MAGMA  2.3.0 Matrix Algebra for GPU and Multicore Architectures
trsv: Triangular matrix-vector solve

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