MAGMA  2.0.0
Matrix Algebra for GPU and Multicore Architectures
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single precision

Functions

magma_int_t magma_sgerbt_batched (magma_bool_t gen, magma_int_t n, magma_int_t nrhs, float **dA_array, magma_int_t ldda, float **dB_array, magma_int_t lddb, float *U, float *V, magma_int_t *info, magma_int_t batchCount, magma_queue_t queue)
 SGERBT solves a system of linear equations A * X = B where A is a general n-by-n matrix and X and B are n-by-nrhs matrices. More...
 
magma_int_t magma_sgerbt_gpu (magma_bool_t gen, magma_int_t n, magma_int_t nrhs, magmaFloat_ptr dA, magma_int_t ldda, magmaFloat_ptr dB, magma_int_t lddb, float *U, float *V, magma_int_t *info)
 SGERBT solves a system of linear equations A * X = B where A is a general n-by-n matrix and X and B are n-by-nrhs matrices. More...
 
magma_int_t magma_sgerfs_nopiv_gpu (magma_trans_t trans, magma_int_t n, magma_int_t nrhs, magmaFloat_ptr dA, magma_int_t ldda, magmaFloat_ptr dB, magma_int_t lddb, magmaFloat_ptr dX, magma_int_t lddx, magmaFloat_ptr dworkd, magmaFloat_ptr dAF, magma_int_t *iter, magma_int_t *info)
 SGERFS improves the computed solution to a system of linear equations. More...
 
magma_int_t magma_sgetrf (magma_int_t m, magma_int_t n, float *A, magma_int_t lda, magma_int_t *ipiv, magma_int_t *info)
 SGETRF computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges. More...
 
magma_int_t magma_sgetrf2_mgpu (magma_int_t ngpu, magma_int_t m, magma_int_t n, magma_int_t nb, magma_int_t offset, magmaFloat_ptr d_lAT[], magma_int_t lddat, magma_int_t *ipiv, magmaFloat_ptr d_lAP[], float *W, magma_int_t ldw, magma_queue_t queues[][2], magma_int_t *info)
 SGETRF computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges. More...
 
magma_int_t magma_sgetrf_batched (magma_int_t m, magma_int_t n, float **dA_array, magma_int_t ldda, magma_int_t **ipiv_array, magma_int_t *info_array, magma_int_t batchCount, magma_queue_t queue)
 SGETRF computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges. More...
 
magma_int_t magma_sgetrf_gpu (magma_int_t m, magma_int_t n, magmaFloat_ptr dA, magma_int_t ldda, magma_int_t *ipiv, magma_int_t *info)
 SGETRF computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges. More...
 
magma_int_t magma_sgetrf_m (magma_int_t ngpu, magma_int_t m, magma_int_t n, float *A, magma_int_t lda, magma_int_t *ipiv, magma_int_t *info)
 SGETRF_m computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges. More...
 
magma_int_t magma_sgetrf_mgpu (magma_int_t ngpu, magma_int_t m, magma_int_t n, magmaFloat_ptr d_lA[], magma_int_t ldda, magma_int_t *ipiv, magma_int_t *info)
 SGETRF computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges. More...
 
magma_int_t magma_sgetrf_nopiv (magma_int_t m, magma_int_t n, float *A, magma_int_t lda, magma_int_t *info)
 SGETRF_NOPIV computes an LU factorization of a general M-by-N matrix A without pivoting. More...
 
magma_int_t magma_sgetrf_nopiv_batched (magma_int_t m, magma_int_t n, float **dA_array, magma_int_t ldda, magma_int_t *info_array, magma_int_t batchCount, magma_queue_t queue)
 SGETRF computes an LU factorization of a general M-by-N matrix A without pivoting. More...
 
magma_int_t magma_sgetrf_nopiv_gpu (magma_int_t m, magma_int_t n, magmaFloat_ptr dA, magma_int_t ldda, magma_int_t *info)
 SGETRF_NOPIV_GPU computes an LU factorization of a general M-by-N matrix A without any pivoting. More...
 
magma_int_t magma_sgetrf_recpanel_batched (magma_int_t m, magma_int_t n, magma_int_t min_recpnb, float **dA_array, magma_int_t ldda, magma_int_t **dipiv_array, magma_int_t **dpivinfo_array, float **dX_array, magma_int_t dX_length, float **dinvA_array, magma_int_t dinvA_length, float **dW1_displ, float **dW2_displ, float **dW3_displ, float **dW4_displ, float **dW5_displ, magma_int_t *info_array, magma_int_t gbstep, magma_int_t batchCount, magma_queue_t queue)
 This is an internal routine that might have many assumption. More...
 
magma_int_t magma_sgetrf_panel_nopiv_batched (magma_int_t m, magma_int_t nb, float **dA_array, magma_int_t ldda, float **dX_array, magma_int_t dX_length, float **dinvA_array, magma_int_t dinvA_length, float **dW0_displ, float **dW1_displ, float **dW2_displ, float **dW3_displ, float **dW4_displ, magma_int_t *info_array, magma_int_t gbstep, magma_int_t batchCount, magma_queue_t queue)
 this is an internal routine that might have many assumption. More...
 
magma_int_t magma_sgetri_gpu (magma_int_t n, magmaFloat_ptr dA, magma_int_t ldda, magma_int_t *ipiv, magmaFloat_ptr dwork, magma_int_t lwork, magma_int_t *info)
 SGETRI computes the inverse of a matrix using the LU factorization computed by SGETRF. More...
 
