\( x = op(A^{-1})\; b \) More...

Functions
void	magma_ctrsv (magma_uplo_t uplo, magma_trans_t trans, magma_diag_t diag, magma_int_t n, magmaFloatComplex_const_ptr dA, magma_int_t ldda, magmaFloatComplex_ptr dx, magma_int_t incx, magma_queue_t queue)
	Solve triangular matrix-vector system (one right-hand side). More...

void	magma_dtrsv (magma_uplo_t uplo, magma_trans_t trans, magma_diag_t diag, magma_int_t n, magmaDouble_const_ptr dA, magma_int_t ldda, magmaDouble_ptr dx, magma_int_t incx, magma_queue_t queue)
	Solve triangular matrix-vector system (one right-hand side). More...

void	magma_strsv (magma_uplo_t uplo, magma_trans_t trans, magma_diag_t diag, magma_int_t n, magmaFloat_const_ptr dA, magma_int_t ldda, magmaFloat_ptr dx, magma_int_t incx, magma_queue_t queue)
	Solve triangular matrix-vector system (one right-hand side). More...

void	magma_ztrsv (magma_uplo_t uplo, magma_trans_t trans, magma_diag_t diag, magma_int_t n, magmaDoubleComplex_const_ptr dA, magma_int_t ldda, magmaDoubleComplex_ptr dx, magma_int_t incx, magma_queue_t queue)
	Solve triangular matrix-vector system (one right-hand side). More...

void	magmablas_ctrsv (magma_uplo_t uplo, magma_trans_t trans, magma_diag_t diag, magma_int_t n, magmaFloatComplex_const_ptr dA, magma_int_t ldda, magmaFloatComplex_ptr db, magma_int_t incb, magma_queue_t queue)
	ctrsv solves one of the matrix equations on gpu More...

void	magmablas_dtrsv (magma_uplo_t uplo, magma_trans_t trans, magma_diag_t diag, magma_int_t n, magmaDouble_const_ptr dA, magma_int_t ldda, magmaDouble_ptr db, magma_int_t incb, magma_queue_t queue)
	dtrsv solves one of the matrix equations on gpu More...

void	magmablas_strsv (magma_uplo_t uplo, magma_trans_t trans, magma_diag_t diag, magma_int_t n, magmaFloat_const_ptr dA, magma_int_t ldda, magmaFloat_ptr db, magma_int_t incb, magma_queue_t queue)
	strsv solves one of the matrix equations on gpu More...

void	magmablas_ztrsv (magma_uplo_t uplo, magma_trans_t trans, magma_diag_t diag, magma_int_t n, magmaDoubleComplex_const_ptr dA, magma_int_t ldda, magmaDoubleComplex_ptr db, magma_int_t incb, magma_queue_t queue)
	ztrsv solves one of the matrix equations on gpu More...

Detailed Description

\( x = op(A^{-1})\; b \)

Function Documentation

void magma_ctrsv	(	magma_uplo_t	uplo,
		magma_trans_t	trans,
		magma_diag_t	diag,
		magma_int_t	n,
		magmaFloatComplex_const_ptr	dA,
		magma_int_t	ldda,
		magmaFloatComplex_ptr	dx,
		magma_int_t	incx,
		magma_queue_t	queue
	)

Solve triangular matrix-vector system (one right-hand side).

\( A x = b \) (trans == MagmaNoTrans), or
\( A^T x = b \) (trans == MagmaTrans), or
\( A^H x = b \) (trans == MagmaConjTrans).

Parameters

[in]	uplo	Whether the upper or lower triangle of A is referenced.
[in]	trans	Operation to perform on A.
[in]	diag	Whether the diagonal of A is assumed to be unit or non-unit.
[in]	n	Number of rows and columns of A. n >= 0.
[in]	dA	COMPLEX array of dimension (ldda,n), ldda >= max(1,n). The n-by-n matrix A, on GPU device.
[in]	ldda	Leading dimension of dA.
[in,out]	dx	COMPLEX array on GPU device. On entry, the n element RHS vector b of dimension (1 + (n-1)*incx). On exit, overwritten with the solution vector x.
[in]	incx	Stride between consecutive elements of dx. incx != 0.
[in]	queue	magma_queue_t Queue to execute in.

void magma_dtrsv	(	magma_uplo_t	uplo,
		magma_trans_t	trans,
		magma_diag_t	diag,
		magma_int_t	n,
		magmaDouble_const_ptr	dA,
		magma_int_t	ldda,
		magmaDouble_ptr	dx,
		magma_int_t	incx,
		magma_queue_t	queue
	)

Solve triangular matrix-vector system (one right-hand side).

