double precision
[Level-3 BLAS]

Functions

magma_int_t magma_dtrsm_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, double alpha, double *A, magma_int_t lda, double *B, magma_int_t ldb)
 DTRSM 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_dgemm (magma_trans_t transA, magma_trans_t transB, magma_int_t m, magma_int_t n, magma_int_t k, double alpha, magmaDouble_const_ptr dA, magma_int_t ldda, magmaDouble_const_ptr dB, magma_int_t lddb, double beta, magmaDouble_ptr dC, magma_int_t lddc)
 Perform matrix-matrix product, $ C = \alpha op(A) op(B) + \beta C $.
void magma_dsymm (magma_side_t side, magma_uplo_t uplo, magma_int_t m, magma_int_t n, double alpha, magmaDouble_const_ptr dA, magma_int_t ldda, magmaDouble_const_ptr dB, magma_int_t lddb, double beta, magmaDouble_ptr dC, magma_int_t lddc)
 Perform symmetric matrix-matrix product.
void magma_dsyrk (magma_uplo_t uplo, magma_trans_t trans, magma_int_t n, magma_int_t k, double alpha, magmaDouble_const_ptr dA, magma_int_t ldda, double beta, magmaDouble_ptr dC, magma_int_t lddc)
 Perform symmetric rank-k update.
void magma_dsyr2k (magma_uplo_t uplo, magma_trans_t trans, magma_int_t n, magma_int_t k, double alpha, magmaDouble_const_ptr dA, magma_int_t ldda, magmaDouble_const_ptr dB, magma_int_t lddb, double beta, magmaDouble_ptr dC, magma_int_t lddc)
 Perform symmetric rank-2k update.
void magma_dtrmm (magma_side_t side, magma_uplo_t uplo, magma_trans_t trans, magma_diag_t diag, magma_int_t m, magma_int_t n, double alpha, magmaDouble_const_ptr dA, magma_int_t ldda, magmaDouble_ptr dB, magma_int_t lddb)
 Perform triangular matrix-matrix product.
void magma_dtrsm (magma_side_t side, magma_uplo_t uplo, magma_trans_t trans, magma_diag_t diag, magma_int_t m, magma_int_t n, double alpha, magmaDouble_const_ptr dA, magma_int_t ldda, magmaDouble_ptr dB, magma_int_t lddb)
 Solve triangular matrix-matrix system (multiple right-hand sides).
void magmablas_dgemm_batched (magma_trans_t transA, magma_trans_t transB, magma_int_t m, magma_int_t n, magma_int_t k, double alpha, double const *const *dA_array, magma_int_t ldda, double const *const *dB_array, magma_int_t lddb, double beta, double **dC_array, magma_int_t lddc, magma_int_t batchCount, magma_queue_t queue)
 DGEMM performs one of the matrix-matrix operations.
void magmablas_dgemm (magma_trans_t transA, magma_trans_t transB, magma_int_t m, magma_int_t n, magma_int_t k, double alpha, magmaDouble_const_ptr dA, magma_int_t ldda, magmaDouble_const_ptr dB, magma_int_t lddb, double beta, magmaDouble_ptr dC, magma_int_t lddc)
 DGEMM performs one of the matrix-matrix operations.
void magmablas_dgemm_batched_lg (magma_trans_t transA, magma_trans_t transB, magma_int_t m, magma_int_t n, magma_int_t k, double alpha, double const *const *dA_array, magma_int_t ldda, double const *const *dB_array, magma_int_t lddb, double beta, double **dC_array, magma_int_t lddc, magma_int_t batchCount, magma_queue_t queue)
 DGEMM performs one of the matrix-matrix operations.
void magmablas_dgemm_batched_k32 (magma_trans_t transA, magma_trans_t transB, magma_int_t m, magma_int_t n, magma_int_t k, double alpha, double const *const *dA_array, magma_int_t ldda, double const *const *dB_array, magma_int_t lddb, double beta, double **dC_array, magma_int_t lddc, magma_int_t batchCount, magma_queue_t queue)
 DGEMM performs one of the matrix-matrix operations.
void magmablas_dgemm_reduce (magma_int_t m, magma_int_t n, magma_int_t k, double alpha, magmaDouble_const_ptr dA, magma_int_t ldda, magmaDouble_const_ptr dB, magma_int_t lddb, double beta, magmaDouble_ptr dC, magma_int_t lddc)
 DGEMM_REDUCE performs one of the matrix-matrix operations.
void magmablas_dgemm_tesla (magma_trans_t transA, magma_trans_t transB, magma_int_t m, magma_int_t n, magma_int_t k, double alpha, const double *A, magma_int_t lda, const double *B, magma_int_t ldb, double beta, double *C, magma_int_t ldc)
 DGEMM performs one of the matrix-matrix operations.
__global__ void dgemm_kernel_N_N_64_16_16_16_4 (double *__restrict__ C, const double *__restrict__ A, const double *__restrict__ B, int m, int n, int k, int lda, int ldb, int ldc, double alpha, double beta)
 Purpose: -------- This routine computes C = alpha * A*B + beta * C.
__global__ void dgemm_kernel_N_N_64_16_16_16_4_special (double *__restrict__ C, const double *__restrict__ A, const double *__restrict__ B, int m, int n, int k, int lda, int ldb, int ldc, double alpha, double beta)
 Purpose: -------- This routine computes C = alpha * A*B + beta * C.
__global__ void dgemm_kernel_N_T_64_16_4_16_4 (double *__restrict__ C, const double *__restrict__ A, const double *__restrict__ B, int m, int n, int k, int lda, int ldb, int ldc, double alpha, double beta)
 Purpose: -------- This routine computes C = alpha * A*B^T + beta * C.
