/***************************************************************************//**
*
* @ingroup PLASMA_Complex64_t_Tile
*
* PLASMA_zgetri_Tile - Computes the inverse of a matrix using the LU factorization
* computed by PLASMA_zgetrf.
* This method inverts U and then computes inv(A) by solving the system
* inv(A)*L = inv(U) for inv(A).
* Tile equivalent of PLASMA_zgetri().
* Operates on matrices stored by tiles.
* All matrices are passed through descriptors.
* All dimensions are taken from the descriptors.
*
*******************************************************************************
*
* @param[in,out] A
* On entry, the triangular factor L or U from the
* factorization A = P*L*U as computed by PLASMA_zgetrf.
* On exit, if return value = 0, the inverse of the original
* matrix A.
*
* @param[in] IPIV
* The pivot indices that define the permutations
* as returned by PLASMA_zgetrf.
*
*******************************************************************************
*
* @return
* \retval PLASMA_SUCCESS successful exit
* \retval >0 if i, the (i,i) element of the factor U is
* exactly zero; The matrix is singular
* and its inverse could not be computed.
*
*******************************************************************************
*
* @sa PLASMA_zgetri
* @sa PLASMA_zgetri_Tile_Async
* @sa PLASMA_cgetri_Tile
* @sa PLASMA_dgetri_Tile
* @sa PLASMA_sgetri_Tile
* @sa PLASMA_zgetrf_Tile
*
******************************************************************************/
int PLASMA_zgetri_Tile(PLASMA_desc *A, int *IPIV)
{
plasma_context_t *plasma;
PLASMA_sequence *sequence = NULL;
PLASMA_request request = PLASMA_REQUEST_INITIALIZER;
PLASMA_desc descW;
int status;
plasma = plasma_context_self();
if (plasma == NULL) {
plasma_fatal_error("PLASMA_zgetri_Tile", "PLASMA not initialized");
return PLASMA_ERR_NOT_INITIALIZED;
}
plasma_sequence_create(plasma, &sequence);
/* Allocate workspace */
PLASMA_Alloc_Workspace_zgetri_Tile_Async(A, &descW);
PLASMA_zgetri_Tile_Async(A, IPIV, &descW, sequence, &request);
plasma_dynamic_sync();
plasma_desc_mat_free(&(descW));
status = sequence->status;
plasma_sequence_destroy(plasma, sequence);
return status;
}
/** ****************************************************************************
*
* @ingroup InPlaceTransformation
*
* PLASMA_dgecfi convert the matrice A in place from format f_in to
* format f_out
*
*******************************************************************************
*
* @param[in] m
* Number of rows of matrix A
*
* @param[in] n
* Number of columns of matrix A
*
* @param[in,out] A
* Matrix of size L*m*n
*
* @param[in] f_in
* Original format of the matrix A. Must be part of (PlasmaCM, PlasmaRM,
* PlasmaCCRB, PlasmaCRRB, PlasmaRCRB, PlasmaRRRB)
*
* @param[in] imb
* Number of rows of each block in original format
*
* @param[in] inb
* Number of columns of each block in original format
*
* @param[in] f_out
* Format requested for the matrix A. Must be part of (PlasmaCM, PlasmaRM,
* PlasmaCCRB, PlasmaCRRB, PlasmaRCRB, PlasmaRRRB)
*
* @param[in] omb
* Number of rows of each block in requested format
*
* @param[in] onb
* Number of columns of each block in requested format
*
*******************************************************************************
*
* @sa PLASMA_dgecfi_Async
*
******************************************************************************/
int PLASMA_dgecfi(int m, int n, double *A,
PLASMA_enum f_in, int imb, int inb,
PLASMA_enum f_out, int omb, int onb)
{
plasma_context_t *plasma;
PLASMA_sequence *sequence = NULL;
PLASMA_request request = PLASMA_REQUEST_INITIALIZER;
int status;
plasma = plasma_context_self();
if (plasma == NULL) {
plasma_fatal_error(__func__, "PLASMA not initialized");
return PLASMA_ERR_NOT_INITIALIZED;
}
plasma_sequence_create(plasma, &sequence);
PLASMA_dgecfi_Async( m, n, A,
f_in, imb, inb,
f_out, omb, onb,
sequence, &request);
plasma_dynamic_sync();
status = sequence->status;
plasma_sequence_destroy(plasma, sequence);
return status;
}
/***************************************************************************//**
*
* @ingroup float
*
* PLASMA_sgesv - Computes the solution to a system of linear equations A * X = B,
* where A is an N-by-N matrix and X and B are N-by-NRHS matrices.
* The tile LU decomposition with partial tile pivoting and row interchanges is used to factor A.
* The factored form of A is then used to solve the system of equations A * X = B.
*
*******************************************************************************
*
* @param[in] N
* The number of linear equations, i.e., the order of the matrix A. N >= 0.
*
* @param[in] NRHS
* The number of right hand sides, i.e., the number of columns of the matrix B.
* NRHS >= 0.
*
* @param[in,out] A
* On entry, the N-by-N coefficient matrix A.
* On exit, the tile L and U factors from the factorization.
*
* @param[in] LDA
* The leading dimension of the array A. LDA >= max(1,N).
*
* @param[out] IPIV
* On exit, the pivot indices that define the permutations.
*
* @param[in,out] B
* On entry, the N-by-NRHS matrix of right hand side matrix B.
* On exit, if return value = 0, the N-by-NRHS solution matrix X.
*
* @param[in] LDB
* The leading dimension of the array B. LDB >= max(1,N).
*
*******************************************************************************
*
* @return
* \retval PLASMA_SUCCESS successful exit
* \retval <0 if -i, the i-th argument had an illegal value
* \retval >0 if i, U(i,i) is exactly zero. The factorization has been completed,
* but the factor U is exactly singular, so the solution could not be computed.
*
*******************************************************************************
*
* @sa PLASMA_sgesv_Tile
* @sa PLASMA_sgesv_Tile_Async
* @sa PLASMA_cgesv
* @sa PLASMA_dgesv
* @sa PLASMA_sgesv
*
******************************************************************************/
int PLASMA_sgesv(int N, int NRHS,
float *A, int LDA,
int *IPIV,
float *B, int LDB)
{
int NB, IB, IBNB, NT;
int status;
plasma_context_t *plasma;
PLASMA_sequence *sequence = NULL;
PLASMA_request request = PLASMA_REQUEST_INITIALIZER;
PLASMA_desc descA, descB;
plasma = plasma_context_self();
if (plasma == NULL) {
plasma_error("PLASMA_sgesv", "PLASMA not initialized");
return PLASMA_ERR_NOT_INITIALIZED;
}
/* Check input arguments */
if (N < 0) {
plasma_error("PLASMA_sgesv", "illegal value of N");
return -1;
}
if (NRHS < 0) {
plasma_error("PLASMA_sgesv", "illegal value of NRHS");
return -2;
}
if (LDA < max(1, N)) {
plasma_error("PLASMA_sgesv", "illegal value of LDA");
return -4;
}
if (LDB < max(1, N)) {
plasma_error("PLASMA_sgesv", "illegal value of LDB");
return -8;
}
/* Quick return */
if (min(N, NRHS) == 0)
return PLASMA_SUCCESS;
/* Tune NB & IB depending on M, N & NRHS; Set NBNB */
status = plasma_tune(PLASMA_FUNC_SGESV, N, N, NRHS);
if (status != PLASMA_SUCCESS) {
plasma_error("PLASMA_sgesv", "plasma_tune() failed");
return status;
}
/* Set NT & NTRHS */
NB = PLASMA_NB;
IB = PLASMA_IB;
IBNB = IB*NB;
NT = (N%NB==0) ? (N/NB) : (N/NB+1);
plasma_sequence_create(plasma, &sequence);
if ( PLASMA_TRANSLATION == PLASMA_OUTOFPLACE ) {
plasma_sooplap2tile( descA, A, NB, NB, LDA, N, 0, 0, N, N , plasma_desc_mat_free(&(descA)) );
plasma_sooplap2tile( descB, B, NB, NB, LDB, NRHS, 0, 0, N, NRHS, plasma_desc_mat_free(&(descA)); plasma_desc_mat_free(&(descB)));
} else {
/***************************************************************************//**
*
* @ingroup PLASMA_Complex64_t
*
* PLASMA_zpotrs - Solves a system of linear equations A * X = B with a symmetric positive
* definite (or Hermitian positive definite in the complex case) matrix A using the Cholesky
* factorization A = U**H*U or A = L*L**H computed by PLASMA_zpotrf.
*
*******************************************************************************
*
* @param[in] uplo
* = PlasmaUpper: Upper triangle of A is stored;
* = PlasmaLower: Lower triangle of A is stored.
*
* @param[in] N
* The order of the matrix A. N >= 0.
*
* @param[in] NRHS
* The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
*
* @param[in] A
* The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H,
* computed by PLASMA_zpotrf.
*
* @param[in] LDA
* The leading dimension of the array A. LDA >= max(1,N).
*
* @param[in,out] B
* On entry, the N-by-NRHS right hand side matrix B.
* On exit, if return value = 0, the N-by-NRHS solution matrix X.
*
* @param[in] LDB
* The leading dimension of the array B. LDB >= max(1,N).
*
*******************************************************************************
*
* @return
* \retval PLASMA_SUCCESS successful exit
* \retval <0 if -i, the i-th argument had an illegal value
*
*******************************************************************************
*
* @sa PLASMA_zpotrs_Tile
* @sa PLASMA_zpotrs_Tile_Async
* @sa PLASMA_cpotrs
* @sa PLASMA_dpotrs
* @sa PLASMA_spotrs
* @sa PLASMA_zpotrf
*
******************************************************************************/
int PLASMA_zpotrs(PLASMA_enum uplo, int N, int NRHS,
PLASMA_Complex64_t *A, int LDA,
PLASMA_Complex64_t *B, int LDB)
{
int NB;
int status;
plasma_context_t *plasma;
PLASMA_sequence *sequence = NULL;
PLASMA_request request = PLASMA_REQUEST_INITIALIZER;
PLASMA_desc descA, descB;
plasma = plasma_context_self();
if (plasma == NULL) {
plasma_fatal_error("PLASMA_zpotrs", "PLASMA not initialized");
return PLASMA_ERR_NOT_INITIALIZED;
}
/* Check input arguments */
if (uplo != PlasmaUpper && uplo != PlasmaLower) {
plasma_error("PLASMA_zpotrs", "illegal value of uplo");
return -1;
}
if (N < 0) {
plasma_error("PLASMA_zpotrs", "illegal value of N");
return -2;
}
if (NRHS < 0) {
plasma_error("PLASMA_zpotrs", "illegal value of NRHS");
return -3;
}
if (LDA < max(1, N)) {
plasma_error("PLASMA_zpotrs", "illegal value of LDA");
return -5;
}
if (LDB < max(1, N)) {
plasma_error("PLASMA_zpotrs", "illegal value of LDB");
return -7;
}
/* Quick return */
if (min(N, NRHS) == 0)
return PLASMA_SUCCESS;
/* Tune NB depending on M, N & NRHS; Set NBNB */
status = plasma_tune(PLASMA_FUNC_ZPOSV, N, N, NRHS);
if (status != PLASMA_SUCCESS) {
plasma_error("PLASMA_zpotrs", "plasma_tune() failed");
return status;
}
/* Set NT & NTRHS */
NB = PLASMA_NB;
plasma_sequence_create(plasma, &sequence);
if ( PLASMA_TRANSLATION == PLASMA_OUTOFPLACE ) {
plasma_zooplap2tile( descA, A, NB, NB, LDA, N, 0, 0, N, N , plasma_desc_mat_free(&(descA)) );
plasma_zooplap2tile( descB, B, NB, NB, LDB, NRHS, 0, 0, N, NRHS, plasma_desc_mat_free(&(descA)); plasma_desc_mat_free(&(descB)));
} else {
/***************************************************************************//**
*
* @ingroup float
*
* PLASMA_splgsy - Generate a random hermitian matrix by tiles.
*
*******************************************************************************
*
* @param[in] bump
* The value to add to the diagonal to be sure
* to have a positive definite matrix.
*
* @param[in] N
* The order of the matrix A. N >= 0.
*
* @param[out] A
* On exit, The random hermitian matrix A generated.
*
* @param[in] LDA
* The leading dimension of the array A. LDA >= max(1,M).
*
* @param[in] seed
* The seed used in the random generation.
*
*******************************************************************************
*
* @return
* \retval PLASMA_SUCCESS successful exit
* \retval <0 if -i, the i-th argument had an illegal value
*
*******************************************************************************
*
* @sa PLASMA_splgsy_Tile
* @sa PLASMA_splgsy_Tile_Async
* @sa PLASMA_cplgsy
* @sa PLASMA_dplgsy
* @sa PLASMA_splgsy
* @sa PLASMA_splrnt
* @sa PLASMA_splgsy
*
******************************************************************************/
int PLASMA_splgsy( float bump, int N,
float *A, int LDA,
unsigned long long int seed )
{
int NB;
int status;
plasma_context_t *plasma;
PLASMA_sequence *sequence = NULL;
PLASMA_request request = PLASMA_REQUEST_INITIALIZER;
PLASMA_desc descA;
plasma = plasma_context_self();
if (plasma == NULL) {
plasma_fatal_error("PLASMA_splgsy", "PLASMA not initialized");
return PLASMA_ERR_NOT_INITIALIZED;
}
/* Check input arguments */
if (N < 0) {
plasma_error("PLASMA_splgsy", "illegal value of N");
return -2;
}
if (LDA < max(1, N)) {
plasma_error("PLASMA_splgsy", "illegal value of LDA");
return -4;
}
/* Quick return */
if (max(0, N) == 0)
return PLASMA_SUCCESS;
/* Tune NB depending on M, N & NRHS; Set NBNB */
status = plasma_tune(PLASMA_FUNC_SGEMM, N, N, 0);
if (status != PLASMA_SUCCESS) {
plasma_error("PLASMA_splgsy", "plasma_tune() failed");
return status;
}
/* Set NT */
NB = PLASMA_NB;
plasma_sequence_create(plasma, &sequence);
descA = plasma_desc_init(
PlasmaRealFloat, NB, NB, NB*NB,
LDA, N, 0, 0, N, N);
descA.mat = A;
/* Call the tile interface */
PLASMA_splgsy_Tile_Async( bump, &descA, seed, sequence, &request );
plasma_siptile2lap( descA, A, NB, NB, LDA, N );
plasma_dynamic_sync();
status = sequence->status;
plasma_sequence_destroy(plasma, sequence);
return status;
}
/***************************************************************************//**
*
* @ingroup PLASMA_Complex64_t_Tile
*
* PLASMA_zlansy_Tile - Tile equivalent of PLASMA_zlansy().
* Operates on matrices stored by tiles.
* All matrices are passed through descriptors.
* All dimensions are taken from the descriptors.
*
*******************************************************************************
*
* @param[in] norm
* = PlasmaMaxNorm: Max norm
* = PlasmaOneNorm: One norm
* = PlasmaInfNorm: Infinity norm
* = PlasmaFrobeniusNorm: Frobenius norm
*
* @param[in] uplo
* = PlasmaUpper: Upper triangle of A is stored;
* = PlasmaLower: Lower triangle of A is stored.
*
* @param[in] A
* On entry, the triangular factor U or L.