magma_int_t magma_sgetri_outofplace_batched (magma_int_t n, float **dA_array, magma_int_t ldda, magma_int_t **dipiv_array, float **dinvA_array, magma_int_t lddia, magma_int_t *info_array, magma_int_t batchCount, magma_queue_t queue)
 SGETRI computes the inverse of a matrix using the LU factorization computed by SGETRF. More...
 
magma_int_t magma_sgetrs_batched (magma_trans_t trans, magma_int_t n, magma_int_t nrhs, float **dA_array, magma_int_t ldda, magma_int_t **dipiv_array, float **dB_array, magma_int_t lddb, magma_int_t batchCount, magma_queue_t queue)
 SGETRS solves a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general N-by-N matrix A using the LU factorization computed by SGETRF. More...
 
magma_int_t magma_sgetrs_gpu (magma_trans_t trans, magma_int_t n, magma_int_t nrhs, magmaFloat_ptr dA, magma_int_t ldda, magma_int_t *ipiv, magmaFloat_ptr dB, magma_int_t lddb, magma_int_t *info)
 SGETRS solves a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general N-by-N matrix A using the LU factorization computed by SGETRF_GPU. More...
 
magma_int_t magma_sgetrs_nopiv_batched (magma_trans_t trans, magma_int_t n, magma_int_t nrhs, float **dA_array, magma_int_t ldda, float **dB_array, magma_int_t lddb, magma_int_t *info_array, magma_int_t batchCount, magma_queue_t queue)
 SGETRS solves a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general N-by-N matrix A using the LU factorization without pivoting computed by SGETRF_NOPIV. More...
 
magma_int_t magma_sgetrs_nopiv_gpu (magma_trans_t trans, magma_int_t n, magma_int_t nrhs, magmaFloat_ptr dA, magma_int_t ldda, magmaFloat_ptr dB, magma_int_t lddb, magma_int_t *info)
 SGETRS solves a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general N-by-N matrix A using the LU factorization computed by SGETRF_NOPIV_GPU. More...
 
magma_int_t magma_strtri (magma_uplo_t uplo, magma_diag_t diag, magma_int_t n, float *A, magma_int_t lda, magma_int_t *info)
 STRTRI computes the inverse of a real upper or lower triangular matrix A. More...
 
magma_int_t magma_strtri_gpu (magma_uplo_t uplo, magma_diag_t diag, magma_int_t n, magmaFloat_ptr dA, magma_int_t ldda, magma_int_t *info)
 STRTRI computes the inverse of a real upper or lower triangular matrix dA. More...
 

Detailed Description

Function Documentation

magma_int_t magma_sgerbt_batched ( magma_bool_t  gen,
magma_int_t  n,
magma_int_t  nrhs,
float **  dA_array,
magma_int_t  ldda,
float **  dB_array,
magma_int_t  lddb,
float *  U,
float *  V,
magma_int_t *  info,
magma_int_t  batchCount,
magma_queue_t  queue 
)

SGERBT solves a system of linear equations A * X = B where A is a general n-by-n matrix and X and B are n-by-nrhs matrices.

Random Butterfly Tranformation is applied on A and B, then the LU decomposition with no pivoting is used to factor A as A = L * U, where L is unit lower triangular, and U is upper triangular. The factored form of A is then used to solve the system of equations A * X = B.

This is a batched version that solves batchCount matrices in parallel. dA, dB, and info become arrays with one entry per matrix.

Parameters
[in]genmagma_bool_t
  • = MagmaTrue: new matrices are generated for U and V
  • = MagmaFalse: matrices U and V given as parameter are used
[in]nINTEGER The order of the matrix A. n >= 0.
[in]nrhsINTEGER The number of right hand sides, i.e., the number of columns of the matrix B. nrhs >= 0.
[in,out]dA_arrayArray of pointers, dimension (batchCount). Each is a REAL array on the GPU, dimension (LDDA,N). On entry, each pointer is an M-by-N matrix to be factored. On exit, the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored.
[in]lddaINTEGER The leading dimension of each array A. LDDA >= max(1,M).
[in,out]dB_arrayArray of pointers, dimension (batchCount). Each is a REAL array on the GPU, dimension (LDDB,N). On entry, each pointer is an right hand side matrix B. On exit, each pointer is the solution matrix X.
[in]lddbINTEGER The leading dimension of the array B. LDB >= max(1,N).
[in,out]UREAL array, dimension (2,n) Random butterfly matrix, if gen = MagmaTrue U is generated and returned as output; else we use U given as input. CPU memory
[in,out]VREAL array, dimension (2,n) Random butterfly matrix, if gen = MagmaTrue V is generated and returned as output; else we use U given as input. CPU memory
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed.
[in]batchCountINTEGER The number of matrices to operate on.
[in]queuemagma_queue_t Queue to execute in.
magma_int_t magma_sgerbt_gpu ( magma_bool_t  gen,
magma_int_t  n,
magma_int_t  nrhs,
magmaFloat_ptr  dA,
magma_int_t  ldda,
magmaFloat_ptr  dB,
magma_int_t  lddb,
float *  U,
float *  V,
magma_int_t *  info 
)

SGERBT solves a system of linear equations A * X = B where A is a general n-by-n matrix and X and B are n-by-nrhs matrices.

