NB*NB, where NB = 128.
[out] dX REAL array of dimension ( m, n ). On exit it contain the solution matrix X.
void magmablas_strsm_outofplace_batched ( magma_side_t  side,
magma_uplo_t  uplo,
magma_trans_t  transA,
magma_diag_t  diag,
magma_int_t  flag,
magma_int_t  m,
magma_int_t  n,
float  alpha,
float **  dA_array,
magma_int_t  ldda,
float **  dB_array,
magma_int_t  lddb,
float **  dX_array,
magma_int_t  lddx,
float **  dinvA_array,
magma_int_t  dinvA_length,
float **  dA_displ,
float **  dB_displ,
float **  dX_displ,
float **  dinvA_displ,
magma_int_t  resetozero,
magma_int_t  batchCount,
magma_queue_t  queue 
)

strsm_work solves one of the matrix equations on gpu

op(A)*X = alpha*B, or X*op(A) = alpha*B,

where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower triangular matrix and op(A) is one of

op(A) = A, or op(A) = A^T, or op(A) = A^H.

The matrix X is overwritten on B.

This is an asynchronous version of magmablas_strsm with flag, d_dinvA and dX workspaces as arguments.

Parameters:
[in] side magma_side_t. On entry, side specifies whether op(A) appears on the left or right of X as follows:

  • = MagmaLeft: op(A)*X = alpha*B.
  • = MagmaRight: X*op(A) = alpha*B.
[in] uplo magma_uplo_t. On entry, uplo specifies whether the matrix A is an upper or lower triangular matrix as follows:

  • = MagmaUpper: A is an upper triangular matrix.
  • = MagmaLower: A is a lower triangular matrix.
[in] transA magma_trans_t. On entry, transA specifies the form of op(A) to be used in the matrix multiplication as follows:

  • = MagmaNoTrans: op(A) = A.
  • = MagmaTrans: op(A) = A^T.
  • = MagmaConjTrans: op(A) = A^H.
[in] diag magma_diag_t. On entry, diag specifies whether or not A is unit triangular as follows:

  • = MagmaUnit: A is assumed to be unit triangular.
  • = MagmaNonUnit: A is not assumed to be unit triangular.
[in] m INTEGER. On entry, m specifies the number of rows of B. m >= 0.
[in] n INTEGER. On entry, n specifies the number of columns of B. n >= 0.
[in] alpha REAL. On entry, alpha specifies the scalar alpha. When alpha is zero then A is not referenced and B need not be set before entry.
[in] dA REAL array of dimension ( ldda, k ), where k is m when side = MagmaLeft and is n when side = MagmaRight. Before entry with uplo = MagmaUpper, the leading k by k upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. Before entry with uplo = MagmaLower, the leading k by k lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. Note that when diag = MagmaUnit, the diagonal elements of A are not referenced either, but are assumed to be unity.
[in] ldda INTEGER. On entry, ldda specifies the first dimension of A. When side = MagmaLeft, ldda >= max( 1, m ), when side = MagmaRight, 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 right-hand side matrix B.
[in] lddb INTEGER. On entry, lddb specifies the first dimension of B. lddb >= max( 1, m ).
[in] flag BOOLEAN. If flag is true, invert diagonal blocks. If flag is false, assume diagonal blocks (stored in d_dinvA) are already inverted.
d_dinvA (workspace) on device. If side == MagmaLeft, d_dinvA must be of size >= ceil(m/TRI_NB)*TRI_NB*TRI_NB, If side == MagmaRight, d_dinvA must be of size >= ceil(n/TRI_NB)*TRI_NB*TRI_NB, where TRI_NB = 128.
[out] dX REAL array of dimension ( lddx, n ). On exit it contain the solution matrix X.
void magmablas_strsm_work ( magma_side_t  side,
magma_uplo_t  uplo,
magma_trans_t  transA,
magma_diag_t  diag,
magma_int_t  m,
magma_int_t  n,
float  alpha,
magmaFloat_const_ptr  dA,
magma_int_t  ldda,
magmaFloat_ptr  dB,
magma_int_t  lddb,
magma_int_t  flag,
magmaFloat_ptr  d_dinvA,
magmaFloat_ptr  dX 
)
void magmablas_strsm_work_batched ( magma_side_t  side,
magma_uplo_t  uplo,
magma_trans_t  transA,
magma_diag_t  diag,
magma_int_t  flag,
magma_int_t  m,
magma_int_t  n,
float  alpha,
float **  dA_array,
magma_int_t  ldda,
float **  dB_array,
magma_int_t  lddb,
float **  dX_array,
magma_int_t  lddx,
float **  dinvA_array,
magma_int_t  dinvA_length,
float **  dA_displ,
float **  dB_displ,
float **  dX_displ,
float **  dinvA_displ,
magma_int_t  resetozero,
magma_int_t  batchCount,
magma_queue_t  queue 
)
void magmablas_strtri_diag ( magma_uplo_t  uplo,
magma_diag_t  diag,
magma_int_t  n,
magmaFloat_const_ptr  dA,
magma_int_t  ldda,
magmaFloat_ptr  d_dinvA 
)
void magmablas_strtri_diag_batched ( magma_uplo_t  uplo,
magma_diag_t  diag,
magma_int_t  n,
float const *const *  dA_array,
magma_int_t  ldda,
float **  dinvA_array,
magma_int_t  resetozero,
magma_int_t  batchCount,
magma_queue_t  queue 
)

