Representation of cluster operators used to describe weights and transformations of cluster bases. More...

Data Structures
struct	_clusteroperator
	Representation of a cluster operator. More...

Typedefs
typedef struct _clusteroperator	clusteroperator
	Representation of a cluster operator.

typedef clusteroperator*	pclusteroperator
	Pointer to clusteroperator object.

typedef const clusteroperator*	pcclusteroperator
	Pointer to constant clusterbasis object.

Functions
pclusteroperator	init_clusteroperator (pclusteroperator co, pccluster t)
	Initialize a clusteroperator object. More...

pclusteroperator	init_leaf_clusteroperator (pclusteroperator co, pccluster t)
	Initialize a clusteroperator object for a leaf. More...

void	uninit_clusteroperator (pclusteroperator co)
	Uninitializes a clusteroperator object. More...

pclusteroperator	new_clusteroperator (pccluster t)
	Create a new clusteroperator object. More...

pclusteroperator	new_leaf_clusteroperator (pccluster t)
	Creates a new clusteroperator object for a leaf. More...

void	del_clusteroperator (pclusteroperator co)
	Delete a clusteroperator object. More...

void	removesons_clusteroperator (pclusteroperator co)
	Turn this clusteroperator into a leaf. More...

void	ref_clusteroperator (pclusteroperator*ptr, pclusteroperator co)
	Set a pointer to a clusterbasis object, increase its reference counter, and decrease reference counter of original pointer target. More...

void	unref_clusteroperator (pclusteroperator co)
	Reduce the reference counter of a clusteroperator object. More...

void	update_clusteroperator (pclusteroperator co)
	Updates bookkeeping information. More...

void	resize_clusteroperator (pclusteroperator co, uint krow, uint kcol)
	Change the number of rows and columns of a cluster operator and resize `cb->C` accordingly. More...

pclusteroperator	identify_son_clusterweight_clusteroperator (pcclusteroperator cwf, pccluster t)
	Find son clusteroperator matching a given cluster. More...

pclusteroperator	build_from_cluster_clusteroperator (pccluster t)
	Construct a clusteroperator matching a cluster tree. More...

pclusteroperator	build_from_clusterbasis_clusteroperator (pcclusterbasis cb)
	Construct a clusteroperator matching a clusterbasis. More...

uint	getactives_clusteroperator ()
	Get number of active clusteroperator objects. More...

size_t	getsize_clusteroperator (pcclusteroperator co)
	Get the size of a given clusteroperator object. More...

void	print_tree_clusteroperator (pcclusteroperator co)
	Print the tree structure of a clusteroperator. More...

void	norm2diff_clusteroperator (pcclusteroperator co1, pcclusteroperator co2)
	Compute and print the norms and norm differences of the coefficient matrices of two cluster operators. More...

real	compareweights_clusteroperator (pcclusteroperator co1, pcclusteroperator co2)
	Compare two cluster weights. More...

pclusteroperator*	enumerate_clusteroperator (pccluster t, pclusteroperator co)
	Enumerate clusteroperator according to cluster tree. More...

void	basisproduct_clusteroperator (pcclusterbasis cb1, pcclusterbasis cb2, pclusteroperator pr)
	Compute the cluster basis product $Z_t = V_{1,t}^* V_{2,t}$ . More...

Detailed Description

Representation of cluster operators used to describe weights and transformations of cluster bases.

The clusteroperator class represents a cluster operator $(Z_t)_{t\in\mathcal{T}_{\mathcal{I}}}$ corresponding to a cluster basis $(V_t)_{t\in\mathcal{T}_{\mathcal{I}}}$ such that $Z_t$ and $V_t$ have the same number of columns.

Weight matrices for a cluster basis can be obtained using weight_clusterbasis_clusteroperator , total weight matrices for an h2matrix are available via totalweights_h2matrix.

Function Documentation

void basisproduct_clusteroperator	(	pcclusterbasis	cb1,
		pcclusterbasis	cb2,
		pclusteroperator	pr
	)

Compute the cluster basis product $Z_t = V_{1,t}^* V_{2,t}$ .

pr can only have sons if both cb1 and cb2 do. If pr is a leaf, currently either cb1 or cb2 has to be a leaf.

Parameters

cb1	First cluster basis.
cb2	Second cluster basis.
pr	Target cluster operator.

pclusteroperator build_from_cluster_clusteroperator ( pccluster t )

Construct a clusteroperator matching a cluster tree.

Constructs a clusteroperator for a cluster and its descendants.

Row and column numbers will be set to zero.

Parameters

t	Root cluster.

Returns: clusteroperator for t and its descendants.

pclusteroperator build_from_clusterbasis_clusteroperator ( pcclusterbasis cb )

Construct a clusteroperator matching a clusterbasis.

Constructs a clusteroperator for a clusterbasis and its descendants.

Row numbers will be set to zero, column numbers will be set to the ranks of the corresponding cluster basis.

Parameters

cb	Root clusterbasis.

Returns: clusteroperator for cb and its descendants.

real compareweights_clusteroperator	(	pcclusteroperator	co1,
		pcclusteroperator	co2
	)

Compare two cluster weights.

Compare the Gramians of two cluster operators $(Z_{t,1})_t$ and $(Z_{2,t})_t$ , i.e., compute $\frac{\|Z_{t,1}^* Z_{t,1} - Z_{t,2}^* Z_{t,2}\|_2} {\|Z_{t,1}^* Z_{t,1}\|_2\|_2}$ for all clusters and return the maximum. This approach makes the result invariant under orthogonal transformations applied to the rows.

Parameters

co1	First clusteroperator $Z_{1,t}$ .
co2	Second clusteroperator $Z_{2,t}$ .

