gesv: Solves Ax = b using LU factorization (driver)

Functions
magma_int_t	magma_cgesv_batched (magma_int_t n, magma_int_t nrhs, magmaFloatComplex **dA_array, magma_int_t ldda, magma_int_t **dipiv_array, magmaFloatComplex **dB_array, magma_int_t lddb, magma_int_t *dinfo_array, magma_int_t batchCount, magma_queue_t queue)
	CGESV 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.
magma_int_t	magma_dgesv_batched (magma_int_t n, magma_int_t nrhs, double **dA_array, magma_int_t ldda, magma_int_t **dipiv_array, double **dB_array, magma_int_t lddb, magma_int_t *dinfo_array, magma_int_t batchCount, magma_queue_t queue)
	DGESV 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.
magma_int_t	magma_sgesv_batched (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 *dinfo_array, magma_int_t batchCount, magma_queue_t queue)
	SGESV 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.
magma_int_t	magma_zgesv_batched (magma_int_t n, magma_int_t nrhs, magmaDoubleComplex **dA_array, magma_int_t ldda, magma_int_t **dipiv_array, magmaDoubleComplex **dB_array, magma_int_t lddb, magma_int_t *dinfo_array, magma_int_t batchCount, magma_queue_t queue)
	ZGESV 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.
magma_int_t	magma_cgesv_batched_small (magma_int_t n, magma_int_t nrhs, magmaFloatComplex **dA_array, magma_int_t ldda, magma_int_t **dipiv_array, magmaFloatComplex **dB_array, magma_int_t lddb, magma_int_t *dinfo_array, magma_int_t batchCount, magma_queue_t queue)
	CGESV 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.
magma_int_t	magma_dgesv_batched_small (magma_int_t n, magma_int_t nrhs, double **dA_array, magma_int_t ldda, magma_int_t **dipiv_array, double **dB_array, magma_int_t lddb, magma_int_t *dinfo_array, magma_int_t batchCount, magma_queue_t queue)
	DGESV 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.
magma_int_t	magma_sgesv_batched_small (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 *dinfo_array, magma_int_t batchCount, magma_queue_t queue)
	SGESV 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.
magma_int_t	magma_zgesv_batched_small (magma_int_t n, magma_int_t nrhs, magmaDoubleComplex **dA_array, magma_int_t ldda, magma_int_t **dipiv_array, magmaDoubleComplex **dB_array, magma_int_t lddb, magma_int_t *dinfo_array, magma_int_t batchCount, magma_queue_t queue)
	ZGESV 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.

Detailed Description

Function Documentation

magma_cgesv_batched()

magma_int_t magma_cgesv_batched	(	magma_int_t	n,
		magma_int_t	nrhs,
		magmaFloatComplex **	dA_array,
		magma_int_t	ldda,
		magma_int_t **	dipiv_array,
		magmaFloatComplex **	dB_array,
		magma_int_t	lddb,
		magma_int_t *	dinfo_array,
		magma_int_t	batchCount,
		magma_queue_t	queue )

CGESV 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.

The LU decomposition with partial pivoting and row interchanges is used to factor A as A = P * L * U, where P is a permutation matrix, 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 N-by-N matrices in parallel. dA, dB, ipiv, and info become arrays with one entry per matrix.

Parameters

[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,out]	dA_array	Array of pointers, dimension (batchCount). Each is a COMPLEX 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]	ldda	INTEGER The leading dimension of each array A. LDDA >= max(1,M).
[out]	dipiv_array	Array 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_array	Array of pointers, dimension (batchCount). Each is a COMPLEX 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]	lddb	INTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]	dinfo_array	Array 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]	batchCount	INTEGER The number of matrices to operate on.
[in]	queue	magma_queue_t Queue to execute in.

magma_dgesv_batched()

magma_int_t magma_dgesv_batched	(	magma_int_t	n,
		magma_int_t	nrhs,
		double **	dA_array,
		magma_int_t	ldda,
		magma_int_t **	dipiv_array,
		double **	dB_array,
		magma_int_t	lddb,
		magma_int_t *	dinfo_array,
		magma_int_t	batchCount,
		magma_queue_t	queue )

DGESV 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.