Inverts the NB x NB diagonal blocks of a triangular matrix.

This routine is used in strsm.

Same as strtri_diag, but adds queue argument. strtri_diag inverts the NB x NB diagonal blocks of A.

Parameters:
[in] uplo magma_uplo_t. On entry, uplo specifies whether the matrix A is an upper or lower triangular matrix as follows:

  • = MagmaUpper: A is an upper triangular matrix.
  • = MagmaLower: A is a lower triangular matrix.
[in] diag magma_diag_t. On entry, diag specifies whether or not A is unit triangular as follows:

  • = MagmaUnit: A is assumed to be unit triangular.
  • = MagmaNonUnit: A is not assumed to be unit triangular.
[in] n INTEGER. On entry, n specifies the order of the matrix A. N >= 0.
[in] dA_array REAL array of dimension ( ldda, n ) The triangular matrix A.
If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced.
If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced.
If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1.
[in] ldda INTEGER. The leading dimension of the array A. LDDA >= max(1,N).
[out] dinvA_array REAL array of dimension (NB, ceil(n/NB)*NB), where NB = 128. On exit, contains inverses of the NB-by-NB diagonal blocks of A.
[in] queue magma_queue_t Queue to execute in.
void magmablas_strtri_diag_q ( magma_uplo_t  uplo,
magma_diag_t  diag,
magma_int_t  n,
magmaFloat_const_ptr  dA,
magma_int_t  ldda,
magmaFloat_ptr  d_dinvA,
magma_queue_t  queue 
)

Inverts the NB x NB diagonal blocks of a triangular matrix.

This routine is used in strsm.

Same as strtri_diag, but adds queue argument. strtri_diag inverts the NB x NB diagonal blocks of A.

Parameters:
[in] uplo magma_uplo_t. On entry, uplo specifies whether the matrix A is an upper or lower triangular matrix as follows:

  • = MagmaUpper: A is an upper triangular matrix.
  • = MagmaLower: A is a lower triangular matrix.
[in] diag magma_diag_t. On entry, diag specifies whether or not A is unit triangular as follows:

