public void EigenvalueDecompositionConstructorTest2()
{
// Asymmetric test
double[][] A =
{
new double[] { 5, 2, 1 },
new double[] { 1, 4, 1 },
new double[] { -1, 2, 3 }
};
var target = new JaggedEigenvalueDecomposition(A);
var D = target.DiagonalMatrix;
var Q = target.Eigenvectors;
double[][] expectedD =
{
new double[] { 6, 0, 0 },
new double[] { 0, 4, 0 },
new double[] { 0, 0, 2 }
};
// Decomposition identity
var actualA = Matrix.Multiply(Matrix.Multiply(Q, D), Q.Inverse());
Assert.IsTrue(Matrix.IsEqual(expectedD, D, 1e-5));
Assert.IsTrue(Matrix.IsEqual(A, actualA, 1e-5));
Assert.IsTrue(Matrix.IsEqual(A, target.Reverse(), 1e-5));
}
public void SolveForEigen(double[][] matrix)
{
if (matrix.Rows() != matrix.Columns())
{
throw new ArgumentException("Must be quadratic");
}
JaggedEigenvalueDecomposition evd = new JaggedEigenvalueDecomposition(matrix, true, false, true);
ComponentVectors = evd.Eigenvectors.Transpose();
Eigenvalues = evd.RealEigenvalues;
}
public void InverseTestNaN()
{
int n = 5;
var I = Matrix.Identity(n);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
double[][] value = Matrix.JaggedMagic(n);
value[i][j] = double.NaN;
var target = new JaggedEigenvalueDecomposition(value);
}
}
}
public void EigenvalueDecompositionConstructorTest()
{
// Symmetric test
double[][] A =
{
new double[] { 4, 2 },
new double[] { 2, 4 }
};
var target = new JaggedEigenvalueDecomposition(A);
var D = target.DiagonalMatrix;
var Q = target.Eigenvectors;
double[][] expectedD =
{
new double[] { 2, 0 },
new double[] { 0, 6 }
};
double[][] expectedQ =
{
new double[] { 0.7071, 0.7071 },
new double[] { -0.7071, 0.7071 }
};
Assert.IsTrue(Matrix.IsEqual(expectedD, D, 0.00001));
Assert.IsTrue(Matrix.IsEqual(expectedQ, Q, 0.0001));
// Decomposition identity
var actualA = Matrix.Dot(Matrix.Dot(Q, D), Q.Inverse());
Assert.IsTrue(Matrix.IsEqual(expectedD, D, 0.00001));
Assert.IsTrue(Matrix.IsEqual(A, actualA, 0.0001));
Assert.AreSame(target.DiagonalMatrix, target.DiagonalMatrix);
}
/// <summary>
/// Learns a model that can map the given inputs to the desired outputs.
/// </summary>
/// <param name="x">The model inputs.</param>
/// <param name="weights">The weight of importance for each input sample.</param>
/// <returns>
/// A model that has learned how to produce suitable outputs
/// given the input data <paramref name="x" />.
/// </returns>
public MultivariateKernelRegression Learn(double[][] x, double[] weights = null)
{
this.sourceCentered = null;
this.StandardDeviations = null;
this.featureMean = null;
this.featureGrandMean = 0;
double[][] K;
if (Method == PrincipalComponentMethod.KernelMatrix)
{
K = x;
if (centerFeatureSpace) // Center the Gram (Kernel) Matrix if requested
{
K = Accord.Statistics.Kernels.Kernel.Center(K, out featureMean, out featureGrandMean); // do not overwrite
}
}
else
{
this.NumberOfInputs = x.Columns();
this.Means = x.Mean(dimension: 0);
this.sourceCentered = Overwrite ? x : Jagged.CreateAs(x);
x.Subtract(Means, dimension: 0, result: sourceCentered);
if (Method == PrincipalComponentMethod.Standardize)
{
this.StandardDeviations = x.StandardDeviation(Means);
sourceCentered.Divide(StandardDeviations, dimension: 0, result: sourceCentered);
}
// Create the Gram (Kernel) Matrix
K = kernel.ToJagged(x: sourceCentered);
if (centerFeatureSpace) // Center the Gram (Kernel) Matrix if requested
{
K = Accord.Statistics.Kernels.Kernel.Center(K, out featureMean, out featureGrandMean, result: K); // overwrite
}
}
// Perform the Eigenvalue Decomposition (EVD) of the Kernel matrix
var evd = new JaggedEigenvalueDecomposition(K,
assumeSymmetric: true, sort: true);
// Gets the Eigenvalues and corresponding Eigenvectors
int numberOfSamples = x.Length;
double[] evals = evd.RealEigenvalues;
double[][] eigs = evd.Eigenvectors;
int nonzero = evd.Rank;
if (NumberOfInputs != 0)
{
nonzero = Math.Min(nonzero, NumberOfInputs);
}
if (NumberOfOutputs != 0)
{
nonzero = Math.Min(nonzero, NumberOfOutputs);
}
// Eliminate unwanted components
eigs = eigs.Get(null, 0, nonzero);
evals = evals.Get(0, nonzero);
// Normalize eigenvectors
if (centerFeatureSpace)
{
eigs.Divide(evals.Sqrt(), dimension: 0, result: eigs);
}
if (Whiten)
{
eigs.Divide(evals.Sqrt(), dimension: 0, result: eigs);
}
//this.Eigenvalues = evals.Divide(numberOfSamples - 1);
this.Eigenvalues = evals;
this.SingularValues = evals.Divide(numberOfSamples - 1).Sqrt();
this.ComponentVectors = eigs.Transpose();
if (allowReversion)
{
// Project the original data into principal component space
this.result = Matrix.Dot(K, eigs).ToMatrix();
}
// Computes additional information about the analysis and creates the
// object-oriented structure to hold the principal components found.