* On exit, if UPLO = 'U', the upper triangle of A is
* overwritten with the upper triangle of the product U * U';
* if UPLO = 'L', the lower triangle of A is overwritten with
* the lower triangle of the product L' * L.
*
*******************************************************************************
*
* @return
* \retval PLASMA_SUCCESS successful exit
*
*******************************************************************************
*
* @sa PLASMA_zlansy
* @sa PLASMA_zlansy_Tile_Async
* @sa PLASMA_clansy_Tile
* @sa PLASMA_dlansy_Tile
* @sa PLASMA_slansy_Tile
*
******************************************************************************/
double PLASMA_zlansy_Tile(PLASMA_enum norm, PLASMA_enum uplo, PLASMA_desc *A)
{
plasma_context_t *plasma;
PLASMA_sequence *sequence = NULL;
PLASMA_request request = PLASMA_REQUEST_INITIALIZER;
double value;
plasma = plasma_context_self();
if (plasma == NULL) {
plasma_fatal_error("PLASMA_zlansy_Tile", "PLASMA not initialized");
return PLASMA_ERR_NOT_INITIALIZED;
}
plasma_sequence_create(plasma, &sequence);
PLASMA_zlansy_Tile_Async(norm, uplo, A, &value, sequence, &request);
plasma_dynamic_sync();
plasma_sequence_destroy(plasma, sequence);
return value;
}
/***************************************************************************//**
*
* @ingroup PLASMA_Complex64_t_Tile
*
* PLASMA_zlaswp_Tile - performs a series of row interchanges on the matrix A.
* One row interchange is initiated for each of rows K1 through K2 of A.
* Tile equivalent of PLASMA_zlaswp().
* Operates on matrices stored by tiles.
* All matrices are passed through descriptors.
* All dimensions are taken from the descriptors.
*
*******************************************************************************
*
* @param[in] A
* The tile factors L and U from the factorization, computed by PLASMA_zgetrf.
*
* @param[in] K1
* The first element of IPIV for which a row interchange will
* be done.
*
* @param[in] K2
* The last element of IPIV for which a row interchange will
* be done.
*
* @param[in] IPIV
* The pivot indices from PLASMA_zgetrf.
*
* @param[in] INCX
* The increment between successive values of IPIV. If IPIV
* is negative, the pivots are applied in reverse order.
*
*******************************************************************************
*
* @return
* \retval PLASMA_SUCCESS successful exit
*
*******************************************************************************
*
* @sa PLASMA_zlaswp
* @sa PLASMA_zlaswp_Tile_Async
* @sa PLASMA_claswp_Tile
* @sa PLASMA_dlaswp_Tile
* @sa PLASMA_slaswp_Tile
* @sa PLASMA_zgetrf_Tile
*
******************************************************************************/
int PLASMA_zlaswp_Tile(PLASMA_desc *A, int K1, int K2, int *IPIV, int INCX)
{
plasma_context_t *plasma;
PLASMA_sequence *sequence = NULL;
PLASMA_request request = PLASMA_REQUEST_INITIALIZER;
int status;
plasma = plasma_context_self();
if (plasma == NULL) {
plasma_fatal_error("PLASMA_zlaswp_Tile", "PLASMA not initialized");
return PLASMA_ERR_NOT_INITIALIZED;
}
plasma_sequence_create(plasma, &sequence);
PLASMA_zlaswp_Tile_Async(A, K1, K2, IPIV, INCX, sequence, &request);
plasma_dynamic_sync();
status = sequence->status;
plasma_sequence_destroy(plasma, sequence);
return status;
}
/***************************************************************************//**
*
* @ingroup PLASMA_Complex32_t_Tile
*
* PLASMA_cpotrf_Tile - Computes the Cholesky factorization of a symmetric positive definite
* or Hermitian positive definite matrix.
* Tile equivalent of PLASMA_cpotrf().
* Operates on matrices stored by tiles.
* All matrices are passed through descriptors.
* All dimensions are taken from the descriptors.
*
*******************************************************************************
*
* @param[in] uplo
* = PlasmaUpper: Upper triangle of A is stored;
* = PlasmaLower: Lower triangle of A is stored.
*
* @param[in] A
* On entry, the symmetric positive definite (or Hermitian) matrix A.
* If uplo = PlasmaUpper, the leading N-by-N upper triangular part of A
* contains the upper triangular part of the matrix A, 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 part of the matrix A, and the strictly upper triangular part of A is not
* referenced.
* On exit, if return value = 0, the factor U or L from the Cholesky factorization
* A = U**H*U or A = L*L**H.
*
*******************************************************************************
*
* @return
* \retval PLASMA_SUCCESS successful exit
* \retval >0 if i, the leading minor of order i of A is not positive definite, so the
* factorization could not be completed, and the solution has not been computed.
*
*******************************************************************************
*
* @sa PLASMA_cpotrf
* @sa PLASMA_cpotrf_Tile_Async
* @sa PLASMA_cpotrf_Tile
* @sa PLASMA_dpotrf_Tile
* @sa PLASMA_spotrf_Tile
* @sa PLASMA_cpotrs_Tile
*
******************************************************************************/
int PLASMA_cpotrf_Tile(PLASMA_enum uplo, PLASMA_desc *A)
{
plasma_context_t *plasma;
PLASMA_sequence *sequence = NULL;
PLASMA_request request = PLASMA_REQUEST_INITIALIZER;
int status;
plasma = plasma_context_self();
if (plasma == NULL) {
plasma_fatal_error("PLASMA_cpotrf_Tile", "PLASMA not initialized");
return PLASMA_ERR_NOT_INITIALIZED;
}
plasma_sequence_create(plasma, &sequence);
PLASMA_cpotrf_Tile_Async(uplo, A, sequence, &request);
plasma_dynamic_sync();
status = sequence->status;
plasma_sequence_destroy(plasma, sequence);
return status;
}
/***************************************************************************//**
*
* @ingroup float_Tile
*
* PLASMA_splgsy_Tile - Generate a random hermitian matrix by tiles.
* Tile equivalent of PLASMA_splgsy().
* Operates on matrices stored by tiles.
* All matrices are passed through descriptors.
* All dimensions are taken from the descriptors.
*
*******************************************************************************
*
* @param[in] bump
* The value to add to the diagonal to be sure
* to have a positive definite matrix.
*
* @param[in] A
* On exit, The random hermitian matrix A generated.
*
* @param[in] seed
* The seed used in the random generation.
*
*******************************************************************************
*
* @return
* \retval PLASMA_SUCCESS successful exit
*
*******************************************************************************
*
* @sa PLASMA_splgsy
* @sa PLASMA_splgsy_Tile_Async
* @sa PLASMA_cplgsy_Tile
* @sa PLASMA_dplgsy_Tile
* @sa PLASMA_splgsy_Tile
* @sa PLASMA_splrnt_Tile
* @sa PLASMA_splgsy_Tile
*
******************************************************************************/
int PLASMA_splgsy_Tile( float bump, PLASMA_desc *A,
unsigned long long int seed )
{
plasma_context_t *plasma;
PLASMA_sequence *sequence = NULL;
PLASMA_request request = PLASMA_REQUEST_INITIALIZER;
int status;
plasma = plasma_context_self();
if (plasma == NULL) {
plasma_fatal_error("PLASMA_splgsy_Tile", "PLASMA not initialized");
return PLASMA_ERR_NOT_INITIALIZED;
}
plasma_sequence_create(plasma, &sequence);
PLASMA_splgsy_Tile_Async( bump, A, seed, sequence, &request );
plasma_dynamic_sync();
status = sequence->status;
plasma_sequence_destroy(plasma, sequence);
return status;
}
/***************************************************************************//**
*
* @ingroup double
*
* PLASMA_dormlq - overwrites the general M-by-N matrix C with Q*C, where Q is an orthogonal
* matrix (unitary in the complex case) defined as the product of elementary reflectors returned
* by PLASMA_dgelqf. Q is of order M.
*
*******************************************************************************
*
* @param[in] side
* Intended usage:
* = PlasmaLeft: apply Q or Q**T from the left;
* = PlasmaRight: apply Q or Q**T from the right.
* Currently only PlasmaLeft is supported.
*
* @param[in] trans
* Intended usage:
* = PlasmaNoTrans: no transpose, apply Q;
* = PlasmaTrans: ugate transpose, apply Q**T.
* Currently only PlasmaTrans is supported.
*
* @param[in] M
* The number of rows of the matrix C. M >= 0.
*
* @param[in] N
* The number of columns of the matrix C. N >= 0.
*
* @param[in] K
* The number of rows of elementary tile reflectors whose product defines the matrix Q.
* M >= K >= 0.
*
* @param[in] A
* Details of the LQ factorization of the original matrix A as returned by PLASMA_dgelqf.
*
* @param[in] LDA
* The leading dimension of the array A. LDA >= max(1,K).
*
* @param[in] T
* Auxiliary factorization data, computed by PLASMA_dgelqf.
*
* @param[in,out] B
* On entry, the M-by-N matrix B.
* On exit, B is overwritten by Q*B or Q**T*B.
*
* @param[in] LDB
* The leading dimension of the array C. LDC >= max(1,M).
*
*******************************************************************************
*
* @return
* \retval PLASMA_SUCCESS successful exit
* \retval <0 if -i, the i-th argument had an illegal value
*
*******************************************************************************
*
* @sa PLASMA_dormlq_Tile
* @sa PLASMA_dormlq_Tile_Async
* @sa PLASMA_cunmlq
* @sa PLASMA_dormlq
* @sa PLASMA_sormlq
* @sa PLASMA_dgelqf
*
******************************************************************************/
int PLASMA_dormlq(PLASMA_enum side, PLASMA_enum trans, int M, int N, int K,
double *A, int LDA,
double *T,
double *B, int LDB)
{
int NB, IB, IBNB, KT, NT, An;
int status;
plasma_context_t *plasma;
PLASMA_sequence *sequence = NULL;
PLASMA_request request = PLASMA_REQUEST_INITIALIZER;
PLASMA_desc descA, descB, descT;
plasma = plasma_context_self();
if (plasma == NULL) {
plasma_fatal_error("PLASMA_dormlq", "PLASMA not initialized");
return PLASMA_ERR_NOT_INITIALIZED;
}
if (side == PlasmaLeft)
An = M;
else
An = N;
/* Check input arguments */
if ( (side != PlasmaLeft) && (side != PlasmaRight) ) {
plasma_error("PLASMA_dormlq", "illegal value of side");
return -1;
}
if ( (trans != PlasmaTrans) && (trans != PlasmaNoTrans) ){
plasma_error("PLASMA_dormlq", "illegal value of trans");
return -2;
}
if (M < 0) {
plasma_error("PLASMA_dormlq", "illegal value of M");
return -3;
}
if (N < 0) {
plasma_error("PLASMA_dormlq", "illegal value of N");
return -4;
}
if ((K < 0) || (K > An)) {
plasma_error("PLASMA_dormlq", "illegal value of K");
return -5;
}
if (LDA < max(1, K)) {
plasma_error("PLASMA_dormlq", "illegal value of LDA");
return -7;
}
if (LDB < max(1, M)) {
plasma_error("PLASMA_dormlq", "illegal value of LDB");
return -10;
}
/* Quick return - currently NOT equivalent to LAPACK's:
* CALL DLASET( 'Full', MAX( M, N ), NRHS, ZERO, ZERO, B, LDB ) */
if (min(M, min(N, K)) == 0)
return PLASMA_SUCCESS;
/* Tune NB & IB depending on M, N & NRHS; Set NBNB */
status = plasma_tune(PLASMA_FUNC_DGELS, M, K, N);
if (status != PLASMA_SUCCESS) {
plasma_error("PLASMA_dormlq", "plasma_tune() failed");
return status;
}
/* Set MT, NT & NTRHS */
NB = PLASMA_NB;
IB = PLASMA_IB;
IBNB = IB*NB;
KT = ( K%NB==0) ? (K /NB) : (K /NB+1);
NT = (An%NB==0) ? (An/NB) : (An/NB+1);
plasma_sequence_create(plasma, &sequence);
if (plasma->householder == PLASMA_FLAT_HOUSEHOLDER) {
descT = plasma_desc_init(
PlasmaRealDouble,
IB, NB, IBNB,
KT*IB, NT*NB, 0, 0, KT*IB, NT*NB);
}
else {
/* Double the size of T to accomodate the tree reduction phase */
descT = plasma_desc_init(
PlasmaRealDouble,
IB, NB, IBNB,
KT*IB, 2*NT*NB, 0, 0, KT*IB, 2*NT*NB);
}
descT.mat = T;
if ( PLASMA_TRANSLATION == PLASMA_OUTOFPLACE ) {
plasma_dooplap2tile( descA, A, NB, NB, LDA, An, 0, 0, K, An, plasma_desc_mat_free(&(descA)) );
plasma_dooplap2tile( descB, B, NB, NB, LDB, N, 0, 0, M, N, plasma_desc_mat_free(&(descA)); plasma_desc_mat_free(&(descB)));
} else {
/***************************************************************************//**
*
* @ingroup PLASMA_Complex32_t
*
* PLASMA_cgelqs - Compute a minimum-norm solution min || A*X - B || using the LQ factorization
* A = L*Q computed by PLASMA_cgelqf.
*
*******************************************************************************
*
* @param[in] M
* The number of rows of the matrix A. M >= 0.
*
* @param[in] N
* The number of columns of the matrix A. N >= M >= 0.
*
* @param[in] NRHS
* The number of columns of B. NRHS >= 0.
*
* @param[in] A
* Details of the LQ factorization of the original matrix A as returned by PLASMA_cgelqf.
*
* @param[in] LDA
* The leading dimension of the array A. LDA >= M.
*
* @param[in] T
* Auxiliary factorization data, computed by PLASMA_cgelqf.
*
* @param[in,out] B
* On entry, the M-by-NRHS right hand side matrix B.
* On exit, the N-by-NRHS solution matrix X.
*
* @param[in] LDB
* The leading dimension of the array B. LDB >= N.