Random Butterfly Tranformation is applied on A and B, then the LU decomposition with no pivoting is used to factor A as A = L * U, where L is unit lower triangular, and U is upper triangular. The factored form of A is then used to solve the system of equations A * X = B.

Parameters
[in]genmagma_bool_t
  • = MagmaTrue: new matrices are generated for U and V
  • = MagmaFalse: matrices U and V given as parameter are used
[in]nINTEGER The order of the matrix A. n >= 0.
[in]nrhsINTEGER The number of right hand sides, i.e., the number of columns of the matrix B. nrhs >= 0.
[in,out]dAREAL array, dimension (LDA,n). On entry, the M-by-n matrix to be factored. On exit, the factors L and U from the factorization A = L*U; the unit diagonal elements of L are not stored.
[in]lddaINTEGER The leading dimension of the array A. LDA >= max(1,n).
[in,out]dBREAL array, dimension (LDB,nrhs) On entry, the right hand side matrix B. On exit, the solution matrix X.
[in]lddbINTEGER The leading dimension of the array B. LDB >= max(1,n).
[in,out]UREAL array, dimension (2,n) Random butterfly matrix, if gen = MagmaTrue U is generated and returned as output; else we use U given as input. CPU memory
[in,out]VREAL array, dimension (2,n) Random butterfly matrix, if gen = MagmaTrue V is generated and returned as output; else we use U given as input. CPU memory
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed.
magma_int_t magma_sgerfs_nopiv_gpu ( magma_trans_t  trans,
magma_int_t  n,
magma_int_t  nrhs,
magmaFloat_ptr  dA,
magma_int_t  ldda,
magmaFloat_ptr  dB,
magma_int_t  lddb,
magmaFloat_ptr  dX,
magma_int_t  lddx,
magmaFloat_ptr  dworkd,
magmaFloat_ptr  dAF,
magma_int_t *  iter,
magma_int_t *  info 
)

SGERFS improves the computed solution to a system of linear equations.

The iterative refinement process is stopped if ITER > ITERMAX or for all the RHS we have: RNRM < SQRT(n)*XNRM*ANRM*EPS*BWDMAX where o ITER is the number of the current iteration in the iterative refinement process o RNRM is the infinity-norm of the residual o XNRM is the infinity-norm of the solution o ANRM is the infinity-operator-norm of the matrix A o EPS is the machine epsilon returned by SLAMCH('Epsilon') The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00 respectively.

Parameters
[in]transmagma_trans_t Specifies the form of the system of equations:
  • = MagmaNoTrans: A * X = B (No transpose)
  • = MagmaTrans: A**T * X = B (Transpose)
  • = MagmaConjTrans: A**H * X = B (Conjugate transpose)
[in]nINTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0.
[in]nrhsINTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in]dAREAL array on the GPU, dimension (ldda,N) the N-by-N coefficient matrix A.
[in]lddaINTEGER The leading dimension of the array dA. ldda >= max(1,N).
[in]dBREAL array on the GPU, dimension (lddb,NRHS) The N-by-NRHS right hand side matrix B.
[in]lddbINTEGER The leading dimension of the array dB. lddb >= max(1,N).
[in,out]dXREAL array on the GPU, dimension (lddx,NRHS) On entry, the solution matrix X, as computed by SGETRS_NOPIV. On exit, the improved solution matrix X.
[in]lddxINTEGER The leading dimension of the array dX. lddx >= max(1,N).
dworkd(workspace) REAL array on the GPU, dimension (N*NRHS) This array is used to hold the residual vectors.
dAFREAL array on the GPU, dimension (ldda,n) The factors L and U from the factorization A = L*U as computed by SGETRF_NOPIV.
[out]iterINTEGER
  • < 0: iterative refinement has failed, real factorization has been performed
    • -1 : the routine fell back to full precision for implementation- or machine-specific reasons
    • -2 : narrowing the precision induced an overflow, the routine fell back to full precision
    • -3 : failure of SGETRF
    • -31: stop the iterative refinement after the 30th iteration
  • > 0: iterative refinement has been successfully used. Returns the number of iterations
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if info = -i, the i-th argument had an illegal value
  • > 0: if info = i, U(i,i) computed in REAL is exactly zero. The factorization has been completed, but the factor U is exactly singular, so the solution could not be computed.
magma_int_t magma_sgetrf ( magma_int_t  m,
magma_int_t  n,
float *  A,
magma_int_t  lda,
magma_int_t *  ipiv,
magma_int_t *  info 
)

SGETRF computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges.

This version does not require work space on the GPU passed as input. GPU memory is allocated in the routine.

The factorization has the form A = P * L * U where P is a permutation matrix, L is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and U is upper triangular (upper trapezoidal if m < n).

This is the right-looking Level 3 BLAS version of the algorithm.

It uses 2 queues to overlap communication and computation.

Parameters
[in]mINTEGER The number of rows of the matrix A. M >= 0.
[in]nINTEGER The number of columns of the matrix A. N >= 0.
[in,out]AREAL array, dimension (LDA,N) On entry, the M-by-N matrix to be factored. On exit, the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored.
Higher performance is achieved if A is in pinned memory, e.g. allocated using magma_malloc_pinned.
[in]ldaINTEGER The leading dimension of the array A. LDA >= max(1,M).
[out]ipivINTEGER array, dimension (min(M,N)) The pivot indices; for 1 <= i <= min(M,N), row i of the matrix was interchanged with row IPIV(i).
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed.
  • > 0: if INFO = 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.
magma_int_t magma_sgetrf2_mgpu ( magma_int_t  ngpu,
magma_int_t  m,
magma_int_t  n,
magma_int_t  nb,
magma_int_t  offset,
magmaFloat_ptr  d_lAT[],
magma_int_t  lddat,
magma_int_t *  ipiv,
magmaFloat_ptr  d_lAP[],
float *  W,
magma_int_t  ldw,
magma_queue_t  queues[][2],
magma_int_t *  info 
)

SGETRF computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges.