CreateComponents();
Accord.Diagnostics.Debug.Assert(NumberOfOutputs > 0);
return(CreateRegression());
}
/// <summary>
/// Learns a model that can map the given inputs to the desired outputs.
/// </summary>
///
/// <param name="x">The model inputs.</param>
/// <param name="weights">The weight of importance for each input sample.</param>
///
/// <returns>
/// A model that has learned how to produce suitable outputs
/// given the input data <paramref name="x" />.
/// </returns>
///
public MultivariateLinearRegression Learn(double[][] x, double[] weights = null)
{
this.NumberOfInputs = x.Columns();
if (Method == PrincipalComponentMethod.Center || Method == PrincipalComponentMethod.Standardize)
{
this.Means = x.Mean(dimension: 0);
double[][] matrix = Overwrite ? x : Jagged.CreateAs(x);
x.Subtract(Means, dimension: 0, result: matrix);
if (Method == PrincipalComponentMethod.Standardize)
{
this.StandardDeviations = x.StandardDeviation(Means);
matrix.Divide(StandardDeviations, dimension: 0, result: matrix);
}
// The principal components of 'Source' are the eigenvectors of Cov(Source). Thus if we
// calculate the SVD of 'matrix' (which is Source standardized), the columns of matrix V
// (right side of SVD) will be the principal components of Source.
// Perform the Singular Value Decomposition (SVD) of the matrix
var svd = new JaggedSingularValueDecomposition(matrix,
computeLeftSingularVectors: false,
computeRightSingularVectors: true,
autoTranspose: true, inPlace: true);
SingularValues = svd.Diagonal;
Eigenvalues = SingularValues.Pow(2);
Eigenvalues.Divide(x.Rows() - 1, result: Eigenvalues);
ComponentVectors = svd.RightSingularVectors.Transpose();
}
else if (Method == PrincipalComponentMethod.CovarianceMatrix ||
Method == PrincipalComponentMethod.CorrelationMatrix)
{
// We only have the covariance matrix. Compute the Eigenvalue decomposition
var evd = new JaggedEigenvalueDecomposition(x,
assumeSymmetric: true, sort: true);
// Gets the Eigenvalues and corresponding Eigenvectors
Eigenvalues = evd.RealEigenvalues;
SingularValues = Eigenvalues.Sqrt();
ComponentVectors = evd.Eigenvectors.Transpose();
}
else
{
// The method type should have been validated before we even entered this section
throw new InvalidOperationException("Invalid method, this should never happen: {0}".Format(Method));
}
if (Whiten)
{
ComponentVectors.Divide(SingularValues, dimension: 1, result: ComponentVectors);
}
// Computes additional information about the analysis and creates the
// object-oriented structure to hold the principal components found.
CreateComponents();
return(CreateRegression());
}
public MultivariateLinearRegression Learn(double[][] x, double[] weights = null)
{
this.NumberOfInputs = x.Columns();
if (Method == PrincipalComponentMethod.Center || Method == PrincipalComponentMethod.Standardize)
{
if (weights == null)
{
this.Means = x.Mean(dimension: 0);
double[][] matrix = Overwrite ? x : Jagged.CreateAs(x);
x.Subtract(Means, dimension: (VectorType)0, result: matrix);
if (Method == PrincipalComponentMethod.Standardize)
{
this.StandardDeviations = x.StandardDeviation(Means);
matrix.Divide(StandardDeviations, dimension: (VectorType)0, result: matrix);
}
var svd = new JaggedSingularValueDecomposition(matrix,
computeLeftSingularVectors: false,
computeRightSingularVectors: true,
autoTranspose: true, inPlace: true);
SingularValues = svd.Diagonal;
Eigenvalues = SingularValues.Pow(2);
Eigenvalues.Divide(x.Rows() - 1, result: Eigenvalues);
ComponentVectors = svd.RightSingularVectors.Transpose();
}
else
{
this.Means = x.WeightedMean(weights: weights);
double[][] matrix = Overwrite ? x : Jagged.CreateAs(x);
x.Subtract(Means, dimension: (VectorType)0, result: matrix);
if (Method == PrincipalComponentMethod.Standardize)
{
this.StandardDeviations = x.WeightedStandardDeviation(weights, Means);
matrix.Divide(StandardDeviations, dimension: (VectorType)0, result: matrix);
}
double[,] cov = x.WeightedCovariance(weights, Means);
var evd = new EigenvalueDecomposition(cov,
assumeSymmetric: true, sort: true);
Eigenvalues = evd.RealEigenvalues;
SingularValues = Eigenvalues.Sqrt();
ComponentVectors = Jagged.Transpose(evd.Eigenvectors);
}
}
else if (Method == PrincipalComponentMethod.CovarianceMatrix ||
Method == PrincipalComponentMethod.CorrelationMatrix)
{
if (weights != null)
{
throw new Exception();
}
var evd = new JaggedEigenvalueDecomposition(x,
assumeSymmetric: true, sort: true);
Eigenvalues = evd.RealEigenvalues;
SingularValues = Eigenvalues.Sqrt();
ComponentVectors = evd.Eigenvectors.Transpose();
}
else
{
throw new InvalidOperationException("Invalid method, this should never happen: {0}".Format(Method));
}
if (Whiten)
{
ComponentVectors.Divide(SingularValues, dimension: (VectorType)1, result: ComponentVectors);
}
CreateComponents();
return(CreateRegression());
}