Representation of a directional cluster basis. More...

#include <dclusterbasis.h>

Data Fields
pcdcluster	t
	Corresponding directional cluster.

uint	directions
	Number of directions, matches `t->directions` if `t->direction > 0`, otherwise equals one.

uint *	k
	Ranks, i.e., number of columns of $V_{t,\iota}$ , type `uint k[directions]`

uint *	koff
	Partial sums of direction ranks for forward_dclusterbasis and backward_dclusterbasis, `koff[iota]=` $\sum_{\kappa=0}^{\iota-1} k_\kappa$ , type `uint koff[directions+1]`

uint	ktree
	Sum of ranks in the entire subtree.

uint	kbranch
	Maximum of rank sums along all branches in the subtree.

pamatrix	V
	Matrices $V_{t,\iota}$ , only stored if `t->sons==0`, type `amatrix V[directions]`

pamatrix *	E
	Transfer matrices $E_{t',\iota}$ for all sons, type `amatrix E[sons][directions]`

uint	sons
	Number of sons.

pdclusterbasis *	son
	Pointers to sons.

uint **	dirson
	Son directions corresponding to this cluster's directions, type `uint dirson[sons][directions]`

Detailed Description

Representation of a directional cluster basis.

A directional cluster basis is a family $(V_{t,\iota})_{t\in\ctI,\iota\in D_t}$ of matrices that assigns each cluster $t\in\ctI$ and each direction $\iota\in D_t$ corresponding to this cluster a basis of a subspace of $\bbbr^{\hat t}$ spanned by the columns of $V_{t,\iota}$ .

For the sake of efficiency, cluster bases are usually stored in nested representation, i.e., if $t$ has sons, $V_{t,\iota}$ is represented implicitly by $V_{t,\iota}|_{\hat t'}=V_{t',\kappa} E_{t',\iota}$ using transfer matrices $E_{t',\iota}$ , where $\kappa \in D_{t'}$ is a suitable direction of the son $t'$ .

The documentation for this struct was generated from the following file:

Library/dclusterbasis.h

Data Fields

Detailed Description