Returns: Maximum of relative errors for all clusters in subtree.

void del_clusteroperator ( pclusteroperator co )

Delete a clusteroperator object.

Releases the storage corresponding to the object. If this clusteroperator references sons, these sons are unreferenced.

Only objects with cb->refs==0 may be deleted.

Parameters

co	Object to be deleted.

pclusteroperator* enumerate_clusteroperator	(	pccluster	t,
		pclusteroperator	co
	)

Enumerate clusteroperator according to cluster tree.

The clusteroperator elements are enumerated in an array of size t->desc. The enumeration starts with 0 assigned to the root and then proceeds with co->son[0] corresponding to the entries 1 to cb->son[0]->desc in the array and ending with co->son[sons-1] corresponding to the last t->son[sons-1]->desc entries.

Parameters

t	Cluster tree.
co	Cluster operator matching the cluster tree given by `t`.

Returns: Array of size t->desc containing pointers to the clusteroperator objects corresponding to co and its descendants.

uint getactives_clusteroperator ( )

Get number of active clusteroperator objects.

Returns: Number of active clusteroperator objects.

size_t getsize_clusteroperator ( pcclusteroperator co )

Get the size of a given clusteroperator object.

Yields the total size of this object and all its descendants.

Parameters

co	clusteroperator root.

Returns: Size of allocated storage in bytes.

pclusteroperator identify_son_clusterweight_clusteroperator	(	pcclusteroperator	cwf,
		pccluster	t
	)

Find son clusteroperator matching a given cluster.

Find a son of cwf matching the cluster t. Returns cwf if no son was found.

Parameters

cwf	Father clusteroperator.
t	Son cluster.

Returns: Son of cwf with cwf->son[i]->t==t if it exists and cwf otherwise.

pclusteroperator init_clusteroperator	(	pclusteroperator	co,
		pccluster	t
	)

Initialize a clusteroperator object.

Sets up the components of the object. If t is not a leaf, the array son is allocated, otherwise it is set to null.

Remarks: Should always be matched by a call to uninit_clusteroperator.

Parameters

co	Object to be initialized.
t	Corresponding cluster.

Returns: Initialized clusteroperator object.

pclusteroperator init_leaf_clusteroperator	(	pclusteroperator	co,
		pccluster	t
	)

Initialize a clusteroperator object for a leaf.

Sets up the components of the object. Sets son to null. If t->sons>0, this yields a partial cluster operator.

Remarks: Should always be matched by a call to uninit_clusteroperator.

Parameters

co	Object to be initialized.
t	Corresponding cluster.

Returns: Initialized clusteroperator object.

pclusteroperator new_clusteroperator ( pccluster t )

Create a new clusteroperator object.

Allocates storage for the object and sets up its components.

Remarks: Should always be matched by a call to del_clusteroperator. This call happens automatically if the last object referencing this object (see ref_clusteroperator) is deleted.

Parameters

t	corresponding cluster.

Returns: Returns the newly created clusteroperator object.

pclusteroperator new_leaf_clusteroperator ( pccluster t )

Creates a new clusteroperator object for a leaf.

Allocates storage for the object and sets up its components.

Remarks: Should always be matched by a call to del_clusteroperator. This call happens automatically if the last object referencing this object (see ref_clusteroperator) is deleted.

Parameters

t	Corresponding cluster.

Returns: Returns the newly created clusteroperator object.

void norm2diff_clusteroperator	(	pcclusteroperator	co1,
		pcclusteroperator	co2
	)

Compute and print the norms and norm differences of the coefficient matrices of two cluster operators.

Todo:: Usually a function called norm2diff should return a value, e.g., the maximal norm, instead of printing to stdout.

Parameters

co1	First clusteroperator.
co2	Second clusteroperator.

void print_tree_clusteroperator ( pcclusteroperator co )

Print the tree structure of a clusteroperator.

Parameters

co	Root clusteroperator.

void ref_clusteroperator	(	pclusteroperator*	ptr,
		pclusteroperator	co
	)

Set a pointer to a clusterbasis object, increase its reference counter, and decrease reference counter of original pointer target.

Parameters

ptr	Pointer to the pclusteroperator variable that will be changed.
co	clusteroperator that will be referenced.

void removesons_clusteroperator ( pclusteroperator co )

Turn this clusteroperator into a leaf.

Unreferences all sons, sets co->sons to zero and co->son to null.

Parameters

co	Target cluster operator.

void resize_clusteroperator	(	pclusteroperator	co,
		uint	krow,
		uint	kcol
	)

Change the number of rows and columns of a cluster operator and resize cb->C accordingly.

Parameters

co	Cluster operator that will be changed.
krow	New number of rows.
kcol	New number of columns.

void uninit_clusteroperator ( pclusteroperator co )

Uninitializes a clusteroperator object.

Invalidates pointers, freeing corresponding storage if appropriate, and prepares the object for deletion.

If this clusteroperator references sons, these sons are unreferenced.

Only objects with cb->refs==0 may be uninitialized.

Parameters

co	Object to be uninitialized.

void unref_clusteroperator ( pclusteroperator co )

Reduce the reference counter of a clusteroperator object.

If the reference counter reaches zero, the object is deleted.

Remarks: Use ref_clusteroperator with cb=NULL instead, since this guarantees that the pointer is properly invalidated.

Parameters

co	clusteroperator that will be unreferenced.

void update_clusteroperator ( pclusteroperator co )

Updates bookkeeping information.

This function should be called after the sons of a clusteroperator have been changed.

Remarks: This function will not update the sons recursively.

Parameters

co	clusteroperator that will be updated.

Data Structures

Typedefs

Functions

Detailed Description

Function Documentation