Functions for turning an amatrix, hmatrix or h2matrix into an h2matrix. More...

Data Structures
struct	_truncblock
	Description of basis and weights for one submatrix in the unification algorithm. More...

Typedefs
typedef struct _truncblock	truncblock
	Cluster basis and weights for use in the unification algorithm.

typedef truncblock *	ptruncblock
	Pointer to truncblock object.

Functions
ph2matrix	compress_amatrix_h2matrix (pcamatrix G, pcblock b, pctruncmode tm, real eps)
	Approximate a matrix, represented by an amatrix object, by an $\mathcal{H}^2$ -matrix. More...

ph2matrix	compress_hmatrix_h2matrix (pchmatrix G, pctruncmode tm, real eps)
	Approximate a hierarchical matrix, represented by an hmatrix object, by an $\mathcal{H}^2$ -matrix. More...

ph2matrix	compress_h2matrix_h2matrix (pch2matrix G, bool rbortho, bool cbortho, pctruncmode tm, real eps)
	Approximate an $\mathcal{H}^2$ -matrix, represented by an h2matrix object, by a recompressed $\mathcal{H}^2$ -matrix. More...

ph2matrix	compress_symmetric_h2matrix_h2matrix (pch2matrix G, bool rbortho, pctruncmode tm, real eps)
	Approximate a symmetric $\mathcal{H}^2$ -matrix, represented by an h2matrix object, by a recompressed $\mathcal{H}^2$ -matrix. More...

void	rowweights_h2matrix (pch2matrix G, pcclusteroperator rbw, pcclusteroperator cbw, pctruncmode tm, pclusteroperator rlw)
	Prepare local row weights for a given $\mathcal{H}^2$ -matrix. More...

void	colweights_h2matrix (pch2matrix G, pcclusteroperator rbw, pcclusteroperator cbw, pctruncmode tm, pclusteroperator clw)
	Prepare local column weights for a given $\mathcal{H}^2$ -matrix. More...

void	localweights_h2matrix (pch2matrix G, pcclusteroperator rbw, pcclusteroperator cbw, pctruncmode tm, pclusteroperator rlw, pclusteroperator clw)
	Prepare local weights for a given $\mathcal{H}^2$ -matrix. More...

void	accumulate_clusteroperator (pcclusterbasis cb, pctruncmode tm, pclusteroperator lw)
	Merge the local weights of clusters with the weights inherited from their ancestors in order to obtain total weights. More...

void	totalweights_h2matrix (pch2matrix G, bool rbortho, bool cbortho, pctruncmode tm, pclusteroperator rw, pclusteroperator cw)
	Construct total weights for a given $\mathcal{H}^2$ -matrix. More...

void	truncate_clusterbasis (pcclusterbasis cb, pcclusteroperator cw, pcclusteroperator clw, pctruncmode tm, real eps, pclusterbasis cbnew, pclusteroperator old2new)
	Compute a truncated cluster basis. More...

pclusterbasis	buildrowbasis_h2matrix (pch2matrix G, bool rbortho, bool cbortho, pctruncmode tm, real eps, pclusteroperator old2new)
	Construct an improved row basis for an $\mathcal{H}^2$ -matrix. More...

pclusterbasis	buildcolbasis_h2matrix (pch2matrix G, bool rbortho, bool cbortho, pctruncmode tm, real eps, pclusteroperator old2new)
	Construct an improved row basis for an $\mathcal{H}^2$ -matrix. More...

void	truncrowbasis_h2matrix (ph2matrix G, bool rbortho, bool cbortho, pctruncmode tm, real eps, pclusterbasis rbnew, pclusteroperator old2new)
	Construct an improved row basis for an $\mathcal{H}^2$ -matrix. More...

void	trunccolbasis_h2matrix (ph2matrix G, bool rbortho, bool cbortho, pctruncmode tm, real eps, pclusterbasis cbnew, pclusteroperator old2new)
	Construct an improved column basis for an $\mathcal{H}^2$ -matrix. More...