*
*******************************************************************************
*
* @return
* \retval PLASMA_SUCCESS successful exit
* \retval <0 if -i, the i-th argument had an illegal value
*
*******************************************************************************
*
* @sa PLASMA_cgelqs_Tile
* @sa PLASMA_cgelqs_Tile_Async
* @sa PLASMA_cgelqs
* @sa PLASMA_dgelqs
* @sa PLASMA_sgelqs
* @sa PLASMA_cgelqf
*
******************************************************************************/
int PLASMA_cgelqs(int M, int N, int NRHS,
PLASMA_Complex32_t *A, int LDA,
PLASMA_Complex32_t *T,
PLASMA_Complex32_t *B, int LDB)
{
int NB, IB, IBNB, MT, NT;
int status;
plasma_context_t *plasma;
PLASMA_sequence *sequence = NULL;
PLASMA_request request = PLASMA_REQUEST_INITIALIZER;
PLASMA_desc descA, descB, descT;
plasma = plasma_context_self();
if (plasma == NULL) {
plasma_fatal_error("PLASMA_cgelqs", "PLASMA not initialized");
return PLASMA_ERR_NOT_INITIALIZED;
}
/* Check input arguments */
if (M < 0) {
plasma_error("PLASMA_cgelqs", "illegal value of M");
return -1;
}
if (N < 0 || M > N) {
plasma_error("PLASMA_cgelqs", "illegal value of N");
return -2;
}
if (NRHS < 0) {
plasma_error("PLASMA_cgelqs", "illegal value of N");
return -3;
}
if (LDA < max(1, M)) {
plasma_error("PLASMA_cgelqs", "illegal value of LDA");
return -5;
}
if (LDB < max(1, max(1, N))) {
plasma_error("PLASMA_cgelqs", "illegal value of LDB");
return -8;
}
/* Quick return */
if (min(M, min(N, NRHS)) == 0) {
return PLASMA_SUCCESS;
}
/* Tune NB & IB depending on M, N & NRHS; Set NBNBSIZE */
status = plasma_tune(PLASMA_FUNC_CGELS, M, N, NRHS);
if (status != PLASMA_SUCCESS) {
plasma_error("PLASMA_cgelqs", "plasma_tune() failed");
return status;
}
/* Set MT, NT & NTRHS */
NB = PLASMA_NB;
IB = PLASMA_IB;
IBNB = IB*NB;
MT = (M%NB==0) ? (M/NB) : (M/NB+1);
NT = (N%NB==0) ? (N/NB) : (N/NB+1);
plasma_sequence_create(plasma, &sequence);
if (plasma->householder == PLASMA_FLAT_HOUSEHOLDER) {
descT = plasma_desc_init(
PlasmaComplexFloat,
IB, NB, IBNB,
MT*IB, NT*NB, 0, 0, MT*IB, NT*NB);
}
else {
/* Double the size of T to accomodate the tree reduction phase */
descT = plasma_desc_init(
PlasmaComplexFloat,
IB, NB, IBNB,
MT*IB, 2*NT*NB, 0, 0, MT*IB, 2*NT*NB);
}
descT.mat = T;
if ( PLASMA_TRANSLATION == PLASMA_OUTOFPLACE ) {
plasma_cooplap2tile( descA, A, NB, NB, LDA, N, 0, 0, M, N , plasma_desc_mat_free(&(descA)) );
plasma_cooplap2tile( descB, B, NB, NB, LDB, NRHS, 0, 0, N, NRHS, plasma_desc_mat_free(&(descA)); plasma_desc_mat_free(&(descB)));
} else {
/***************************************************************************//**
*
* @ingroup float
*
* PLASMA_sgemm - Performs one of the matrix-matrix operations
*
* \f[ C = \alpha [op( A )\times op( B )] + \beta C \f],
*
* where op( X ) is one of
*
* op( X ) = X or op( X ) = X' or op( X ) = g( X' )
*
* 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.
*
*******************************************************************************
*
* @param[in] transA
* Specifies whether the matrix A is transposed, not transposed or ugate transposed:
* = PlasmaNoTrans: A is not transposed;
* = PlasmaTrans: A is transposed;
* = PlasmaTrans: A is ugate transposed.
*
* @param[in] transB
* Specifies whether the matrix B is transposed, not transposed or ugate transposed:
* = PlasmaNoTrans: B is not transposed;
* = PlasmaTrans: B is transposed;
* = PlasmaTrans: B is ugate transposed.
*
* @param[in] M
* M specifies the number of rows of the matrix op( A ) and of the matrix C. M >= 0.
*
* @param[in] N
* N specifies the number of columns of the matrix op( B ) and of the matrix C. N >= 0.
*
* @param[in] K
* K specifies the number of columns of the matrix op( A ) and the number of rows of
* the matrix op( B ). K >= 0.
*
* @param[in] alpha
* alpha specifies the scalar alpha
*
* @param[in] A
* A is a LDA-by-ka matrix, where ka is K when transA = PlasmaNoTrans,
* and is M otherwise.
*
* @param[in] LDA
* The leading dimension of the array A. LDA >= max(1,M).
*
* @param[in] B
* B is a LDB-by-kb matrix, where kb is N when transB = PlasmaNoTrans,
* and is K otherwise.
*
* @param[in] LDB
* The leading dimension of the array B. LDB >= max(1,N).
*
* @param[in] beta
* beta specifies the scalar beta
*
* @param[in,out] C
* C is a LDC-by-N matrix.
* On exit, the array is overwritten by the M by N matrix ( alpha*op( A )*op( B ) + beta*C )
*
* @param[in] LDC
* The leading dimension of the array C. LDC >= max(1,M).
*
*******************************************************************************
*
* @return
* \retval PLASMA_SUCCESS successful exit
*
*******************************************************************************
*
* @sa PLASMA_sgemm_Tile
* @sa PLASMA_cgemm
* @sa PLASMA_dgemm
* @sa PLASMA_sgemm
*
******************************************************************************/
int PLASMA_sgemm(PLASMA_enum transA, PLASMA_enum transB, int M, int N, int K,
float alpha, float *A, int LDA,
float *B, int LDB,
float beta, float *C, int LDC)
{
int NB;
int Am, An, Bm, Bn;
int status;
PLASMA_desc descA, descB, descC;
plasma_context_t *plasma;
PLASMA_sequence *sequence = NULL;
PLASMA_request request = PLASMA_REQUEST_INITIALIZER;
plasma = plasma_context_self();
if (plasma == NULL) {
plasma_fatal_error("PLASMA_sgemm", "PLASMA not initialized");
return PLASMA_ERR_NOT_INITIALIZED;
}
/* Check input arguments */
if ((transA != PlasmaNoTrans) && (transA != PlasmaTrans) && (transA != PlasmaTrans)) {
plasma_error("PLASMA_sgemm", "illegal value of transA");
return -1;
}
if ((transB != PlasmaNoTrans) && (transB != PlasmaTrans) && (transB != PlasmaTrans)) {
plasma_error("PLASMA_sgemm", "illegal value of transB");
return -2;
}
if ( transA == PlasmaNoTrans ) {
Am = M;
An = K;
} else {
Am = K;
An = M;
}
if ( transB == PlasmaNoTrans ) {
Bm = K;
Bn = N;
} else {
Bm = N;
Bn = K;
}
if (M < 0) {
plasma_error("PLASMA_sgemm", "illegal value of M");
return -3;
}
if (N < 0) {
plasma_error("PLASMA_sgemm", "illegal value of N");
return -4;
}
if (K < 0) {
plasma_error("PLASMA_sgemm", "illegal value of N");
return -5;
}
if (LDA < max(1, Am)) {
plasma_error("PLASMA_sgemm", "illegal value of LDA");
return -8;
}
if (LDB < max(1, Bm)) {
plasma_error("PLASMA_sgemm", "illegal value of LDB");
return -10;
}
if (LDC < max(1, M)) {
plasma_error("PLASMA_sgemm", "illegal value of LDC");
return -13;
}
/* Quick return */
if (M == 0 || N == 0 ||
((alpha == (float)0.0 || K == 0) && beta == (float)1.0))
return PLASMA_SUCCESS;
/* Tune NB depending on M, N & NRHS; Set NBNBSIZE */
status = plasma_tune(PLASMA_FUNC_SGEMM, M, N, 0);
if (status != PLASMA_SUCCESS) {
plasma_error("PLASMA_sgemm", "plasma_tune() failed");
return status;
}
/* Set MT & NT & KT */
NB = PLASMA_NB;
plasma_sequence_create(plasma, &sequence);
if ( PLASMA_TRANSLATION == PLASMA_OUTOFPLACE ) {
plasma_sooplap2tile( descA, A, NB, NB, LDA, An, 0, 0, Am, An, plasma_desc_mat_free(&(descA)) );
plasma_sooplap2tile( descB, B, NB, NB, LDB, Bn, 0, 0, Bm, Bn, plasma_desc_mat_free(&(descA)); plasma_desc_mat_free(&(descB)));
plasma_sooplap2tile( descC, C, NB, NB, LDC, N, 0, 0, M, N, plasma_desc_mat_free(&(descA)); plasma_desc_mat_free(&(descB)); plasma_desc_mat_free(&(descC)));
} else {
/***************************************************************************//**
*
* @ingroup PLASMA_Complex32_t
*
* PLASMA_cpotrf - Computes the Cholesky factorization of a symmetric positive definite
* (or Hermitian positive definite in the complex case) matrix A.
* The factorization has the form
*
* \f[ A = \{_{L\times L^H, if uplo = PlasmaLower}^{U^H\times U, if uplo = PlasmaUpper} \f]
*
* where U is an upper triangular matrix and L is a lower triangular matrix.
*
*******************************************************************************
*
* @param[in] uplo
* = PlasmaUpper: Upper triangle of A is stored;
* = PlasmaLower: Lower triangle of A is stored.
*
* @param[in] N
* The order of the matrix A. N >= 0.
*
* @param[in,out] A
* On entry, the symmetric positive definite (or Hermitian) matrix A.
* If uplo = PlasmaUpper, the leading N-by-N upper triangular part of A
* contains the upper triangular part of the matrix A, 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 part of the matrix A, and the strictly upper triangular part of A is not
* referenced.
* On exit, if return value = 0, the factor U or L from the Cholesky factorization
* A = U**H*U or A = L*L**H.
*
* @param[in] LDA
* The leading dimension of the array A. LDA >= max(1,N).
*
*******************************************************************************
*
* @return
* \retval PLASMA_SUCCESS successful exit
* \retval <0 if -i, the i-th argument had an illegal value
* \retval >0 if i, the leading minor of order i of A is not positive definite, so the
* factorization could not be completed, and the solution has not been computed.
*
*******************************************************************************
*
* @sa PLASMA_cpotrf_Tile
* @sa PLASMA_cpotrf_Tile_Async
* @sa PLASMA_cpotrf
* @sa PLASMA_dpotrf
* @sa PLASMA_spotrf
* @sa PLASMA_cpotrs
*
******************************************************************************/
int PLASMA_cpotrf(PLASMA_enum uplo, int N,
PLASMA_Complex32_t *A, int LDA)
{
int NB;
int status;
plasma_context_t *plasma;
PLASMA_sequence *sequence = NULL;
PLASMA_request request = PLASMA_REQUEST_INITIALIZER;
PLASMA_desc descA;
plasma = plasma_context_self();
if (plasma == NULL) {
plasma_fatal_error("PLASMA_cpotrf", "PLASMA not initialized");
return PLASMA_ERR_NOT_INITIALIZED;
}
/* Check input arguments */
if (uplo != PlasmaUpper && uplo != PlasmaLower) {
plasma_error("PLASMA_cpotrf", "illegal value of uplo");
return -1;
}
if (N < 0) {
plasma_error("PLASMA_cpotrf", "illegal value of N");
return -2;
}
if (LDA < max(1, N)) {
plasma_error("PLASMA_cpotrf", "illegal value of LDA");
return -4;
}
/* Quick return */
if (max(N, 0) == 0)
return PLASMA_SUCCESS;
/* Tune NB depending on M, N & NRHS; Set NBNB */
status = plasma_tune(PLASMA_FUNC_CPOSV, N, N, 0);
if (status != PLASMA_SUCCESS) {
plasma_error("PLASMA_cpotrf", "plasma_tune() failed");
return status;
}
/* Set NT */
NB = PLASMA_NB;
plasma_sequence_create(plasma, &sequence);
if ( PLASMA_TRANSLATION == PLASMA_OUTOFPLACE ) {
plasma_cooplap2tile( descA, A, NB, NB, LDA, N, 0, 0, N, N, plasma_desc_mat_free(&(descA)) );
} else {
plasma_ciplap2tile( descA, A, NB, NB, LDA, N, 0, 0, N, N);
}
/* Call the tile interface */
PLASMA_cpotrf_Tile_Async(uplo, &descA, sequence, &request);
if ( PLASMA_TRANSLATION == PLASMA_OUTOFPLACE ) {
plasma_cooptile2lap( descA, A, NB, NB, LDA, N );
plasma_dynamic_sync();
plasma_desc_mat_free(&descA);
} else {
plasma_ciptile2lap( descA, A, NB, NB, LDA, N );
plasma_dynamic_sync();
}
status = sequence->status;
plasma_sequence_destroy(plasma, sequence);
return status;
}
/***************************************************************************//**
*
* @ingroup float
*
* PLASMA_sgelqf - Computes the tile LQ factorization of a complex M-by-N matrix A: A = L * Q.
*
*******************************************************************************
*
* @param[in] M
* The number of rows of the matrix A. M >= 0.
*
* @param[in] N
* The number of columns of the matrix A. N >= 0.
*
* @param[in,out] A
* On entry, the M-by-N matrix A.
* On exit, the elements on and below the diagonal of the array contain the m-by-min(M,N)
* lower trapezoidal matrix L (L is lower triangular if M <= N); the elements above the
* diagonal represent the unitary matrix Q as a product of elementary reflectors, stored
* by tiles.
*
* @param[in] LDA
* The leading dimension of the array A. LDA >= max(1,M).
*
* @param[out] T
* On exit, auxiliary factorization data, required by PLASMA_sgelqs to solve the system
* of equations.
*
*******************************************************************************
*
* @return
* \retval PLASMA_SUCCESS successful exit
* \retval <0 if -i, the i-th argument had an illegal value
*
*******************************************************************************
*
* @sa PLASMA_sgelqf_Tile
* @sa PLASMA_sgelqf_Tile_Async
* @sa PLASMA_cgelqf
* @sa PLASMA_dgelqf
* @sa PLASMA_sgelqf
* @sa PLASMA_sgelqs
*
******************************************************************************/
int PLASMA_sgelqf(int M, int N,
float *A, int LDA,
float *T)
{
int NB, IB, IBNB, MT, NT;
int status;
plasma_context_t *plasma;
PLASMA_sequence *sequence = NULL;
PLASMA_request request = PLASMA_REQUEST_INITIALIZER;
PLASMA_desc descA, descT;
plasma = plasma_context_self();
if (plasma == NULL) {
plasma_fatal_error("PLASMA_sgelqf", "PLASMA not initialized");
return PLASMA_ERR_NOT_INITIALIZED;
}
/* Check input arguments */
if (M < 0) {
plasma_error("PLASMA_sgelqf", "illegal value of M");
return -1;
}
if (N < 0) {
plasma_error("PLASMA_sgelqf", "illegal value of N");
return -2;
}
if (LDA < max(1, M)) {
plasma_error("PLASMA_sgelqf", "illegal value of LDA");
return -4;
}
/* Quick return */
if (min(M, N) == 0)
return PLASMA_SUCCESS;
/* Tune NB & IB depending on M, N & NRHS; Set NBNBSIZE */
status = plasma_tune(PLASMA_FUNC_SGELS, M, N, 0);
if (status != PLASMA_SUCCESS) {
plasma_error("PLASMA_sgelqf", "plasma_tune() failed");
return status;
}
/* Set MT & NT */
NB = PLASMA_NB;
IB = PLASMA_IB;
IBNB = IB*NB;
MT = (M%NB==0) ? (M/NB) : (M/NB+1);
NT = (N%NB==0) ? (N/NB) : (N/NB+1);
plasma_sequence_create(plasma, &sequence);
if (plasma->householder == PLASMA_FLAT_HOUSEHOLDER) {
descT = plasma_desc_init(
PlasmaRealFloat,
IB, NB, IBNB,
MT*IB, NT*NB, 0, 0, MT*IB, NT*NB);
}
else {
/* Double the size of T to accomodate the tree reduction phase */
descT = plasma_desc_init(
PlasmaRealFloat,
IB, NB, IBNB,
MT*IB, 2*NT*NB, 0, 0, MT*IB, 2*NT*NB);
}
descT.mat = T;
if ( PLASMA_TRANSLATION == PLASMA_OUTOFPLACE ) {
plasma_sooplap2tile( descA, A, NB, NB, LDA, N, 0, 0, M, N, plasma_desc_mat_free(&(descA)) );
} else {
plasma_siplap2tile( descA, A, NB, NB, LDA, N, 0, 0, M, N);
}
/* Call the tile interface */
PLASMA_sgelqf_Tile_Async(&descA, &descT, sequence, &request);
if ( PLASMA_TRANSLATION == PLASMA_OUTOFPLACE ) {
plasma_sooptile2lap( descA, A, NB, NB, LDA, N );
plasma_dynamic_sync();
plasma_desc_mat_free(&descA);
} else {
plasma_siptile2lap( descA, A, NB, NB, LDA, N );
plasma_dynamic_sync();
}
status = sequence->status;
plasma_sequence_destroy(plasma, sequence);
return status;
}
/***************************************************************************//**
*
* @ingroup PLASMA_Complex64_t
*
* PLASMA_zgetrs_incpiv - Solves a system of linear equations A * X = B, with a general N-by-N matrix A
* using the tile LU factorization computed by PLASMA_zgetrf_incpiv.
