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MAGMA
1.5.0
Matrix Algebra for GPU and Multicore Architectures
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Functions | |
void | magmablas_zgemv_batched (magma_trans_t trans, magma_int_t m, magma_int_t n, magmaDoubleComplex alpha, magmaDoubleComplex **A_array, magma_int_t lda, magmaDoubleComplex **x_array, magma_int_t incx, magmaDoubleComplex beta, magmaDoubleComplex **y_array, magma_int_t incy, magma_int_t batchCount) |
This routine computes Y = alpha opt(A) x + beta y, on the GPU, where A = A_array[i],x = x_array[i] and y = y_array[i], i=[0,batchCount-1]. More... | |
magma_int_t | magmablas_zhemv_work (magma_uplo_t uplo, magma_int_t n, magmaDoubleComplex alpha, const magmaDoubleComplex *A, magma_int_t lda, const magmaDoubleComplex *x, magma_int_t incx, magmaDoubleComplex beta, magmaDoubleComplex *y, magma_int_t incy, magmaDoubleComplex *dwork, magma_int_t lwork) |
magmablas_zhemv_work performs the matrix-vector operation: More... | |
magma_int_t | magmablas_zhemv (magma_uplo_t uplo, magma_int_t n, magmaDoubleComplex alpha, const magmaDoubleComplex *A, magma_int_t lda, const magmaDoubleComplex *x, magma_int_t incx, magmaDoubleComplex beta, magmaDoubleComplex *y, magma_int_t incy) |
magmablas_zhemv performs the matrix-vector operation: More... | |
magma_int_t | magmablas_zhemv_mgpu_offset (magma_uplo_t uplo, magma_int_t n, magmaDoubleComplex alpha, magmaDoubleComplex **A, magma_int_t lda, magmaDoubleComplex **x, magma_int_t incx, magmaDoubleComplex beta, magmaDoubleComplex **y, magma_int_t incy, magmaDoubleComplex **work, magma_int_t lwork, magma_int_t num_gpus, magma_int_t nb, magma_int_t offset, magma_queue_t stream[][10]) |
magmablas_zhemv performs the matrix-vector operation: More... | |
magma_int_t | magmablas_zsymv_work (magma_uplo_t uplo, magma_int_t n, magmaDoubleComplex alpha, const magmaDoubleComplex *A, magma_int_t lda, const magmaDoubleComplex *x, magma_int_t incx, magmaDoubleComplex beta, magmaDoubleComplex *y, magma_int_t incy, magmaDoubleComplex *dwork, magma_int_t lwork) |
magmablas_zsymv_work performs the matrix-vector operation: More... | |
magma_int_t | magmablas_zsymv (magma_uplo_t uplo, magma_int_t n, magmaDoubleComplex alpha, const magmaDoubleComplex *A, magma_int_t lda, const magmaDoubleComplex *x, magma_int_t incx, magmaDoubleComplex beta, magmaDoubleComplex *y, magma_int_t incy) |
magmablas_zsymv performs the matrix-vector operation: More... | |
void magmablas_zgemv_batched | ( | magma_trans_t | trans, |
magma_int_t | m, | ||
magma_int_t | n, | ||
magmaDoubleComplex | alpha, | ||
magmaDoubleComplex ** | A_array, | ||
magma_int_t | lda, | ||
magmaDoubleComplex ** | x_array, | ||
magma_int_t | incx, | ||
magmaDoubleComplex | beta, | ||
magmaDoubleComplex ** | y_array, | ||
magma_int_t | incy, | ||
magma_int_t | batchCount | ||
) |
This routine computes Y = alpha opt(A) x + beta y, on the GPU, where A = A_array[i],x = x_array[i] and y = y_array[i], i=[0,batchCount-1].
This is a batched version.
