Functions | |
void | magma_sgemv (magma_trans_t transA, magma_int_t m, magma_int_t n, float alpha, const float *dA, magma_int_t ldda, const float *dx, magma_int_t incx, float beta, float *dy, magma_int_t incy) |
Perform matrix-vector product. | |
void | magma_sger (magma_int_t m, magma_int_t n, float alpha, const float *dx, magma_int_t incx, const float *dy, magma_int_t incy, float *dA, magma_int_t ldda) |
Perform rank-1 update, ![]() | |
void | magma_ssymv (magma_uplo_t uplo, magma_int_t n, float alpha, const float *dA, magma_int_t ldda, const float *dx, magma_int_t incx, float beta, float *dy, magma_int_t incy) |
Perform symmetric matrix-vector product, ![]() | |
void | magma_ssyr (magma_uplo_t uplo, magma_int_t n, float alpha, const float *dx, magma_int_t incx, float *dA, magma_int_t ldda) |
Perform symmetric rank-1 update, ![]() | |
void | magma_ssyr2 (magma_uplo_t uplo, magma_int_t n, float alpha, const float *dx, magma_int_t incx, const float *dy, magma_int_t incy, float *dA, magma_int_t ldda) |
Perform symmetric rank-2 update, ![]() | |
void | magma_strmv (magma_uplo_t uplo, magma_trans_t trans, magma_diag_t diag, magma_int_t n, const float *dA, magma_int_t ldda, float *dx, magma_int_t incx) |
Perform triangular matrix-vector product. | |
void | magma_strsv (magma_uplo_t uplo, magma_trans_t trans, magma_diag_t diag, magma_int_t n, const float *dA, magma_int_t ldda, float *dx, magma_int_t incx) |
Solve triangular matrix-vector system (one right-hand side). | |
void | magmablas_sgemv_conjv (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) |
SGEMV_CONJV performs the matrix-vector operation. | |
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. | |
void | magmablas_sswapblk (magma_order_t order, magma_int_t n, float *dA1T, magma_int_t lda1, float *dA2T, magma_int_t lda2, magma_int_t i1, magma_int_t i2, const magma_int_t *ipiv, magma_int_t inci, magma_int_t offset) |
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: | |
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: | |
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: |
void magma_sgemv | ( | magma_trans_t | transA, | |
magma_int_t | m, | |||
magma_int_t | n, | |||
float | alpha, | |||
const float * | dA, | |||
magma_int_t | ldda, | |||
const float * | dx, | |||
magma_int_t | incx, | |||
float | beta, | |||
float * | dy, | |||
magma_int_t | incy | |||
) |
Perform matrix-vector product.
(transA == MagmaNoTrans), or
(transA == MagmaTrans), or
(transA == MagmaConjTrans).
[in] | transA | Operation to perform on A. |
[in] | m | Number of rows of A. m >= 0. |
[in] | n | Number of columns of A. n >= 0. |
[in] | alpha | Scalar ![]() |
[in] | dA | REAL array of dimension (ldda,n), ldda >= max(1,m). The m-by-n matrix A, on GPU device. |
[in] | ldda | Leading dimension of dA. |
[in] | dx | REAL array on GPU device. If transA == MagmaNoTrans, the n element vector x of dimension (1 + (n-1)*incx); otherwise, the m element vector x of dimension (1 + (m-1)*incx). |
[in] | incx | Stride between consecutive elements of dx. incx != 0. |
[in] | beta | Scalar ![]() |
[in,out] | dy | REAL array on GPU device. If transA == MagmaNoTrans, the m element vector y of dimension (1 + (m-1)*incy); otherwise, the n element vector y of dimension (1 + (n-1)*incy). |
[in] | incy | Stride between consecutive elements of dy. incy != 0. |
void magma_sger | ( | magma_int_t | m, | |
magma_int_t | n, | |||
float | alpha, | |||
const float * | dx, | |||
magma_int_t | incx, | |||
const float * | dy, | |||
magma_int_t | incy, | |||
float * | dA, | |||
magma_int_t | ldda | |||
) |
Perform rank-1 update, .