*
*******************************************************************************
*
* @param[in] trans
* Intended to specify the the form of the system of equations:
* = PlasmaNoTrans: A * X = B (No transpose)
* = PlasmaTrans: A**T * X = B (Transpose)
* = PlasmaConjTrans: A**H * X = B (Conjugate transpose)
* Currently only PlasmaNoTrans is supported.
*
* @param[in] N
* The order of the matrix A. N >= 0.
*
* @param[in] NRHS
* The number of right hand sides, i.e., the number of columns of the matrix B.
* NRHS >= 0.
*
* @param[in] A
* The tile factors L and U from the factorization, computed by PLASMA_zgetrf_incpiv.
*
* @param[in] LDA
* The leading dimension of the array A. LDA >= max(1,N).
*
* @param[in] L
* Auxiliary factorization data, related to the tile L factor, computed by PLASMA_zgetrf_incpiv.
*
* @param[in] IPIV
* The pivot indices from PLASMA_zgetrf_incpiv (not equivalent to LAPACK).
*
* @param[in,out] B
* On entry, the N-by-NRHS matrix of right hand side matrix B.
* On exit, the solution matrix X.
*
* @param[in] LDB
* The leading dimension of the array B. LDB >= max(1,N).
*
*******************************************************************************
*
* @return
* \retval PLASMA_SUCCESS successful exit
* \return <0 if -i, the i-th argument had an illegal value
*
*******************************************************************************
*
* @sa PLASMA_zgetrs_incpiv_Tile
* @sa PLASMA_zgetrs_incpiv_Tile_Async
* @sa PLASMA_cgetrs_incpiv
* @sa PLASMA_dgetrs_incpiv
* @sa PLASMA_sgetrs_incpiv
* @sa PLASMA_zgetrf_incpiv
*
******************************************************************************/
int PLASMA_zgetrs_incpiv(PLASMA_enum trans, int N, int NRHS,
PLASMA_Complex64_t *A, int LDA,
PLASMA_Complex64_t *L, int *IPIV,
PLASMA_Complex64_t *B, int LDB)
{
int NB, IB, IBNB, NT;
int status;
plasma_context_t *plasma;
PLASMA_sequence *sequence = NULL;
PLASMA_request request = PLASMA_REQUEST_INITIALIZER;
PLASMA_desc descA, descB, descL;
plasma = plasma_context_self();
if (plasma == NULL) {
plasma_fatal_error("PLASMA_zgetrs_incpiv", "PLASMA not initialized");
return PLASMA_ERR_NOT_INITIALIZED;
}
/* Check input arguments */
if (trans != PlasmaNoTrans) {
plasma_error("PLASMA_zgetrs_incpiv", "only PlasmaNoTrans supported");
return PLASMA_ERR_NOT_SUPPORTED;
}
if (N < 0) {
plasma_error("PLASMA_zgetrs_incpiv", "illegal value of N");
return -2;
}
if (NRHS < 0) {
plasma_error("PLASMA_zgetrs_incpiv", "illegal value of NRHS");
return -3;
}
if (LDA < max(1, N)) {
plasma_error("PLASMA_zgetrs_incpiv", "illegal value of LDA");
return -5;
}
if (LDB < max(1, N)) {
plasma_error("PLASMA_zgetrs_incpiv", "illegal value of LDB");
return -9;
}
/* Quick return */
if (min(N, NRHS) == 0)
return PLASMA_SUCCESS;
/* Tune NB & IB depending on N & NRHS; Set NBNBSIZE */
status = plasma_tune(PLASMA_FUNC_ZGESV, N, N, NRHS);
if (status != PLASMA_SUCCESS) {
plasma_error("PLASMA_zgetrs_incpiv", "plasma_tune() failed");
return status;
}
/* Set NT & NTRHS */
NB = PLASMA_NB;
IB = PLASMA_IB;
IBNB = IB*NB;
NT = (N%NB==0) ? (N/NB) : (N/NB+1);
plasma_sequence_create(plasma, &sequence);
descL = plasma_desc_init(
PlasmaComplexDouble,
IB, NB, IBNB,
NT*IB, NT*NB, 0, 0, NT*IB, NT*NB);
descL.mat = L;
if ( PLASMA_TRANSLATION == PLASMA_OUTOFPLACE ) {
plasma_zooplap2tile( descA, A, NB, NB, LDA, N, 0, 0, N, N , plasma_desc_mat_free(&(descA)) );
plasma_zooplap2tile( descB, B, NB, NB, LDB, NRHS, 0, 0, N, NRHS, plasma_desc_mat_free(&(descA)); plasma_desc_mat_free(&(descB)));
} else {
/***************************************************************************//**
*
* @ingroup double
*
* PLASMA_dtrmm - Computes B = alpha*op( A )*B or B = alpha*B*op( A ).
*
*******************************************************************************
*
* @param[in] side
* Specifies whether A appears on the left or on the right of X:
* = PlasmaLeft: A*X = B
* = PlasmaRight: X*A = B
*
* @param[in] uplo
* Specifies whether the matrix A is upper triangular or lower triangular:
* = PlasmaUpper: Upper triangle of A is stored;
* = PlasmaLower: Lower triangle of A is stored.
*
* @param[in] transA
* Specifies whether the matrix A is transposed, not transposed or ugate transposed:
* = PlasmaNoTrans: A is transposed;
* = PlasmaTrans: A is not transposed;
* = PlasmaTrans: A is ugate transposed.
*
* @param[in] diag
* Specifies whether or not A is unit triangular:
* = PlasmaNonUnit: A is non unit;
* = PlasmaUnit: A us unit.
*
* @param[in] N
* The order of the matrix A. N >= 0.
*
* @param[in] NRHS
* The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
*
* @param[in] alpha
* alpha specifies the scalar alpha.
*
* @param[in] A
* The triangular matrix A. If uplo = PlasmaUpper, the leading N-by-N upper triangular
* part of the array A contains the upper triangular matrix, and the strictly lower
* triangular part of A is not referenced. If uplo = PlasmaLower, the leading N-by-N
* lower triangular part of the array A contains the lower triangular matrix, and the
* strictly upper triangular part of A is not referenced. If diag = PlasmaUnit, the
* diagonal elements of A are also not referenced and are assumed to be 1.
*
* @param[in] LDA
* The leading dimension of the array A. LDA >= max(1,N).
*
* @param[in,out] B
* On entry, the N-by-NRHS right hand side matrix B.
* On exit, if return value = 0, the N-by-NRHS solution matrix X.
*
* @param[in] LDB
* The leading dimension of the array B. LDB >= max(1,N).
*
*******************************************************************************
*
* @return
* \retval PLASMA_SUCCESS successful exit
* \retval <0 if -i, the i-th argument had an illegal value
*
*******************************************************************************
*
* @sa PLASMA_dtrmm_Tile
* @sa PLASMA_dtrmm_Tile_Async
* @sa PLASMA_ctrmm
* @sa PLASMA_dtrmm
* @sa PLASMA_strmm
*
******************************************************************************/
int PLASMA_dtrmm(PLASMA_enum side, PLASMA_enum uplo,
PLASMA_enum transA, PLASMA_enum diag,
int N, int NRHS, double alpha,
double *A, int LDA,
double *B, int LDB)
{
int NB, NA;
int status;
plasma_context_t *plasma;
PLASMA_sequence *sequence = NULL;
PLASMA_request request = PLASMA_REQUEST_INITIALIZER;
PLASMA_desc descA, descB;
plasma = plasma_context_self();
if (plasma == NULL) {
plasma_fatal_error("PLASMA_dtrmm", "PLASMA not initialized");
return PLASMA_ERR_NOT_INITIALIZED;
}
/* Check input arguments */
if (side != PlasmaLeft && side != PlasmaRight) {
plasma_error("PLASMA_dtrmm", "illegal value of side");
return -1;
}
if (uplo != PlasmaUpper && uplo != PlasmaLower) {
plasma_error("PLASMA_dtrmm", "illegal value of uplo");
return -2;
}
if (transA != PlasmaTrans && transA != PlasmaNoTrans && transA != PlasmaTrans ) {
plasma_error("PLASMA_dtrmm", "illegal value of transA");
return -3;
}
if (diag != PlasmaUnit && diag != PlasmaNonUnit) {
plasma_error("PLASMA_dtrmm", "illegal value of diag");
return -4;
}
if (N < 0) {
plasma_error("PLASMA_dtrmm", "illegal value of N");
return -5;
}
if (NRHS < 0) {
plasma_error("PLASMA_dtrmm", "illegal value of NRHS");
return -6;
}
if (LDA < max(1, N)) {
plasma_error("PLASMA_dtrmm", "illegal value of LDA");
return -8;
}
if (LDB < max(1, N)) {
plasma_error("PLASMA_dtrmm", "illegal value of LDB");
return -10;
}
/* Quick return */
if (min(N, NRHS) == 0)
return PLASMA_SUCCESS;
/* Tune NB depending on M, N & NRHS; Set NBNB */
status = plasma_tune(PLASMA_FUNC_DPOSV, N, N, NRHS);
if (status != PLASMA_SUCCESS) {
plasma_error("PLASMA_dtrmm", "plasma_tune() failed");
return status;
}
/* Set NT & NTRHS */
NB = PLASMA_NB;
if (side == PlasmaLeft) {
NA = N;
} else {
NA = NRHS;
}
plasma_sequence_create(plasma, &sequence);
if ( PLASMA_TRANSLATION == PLASMA_OUTOFPLACE ) {
plasma_dooplap2tile( descA, A, NB, NB, LDA, NA, 0, 0, NA, NA, plasma_desc_mat_free(&(descA)) );
plasma_dooplap2tile( descB, B, NB, NB, LDB, NRHS, 0, 0, N, NRHS, plasma_desc_mat_free(&(descA)); plasma_desc_mat_free(&(descB)));
} else {
/***************************************************************************//**
*
* @ingroup PLASMA_Complex64_t
*
* PLASMA_zlansy returns the value
*
* zlansy = ( max(abs(A(i,j))), NORM = PlasmaMaxNorm
* (
* ( norm1(A), NORM = PlasmaOneNorm
* (
* ( normI(A), NORM = PlasmaInfNorm
* (
* ( normF(A), NORM = PlasmaFrobeniusNorm
*
* where norm1 denotes the one norm of a matrix (maximum column sum),
* normI denotes the infinity norm of a matrix (maximum row sum) and
* normF denotes the Frobenius norm of a matrix (square root of sum
* of squares). Note that max(abs(A(i,j))) is not a consistent matrix
* norm.
*
*******************************************************************************
*
* @param[in] norm
* = PlasmaMaxNorm: Max norm
* = PlasmaOneNorm: One norm
* = PlasmaInfNorm: Infinity norm
* = PlasmaFrobeniusNorm: Frobenius norm
*
* @param[in] uplo
* = PlasmaUpper: Upper triangle of A is stored;
* = PlasmaLower: Lower triangle of A is stored.
*
* @param[in] N
* The number of columns/rows of the matrix A. N >= 0. When N = 0,
* the returned value is set to zero.
*
* @param[in] A
* The N-by-N matrix A.
*
* @param[in] LDA
* The leading dimension of the array A. LDA >= max(1,N).
*
*******************************************************************************
*
* @return
* \retval the norm described above.
*
*******************************************************************************
*
* @sa PLASMA_zlansy_Tile
* @sa PLASMA_zlansy_Tile_Async
* @sa PLASMA_clansy
* @sa PLASMA_dlansy
* @sa PLASMA_slansy
*
******************************************************************************/
double PLASMA_zlansy(PLASMA_enum norm, PLASMA_enum uplo, int N,
PLASMA_Complex64_t *A, int LDA)
{
int NB;
int status;
double value;
plasma_context_t *plasma;
PLASMA_sequence *sequence = NULL;
PLASMA_request request = PLASMA_REQUEST_INITIALIZER;
PLASMA_desc descA;
plasma = plasma_context_self();
if (plasma == NULL) {
plasma_fatal_error("PLASMA_zlansy", "PLASMA not initialized");
return PLASMA_ERR_NOT_INITIALIZED;
}
/* Check input arguments */
if ( (norm != PlasmaMaxNorm) && (norm != PlasmaOneNorm)
&& (norm != PlasmaInfNorm) && (norm != PlasmaFrobeniusNorm) ) {
plasma_error("PLASMA_zlansy", "illegal value of norm");
return -1;
}
if ( (uplo != PlasmaUpper) && (uplo != PlasmaLower) ) {
plasma_error("PLASMA_zlansy", "illegal value of uplo");
return -2;
}
if (N < 0) {
plasma_error("PLASMA_zlansy", "illegal value of N");
return -3;
}
if (LDA < max(1, N)) {
plasma_error("PLASMA_zlansy", "illegal value of LDA");
return -5;
}
/* Quick return */
if ( N == 0)
return (double)0.0;
/* Tune NB depending on M, N & NRHS; Set NBNB */
status = plasma_tune(PLASMA_FUNC_ZGEMM, N, N, 0);
if (status != PLASMA_SUCCESS) {
plasma_error("PLASMA_zlansy", "plasma_tune() failed");
return status;
}
/* Set NT */
NB = PLASMA_NB;
plasma_sequence_create(plasma, &sequence);
if ( PLASMA_TRANSLATION == PLASMA_OUTOFPLACE ) {
plasma_zooplap2tile( descA, A, NB, NB, LDA, N, 0, 0, N, N, sequence, &request,
plasma_desc_mat_free(&(descA)) );
} else {
plasma_ziplap2tile( descA, A, NB, NB, LDA, N, 0, 0, N, N,
sequence, &request);
}
/* Call the tile interface */
PLASMA_zlansy_Tile_Async(norm, uplo, &descA, &value, sequence, &request);
if ( PLASMA_TRANSLATION == PLASMA_OUTOFPLACE ) {
plasma_dynamic_sync();
plasma_desc_mat_free(&descA);
} else {
plasma_ziptile2lap( descA, A, NB, NB, LDA, N, sequence, &request);
plasma_dynamic_sync();
}
plasma_sequence_destroy(plasma, sequence);
return value;
}
/***************************************************************************//**
*
* @ingroup PLASMA_Complex64_t
*
* PLASMA_zunglq - Generates an M-by-N matrix Q with orthonormal rows, which is defined as the
* first M rows of a product of the elementary reflectors returned by PLASMA_zgelqf.
