ABlockedData: General abstract class that allows computation of and SVD on a large matrix that is separated into several blocks. More...

Detailed Description

ABlockedData: General abstract class that allows computation of and SVD on a large matrix that is separated into several blocks.

Author: Daniel Wirtz

Date: 2012-07-11

Change in 0.6:: (Daniel Wirtz, 2012-10-01) Added an optional Vexclude matrix argument to exclude a given space from the data

New in 0.6:: (Daniel Wirtz, 2012-07-11) Added this class.

This class is part of the framework

KerMor - Model Order Reduction using Kernels

Homepage http://www.morepas.org/software/index.html
Documentation http://www.morepas.org/software/kermor/index.html
License KerMor license conditions

Definition at line 18 of file ABlockedData.m.

Public Member Functions
function [ matrix< double > U , matrix < double > S , matrix< double > V ] =	getSVD (integer k,matrix< double > Vexclude,colvec< integer > targetdims)
	Computes an SVD on this blockwise matrix \(A = USV^T\). More...

function prod =	mtimes ()
	Need left-sided matrix multiplication if RHS singular vectors V should be returned. More...

function A =	toMemoryMatrix ()
	Converts this FileMatrix to a full double matrix. More...

virtual function varargout =	size (dim)

virtual function n =	getNumBlocks ()

virtual function B =	getBlock (nr)

Static Public Member Functions
static function res =	test_BlockSVD_vs_SVD ()

Public Attributes
double	MinRelSingularValueSize = 1e-20
	The minimum relative value of singular values that triggers selection of the compared to the largest one. More...

Public Attributes inherited from handle
	addlistener
	Creates a listener for the specified event and assigns a callback function to execute when the event occurs. More...

	notify
	Broadcast a notice that a specific event is occurring on a specified handle object or array of handle objects. More...

	delete
	Handle object destructor method that is called when the object's lifecycle ends. More...

	disp
	Handle object disp method which is called by the display method. See the MATLAB disp function. More...

	display
	Handle object display method called when MATLAB software interprets an expression returning a handle object that is not terminated by a semicolon. See the MATLAB display function. More...

	findobj
	Finds objects matching the specified conditions from the input array of handle objects. More...

	findprop
	Returns a meta.property objects associated with the specified property name. More...

	fields
	Returns a cell array of string containing the names of public properties. More...

	fieldnames
	Returns a cell array of string containing the names of public properties. See the MATLAB fieldnames function. More...

	isvalid
	Returns a logical array in which elements are true if the corresponding elements in the input array are valid handles. This method is Sealed so you cannot override it in a handle subclass. More...

	eq
	Relational functions example. See details for more information. More...

	transpose
	Transposes the elements of the handle object array. More...

	permute
	Rearranges the dimensions of the handle object array. See the MATLAB permute function. More...

	reshape
	hanges the dimensions of the handle object array to the specified dimensions. See the MATLAB reshape function. More...

	sort
	ort the handle objects in any array in ascending or descending order. More...

Member Function Documentation

virtual function B = data.ABlockedData.getBlock ( nr )

pure virtual

Implemented in data.FileMatrix, data.MemoryTrajectoryData, data.ATrajectoryData, data.AxBlockData, data.JoinedBlockData, and data.FinDiffBlockData.

Referenced by getSVD(), and toMemoryMatrix().

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virtual function n = data.ABlockedData.getNumBlocks ( )

pure virtual

Implemented in data.FileMatrix, data.MemoryTrajectoryData, data.ATrajectoryData, data.AxBlockData, data.JoinedBlockData, and data.FinDiffBlockData.

Referenced by getSVD(), and toMemoryMatrix().

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function [ matrix< double > U , matrix< double > S , matrix< double > V ] = data.ABlockedData.getSVD	(	integer	k,
		matrix< double >	Vexclude,
		colvec< integer >	targetdims
	)

Computes an SVD on this blockwise matrix \(A = USV^T\).

Parameters

k	The number of largest singular values and vectors to compute. Default: all
Vexclude	A matrix containing orthonormal columns, whose spanned space is to be excluded from the SVD. If targetdims are given, the first dimension must match the targeted dimension's size. Default: []
targetdims	The dimensions on which to perform the SVD. Selects all by default. Default: `:`

Return values

U	The left-hand side singular vectors \(U\) of the decomposition \(U\Sigma V^T = A\).
S	The singular values \(\Sigma\) of the decomposition \(U\Sigma V^T = A\).
V	The transposed right-hand side singular vectors \(V\) of the decomposition \(U\Sigma V = A\).

Definition at line 55 of file ABlockedData.m.

References KerMor.App(), getBlock(), getNumBlocks(), MinRelSingularValueSize, size(), and t.

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