single-complex precision
[LU solve: computational]

Functions

magma_int_t magma_cgetrf (magma_int_t m, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, magma_int_t *ipiv, magma_int_t *info)
 CGETRF computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges.
magma_int_t magma_cgetrf2_mgpu (magma_int_t num_gpus, magma_int_t m, magma_int_t n, magma_int_t nb, magma_int_t offset, magmaFloatComplex *d_lAT[], magma_int_t lddat, magma_int_t *ipiv, magmaFloatComplex *d_lAP[], magmaFloatComplex *w, magma_int_t ldw, magma_queue_t stream[][2], magma_int_t *info)
 CGETRF computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges.
magma_int_t magma_cgetrf_gpu (magma_int_t m, magma_int_t n, magmaFloatComplex *dA, magma_int_t ldda, magma_int_t *ipiv, magma_int_t *info)
 CGETRF computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges.
magma_int_t magma_cgetrf_m (magma_int_t num_gpus, magma_int_t m, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, magma_int_t *ipiv, magma_int_t *info)
 CGETRF_m computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges.
magma_int_t magma_cgetrf_mgpu (magma_int_t num_gpus, magma_int_t m, magma_int_t n, magmaFloatComplex **d_lA, magma_int_t ldda, magma_int_t *ipiv, magma_int_t *info)
 CGETRF computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges.
magma_int_t magma_cgetrf_nopiv (magma_int_t m, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, magma_int_t *info)
 CGETRF_NOPIV computes an LU factorization of a general M-by-N matrix A without pivoting.
magma_int_t magma_cgetrf_nopiv_gpu (magma_int_t m, magma_int_t n, magmaFloatComplex *dA, magma_int_t ldda, magma_int_t *info)
 CGETRF_NOPIV_GPU computes an LU factorization of a general M-by-N matrix A without any pivoting.
magma_int_t magma_cgetri_gpu (magma_int_t n, magmaFloatComplex *dA, magma_int_t ldda, magma_int_t *ipiv, magmaFloatComplex *dwork, magma_int_t lwork, magma_int_t *info)
 CGETRI computes the inverse of a matrix using the LU factorization computed by CGETRF.
magma_int_t magma_cgetrs_gpu (magma_trans_t trans, magma_int_t n, magma_int_t nrhs, magmaFloatComplex *dA, magma_int_t ldda, magma_int_t *ipiv, magmaFloatComplex *dB, magma_int_t lddb, magma_int_t *info)
 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 CGETRF_GPU.

Function Documentation

magma_int_t magma_cgetrf ( magma_int_t  m,
magma_int_t  n,
magmaFloatComplex *  A,
magma_int_t  lda,
magma_int_t *  ipiv,
magma_int_t *  info 
)

CGETRF 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.

If the current stream is NULL, this version replaces it with a new stream to overlap computation with communication.

Parameters:
[in] m INTEGER The number of rows of the matrix A. M >= 0.
[in] n INTEGER The number of columns of the matrix A. N >= 0.
[in,out] A COMPLEX 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] lda INTEGER The leading dimension of the array A. LDA >= max(1,M).
[out] ipiv 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 INTEGER

  • = 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_cgetrf2_mgpu ( magma_int_t  num_gpus,
magma_int_t  m,
magma_int_t  n,
magma_int_t  nb,
magma_int_t  offset,
magmaFloatComplex *  d_lAT[],
magma_int_t  lddat,
magma_int_t *  ipiv,
magmaFloatComplex *  d_lAP[],
magmaFloatComplex *  w,
magma_int_t  ldw,
magma_queue_t  stream[][2],
magma_int_t *  info 
)

CGETRF 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] num_gpus INTEGER The number of GPUs to be used for the factorization.
[in] m INTEGER The number of rows of the matrix A. M >= 0.
[in] n INTEGER The number of columns of the matrix A. N >= 0.
[in,out] d_lAT COMPLEX array of pointers on the GPU, dimension (num_gpus). 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] lddat INTEGER The leading dimension of the array d_lAT[d]. LDDA >= max(1,M).
[out] ipiv 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).
(workspace) on device d_lAP COMPLEX array of pointers on the GPU, dimension (num_gpus). d_lAP[d] is the workspace on d-th GPU. Each local workspace must be of size (3+num_gpus)*nb*maxm, where maxm is m rounded up to a multiple of 32 and nb is the block size.
(workspace) w COMPLEX array, dimension (num_gpus*nb*maxm). It is used to store panel on CPU.
[in] ldw INTEGER The leading dimension of the workspace w.
[in] stream magma_queue_t stream[d] points to the streams for the d-th GPU to execute in. Each GPU require two streams.
[out] info INTEGER

  • = 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_cgetrf_gpu ( magma_int_t  m,
magma_int_t  n,
magmaFloatComplex *  dA,
magma_int_t  ldda,
magma_int_t *  ipiv,
magma_int_t *  info 
)

CGETRF 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.

If the current stream is NULL, this version replaces it with a new stream to overlap computation with communication.