\( A x = b \) (trans == MagmaNoTrans), or
\( A^T x = b \) (trans == MagmaTrans), or
\( A^H x = b \) (trans == MagmaConjTrans).

Parameters

[in]	uplo	Whether the upper or lower triangle of A is referenced.
[in]	trans	Operation to perform on A.
[in]	diag	Whether the diagonal of A is assumed to be unit or non-unit.
[in]	n	Number of rows and columns of A. n >= 0.
[in]	dA	DOUBLE PRECISION array of dimension (ldda,n), ldda >= max(1,n). The n-by-n matrix A, on GPU device.
[in]	ldda	Leading dimension of dA.
[in,out]	dx	DOUBLE PRECISION array on GPU device. On entry, the n element RHS vector b of dimension (1 + (n-1)*incx). On exit, overwritten with the solution vector x.
[in]	incx	Stride between consecutive elements of dx. incx != 0.
[in]	queue	magma_queue_t Queue to execute in.

void magma_strsv	(	magma_uplo_t	uplo,
		magma_trans_t	trans,
		magma_diag_t	diag,
		magma_int_t	n,
		magmaFloat_const_ptr	dA,
		magma_int_t	ldda,
		magmaFloat_ptr	dx,
		magma_int_t	incx,
		magma_queue_t	queue
	)

Solve triangular matrix-vector system (one right-hand side).

\( A x = b \) (trans == MagmaNoTrans), or
\( A^T x = b \) (trans == MagmaTrans), or
\( A^H x = b \) (trans == MagmaConjTrans).

Parameters

[in]	uplo	Whether the upper or lower triangle of A is referenced.
[in]	trans	Operation to perform on A.
[in]	diag	Whether the diagonal of A is assumed to be unit or non-unit.
[in]	n	Number of rows and columns of A. n >= 0.
[in]	dA	REAL array of dimension (ldda,n), ldda >= max(1,n). The n-by-n matrix A, on GPU device.
[in]	ldda	Leading dimension of dA.
[in,out]	dx	REAL array on GPU device. On entry, the n element RHS vector b of dimension (1 + (n-1)*incx). On exit, overwritten with the solution vector x.
[in]	incx	Stride between consecutive elements of dx. incx != 0.
[in]	queue	magma_queue_t Queue to execute in.

void magma_ztrsv	(	magma_uplo_t	uplo,
		magma_trans_t	trans,
		magma_diag_t	diag,
		magma_int_t	n,
		magmaDoubleComplex_const_ptr	dA,
		magma_int_t	ldda,
		magmaDoubleComplex_ptr	dx,
		magma_int_t	incx,
		magma_queue_t	queue
	)

Solve triangular matrix-vector system (one right-hand side).

\( A x = b \) (trans == MagmaNoTrans), or
\( A^T x = b \) (trans == MagmaTrans), or
\( A^H x = b \) (trans == MagmaConjTrans).

Parameters

[in]	uplo	Whether the upper or lower triangle of A is referenced.
[in]	trans	Operation to perform on A.
[in]	diag	Whether the diagonal of A is assumed to be unit or non-unit.
[in]	n	Number of rows and columns of A. n >= 0.
[in]	dA	COMPLEX_16 array of dimension (ldda,n), ldda >= max(1,n). The n-by-n matrix A, on GPU device.
[in]	ldda	Leading dimension of dA.
[in,out]	dx	COMPLEX_16 array on GPU device. On entry, the n element RHS vector b of dimension (1 + (n-1)*incx). On exit, overwritten with the solution vector x.
[in]	incx	Stride between consecutive elements of dx. incx != 0.
[in]	queue	magma_queue_t Queue to execute in.

void magmablas_ctrsv	(	magma_uplo_t	uplo,
		magma_trans_t	trans,
		magma_diag_t	diag,
		magma_int_t	n,
		magmaFloatComplex_const_ptr	dA,
		magma_int_t	ldda,
		magmaFloatComplex_ptr	db,
		magma_int_t	incb,
		magma_queue_t	queue
	)

ctrsv solves one of the matrix equations on gpu

op(A)*x = B,   or
x*op(A) = B,

where alpha is a scalar, X and B are vectors, A is a unit, or non-unit, upper or lower triangular matrix and op(A) is one of

op(A) = A,    or
op(A) = A^T,  or
op(A) = A^H.