__global__ void dgemm_kernel_T_N_32_32_8_8_8 (double *__restrict__ C, const double *__restrict__ A, const double *__restrict__ B, int m, int n, int k, int lda, int ldb, int ldc, double alpha, double beta)
 Purpose: -------- This routine computes C = alpha * A^T*B + beta * C.
__global__ void dgemm_kernel_T_T_64_16_16_16_4 (double *__restrict__ C, const double *__restrict__ A, const double *__restrict__ B, int m, int n, int k, int lda, int ldb, int ldc, double alpha, double beta)
 Purpose: -------- This routine computes C = alpha * A^T*B^T + beta * C.
__global__ void dgemm_kernel_T_T_64_16_16_16_4_special (double *__restrict__ C, const double *__restrict__ A, const double *__restrict__ B, int m, int n, int k, int lda, int ldb, int ldc, double alpha, double beta)
 Purpose: -------- This routine computes C = alpha * A^T*B^T + beta * C.
void magmablas_dsyr2k_mgpu2 (magma_uplo_t uplo, magma_trans_t trans, magma_int_t n, magma_int_t k, double alpha, magmaDouble_ptr dA[], magma_int_t ldda, magma_int_t a_offset, 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 ngpu, magma_int_t nb, magma_queue_t queues[][20], magma_int_t nqueue)
 DSYR2K performs one of the symmetric rank 2k operations.
void magmablas_dsyr2k_mgpu_spec (magma_uplo_t uplo, magma_trans_t trans, magma_int_t n, magma_int_t k, double alpha, magmaDouble_ptr dA[], magma_int_t ldda, magma_int_t a_offset, 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 ngpu, magma_int_t nb, magma_queue_t queues[][20], magma_int_t nqueue)
 DSYR2K performs one of the symmetric rank 2k operations.
void magmablas_dsyrk_batched (magma_uplo_t uplo, magma_trans_t trans, magma_int_t n, magma_int_t k, double alpha, double const *const *dA_array, magma_int_t ldda, double beta, double **dC_array, magma_int_t lddc, magma_int_t batchCount, magma_queue_t queue)
 DSYRK performs one of the symmetric rank k operations.
void magmablas_dsyrk_batched_lg (magma_uplo_t uplo, magma_trans_t trans, magma_int_t n, magma_int_t k, double alpha, double const *const *dA_array, magma_int_t ldda, double beta, double **dC_array, magma_int_t lddc, magma_int_t batchCount, magma_queue_t queue)
 DSYRK performs one of the symmetric rank k operations.
void magmablas_dsyrk_batched_k32 (magma_uplo_t uplo, magma_trans_t trans, magma_int_t n, magma_int_t k, double alpha, double const *const *dA_array, magma_int_t ldda, double beta, double **dC_array, magma_int_t lddc, magma_int_t batchCount, magma_queue_t queue)
 DSYRK performs one of the symmetric rank k operations.
void magmablas_dtrsm_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, double alpha, magmaDouble_const_ptr dA, magma_int_t ldda, magmaDouble_ptr dB, magma_int_t lddb, magma_int_t flag, magmaDouble_ptr d_dinvA, magmaDouble_ptr dX)
 dtrsm_outofplace solves one of the matrix equations on gpu
void magmablas_dtrsm_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, double alpha, magmaDouble_const_ptr dA, magma_int_t ldda, magmaDouble_ptr dB, magma_int_t lddb, magma_int_t flag, magmaDouble_ptr d_dinvA, magmaDouble_ptr dX)
void magmablas_dtrsm (magma_side_t side, magma_uplo_t uplo, magma_trans_t transA, magma_diag_t diag, magma_int_t m, magma_int_t n, double alpha, magmaDouble_const_ptr dA, magma_int_t ldda, magmaDouble_ptr dB, magma_int_t lddb)
void magmablas_dtrsm_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, double alpha, double **dA_array, magma_int_t ldda, double **dB_array, magma_int_t lddb, double **dX_array, magma_int_t lddx, double **dinvA_array, magma_int_t dinvA_length, double **dA_displ, double **dB_displ, double **dX_displ, double **dinvA_displ, magma_int_t resetozero, magma_int_t batchCount, magma_queue_t queue)
 dtrsm_work solves one of the matrix equations on gpu
void magmablas_dtrsm_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, double alpha, double **dA_array, magma_int_t ldda, double **dB_array, magma_int_t lddb, double **dX_array, magma_int_t lddx, double **dinvA_array, magma_int_t dinvA_length, double **dA_displ, double **dB_displ, double **dX_displ, double **dinvA_displ, magma_int_t resetozero, magma_int_t batchCount, magma_queue_t queue)
void magmablas_dtrsm_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, double alpha, double **dA_array, magma_int_t ldda, double **dB_array, magma_int_t lddb, magma_int_t batchCount, magma_queue_t queue)
void magmablas_dtrtri_diag_q (magma_uplo_t uplo, magma_diag_t diag, magma_int_t n, magmaDouble_const_ptr dA, magma_int_t ldda, magmaDouble_ptr d_dinvA, magma_queue_t queue)
 Inverts the NB x NB diagonal blocks of a triangular matrix.
void magmablas_dtrtri_diag (magma_uplo_t uplo, magma_diag_t diag, magma_int_t n, magmaDouble_const_ptr dA, magma_int_t ldda, magmaDouble_ptr d_dinvA)
void magmablas_dtrtri_diag_batched (magma_uplo_t uplo, magma_diag_t diag, magma_int_t n, double const *const *dA_array, magma_int_t ldda, double **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