The factorization has the form A = P * L * U where P is a permutation matrix, L is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and U is upper triangular (upper trapezoidal if m < n).

This is the right-looking Level 3 BLAS version of the algorithm. Use two buffer to send panels.

Parameters
[in]ngpuINTEGER Number of GPUs to use. ngpu > 0.
[in]mINTEGER The number of rows of the matrix A. M >= 0.
[in]nINTEGER The number of columns of the matrix A. N >= 0.
[in]nbINTEGER The block size used for the matrix distribution.
[in]offsetINTEGER The first row and column indices of the submatrix that this routine will factorize.
[in,out]d_lATREAL array of pointers on the GPU, dimension (ngpu). On entry, the M-by-N matrix A distributed over GPUs (d_lAT[d] points to the local matrix on d-th GPU). It uses a 1D block column cyclic format (with the block size nb), and each local matrix is stored by row. On exit, the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored.
[in]lddatINTEGER The leading dimension of the array d_lAT[d]. LDDA >= max(1,M).
[out]ipivINTEGER array, dimension (min(M,N)) The pivot indices; for 1 <= i <= min(M,N), row i of the matrix was interchanged with row IPIV(i).
[in]d_lAPREAL array of pointers on the GPU, dimension (ngpu). d_lAP[d] is the workspace on d-th GPU. Each local workspace must be of size (3+ngpu)*nb*maxm, where maxm is m rounded up to a multiple of 32 and nb is the block size.
[in]WREAL array, dimension (ngpu*nb*maxm). It is used to store panel on CPU.
[in]ldwINTEGER The leading dimension of the workspace w.
[in]queuesmagma_queue_t queues[d] points to the queues for the d-th GPU to execute in. Each GPU require two queues.
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed.
  • > 0: if INFO = 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.
magma_int_t magma_sgetrf_batched ( magma_int_t  m,
magma_int_t  n,
float **  dA_array,
magma_int_t  ldda,
magma_int_t **  ipiv_array,
magma_int_t *  info_array,
magma_int_t  batchCount,
magma_queue_t  queue 
)

SGETRF computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges.

The factorization has the form A = P * L * U where P is a permutation matrix, L is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and U is upper triangular (upper trapezoidal if m < n).

This is the right-looking Level 3 BLAS version of the algorithm.

This is a batched version that factors batchCount M-by-N matrices in parallel. dA, ipiv, and info become arrays with one entry per matrix.

Parameters
[in]mINTEGER The number of rows of each matrix A. M >= 0.
[in]nINTEGER The number of columns of each matrix A. N >= 0.
[in,out]dA_arrayArray of pointers, dimension (batchCount). Each is a REAL array on the GPU, dimension (LDDA,N). On entry, each pointer is an M-by-N matrix to be factored. On exit, the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored.
[in]lddaINTEGER The leading dimension of each array A. LDDA >= max(1,M).
[out]ipiv_arrayArray of pointers, dimension (batchCount), for corresponding matrices. Each is an INTEGER array, dimension (min(M,N)) The pivot indices; for 1 <= i <= min(M,N), row i of the matrix was interchanged with row IPIV(i).
[out]info_arrayArray of INTEGERs, dimension (batchCount), for corresponding matrices.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed.
  • > 0: if INFO = 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.
[in]batchCountINTEGER The number of matrices to operate on.
[in]queuemagma_queue_t Queue to execute in.
magma_int_t magma_sgetrf_gpu ( magma_int_t  m,
magma_int_t  n,
magmaFloat_ptr  dA,
magma_int_t  ldda,
magma_int_t *  ipiv,
magma_int_t *  info 
)

SGETRF computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges.

The factorization has the form A = P * L * U where P is a permutation matrix, L is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and U is upper triangular (upper trapezoidal if m < n).

This is the right-looking Level 3 BLAS version of the algorithm.

Parameters
[in]mINTEGER The number of rows of the matrix A. M >= 0.
[in]nINTEGER The number of columns of the matrix A. N >= 0.
[in,out]dAREAL array on the GPU, dimension (LDDA,N). On entry, the M-by-N matrix to be factored. On exit, the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored.
[in]lddaINTEGER The leading dimension of the array A. LDDA >= max(1,M).
[out]ipivINTEGER array, dimension (min(M,N)) The pivot indices; for 1 <= i <= min(M,N), row i of the matrix was interchanged with row IPIV(i).
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed.
  • > 0: if INFO = 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.
magma_int_t magma_sgetrf_m ( magma_int_t  ngpu,
magma_int_t  m,
magma_int_t  n,
float *  A,
magma_int_t  lda,
magma_int_t *  ipiv,
magma_int_t *  info 
)

SGETRF_m computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges.

This version does not require work space on the GPU passed as input. GPU memory is allocated in the routine. The matrix may exceed the GPU memory.