ph2matrix	build_projected_h2matrix (pch2matrix G, pclusterbasis rb, pcclusteroperator ro, pclusterbasis cb, pcclusteroperator co)
	Construct an $\mathcal{H}^2$ -matrix approximation of a given $\mathcal{H}^2$ -matrix in new cluster bases by blockwise projection. More...

void	project_inplace_h2matrix (ph2matrix G, pclusterbasis rb, pcclusteroperator ro, pclusterbasis cb, pcclusteroperator co)
	Switch the cluster bases of an $\mathcal{H}^2$ -matrix by applying blockwise projections. More...

void	orthoweight_clusterbasis (pclusterbasis cb)
	Compute cluster weights and store them in the cluster basis. More...

void	totalweight_row_clusteroperator (pclusterbasis rb, pclusteroperator rw, pctruncmode tm)
	Compute total row weights of a matrix. More...

void	totalweight_col_clusteroperator (pclusterbasis cb, pclusteroperator cw, pctruncmode tm)
	Compute total column weights of a matrix. More...

void	truncate_inplace_clusterbasis (pclusterbasis cb, pclusteroperator cw, pctruncmode tm, real eps)
	Replace a cluster basis with a truncated basis. More...

void	recompress_inplace_h2matrix (ph2matrix G, pctruncmode tm, real eps)
	Recompress an $\mathcal{H}^2$ -matrix. More...

ptruncblock	new_truncblock (pcclusterbasis cb, pcclusteroperator cw, ptruncblock next)
	Create a new truncblock object. More...

void	del_truncblock (ptruncblock tb)
	Delete a list of truncblock objects. More...

ptruncblock	reverse_truncblock (ptruncblock tb)
	Reverse the order of a list of truncblock objects. More...

pclusterbasis	unify_clusterbasis (pccluster t, ptruncblock tb, pctruncmode tm, real eps, pclusteroperator*cw)
	Construct a unified cluster basis. More...

void	unify_h2matrix (ph2matrix G, pclusteroperatorrw1, pclusteroperatorcw1, pctruncmode tm, real eps, pclusteroperatorrw, pclusteroperatorcw)
	Unify $\mathcal{H}^2$ -submatrices into a large $\mathcal{H}^2$ -matrix. More...

void	unify_parallel_h2matrix (ph2matrix G, uint pardepth, pclusteroperatorrw1, pclusteroperatorcw1, pctruncmode tm, real eps, pclusteroperatorrw, pclusteroperatorcw)
	Unify $\mathcal{H}^2$ -submatrices into a large $\mathcal{H}^2$ -matrix, experimental parallel implementation. More...

void	convert_rkmatrix_uniform (pcrkmatrix r, puniform u, pctruncmode tm, pclusteroperatorrw, pclusteroperatorcw)
	Converts an rkmatrix into a uniform matrix. More...

pclusterbasis	buildrowbasis_hmatrix (pchmatrix G, pctruncmode tm, real eps)
	Construct a row basis for a hierarchical matrix. More...

pclusterbasis	buildcolbasis_hmatrix (pchmatrix G, pctruncmode tm, real eps)
	Construct a column basis for a hierarchical matrix. More...

ph2matrix	build_projected_hmatrix_h2matrix (pchmatrix G, pclusterbasis rb, pclusterbasis cb)
	Construct an $\mathcal{H}^2$ -matrix approximation of a given hierarchical matrix in given cluster bases by blockwise projection. More...

pclusterbasis	buildrowbasis_amatrix (pcamatrix G, pcblock b, pctruncmode tm, real eps)
	Construct a row basis for an array matrix. More...

pclusterbasis	buildcolbasis_amatrix (pcamatrix G, pcblock b, pctruncmode tm, real eps)
	Construct a column basis for an array matrix. More...

ph2matrix	build_projected_amatrix_h2matrix (pcamatrix G, pcblock b, pclusterbasis rb, pclusterbasis cb)
	Construct an $\mathcal{H}^2$ -matrix approximation of a given array matrix in given cluster bases by blockwise projection. More...

Detailed Description

Functions for turning an amatrix, hmatrix or h2matrix into an h2matrix.