__global__ void dgemm_kernel_N_N_64_16_16_16_4 ( double *__restrict__  C,
const double *__restrict__  A,
const double *__restrict__  B,
int  m,
int  n,
int  k,
int  lda,
int  ldb,
int  ldc,
double  alpha,
double  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 dgemm_kernel_N_N_64_16_16_16_4_special ( double *__restrict__  C,
const double *__restrict__  A,
const double *__restrict__  B,
int  m,
int  n,
int  k,
int  lda,
int  ldb,
int  ldc,
double  alpha,
double  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 dgemm_kernel_N_T_64_16_4_16_4 ( double *__restrict__  C,
const double *__restrict__  A,
const double *__restrict__  B,
int  m,
int  n,
int  k,
int  lda,
int  ldb,
int  ldc,
double  alpha,
double  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 dgemm_kernel_T_N_32_32_8_8_8 ( double *__restrict__  C,
const double *__restrict__  A,
const double *__restrict__  B,
int  m,
int  n,
int  k,
int  lda,
int  ldb,
int  ldc,
double  alpha,
double  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 dgemm_kernel_T_T_64_16_16_16_4 ( double *__restrict__  C,
const double *__restrict__  A,
const double *__restrict__  B,
int  m,
int  n,
int  k,
int  lda,
int  ldb,
int  ldc,
double  alpha,
double  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 dgemm_kernel_T_T_64_16_16_16_4_special ( double *__restrict__  C,
const double *__restrict__  A,
const double *__restrict__  B,
int  m,
int  n,
int  k,
int  lda,
int  ldb,
int  ldc,
double  alpha,
double  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.