*
*******************************************************************************
*
* @param[in] M
* The number of rows of the matrix Q. M >= 0.
*
* @param[in] N
* The number of columns of the matrix Q. N >= M.
*
* @param[in] K
* The number of rows of elementary tile reflectors whose product defines the matrix Q.
* M >= K >= 0.
*
* @param[in] A
* Details of the LQ factorization of the original matrix A as returned by PLASMA_zgelqf.
*
* @param[in] LDA
* The leading dimension of the array A. LDA >= max(1,M).
*
* @param[in] T
* Auxiliary factorization data, computed by PLASMA_zgelqf.
*
* @param[out] Q
* On exit, the M-by-N matrix Q.
*
* @param[in] LDQ
* The leading dimension of the array Q. LDQ >= max(1,M).
*
*******************************************************************************
*
* @return
* \retval PLASMA_SUCCESS successful exit
* \retval PLASMA_SUCCESS <0 if -i, the i-th argument had an illegal value
*
*******************************************************************************
*
* @sa PLASMA_zunglq_Tile
* @sa PLASMA_zunglq_Tile_Async
* @sa PLASMA_cunglq
* @sa PLASMA_dorglq
* @sa PLASMA_sorglq
* @sa PLASMA_zgelqf
*
******************************************************************************/
int PLASMA_zunglq(int M, int N, int K,
PLASMA_Complex64_t *A, int LDA,
PLASMA_Complex64_t *T,
PLASMA_Complex64_t *Q, int LDQ)
{
int NB, IB, IBNB, KT, NT;
int status;
plasma_context_t *plasma;
PLASMA_sequence *sequence = NULL;
PLASMA_request request = PLASMA_REQUEST_INITIALIZER;
PLASMA_desc descA, descQ, descT;
plasma = plasma_context_self();
if (plasma == NULL) {
plasma_fatal_error("PLASMA_zunglq", "PLASMA not initialized");
return PLASMA_ERR_NOT_INITIALIZED;
}
if (M < 0) {
plasma_error("PLASMA_zunglq", "illegal value of M");
return -1;
}
if (N < M) {
plasma_error("PLASMA_zunglq", "illegal value of N");
return -2;
}
if (K < 0 || K > M) {
plasma_error("PLASMA_zunglq", "illegal value of K");
return -3;
}
if (LDA < max(1, M)) {
plasma_error("PLASMA_zunglq", "illegal value of LDA");
return -5;
}
if (LDQ < max(1, M)) {
plasma_error("PLASMA_zunglq", "illegal value of LDQ");
return -8;
}
/* Quick return - currently NOT equivalent to LAPACK's:
* CALL DLASET( 'Full', MAX( M, N ), NRHS, ZERO, ZERO, B, LDQ ) */
if (min(M, min(N, K)) == 0)
return PLASMA_SUCCESS;
/* Tune NB & IB depending on M, N & NRHS; Set NBNB */
status = plasma_tune(PLASMA_FUNC_ZGELS, M, N, 0);
if (status != PLASMA_SUCCESS) {
plasma_error("PLASMA_zunglq", "plasma_tune() failed");
return status;
}
/* Set MT & NT */
NB = PLASMA_NB;
IB = PLASMA_IB;
IBNB = IB*NB;
NT = (N%NB==0) ? (N/NB) : (N/NB+1);
KT = (K%NB==0) ? (K/NB) : (K/NB+1);
plasma_sequence_create(plasma, &sequence);
if (plasma->householder == PLASMA_FLAT_HOUSEHOLDER) {
descT = plasma_desc_init(
PlasmaComplexDouble,
IB, NB, IBNB,
KT*IB, NT*NB, 0, 0, KT*IB, NT*NB);
}
else {
/* Double the size of T to accomodate the tree reduction phase */
descT = plasma_desc_init(
PlasmaComplexDouble,
IB, NB, IBNB,
KT*IB, 2*NT*NB, 0, 0, KT*IB, 2*NT*NB);
}
descT.mat = T;
if ( PLASMA_TRANSLATION == PLASMA_OUTOFPLACE ) {
plasma_zooplap2tile( descA, A, NB, NB, LDA, N, 0, 0, K, N, plasma_desc_mat_free(&(descA)) );
plasma_zooplap2tile( descQ, Q, NB, NB, LDQ, N, 0, 0, M, N, plasma_desc_mat_free(&(descA)); plasma_desc_mat_free(&(descQ)));
} else {
/***************************************************************************//**
*
* @ingroup PLASMA_Complex64_t
*
* PLASMA_zgetri - Computes the inverse of a matrix using the LU factorization
* computed by PLASMA_zgetrf.
* This method inverts U and then computes inv(A) by solving the system
* inv(A)*L = inv(U) for inv(A).
*
*******************************************************************************
*
* @param[in] N
* The order of the matrix A. N >= 0.
*
* @param[in,out] A
* On entry, the triangular factor L or U from the
* factorization A = P*L*U as computed by PLASMA_zgetrf.
* On exit, if return value = 0, the inverse of the original
* matrix A.
*
* @param[in] LDA
* The leading dimension of the array A. LDA >= max(1,N).
*
* @param[in] IPIV
* The pivot indices that define the permutations
* as returned by PLASMA_zgetrf.
*
*******************************************************************************
*
* @return
* \retval PLASMA_SUCCESS successful exit
* \retval <0 if -i, the i-th argument had an illegal value
* \retval >0 if i, the (i,i) element of the factor U is
* exactly zero; The matrix is singular
* and its inverse could not be computed.
*
*******************************************************************************
*
* @sa PLASMA_zgetri_Tile
* @sa PLASMA_zgetri_Tile_Async
* @sa PLASMA_cgetri
* @sa PLASMA_dgetri
* @sa PLASMA_sgetri
* @sa PLASMA_zgetrf
*
******************************************************************************/
int PLASMA_zgetri(int N,
PLASMA_Complex64_t *A, int LDA,
int *IPIV)
{
int NB;
int status;
plasma_context_t *plasma;
PLASMA_sequence *sequence = NULL;
PLASMA_request request = PLASMA_REQUEST_INITIALIZER;
PLASMA_desc descA;
PLASMA_desc descW;
plasma = plasma_context_self();
if (plasma == NULL) {
plasma_fatal_error("PLASMA_zgetri", "PLASMA not initialized");
return PLASMA_ERR_NOT_INITIALIZED;
}
/* Check input arguments */
if (N < 0) {
plasma_error("PLASMA_zgetri", "illegal value of N");
return -1;
}
if (LDA < max(1, N)) {
plasma_error("PLASMA_zgetri", "illegal value of LDA");
return -3;
}
/* Quick return */
if (max(N, 0) == 0)
return PLASMA_SUCCESS;
/* Tune NB depending on M, N & NRHS; Set NBNB */
status = plasma_tune(PLASMA_FUNC_ZGESV, N, N, 0);
if (status != PLASMA_SUCCESS) {
plasma_error("PLASMA_zgetri", "plasma_tune() failed");
return status;
}
/* Set NT */
NB = PLASMA_NB;
plasma_sequence_create(plasma, &sequence);
if ( PLASMA_TRANSLATION == PLASMA_OUTOFPLACE ) {
plasma_zooplap2tile( descA, A, NB, NB, LDA, N, 0, 0, N, N, sequence, &request,
plasma_desc_mat_free(&(descA)) );
} else {
plasma_ziplap2tile( descA, A, NB, NB, LDA, N, 0, 0, N, N,
sequence, &request);
}
/* Allocate workspace */
PLASMA_Alloc_Workspace_zgetri_Tile_Async(&descA, &descW);
/* Call the tile interface */
PLASMA_zgetri_Tile_Async(&descA, IPIV, &descW, sequence, &request);
if ( PLASMA_TRANSLATION == PLASMA_OUTOFPLACE ) {
plasma_zooptile2lap( descA, A, NB, NB, LDA, N, sequence, &request);
plasma_dynamic_sync();
plasma_desc_mat_free(&descA);
} else {
plasma_ziptile2lap( descA, A, NB, NB, LDA, N, sequence, &request);
plasma_dynamic_sync();
}
plasma_desc_mat_free(&(descW));
status = sequence->status;
plasma_sequence_destroy(plasma, sequence);
return status;
}
/***************************************************************************//**
*
* @ingroup double
*
* PLASMA_dgels - solves overdetermined or underdetermined linear systems involving an M-by-N
* matrix A using the QR or the LQ factorization of A. It is assumed that A has full rank.
* The following options are provided:
*
* # trans = PlasmaNoTrans and M >= N: find the least squares solution of an overdetermined
* system, i.e., solve the least squares problem: minimize || B - A*X ||.
*
* # trans = PlasmaNoTrans and M < N: find the minimum norm solution of an underdetermined
* system A * X = B.
*
* Several right hand side vectors B and solution vectors X can be handled in a single call;
* they are stored as the columns of the M-by-NRHS right hand side matrix B and the N-by-NRHS
* solution matrix X.
*
*******************************************************************************
*
* @param[in] trans
* Intended usage:
* = PlasmaNoTrans: the linear system involves A;
* = PlasmaTrans: the linear system involves A**T.
* Currently only PlasmaNoTrans is supported.
*
* @param[in] M
* The number of rows of the matrix A. M >= 0.
*
* @param[in] N
* The number of columns of the matrix A. N >= 0.
*
* @param[in] NRHS
* The number of right hand sides, i.e., the number of columns of the matrices B and X.
* NRHS >= 0.
*
* @param[in,out] A
* On entry, the M-by-N matrix A.
* On exit,
* if M >= N, A is overwritten by details of its QR factorization as returned by
* PLASMA_dgeqrf;
* if M < N, A is overwritten by details of its LQ factorization as returned by
* PLASMA_dgelqf.
*
* @param[in] LDA
* The leading dimension of the array A. LDA >= max(1,M).
*
* @param[out] T
* On exit, auxiliary factorization data.
*
* @param[in,out] B
* On entry, the M-by-NRHS matrix B of right hand side vectors, stored columnwise;
* On exit, if return value = 0, B is overwritten by the solution vectors, stored
* columnwise:
* if M >= N, rows 1 to N of B contain the least squares solution vectors; the residual
* sum of squares for the solution in each column is given by the sum of squares of the
* modulus of elements N+1 to M in that column;
* if M < N, rows 1 to N of B contain the minimum norm solution vectors;
*
* @param[in] LDB
* The leading dimension of the array B. LDB >= MAX(1,M,N).
*
*******************************************************************************
*
* @return
* \retval PLASMA_SUCCESS successful exit
* \retval <0 if -i, the i-th argument had an illegal value
*
*******************************************************************************
*
* @sa PLASMA_dgels_Tile
* @sa PLASMA_dgels_Tile_Async
* @sa PLASMA_cgels
* @sa PLASMA_dgels
* @sa PLASMA_sgels
*
******************************************************************************/
int PLASMA_dgels(PLASMA_enum trans, int M, int N, int NRHS,
double *A, int LDA,
double *T,
double *B, int LDB)
{
int i, j;
int NB, IB, IBNB, MT, NT;
int status;
plasma_context_t *plasma;
PLASMA_sequence *sequence = NULL;
PLASMA_request request = PLASMA_REQUEST_INITIALIZER;
PLASMA_desc descA, descB, descT;
plasma = plasma_context_self();
if (plasma == NULL) {
plasma_fatal_error("PLASMA_dgels", "PLASMA not initialized");
return PLASMA_ERR_NOT_INITIALIZED;
}
/* Check input arguments */
if (trans != PlasmaNoTrans) {
plasma_error("PLASMA_dgels", "only PlasmaNoTrans supported");
return PLASMA_ERR_NOT_SUPPORTED;
}
if (M < 0) {
plasma_error("PLASMA_dgels", "illegal value of M");
return -2;
}
if (N < 0) {
plasma_error("PLASMA_dgels", "illegal value of N");
return -3;
}
if (NRHS < 0) {
plasma_error("PLASMA_dgels", "illegal value of NRHS");
return -4;
}
if (LDA < max(1, M)) {
plasma_error("PLASMA_dgels", "illegal value of LDA");
return -6;
}
if (LDB < max(1, max(M, N))) {
plasma_error("PLASMA_dgels", "illegal value of LDB");
return -9;
}
/* Quick return */
if (min(M, min(N, NRHS)) == 0) {
for (i = 0; i < max(M, N); i++)
for (j = 0; j < NRHS; j++)
B[j*LDB+i] = 0.0;
return PLASMA_SUCCESS;
}
/* Tune NB & IB depending on M, N & NRHS; Set NBNB */
status = plasma_tune(PLASMA_FUNC_DGELS, M, N, NRHS);
if (status != PLASMA_SUCCESS) {
plasma_error("PLASMA_dgels", "plasma_tune() failed");
return status;
}
/* Set MT, NT & NTRHS */
NB = PLASMA_NB;
IB = PLASMA_IB;
IBNB = IB*NB;
NT = (N%NB==0) ? (N/NB) : (N/NB+1);
MT = (M%NB==0) ? (M/NB) : (M/NB+1);
plasma_sequence_create(plasma, &sequence);
if (plasma->householder == PLASMA_FLAT_HOUSEHOLDER) {
descT = plasma_desc_init(
PlasmaRealDouble,
IB, NB, IBNB,
MT*IB, NT*NB, 0, 0, MT*IB, NT*NB);
}
else {
/* Double the size of T to accomodate the tree reduction phase */
descT = plasma_desc_init(
PlasmaRealDouble,
IB, NB, IBNB,
MT*IB, 2*NT*NB, 0, 0, MT*IB, 2*NT*NB);
}
descT.mat = T;
if ( M >= N ) {
if ( PLASMA_TRANSLATION == PLASMA_OUTOFPLACE ) {
plasma_dooplap2tile( descA, A, NB, NB, LDA, N, 0, 0, M, N , plasma_desc_mat_free(&(descA)) );
plasma_dooplap2tile( descB, B, NB, NB, LDB, NRHS, 0, 0, M, NRHS, plasma_desc_mat_free(&(descA)); plasma_desc_mat_free(&(descB)));
} else {
/***************************************************************************//**
*
* @ingroup PLASMA_Complex32_t
*
* PLASMA_csyrk - Performs one of the hermitian rank k operations
*
* \f[ C = \alpha [ op( A ) \times conjfg( op( A )' )] + \beta C \f],
*
* where op( X ) is one of
*
* op( X ) = X or op( X ) = conjfg( X' )
*
* where alpha and beta are real scalars, C is an n-by-n hermitian
* matrix and A is an n-by-k matrix in the first case and a k-by-n
* matrix in the second case.
*
*******************************************************************************
*
* @param[in] uplo
* = PlasmaUpper: Upper triangle of C is stored;
* = PlasmaLower: Lower triangle of C is stored.
*
* @param[in] trans
* Specifies whether the matrix A is transposed or conjfugate transposed:
* = PlasmaNoTrans: A is not transposed;
* = PlasmaTrans : A is transposed.
*
* @param[in] N
* N specifies the order of the matrix C. N must be at least zero.
*
* @param[in] K
* K specifies the number of columns of the matrix op( A ).
*
* @param[in] alpha
* alpha specifies the scalar alpha.