The functions in this module can be used to convert array matrices and hierarchical matrices into $\mathcal{H}^2$ -matrices and to recompress $\mathcal{H}^2$ -matrices. The module also provides a unification algorithm that takes a block matrix consisting of independent $\mathcal{H}^2$ -matrices and turns it into an $\mathcal{H}^2$ -matrix with unified row and column bases.

Function Documentation

void accumulate_clusteroperator	(	pcclusterbasis	cb,
		pctruncmode	tm,
		pclusteroperator	lw
	)

Merge the local weights of clusters with the weights inherited from their ancestors in order to obtain total weights.

Finds matrices $Z_t$ with $P_t Z_t = \begin{pmatrix} Z^+_t\\ \zeta_{\rm age} Z_{t^+} E_t^* \end{pmatrix}$ , where $t^+$ is the father of the cluster $t$ and $P_t$ is orthogonal.

Parameters

cb	Cluster basis.
tm	Truncation mode, supplies $\zeta_{\rm age}$ .
lw	Cluster operator, contains and is overwritten by .

ph2matrix build_projected_amatrix_h2matrix	(	pcamatrix	G,
		pcblock	b,
		pclusterbasis	rb,
		pclusterbasis	cb
	)

Construct an $\mathcal{H}^2$ -matrix approximation of a given array matrix in given cluster bases by blockwise projection.

Parameters

G	Original matrix.
b	Block tree.
rb	New row basis.
cb	New column basis.

Returns: Approximating $\mathcal{H}^2$ -matrix.

ph2matrix build_projected_h2matrix	(	pch2matrix	G,
		pclusterbasis	rb,
		pcclusteroperator	ro,
		pclusterbasis	cb,
		pcclusteroperator	co
	)

Construct an $\mathcal{H}^2$ -matrix approximation of a given $\mathcal{H}^2$ -matrix in new cluster bases by blockwise projection.

Parameters

G	Original matrix.
rb	New row basis.
ro	Basis change from old row basis `G->rb` to new basis `rb`.
cb	New column basis.
co	Basis change from old column basis `G->cb` to new basis `cb`.

Returns: Approximating $\mathcal{H}^2$ -matrix.

ph2matrix build_projected_hmatrix_h2matrix	(	pchmatrix	G,
		pclusterbasis	rb,
		pclusterbasis	cb
	)

Construct an $\mathcal{H}^2$ -matrix approximation of a given hierarchical matrix in given cluster bases by blockwise projection.

Parameters

G	Original matrix.
rb	New row basis.
cb	New column basis.

Returns: Approximating $\mathcal{H}^2$ -matrix.

pclusterbasis buildcolbasis_amatrix	(	pcamatrix	G,
		pcblock	b,
		pctruncmode	tm,
		real	eps
	)

Construct a column basis for an array matrix.

Parameters

G	Original matrix .
b	Block tree.
tm	Truncation mode.
eps	Truncation accuracy.

Returns: New column cluster basis.

pclusterbasis buildcolbasis_h2matrix	(	pch2matrix	G,
		bool	rbortho,
		bool	cbortho,
		pctruncmode	tm,
		real	eps,
		pclusteroperator	old2new
	)

Construct an improved row basis for an $\mathcal{H}^2$ -matrix.

Parameters

G	Original matrix .
rbortho	Set if the original row basis is orthogonal, this allows the algorithm to avoid computing row weights.
cbortho	Set if the original column basis is orthogonal, this allows the algorithm to avoid computing column weights.
tm	Truncation mode.
eps	Truncation accuracy.
old2new	Cluster operator describing the change of basis from `G->cb` to the new basis.

Returns: New column cluster basis.

pclusterbasis buildcolbasis_hmatrix	(	pchmatrix	G,
		pctruncmode	tm,
		real	eps
	)

Construct a column basis for a hierarchical matrix.

Parameters

G	Original matrix .
tm	Truncation mode.
eps	Truncation accuracy.

Returns: New column cluster basis.

pclusterbasis buildrowbasis_amatrix	(	pcamatrix	G,
		pcblock	b,
		pctruncmode	tm,
		real	eps
	)

Construct a row basis for an array matrix.

