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MAGMA
1.5.0
Matrix Algebra for GPU and Multicore Architectures
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Functions | |
void | magmablas_sgemv (magma_trans_t trans, magma_int_t m, magma_int_t n, float alpha, const float *A, magma_int_t lda, const float *x, magma_int_t incx, float beta, float *y, magma_int_t incy) |
This routine computes: 1) y = A x if trans == 'N' or 'n', alpha == 1, beta == 0, and incx == incy == 1 (using magmablas code) 2) y = alpha A^T x if trans == 'T' or 't', beta == 0, and incx == incy == 1 (using magmablas code) 3) y = alpha A^trans x + beta y otherwise, using CUBLAS. More... | |
void | magmablas_sgemv_tesla (magma_trans_t trans, magma_int_t m, magma_int_t n, float alpha, const float *A, magma_int_t lda, const float *x, magma_int_t incx, float beta, float *y, magma_int_t incy) |
This routine computes: 1) y = A x if trans == 'N' or 'n', alpha == 1, beta == 0, and incx == incy == 1 (using magmablas code) 2) y = alpha A^T x if trans == 'T' or 't', beta == 0, and incx == incy == 1 (using magmablas code) 3) y = alpha A^TRANS x + beta y otherwise, using CUBLAS. More... | |
magma_int_t | magmablas_ssymv_work (magma_uplo_t uplo, magma_int_t n, float alpha, const float *A, magma_int_t lda, const float *x, magma_int_t incx, float beta, float *y, magma_int_t incy, float *dwork, magma_int_t lwork) |
magmablas_ssymv_work performs the matrix-vector operation: More... | |
magma_int_t | magmablas_ssymv (magma_uplo_t uplo, magma_int_t n, float alpha, const float *A, magma_int_t lda, const float *x, magma_int_t incx, float beta, float *y, magma_int_t incy) |
magmablas_ssymv performs the matrix-vector operation: More... | |
magma_int_t | magmablas_ssymv_mgpu_offset (magma_uplo_t uplo, magma_int_t n, float alpha, float **A, magma_int_t lda, float **x, magma_int_t incx, float beta, float **y, magma_int_t incy, float **work, magma_int_t lwork, magma_int_t num_gpus, magma_int_t nb, magma_int_t offset, magma_queue_t stream[][10]) |
magmablas_ssymv performs the matrix-vector operation: More... | |
void magmablas_sgemv | ( | magma_trans_t | trans, |
magma_int_t | m, | ||
magma_int_t | n, | ||
float | alpha, | ||
const float * | A, | ||
magma_int_t | lda, | ||
const float * | x, | ||
magma_int_t | incx, | ||
float | beta, | ||
float * | y, | ||
magma_int_t | incy | ||
) |
This routine computes: 1) y = A x if trans == 'N' or 'n', alpha == 1, beta == 0, and incx == incy == 1 (using magmablas code) 2) y = alpha A^T x if trans == 'T' or 't', beta == 0, and incx == incy == 1 (using magmablas code) 3) y = alpha A^trans x + beta y otherwise, using CUBLAS.
[in] | trans | magma_trans_t On entry, TRANS specifies the operation to be performed as follows:
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[in] | m | INTEGER On entry, m specifies the number of rows of the matrix A. |
[in] | n | INTEGER On entry, n specifies the number of columns of the matrix A |
[in] | alpha | REAL On entry, ALPHA specifies the scalar alpha. |
[in] | A | REAL array of dimension ( LDA, n ) on the GPU. |
[in] | lda | INTEGER LDA specifies the leading dimension of A. |
[in] | x | REAL array of dimension n if trans == 'n' m if trans == 't' |
[in] | incx | Specifies the increment for the elements of X. INCX must not be zero. |
[in] | beta | REAL On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. |
[out] | y | REAL array of dimension m if trans == 'n' n if trans == 't' |
[in] | incy | Specifies the increment for the elements of Y. INCY must not be zero. |
void magmablas_sgemv_tesla | ( | magma_trans_t | trans, |
magma_int_t | m, | ||
magma_int_t | n, | ||
float | alpha, | ||
const float * | A, | ||
magma_int_t | lda, | ||
const float * | x, | ||
magma_int_t | incx, | ||
float | beta, | ||
float * | y, | ||
magma_int_t | incy | ||
) |
This routine computes: 1) y = A x if trans == 'N' or 'n', alpha == 1, beta == 0, and incx == incy == 1 (using magmablas code) 2) y = alpha A^T x if trans == 'T' or 't', beta == 0, and incx == incy == 1 (using magmablas code) 3) y = alpha A^TRANS x + beta y otherwise, using CUBLAS.