The LU decomposition with partial pivoting and row interchanges is used to factor A as A = P * L * U, where P is a permutation matrix, 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 N-by-N matrices in parallel. dA, dB, ipiv, and info become arrays with one entry per matrix.

Parameters

[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,out]	dA_array	Array of pointers, dimension (batchCount). Each is a DOUBLE PRECISION 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]	ldda	INTEGER The leading dimension of each array A. LDDA >= max(1,M).
[out]	dipiv_array	Array 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_array	Array of pointers, dimension (batchCount). Each is a DOUBLE PRECISION 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]	lddb	INTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]	dinfo_array	Array 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]	batchCount	INTEGER The number of matrices to operate on.
[in]	queue	magma_queue_t Queue to execute in.

magma_sgesv_batched()

magma_int_t magma_sgesv_batched	(	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 *	dinfo_array,
		magma_int_t	batchCount,
		magma_queue_t	queue )

SGESV 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.

The LU decomposition with partial pivoting and row interchanges is used to factor A as A = P * L * U, where P is a permutation matrix, 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 N-by-N matrices in parallel. dA, dB, ipiv, and info become arrays with one entry per matrix.

Parameters

[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,out]	dA_array	Array 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]	ldda	INTEGER The leading dimension of each array A. LDDA >= max(1,M).
[out]	dipiv_array	Array 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_array	Array 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]	lddb	INTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]	dinfo_array	Array 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]	batchCount	INTEGER The number of matrices to operate on.
[in]	queue	magma_queue_t Queue to execute in.

magma_zgesv_batched()

magma_int_t magma_zgesv_batched	(	magma_int_t	n,
		magma_int_t	nrhs,
		magmaDoubleComplex **	dA_array,
		magma_int_t	ldda,
		magma_int_t **	dipiv_array,
		magmaDoubleComplex **	dB_array,
		magma_int_t	lddb,
		magma_int_t *	dinfo_array,
		magma_int_t	batchCount,
		magma_queue_t	queue )

ZGESV 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.

The LU decomposition with partial pivoting and row interchanges is used to factor A as A = P * L * U, where P is a permutation matrix, 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 N-by-N matrices in parallel. dA, dB, ipiv, and info become arrays with one entry per matrix.

Parameters

[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,out]	dA_array	Array of pointers, dimension (batchCount). Each is a COMPLEX_16 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]	ldda	INTEGER The leading dimension of each array A. LDDA >= max(1,M).
[out]	dipiv_array	Array 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_array	Array of pointers, dimension (batchCount). Each is a COMPLEX_16 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]	lddb	INTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]	dinfo_array	Array 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]	batchCount	INTEGER The number of matrices to operate on.
[in]	queue	magma_queue_t Queue to execute in.

magma_cgesv_batched_small()

magma_int_t magma_cgesv_batched_small	(	magma_int_t	n,
		magma_int_t	nrhs,
		magmaFloatComplex **	dA_array,
		magma_int_t	ldda,
		magma_int_t **	dipiv_array,
		magmaFloatComplex **	dB_array,
		magma_int_t	lddb,
		magma_int_t *	dinfo_array,
		magma_int_t	batchCount,
		magma_queue_t	queue )

CGESV 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.

The LU decomposition with partial pivoting and row interchanges is used to factor A as A = P * L * U, where P is a permutation matrix, 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 N-by-N matrices in parallel. dA, dB, ipiv, and info become arrays with one entry per matrix.