Parameters:
[in] m INTEGER The number of rows of the matrix A. M >= 0.
[in] n INTEGER The number of columns of the matrix A. N >= 0.
[in,out] dA COMPLEX 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] ldda INTEGER The leading dimension of the array A. LDDA >= max(1,M).
[out] ipiv 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 INTEGER

  • = 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_cgetrf_m ( magma_int_t  num_gpus,
magma_int_t  m,
magma_int_t  n,
magmaFloatComplex *  A,
magma_int_t  lda,
magma_int_t *  ipiv,
magma_int_t *  info 
)

CGETRF_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] num_gpus INTEGER The number of GPUs. num_gpus > 0.
[in] m INTEGER The number of rows of the matrix A. M >= 0.
[in] n INTEGER The number of columns of the matrix A. N >= 0.
[in,out] A COMPLEX 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] lda INTEGER The leading dimension of the array A. LDA >= max(1,M).
[out] ipiv 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 INTEGER

  • = 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_cgetrf_mgpu ( magma_int_t  num_gpus,
magma_int_t  m,
magma_int_t  n,
magmaFloatComplex **  d_lA,
magma_int_t  ldda,
magma_int_t *  ipiv,
magma_int_t *  info 
)

CGETRF 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] num_gpus INTEGER The number of GPUs to be used for the factorization.
[in] m INTEGER The number of rows of the matrix A. M >= 0.
[in] n INTEGER The number of columns of the matrix A. N >= 0.
[in,out] d_lA COMPLEX array of pointers on the GPU, dimension (num_gpus). 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] ldda INTEGER The leading dimension of the array d_lA. LDDA >= max(1,M).
[out] ipiv 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 INTEGER

  • = 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_cgetrf_nopiv ( magma_int_t  m,
magma_int_t  n,
magmaFloatComplex *  A,
magma_int_t  lda,
magma_int_t *  info 
)

CGETRF_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.

Parameters:
[in] m INTEGER The number of rows of the matrix A. M >= 0.
[in] n INTEGER The number of columns of the matrix A. N >= 0.
[in,out] A COMPLEX 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] lda INTEGER The leading dimension of the array A. LDA >= max(1,M).
[out] info INTEGER

  • = 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_cgetrf_nopiv_gpu ( magma_int_t  m,
magma_int_t  n,
magmaFloatComplex *  dA,
magma_int_t  ldda,
magma_int_t *  info 
)

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

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] m INTEGER The number of rows of the matrix A. M >= 0.
[in] n INTEGER The number of columns of the matrix A. N >= 0.
[in,out] dA COMPLEX 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] ldda INTEGER The leading dimension of the array A. LDDA >= max(1,M).
[out] info INTEGER

  • = 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_cgetri_gpu ( magma_int_t  n,
magmaFloatComplex *  dA,
magma_int_t  ldda,
magma_int_t *  ipiv,
magmaFloatComplex *  dwork,
magma_int_t  lwork,
magma_int_t *  info 
)

CGETRI computes the inverse of a matrix using the LU factorization computed by CGETRF.

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 CGESV, or CGETRF and CGETRS, 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] n INTEGER The order of the matrix A. N >= 0.
[in,out] dA COMPLEX array on the GPU, dimension (LDDA,N) On entry, the factors L and U from the factorization A = P*L*U as computed by CGETRF_GPU. On exit, if INFO = 0, the inverse of the original matrix A.
[in] ldda INTEGER The leading dimension of the array A. LDDA >= max(1,N).
[in] ipiv INTEGER array, dimension (N) The pivot indices from CGETRF; for 1 <= i <= N, row i of the matrix was interchanged with row IPIV(i).
[out] dwork (workspace) COMPLEX array on the GPU, dimension (MAX(1,LWORK))
[in] lwork INTEGER The dimension of the array DWORK. LWORK >= N*NB, where NB is the optimal blocksize returned by magma_get_cgetri_nb(n).
Unlike LAPACK, this version does not currently support a workspace query, because the workspace is on the GPU.
[out] info INTEGER

  • = 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_cgetrs_gpu ( magma_trans_t  trans,
magma_int_t  n,
magma_int_t  nrhs,
magmaFloatComplex *  dA,
magma_int_t  ldda,
magma_int_t *  ipiv,
magmaFloatComplex *  dB,
magma_int_t  lddb,
magma_int_t *  info 
)

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 CGETRF_GPU.

Parameters:
[in] trans magma_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] n INTEGER The order of the matrix A. N >= 0.
[in] nrhs INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in] dA COMPLEX array on the GPU, dimension (LDA,N) The factors L and U from the factorization A = P*L*U as computed by CGETRF_GPU.
[in] ldda INTEGER The leading dimension of the array A. LDA >= max(1,N).
[in] ipiv INTEGER array, dimension (N) The pivot indices from CGETRF; for 1 <= i <= N, row i of the matrix was interchanged with row IPIV(i).
[in,out] dB COMPLEX array on the GPU, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.
[in] lddb INTEGER The leading dimension of the array B. LDB >= max(1,N).
[out] info INTEGER

  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

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