MAGMA  2.3.0 Matrix Algebra for GPU and Multicore Architectures
symv: Symmetric matrix-vector multiply

$$y = \alpha Ax + \beta y$$ More...

## Functions

void magma_csymv (magma_uplo_t uplo, magma_int_t n, magmaFloatComplex alpha, magmaFloatComplex_const_ptr dA, magma_int_t ldda, magmaFloatComplex_const_ptr dx, magma_int_t incx, magmaFloatComplex beta, magmaFloatComplex_ptr dy, magma_int_t incy, magma_queue_t queue)
Perform symmetric matrix-vector product, $$y = \alpha A x + \beta y,$$ where $$A$$ is symmetric. More...

void magma_dsymv (magma_uplo_t uplo, magma_int_t n, double alpha, magmaDouble_const_ptr dA, magma_int_t ldda, magmaDouble_const_ptr dx, magma_int_t incx, double beta, magmaDouble_ptr dy, magma_int_t incy, magma_queue_t queue)
Perform symmetric matrix-vector product, $$y = \alpha A x + \beta y,$$ where $$A$$ is symmetric. More...

void magma_ssymv (magma_uplo_t uplo, magma_int_t n, float alpha, magmaFloat_const_ptr dA, magma_int_t ldda, magmaFloat_const_ptr dx, magma_int_t incx, float beta, magmaFloat_ptr dy, magma_int_t incy, magma_queue_t queue)
Perform symmetric matrix-vector product, $$y = \alpha A x + \beta y,$$ where $$A$$ is symmetric. More...

Perform symmetric matrix-vector product, $$y = \alpha A x + \beta y,$$ where $$A$$ is symmetric. More...

magma_int_t magmablas_csymv_work (magma_uplo_t uplo, magma_int_t n, magmaFloatComplex alpha, magmaFloatComplex_const_ptr dA, magma_int_t ldda, magmaFloatComplex_const_ptr dx, magma_int_t incx, magmaFloatComplex beta, magmaFloatComplex_ptr dy, magma_int_t incy, magmaFloatComplex_ptr dwork, magma_int_t lwork, magma_queue_t queue)
magmablas_csymv_work performs the matrix-vector operation: More...

magma_int_t magmablas_csymv (magma_uplo_t uplo, magma_int_t n, magmaFloatComplex alpha, magmaFloatComplex_const_ptr dA, magma_int_t ldda, magmaFloatComplex_const_ptr dx, magma_int_t incx, magmaFloatComplex beta, magmaFloatComplex_ptr dy, magma_int_t incy, magma_queue_t queue)
magmablas_csymv performs the matrix-vector operation: More...

magmablas_zsymv_work performs the matrix-vector operation: More...

magmablas_zsymv performs the matrix-vector operation: More...

## Detailed Description

$$y = \alpha Ax + \beta y$$

## Function Documentation

 void magma_csymv ( magma_uplo_t uplo, magma_int_t n, magmaFloatComplex alpha, magmaFloatComplex_const_ptr dA, magma_int_t ldda, magmaFloatComplex_const_ptr dx, magma_int_t incx, magmaFloatComplex beta, magmaFloatComplex_ptr dy, magma_int_t incy, magma_queue_t queue )

Perform symmetric matrix-vector product, $$y = \alpha A x + \beta y,$$ where $$A$$ is symmetric.

Parameters
 [in] uplo Whether the upper or lower triangle of A is referenced. [in] n Number of rows and columns of A. n >= 0. [in] alpha Scalar $$\alpha$$ [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] dx COMPLEX array on GPU device. The m element vector x of dimension (1 + (m-1)*incx). [in] incx Stride between consecutive elements of dx. incx != 0. [in] beta Scalar $$\beta$$ [in,out] dy COMPLEX array on GPU device. The n element vector y of dimension (1 + (n-1)*incy). [in] incy Stride between consecutive elements of dy. incy != 0. [in] queue magma_queue_t Queue to execute in.
 void magma_dsymv ( magma_uplo_t uplo, magma_int_t n, double alpha, magmaDouble_const_ptr dA, magma_int_t ldda, magmaDouble_const_ptr dx, magma_int_t incx, double beta, magmaDouble_ptr dy, magma_int_t incy, magma_queue_t queue )

Perform symmetric matrix-vector product, $$y = \alpha A x + \beta y,$$ where $$A$$ is symmetric.