void magma_dgemm ( magma_trans_t  transA,
magma_trans_t  transB,
magma_int_t  m,
magma_int_t  n,
magma_int_t  k,
double  alpha,
magmaDouble_const_ptr  dA,
magma_int_t  ldda,
magmaDouble_const_ptr  dB,
magma_int_t  lddb,
double  beta,
magmaDouble_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 DOUBLE_PRECISION 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 DOUBLE_PRECISION 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 DOUBLE_PRECISION 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_dsymm ( magma_side_t  side,
magma_uplo_t  uplo,
magma_int_t  m,
magma_int_t  n,
double  alpha,
magmaDouble_const_ptr  dA,
magma_int_t  ldda,
magmaDouble_const_ptr  dB,
magma_int_t  lddb,
double  beta,
magmaDouble_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 DOUBLE_PRECISION 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 DOUBLE_PRECISION 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 DOUBLE_PRECISION 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_dsyr2k ( magma_uplo_t  uplo,
magma_trans_t  trans,
magma_int_t  n,
magma_int_t  k,
double  alpha,
magmaDouble_const_ptr  dA,
magma_int_t  ldda,
magmaDouble_const_ptr  dB,
magma_int_t  lddb,
double  beta,
magmaDouble_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 DOUBLE_PRECISION 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 DOUBLE_PRECISION 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 DOUBLE_PRECISION 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_dsyrk ( magma_uplo_t  uplo,
magma_trans_t  trans,
magma_int_t  n,
magma_int_t  k,
double  alpha,
magmaDouble_const_ptr  dA,
magma_int_t  ldda,
double  beta,
magmaDouble_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 DOUBLE_PRECISION 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 DOUBLE_PRECISION 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_dtrmm ( magma_side_t  side,
magma_uplo_t  uplo,
magma_trans_t  trans,
magma_diag_t  diag,
magma_int_t  m,
magma_int_t  n,
double  alpha,
magmaDouble_const_ptr  dA,
magma_int_t  ldda,
magmaDouble_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 DOUBLE_PRECISION 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 DOUBLE_PRECISION 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_dtrsm ( magma_side_t  side,
magma_uplo_t  uplo,
magma_trans_t  trans,
magma_diag_t  diag,
magma_int_t  m,
magma_int_t  n,
double  alpha,
magmaDouble_const_ptr  dA,
magma_int_t  ldda,
magmaDouble_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 DOUBLE_PRECISION 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 DOUBLE_PRECISION 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_dtrsm_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,
double  alpha,
double *  A,
magma_int_t  lda,
double *  B,
magma_int_t  ldb 
)