Parameters

G	Original matrix .
b	Block tree.
tm	Truncation mode.
eps	Truncation accuracy.

Returns: New row cluster basis.

pclusterbasis buildrowbasis_h2matrix	(	pch2matrix	G,
		bool	rbortho,
		bool	cbortho,
		pctruncmode	tm,
		real	eps,
		pclusteroperator	old2new
	)

Construct an improved row basis for an $\mathcal{H}^2$ -matrix.

Parameters

G	Original matrix .
rbortho	Set if the original row basis is orthogonal, this allows the algorithm to avoid computing row weights.
cbortho	Set if the original column basis is orthogonal, this allows the algorithm to avoid computing column weights.
tm	Truncation mode.
eps	Truncation accuracy.
old2new	Cluster operator describing the change of basis from `G->rb` to the new basis.

Returns: New row cluster basis.

pclusterbasis buildrowbasis_hmatrix	(	pchmatrix	G,
		pctruncmode	tm,
		real	eps
	)

Construct a row basis for a hierarchical matrix.

Parameters

G	Original matrix .
tm	Truncation mode.
eps	Truncation accuracy.

Returns: New row cluster basis.

void colweights_h2matrix	(	pch2matrix	G,
		pcclusteroperator	rbw,
		pcclusteroperator	cbw,
		pctruncmode	tm,
		pclusteroperator	clw
	)

Prepare local column weights for a given $\mathcal{H}^2$ -matrix.

Finds matrices $Z^+_s$ with $\begin{pmatrix} G_{t_1,s}\\ \vdots\\ G_{t_\tau,s} \end{pmatrix} = P_s Z^+_s W_s^*$ , where $(t_1,s),\ldots,(t_\tau,s)$ are the admissible blocks connected to the column cluster $s$ and $P_s$ is orthogonal.

Remarks: If row and column weights have to be computed, consider using localweights_h2matrix.

Parameters

G	Source matrix .
rbw	Basis weights for the row basis, can be obtained by weight_clusterbasis_clusteroperator. If this is a null pointer, the row basis is assumed to be orthogonal, so no weights are required.
cbw	Basis weights for the column basis, can be obtained by weight_clusterbasis_clusteroperator. If this is a null pointer, the column basis is assumed to be orthogonal, so no weights are required.
tm	Truncation mode.
clw	Will be filled with the local column weights, can be initialized by build_from_clusterbasis_clusteroperator. If the cluster operator already contains something, the local weights will be merged with the original contents.

ph2matrix compress_amatrix_h2matrix	(	pcamatrix	G,
		pcblock	b,
		pctruncmode	tm,
		real	eps
	)

Approximate a matrix, represented by an amatrix object, by an $\mathcal{H}^2$ -matrix.

Parameters

G	Source matrix .
b	Block tree, rows and columns have to match .
tm	Truncation mode.
eps	Truncation accuracy.

Returns: $\mathcal{H}^2$ -matrix approximation of .

ph2matrix compress_h2matrix_h2matrix	(	pch2matrix	G,
		bool	rbortho,
		bool	cbortho,
		pctruncmode	tm,
		real	eps
	)

Approximate an $\mathcal{H}^2$ -matrix, represented by an h2matrix object, by a recompressed $\mathcal{H}^2$ -matrix.

Parameters

G	Source matrix .
rbortho	Set if the original row basis is orthogonal, this allows the algorithm to avoid computing row weights.
cbortho	Set if the original column basis is orthogonal, this allows the algorithm to avoid computing column weights.
tm	Truncation mode.
eps	Truncation accuracy.

Returns: $\mathcal{H}^2$ -matrix approximation of .

ph2matrix compress_hmatrix_h2matrix	(	pchmatrix	G,
		pctruncmode	tm,
		real	eps
	)

Approximate a hierarchical matrix, represented by an hmatrix object, by an $\mathcal{H}^2$ -matrix.

Parameters

G	Source matrix .
tm	Truncation mode.
eps	Truncation accuracy.