*
* @param[in] A
* A is a LDA-by-ka matrix, where ka is K when trans = PlasmaNoTrans,
* and is N otherwise.
*
* @param[in] LDA
* The leading dimension of the array A. LDA must be at least
* max( 1, N ), otherwise LDA must be at least max( 1, K ).
*
* @param[in] beta
* beta specifies the scalar beta
*
* @param[in,out] C
* C is a LDC-by-N matrix.
* On exit, the array uplo part of the matrix is overwritten
* by the uplo part of the updated matrix.
*
* @param[in] LDC
* The leading dimension of the array C. LDC >= max( 1, N ).
*
*******************************************************************************
*
* @return
* \retval PLASMA_SUCCESS successful exit
*
*******************************************************************************
*
* @sa PLASMA_csyrk_Tile
* @sa PLASMA_csyrk
* @sa PLASMA_dsyrk
* @sa PLASMA_ssyrk
*
******************************************************************************/
int PLASMA_csyrk(PLASMA_enum uplo, PLASMA_enum trans, int N, int K,
PLASMA_Complex32_t alpha, PLASMA_Complex32_t *A, int LDA,
PLASMA_Complex32_t beta, PLASMA_Complex32_t *C, int LDC)
{
int NB;
int Am, An;
int status;
PLASMA_desc descA, descC;
plasma_context_t *plasma;
PLASMA_sequence *sequence = NULL;
PLASMA_request request = PLASMA_REQUEST_INITIALIZER;
plasma = plasma_context_self();
if (plasma == NULL) {
plasma_fatal_error("PLASMA_csyrk", "PLASMA not initialized");
return PLASMA_ERR_NOT_INITIALIZED;
}
/* Check input arguments */
if ((uplo != PlasmaUpper) && (uplo != PlasmaLower)) {
plasma_error("PLASMA_csyrk", "illegal value of uplo");
return -1;
}
if ((trans != PlasmaNoTrans) && (trans != PlasmaTrans)) {
plasma_error("PLASMA_csyrk", "illegal value of trans");
return -2;
}
if ( trans == PlasmaNoTrans ) {
Am = N; An = K;
} else {
Am = K; An = N;
}
if (N < 0) {
plasma_error("PLASMA_csyrk", "illegal value of N");
return -3;
}
if (K < 0) {
plasma_error("PLASMA_csyrk", "illegal value of K");
return -4;
}
if (LDA < max(1, Am)) {
plasma_error("PLASMA_csyrk", "illegal value of LDA");
return -7;
}
if (LDC < max(1, N)) {
plasma_error("PLASMA_csyrk", "illegal value of LDC");
return -10;
}
/* Quick return */
if (N == 0 ||
((alpha == (PLASMA_Complex32_t)0.0 || K == 0.0) && beta == (PLASMA_Complex32_t)1.0))
return PLASMA_SUCCESS;
/* Tune NB depending on M, N & NRHS; Set NBNBSIZE */
status = plasma_tune(PLASMA_FUNC_CSYRK, N, K, 0);
if (status != PLASMA_SUCCESS) {
plasma_error("PLASMA_csyrk", "plasma_tune() failed");
return status;
}
/* Set MT & NT & KT */
NB = PLASMA_NB;
plasma_sequence_create(plasma, &sequence);
if ( PLASMA_TRANSLATION == PLASMA_OUTOFPLACE ) {
plasma_cooplap2tile( descA, A, NB, NB, LDA, An, 0, 0, Am, An, plasma_desc_mat_free(&(descA)) );
plasma_cooplap2tile( descC, C, NB, NB, LDC, N, 0, 0, N, N, plasma_desc_mat_free(&(descA)); plasma_desc_mat_free(&(descC)));
} else {
/***************************************************************************//**
*
* @ingroup PLASMA_Complex32_t
*
* PLASMA_cgetrf - Computes an LU factorization of a general M-by-N matrix A
* using the tile LU algorithm with partial tile pivoting with row interchanges.
*
*******************************************************************************
*
* @param[in] M
* The number of rows of the matrix A. M >= 0.
*
* @param[in] N
* The number of columns of the matrix A. N >= 0.
*
* @param[in,out] A
* On entry, the M-by-N matrix to be factored.
* On exit, the tile factors L and U from the factorization.
*
* @param[in] LDA
* The leading dimension of the array A. LDA >= max(1,M).
*
* @param[out] IPIV
* The pivot indices that define the permutations.
*
*******************************************************************************
*
* @return
* \retval PLASMA_SUCCESS successful exit
* \retval <0 if -i, the i-th argument had an illegal value
* \retval >0 if i, U(i,i) is exactly zero. The factorization has been completed,
* but the factor U is exactly singular, and division by zero will occur
* if it is used to solve a system of equations.
*
*******************************************************************************
*
* @sa PLASMA_cgetrf_Tile
* @sa PLASMA_cgetrf_Tile_Async
* @sa PLASMA_cgetrf
* @sa PLASMA_dgetrf
* @sa PLASMA_sgetrf
*
******************************************************************************/
int PLASMA_cgetrf(int M, int N,
PLASMA_Complex32_t *A, int LDA,
int *IPIV)
{
int NB, NBNB, minMN;
int status;
PLASMA_desc descA ;
plasma_context_t *plasma;
PLASMA_sequence *sequence = NULL;
PLASMA_request request = PLASMA_REQUEST_INITIALIZER;
plasma = plasma_context_self();
if (plasma == NULL) {
plasma_fatal_error("PLASMA_cgetrf", "PLASMA not initialized");
return PLASMA_ERR_NOT_INITIALIZED;
}
/* Check input arguments */
if (M < 0) {
plasma_error("PLASMA_cgetrf", "illegal value of M");
return -1;
}
if (N < 0) {
plasma_error("PLASMA_cgetrf", "illegal value of N");
return -2;
}
if (LDA < max(1, M)) {
plasma_error("PLASMA_cgetrf", "illegal value of LDA");
return -4;
}
/* Quick return */
if (min(M, N) == 0)
return PLASMA_SUCCESS;
/* Tune NB & IB depending on M, N & NRHS; Set NBNBSIZE */
status = plasma_tune(PLASMA_FUNC_CGESV, M, N, 0);
if (status != PLASMA_SUCCESS) {
plasma_error("PLASMA_cgetrf", "plasma_tune() failed");
return status;
}
/* Set NT & NTRHS */
NB = PLASMA_NB;
NBNB = NB*NB;
plasma_sequence_create(plasma, &sequence);
descA = plasma_desc_init(
PlasmaComplexFloat,
NB, NB, NBNB,
LDA, N, 0, 0, M, N);
descA.mat = A;
minMN = min(M, N);
memset(IPIV, 0, minMN*sizeof(int));
/* Call the tile interface */
plasma_dynamic_call_4(plasma_pcgetrf_reclap,
PLASMA_desc, descA,
int*, IPIV,
PLASMA_sequence*, sequence,
PLASMA_request*, &request);
plasma_dynamic_sync();
/*
* Generate the correct IPIV (Has to be move in a task)
*/
{
int i, inc, tmp, j;
for(i=1; i<descA.mt; i++) {
inc = i*descA.mb;
tmp = min( minMN - inc, descA.mb);
if ( tmp < 1 )
break;
for (j=0; j<tmp; j++)
IPIV[inc+j] = IPIV[inc+j] + inc;
}
}
status = sequence->status;
plasma_sequence_destroy(plasma, sequence);
return status;
}
/***************************************************************************//**
*
* @ingroup float
*
* PLASMA_ssygv - Computes all eigenvalues and, optionally,
* eigenvectors of a complex generalized Hermitian-definite
* eigenproblem of the form: A*x=(lambda)*B*x, A*Bx=(lambda)*x, or
* B*A*x=(lambda)*x.
* Here A and B are assumed to be Hermitian and B is also positive
* definite.
* Note: Only PlasmaNoVec supported!
*
*******************************************************************************
*
* @param[in] PlasmaItype
* Intended usage:
* = 1: A*x=(lambda)*B*x
* = 2: A*Bx=(lambda)*x
* = 3: B*A*x=(lambda)*x
*
* @param[in] jobz
* Intended usage:
* = PlasmaNoVec: computes eigenvalues only;
* = PlasmaVec: computes eigenvalues and eigenvectors.
* Note: Only PlasmaNoVec supported!
*
* @param[in] uplo
* Specifies whether the matrix A is upper triangular or
* lower triangular:
* = PlasmaUpper: Upper triangle of A and B are stored;
* = PlasmaLower: Lower triangle of A and B are stored.
*
* @param[in] N
* The order of the matrix A. N >= 0.
*
* @param[in,out] A
* On entry, the symmetric (or Hermitian) matrix A.
* If uplo = PlasmaUpper, the leading N-by-N upper triangular
* part of A contains the upper triangular part of the matrix
* A, and the strictly lower triangular part of A is not
* referenced.
* If uplo = PlasmaLower, the leading N-by-N lower triangular
* part of A contains the lower triangular part of the matrix
* A, and the strictly upper triangular part of A is not
* referenced.
* On exit, if jobz = PlasmaVec, then if return value = 0, A
* contains the matrix Z of eigenvectors.
* The eigenvectors are normalized as follows:
* if ITYPE = 1 or 2, Z**T*B*Z = I;
* if ITYPE = 3, Z**T*inv(B)*Z = I.
* If jobz = PlasmaNoVec, then on exit the lower triangle (if
* uplo = PlasmaLower) or the upper triangle (if uplo =
* PlasmaUpper) of A, including the diagonal, is destroyed.
*
* @param[in] LDA
* The leading dimension of the array A. LDA >= max(1,N).
*
* @param[in,out] B
* On entry, the symmetric (or Hermitian) positive definite
* matrix B.
* If uplo = PlasmaUpper, the leading N-by-N upper triangular
* part of B contains the upper triangular part of the matrix
* B, and the strictly lower triangular part of B is not
* referenced.
* If uplo = PlasmaLower, the leading N-by-N lower triangular
* part of B contains the lower triangular part of the matrix
* B, and the strictly upper triangular part of B is not
* referenced.
* On exit, if return value <= N, the part of B containing
* the matrix is overwritten by the triangular factor U or L
* from the Cholesky factorization B = U**T*U or B = L*L**T.
*
* @param[in] LDB
* The leading dimension of the array B. LDA >= max(1,N).
*
* @param[out] W
* On exit, if info = 0, the eigenvalues.
*
* @param[in, out] descT
* On entry, descriptor as return by PLASMA_Alloc_Workspace_ssygv
* On exit, contains auxiliary factorization data.
*
* @param[out] Q
* On exit, if jobz = PlasmaVec and info = 0, the eigenvectors.
*
* @param[in] LDQ
* The leading dimension of Q.
*
*******************************************************************************
*
* @return
* \retval PLASMA_SUCCESS successful exit
* \retval <0 if -i, the i-th argument had an illegal value
* \retval <=N if INFO = i, plasma_ssygv failed to converge; i
* off-diagonal elements of an intermediate tridiagonal
* form did not converge to zero.
* \retval >N if INFO = N + i, for 1 <= i <= N, then the leading
* minor of order i of B is not positive definite.
* The factorization of B could not be completed and
* no eigenvalues or eigenvectors were computed.
*
*******************************************************************************
*
* @sa PLASMA_ssygv_Tile
* @sa PLASMA_ssygv_Tile_Async
* @sa PLASMA_chegv
* @sa PLASMA_dsygv
* @sa PLASMA_ssygv
*
******************************************************************************/
int PLASMA_ssygv(PLASMA_enum itype, PLASMA_enum jobz, PLASMA_enum uplo, int N,
float *A, int LDA,
float *B, int LDB,
float *W,
PLASMA_desc *descT,
float *Q, int LDQ)
{
int NB, IB, IBNB, NT;
int status;
plasma_context_t *plasma;
PLASMA_sequence *sequence = NULL;
PLASMA_request request = PLASMA_REQUEST_INITIALIZER;
PLASMA_desc descA, descB, descQ;
plasma = plasma_context_self();
if (plasma == NULL) {
plasma_error("PLASMA_ssygv", "PLASMA not initialized");
return PLASMA_ERR_NOT_INITIALIZED;
}
/* Tune NB & IB depending on N; Set NBNB */
status = plasma_tune(PLASMA_FUNC_SSYGV, N, N, 0);
if (status != PLASMA_SUCCESS) {
plasma_error("PLASMA_ssygv", "plasma_tune() failed");
return status;
}
/* Set NT */
NB = PLASMA_NB;
IB = PLASMA_IB;
IBNB = IB*NB;
NT = (N%NB==0) ? (N/NB) : (N/NB+1);
/* Check input arguments */
if (itype != 1 && itype != 2 && itype != 3) {
plasma_error("PLASMA_ssygv", "Illegal value of itype");
return -1;
}
if (jobz != PlasmaNoVec && jobz != PlasmaVec) {
plasma_error("PLASMA_ssygv", "illegal value of jobz");
return -2;
}
if (uplo != PlasmaLower && uplo!= PlasmaUpper) {
plasma_error("PLASMA_ssygv", "only PlasmaLower supported");
return -3;
}
if (N < 0) {
plasma_error("PLASMA_ssygv", "illegal value of N");
return -4;
}
if (LDA < max(1, N)) {
plasma_error("PLASMA_ssygv", "illegal value of LDA");
return -6;
}
if (LDB < max(1, N)) {
plasma_error("PLASMA_ssygv", "illegal value of LDB");
return -8;
}
if ( (plasma_desc_check(descT) != PLASMA_SUCCESS) ||
( descT->m != NT*IB ) || (descT->n != NT*NB) ) {
plasma_error("PLASMA_ssygv", "invalid T descriptor");
return -10;
}
if (LDQ < max(1, N)) {
plasma_error("PLASMA_ssygv", "illegal value of LDQ");
return -12;
}
/* Quick return */
if (N == 0)
return PLASMA_SUCCESS;
if (jobz == PlasmaVec) {
plasma_error("PLASMA_ssygv", "computing the eigenvectors is not supported in this version");
return -1;
}
plasma_sequence_create(plasma, &sequence);
if ( PLASMA_TRANSLATION == PLASMA_OUTOFPLACE ) {
plasma_sooplap2tile( descA, A, NB, NB, LDA, N, 0, 0, N, N,
plasma_desc_mat_free(&(descA)) );
plasma_sooplap2tile( descB, B, NB, NB, LDB, N, 0, 0, N, N,
plasma_desc_mat_free(&(descA)); plasma_desc_mat_free(&(descB)) );
if (jobz == PlasmaVec) {
/* No need for conversion, it's just output */
plasma_sdesc_alloc( descQ, NB, NB, LDQ, N, 0, 0, N, N,
plasma_desc_mat_free(&(descA)); plasma_desc_mat_free(&(descB)); plasma_desc_mat_free(&(descQ)) );
}
/***************************************************************************//**
*
* @ingroup PLASMA_Complex64_t
*
* PLASMA_zhemm - Performs one of the matrix-matrix operations
*
* \f[ C = \alpha \times A \times B + \beta \times C \f]
*
* or
*
* \f[ C = \alpha \times B \times A + \beta \times C \f]
*
* where alpha and beta are scalars, A is an hermitian matrix and B and
* C are m by n matrices.