DTRSM 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 DOUBLE_PRECISION. 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 DOUBLE_PRECISION 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 DOUBLE_PRECISION 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_dgemm ( magma_trans_t  transA,
magma_trans_t  transB,
magma_int_t  m,
magma_int_t  n,
magma_int_t  k,
double  alpha,
magmaDouble_const_ptr  dA,
magma_int_t  ldda,
magmaDouble_const_ptr  dB,
magma_int_t  lddb,
double  beta,
magmaDouble_ptr  dC,
magma_int_t  lddc 
)

DGEMM 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 DOUBLE_PRECISION On entry, ALPHA specifies the scalar alpha.
[in] dA DOUBLE_PRECISION 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 DOUBLE_PRECISION 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 DOUBLE_PRECISION. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then dC need not be set on input.
[in,out] dC DOUBLE_PRECISION 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_dgemm_batched ( magma_trans_t  transA,
magma_trans_t  transB,
magma_int_t  m,
magma_int_t  n,
magma_int_t  k,
double  alpha,
double const *const *  dA_array,
magma_int_t  ldda,
double const *const *  dB_array,
magma_int_t  lddb,
double  beta,
double **  dC_array,
magma_int_t  lddc,
magma_int_t  batchCount,
magma_queue_t  queue 
)

DGEMM 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 DOUBLE_PRECISION On entry, ALPHA specifies the scalar alpha.
[in] dA DOUBLE_PRECISION 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 DOUBLE_PRECISION 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 DOUBLE_PRECISION. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then dC need not be set on input.
[in,out] dC DOUBLE_PRECISION 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_dgemm_batched_k32 ( magma_trans_t  transA,
magma_trans_t  transB,
magma_int_t  m,
magma_int_t  n,
magma_int_t  k,
double  alpha,
double const *const *  dA_array,
magma_int_t  ldda,
double const *const *  dB_array,
magma_int_t  lddb,
double  beta,
double **  dC_array,
magma_int_t  lddc,
magma_int_t  batchCount,
magma_queue_t  queue 
)

DGEMM 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 DOUBLE_PRECISION On entry, ALPHA specifies the scalar alpha.
[in] dA DOUBLE_PRECISION 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 DOUBLE_PRECISION 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 DOUBLE_PRECISION. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then dC need not be set on input.
[in,out] dC DOUBLE_PRECISION 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_dgemm_batched_lg ( magma_trans_t  transA,
magma_trans_t  transB,
magma_int_t  m,
magma_int_t  n,
magma_int_t  k,
double  alpha,
double const *const *  dA_array,
magma_int_t  ldda,
double const *const *  dB_array,
magma_int_t  lddb,
double  beta,
double **  dC_array,
magma_int_t  lddc,
magma_int_t  batchCount,
magma_queue_t  queue 
)

DGEMM 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 DOUBLE_PRECISION On entry, ALPHA specifies the scalar alpha.
[in] dA DOUBLE_PRECISION 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 DOUBLE_PRECISION 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 DOUBLE_PRECISION. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then dC need not be set on input.
[in,out] dC DOUBLE_PRECISION 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_dgemm_reduce ( magma_int_t  m,
magma_int_t  n,
magma_int_t  k,
double  alpha,
magmaDouble_const_ptr  dA,
magma_int_t  ldda,
magmaDouble_const_ptr  dB,
magma_int_t  lddb,
double  beta,
magmaDouble_ptr  dC,
magma_int_t  lddc 
)

DGEMM_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_dgemm_tesla ( magma_trans_t  transA,
magma_trans_t  transB,
magma_int_t  m,
magma_int_t  n,
magma_int_t  k,
double  alpha,
const double *  A,
magma_int_t  lda,
const double *  B,
magma_int_t  ldb,
double  beta,
double *  C,
magma_int_t  ldc 
)

