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

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

Functions

void magmablas_ctrsv_batched (magma_uplo_t uplo, magma_trans_t trans, magma_diag_t diag, magma_int_t n, magmaFloatComplex **A_array, magma_int_t lda, magmaFloatComplex **b_array, magma_int_t incb, magma_int_t batchCount, magma_queue_t queue)
 ctrsv solves one of the matrix equations on gpu More...
 
void magmablas_dtrsv_batched (magma_uplo_t uplo, magma_trans_t trans, magma_diag_t diag, magma_int_t n, double **A_array, magma_int_t lda, double **b_array, magma_int_t incb, magma_int_t batchCount, magma_queue_t queue)
 dtrsv solves one of the matrix equations on gpu More...
 
void magmablas_strsv_batched (magma_uplo_t uplo, magma_trans_t trans, magma_diag_t diag, magma_int_t n, float **A_array, magma_int_t lda, float **b_array, magma_int_t incb, magma_int_t batchCount, magma_queue_t queue)
 strsv solves one of the matrix equations on gpu More...
 
void magmablas_ztrsv_batched (magma_uplo_t uplo, magma_trans_t trans, magma_diag_t diag, magma_int_t n, magmaDoubleComplex **A_array, magma_int_t lda, magmaDoubleComplex **b_array, magma_int_t incb, magma_int_t batchCount, magma_queue_t queue)
 ztrsv solves one of the matrix equations on gpu More...
 

Detailed Description

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


Function Documentation

void magmablas_ctrsv_batched ( magma_uplo_t  uplo,
magma_trans_t  trans,
magma_diag_t  diag,
magma_int_t  n,
magmaFloatComplex **  A_array,
magma_int_t  lda,
magmaFloatComplex **  b_array,
magma_int_t  incb,
magma_int_t  batchCount,
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]uplomagma_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]transmagma_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]diagmagma_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]nINTEGER. On entry, n N specifies the order of the matrix A. n >= 0.
[in]A_arrayArray of pointers, dimension (batchCount). Each is a COMPLEX array A 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]ldaINTEGER. On entry, lda specifies the first dimension of A. lda >= max( 1, n ).
[in]b_arrayArray of pointers, dimension (batchCount). Each is a COMPLEX array of dimension n On exit, b is overwritten with the solution vector X.
[in]incbINTEGER. On entry, incb specifies the increment for the elements of b. incb must not be zero. Unchanged on exit.
[in]batchCountINTEGER The number of matrices to operate on.
[in]queuemagma_queue_t Queue to execute in.
void magmablas_dtrsv_batched ( magma_uplo_t  uplo,
magma_trans_t  trans,
magma_diag_t  diag,
magma_int_t  n,
double **  A_array,
magma_int_t  lda,
double **  b_array,
magma_int_t  incb,
magma_int_t  batchCount,
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]uplomagma_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]transmagma_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]diagmagma_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]nINTEGER. On entry, n N specifies the order of the matrix A. n >= 0.
[in]A_arrayArray of pointers, dimension (batchCount). Each is a DOUBLE PRECISION array A 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]ldaINTEGER. On entry, lda specifies the first dimension of A. lda >= max( 1, n ).
[in]b_arrayArray of pointers, dimension (batchCount). Each is a DOUBLE PRECISION array of dimension n On exit, b is overwritten with the solution vector X.
[in]incbINTEGER. On entry, incb specifies the increment for the elements of b. incb must not be zero. Unchanged on exit.
[in]batchCountINTEGER The number of matrices to operate on.
[in]queuemagma_queue_t Queue to execute in.
void magmablas_strsv_batched ( magma_uplo_t  uplo,
magma_trans_t  trans,
magma_diag_t  diag,
magma_int_t  n,
float **  A_array,
magma_int_t  lda,
float **  b_array,
magma_int_t  incb,
magma_int_t  batchCount,
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]uplomagma_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]transmagma_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]diagmagma_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]nINTEGER. On entry, n N specifies the order of the matrix A. n >= 0.
[in]A_arrayArray of pointers, dimension (batchCount). Each is a REAL array A 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]ldaINTEGER. On entry, lda specifies the first dimension of A. lda >= max( 1, n ).
[in]b_arrayArray of pointers, dimension (batchCount). Each is a REAL array of dimension n On exit, b is overwritten with the solution vector X.
[in]incbINTEGER. On entry, incb specifies the increment for the elements of b. incb must not be zero. Unchanged on exit.
[in]batchCountINTEGER The number of matrices to operate on.
[in]queuemagma_queue_t Queue to execute in.
void magmablas_ztrsv_batched ( magma_uplo_t  uplo,
magma_trans_t  trans,
magma_diag_t  diag,
magma_int_t  n,
magmaDoubleComplex **  A_array,
magma_int_t  lda,
magmaDoubleComplex **  b_array,
magma_int_t  incb,
magma_int_t  batchCount,
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]uplomagma_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]transmagma_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]diagmagma_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]nINTEGER. On entry, n N specifies the order of the matrix A. n >= 0.
[in]A_arrayArray of pointers, dimension (batchCount). Each is a COMPLEX_16 array A 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]ldaINTEGER. On entry, lda specifies the first dimension of A. lda >= max( 1, n ).
[in]b_arrayArray of pointers, dimension (batchCount). Each is a COMPLEX_16 array of dimension n On exit, b is overwritten with the solution vector X.
[in]incbINTEGER. On entry, incb specifies the increment for the elements of b. incb must not be zero. Unchanged on exit.
[in]batchCountINTEGER The number of matrices to operate on.
[in]queuemagma_queue_t Queue to execute in.