[in] | trans | CHARACTER*1. On entry, TRANS specifies the form of op( A ) to be used in the matrix multiplication as follows: = 'N': op( A ) = A. = 'T': op( A ) = A**T. = 'C': op( A ) = A**H. |
[in] | m | INTEGER. On entry, M specifies the number of rows of the matrix opt(A). |
[in] | n | INTEGER. On entry, N specifies the number of columns of the matrix opt(A) |
[in] | alpha | COMPLEX*16. On entry, ALPHA specifies the scalar alpha. |
[in] | A_array | A = A_array[i] A: COMPLEX*16 array of dimension ( LDA, n ) on the GPU. |
[in] | lda | INTEGER. LDA specifies the leading dimension of A. |
[in] | x_array | x = x_array[i] x: COMPLEX*16 array of dimension n. |
[in] | beta | DOUBLE PRECISION. On entry, BETA specifies the scalar beta. |
[out] | y_array | y = y_array[i]: y: COMPLEX*16 array of dimension n. On exit y = alpha opt(A) x + beta y. |
[in] | batchCount | INTEGER number of pointers contained in A_array, x_array and y_array. |
magma_int_t magmablas_zhemv | ( | magma_uplo_t | uplo, |
magma_int_t | n, | ||
magmaDoubleComplex | alpha, | ||
const magmaDoubleComplex * | A, | ||
magma_int_t | lda, | ||
const magmaDoubleComplex * | x, | ||
magma_int_t | incx, | ||
magmaDoubleComplex | beta, | ||
magmaDoubleComplex * | y, | ||
magma_int_t | incy | ||
) |
magmablas_zhemv 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.
[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:
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[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] | A | 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 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] | lda | INTEGER. 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] | x | 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] | y | 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. |
magma_int_t magmablas_zhemv_mgpu_offset | ( | magma_uplo_t | uplo, |
magma_int_t | n, | ||
magmaDoubleComplex | alpha, | ||
magmaDoubleComplex ** | A, | ||
magma_int_t | lda, | ||
magmaDoubleComplex ** | x, | ||
magma_int_t | incx, | ||
magmaDoubleComplex | beta, | ||
magmaDoubleComplex ** | y, | ||
magma_int_t | incy, | ||
magmaDoubleComplex ** | work, | ||
magma_int_t | lwork, | ||
magma_int_t | num_gpus, | ||
magma_int_t | nb, | ||
magma_int_t | offset, | ||
magma_queue_t | stream[][10] | ||
) |
magmablas_zhemv 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.
[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:
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[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] | A | 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 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] | lda | INTEGER. 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] | x | 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] | y | 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. |
magma_int_t magmablas_zhemv_work | ( | magma_uplo_t | uplo, |
magma_int_t | n, | ||
magmaDoubleComplex | alpha, | ||
const magmaDoubleComplex * | A, | ||
magma_int_t | lda, | ||
const magmaDoubleComplex * | x, | ||
magma_int_t | incx, | ||
magmaDoubleComplex | beta, | ||
magmaDoubleComplex * | y, | ||
magma_int_t | incy, | ||
magmaDoubleComplex * | dwork, | ||
magma_int_t | lwork | ||
) |
magmablas_zhemv_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.
[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:
|
[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] | A | 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 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] | lda | INTEGER. 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] | x | 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] | y | 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 >= LDA * ceil( N / NB_X ), where NB_X = 64. |
MAGMA implements zhemv 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_zhemv_work requires users to provide a workspace, while magmablas_zhemv is a wrapper routine allocating the workspace inside the routine and provides the same interface as cublas.
If users need to call zhemv frequently, we suggest using magmablas_zhemv_work instead of magmablas_zhemv. As the overhead to allocate and free in device memory in magmablas_zhemv 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_zsymv | ( | magma_uplo_t | uplo, |
magma_int_t | n, | ||
magmaDoubleComplex | alpha, | ||
const magmaDoubleComplex * | A, | ||
magma_int_t | lda, | ||
const magmaDoubleComplex * | x, | ||
magma_int_t | incx, | ||
magmaDoubleComplex | beta, | ||
magmaDoubleComplex * | y, | ||
magma_int_t | incy | ||
) |
magmablas_zsymv 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.
[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:
|
[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] | A | 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 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] | lda | INTEGER. 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] | x | 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] | y | 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. |
magma_int_t magmablas_zsymv_work | ( | magma_uplo_t | uplo, |
magma_int_t | n, | ||
magmaDoubleComplex | alpha, | ||
const magmaDoubleComplex * | A, | ||
magma_int_t | lda, | ||
const magmaDoubleComplex * | x, | ||
magma_int_t | incx, | ||
magmaDoubleComplex | beta, | ||
magmaDoubleComplex * | y, | ||
magma_int_t | incy, | ||
magmaDoubleComplex * | dwork, | ||
magma_int_t | lwork | ||
) |
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.
[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:
|
[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] | A | 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 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] | lda | INTEGER. 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] | x | 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] | y | 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 >= LDA * ceil( N / NB_X ), where NB_X = 64. |
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.