DGEMM 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 DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha.
[in] A DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then C need not be set on input.
[in,out] C DOUBLE PRECISION 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_dsyr2k_mgpu2 ( magma_uplo_t  uplo,
magma_trans_t  trans,
magma_int_t  n,
magma_int_t  k,
double  alpha,
magmaDouble_ptr  dA[],
magma_int_t  ldda,
magma_int_t  a_offset,
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  ngpu,
magma_int_t  nb,
magma_queue_t  queues[][20],
magma_int_t  nqueue 
)

DSYR2K 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 DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha.
[in] dA DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION. On entry, BETA specifies the scalar beta.
[in,out] dC DOUBLE PRECISION 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_dsyr2k_mgpu_spec ( magma_uplo_t  uplo,
magma_trans_t  trans,
magma_int_t  n,
magma_int_t  k,
double  alpha,
magmaDouble_ptr  dA[],
magma_int_t  ldda,
magma_int_t  a_offset,
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  ngpu,
magma_int_t  nb,
magma_queue_t  queues[][20],
magma_int_t  nqueue 
)

DSYR2K 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 DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha.
[in] dA DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION. On entry, BETA specifies the scalar beta.
[in,out] dC DOUBLE PRECISION 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_dsyrk_batched ( magma_uplo_t  uplo,
magma_trans_t  trans,
magma_int_t  n,
magma_int_t  k,
double  alpha,
double const *const *  dA_array,
magma_int_t  ldda,
double  beta,
double **  dC_array,
magma_int_t  lddc,
magma_int_t  batchCount,
magma_queue_t  queue 
)

DSYRK performs one of the symmetric rank k operations.

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

or

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

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

Parameters ----------

Parameters:
[in] uplo 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 DOUBLE PRECISION On entry, ALPHA specifies the scalar alpha.
[in] dA DOUBLE_PRECISION array of DIMENSION ( ldda, ka ), where ka is k when trans = MagmaNoTrans, and is n otherwise. Before entry with trans = MagmaNoTrans, the leading 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 DOUBLE PRECISION. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then dC need not be set on input.
[in,out] dC DOUBLE_PRECISION 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_dsyrk_batched_k32 ( magma_uplo_t  uplo,
magma_trans_t  trans,
magma_int_t  n,
magma_int_t  k,
double  alpha,
double const *const *  dA_array,
magma_int_t  ldda,
double  beta,
double **  dC_array,
magma_int_t  lddc,
magma_int_t  batchCount,
magma_queue_t  queue 
)

DSYRK performs one of the symmetric rank k operations.

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

or

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

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

Parameters ----------

Parameters:
[in] uplo 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 DOUBLE PRECISION On entry, ALPHA specifies the scalar alpha.
[in] dA DOUBLE_PRECISION array of DIMENSION ( ldda, ka ), where ka is k when trans = MagmaNoTrans, and is n otherwise. Before entry with trans = MagmaNoTrans, the leading 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 DOUBLE PRECISION. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then dC need not be set on input.
[in,out] dC DOUBLE_PRECISION 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_dsyrk_batched_lg ( magma_uplo_t  uplo,
magma_trans_t  trans,
magma_int_t  n,
magma_int_t  k,
double  alpha,
double const *const *  dA_array,
magma_int_t  ldda,
double  beta,
double **  dC_array,
magma_int_t  lddc,
magma_int_t  batchCount,
magma_queue_t  queue 
)

DSYRK performs one of the symmetric rank k operations.

