Uniform matrices with directional cluster bases. More...

Data Structures
struct	_duniform
	Uniform matrices with directional cluster bases. More...

Typedefs
typedef struct _duniform	duniform
	Uniform matrices with directional cluster bases.

typedef duniform *	pduniform
	Pointer to duniform objects.

typedef const duniform *	pcduniform
	Pointer to constant duniform objects.

Functions
pduniform	new_duniform (pdclusterbasis rb, uint rd, pdclusterbasis cb, uint cd)
	Create a new duniform object. More...

void	del_duniform (pduniform u)
	Delete a duniform object. More...

size_t	getsize_duniform (pcduniform u)
	Compute the storage size of a duniform object. More...

void	clear_duniform (pduniform u)
	Set a duniform matrix to zero. More...

void	copy_duniform (pcduniform src, pduniform trg)
	Copy a duniform matrix. More...

void	fastaddeval_duniform_avector (field alpha, pcduniform u, pcavector xt, pavector yt)
	Fast matrix-vector multiplication. More...

void	fastaddevaltrans_duniform_avector (field alpha, pcduniform u, pcavector xt, pavector yt)
	Fast adjoint matrix-vector multiplication. More...

void	slowaddeval_duniform_avector (field alpha, pcduniform u, pcavector x, pavector y)
	Slow matrix-vector multiplication $y \gets y + \alpha G x$ . More...

void	slowaddevaltrans_duniform_avector (field alpha, pcduniform u, pcavector x, pavector y)
	Slow adjoint matrix-vector multiplication $y \gets y + \alpha G^* x$ . More...

void	expand_duniform (field alpha, pcduniform u, pamatrix G)
	Convert a duniform matrix to a dense matrix. More...

real	norm2_fast_duniform (pcduniform u, pcdclusteroperator ro, pcdclusteroperator co)
	Will compute the Euclidean norm of the coupling matrix or of the product of one or two weight matrices with the coupling matrix. More...

real	normfrob_fast_duniform (pcduniform u, pcdclusteroperator ro, pcdclusteroperator co)
	Will compute the Frobenius norm of the coupling matrix or of the product of one or two weight matrices with the coupling matrix. More...

void	add_projected_duniform (pcduniform u, pcdclusteroperator ro, pcdclusteroperator co, pduniform unew)
	Addition of two duniform matrices even with different directional cluster basis. More...

Detailed Description

Uniform matrices with directional cluster bases.

Function Documentation

void add_projected_duniform	(	pcduniform	u,
		pcdclusteroperator	ro,
		pcdclusteroperator	co,
		pduniform	unew
	)

Addition of two duniform matrices even with different directional cluster basis.

Add to the duniform matrix $S_{b,\text{new}}$ another duniform matrix $\tilde S$ . Where $\tilde S$ depends on the equality of the row- and column basis. The matrix can be either

$\tilde S = S_{b}, \quad \tilde S = C_{t, rd} S_{b} \quad \tilde S = S_{b} C_{s, cd}^{*} \text{ or } \quad \tilde S = C_{t, rd} S_{b} C_{s, cd}^{*},$

where $rd, cd $ denotes the directions corresponding to $S_{b}$ .

Parameters

u	Source duniform matrix with corresponding .
ro	dclusteroperator describes the basis-change for the directional row cluster basis with corresponding weight matrix $C_{t, rd}$ .
co	dclusteroperator describes the basis-change for the directional column cluster basis with corresponding weight matrix $C_{s, cd}$ .
unew	Source duniform matrix with corresponding $S_{b, \text{new}}$ .

void clear_duniform ( pduniform u )

Set a duniform matrix to zero.

Parameters

u Matrix.

void copy_duniform	(	pcduniform	src,
		pduniform	trg
	)

Copy a duniform matrix.

Parameters

src	Source matrix.
trg	Target matrix.

void del_duniform ( pduniform u )

Delete a duniform object.

Parameters

u	Object to be deleted.

void expand_duniform	(	field	alpha,
		pcduniform	u,
		pamatrix	G
	)

Convert a duniform matrix to a dense matrix.

Adds $\alpha V_{t c} S_{ts} W_{s c}^*$ to a matrix $G$ .

Parameters

alpha	Scaling factor $\alpha$ .
u	Source matrix.
G	Target matrix.

void fastaddeval_duniform_avector	(	field	alpha,
		pcduniform	u,
		pcavector	xt,
		pavector	yt
	)

Fast matrix-vector multiplication.

Multiply the transformed coefficients in xt by the coupling matrix and add the result to yt.

