MAGMA  1.5.0
Matrix Algebra for GPU and Multicore Architectures
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single-complex precision

Functions

magma_int_t magmablas_chemv_work (magma_uplo_t uplo, magma_int_t n, magmaFloatComplex alpha, const magmaFloatComplex *A, magma_int_t lda, const magmaFloatComplex *x, magma_int_t incx, magmaFloatComplex beta, magmaFloatComplex *y, magma_int_t incy, magmaFloatComplex *dwork, magma_int_t lwork)
 magmablas_chemv_work performs the matrix-vector operation: More...
 
magma_int_t magmablas_chemv (magma_uplo_t uplo, magma_int_t n, magmaFloatComplex alpha, const magmaFloatComplex *A, magma_int_t lda, const magmaFloatComplex *x, magma_int_t incx, magmaFloatComplex beta, magmaFloatComplex *y, magma_int_t incy)
 magmablas_chemv performs the matrix-vector operation: More...
 
magma_int_t magmablas_chemv_mgpu_offset (magma_uplo_t uplo, magma_int_t n, magmaFloatComplex alpha, magmaFloatComplex **A, magma_int_t lda, magmaFloatComplex **x, magma_int_t incx, magmaFloatComplex beta, magmaFloatComplex **y, magma_int_t incy, magmaFloatComplex **work, magma_int_t lwork, magma_int_t num_gpus, magma_int_t nb, magma_int_t offset, magma_queue_t stream[][10])
 magmablas_chemv performs the matrix-vector operation: More...
 
magma_int_t magmablas_csymv_work (magma_uplo_t uplo, magma_int_t n, magmaFloatComplex alpha, const magmaFloatComplex *A, magma_int_t lda, const magmaFloatComplex *x, magma_int_t incx, magmaFloatComplex beta, magmaFloatComplex *y, magma_int_t incy, magmaFloatComplex *dwork, magma_int_t lwork)
 magmablas_csymv_work performs the matrix-vector operation: More...
 
magma_int_t magmablas_csymv (magma_uplo_t uplo, magma_int_t n, magmaFloatComplex alpha, const magmaFloatComplex *A, magma_int_t lda, const magmaFloatComplex *x, magma_int_t incx, magmaFloatComplex beta, magmaFloatComplex *y, magma_int_t incy)
 magmablas_csymv performs the matrix-vector operation: More...
 

Detailed Description

Function Documentation

magma_int_t magmablas_chemv ( magma_uplo_t  uplo,
magma_int_t  n,
magmaFloatComplex  alpha,
const magmaFloatComplex *  A,
magma_int_t  lda,
const magmaFloatComplex *  x,
magma_int_t  incx,
magmaFloatComplex  beta,
magmaFloatComplex *  y,
magma_int_t  incy 
)

magmablas_chemv 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 Hermitian matrix.

Parameters
[in]uplomagma_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]nINTEGER. On entry, N specifies the order of the matrix A. N must be at least zero.
[in]alphaCOMPLEX. On entry, ALPHA specifies the scalar alpha.
[in]ACOMPLEX 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 part of the Hermitian 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 Hermitian 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]ldaINTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ). It is recommended that lda is multiple of 16. Otherwise performance would be deteriorated as the memory accesses would not be fully coalescent.
[in]xCOMPLEX array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x.
[in]incxINTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero.
[in]betaCOMPLEX. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input.
[in,out]yCOMPLEX 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]incyINTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero.
magma_int_t magmablas_chemv_mgpu_offset ( magma_uplo_t  uplo,
magma_int_t  n,
magmaFloatComplex  alpha,
magmaFloatComplex **  A,
magma_int_t  lda,
magmaFloatComplex **  x,
magma_int_t  incx,
magmaFloatComplex  beta,
magmaFloatComplex **  y,
magma_int_t  incy,
magmaFloatComplex **  work,
magma_int_t  lwork,
magma_int_t  num_gpus,
magma_int_t  nb,
magma_int_t  offset,
magma_queue_t  stream[][10] 
)

magmablas_chemv 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 hermitian matrix.