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

or

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

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

Parameters ----------

Parameters:
[in] uplo 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 DOUBLE PRECISION On entry, ALPHA specifies the scalar alpha.
[in] dA DOUBLE_PRECISION array of DIMENSION ( ldda, ka ), where ka is k when trans = MagmaNoTrans, and is n otherwise. Before entry with trans = MagmaNoTrans, the leading 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 DOUBLE PRECISION. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then dC need not be set on input.
[in,out] dC DOUBLE_PRECISION 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_dtrsm ( magma_side_t  side,
magma_uplo_t  uplo,
magma_trans_t  transA,
magma_diag_t  diag,
magma_int_t  m,
magma_int_t  n,
double  alpha,
magmaDouble_const_ptr  dA,
magma_int_t  ldda,
magmaDouble_ptr  dB,
magma_int_t  lddb 
)
void magmablas_dtrsm_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,
double  alpha,
double **  dA_array,
magma_int_t  ldda,
double **  dB_array,
magma_int_t  lddb,
magma_int_t  batchCount,
magma_queue_t  queue 
)
void magmablas_dtrsm_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,
double  alpha,
magmaDouble_const_ptr  dA,
magma_int_t  ldda,
magmaDouble_ptr  dB,
magma_int_t  lddb,
magma_int_t  flag,
magmaDouble_ptr  d_dinvA,
magmaDouble_ptr  dX 
)

dtrsm_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_dtrsm 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 DOUBLE_PRECISION. 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 DOUBLE_PRECISION 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 DOUBLE_PRECISION 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 DOUBLE_PRECISION array of dimension ( m, n ). On exit it contain the solution matrix X.
void magmablas_dtrsm_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,
double  alpha,
double **  dA_array,
magma_int_t  ldda,
double **  dB_array,
magma_int_t  lddb,
double **  dX_array,
magma_int_t  lddx,
double **  dinvA_array,
magma_int_t  dinvA_length,
double **  dA_displ,
double **  dB_displ,
double **  dX_displ,
double **  dinvA_displ,
magma_int_t  resetozero,
magma_int_t  batchCount,
magma_queue_t  queue 
)

dtrsm_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_dtrsm 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 DOUBLE_PRECISION. 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 DOUBLE_PRECISION 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 DOUBLE_PRECISION 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 DOUBLE_PRECISION array of dimension ( lddx, n ). On exit it contain the solution matrix X.
void magmablas_dtrsm_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,
double  alpha,
magmaDouble_const_ptr  dA,
magma_int_t  ldda,
magmaDouble_ptr  dB,
magma_int_t  lddb,
magma_int_t  flag,
magmaDouble_ptr  d_dinvA,
magmaDouble_ptr  dX 
)
void magmablas_dtrsm_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,
double  alpha,
double **  dA_array,
magma_int_t  ldda,
double **  dB_array,
magma_int_t  lddb,
double **  dX_array,
magma_int_t  lddx,
double **  dinvA_array,
magma_int_t  dinvA_length,
double **  dA_displ,
double **  dB_displ,
double **  dX_displ,
double **  dinvA_displ,
magma_int_t  resetozero,
magma_int_t  batchCount,
magma_queue_t  queue 
)
void magmablas_dtrtri_diag ( magma_uplo_t  uplo,
magma_diag_t  diag,
magma_int_t  n,
magmaDouble_const_ptr  dA,
magma_int_t  ldda,
magmaDouble_ptr  d_dinvA 
)
void magmablas_dtrtri_diag_batched ( magma_uplo_t  uplo,
magma_diag_t  diag,
magma_int_t  n,
double const *const *  dA_array,
magma_int_t  ldda,
double **  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 dtrsm.

Same as dtrtri_diag, but adds queue argument. dtrtri_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 DOUBLE_PRECISION 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 DOUBLE_PRECISION 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_dtrtri_diag_q ( magma_uplo_t  uplo,
magma_diag_t  diag,
magma_int_t  n,
magmaDouble_const_ptr  dA,
magma_int_t  ldda,
magmaDouble_ptr  d_dinvA,
magma_queue_t  queue 
)

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

This routine is used in dtrsm.

Same as dtrtri_diag, but adds queue argument. dtrtri_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 DOUBLE_PRECISION 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 DOUBLE_PRECISION 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.

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