gerbt: Apply random butterfly transformation (RBT)

Functions
magma_int_t	magma_cgerbt_batched (magma_bool_t gen, magma_int_t n, magma_int_t nrhs, magmaFloatComplex **dA_array, magma_int_t ldda, magmaFloatComplex **dB_array, magma_int_t lddb, magmaFloatComplex *U, magmaFloatComplex *V, magma_int_t *info, magma_int_t batchCount, magma_queue_t queue)
	CGERBT 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_dgerbt_batched (magma_bool_t gen, magma_int_t n, magma_int_t nrhs, double **dA_array, magma_int_t ldda, double **dB_array, magma_int_t lddb, double *U, double *V, magma_int_t *info, magma_int_t batchCount, magma_queue_t queue)
	DGERBT 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_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.
magma_int_t	magma_zgerbt_batched (magma_bool_t gen, magma_int_t n, magma_int_t nrhs, magmaDoubleComplex **dA_array, magma_int_t ldda, magmaDoubleComplex **dB_array, magma_int_t lddb, magmaDoubleComplex *U, magmaDoubleComplex *V, magma_int_t *info, magma_int_t batchCount, magma_queue_t queue)
	ZGERBT 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_cgerbt_batched()

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

CGERBT 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]	gen	magma_bool_t = MagmaTrue: new matrices are generated for U and V = MagmaFalse: matrices U and V given as parameter are used
[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).
[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).
[in,out]	U	COMPLEX 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]	V	COMPLEX 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]	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.
[in]	batchCount	INTEGER The number of matrices to operate on.
[in]	queue	magma_queue_t Queue to execute in.

magma_dgerbt_batched()

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

DGERBT 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]	gen	magma_bool_t = MagmaTrue: new matrices are generated for U and V = MagmaFalse: matrices U and V given as parameter are used
[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).
[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).
[in,out]	U	DOUBLE PRECISION 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]	V	DOUBLE PRECISION 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]	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.
[in]	batchCount	INTEGER The number of matrices to operate on.
[in]	queue	magma_queue_t Queue to execute in.

magma_sgerbt_batched()

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]	gen	magma_bool_t = MagmaTrue: new matrices are generated for U and V = MagmaFalse: matrices U and V given as parameter are used
[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).
[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).
[in,out]	U	REAL 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]	V	REAL 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]	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.
[in]	batchCount	INTEGER The number of matrices to operate on.
[in]	queue	magma_queue_t Queue to execute in.

magma_zgerbt_batched()

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

ZGERBT 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]	gen	magma_bool_t = MagmaTrue: new matrices are generated for U and V = MagmaFalse: matrices U and V given as parameter are used
[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).
[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).
[in,out]	U	COMPLEX_16 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]	V	COMPLEX_16 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]	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.
[in]	batchCount	INTEGER The number of matrices to operate on.
[in]	queue	magma_queue_t Queue to execute in.