[in] | trans | magma_trans_t On entry, TRANS specifies the operation to be performed as follows:
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[in] | m | INTEGER On entry, M specifies the number of rows of the matrix A. |
[in] | n | INTEGER On entry, N specifies the number of columns of the matrix A |
[in] | alpha | REAL On entry, ALPHA specifies the scalar alpha. |
[in] | A | REAL array of dimension (LDA, N) on the GPU. |
[in] | lda | INTEGER LDA specifies the leading dimension of A. |
[in] | x | REAL array of dimension n if trans == 'n' m if trans == 't' |
[in] | incx | Specifies the increment for the elements of X. INCX must not be zero. |
[in] | beta | REAL On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. |
[out] | y | REAL array of dimension m if trans == 'n' n if trans == 't' |
[in] | incy | Specifies the increment for the elements of Y. INCY must not be zero. |
magma_int_t magmablas_ssymv | ( | magma_uplo_t | uplo, |
magma_int_t | n, | ||
float | alpha, | ||
const float * | A, | ||
magma_int_t | lda, | ||
const float * | x, | ||
magma_int_t | incx, | ||
float | beta, | ||
float * | y, | ||
magma_int_t | incy | ||
) |
magmablas_ssymv 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 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:
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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 | REAL. On entry, ALPHA specifies the scalar alpha. |
[in] | A | 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 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 | REAL 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 | REAL. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. |
[in,out] | y | REAL 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_ssymv_mgpu_offset | ( | magma_uplo_t | uplo, |
magma_int_t | n, | ||
float | alpha, | ||
float ** | A, | ||
magma_int_t | lda, | ||
float ** | x, | ||
magma_int_t | incx, | ||
float | beta, | ||
float ** | y, | ||
magma_int_t | incy, | ||
float ** | work, | ||
magma_int_t | lwork, | ||
magma_int_t | num_gpus, | ||
magma_int_t | nb, | ||
magma_int_t | offset, | ||
magma_queue_t | stream[][10] | ||
) |
magmablas_ssymv 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 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:
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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 | REAL. On entry, ALPHA specifies the scalar alpha. |
[in] | A | 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 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 | REAL 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 | REAL. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. |
[in,out] | y | REAL 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_ssymv_work | ( | magma_uplo_t | uplo, |
magma_int_t | n, | ||
float | alpha, | ||
const float * | A, | ||
magma_int_t | lda, | ||
const float * | x, | ||
magma_int_t | incx, | ||
float | beta, | ||
float * | y, | ||
magma_int_t | incy, | ||
float * | dwork, | ||
magma_int_t | lwork | ||
) |
magmablas_ssymv_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 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:
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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 | REAL. On entry, ALPHA specifies the scalar alpha. |
[in] | A | 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 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 | REAL 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 | REAL. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. |
[in,out] | y | REAL 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) REAL 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 ssymv 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_ssymv_work requires users to provide a workspace, while magmablas_ssymv is a wrapper routine allocating the workspace inside the routine and provides the same interface as cublas.
If users need to call ssymv frequently, we suggest using magmablas_ssymv_work instead of magmablas_ssymv. As the overhead to allocate and free in device memory in magmablas_ssymv would hurt performance. Our tests show that this penalty is about 10 Gflop/s when the matrix size is around 10000.