*
*******************************************************************************
*
* @param[in] side
* Specifies whether the hermitian matrix A appears on the
* left or right in the operation as follows:
* = PlasmaLeft: \f[ C = \alpha \times A \times B + \beta \times C \f]
* = PlasmaRight: \f[ C = \alpha \times B \times A + \beta \times C \f]
*
* @param[in] uplo
* Specifies whether the upper or lower triangular part of
* the hermitian matrix A is to be referenced as follows:
* = PlasmaLower: Only the lower triangular part of the
* hermitian matrix A is to be referenced.
* = PlasmaUpper: Only the upper triangular part of the
* hermitian matrix A is to be referenced.
*
* @param[in] M
* Specifies the number of rows of the matrix C. M >= 0.
*
* @param[in] N
* Specifies the number of columns of the matrix C. N >= 0.
*
* @param[in] alpha
* Specifies the scalar alpha.
*
* @param[in] A
* A is a LDA-by-ka matrix, where ka is M when side = PlasmaLeft,
* and is N otherwise. Only the uplo triangular part is referenced.
*
* @param[in] LDA
* The leading dimension of the array A. LDA >= max(1,ka).
*
* @param[in] B
* B is a LDB-by-N matrix, where the leading M-by-N part of
* the array B must contain the matrix B.
*
* @param[in] LDB
* The leading dimension of the array B. LDB >= max(1,M).
*
* @param[in] beta
* Specifies the scalar beta.
*
* @param[in,out] C
* C is a LDC-by-N matrix.
* On exit, the array is overwritten by the M by N updated matrix.
*
* @param[in] LDC
* The leading dimension of the array C. LDC >= max(1,M).
*
*******************************************************************************
*
* @return
* \retval PLASMA_SUCCESS successful exit
*
*******************************************************************************
*
* @sa PLASMA_zhemm_Tile
* @sa PLASMA_chemm
* @sa PLASMA_dhemm
* @sa PLASMA_shemm
*
******************************************************************************/
int PLASMA_zhemm(PLASMA_enum side, PLASMA_enum uplo, int M, int N,
PLASMA_Complex64_t alpha, PLASMA_Complex64_t *A, int LDA,
PLASMA_Complex64_t *B, int LDB,
PLASMA_Complex64_t beta, PLASMA_Complex64_t *C, int LDC)
{
int NB;
int Am;
int status;
PLASMA_desc descA, descB, descC;
plasma_context_t *plasma;
PLASMA_sequence *sequence = NULL;
PLASMA_request request = PLASMA_REQUEST_INITIALIZER;
plasma = plasma_context_self();
if (plasma == NULL) {
plasma_fatal_error("PLASMA_zhemm", "PLASMA not initialized");
return PLASMA_ERR_NOT_INITIALIZED;
}
/* Check input arguments */
if ( (side != PlasmaLeft) && (side != PlasmaRight) ){
plasma_error("PLASMA_zhemm", "illegal value of side");
return -1;
}
if ((uplo != PlasmaLower) && (uplo != PlasmaUpper)) {
plasma_error("PLASMA_zhemm", "illegal value of uplo");
return -2;
}
Am = ( side == PlasmaLeft ) ? M : N;
if (M < 0) {
plasma_error("PLASMA_zhemm", "illegal value of M");
return -3;
}
if (N < 0) {
plasma_error("PLASMA_zhemm", "illegal value of N");
return -4;
}
if (LDA < max(1, Am)) {
plasma_error("PLASMA_zhemm", "illegal value of LDA");
return -7;
}
if (LDB < max(1, M)) {
plasma_error("PLASMA_zhemm", "illegal value of LDB");
return -9;
}
if (LDC < max(1, M)) {
plasma_error("PLASMA_zhemm", "illegal value of LDC");
return -12;
}
/* Quick return */
if (M == 0 || N == 0 ||
((alpha == (PLASMA_Complex64_t)0.0) && beta == (PLASMA_Complex64_t)1.0))
return PLASMA_SUCCESS;
/* Tune NB depending on M, N & NRHS; Set NBNBSIZE */
status = plasma_tune(PLASMA_FUNC_ZHEMM, M, N, 0);
if (status != PLASMA_SUCCESS) {
plasma_error("PLASMA_zhemm", "plasma_tune() failed");
return status;
}
/* Set MT & NT & KT */
NB = PLASMA_NB;
plasma_sequence_create(plasma, &sequence);
if ( PLASMA_TRANSLATION == PLASMA_OUTOFPLACE ) {
plasma_zooplap2tile( descA, A, NB, NB, LDA, Am, 0, 0, Am, Am,
plasma_desc_mat_free(&(descA)) );
plasma_zooplap2tile( descB, B, NB, NB, LDB, N, 0, 0, M, N,
plasma_desc_mat_free(&(descA)); plasma_desc_mat_free(&(descB)));
plasma_zooplap2tile( descC, C, NB, NB, LDC, N, 0, 0, M, N,
plasma_desc_mat_free(&(descA)); plasma_desc_mat_free(&(descB)); plasma_desc_mat_free(&(descC)));
} else {
/***************************************************************************//**
*
* @ingroup float
*
* PLASMA_ssytrd - reduces a complex Hermitian matrix A to real symmetric
* tridiagonal form S using a two-stage approach
* First stage: reduction to band tridiagonal form (unitary Q1);
* Second stage: reduction from band to tridiagonal form (unitary
* Q2). Let Q = Q1 * Q2 be the global unitary transformation; Q**T *
* A * Q = S.
* Not LAPACK compliant as A does not contain the T elements
* Note: Only PlasmaNoVec supported!
*
*******************************************************************************
*
* @param[in] jobz
* Intended usage:
* = PlasmaNoVec: computes eigenvalues only;
* = PlasmaVec: computes eigenvalues and eigenvectors.
* Note: Only PlasmaNoVec supported!
*
* @param[in] uplo
* Specifies whether the matrix A is upper triangular or
* lower triangular:
* = PlasmaUpper: Upper triangle of A is stored;
* = PlasmaLower: Lower triangle of A is stored.
*
* @param[in] N
* The order of the matrix A. N >= 0.
*
* @param[in,out] A
* On entry, the symmetric (or Hermitian) matrix A.
* If uplo = PlasmaUpper, the leading N-by-N upper triangular
* part of A contains the upper triangular part of the matrix
* A, and the strictly lower triangular part of A is not
* referenced.
* If uplo = PlasmaLower, the leading N-by-N lower triangular
* part of A contains the lower triangular part of the matrix
* A, and the strictly upper triangular part of A is not
* referenced.
* On exit, the lower triangle (if uplo = PlasmaLower) or the
* upper triangle (if uplo = PlasmaUpper) of A, including the
* diagonal, is destroyed.
*
* @param[in] LDA
* The leading dimension of the array A. LDA >= max(1,N).
*
* @param[out] D
* On exit, the diagonal elements of the tridiagonal matrix:
* D(i) = A(i,i).
*
* @param[out] E
* On exit, he off-diagonal elements of the tridiagonal matrix:
* E(i) = A(i,i+1) if uplo = PlasmaUpper, E(i) = A(i+1,i) if uplo = PlasmaLower.
*
* @param[in, out] descT
* On entry, descriptor as return by PLASMA_Alloc_Workspace_ssyev
* On exit, contains auxiliary factorization data.
*
* @param[out] Q
* On exit, if jobz = PlasmaVec and info = 0, the eigenvectors.
*
* @param[in] LDQ
* The leading dimension of the array Q. LDQ >= max(1,N).
*
*******************************************************************************
*
* @return
* \retval PLASMA_SUCCESS successful exit
* \retval <0 if -i, the i-th argument had an illegal value
* \retval >0 if INFO = i, the algorithm failed to converge; i
* off-diagonal elements of an intermediate tridiagonal
* form did not converge to zero.
*
*******************************************************************************
*
* @sa PLASMA_ssytrd_Tile
* @sa PLASMA_ssytrd_Tile_Async
* @sa PLASMA_chetrd
* @sa PLASMA_dsytrd
* @sa PLASMA_ssytrd
*
******************************************************************************/
int PLASMA_ssytrd(PLASMA_enum jobz, PLASMA_enum uplo, int N,
float *A, int LDA,
float *D,
float *E,
PLASMA_desc *descT,
float *Q, int LDQ)
{
int NB, IB, IBNB, NT;
int status;
plasma_context_t *plasma;
PLASMA_sequence *sequence = NULL;
PLASMA_request request = PLASMA_REQUEST_INITIALIZER;
PLASMA_desc descA, descQ;
plasma = plasma_context_self();
if (plasma == NULL) {
plasma_error("PLASMA_ssytrd", "PLASMA not initialized");
return PLASMA_ERR_NOT_INITIALIZED;
}
/* Tune NB & IB depending on N; Set NBNB */
status = plasma_tune(PLASMA_FUNC_SSYTRD, N, N, 0);
if (status != PLASMA_SUCCESS) {
plasma_error("PLASMA_ssytrd", "plasma_tune() failed");
return status;
}
/* Set NT */
NB = PLASMA_NB;
IB = PLASMA_IB;
IBNB = IB*NB;
NT = (N%NB==0) ? (N/NB) : (N/NB+1);
/* Check input arguments */
if (jobz != PlasmaNoVec && jobz != PlasmaVec) {
plasma_error("PLASMA_ssytrd", "illegal value of jobz");
return -1;
}
if (uplo != PlasmaLower && uplo != PlasmaUpper) {
plasma_error("PLASMA_ssytrd", "illegal value of uplo");
return -2;
}
if (N < 0) {
plasma_error("PLASMA_ssytrd", "illegal value of N");
return -3;
}
if (LDA < max(1, N)) {
plasma_error("PLASMA_ssytrd", "illegal value of LDA");
return -5;
}
if ( (plasma_desc_check(descT) != PLASMA_SUCCESS) ||
( descT->m != NT*IB ) || (descT->n != NT*NB) ) {
plasma_error("PLASMA_ssytrd", "invalid T descriptor");
return -8;
}
if (LDQ < max(1, N)) {
plasma_error("PLASMA_ssytrd", "illegal value of LDQ");
return -10;
}
/* Quick return */
if (N == 0)
return PLASMA_SUCCESS;
if (jobz == PlasmaVec) {
plasma_error("PLASMA_ssytrd", "computing the eigenvectors is not supported in this version");
return -1;
}
plasma_sequence_create(plasma, &sequence);
if ( PLASMA_TRANSLATION == PLASMA_OUTOFPLACE ) {
plasma_sooplap2tile( descA, A, NB, NB, LDA, N, 0, 0, N, N , plasma_desc_mat_free(&(descA)) );
if (jobz == PlasmaVec) {
plasma_sooplap2tile( descQ, Q, NB, NB, LDQ, N, 0, 0, N, N , plasma_desc_mat_free(&(descQ)) );
}
} else {
plasma_siplap2tile( descA, A, NB, NB, LDA, N, 0, 0, N, N );
if (jobz == PlasmaVec)
plasma_siplap2tile( descQ, Q, NB, NB, LDQ, N, 0, 0, N, N );
}
/* Call the tile interface */
PLASMA_ssytrd_Tile_Async(jobz, uplo, &descA, D, E, descT, &descQ, sequence, &request);
if ( PLASMA_TRANSLATION == PLASMA_OUTOFPLACE ) {
plasma_sooptile2lap( descA, A, NB, NB, LDA, N );
if (jobz == PlasmaVec) {
plasma_sooptile2lap( descQ, Q, NB, NB, LDQ, N );
}
plasma_dynamic_sync();
plasma_desc_mat_free(&descA);
if (jobz == PlasmaVec)
plasma_desc_mat_free(&descQ);
} else {
plasma_siptile2lap( descA, A, NB, NB, LDA, N );
if (jobz == PlasmaVec)
plasma_siptile2lap( descQ, Q, NB, NB, LDQ, N );
plasma_dynamic_sync();
}
status = sequence->status;
plasma_sequence_destroy(plasma, sequence);
return status;
}
/***************************************************************************//**
*
* @ingroup PLASMA_Complex64_t
*
* PLASMA_zcposv - Computes the solution to a system of linear equations A * X = B,
* where A is an N-by-N symmetric positive definite (or Hermitian positive definite
* in the complex case) matrix and X and B are N-by-NRHS matrices.
* The Cholesky decomposition is used to factor A as
*
* A = U**H * U, if uplo = PlasmaUpper, or
* A = L * L**H, if uplo = PlasmaLower,
*
* where U is an upper triangular matrix and L is a lower triangular matrix.
* The factored form of A is then used to solve the system of equations A * X = B.
*
* PLASMA_zcposv first attempts to factorize the matrix in COMPLEX and use this
* factorization within an iterative refinement procedure to produce a
* solution with COMPLEX*16 normwise backward error quality (see below).
* If the approach fails the method switches to a COMPLEX*16
* factorization and solve.
*
* The iterative refinement is not going to be a winning strategy if
* the ratio COMPLEX performance over COMPLEX*16 performance is too
* small. A reasonable strategy should take the number of right-hand
* sides and the size of the matrix into account. This might be done
* with a call to ILAENV in the future. Up to now, we always try
* iterative refinement.
*
* The iterative refinement process is stopped if ITER > ITERMAX or
* for all the RHS we have: RNRM < N*XNRM*ANRM*EPS*BWDMAX
* where:
*
* - ITER is the number of the current iteration in the iterative refinement process
* - RNRM is the infinity-norm of the residual
* - XNRM is the infinity-norm of the solution
* - ANRM is the infinity-operator-norm of the matrix A
* - EPS is the machine epsilon returned by DLAMCH('Epsilon').
*
* Actually, in its current state (PLASMA 2.1.0), the test is slightly relaxed.
*
* The values ITERMAX and BWDMAX are fixed to 30 and 1.0D+00 respectively.
*
*******************************************************************************
*
* @param[in] uplo
* Specifies whether the matrix A is upper triangular or lower triangular:
* = PlasmaUpper: Upper triangle of A is stored;
* = PlasmaLower: Lower triangle of A is stored.
*
* @param[in] N
* The number of linear equations, i.e., the order of the matrix A. N >= 0.
*
* @param[in] NRHS
* The number of right hand sides, i.e., the number of columns of the matrix B.
* NRHS >= 0.
*
* @param[in] A
* The N-by-N symmetric positive definite (or Hermitian) coefficient matrix A.
* If uplo = PlasmaUpper, the leading N-by-N upper triangular part of A
* contains the upper triangular part of the matrix A, 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 part of the matrix A, and the strictly upper triangular part of A is not
* referenced.
* This matrix is not modified.
*
* @param[in] LDA
* The leading dimension of the array A. LDA >= max(1,N).
*
* @param[in] B
* The N-by-NRHS matrix of right hand side matrix B.
*
* @param[in] LDB
* The leading dimension of the array B. LDB >= max(1,N).
*
* @param[out] X
* If return value = 0, the N-by-NRHS solution matrix X.
*
* @param[in] LDX
* The leading dimension of the array B. LDX >= max(1,N).
*
* @param[out] ITER
* The number of the current iteration in the iterative refinement process
*
*******************************************************************************
*
* @return
* \retval PLASMA_SUCCESS successful exit
* \retval <0 if -i, the i-th argument had an illegal value
* \retval >0 if i, the leading minor of order i of A is not positive definite, so the
* factorization could not be completed, and the solution has not been computed.
