Class SvdAndPca

contains methods and test example to do Singular Value decomposition and Principal Components Analysis

IMPORTANT NOTE: The underlying storage of the Matrix class is a one dimensional array in column-major order (column by column). NOT Row by row!!.

Inheritance

Object

SvdAndPca

Inherited Members

Object.Equals(Object)

Object.Equals(Object, Object)

Object.GetHashCode()

Object.GetType()

Object.MemberwiseClone()

Object.ReferenceEquals(Object, Object)

Object.ToString()

Namespace: TowseyLibrary

Assembly: TowseyLibrary.dll

Syntax

public static class SvdAndPca

Methods

EigenVectors(Double[,])

returns the eigen values and eigen vectors of a matrix IMPORTANT: THIS METHOD NEEDS DEBUGGING. IT RETURNS THE NEGATIVE VALUES OF THE EIGEN VECTORS ON A TOY EXMAPLE double[,] matrix = { { 3.0, -1.0 }, { -1.0, 3.0 } }; eigen values are correct ie, 2.0, 4.0; but in the wrong order.

Declaration

public static Tuple<double[], double[, ]> EigenVectors(double[, ] matrix)

Parameters

Type	Name	Description
Double[,]	matrix

Returns

Type	Description
Tuple<Double[], Double[,]>

ExampleOfSVD_1()

Declaration

public static void ExampleOfSVD_1()

ExampleOfSVD_2()

Declaration

public static void ExampleOfSVD_2()

ExampleOfSVD_3()

These examples are used to do Wavelet Packet Decomposition and then do SVD on the returned WPD trees.

Declaration

public static void ExampleOfSVD_3()

SingularValueDecompositionOutput(Double[,])

Declaration

public static Tuple<Vector<double>, Matrix<double>> SingularValueDecompositionOutput(double[, ] matrix)

Parameters

Type	Name	Description
Double[,]	matrix

Returns

Type	Description
Tuple<MathNet.Numerics.LinearAlgebra.Vector<Double>, MathNet.Numerics.LinearAlgebra.Matrix<Double>>

SingularValueDecompositionVector(Double[,])

The singular value decomposition of an M by N rectangular matrix A has the form A(mxn) = U(mxm) * S(mxn) * V'(nxn) where U is an orthogonal matrix, whose columns are the left singular vectors; S is a diagonal matrix, whose min(m,n) diagonal entries are the singular values; V is an orthogonal matrix, whose columns are the right singular vectors; Note 1: the transpose of V is used in the decomposition, and that the diagonal matrix S is typically stored as a vector. Note 2: the values on the diagonal of S are the square-root of the eigenvalues.

THESE TWO METHODS HAVE BEEN TESTED ON TOY EXAMPLES AND returned correct values.

Declaration

public static double[] SingularValueDecompositionVector(double[, ] matrix)

Parameters

Type	Name	Description
Double[,]	matrix

Returns

Type	Description
Double[]

TestEigenValues()

Declaration

public static void TestEigenValues()