  • = MagmaUnit: A is assumed to be unit triangular.
  • = MagmaNonUnit: A is not assumed to be unit triangular.
[in] n INTEGER. On entry, n specifies the order of the matrix A. N >= 0.
[in] dA REAL array of dimension ( ldda, n ) The triangular matrix A.
If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced.
If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced.
If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1.
[in] ldda INTEGER. The leading dimension of the array A. LDDA >= max(1,N).
[out] d_dinvA REAL array of dimension (NB, ceil(n/NB)*NB), where NB = 128. On exit, contains inverses of the NB-by-NB diagonal blocks of A.
[in] queue magma_queue_t Queue to execute in.
__global__ void sgemm_kernel_N_N_64_16_16_16_4 ( float *__restrict__  C,
const float *__restrict__  A,
const float *__restrict__  B,
int  m,
int  n,
int  k,
int  lda,
int  ldb,
int  ldc,
float  alpha,
float  beta 
)

Purpose: -------- This routine computes C = alpha * A*B + beta * C.

B is put into shared memory Parameters Used: blk_M=64 blk_N=16 blk_K=16 nthd_x=16 nthd_y=4

This code should run for any matrix size. This kernel outperforms cuda-2.2 when m, n, k >= 512

__global__ void sgemm_kernel_N_N_64_16_16_16_4_special ( float *__restrict__  C,
const float *__restrict__  A,
const float *__restrict__  B,
int  m,
int  n,
int  k,
int  lda,
int  ldb,
int  ldc,
float  alpha,
float  beta 
)

Purpose: -------- This routine computes C = alpha * A*B + beta * C.

B is put into shared memory Parameters Used: blk_M=64 blk_N=16 blk_K=16 nthd_x=16 nthd_y=4

This kernel is for matrices divisible by the corresponding blocking sizes.

__global__ void sgemm_kernel_N_T_64_16_4_16_4 ( float *__restrict__  C,
const float *__restrict__  A,
const float *__restrict__  B,
int  m,
int  n,
int  k,
int  lda,
int  ldb,
int  ldc,
float  alpha,
float  beta 
)

Purpose: -------- This routine computes C = alpha * A*B^T + beta * C.

B is put into shared memory Parameters Used: blk_M=64 blk_N=16 blk_K=4 nthd_x=16 nthd_y=4

This code should run for any matrix size.

__global__ void sgemm_kernel_T_N_32_32_8_8_8 ( float *__restrict__  C,
const float *__restrict__  A,
const float *__restrict__  B,
int  m,
int  n,
int  k,
int  lda,
int  ldb,
int  ldc,
float  alpha,
float  beta 
)

Purpose: -------- This routine computes C = alpha * A^T*B + beta * C.

B is put into shared memory Parameters Used: blk_M=32 blk_N=32 blk_K=8 nthd_x=8 nthd_y=8

This code should run for any matrix size.

__global__ void sgemm_kernel_T_T_64_16_16_16_4 ( float *__restrict__  C,
const float *__restrict__  A,
const float *__restrict__  B,
int  m,
int  n,
int  k,
int  lda,
int  ldb,
int  ldc,
float  alpha,
float  beta 
)

Purpose: -------- This routine computes C = alpha * A^T*B^T + beta * C.

B is put into shared memory Parameters Used: blk_M=64 blk_N=16 blk_K=16 nthd_x=16 nthd_y=4

This code should run for any matrix size. This kernel outperforms cuda-2.2 when m, n, k >= 512

__global__ void sgemm_kernel_T_T_64_16_16_16_4_special ( float *__restrict__  C,
const float *__restrict__  A,
const float *__restrict__  B,
int  m,
int  n,
int  k,
int  lda,
int  ldb,
int  ldc,
float  alpha,
float  beta 
)

Purpose: -------- This routine computes C = alpha * A^T*B^T + beta * C.

B is put into shared memory Parameters Used: blk_M=64 blk_N=16 blk_K=16 nthd_x=16 nthd_y=4

This kernel is for matrices divisible by the corresponding blocking sizes.


Generated on 3 May 2015 for MAGMA by  doxygen 1.6.1