edu.umbc.cs.maple.utils
Class ColtSGTUtils

java.lang.Object
  edu.umbc.cs.maple.utils.ColtSGTUtils

public class ColtSGTUtils
extends java.lang.Object

Various utility functions for Spectral Graph Theory using the COLT matrix library.

Copyright (c) 2008 Eric Eaton

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/.

Version:

0.1

Author:

Eric Eaton (EricEaton@umbc.edu)
University of Maryland Baltimore County

Nested Class Summary

static class	ColtSGTUtils.KeyEigenvalues
static class	ColtSGTUtils.LaplacianType

Constructor Summary

ColtSGTUtils()

Method Summary

static cern.colt.matrix.DoubleMatrix2D	directedWeightedAdjacencyToLaplacian(cern.colt.matrix.DoubleMatrix2D adjacencyMatrix, ColtSGTUtils.LaplacianType laplacianType) Computes the Laplacian matrix for a directed weighted adjacency matrix A.
static void	main(java.lang.String[] args)
static void	mainAssist(double[][] A)
static cern.colt.matrix.DoubleMatrix2D	projectFunctionToBasis(cern.colt.matrix.DoubleMatrix2D basisVectors, cern.colt.matrix.DoubleMatrix2D f) Computes the projection of a function onto another basis.
static cern.colt.matrix.DoubleMatrix2D[]	resolution(cern.colt.matrix.DoubleMatrix2D A, int resolution, ColtSGTUtils.KeyEigenvalues keyEigenvalues) Computes the specified resolution of matrix A.
static cern.colt.matrix.DoubleMatrix2D[]	resolutionGraphFunction(cern.colt.matrix.DoubleMatrix2D graphLaplacian, cern.colt.matrix.DoubleMatrix2D f, int resolution) Computes the specified resolution of a function on a graph.
static cern.colt.matrix.DoubleMatrix2D	undirectedWeightedAdjacencyToLaplacian(cern.colt.matrix.DoubleMatrix2D adjacencyMatrix, ColtSGTUtils.LaplacianType laplacianType) Computes the Laplacian matrix for an undirected weighted adjacency matrix A.
static cern.colt.matrix.DoubleMatrix2D	weightedAdjacencyToLaplacian(cern.colt.matrix.DoubleMatrix2D adjacencyMatrix, ColtSGTUtils.LaplacianType laplacianType) Computes the Laplacian matrix for a weighted adjacency matrix A.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

ColtSGTUtils

public ColtSGTUtils()

Method Detail

weightedAdjacencyToLaplacian

public static cern.colt.matrix.DoubleMatrix2D weightedAdjacencyToLaplacian(cern.colt.matrix.DoubleMatrix2D adjacencyMatrix,
                                                                           ColtSGTUtils.LaplacianType laplacianType)

Computes the Laplacian matrix for a weighted adjacency matrix A. Automatically detects whether the adjacency matrix is directed or undirected.

Parameters:

adjacencyMatrix - the adjacency matrix

laplacianType - whether to use the normalized or combinatorial form of the Laplacian

undirectedWeightedAdjacencyToLaplacian

public static cern.colt.matrix.DoubleMatrix2D undirectedWeightedAdjacencyToLaplacian(cern.colt.matrix.DoubleMatrix2D adjacencyMatrix,
                                                                                     ColtSGTUtils.LaplacianType laplacianType)

Computes the Laplacian matrix for an undirected weighted adjacency matrix A. Coded from Section 1.4 of Chung's Spectral Graph Theory

Parameters:

adjacencyMatrix - the adjacency matrix

laplacianType - whether to use the normalized or combinatorial form of the Laplacian

directedWeightedAdjacencyToLaplacian

public static cern.colt.matrix.DoubleMatrix2D directedWeightedAdjacencyToLaplacian(cern.colt.matrix.DoubleMatrix2D adjacencyMatrix,
                                                                                   ColtSGTUtils.LaplacianType laplacianType)

Computes the Laplacian matrix for a directed weighted adjacency matrix A.

Parameters:

adjacencyMatrix - the adjacency matrix

laplacianType - whether to use the normalized or combinatorial form of the Laplacian

resolution

public static cern.colt.matrix.DoubleMatrix2D[] resolution(cern.colt.matrix.DoubleMatrix2D A,
                                                           int resolution,
                                                           ColtSGTUtils.KeyEigenvalues keyEigenvalues)

Computes the specified resolution of matrix A.

Parameters:

A - the matrix

resolution - the resolution

keyEigenvalues - specifies whether the top LARGEST or SMALLEST eigenvalues should be taken. LARGEST should be the choice for most applications; SMALLEST should be the choice for eigenvectors of the graph Laplacian.

Returns:

three matrices M[3] M[0]: Ak, A at the specified resolution M[1]: Qk, the eigenvectors used to compose Ak M[2]: Lk, the eigenvalues used to compose Ak

resolutionGraphFunction

public static cern.colt.matrix.DoubleMatrix2D[] resolutionGraphFunction(cern.colt.matrix.DoubleMatrix2D graphLaplacian,
                                                                        cern.colt.matrix.DoubleMatrix2D f,
                                                                        int resolution)

Computes the specified resolution of a function on a graph.

Parameters:

graphLaplacian - the graph Laplacian

f - the function values on the vertices of the graph

resolution - the resolution

Returns:

three matrices M[3] M[0]: fk, f at the specified resolution on the graph M[1]: Qk, the eigenfunctions of the graph Laplacian used in the computation M[2]: Lk, the eigenvalues of the graph Laplacian used in the computation

projectFunctionToBasis

public static cern.colt.matrix.DoubleMatrix2D projectFunctionToBasis(cern.colt.matrix.DoubleMatrix2D basisVectors,
                                                                     cern.colt.matrix.DoubleMatrix2D f)

Computes the projection of a function onto another basis.

Parameters:

basisVectors - the basis vectors

f - the function values on the vertices of the graph

Returns:

one matrix f on the basis vectors

main

public static void main(java.lang.String[] args)

mainAssist

public static void mainAssist(double[][] A)