The vector x is overwritten on b.

Parameters

[in]	uplo	magma_uplo_t. On entry, uplo specifies whether the matrix A is an upper or lower triangular matrix as follows: = MagmaUpper: A is an upper triangular matrix. = MagmaLower: A is a lower triangular matrix.
[in]	trans	magma_trans_t. On entry, trans specifies the form of op(A) to be used in the matrix multiplication as follows: = MagmaNoTrans: op(A) = A. = MagmaTrans: op(A) = A^T. = MagmaConjTrans: op(A) = A^H.
[in]	diag	magma_diag_t. On entry, diag specifies whether or not A is unit triangular as follows: = MagmaUnit: A is assumed to be unit triangular. = MagmaNonUnit: A is not assumed to be unit triangular.
[in]	n	INTEGER. On entry, n N specifies the order of the matrix A. n >= 0.
[in]	dA	COMPLEX array of dimension ( lda, n ) Before entry with uplo = MagmaUpper, the leading n by n upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. Before entry with uplo = MagmaLower, the leading n by n lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. Note that when diag = MagmaUnit, the diagonal elements of A are not referenced either, but are assumed to be unity.
[in]	ldda	INTEGER. On entry, lda specifies the first dimension of A. lda >= max( 1, n ).
[in]	db	COMPLEX array of dimension n On exit, b is overwritten with the solution vector X.
[in]	incb	INTEGER. On entry, incb specifies the increment for the elements of b. incb must not be zero. Unchanged on exit.
[in]	queue	magma_queue_t Queue to execute in.

void magmablas_dtrsv	(	magma_uplo_t	uplo,
		magma_trans_t	trans,
		magma_diag_t	diag,
		magma_int_t	n,
		magmaDouble_const_ptr	dA,
		magma_int_t	ldda,
		magmaDouble_ptr	db,
		magma_int_t	incb,
		magma_queue_t	queue
	)

dtrsv solves one of the matrix equations on gpu

op(A)*x = B,   or
x*op(A) = B,

where alpha is a scalar, X and B are vectors, A is a unit, or non-unit, upper or lower triangular matrix and op(A) is one of

op(A) = A,    or
op(A) = A^T,  or
op(A) = A^H.

The vector x is overwritten on b.

Parameters

[in]	uplo	magma_uplo_t. On entry, uplo specifies whether the matrix A is an upper or lower triangular matrix as follows: = MagmaUpper: A is an upper triangular matrix. = MagmaLower: A is a lower triangular matrix.
[in]	trans	magma_trans_t. On entry, trans specifies the form of op(A) to be used in the matrix multiplication as follows: = MagmaNoTrans: op(A) = A. = MagmaTrans: op(A) = A^T. = MagmaConjTrans: op(A) = A^H.
[in]	diag	magma_diag_t. On entry, diag specifies whether or not A is unit triangular as follows: = MagmaUnit: A is assumed to be unit triangular. = MagmaNonUnit: A is not assumed to be unit triangular.
[in]	n	INTEGER. On entry, n N specifies the order of the matrix A. n >= 0.
[in]	dA	DOUBLE PRECISION array of dimension ( lda, n ) Before entry with uplo = MagmaUpper, the leading n by n upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. Before entry with uplo = MagmaLower, the leading n by n lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. Note that when diag = MagmaUnit, the diagonal elements of A are not referenced either, but are assumed to be unity.
[in]	ldda	INTEGER. On entry, lda specifies the first dimension of A. lda >= max( 1, n ).
[in]	db	DOUBLE PRECISION array of dimension n On exit, b is overwritten with the solution vector X.
[in]	incb	INTEGER. On entry, incb specifies the increment for the elements of b. incb must not be zero. Unchanged on exit.
[in]	queue	magma_queue_t Queue to execute in.

void magmablas_strsv	(	magma_uplo_t	uplo,
		magma_trans_t	trans,
		magma_diag_t	diag,
		magma_int_t	n,
		magmaFloat_const_ptr	dA,
		magma_int_t	ldda,
		magmaFloat_ptr	db,
		magma_int_t	incb,
		magma_queue_t	queue
	)

strsv solves one of the matrix equations on gpu

op(A)*x = B,   or
x*op(A) = B,

where alpha is a scalar, X and B are vectors, A is a unit, or non-unit, upper or lower triangular matrix and op(A) is one of

op(A) = A,    or
op(A) = A^T,  or
op(A) = A^H.