Returns: $\mathcal{H}^2$ -matrix approximation of .

ph2matrix compress_symmetric_h2matrix_h2matrix	(	pch2matrix	G,
		bool	rbortho,
		pctruncmode	tm,
		real	eps
	)

Approximate a symmetric $\mathcal{H}^2$ -matrix, represented by an h2matrix object, by a recompressed $\mathcal{H}^2$ -matrix.

Since the matrix is symmetric, we assume the row and column cluster basis are identical, i.e., G->rb==G->cb.

Parameters

G	Source matrix .
rbortho	Set if the original row and column basis is orthogonal, this allows the algorithm to avoid computing row weights.
tm	Truncation mode.
eps	Truncation accuracy.

Returns: $\mathcal{H}^2$ -matrix approximation of .

void convert_rkmatrix_uniform	(	pcrkmatrix	r,
		puniform	u,
		pctruncmode	tm,
		pclusteroperator*	rw,
		pclusteroperator*	cw
	)

Converts an rkmatrix into a uniform matrix.

Returns an exact representation of an rkmatrix by a new uniform matrix with new orthogonal row and column cluster bases and also computes corresponding total weight matrices. This function is intended for use with unify_h2matrix in order to convert rkmatrix approximations of leaves into h2matrix objects.

Parameters

r	Original matrix.
u	Uniform matrix, will be overwritten.
tm	Truncation mode, used to set of weight matrices correctly.
rw	If not a null pointer, will be set to point to a new clusteroperator tree containing the total row weights of the new uniform matrix.
cw	If not a null pointer, will be set to point to a new clusteroperator tree containing the total column weights of the new uniform matrix.

void del_truncblock ( ptruncblock tb )

Delete a list of truncblock objects.

Parameters

tb	Head of list.

void localweights_h2matrix	(	pch2matrix	G,
		pcclusteroperator	rbw,
		pcclusteroperator	cbw,
		pctruncmode	tm,
		pclusteroperator	rlw,
		pclusteroperator	clw
	)

Prepare local weights for a given $\mathcal{H}^2$ -matrix.

Finds matrices $Z^+_t$ with $\begin{pmatrix} G_{t,s_1} & \cdots & G_{t,s_\sigma} \end{pmatrix} = V_t (Z^+_t)^* P_t$ , where $(t,s_1),\ldots,(t,s_\sigma)$ are the admissible blocks connected to the row cluster $t$ and $P_t$ is orthogonal and matrices $Z^+_s$ with $\begin{pmatrix} G_{t_1,s}\\ \vdots\\ G_{t_\tau,s} \end{pmatrix} = Z^+_s W_s^* P_s$ , where $(t_1,s),\ldots,(t_\tau,s)$ are the admissible blocks connected to the column cluster $s$ and $P_s$ is orthogonal.

This algorithm is more efficient than calling rowweights_h2matrix and colweights_h2matrix individually, since it passes only once through the matrix.

Parameters

G	Source matrix .
rbw	Basis weights for the row basis, can be obtained by weight_clusterbasis_clusteroperator. If this is a null pointer, the row basis is assumed to be orthogonal, so no weights are required.
cbw	Basis weights for the column basis, can be obtained by weight_clusterbasis_clusteroperator. If this is a null pointer, the column basis is assumed to be orthogonal, so no weights are required.
tm	Truncation mode.
rlw	Will be filled with the local row weights, can be initialized by build_from_clusterbasis_clusteroperator. If the cluster operator already contains something, the local weights will be merged with the original contents.
clw	Will be filled with the local column weights, can be initialized by build_from_clusterbasis_clusteroperator. If the cluster operator already contains something, the local weights will be merged with the original contents.

ptruncblock new_truncblock	(	pcclusterbasis	cb,
		pcclusteroperator	cw,
		ptruncblock	next
	)

Create a new truncblock object.

Parameters

cb	Cluster basis of the corresponding submatrix.
cw	Total weights for `cb`.
next	Next truncblock in list.

Returns: Returns the newly created truncblock object.

void orthoweight_clusterbasis ( pclusterbasis cb )

Compute cluster weights and store them in the cluster basis.

The weights are the factors $R_t$ of the skinny QR decomposition $V_t = Q_t R_t$ .

