Low-rank dense routines

Set of low-rank routines for dense matrices. More...

Functions
int	starsh_dense_dsvfr (int size, double *S, double tol)
	Returns rank of double precision singular values. More...
void	starsh_dense_dlrsdd (int nrows, int ncols, double *D, int ldD, double *U, int ldU, double *V, int ldV, int *rank, int maxrank, double tol, double *work, int lwork, int *iwork)
	SVD approximation of a dense double precision matrix. More...
void	starsh_dense_dlrrsdd (int nrows, int ncols, double *D, int ldD, double *U, int ldU, double *V, int ldV, int *rank, int maxrank, int oversample, double tol, double *work, int lwork, int *iwork)
	Randomized SVD approximation of a dense double precision matrix. More...
void	starsh_dense_dlrqp3 (int nrows, int ncols, double *D, int ldD, double *U, int ldU, double *V, int ldV, int *rank, int maxrank, int oversample, double tol, double *work, int lwork, int *iwork)
	Rank-revealing QR approximation of a dense double precision matrix. More...
void	starsh_dense_dlrna (int nrows, int ncols, double *D, double *U, double *V, int *rank, int maxrank, double tol, double *work, int lwork, int *iwork)
	Fake approximation schemes, that returns rank=-1. More...
void	starsh_dense_dlrsdd_starpu (void *buffers[], void *cl_arg)
	STARPU kernel for DGESDD on a tile.
void	starsh_dense_dlrrsdd_starpu (void *buffers[], void *cl_arg)
	STARPU kernel for 1-way randomized SVD on a tile.
void	starsh_dense_dlrqp3_starpu (void *buffers[], void *cl_arg)
	STARPU kernel for RRQR on a tile.
void	starsh_dense_kernel_starpu (void *buffers[], void *cl_arg)
	STARPU kernel for matrix kernel.
void	starsh_dense_dgemm_starpu (void *buffers[], void *cl_arg)
	STARPU kernel for matrix kernel.
void	starsh_dense_fake_init_starpu (void *buffers[], void *cl_arg)
	STARPU kernel for matrix kernel.

Detailed Description

Set of low-rank routines for dense matrices.

Function Documentation

starsh_dense_dlrna()

void starsh_dense_dlrna	(	int	nrows,
		int	ncols,
		double *	D,
		double *	U,
		double *	V,
		int *	rank,
		int	maxrank,
		double	tol,
		double *	work,
		int	lwork,
		int *	iwork
	)

Fake approximation schemes, that returns rank=-1.

This function calls LAPACK and BLAS routines, so integer types are int instead of STARSH_int.

Parameters

[in]	nrows	Number of rows of a matrix.
[in]	ncols	Number of columns of a matrix.
[in,out]	D	Pointer to dense matrix.
[out]	U	Pointer to low-rank factor U.
[out]	V	Pointer to low-rank factor V.
[out]	rank	Address of rank variable.
[in]	maxrank	Maximum possible rank.
[in]	tol	Relative error for approximation.
[in]	work	Working array.
[in]	lwork	Size of work array.
[in]	iwork	Temporary integer array.

starsh_dense_dlrqp3()

void starsh_dense_dlrqp3	(	int	nrows,
		int	ncols,
		double *	D,
		int	ldD,
		double *	U,
		int	ldU,
		double *	V,
		int	ldV,
		int *	rank,
		int	maxrank,
		int	oversample,
		double	tol,
		double *	work,
		int	lwork,
		int *	iwork
	)

Rank-revealing QR approximation of a dense double precision matrix.

This function calls LAPACK and BLAS routines, so integer types are int instead of STARSH_int.

Parameters

[in]	nrows	Number of rows of a matrix.
[in]	ncols	Number of columns of a matrix.
[in,out]	D	Pointer to dense matrix.
[in]	ldD	leading dimensions of D.
[out]	U	Pointer to low-rank factor U.
[in]	ldU	leading dimensions of U.
[out]	V	Pointer to low-rank factor V.
[in]	ldV	leading dimensions of V.
[out]	rank	Address of rank variable.
[in]	maxrank	Maximum possible rank.
[in]	oversample
[in]	tol	Relative error for approximation.
[in]	work	Working array.
[in]	lwork	Size of work array.
[in]	iwork	Temporary integer array.

starsh_dense_dlrrsdd()

void starsh_dense_dlrrsdd	(	int	nrows,
		int	ncols,
		double *	D,
		int	ldD,
		double *	U,
		int	ldU,
		double *	V,
		int	ldV,
		int *	rank,
		int	maxrank,
		int	oversample,
		double	tol,
		double *	work,
		int	lwork,
		int *	iwork
	)

Randomized SVD approximation of a dense double precision matrix.

This function calls LAPACK and BLAS routines, so integer types are int instead of STARSH_int.

Parameters

[in]	nrows	Number of rows of a matrix.
[in]	ncols	Number of columns of a matrix.
[in,out]	D	Pointer to dense matrix.
[in]	ldD	leading dimensions of D.
[out]	U	Pointer to low-rank factor U.
[in]	ldU	leading dimensions of U.
[out]	V	Pointer to low-rank factor V.
[in]	ldV	leading dimensions of V.
[out]	rank	Address of rank variable.
[in]	maxrank	Maximum possible rank.
[in]	oversample	Size of oversampling subset.
[in]	tol	Relative error for approximation.
[in]	work	Working array.
[in]	lwork	Size of work array.
[in]	iwork	Temporary integer array.

starsh_dense_dlrsdd()

void starsh_dense_dlrsdd	(	int	nrows,
		int	ncols,
		double *	D,
		int	ldD,
		double *	U,
		int	ldU,
		double *	V,
		int	ldV,
		int *	rank,
		int	maxrank,
		double	tol,
		double *	work,
		int	lwork,
		int *	iwork
	)

SVD approximation of a dense double precision matrix.

This function calls LAPACK and BLAS routines, so integer types are int instead of STARSH_int.

Parameters

[in]	nrows	Number of rows of a matrix.
[in]	ncols	Number of columns of a matrix.
[in,out]	D	Pointer to dense matrix.
[in]	ldD	leading dimensions of D.
[out]	U	Pointer to low-rank factor U.
[in]	ldU	leading dimensions of U.
[out]	V	Pointer to low-rank factor V.
[in]	ldV	leading dimensions of V.
[out]	rank	Address of rank variable.
[in]	maxrank	Maximum possible rank.
[in]	tol	Relative error for approximation.
[in]	work	Working array.
[in]	lwork	Size of work array.
[in]	iwork	Temporary integer array.

starsh_dense_dsvfr()

int starsh_dense_dsvfr	(	int	size,
		double *	S,
		double	tol
	)

Returns rank of double precision singular values.

Tries ranks size, size-1, size-2 and so on. May be accelerated by binary search, but it requires additional temporary memory to be allocated.

Parameters

[in]	size	Number of singular values.
[in]	S	Array of singular values.
[in]	tol	Relative error tolerance.

Returns

rank in terms of relative error in Frobenius norm.