[in] | m | Number of rows of A. m >= 0. |
[in] | n | Number of columns of A. n >= 0. |
[in] | alpha | Scalar ![]() |
[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] | 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,out] | dA | REAL array on GPU device. The m-by-n matrix A of dimension (ldda,n), ldda >= max(1,m). |
[in] | ldda | Leading dimension of dA. |
void magma_ssymv | ( | magma_uplo_t | uplo, | |
magma_int_t | n, | |||
float | alpha, | |||
const float * | dA, | |||
magma_int_t | ldda, | |||
const float * | dx, | |||
magma_int_t | incx, | |||
float | beta, | |||
float * | dy, | |||
magma_int_t | incy | |||
) |
Perform symmetric matrix-vector product, .
[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 ![]() |
[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 ![]() |
[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. |
void magma_ssyr | ( | magma_uplo_t | uplo, | |
magma_int_t | n, | |||
float | alpha, | |||
const float * | dx, | |||
magma_int_t | incx, | |||
float * | dA, | |||
magma_int_t | ldda | |||
) |
Perform symmetric rank-1 update, .
[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 ![]() |
[in] | dx | REAL array on GPU device. The n element vector x of dimension (1 + (n-1)*incx). |
[in] | incx | Stride between consecutive elements of dx. incx != 0. |
[in,out] | 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. |
void magma_ssyr2 | ( | magma_uplo_t | uplo, | |
magma_int_t | n, | |||
float | alpha, | |||
const float * | dx, | |||
magma_int_t | incx, | |||
const float * | dy, | |||
magma_int_t | incy, | |||
float * | dA, | |||
magma_int_t | ldda | |||
) |
Perform symmetric rank-2 update, .
[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 ![]() |
[in] | dx | REAL array on GPU device. The n element vector x of dimension (1 + (n-1)*incx). |
[in] | incx | Stride between consecutive elements of dx. incx != 0. |
[in] | 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,out] | 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. |
void magma_strmv | ( | magma_uplo_t | uplo, | |
magma_trans_t | trans, | |||
magma_diag_t | diag, | |||
magma_int_t | n, | |||
const float * | dA, | |||
magma_int_t | ldda, | |||
float * | dx, | |||
magma_int_t | incx | |||
) |
Perform triangular matrix-vector product.
(trans == MagmaNoTrans), or
(trans == MagmaTrans), or
(trans == MagmaConjTrans).
[in] | uplo | Whether the upper or lower triangle of A is referenced. |
[in] | trans | Operation to perform on A. |
[in] | diag | Whether the diagonal of A is assumed to be unit or non-unit. |
[in] | n | Number of rows and columns of A. n >= 0. |
[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 n element vector x of dimension (1 + (n-1)*incx). |
[in] | incx | Stride between consecutive elements of dx. incx != 0. |
void magma_strsv | ( | magma_uplo_t | uplo, | |
magma_trans_t | trans, | |||
magma_diag_t | diag, | |||
magma_int_t | n, | |||
const float * | dA, | |||
magma_int_t | ldda, | |||
float * | dx, | |||
magma_int_t | incx | |||
) |
Solve triangular matrix-vector system (one right-hand side).
(trans == MagmaNoTrans), or
(trans == MagmaTrans), or
(trans == MagmaConjTrans).
[in] | uplo | Whether the upper or lower triangle of A is referenced. |
[in] | trans | Operation to perform on A. |
[in] | diag | Whether the diagonal of A is assumed to be unit or non-unit. |
[in] | n | Number of rows and columns of A. n >= 0. |
[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,out] | dx | REAL array on GPU device. On entry, the n element RHS vector b of dimension (1 + (n-1)*incx). On exit, overwritten with the solution vector x. |
[in] | incx | Stride between consecutive elements of dx. incx != 0. |
void magmablas_sgemv_conjv | ( | 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 | |||
) |
SGEMV_CONJV performs the matrix-vector operation.
y := alpha*A*conj(x) + beta*y,
where alpha and beta are scalars, x and y are vectors and A is an m by n matrix.
[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 |
[in] | incx | Specifies the increment for the elements of X. INCX must not be zero. |
[in] | beta | DOUBLE 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 |
[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:
|
[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_sswapblk | ( | magma_order_t | order, | |
magma_int_t | n, | |||
float * | dA1T, | |||
magma_int_t | lda1, | |||
float * | dA2T, | |||
magma_int_t | lda2, | |||
magma_int_t | i1, | |||
magma_int_t | i2, | |||
const magma_int_t * | ipiv, | |||
magma_int_t | inci, | |||
magma_int_t | offset | |||
) |
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:
|
[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:
|
[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:
|
[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.