Parameters
 [in] uplo Whether the upper or lower triangle of A is referenced. [in] n Number of rows and columns of A. n >= 0. [in] alpha Scalar $$\alpha$$ [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] dx DOUBLE PRECISION array on GPU device. The m element vector x of dimension (1 + (m-1)*incx). [in] incx Stride between consecutive elements of dx. incx != 0. [in] beta Scalar $$\beta$$ [in,out] dy DOUBLE PRECISION array on GPU device. The n element vector y of dimension (1 + (n-1)*incy). [in] incy Stride between consecutive elements of dy. incy != 0. [in] queue magma_queue_t Queue to execute in.
 void magma_ssymv ( magma_uplo_t uplo, magma_int_t n, float alpha, magmaFloat_const_ptr dA, magma_int_t ldda, magmaFloat_const_ptr dx, magma_int_t incx, float beta, magmaFloat_ptr dy, magma_int_t incy, magma_queue_t queue )

Perform symmetric matrix-vector product, $$y = \alpha A x + \beta y,$$ where $$A$$ is symmetric.

Parameters
 [in] uplo Whether the upper or lower triangle of A is referenced. [in] n Number of rows and columns of A. n >= 0. [in] alpha Scalar $$\alpha$$ [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] dx REAL array on GPU device. The m element vector x of dimension (1 + (m-1)*incx). [in] incx Stride between consecutive elements of dx. incx != 0. [in] beta Scalar $$\beta$$ [in,out] dy REAL array on GPU device. The n element vector y of dimension (1 + (n-1)*incy). [in] incy Stride between consecutive elements of dy. incy != 0. [in] queue magma_queue_t Queue to execute in.

Perform symmetric matrix-vector product, $$y = \alpha A x + \beta y,$$ where $$A$$ is symmetric.

Parameters
 [in] uplo Whether the upper or lower triangle of A is referenced. [in] n Number of rows and columns of A. n >= 0. [in] alpha Scalar $$\alpha$$ [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] dx COMPLEX_16 array on GPU device. The m element vector x of dimension (1 + (m-1)*incx). [in] incx Stride between consecutive elements of dx. incx != 0. [in] beta Scalar $$\beta$$ [in,out] dy COMPLEX_16 array on GPU device. The n element vector y of dimension (1 + (n-1)*incy). [in] incy Stride between consecutive elements of dy. incy != 0. [in] queue magma_queue_t Queue to execute in.
 magma_int_t magmablas_csymv_work ( magma_uplo_t uplo, magma_int_t n, magmaFloatComplex alpha, magmaFloatComplex_const_ptr dA, magma_int_t ldda, magmaFloatComplex_const_ptr dx, magma_int_t incx, magmaFloatComplex beta, magmaFloatComplex_ptr dy, magma_int_t incy, magmaFloatComplex_ptr dwork, magma_int_t lwork, magma_queue_t queue )

magmablas_csymv_work performs the matrix-vector operation:

y := alpha*A*x + beta*y,


where alpha and beta are scalars, x and y are n element vectors and A is an n by n complex symmetric matrix.

Parameters
 [in] uplo magma_uplo_t. On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows: = MagmaUpper: Only the upper triangular part of A is to be referenced. = MagmaLower: Only the lower triangular part of A is to be referenced. [in] n INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero. [in] alpha COMPLEX. On entry, ALPHA specifies the scalar alpha. [in] dA COMPLEX array of DIMENSION ( LDDA, n ). Before entry with UPLO = MagmaUpper, the leading n by n upper triangular part of the array A must contain the upper triangular part of the symmetric 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 part of the symmetric matrix and the strictly upper triangular part of A is not referenced. Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero. [in] ldda INTEGER. On entry, LDDA specifies the first dimension of A as declared in the calling (sub) program. LDDA must be at least max( 1, n ). It is recommended that ldda is multiple of 16. Otherwise performance would be deteriorated as the memory accesses would not be fully coalescent. [in] dx COMPLEX array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. [in] incx INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. [in] beta COMPLEX. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. [in,out] dy COMPLEX array of dimension at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y. On exit, Y is overwritten by the updated vector y. [in] incy INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. [in] dwork (workspace) COMPLEX array on the GPU, dimension (MAX(1, LWORK)), [in] lwork INTEGER. The dimension of the array DWORK. LWORK >= LDDA * ceil( N / NB_X ), where NB_X = 64. [in] queue magma_queue_t. Queue to execute in.