Parameters

[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,out]	dA_array	Array of pointers, dimension (batchCount). Each is a COMPLEX 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]	ldda	INTEGER The leading dimension of each array A. LDDA >= max(1,M).
[out]	dipiv_array	Array 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_array	Array of pointers, dimension (batchCount). Each is a COMPLEX array on the GPU, dimension (LDDB,NRHS). On entry, each pointer is an right hand side matrix B. On exit, each pointer is the solution matrix X.
[in]	lddb	INTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]	dinfo_array	Array 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]	batchCount	INTEGER The number of matrices to operate on.
[in]	queue	magma_queue_t Queue to execute in.

magma_dgesv_batched_small()

magma_int_t magma_dgesv_batched_small	(	magma_int_t	n,
		magma_int_t	nrhs,
		double **	dA_array,
		magma_int_t	ldda,
		magma_int_t **	dipiv_array,
		double **	dB_array,
		magma_int_t	lddb,
		magma_int_t *	dinfo_array,
		magma_int_t	batchCount,
		magma_queue_t	queue )

DGESV 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.

The LU decomposition with partial pivoting and row interchanges is used to factor A as A = P * L * U, where P is a permutation matrix, 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 N-by-N matrices in parallel. dA, dB, ipiv, and info become arrays with one entry per matrix.

Parameters

[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,out]	dA_array	Array of pointers, dimension (batchCount). Each is a DOUBLE PRECISION 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]	ldda	INTEGER The leading dimension of each array A. LDDA >= max(1,M).
[out]	dipiv_array	Array 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_array	Array of pointers, dimension (batchCount). Each is a DOUBLE PRECISION array on the GPU, dimension (LDDB,NRHS). On entry, each pointer is an right hand side matrix B. On exit, each pointer is the solution matrix X.
[in]	lddb	INTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]	dinfo_array	Array 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]	batchCount	INTEGER The number of matrices to operate on.
[in]	queue	magma_queue_t Queue to execute in.

magma_sgesv_batched_small()

magma_int_t magma_sgesv_batched_small	(	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 *	dinfo_array,
		magma_int_t	batchCount,
		magma_queue_t	queue )

SGESV 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.

The LU decomposition with partial pivoting and row interchanges is used to factor A as A = P * L * U, where P is a permutation matrix, 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 N-by-N matrices in parallel. dA, dB, ipiv, and info become arrays with one entry per matrix.

Parameters

[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,out]	dA_array	Array 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]	ldda	INTEGER The leading dimension of each array A. LDDA >= max(1,M).
[out]	dipiv_array	Array 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_array	Array of pointers, dimension (batchCount). Each is a REAL array on the GPU, dimension (LDDB,NRHS). On entry, each pointer is an right hand side matrix B. On exit, each pointer is the solution matrix X.
[in]	lddb	INTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]	dinfo_array	Array 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]	batchCount	INTEGER The number of matrices to operate on.
[in]	queue	magma_queue_t Queue to execute in.

magma_zgesv_batched_small()

magma_int_t magma_zgesv_batched_small	(	magma_int_t	n,
		magma_int_t	nrhs,
		magmaDoubleComplex **	dA_array,
		magma_int_t	ldda,
		magma_int_t **	dipiv_array,
		magmaDoubleComplex **	dB_array,
		magma_int_t	lddb,
		magma_int_t *	dinfo_array,
		magma_int_t	batchCount,
		magma_queue_t	queue )

ZGESV 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.

The LU decomposition with partial pivoting and row interchanges is used to factor A as A = P * L * U, where P is a permutation matrix, 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 N-by-N matrices in parallel. dA, dB, ipiv, and info become arrays with one entry per matrix.

Parameters

[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,out]	dA_array	Array of pointers, dimension (batchCount). Each is a COMPLEX_16 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]	ldda	INTEGER The leading dimension of each array A. LDDA >= max(1,M).
[out]	dipiv_array	Array 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_array	Array of pointers, dimension (batchCount). Each is a COMPLEX_16 array on the GPU, dimension (LDDB,NRHS). On entry, each pointer is an right hand side matrix B. On exit, each pointer is the solution matrix X.
[in]	lddb	INTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]	dinfo_array	Array 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]	batchCount	INTEGER The number of matrices to operate on.
[in]	queue	magma_queue_t Queue to execute in.