*
*******************************************************************************
*
* @sa PLASMA_zcposv_Tile
* @sa PLASMA_zcposv_Tile_Async
* @sa PLASMA_dsposv
* @sa PLASMA_zposv
*
******************************************************************************/
int PLASMA_zcposv(PLASMA_enum uplo, int N, int NRHS,
PLASMA_Complex64_t *A, int LDA,
PLASMA_Complex64_t *B, int LDB,
PLASMA_Complex64_t *X, int LDX, int *ITER)
{
int NB;
int status;
PLASMA_desc descA;
PLASMA_desc descB;
PLASMA_desc descX;
plasma_context_t *plasma;
PLASMA_sequence *sequence = NULL;
PLASMA_request request = PLASMA_REQUEST_INITIALIZER;
plasma = plasma_context_self();
if (plasma == NULL) {
plasma_fatal_error("PLASMA_zcposv", "PLASMA not initialized");
return PLASMA_ERR_NOT_INITIALIZED;
}
/* Check input arguments */
if (uplo != PlasmaUpper && uplo != PlasmaLower) {
plasma_error("PLASMA_zcposv", "illegal value of uplo");
return -1;
}
if (N < 0) {
plasma_error("PLASMA_zcposv", "illegal value of N");
return -2;
}
if (NRHS < 0) {
plasma_error("PLASMA_zcposv", "illegal value of NRHS");
return -3;
}
if (LDA < max(1, N)) {
plasma_error("PLASMA_zcposv", "illegal value of LDA");
return -5;
}
if (LDB < max(1, N)) {
plasma_error("PLASMA_zcposv", "illegal value of LDB");
return -7;
}
if (LDX < max(1, N)) {
plasma_error("PLASMA_zcposv", "illegal value of LDX");
return -10;
}
/* Quick return - currently NOT equivalent to LAPACK's
* LAPACK does not have such check for ZCPOSV */
if (min(N, NRHS) == 0)
return PLASMA_SUCCESS;
/* Tune NB depending on M, N & NRHS; Set NBNBSIZE */
status = plasma_tune(PLASMA_FUNC_ZCPOSV, N, N, NRHS);
if (status != PLASMA_SUCCESS) {
plasma_error("PLASMA_zcposv", "plasma_tune() failed");
return status;
}
NB = PLASMA_NB;
plasma_sequence_create(plasma, &sequence);
/* DOUBLE PRECISION INITIALIZATION */
if ( PLASMA_TRANSLATION == PLASMA_OUTOFPLACE ) {
plasma_zooplap2tile( descA, A, NB, NB, LDA, N, 0, 0, N, N , plasma_desc_mat_free(&(descA)) );
plasma_zooplap2tile( descB, B, NB, NB, LDB, NRHS, 0, 0, N, NRHS, plasma_desc_mat_free(&(descA)); plasma_desc_mat_free(&(descB)) );
plasma_zdesc_alloc( descX, NB, NB, N, NRHS, 0, 0, N, NRHS, plasma_desc_mat_free(&(descA)); plasma_desc_mat_free(&(descB)); plasma_desc_mat_free(&(descX)) );
} else {
/***************************************************************************//**
*
* @ingroup PLASMA_Complex64_t
*
* PLASMA_zgesvd - computes the singular value decomposition (SVD) of a complex
* M-by-N matrix A, optionally computing the left and/or right singular
* vectors. The SVD is written
*
* A = U * SIGMA * transpose(V)
*
* where SIGMA is an M-by-N matrix which is zero except for its
* min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and
* V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA
* are the singular values of A; they are real and non-negative, and
* are returned in descending order. The first min(m,n) columns of
* U and V are the left and right singular vectors of A.
*
* Note that the routine returns V**T, not V.
* Not LAPACK Compliant for now!
* Note: Only PlasmaNoVec supported!
*******************************************************************************
*
* @param[in] jobu
* Specifies options for computing all or part of the matrix U.
* Intended usage:
* = PlasmaVec: all M columns of U are returned in array U;
* = PlasmaNoVec: no columns of U (no left singular vectors) are
* computed.
* Note: Only PlasmaNoVec supported!
*
* @param[in] jobvt
* Specifies options for computing all or part of the matrix V**H.
* Intended usage:
* = PlasmaVec: all M columns of U are returned in array U;
* = PlasmaNoVec: no columns of U (no left singular vectors) are
* computed.
* Note: Only PlasmaNoVec supported!
*
* @param[in] M
* The number of rows of the matrix A. M >= 0.
*
* @param[in] N
* The number of columns of the matrix A. N >= 0.
*
* @param[in,out] A
* On entry, the M-by-N matrix A.
* On exit,
* if JOBU = 'O', A is overwritten with the first min(m,n)
* columns of U (the left singular vectors,
* stored columnwise);
* if JOBVT = 'O', A is overwritten with the first min(m,n)
* rows of V**H (the right singular vectors,
* stored rowwise);
* if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents of A
* are destroyed.
*
* @param[in] LDA
* The leading dimension of the array A. LDA >= max(1,M).
*
* @param[out] S
* The double precision singular values of A, sorted so that S(i) >= S(i+1).
*
* @param[out] U
* (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'.
* If JOBU = 'A', U contains the M-by-M unitary matrix U;
* if JOBU = 'S', U contains the first min(m,n) columns of U
* (the left singular vectors, stored columnwise);
* if JOBU = 'N' or 'O', U is not referenced.
*
* @param[in] LDU
* The leading dimension of the array U. LDU >= 1; if
* JOBU = 'S' or 'A', LDU >= M.
*
* @param[out] VT
* If JOBVT = 'A', VT contains the N-by-N unitary matrix
* V**H;
* if JOBVT = 'S', VT contains the first min(m,n) rows of
* V**H (the right singular vectors, stored rowwise);
* if JOBVT = 'N' or 'O', VT is not referenced.
*
* @param[in] LDVT
* The leading dimension of the array VT. LDVT >= 1; if
* JOBVT = 'A', LDVT >= N; if JOBVT = 'S', LDVT >= min(M,N).
*
* @param[in, out] descT
* On entry, descriptor as return by PLASMA_Alloc_Workspace_zgesvd
* On exit, contains auxiliary factorization data.
*
*
*******************************************************************************
*
* @return
* \retval PLASMA_SUCCESS successful exit
* \retval <0 if -i, the i-th argument had an illegal value
*
*******************************************************************************
*
* @sa PLASMA_zgesvd_Tile
* @sa PLASMA_zgesvd_Tile_Async
* @sa PLASMA_cgesvd
* @sa PLASMA_dgesvd
* @sa PLASMA_sgesvd
*
******************************************************************************/
int PLASMA_zgesvd(PLASMA_enum jobu, PLASMA_enum jobvt, int M, int N,
PLASMA_Complex64_t *A, int LDA,
double *S,
PLASMA_Complex64_t *U, int LDU,
PLASMA_Complex64_t *VT, int LDVT,
PLASMA_desc *descT)
{
int NB, IB, IBNB, minMN, MT, NT, minMTNT;
int status;
plasma_context_t *plasma;
PLASMA_sequence *sequence = NULL;
PLASMA_request request = PLASMA_REQUEST_INITIALIZER;
PLASMA_desc descA, descU, descVT;
plasma = plasma_context_self();
if (plasma == NULL) {
plasma_fatal_error("PLASMA_zgesvd", "PLASMA not initialized");
return PLASMA_ERR_NOT_INITIALIZED;
}
/* Tune NB & IB depending on M & N; Set NBNB */
status = plasma_tune(PLASMA_FUNC_ZGESVD, M, N, 0);
if (status != PLASMA_SUCCESS) {
plasma_error("PLASMA_zgesvd", "plasma_tune() failed");
return status;
}
/* Set MT, NT */
NB = PLASMA_NB;
IB = PLASMA_IB;
IBNB = IB*NB;
MT = (M%NB==0) ? (M/NB) : (M/NB+1);
NT = (N%NB==0) ? (N/NB) : (N/NB+1);
minMN = min(M,N);
minMTNT = min(MT,NT);
/* Check input arguments */
if (jobu != PlasmaNoVec && jobu !=PlasmaVec) {
plasma_error("PLASMA_zgesvd", "illegal value of jobu");
return -1;
}
if (jobvt != PlasmaNoVec && jobvt != PlasmaVec) {
plasma_error("PLASMA_zgesvd", "illegal value of jobvt");
return -2;
}
if (M < 0) {
plasma_error("PLASMA_zgesvd", "illegal value of M");
return -3;
}
if (N < 0) {
plasma_error("PLASMA_zgesvd", "illegal value of N");
return -4;
}
if (LDA < max(1, M)) {
plasma_error("PLASMA_zgesvd", "illegal value of LDA");
return -6;
}
if (LDU < 1) {
plasma_error("PLASMA_zgesvd", "illegal value of LDU");
return -9;
}
if (LDVT < 1) {
plasma_error("PLASMA_zgesvd", "illegal value of LDVT");
return -11;
}
if ( (plasma_desc_check(descT) != PLASMA_SUCCESS) ||
( descT->m != MT*IB ) || (descT->n != NT*NB) ) {
plasma_error("PLASMA_zgesvd", "invalid T descriptor");
return -12;
}
/* Quick return */
if (min(M, N) == 0) {
return PLASMA_SUCCESS;
}
if (jobu == PlasmaVec) {
plasma_error("PLASMA_zgesvd", "computing the singular vectors is not supported in this version");
return -1;
}
if (jobvt == PlasmaVec) {
plasma_error("PLASMA_zgesvd", "computing the singular vectors is not supported in this version");
return -2;
}
plasma_sequence_create(plasma, &sequence);
if ( PLASMA_TRANSLATION == PLASMA_OUTOFPLACE ) {
plasma_zooplap2tile( descA, A, NB, NB, LDA, N, 0, 0, M, N, plasma_desc_mat_free(&(descA)) );
if (jobu == PlasmaVec){
plasma_zooplap2tile( descU, U, NB, NB, LDU, M, 0, 0, M, M, plasma_desc_mat_free(&(descA)); plasma_desc_mat_free(&(descU)));
}
/***************************************************************************//**
*
* @ingroup double
*
* PLASMA_dsygst - reduces a complex Hermitian-definite generalized
* eigenproblem to standard form.
* If PlasmaItype == 1, the problem is A*x = lambda*B*x, and A is
* overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T)
* If PlasmaItype == 2 or 3, the problem is A*B*x = lambda*x or B*A*x
* = lambda*x, and A is overwritten by U*A*U**T or L**T*A*L. B must
* have been previously factorized as U**T*U or L*L**T by
* PLASMA_DPOTRF.
*
*******************************************************************************
*
* @param[in] PlasmaItype
* Intended usage:
* = 1: A*x=(lambda)*B*x
* = 2: A*Bx=(lambda)*x
* = 3: B*A*x=(lambda)*x
*
* @param[in] uplo
* Specifies whether the matrix A is upper triangular or
* lower triangular:
* = PlasmaUpper: Upper triangle of A is stored;
* = PlasmaLower: Lower triangle of A is stored.
*
* @param[in] N
* The order of the matrices A and B. N >= 0.
*
* @param[in,out] A
* On entry, the symmetric (or Hermitian) matrix A.
* If uplo = PlasmaUpper, the leading N-by-N upper triangular
* part of A contains the upper triangular part of the matrix
* A, and the strictly lower triangular part of A is not
* referenced.
* If uplo = PlasmaLower, the leading N-by-N lower triangular
* part of A contains the lower triangular part of the matrix
* A, and the strictly upper triangular part of A is not
* referenced.
* On exit, if return value == 0, the transformed matrix,
* stored in the same format as A.
*
* @param[in] LDA
* The leading dimension of the array A. LDA >= max(1,N).
*
* @param[in,out] B
* On entry, the triangular factor from the Cholesky
* factorization of B, as returned by PLASMA_DPOTRF.
*
* @param[in] LDB
* The leading dimension of the array B. LDB >= max(1,N).
*
*******************************************************************************
*
* @return
* \retval PLASMA_SUCCESS successful exit
* \retval <0 if -i, the i-th argument had an illegal value
*
*******************************************************************************
*
* @sa PLASMA_dsygst_Tile
* @sa PLASMA_dsygst_Tile_Async
* @sa PLASMA_chegst
* @sa PLASMA_dsygst
* @sa PLASMA_ssygst
*
******************************************************************************/
int PLASMA_dsygst(PLASMA_enum itype, PLASMA_enum uplo, int N,
double *A, int LDA,
double *B, int LDB)
{
int NB, IB, IBNB, NT;
int status;
plasma_context_t *plasma;
PLASMA_sequence *sequence = NULL;
PLASMA_request request = PLASMA_REQUEST_INITIALIZER;
PLASMA_desc descA, descB;
plasma = plasma_context_self();
if (plasma == NULL) {
plasma_fatal_error("PLASMA_dsygst", "PLASMA not initialized");
return PLASMA_ERR_NOT_INITIALIZED;
}
/* Check input arguments */
if (itype != 1 && itype != 2 && itype != 3) {
plasma_error("PLASMA_dsygst", "Illegal value of itype");
return -1;
}
if (uplo != PlasmaUpper && uplo != PlasmaLower) {
plasma_error("PLASMA_dsygst", "Illegal value of uplo");
return -2;
}
if (N < 0) {
plasma_error("PLASMA_dsygst", "illegal value of N");
return -3;
}
if (LDA < max(1, N)) {
plasma_error("PLASMA_dsygst", "illegal value of LDA");
return -5;
}
if (LDB < max(1, N)) {
plasma_error("PLASMA_dsygst", "illegal value of LDB");
return -7;
}
/* Quick return */
if (N == 0)
return PLASMA_SUCCESS;
/* Tune NB & IB depending on M, N & NRHS; Set NBNBSIZE */
status = plasma_tune(PLASMA_FUNC_DSYGST, N, N, 0);
if (status != PLASMA_SUCCESS) {
plasma_error("PLASMA_dsygst", "plasma_tune() failed");
return status;
}
/* Set NT */
NB = PLASMA_NB;
IB = PLASMA_IB;
IBNB = IB*NB;
NT = (N%NB==0) ? (N/NB) : (N/NB+1);
plasma_sequence_create(plasma, &sequence);
if ( PLASMA_TRANSLATION == PLASMA_OUTOFPLACE ) {
plasma_dooplap2tile( descA, A, NB, NB, LDA, N, 0, 0, N, N, plasma_desc_mat_free(&(descA)) );
plasma_dooplap2tile( descB, B, NB, NB, LDB, N, 0, 0, N, N, plasma_desc_mat_free(&(descB)) );
} else {
plasma_diplap2tile( descA, A, NB, NB, LDA, N, 0, 0, N, N);
plasma_diplap2tile( descB, B, NB, NB, LDB, N, 0, 0, N, N);
}
/* Call the tile interface */
PLASMA_dsygst_Tile_Async(itype, uplo, &descA, &descB, sequence, &request);
if ( PLASMA_TRANSLATION == PLASMA_OUTOFPLACE ) {
plasma_dooptile2lap( descA, A, NB, NB, LDA, N );
plasma_dooptile2lap( descB, B, NB, NB, LDB, N );
plasma_dynamic_sync();
plasma_desc_mat_free(&descA);
plasma_desc_mat_free(&descB);
} else {
plasma_diptile2lap( descA, A, NB, NB, LDA, N );
plasma_diptile2lap( descB, B, NB, NB, LDB, N );
plasma_dynamic_sync();
}
status = sequence->status;
plasma_sequence_destroy(plasma, sequence);
return status;
}