This function is similar to weight_clusterbasis_clusteroperator, but stores the basis weights in cb->Z instead of in a separate clusteroperator.

Parameters

cb	Target cluster basis, its field `Z` will be overwritten.

void project_inplace_h2matrix	(	ph2matrix	G,
		pclusterbasis	rb,
		pcclusteroperator	ro,
		pclusterbasis	cb,
		pcclusteroperator	co
	)

Switch the cluster bases of an $\mathcal{H}^2$ -matrix by applying blockwise projections.

Parameters

G	Original matrix, will be overwritten by projected matrix.
rb	New row basis.
ro	Basis change from old row basis `G->rb` to new basis `rb`.
cb	New column basis.
co	Basis change from old column basis `G->cb` to new basis `cb`

void recompress_inplace_h2matrix	(	ph2matrix	G,
		pctruncmode	tm,
		real	eps
	)

Recompress an $\mathcal{H}^2$ -matrix.

Replace an $\mathcal{H}^2$ -matrix by a recompressed matrix.

Parameters

G	Original matrix, will be overwritten by the recompressed matrix.
tm	Truncation mode.
eps	Truncation accuracy.

ptruncblock reverse_truncblock ( ptruncblock tb )

Reverse the order of a list of truncblock objects.

Since new blocks are added at the head of a list, reversing the list restores the original order.

Parameters

tb	Head of original list, will be changed.

Returns: Head of reversed list.

void rowweights_h2matrix	(	pch2matrix	G,
		pcclusteroperator	rbw,
		pcclusteroperator	cbw,
		pctruncmode	tm,
		pclusteroperator	rlw
	)

Prepare local row weights for a given $\mathcal{H}^2$ -matrix.

Finds matrices $Z^+_t$ with $\begin{pmatrix} G_{t,s_1} & \cdots & G_{t,s_\sigma} \end{pmatrix} = V_t (Z^+_t)^* P_t^*$ , where $(t,s_1),\ldots,(t,s_\sigma)$ are the admissible blocks connected to the row cluster $t$ and $P_t$ is orthogonal.

Remarks: If row and column weights have to be computed, consider using localweights_h2matrix.

Parameters

G	Source matrix .
rbw	Basis weights for the row basis, can be obtained by weight_clusterbasis_clusteroperator. If this is a null pointer, the row basis is assumed to be orthogonal, so no weights are required.
cbw	Basis weights for the column basis, can be obtained by weight_clusterbasis_clusteroperator. If this is a null pointer, the column basis is assumed to be orthogonal, so no weights are required.
tm	Truncation mode.
rlw	Will be filled with the local row weights, can be initialized by build_from_clusterbasis_clusteroperator. If the cluster operator already contains something, the local weights will be merged with the original contents.

void totalweight_col_clusteroperator	(	pclusterbasis	cb,
		pclusteroperator	cw,
		pctruncmode	tm
	)

Compute total column weights of a matrix.

The column weights are the factor $R_t$ of the skinny QR decomposition $X_t = Q_t R_t$ , where $X_t$ is the total column cluster basis of an $\mathcal{H}^2$ -matrix $X$ .

The matrix $X_t$ is obtained implicitly from the list starting with the pointer clist contained in the cluster basis.

Parameters

cb	Column basis.
cw	Total column weight.
tm	Truncation mode.

void totalweight_row_clusteroperator	(	pclusterbasis	rb,
		pclusteroperator	rw,
		pctruncmode	tm
	)

Compute total row weights of a matrix.

The row weights are the factor $R_t$ of the skinny QR decomposition $X_t = Q_t R_t$ , where $X_t$ is the total row cluster basis of an $\mathcal{H}^2$ -matrix $X$ .

The matrix $X_t$ is obtained implicitly from the list starting with the pointer rlist contained in the cluster basis.

Parameters

rb	Row basis.
rw	Total row weight.
tm	Truncation mode.

void totalweights_h2matrix	(	pch2matrix	G,
		bool	rbortho,
		bool	cbortho,
		pctruncmode	tm,
		pclusteroperator	rw,
		pclusteroperator	cw
	)

Construct total weights for a given $\mathcal{H}^2$ -matrix.