The factorization has the form A = P * L * U where P is a permutation matrix, L is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and U is upper triangular (upper trapezoidal if m < n).

This is the right-looking Level 3 BLAS version of the algorithm.

Note: The factorization of big panel is done calling multiple-gpu-interface. Pivots are applied on GPU within the big panel.

Parameters
[in]ngpuINTEGER Number of GPUs to use. ngpu > 0.
[in]mINTEGER The number of rows of the matrix A. M >= 0.
[in]nINTEGER The number of columns of the matrix A. N >= 0.
[in,out]AREAL array, dimension (LDA,N) On entry, the M-by-N matrix to be factored. On exit, the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored.
Higher performance is achieved if A is in pinned memory, e.g. allocated using magma_malloc_pinned.
[in]ldaINTEGER The leading dimension of the array A. LDA >= max(1,M).
[out]ipivINTEGER array, dimension (min(M,N)) The pivot indices; for 1 <= i <= min(M,N), row i of the matrix was interchanged with row IPIV(i).
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed.
  • > 0: if INFO = 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.
magma_int_t magma_sgetrf_mgpu ( magma_int_t  ngpu,
magma_int_t  m,
magma_int_t  n,
magmaFloat_ptr  d_lA[],
magma_int_t  ldda,
magma_int_t *  ipiv,
magma_int_t *  info 
)

SGETRF computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges.

The factorization has the form A = P * L * U where P is a permutation matrix, L is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and U is upper triangular (upper trapezoidal if m < n).

This is the right-looking Level 3 BLAS version of the algorithm.

Parameters
[in]ngpuINTEGER Number of GPUs to use. ngpu > 0.
[in]mINTEGER The number of rows of the matrix A. M >= 0.
[in]nINTEGER The number of columns of the matrix A. N >= 0.
[in,out]d_lAREAL array of pointers on the GPU, dimension (ngpu). On entry, the M-by-N matrix A distributed over GPUs (d_lA[d] points to the local matrix on d-th GPU). It uses 1D block column cyclic format with the block size of nb, and each local matrix is stored by column. On exit, the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored.
[in]lddaINTEGER The leading dimension of the array d_lA. LDDA >= max(1,M).
[out]ipivINTEGER array, dimension (min(M,N)) The pivot indices; for 1 <= i <= min(M,N), row i of the matrix was interchanged with row IPIV(i).
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed.
  • > 0: if INFO = 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.
magma_int_t magma_sgetrf_nopiv ( magma_int_t  m,
magma_int_t  n,
float *  A,
magma_int_t  lda,
magma_int_t *  info 
)

SGETRF_NOPIV computes an LU factorization of a general M-by-N matrix A without pivoting.

The factorization has the form A = L * U where L is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and U is upper triangular (upper trapezoidal if m < n).

This is the right-looking Level 3 BLAS version of the algorithm.

This is a CPU-only (not accelerated) version.

Parameters
[in]mINTEGER The number of rows of the matrix A. M >= 0.
[in]nINTEGER The number of columns of the matrix A. N >= 0.
[in,out]AREAL array, dimension (LDA,N) On entry, the M-by-N matrix to be factored. On exit, the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored.
[in]ldaINTEGER The leading dimension of the array A. LDA >= max(1,M).
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = 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.
magma_int_t magma_sgetrf_nopiv_batched ( magma_int_t  m,
magma_int_t  n,
float **  dA_array,
magma_int_t  ldda,
magma_int_t *  info_array,
magma_int_t  batchCount,
magma_queue_t  queue 
)

SGETRF computes an LU factorization of a general M-by-N matrix A without pivoting.

The factorization has the form A = L * U where L is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and U is upper triangular (upper trapezoidal if m < n).

This is the right-looking Level 3 BLAS version of the algorithm.

This is a batched version that factors batchCount M-by-N matrices in parallel. dA, and info become arrays with one entry per matrix.

Parameters
[in]mINTEGER The number of rows of each matrix A. M >= 0.
[in]nINTEGER The number of columns of each matrix A. N >= 0.
[in,out]dA_arrayArray of pointers, dimension (batchCount). Each is a REAL array on the GPU, dimension (LDDA,N). On entry, each pointer is an M-by-N matrix to be factored. On exit, the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored.
[in]lddaINTEGER The leading dimension of each array A. LDDA >= max(1,M).
[out]info_arrayArray of INTEGERs, dimension (batchCount), for corresponding matrices.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed.
  • > 0: if INFO = 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.
[in]batchCountINTEGER The number of matrices to operate on.
[in]queuemagma_queue_t Queue to execute in.
magma_int_t magma_sgetrf_nopiv_gpu ( magma_int_t  m,
magma_int_t  n,
magmaFloat_ptr  dA,
magma_int_t  ldda,
magma_int_t *  info 
)

SGETRF_NOPIV_GPU computes an LU factorization of a general M-by-N matrix A without any pivoting.

The factorization has the form A = L * U where L is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and U is upper triangular (upper trapezoidal if m < n).

This is the right-looking Level 3 BLAS version of the algorithm.