Parameters
[in]uplomagma_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]nINTEGER. On entry, N specifies the order of the matrix A. N must be at least zero.
[in]alphaCOMPLEX. On entry, ALPHA specifies the scalar alpha.
[in]ACOMPLEX 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 part of the hermitian 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 hermitian 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]ldaINTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ). It is recommended that lda is multiple of 16. Otherwise performance would be deteriorated as the memory accesses would not be fully coalescent.
[in]xCOMPLEX array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x.
[in]incxINTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero.
[in]betaCOMPLEX. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input.
[in,out]yCOMPLEX 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]incyINTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero.
magma_int_t magmablas_chemv_work ( magma_uplo_t  uplo,
magma_int_t  n,
magmaFloatComplex  alpha,
const magmaFloatComplex *  A,
magma_int_t  lda,
const magmaFloatComplex *  x,
magma_int_t  incx,
magmaFloatComplex  beta,
magmaFloatComplex *  y,
magma_int_t  incy,
magmaFloatComplex *  dwork,
magma_int_t  lwork 
)

magmablas_chemv_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 Hermitian matrix.

Parameters
[in]uplomagma_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]nINTEGER. On entry, N specifies the order of the matrix A. N must be at least zero.
[in]alphaCOMPLEX. On entry, ALPHA specifies the scalar alpha.
[in]ACOMPLEX 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 part of the Hermitian 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 Hermitian 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]ldaINTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ). It is recommended that lda is multiple of 16. Otherwise performance would be deteriorated as the memory accesses would not be fully coalescent.
[in]xCOMPLEX array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x.
[in]incxINTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero.
[in]betaCOMPLEX. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input.
[in,out]yCOMPLEX 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]incyINTEGER. 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]lworkINTEGER. The dimension of the array DWORK. LWORK >= LDA * ceil( N / NB_X ), where NB_X = 64.

MAGMA implements chemv 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_chemv_work requires users to provide a workspace, while magmablas_chemv is a wrapper routine allocating the workspace inside the routine and provides the same interface as cublas.

If users need to call chemv frequently, we suggest using magmablas_chemv_work instead of magmablas_chemv. As the overhead to allocate and free in device memory in magmablas_chemv 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,
const magmaFloatComplex *  A,
magma_int_t  lda,
const magmaFloatComplex *  x,
magma_int_t  incx,
magmaFloatComplex  beta,
magmaFloatComplex *  y,
magma_int_t  incy 
)

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]uplomagma_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]nINTEGER. On entry, N specifies the order of the matrix A. N must be at least zero.
[in]alphaCOMPLEX. On entry, ALPHA specifies the scalar alpha.
[in]ACOMPLEX 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 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]ldaINTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ). It is recommended that lda is multiple of 16. Otherwise performance would be deteriorated as the memory accesses would not be fully coalescent.
[in]xCOMPLEX array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x.
[in]incxINTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero.
[in]betaCOMPLEX. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input.
[in,out]yCOMPLEX 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]incyINTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero.
magma_int_t magmablas_csymv_work ( magma_uplo_t  uplo,
magma_int_t  n,
magmaFloatComplex  alpha,
const magmaFloatComplex *  A,
magma_int_t  lda,
const magmaFloatComplex *  x,
magma_int_t  incx,
magmaFloatComplex  beta,
magmaFloatComplex *  y,
magma_int_t  incy,
magmaFloatComplex *  dwork,
magma_int_t  lwork 
)

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]uplomagma_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]nINTEGER. On entry, N specifies the order of the matrix A. N must be at least zero.
[in]alphaCOMPLEX. On entry, ALPHA specifies the scalar alpha.
[in]ACOMPLEX 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 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]ldaINTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ). It is recommended that lda is multiple of 16. Otherwise performance would be deteriorated as the memory accesses would not be fully coalescent.
[in]xCOMPLEX array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x.
[in]incxINTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero.
[in]betaCOMPLEX. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input.
[in,out]yCOMPLEX 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]incyINTEGER. 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]lworkINTEGER. The dimension of the array DWORK. LWORK >= LDA * ceil( N / NB_X ), where NB_X = 64.

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.