Parameters

alpha	Scaling factor $\alpha$ .
u	Matrix.
xt	Transformed input vector as provided, e.g., by forward_dclusterbasis. Size `u->cb->ktree`.
yt	Transformed output vector, functions like backward_dclusterbasis can be used to obtain the final result. Size `u->rb->ktree`.

void fastaddevaltrans_duniform_avector	(	field	alpha,
		pcduniform	u,
		pcavector	xt,
		pavector	yt
	)

Fast adjoint matrix-vector multiplication.

Multiply the transformed coefficients in xt by the adjoint coupling matrix and add the result to yt.

Parameters

alpha	Scaling factor $\alpha$ .
u	Matrix.
xt	Transformed input vector as provided, e.g., by forward_dclusterbasis. Size `u->rb->ktree`
yt	Transformed output vector, functions like backward_dclusterbasis can be used to obtain the final result. Size `u->cb->ktree`.

size_t getsize_duniform ( pcduniform u )

Compute the storage size of a duniform object.

Parameters

u Object.

Returns: Storage size of u in bytes, not including the cluster bases.

pduniform new_duniform	(	pdclusterbasis	rb,
		uint	rd,
		pdclusterbasis	cb,
		uint	cd
	)

Create a new duniform object.

Parameters

rb	Row cluster basis.
rd	Direction for row basis.
cb	Column cluster basis.
cd	Direction for column basis.

Returns: New object.

real norm2_fast_duniform	(	pcduniform	u,
		pcdclusteroperator	ro,
		pcdclusteroperator	co
	)

Will compute the Euclidean norm of the coupling matrix or of the product of one or two weight matrices with the coupling matrix.

If no directional cluster operator is given, the function will compute $\| S_{b} \|_{2}$ . If a directional row $ ro $ or column cluster operators $ co $ are given

$\| C_{t, rd} S_{b} \|_{2}, \| S_{b} C_{s, cd}^{*} \|_{2} \text{ or } \| C_{t, rd} S_{b} C_{s, cd}^{*} \|_{2} ,$

where $rd, cd $ denotes the directions corresponding to $S_{b}$ , will be computed.

Parameters

u	duniform object for the coupling matrix.
ro	Optional directional row cluster operator. If `ro == NULL`, no $C_{t, rd}$ will be used.
co	Optional directional column cluster operator. If `c0 == NULL`, no $C_{s, cd}$ will be used.

Returns: Approximation of the Euclidean norm of the coupling matrix or of the product of one or two weight matrices with the coupling matrix.

real normfrob_fast_duniform	(	pcduniform	u,
		pcdclusteroperator	ro,
		pcdclusteroperator	co
	)

Will compute the Frobenius norm of the coupling matrix or of the product of one or two weight matrices with the coupling matrix.

If no directional cluster operator is given, the function will compute $\| S_{b} \|_{2}$ . If directional row $ ro $ or column cluster operators $ co $ are given

$\| C_{t, rd} S_{b} \|_{2}, \| S_{b} C_{s, cd}^{*} \|_{2} \text{ or } \| C_{t, rd} S_{b} C_{s, cd}^{*} \|_{2} ,$

where $rd, cd $ denotes the directions corresponding to $S_{b}$ , will be computed.

Parameters

u	duniform object for the coupling matrix.
ro	Optional directional row cluster operator. If `ro == NULL`, no $C_{t, rd}$ will be used.
co	Optional directional column cluster operator. If `co == NULL`, no $C_{s, cd}$ will be used.

Returns: Approximation of the Frbenius norm of the coupling matrix or of the product of one or two weight matrices with the coupling matrix.

void slowaddeval_duniform_avector	(	field	alpha,
		pcduniform	u,
		pcavector	x,
		pavector	y
	)

Slow matrix-vector multiplication $y \gets y + \alpha G x$ .

Intended for debugging, applies forward and backward transformation for each individual block instead of sharing transformed vectors.

Parameters

alpha	Scaling factor $\alpha$ .
u	matrix.
x	Input vector .
y	Output vector .

void slowaddevaltrans_duniform_avector	(	field	alpha,
		pcduniform	u,
		pcavector	x,
		pavector	y
	)

Slow adjoint matrix-vector multiplication $y \gets y + \alpha G^* x$ .

Intended for debugging, applies forward and backward transformation for each individual block instead of sharing transformed vectors.

Parameters

alpha	Scaling factor $\alpha$ .
u	matrix.
x	Input vector .
y	Output vector .

Data Structures

Typedefs

Functions

Detailed Description

Function Documentation