Parameters
[in]mINTEGER The number of rows of the matrix A. M >= 0.
[in]nINTEGER The number of columns of the matrix A. N >= 0.
[in,out]dAREAL array on the GPU, dimension (LDDA,N). On entry, the M-by-N matrix to be factored. On exit, the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored.
[in]lddaINTEGER The leading dimension of the array A. LDDA >= max(1,M).
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed.
  • > 0: if INFO = 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.
magma_int_t magma_sgetrf_panel_nopiv_batched ( magma_int_t  m,
magma_int_t  nb,
float **  dA_array,
magma_int_t  ldda,
float **  dX_array,
magma_int_t  dX_length,
float **  dinvA_array,
magma_int_t  dinvA_length,
float **  dW0_displ,
float **  dW1_displ,
float **  dW2_displ,
float **  dW3_displ,
float **  dW4_displ,
magma_int_t *  info_array,
magma_int_t  gbstep,
magma_int_t  batchCount,
magma_queue_t  queue 
)

this is an internal routine that might have many assumption.

No documentation is available today.

magma_int_t magma_sgetrf_recpanel_batched ( magma_int_t  m,
magma_int_t  n,
magma_int_t  min_recpnb,
float **  dA_array,
magma_int_t  ldda,
magma_int_t **  dipiv_array,
magma_int_t **  dpivinfo_array,
float **  dX_array,
magma_int_t  dX_length,
float **  dinvA_array,
magma_int_t  dinvA_length,
float **  dW1_displ,
float **  dW2_displ,
float **  dW3_displ,
float **  dW4_displ,
float **  dW5_displ,
magma_int_t *  info_array,
magma_int_t  gbstep,
magma_int_t  batchCount,
magma_queue_t  queue 
)

This is an internal routine that might have many assumption.

Documentation is not fully completed

SGETRF_PANEL computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges.

The factorization has the form A = P * L * U where P is a permutation matrix, L is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and U is upper triangular (upper trapezoidal if m < n).

This is the right-looking Level 3 BLAS version of the algorithm.

This is a batched version that factors batchCount M-by-N matrices in parallel. dA, ipiv, and info become arrays with one entry per matrix.

Parameters
[in]mINTEGER The number of rows of each matrix A. M >= 0.
[in]nINTEGER The number of columns of each matrix A. N >= 0.
[in]min_recpnbINTEGER. Internal use. The recursive nb
[in,out]dA_arrayArray of pointers, dimension (batchCount). Each is a REAL array on the GPU, dimension (LDDA,N). On entry, each pointer is an M-by-N matrix to be factored. On exit, the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored.
[in]lddaINTEGER The leading dimension of each array A. LDDA >= max(1,M).
[out]dipiv_arrayArray of pointers, dimension (batchCount), for corresponding matrices. Each is an INTEGER array, dimension (min(M,N)) The pivot indices; for 1 <= i <= min(M,N), row i of the matrix was interchanged with row IPIV(i).
[out]dpivinfo_arrayArray of pointers, dimension (batchCount), for internal use.
[in,out]dX_arrayArray of pointers, dimension (batchCount). Each is a REAL array X of dimension ( lddx, n ). On entry, should be set to 0 On exit, the solution matrix X
[in]dX_lengthINTEGER. The size of each workspace matrix dX
[in,out]dinvA_arrayArray of pointers, dimension (batchCount). Each is a REAL array dinvA, a workspace on device. If side == MagmaLeft, dinvA must be of size >= ceil(m/TRI_NB)*TRI_NB*TRI_NB, If side == MagmaRight, dinvA must be of size >= ceil(n/TRI_NB)*TRI_NB*TRI_NB, where TRI_NB = 128.
[in]dinvA_lengthINTEGER The size of each workspace matrix dinvA
[in]dW1_displWorkspace array of pointers, for internal use.
[in]dW2_displWorkspace array of pointers, for internal use.
[in]dW3_displWorkspace array of pointers, for internal use.
[in]dW4_displWorkspace array of pointers, for internal use.
[in]dW5_displWorkspace array of pointers, for internal use.
[out]info_arrayArray of INTEGERs, dimension (batchCount), for corresponding matrices.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed.
  • > 0: if INFO = 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.
[in]gbstepINTEGER internal use.
[in]batchCountINTEGER The number of matrices to operate on.
[in]queuemagma_queue_t Queue to execute in.
magma_int_t magma_sgetri_gpu ( magma_int_t  n,
magmaFloat_ptr  dA,
magma_int_t  ldda,
magma_int_t *  ipiv,
magmaFloat_ptr  dwork,
magma_int_t  lwork,
magma_int_t *  info 
)

SGETRI computes the inverse of a matrix using the LU factorization computed by SGETRF.

This method inverts U and then computes inv(A) by solving the system inv(A)*L = inv(U) for inv(A).

Note that it is generally both faster and more accurate to use SGESV, or SGETRF and SGETRS, to solve the system AX = B, rather than inverting the matrix and multiplying to form X = inv(A)*B. Only in special instances should an explicit inverse be computed with this routine.

Parameters
[in]nINTEGER The order of the matrix A. N >= 0.
[in,out]dAREAL array on the GPU, dimension (LDDA,N) On entry, the factors L and U from the factorization A = P*L*U as computed by SGETRF_GPU. On exit, if INFO = 0, the inverse of the original matrix A.
[in]lddaINTEGER The leading dimension of the array A. LDDA >= max(1,N).
[in]ipivINTEGER array, dimension (N) The pivot indices from SGETRF; for 1 <= i <= N, row i of the matrix was interchanged with row IPIV(i).
[out]dwork(workspace) REAL array on the GPU, dimension (MAX(1,LWORK))
[in]lworkINTEGER The dimension of the array DWORK. LWORK >= N*NB, where NB is the optimal blocksize returned by magma_get_sgetri_nb(n).
Unlike LAPACK, this version does not currently support a workspace query, because the workspace is on the GPU.
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, U(i,i) is exactly zero; the matrix is singular and its cannot be computed.
magma_int_t magma_sgetri_outofplace_batched ( magma_int_t  n,
float **  dA_array,
magma_int_t  ldda,
magma_int_t **  dipiv_array,
float **  dinvA_array,
magma_int_t  lddia,
magma_int_t *  info_array,
magma_int_t  batchCount,
magma_queue_t  queue 
)

SGETRI computes the inverse of a matrix using the LU factorization computed by SGETRF.