The vector x is overwritten on b.

Parameters

[in]	uplo	magma_uplo_t. On entry, uplo specifies whether the matrix A is an upper or lower triangular matrix as follows: = MagmaUpper: A is an upper triangular matrix. = MagmaLower: A is a lower triangular matrix.
[in]	trans	magma_trans_t. On entry, trans specifies the form of op(A) to be used in the matrix multiplication as follows: = MagmaNoTrans: op(A) = A. = MagmaTrans: op(A) = A^T. = MagmaConjTrans: op(A) = A^H.
[in]	diag	magma_diag_t. On entry, diag specifies whether or not A is unit triangular as follows: = MagmaUnit: A is assumed to be unit triangular. = MagmaNonUnit: A is not assumed to be unit triangular.
[in]	n	INTEGER. On entry, n N specifies the order of the matrix A. n >= 0.
[in]	dA	REAL array of dimension ( lda, n ) Before entry with uplo = MagmaUpper, the leading n by n upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. Before entry with uplo = MagmaLower, the leading n by n lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. Note that when diag = MagmaUnit, the diagonal elements of A are not referenced either, but are assumed to be unity.
[in]	ldda	INTEGER. On entry, lda specifies the first dimension of A. lda >= max( 1, n ).
[in]	db	REAL array of dimension n On exit, b is overwritten with the solution vector X.
[in]	incb	INTEGER. On entry, incb specifies the increment for the elements of b. incb must not be zero. Unchanged on exit.
[in]	queue	magma_queue_t Queue to execute in.

void magmablas_ztrsv	(	magma_uplo_t	uplo,
		magma_trans_t	trans,
		magma_diag_t	diag,
		magma_int_t	n,
		magmaDoubleComplex_const_ptr	dA,
		magma_int_t	ldda,
		magmaDoubleComplex_ptr	db,
		magma_int_t	incb,
		magma_queue_t	queue
	)

ztrsv solves one of the matrix equations on gpu

op(A)*x = B,   or
x*op(A) = B,

where alpha is a scalar, X and B are vectors, A is a unit, or non-unit, upper or lower triangular matrix and op(A) is one of

op(A) = A,    or
op(A) = A^T,  or
op(A) = A^H.

The vector x is overwritten on b.

Parameters

[in]	uplo	magma_uplo_t. On entry, uplo specifies whether the matrix A is an upper or lower triangular matrix as follows: = MagmaUpper: A is an upper triangular matrix. = MagmaLower: A is a lower triangular matrix.
[in]	trans	magma_trans_t. On entry, trans specifies the form of op(A) to be used in the matrix multiplication as follows: = MagmaNoTrans: op(A) = A. = MagmaTrans: op(A) = A^T. = MagmaConjTrans: op(A) = A^H.
[in]	diag	magma_diag_t. On entry, diag specifies whether or not A is unit triangular as follows: = MagmaUnit: A is assumed to be unit triangular. = MagmaNonUnit: A is not assumed to be unit triangular.
[in]	n	INTEGER. On entry, n N specifies the order of the matrix A. n >= 0.
[in]	dA	COMPLEX_16 array of dimension ( lda, n ) Before entry with uplo = MagmaUpper, the leading n by n upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. Before entry with uplo = MagmaLower, the leading n by n lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. Note that when diag = MagmaUnit, the diagonal elements of A are not referenced either, but are assumed to be unity.
[in]	ldda	INTEGER. On entry, lda specifies the first dimension of A. lda >= max( 1, n ).
[in]	db	COMPLEX_16 array of dimension n On exit, b is overwritten with the solution vector X.
[in]	incb	INTEGER. On entry, incb specifies the increment for the elements of b. incb must not be zero. Unchanged on exit.
[in]	queue	magma_queue_t Queue to execute in.

Functions

Detailed Description

Function Documentation