Functions for computing a low rank update for an h2matrix. More...

Functions
real	norm2_rkupdate_uniform (puniform u, uint k)
	Computes the Euclidean norm of the extended coupling matrix of the low rank update multiplied by weight matrices. More...

real	normfrob_rkupdate_uniform (puniform u, uint k)
	Computes the Frobenius norm of the extended coupling matrix of the low rank update multiplied by weight matrices. More...

void	rkupdate_h2matrix (prkmatrix R, ph2matrix Gh2, pclusteroperator rwf, pclusteroperator cwf, ptruncmode tm, real eps)
	Computes the low rank update $G \gets G + R$ . More...

pclusteroperator	prepare_row_clusteroperator (pclusterbasis rb, pclusterbasis cb, ptruncmode tm)
	Prepares the weights of the row clusterbasis used by rkupdate_h2matrix and the arithmetic functions in h2arith. More...

pclusteroperator	prepare_col_clusteroperator (pclusterbasis rb, pclusterbasis cb, ptruncmode tm)
	Prepares the weights of the column clusterbasis used by rkupdate_h2matrix and the arithmetic functions in h2arith. More...

Detailed Description

Functions for computing a low rank update for an h2matrix.

The functions in this module can be used to compute low rank updates for $\mathcal{H}^2$ -matrices. The module also provides functions to initialise the auxilliary structures required by the low rank update and the arithmetic functions in h2arith.

Function Documentation

real norm2_rkupdate_uniform	(	puniform	u,
		uint	k
	)

Computes the Euclidean norm of the extended coupling matrix of the low rank update multiplied by weight matrices.

Depending on given row and column clusterbasis of the uniform matrix this function computes one of the following four values via vector iteration:

$\left\lVert \begin{pmatrix} S_b & \\ & I_k \end{pmatrix} \right\rVert_2, \quad \left\lVert C_t \begin{pmatrix} S_b & \\ & I_k \end{pmatrix} \right\rVert_2, \quad \left\lVert \begin{pmatrix} S_b & \\ & I_k \end{pmatrix} C_s^* \right\rVert_2 \quad \text{or} \quad \left\lVert C_t \begin{pmatrix} S_b & \\ & I_k \end{pmatrix} C_s^* \right\rVert_2$

with $C_t$ =u->rb->Z and $C_s$ =u->cb->Z. $C_t$ is omitted if u->rb->Z==NULL and $C_s$ is omitted if u->cb->Z==NULL

Parameters

u	uniform object
k	rank of the low rank matrix

Returns: Approximation of the Euclidean norm of one of the matrices mentioned above.

real normfrob_rkupdate_uniform	(	puniform	u,
		uint	k
	)

Computes the Frobenius norm of the extended coupling matrix of the low rank update multiplied by weight matrices.

Depending on given row and column clusterbasis of the uniform matrix this functions computed one of the following four values:

$\left\lVert \begin{pmatrix} S_b & \\ & I_k \end{pmatrix} \right\rVert_F, \quad \left\lVert C_t \begin{pmatrix} S_b & \\ & I_k \end{pmatrix} \right\rVert_F, \quad \left\lVert \begin{pmatrix} S_b & \\ & I_k \end{pmatrix} C_s^* \right\rVert_F \quad \text{or} \quad \left\lVert C_t \begin{pmatrix} S_b & \\ & I_k \end{pmatrix} C_s^* \right\rVert_F$

with $C_t$ =u->rb->Z and $C_s$ =u->cb->Z. $C_t$ is omitted if u->rb->Z==NULL and $C_s$ is omitted if u->cb->Z==NULL

Parameters

u	uniform object
k	rank of the low rank matrix

Returns: Approximation of the Frobenius norm of one of the matrices mentioned above.

pclusteroperator prepare_col_clusteroperator	(	pclusterbasis	rb,
		pclusterbasis	cb,
		ptruncmode	tm
	)

Prepares the weights of the column clusterbasis used by rkupdate_h2matrix and the arithmetic functions in h2arith.

Parameters

rb	row clusterbasis
cb	column clusterbasis
tm	options for the total weights

Returns: new clusteroperator

pclusteroperator prepare_row_clusteroperator	(	pclusterbasis	rb,
		pclusterbasis	cb,
		ptruncmode	tm
	)

Prepares the weights of the row clusterbasis used by rkupdate_h2matrix and the arithmetic functions in h2arith.

Parameters

rb	row clusterbasis
cb	column clusterbasis
tm	options for the total weights

Returns: new clusteroperator

void rkupdate_h2matrix	(	prkmatrix	R,
		ph2matrix	Gh2,
		pclusteroperator	rwf,
		pclusteroperator	cwf,
		ptruncmode	tm,
		real	eps
	)

Computes the low rank update $G \gets G + R$ .

Parameters

R	Low-rank matrix .
Gh2	Target matrix .
rwf	has to be the father of the total weights of the row clusterbasis of C, e.g. initialised by prepare_row_clusteroperator
cwf	has to be the father of the total weights of the col clusterbasis of C, e.g. initialised by prepare_col_clusteroperator
tm	options of truncation
eps	tolerance of truncation