This method inverts U and then computes inv(A) by solving the system inv(A)*L = inv(U) for inv(A).

Note that it is generally both faster and more accurate to use SGESV, or SGETRF and SGETRS, to solve the system AX = B, rather than inverting the matrix and multiplying to form X = inv(A)*B. Only in special instances should an explicit inverse be computed with this routine.

Parameters
[in]nINTEGER The order of the matrix A. N >= 0.
[in,out]dA_arrayArray of pointers, dimension (batchCount). Each is a REAL array on the GPU, dimension (LDDA,N) On entry, the factors L and U from the factorization A = P*L*U as computed by SGETRF_GPU. On exit, if INFO = 0, the inverse of the original matrix A.
[in]lddaINTEGER The leading dimension of the array A. LDDA >= max(1,N).
[in]dipiv_arrayArray of pointers, dimension (batchCount), for corresponding matrices. Each is an INTEGER array, dimension (N) The pivot indices; for 1 <= i <= min(M,N), row i of the matrix was interchanged with row IPIV(i).
[out]dinvA_arrayArray of pointers, dimension (batchCount). Each is a REAL array on the GPU, dimension (LDDIA,N) It contains the inverse of the matrix
[in]lddiaINTEGER The leading dimension of the array invA_array. LDDIA >= max(1,N).
[out]info_arrayArray of INTEGERs, dimension (batchCount), for corresponding matrices.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed.
  • > 0: if INFO = 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.
[in]batchCountINTEGER The number of matrices to operate on.
[in]queuemagma_queue_t Queue to execute in.
magma_int_t magma_sgetrs_batched ( magma_trans_t  trans,
magma_int_t  n,
magma_int_t  nrhs,
float **  dA_array,
magma_int_t  ldda,
magma_int_t **  dipiv_array,
float **  dB_array,
magma_int_t  lddb,
magma_int_t  batchCount,
magma_queue_t  queue 
)

SGETRS solves a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general N-by-N matrix A using the LU factorization computed by SGETRF.

This is a batched version that solves batchCount N-by-N matrices in parallel. dA, dB, and ipiv become arrays with one entry per matrix.

Parameters
[in]transmagma_trans_t Specifies the form of the system of equations:
  • = MagmaNoTrans: A * X = B (No transpose)
  • = MagmaTrans: A**T * X = B (Transpose)
  • = MagmaConjTrans: A**H * X = B (Conjugate transpose)
[in]nINTEGER The order of the matrix A. N >= 0.
[in]nrhsINTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in,out]dA_arrayArray of pointers, dimension (batchCount). Each is a REAL array on the GPU, dimension (LDDA,N). On entry, each pointer is an M-by-N matrix to be factored. On exit, the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored.
[in]lddaINTEGER The leading dimension of each array A. LDDA >= max(1,M).
[out]dipiv_arrayArray of pointers, dimension (batchCount), for corresponding matrices. Each is an INTEGER array, dimension (min(M,N)) The pivot indices; for 1 <= i <= min(M,N), row i of the matrix was interchanged with row IPIV(i).
[in,out]dB_arrayArray of pointers, dimension (batchCount). Each is a REAL array on the GPU, dimension (LDDB,N). On entry, each pointer is an right hand side matrix B. On exit, each pointer is the solution matrix X.
[in]lddbINTEGER The leading dimension of the array B. LDB >= max(1,N).
[in]batchCountINTEGER The number of matrices to operate on.
[in]queuemagma_queue_t Queue to execute in.
magma_int_t magma_sgetrs_gpu ( magma_trans_t  trans,
magma_int_t  n,
magma_int_t  nrhs,
magmaFloat_ptr  dA,
magma_int_t  ldda,
magma_int_t *  ipiv,
magmaFloat_ptr  dB,
magma_int_t  lddb,
magma_int_t *  info 
)

SGETRS solves a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general N-by-N matrix A using the LU factorization computed by SGETRF_GPU.

Parameters
[in]transmagma_trans_t Specifies the form of the system of equations:
  • = MagmaNoTrans: A * X = B (No transpose)
  • = MagmaTrans: A**T * X = B (Transpose)
  • = MagmaConjTrans: A**H * X = B (Conjugate transpose)
[in]nINTEGER The order of the matrix A. N >= 0.
[in]nrhsINTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in]dAREAL array on the GPU, dimension (LDDA,N) The factors L and U from the factorization A = P*L*U as computed by SGETRF_GPU.
[in]lddaINTEGER The leading dimension of the array A. LDDA >= max(1,N).
[in]ipivINTEGER array, dimension (N) The pivot indices from SGETRF; for 1 <= i <= N, row i of the matrix was interchanged with row IPIV(i).
[in,out]dBREAL array on the GPU, dimension (LDDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.
[in]lddbINTEGER The leading dimension of the array B. LDDB >= max(1,N).
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
magma_int_t magma_sgetrs_nopiv_batched ( magma_trans_t  trans,
magma_int_t  n,
magma_int_t  nrhs,
float **  dA_array,
magma_int_t  ldda,
float **  dB_array,
magma_int_t  lddb,
magma_int_t *  info_array,
magma_int_t  batchCount,
magma_queue_t  queue 
)

SGETRS solves a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general N-by-N matrix A using the LU factorization without pivoting computed by SGETRF_NOPIV.