Finds matrices $Z_t$ with $G_t = V_t Z_t^* P_t^*$ , where $G_t$ is the total cluster basis and $P_t$ is orthogonal. These are called total row weights. The total column weights are computed by applying the same procedure to $G^*$ instead of $G$ .

Parameters

G	Source matrix .
rbortho	Set if the original row basis is orthogonal, this allows the algorithm to avoid computing row weights.
cbortho	Set if the original column basis is orthogonal, this allows the algorithm to avoid computing column weights.
tm	Truncation mode.
rw	Total row weights, can be initialized by calling build_from_clusterbasis_clusteroperator for the row basis.
cw	Total column weights, can be initialized by build_from_clusterbasis_clusteroperator for the column basis.

void truncate_clusterbasis	(	pcclusterbasis	cb,
		pcclusteroperator	cw,
		pcclusteroperator	clw,
		pctruncmode	tm,
		real	eps,
		pclusterbasis	cbnew,
		pclusteroperator	old2new
	)

Compute a truncated cluster basis.

Reduces the rank of a cluster basis by computing singular value decompositions and choosing the most important left singular vectors to construct a new basis. Both total and local weights can be taken into account, and the local weights will be accumulated on the fly, making a call to accumulate_clusteroperator unnecessary.

Parameters

cb	Original cluster basis.
cw	Total weights, ignored if null pointer.
clw	Local weights, will be accumulated, but not overwritten during the course of the algorithm, ignored if null pointer.
tm	Truncation mode.
eps	Truncation accuracy.
cbnew	New cluster basis, can be initialized with clonestructure_clusterbasis.
old2new	Cluster operator describing the change of basis from `cb` to `cbnew`.

void truncate_inplace_clusterbasis	(	pclusterbasis	cb,
		pclusteroperator	cw,
		pctruncmode	tm,
		real	eps
	)

Replace a cluster basis with a truncated basis.

This function is similar to truncate_clusterbasis, but replaces the old cluster basis by the new one.

Parameters

cb	Old clusterbasis, will be overwritten by truncated cluster basis.
cw	Cluster weights.
tm	Truncation mode.
eps	Truncation accuracy.

void trunccolbasis_h2matrix	(	ph2matrix	G,
		bool	rbortho,
		bool	cbortho,
		pctruncmode	tm,
		real	eps,
		pclusterbasis	cbnew,
		pclusteroperator	old2new
	)

Construct an improved column basis for an $\mathcal{H}^2$ -matrix.

Remarks: Compare to buildcolbasis_h2matrix, this function constructs local weights by only one QR decomposition per cluster instead of one per block. It also handles block weights in a slightly different manner.

Parameters

G	Original matrix .
rbortho	Set if the original row basis is orthogonal, this allows the algorithm to avoid computing row weights.
cbortho	Set if the original column basis is orthogonal, this allows the algorithm to avoid computing column weights.
tm	Truncation mode.
eps	Truncation accuracy.
cbnew	New cluster basis, can be initialized with clonestructure_clusterbasis.
old2new	Cluster operator describing the change of basis from `G->cb` to `cbnew`.

void truncrowbasis_h2matrix	(	ph2matrix	G,
		bool	rbortho,
		bool	cbortho,
		pctruncmode	tm,
		real	eps,
		pclusterbasis	rbnew,
		pclusteroperator	old2new
	)

Construct an improved row basis for an $\mathcal{H}^2$ -matrix.

Remarks: Compare to buildrowbasis_h2matrix, this function constructs local weights by only one QR decomposition per cluster instead of one per block. It also handles block weights in a slightly different manner.

Parameters

G	Original matrix .
rbortho	Set if the original row basis is orthogonal, this allows the algorithm to avoid computing row weights.
cbortho	Set if the original column basis is orthogonal, this allows the algorithm to avoid computing column weights.
tm	Truncation mode.
eps	Truncation accuracy.
rbnew	New cluster basis, can be initialized with clonestructure_clusterbasis.
old2new	Cluster operator describing the change of basis from `G->rb` to `cbnew`.

pclusterbasis unify_clusterbasis	(	pccluster	t,
		ptruncblock	tb,
		pctruncmode	tm,
		real	eps,
		pclusteroperator*	cw
	)

Construct a unified cluster basis.

