MatUtils: Matrix utility functions. More...

Detailed Description

MatUtils: Matrix utility functions.

New in 0.1:: (Daniel Wirtz, 2010-06-02) 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 17 of file MatUtils.m.

Static Public Member Functions
static function [ A , idxmat ] =	laplacemat (h, d1, d2)
	Computes a 2D diffusion sparse matrix with zero neuman boundary conditions. More...

static function matrix < double > A =	divcdivumat (px, py, gradc)
	Computes the 2D matrix for the expression \(\nabla c(x) \cdot \nabla u\) arising in the general spatial-dependent diffusion term \(\nabla\cdot(c(x)\nabla u(x))\). More...

static function A =	laplacemat3D (h, g)
	Computes a 3D laplacian sparse matrix. More...

static function A =	generalizedLaplacemat3D (h, g, sigma)
	Computes a 3D generalized laplacian sparse matrix \(\nabla\cdot\sigma\nabla\). More...

static function Kinv =	getExtendedInverse (Kinv, v, mode)
	For a matrix K with known inverse Kinv the matrix is extended by the vector. More...

static function Asparse =	toSparse (matrix< double > A,rowvec< integer > rowidx, n)
	Converts a full matrix A to a sparse matrix, where the entries of A are split up to the row indices specified by rowidx. More...

static function res =	test_DivCDivUMat ()

static function	test_ExtendedInverseDirect ()
	Tests direct inversion extension for a matrix of size s for a fixed number of experiments each. More...

static function	test_ExtendedInverseSequential ()

Member Function Documentation

function matrix< double > A = MatUtils.divcdivumat	(	px,
		py,
		gradc
	)

static

Computes the 2D matrix for the expression \(\nabla c(x) \cdot \nabla u\) arising in the general spatial-dependent diffusion term \(\nabla\cdot(c(x)\nabla u(x))\).

The coordinates in px and py have to be equally spaced, e.g. meshgrid'ed. Further the coordinate system origin is assumed to be in the top left corner, so x+ to the right and y+ to the bottom (accorcind

Arguments: px: Matrix of x coordinates py: Matrix of y coordinates gradc: Function handle \(\R^2 \to \R^2\) for gradient evaluation of \(grad c(x)\) function at points [px;py].

Author: Daniel Wirtz

Date: 2014-04-07

Return values

A	The matrix with discretized entries

Definition at line 104 of file MatUtils.m.

References k, and t.

Referenced by test_DivCDivUMat().

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function A = MatUtils.generalizedLaplacemat3D	(	h,
		g,
		sigma
	)

static

Computes a 3D generalized laplacian sparse matrix \(\nabla\cdot\sigma\nabla\).

Arguments: h: discretization spatial stepwidth in all three directions g: the general.geometry.RectGrid3D instance describing the geometry. sigma: the conductivity tensor, assumed to be diagonal