This is a batched version that solves batchCount N-by-N matrices in parallel. dA, dB, become arrays with one entry per matrix.

Parameters
[in]transmagma_trans_t Specifies the form of the system of equations:
  • = MagmaNoTrans: A * X = B (No transpose)
  • = MagmaTrans: A**T * X = B (Transpose)
  • = MagmaConjTrans: A**H * X = B (Conjugate transpose)
[in]nINTEGER The order of the matrix A. N >= 0.
[in]nrhsINTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in,out]dA_arrayArray of pointers, dimension (batchCount). Each is a REAL array on the GPU, dimension (LDDA,N). On entry, each pointer is an M-by-N matrix to be factored. On exit, the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored.
[in]lddaINTEGER The leading dimension of each array A. LDDA >= max(1,M).
[in,out]dB_arrayArray of pointers, dimension (batchCount). Each is a REAL array on the GPU, dimension (LDDB,N). On entry, each pointer is an right hand side matrix B. On exit, each pointer is the solution matrix X.
[in]lddbINTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]info_arrayArray of INTEGERs, dimension (batchCount), for corresponding matrices.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed.
  • > 0: if INFO = 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.
[in]batchCountINTEGER The number of matrices to operate on.
[in]queuemagma_queue_t Queue to execute in.
magma_int_t magma_sgetrs_nopiv_gpu ( magma_trans_t  trans,
magma_int_t  n,
magma_int_t  nrhs,
magmaFloat_ptr  dA,
magma_int_t  ldda,
magmaFloat_ptr  dB,
magma_int_t  lddb,
magma_int_t *  info 
)

SGETRS solves a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general N-by-N matrix A using the LU factorization computed by SGETRF_NOPIV_GPU.

Parameters
[in]transmagma_trans_t Specifies the form of the system of equations:
  • = MagmaNoTrans: A * X = B (No transpose)
  • = MagmaTrans: A**T * X = B (Transpose)
  • = MagmaConjTrans: A**H * X = B (Conjugate transpose)
[in]nINTEGER The order of the matrix A. N >= 0.
[in]nrhsINTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in]dAREAL array on the GPU, dimension (LDDA,N) The factors L and U from the factorization A = P*L*U as computed by SGETRF_GPU.
[in]lddaINTEGER The leading dimension of the array A. LDDA >= max(1,N).
[in,out]dBREAL array on the GPU, dimension (LDDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.
[in]lddbINTEGER The leading dimension of the array B. LDDB >= max(1,N).
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
magma_int_t magma_strtri ( magma_uplo_t  uplo,
magma_diag_t  diag,
magma_int_t  n,
float *  A,
magma_int_t  lda,
magma_int_t *  info 
)

STRTRI computes the inverse of a real upper or lower triangular matrix A.

This is the Level 3 BLAS version of the algorithm.

Parameters
[in]uplomagma_uplo_t
  • = MagmaUpper: A is upper triangular;
  • = MagmaLower: A is lower triangular.
[in]diagmagma_diag_t
  • = MagmaNonUnit: A is non-unit triangular;
  • = MagmaUnit: A is unit triangular.
[in]nINTEGER The order of the matrix A. N >= 0.
[in,out]AREAL array, dimension (LDA,N) On entry, the triangular matrix A. If UPLO = MagmaUpper, 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 = MagmaLower, 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 = MagmaUnit, the diagonal elements of A are also not referenced and are assumed to be 1. On exit, the (triangular) inverse of the original matrix, in the same storage format.
[in]ldaINTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, A(i,i) is exactly zero. The triangular matrix is singular and its inverse cannot be computed.
magma_int_t magma_strtri_gpu ( magma_uplo_t  uplo,
magma_diag_t  diag,
magma_int_t  n,
magmaFloat_ptr  dA,
magma_int_t  ldda,
magma_int_t *  info 
)

STRTRI computes the inverse of a real upper or lower triangular matrix dA.

This is the Level 3 BLAS version of the algorithm.

Parameters
[in]uplomagma_uplo_t
  • = MagmaUpper: A is upper triangular;
  • = MagmaLower: A is lower triangular.
[in]diagmagma_diag_t
  • = MagmaNonUnit: A is non-unit triangular;
  • = MagmaUnit: A is unit triangular.
[in]nINTEGER The order of the matrix A. N >= 0.
[in,out]dAREAL array ON THE GPU, dimension (LDDA,N) On entry, the triangular matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of the array dA contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = MagmaLower, the leading N-by-N lower triangular part of the array dA contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = MagmaUnit, the diagonal elements of A are also not referenced and are assumed to be 1. On exit, the (triangular) inverse of the original matrix, in the same storage format.
[in]lddaINTEGER The leading dimension of the array dA. LDDA >= max(1,N).
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, dA(i,i) is exactly zero. The triangular matrix is singular and its inverse cannot be computed. (Singularity check is currently disabled.)