Constructs a cluster basis that can approximate multiple $\mathcal{H}^2$ -matrices simultaneously, e.g., multiple independent sub- $\mathcal{H}^2$ -matrices that have to be merged into a large $\mathcal{H}^2$ -matrix.

Parameters

t	Root of the corresponding cluster tree.
tb	List of truncblock objects describing cluster bases and weights. After the function has completed, the fields `old2new` will contain the basis change operators.
tm	Truncation mode.
eps	Truncation accuracy.
cw	If not a null pointer, will be set to point to a new clusteroperator tree containing the total weights for the new basis. This is useful for recursive unification.

Returns: Unified cluster basis.

void unify_h2matrix	(	ph2matrix	G,
		pclusteroperator*	rw1,
		pclusteroperator*	cw1,
		pctruncmode	tm,
		real	eps,
		pclusteroperator*	rw,
		pclusteroperator*	cw
	)

Unify $\mathcal{H}^2$ -submatrices into a large $\mathcal{H}^2$ -matrix.

Takes a block matrix containing $\mathcal{H}^2$ -matrices and approximates it by a global $\mathcal{H}^2$ -matrix.

Remarks: Differently from everywhere else in the library, G is not a proper $\mathcal{H}^2$ -matrix, since the cluster bases of its immediate submatrices are allowed to differ from each other.

Parameters

G	Block matrix, will be overwritten by a proper $\mathcal{H}^2$ -matrix approximation.
rw1	Total row weights for all submatrices, enumerated in column-major ordering, i.e., `rw1[i+j*G->rsons]` corresponds to the block in row `i` and column `j`.
cw1	Total column weights for all submatrices, enumerated in column-major ordering, i.e., `rw1[i+j*G->rsons]` corresponds to the block in row `i` and column `j`.
tm	Truncation mode.
eps	Truncation accuracy.
rw	If not a null pointer, will be set to point to a new clusteroperator tree containing the total row weights of the new $\mathcal{H}^2$ -matrix.
cw	If not a null pointer, will be set to point to a new clusteroperator tree containing the total column weights of the new $\mathcal{H}^2$ -matrix.

void unify_parallel_h2matrix	(	ph2matrix	G,
		uint	pardepth,
		pclusteroperator*	rw1,
		pclusteroperator*	cw1,
		pctruncmode	tm,
		real	eps,
		pclusteroperator*	rw,
		pclusteroperator*	cw
	)

Unify $\mathcal{H}^2$ -submatrices into a large $\mathcal{H}^2$ -matrix, experimental parallel implementation.

Takes a block matrix containing $\mathcal{H}^2$ -matrices and approximates it by a global $\mathcal{H}^2$ -matrix.

Remarks: Differently from everywhere else in the library, G is not a proper $\mathcal{H}^2$ -matrix, since the cluster bases of its immediate submatrices are allowed to differ from each other.

Parameters

G	Block matrix, will be overwritten by a proper $\mathcal{H}^2$ -matrix approximation.
pardepth	Parallization depth. Parallel threads are spawned only on the next `pardepth` levels of the recursion.
rw1	Total row weights for all submatrices, enumerated in column-major ordering, i.e., `rw1[i+j*G->rsons]` corresponds to the block in row `i` and column `j`.
cw1	Total column weights for all submatrices, enumerated in column-major ordering, i.e., `rw1[i+j*G->rsons]` corresponds to the block in row `i` and column `j`.
tm	Truncation mode.
eps	Truncation accuracy.
rw	If not a null pointer, will be set to point to a new clusteroperator tree containing the total row weights of the new $\mathcal{H}^2$ -matrix.
cw	If not a null pointer, will be set to point to a new clusteroperator tree containing the total column weights of the new $\mathcal{H}^2$ -matrix.

Data Structures

Typedefs

Functions

Detailed Description

Function Documentation