MAGMA implements csymv through two steps: 1) perform the multiplication in each thread block and put the intermediate value in dwork. 2) sum the intermediate values and store the final result in y.

magamblas_csymv_work requires users to provide a workspace, while magmablas_csymv is a wrapper routine allocating the workspace inside the routine and provides the same interface as cublas.

If users need to call csymv frequently, we suggest using magmablas_csymv_work instead of magmablas_csymv. As the overhead to allocate and free in device memory in magmablas_csymv would hurt performance. Our tests show that this penalty is about 10 Gflop/s when the matrix size is around 10000.

 magma_int_t magmablas_csymv ( magma_uplo_t uplo, magma_int_t n, magmaFloatComplex alpha, magmaFloatComplex_const_ptr dA, magma_int_t ldda, magmaFloatComplex_const_ptr dx, magma_int_t incx, magmaFloatComplex beta, magmaFloatComplex_ptr dy, magma_int_t incy, magma_queue_t queue )

magmablas_csymv performs the matrix-vector operation:

y := alpha*A*x + beta*y,


where alpha and beta are scalars, x and y are n element vectors and A is an n by n complex symmetric matrix.

Parameters
 [in] uplo magma_uplo_t. On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows: = MagmaUpper: Only the upper triangular part of A is to be referenced. = MagmaLower: Only the lower triangular part of A is to be referenced. [in] n INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero. [in] alpha COMPLEX. On entry, ALPHA specifies the scalar alpha. [in] dA COMPLEX array of DIMENSION ( LDDA, n ). Before entry with UPLO = MagmaUpper, the leading n by n upper triangular part of the array A must contain the upper triangular part of the symmetric 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 part of the symmetric matrix and the strictly upper triangular part of A is not referenced. Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero. [in] ldda INTEGER. On entry, LDDA specifies the first dimension of A as declared in the calling (sub) program. LDDA must be at least max( 1, n ). It is recommended that ldda is multiple of 16. Otherwise performance would be deteriorated as the memory accesses would not be fully coalescent. [in] dx COMPLEX array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. [in] incx INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. [in] beta COMPLEX. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. [in,out] dy COMPLEX array of dimension at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y. On exit, Y is overwritten by the updated vector y. [in] incy INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. [in] queue magma_queue_t Queue to execute in.

magmablas_zsymv_work performs the matrix-vector operation:

y := alpha*A*x + beta*y,


where alpha and beta are scalars, x and y are n element vectors and A is an n by n complex symmetric matrix.

Parameters
 [in] uplo magma_uplo_t. On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows: = MagmaUpper: Only the upper triangular part of A is to be referenced. = MagmaLower: Only the lower triangular part of A is to be referenced. [in] n INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero. [in] alpha COMPLEX_16. On entry, ALPHA specifies the scalar alpha. [in] dA COMPLEX_16 array of DIMENSION ( LDDA, n ). Before entry with UPLO = MagmaUpper, the leading n by n upper triangular part of the array A must contain the upper triangular part of the symmetric 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 part of the symmetric matrix and the strictly upper triangular part of A is not referenced. Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero. [in] ldda INTEGER. On entry, LDDA specifies the first dimension of A as declared in the calling (sub) program. LDDA must be at least max( 1, n ). It is recommended that ldda is multiple of 16. Otherwise performance would be deteriorated as the memory accesses would not be fully coalescent. [in] dx COMPLEX_16 array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. [in] incx INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. [in] beta COMPLEX_16. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. [in,out] dy COMPLEX_16 array of dimension at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y. On exit, Y is overwritten by the updated vector y. [in] incy INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. [in] dwork (workspace) COMPLEX_16 array on the GPU, dimension (MAX(1, LWORK)), [in] lwork INTEGER. The dimension of the array DWORK. LWORK >= LDDA * ceil( N / NB_X ), where NB_X = 64. [in] queue magma_queue_t. Queue to execute in.

MAGMA implements zsymv through two steps: 1) perform the multiplication in each thread block and put the intermediate value in dwork. 2) sum the intermediate values and store the final result in y.

magamblas_zsymv_work requires users to provide a workspace, while magmablas_zsymv is a wrapper routine allocating the workspace inside the routine and provides the same interface as cublas.

If users need to call zsymv frequently, we suggest using magmablas_zsymv_work instead of magmablas_zsymv. As the overhead to allocate and free in device memory in magmablas_zsymv would hurt performance. Our tests show that this penalty is about 10 Gflop/s when the matrix size is around 10000.

y := alpha*A*x + beta*y,