H2Lib  3.0
Data Fields
_dclusterbasis Struct Reference

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.
 Ranks, i.e., number of columns of $V_{t,\iota}$, type uint k[directions]
 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]
 Transfer matrices $E_{t',\iota}$ for all sons, type amatrix E[sons][directions]
uint sons
 Number of sons.
 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: