public void Transform_SimpleExample_ReturnsExpectedOutput()
{
var m = new Matrix(new[]
{
new [] { 2d, 4d},
new [] { 1d, 3d},
new [] { 0d, 0d},
new [] { 0d, 0d}
});
var svd = new SingularValueDecomposition();
var t = svd.Transform(m);
}
private double regress(double[][] inputs, double[] outputs, out double[,] designMatrix, bool robust)
{
if (inputs.Length != outputs.Length)
{
throw new ArgumentException("Number of input and output samples does not match", "outputs");
}
int rows = inputs.Length; // number of instance points
int cols = inputs[0].Length; // dimension of each point
NumberOfInputs = cols;
ISolverMatrixDecomposition <double> solver;
// Create the problem's design matrix. If we
// have to add an intercept term, add a new
// extra column at the end and fill with 1s.
if (!addIntercept)
{
// Just copy values over
designMatrix = new double[rows, cols];
for (int i = 0; i < inputs.Length; i++)
{
for (int j = 0; j < inputs[i].Length; j++)
{
designMatrix[i, j] = inputs[i][j];
}
}
}
else
{
// Add an intercept term
designMatrix = new double[rows, cols + 1];
for (int i = 0; i < inputs.Length; i++)
{
for (int j = 0; j < inputs[i].Length; j++)
{
designMatrix[i, j] = inputs[i][j];
}
designMatrix[i, cols] = 1;
}
}
// Check if we have an overdetermined or underdetermined
// system to select an appropriate matrix solver method.
if (robust || cols >= rows)
{
// We have more variables than equations, an
// underdetermined system. Solve using a SVD:
solver = new SingularValueDecomposition(designMatrix,
computeLeftSingularVectors: true,
computeRightSingularVectors: true,
autoTranspose: true);
}
else
{
// We have more equations than variables, an
// overdetermined system. Solve using the QR:
solver = new QrDecomposition(designMatrix);
}
// Solve V*C = B to find C (the coefficients)
coefficients = solver.Solve(outputs);
if (addIntercept)
{
intercept = coefficients[coefficients.Length - 1];
}
// Calculate Sum-Of-Squares error
double error = 0.0;
double e;
for (int i = 0; i < outputs.Length; i++)
{
e = outputs[i] - Compute(inputs[i]);
error += e * e;
}
return(error);
}
public static double[,] PseudoInverse(this double[,] m)
{
SingularValueDecomposition svd = new SingularValueDecomposition(m);
return(svd.Solve(Matrix.Diagonal(m.GetLength(0), m.GetLength(1), 1.0)));
}
/// <summary>
/// Parallel (symmetric) iterative algorithm.
/// </summary>
///
/// <returns>
/// Returns a matrix in which each row contains
/// the mixing coefficients for each component.
/// </returns>
///
private double[,] parallel(double[,] X, int components, double[,] winit)
{
// References:
// - Hyvärinen, A (1999). Fast and Robust Fixed-Point
// Algorithms for Independent Component Analysis.
// There are two ways to apply the fixed-unit algorithm to compute the whole
// ICA iteration. The second approach is to perform orthogonalization at once
// using an Eigendecomposition [Hyvärinen]. The Eigendecomposition can in turn
// be converted to a more stable singular value decomposition and be used to
// create a projection basis in the same way as in Principal Component Analysis.
int n = X.GetLength(0);
int m = X.GetLength(1);
// Algorithm initialization
double[,] W0 = winit;
double[,] W = winit;
double[,] K = new double[components, components];
bool stop = false;
int iterations = 0;
double lastChange = 1;
do // until convergence
{
// [Hyvärinen, 1997]'s paper suggests the use of the Eigendecomposition
// to orthogonalize W (after equation 10). However, [E, D] = eig(W'W)
// can be replaced by [U, S] = svd(W), which is more stable and avoids
// computing W'W. Since the singular values are already the square roots
// of the eigenvalues of W'W, the computation of E'*D^(-1/2)*E' reduces
// to U*S^(-1)*U'.
// Perform simultaneous decorrelation of all components at once
var svd = new SingularValueDecomposition(W,
computeLeftSingularVectors: true,
computeRightSingularVectors: false,
autoTranspose: true);
double[] S = svd.Diagonal;
double[,] U = svd.LeftSingularVectors;
// Form orthogonal projection basis K
for (int i = 0; i < components; i++)
{
for (int j = 0; j < components; j++)
{
double s = 0;
for (int k = 0; k < S.Length; k++)
{
if (S[k] != 0.0)
{
s += U[i, k] * U[j, k] / S[k];
}
}
K[i, j] = s;
}
}
// Orthogonalize
W = K.Multiply(W);
// Gets the maximum parameter absolute change
double delta = getMaximumAbsoluteChange(W0, W);
// Check for convergence
if (delta < tolerance * lastChange || iterations >= maxIterations)
{
stop = true;
}
else
{
// Advance to the next iteration
W0 = W; W = new double[components, m];
lastChange = delta;
iterations++;
// For each component (in parallel)
global::Accord.Threading.Tasks.Parallel.For(0, components, i =>
{
double[] wx = new double[n];
double[] dgwx = new double[n];
double[] gwx = new double[n];
double[] means = new double[m];
// Compute wx = w*x
for (int j = 0; j < wx.Length; j++)
{
double s = 0;
for (int k = 0; k < m; k++)
{
s += W0[i, k] * X[j, k];
}
wx[j] = s;
}
// Compute g(wx) and g'(wx)
contrast.Evaluate(wx, gwx, dgwx);
// Compute E{ x*g(w*x) }
for (int j = 0; j < means.Length; j++)
{
for (int k = 0; k < gwx.Length; k++)
{
means[j] += X[k, j] * gwx[k];
}
means[j] /= n;
}
// Compute E{ g'(w*x) }
double mean = Statistics.Tools.Mean(dgwx);
// Compute next update for w according
// to Hyvärinen paper's equation (20).
// w+ = E{ xg(w*x)} - E{ g'(w*x)}*w
for (int j = 0; j < means.Length; j++)
{
W[i, j] = means[j] - mean * W0[i, j];
}
// The normalization to w* will be performed
// in the beginning of the next iteration.
});
}
} while (!stop);
// Return the component basis matrix
return(W); // vectors stored as rows.
}
/// <summary>
/// Performs the regression using the input vectors and output
/// vectors, returning the sum of squared errors of the fit.
/// </summary>
///
/// <param name="inputs">The input vectors to be used in the regression.</param>
/// <param name="outputs">The output values for each input vector.</param>
/// <returns>The Sum-Of-Squares error of the regression.</returns>
///
public virtual double Regress(double[][] inputs, double[][] outputs)
{
if (inputs.Length != outputs.Length)
{
throw new ArgumentException("Number of input and output samples does not match", "outputs");
}
int cols = inputs[0].Length; // inputs
int rows = inputs.Length; // points
if (insertConstant)
{
cols++;
}
for (int c = 0; c < coefficients.GetLength(1); c++)
{
double[] B = new double[cols];
double[,] V = new double[cols, cols];
// Compute V and B matrices
for (int i = 0; i < cols; i++)
{
// Least Squares Matrix
for (int j = 0; j < cols; j++)
{
for (int k = 0; k < rows; k++)
{
if (insertConstant)
{
double a = (i == cols - 1) ? 1 : inputs[k][i];
double b = (j == cols - 1) ? 1 : inputs[k][j];
V[i, j] += a * b;
}
else
{
V[i, j] += inputs[k][i] * inputs[k][j];
}
}
}
// Function to minimize
for (int k = 0; k < rows; k++)
{
if (insertConstant && (i == cols - 1))
{
B[i] += outputs[k][c];
}
else
{
B[i] += inputs[k][i] * outputs[k][c];
}
}
}
// Solve V*C = B to find C (the coefficients)
double[] coef = new SingularValueDecomposition(V).Solve(B);
if (insertConstant)
{
intercepts[c] = coef[coef.Length - 1];
for (int i = 0; i < cols - 1; i++)
{
coefficients[i, c] = coef[i];
}
}
else
{
for (int i = 0; i < cols; i++)
{
coefficients[i, c] = coef[i];
}
}
}
// Calculate Sum-Of-Squares error
double error = 0.0, e;
for (int i = 0; i < outputs.Length; i++)
{
double[] y = Compute(inputs[i]);
for (int c = 0; c < y.Length; c++)
{
e = outputs[i][c] - y[c];
error += e * e;
}
}
return(error);
}
// decompositions
#region svd
protected double[] svd(double[,] m)
{
var svd = new SingularValueDecomposition(m, false, false, true);
return(svd.Diagonal);
}
/// <summary>
/// Calculates the pseudo inverse of the matrix <c>input</c> by means of singular value decomposition.
/// A relative value of <c>100*DBL_EPSILON</c> is used to chop the singular values before calculation.
/// </summary>
/// <param name="input">Input matrix</param>
/// <param name="rank">Returns the rank of the input matrix.</param>
/// <returns>The pseudo inverse of matrix <c>input</c>.</returns>
public static IMatrix PseudoInverse(IROMatrix input, out int rank)
{
MatrixMath.BEMatrix ma = new BEMatrix(input.Rows,input.Columns);
MatrixMath.Copy(input,ma);
SingularValueDecomposition svd = new SingularValueDecomposition(ma);
double[][] B = GetMatrixArray(input.Columns,input.Rows);
/* compute the pseudoinverse in B */
double[] s = svd.Diagonal;
int m = input.Rows;
int n = input.Columns;
int minmn = Math.Min(m,n);
double[][] v = svd.V;
double[][] u = svd.U;
double thresh = (DoubleConstants.DBL_EPSILON*100) * s[0];
for(rank=0; rank<minmn && s[rank]>thresh; rank++)
{
double one_over_denom=1.0/s[rank];
for(int j=0; j<m; j++)
for(int i=0; i<n; i++)
B[i][j]+=v[i][rank]*u[j][rank]*one_over_denom;
}
return new JaggedArrayMatrix(B);
}
public static double SquareMahalanobis(double[] x, double[] y, SingularValueDecomposition svd)
{
return(new SquareMahalanobis(svd).Distance(x, y));
}
public void SingularValueDecompositionConstructorTest1()
{
// This test catches the bug in SingularValueDecomposition in the line
// for (int j = k + 1; j < nu; j++)
// where it should be
// for (int j = k + 1; j < n; j++)
// Test for m-x-n matrices where m < n. The available SVD
// routine was not meant to be used in this case.
double[,] value = new double[, ]
{
{ 1, 2 },
{ 3, 4 },
{ 5, 6 },
{ 7, 8 }
}.Transpose(); // value is 2x4, having less rows than columns.
var target = new SingularValueDecomposition(value, true, true, false);
double[,] actual = target.LeftSingularVectors.Dot(
target.DiagonalMatrix).Dot(target.RightSingularVectors.Transpose());
// Checking the decomposition
Assert.IsTrue(Matrix.IsEqual(actual, value, 1e-2));
Assert.IsTrue(Matrix.IsEqual(target.Reverse(), value, 1e-2));
// Checking values
double[,] U =
{
{ -0.641423027995072, -0.767187395072177 },
{ -0.767187395072177, 0.641423027995072 },
};
// U should be equal
Assert.IsTrue(Matrix.IsEqual(target.LeftSingularVectors, U, 0.001));
double[,] V = // economy svd
{
{ -0.152483233310201, 0.822647472225661, },
{ -0.349918371807964, 0.421375287684580, },
{ -0.547353510305727, 0.0201031031435023, },
{ -0.744788648803490, -0.381169081397574, },
};
var matrix = target.RightSingularVectors.Submatrix(0, 3, 0, 1);
// V can be different, but for the economy SVD it is often equal
Assert.IsTrue(
Matrix.IsEqual(matrix, V, 0.0001));
double[,] S =
{
{ 14.2690954992615, 0.000000000000000 },
{ 0.0000000000000, 0.626828232417543 },
};
// The diagonal values should be equal
Assert.IsTrue(Matrix.IsEqual(target.Diagonal.First(2),
Matrix.Diagonal(S), 0.001));
}
/// <summary>
/// Reverts a set of projected data into it's original form. Complete reverse
/// transformation is not always possible and is not even guaranteed to exist.
/// </summary>
///
/// <remarks>
/// <para>
/// This method works using a closed-form MDS approach as suggested by
/// Kwok and Tsang. It is currently a direct implementation of the algorithm
/// without any kind of optimization.
/// </para>
/// <para>
/// Reference:
/// - http://cmp.felk.cvut.cz/cmp/software/stprtool/manual/kernels/preimage/list/rbfpreimg3.html
/// </para>
/// </remarks>
///
/// <param name="data">The kpca-transformed data.</param>
/// <param name="neighbors">The number of nearest neighbors to use while constructing the pre-image.</param>
///
public double[,] Revert(double[,] data, int neighbors)
{
if (data == null)
{
throw new ArgumentNullException("data");
}
if (sourceCentered == null)
{
throw new InvalidOperationException("The analysis must have been computed first.");
}
if (neighbors < 2)
{
throw new ArgumentOutOfRangeException("neighbors", "At least two neighbors are necessary.");
}
// Verify if the current kernel supports
// distance calculation in feature space.
var distance = kernel as IReverseDistance;
if (distance == null)
{
throw new NotSupportedException(
"Current kernel does not support distance calculation in feature space.");
}
int rows = data.GetLength(0);
var result = Result;
double[,] reversion = new double[rows, sourceCentered.GetLength(1)];
// number of neighbors cannot exceed the number of training vectors.
int nn = System.Math.Min(neighbors, sourceCentered.GetLength(0));
// For each point to be reversed
for (int p = 0; p < rows; p++)
{
// 1. Get the point in feature space
double[] y = data.GetRow(p);
// 2. Select nn nearest neighbors of the feature space
double[,] X = sourceCentered;
double[] d2 = new double[Result.GetLength(0)];
int[] inx = new int[Result.GetLength(0)];
// 2.1 Calculate distances
for (int i = 0; i < X.GetLength(0); i++)
{
inx[i] = i;
d2[i] = distance.ReverseDistance(y, result.GetRow(i).Submatrix(y.Length));
if (Double.IsNaN(d2[i]))
{
d2[i] = Double.PositiveInfinity;
}
}
// 2.2 Order them
Array.Sort(d2, inx);
// 2.3 Select nn neighbors
int def = 0;
for (int i = 0; i < d2.Length && i < nn; i++, def++)
{
if (Double.IsInfinity(d2[i]))
{
break;
}
}
inx = inx.Submatrix(def);
X = X.Submatrix(inx).Transpose(); // X is in input space
d2 = d2.Submatrix(def); // distances in input space
// 3. Perform SVD
// [U,L,V] = svd(X*H);
// TODO: If X has more columns than rows, the SV decomposition should be
// computed on the transpose of X and the left and right vectors should
// be swapped. This should be fixed after more unit tests are elaborated.
SingularValueDecomposition svd = new SingularValueDecomposition(X,
computeLeftSingularVectors: true, computeRightSingularVectors: true,
autoTranspose: false);
double[,] U = svd.LeftSingularVectors;
double[,] L = Matrix.Diagonal(def, svd.Diagonal);
double[,] V = svd.RightSingularVectors;
// 4. Compute projections
// Z = L*V';
double[,] Z = L.Multiply(V.Transpose());
// 5. Calculate distances
// d02 = sum(Z.^2)';
double[] d02 = Matrix.Sum(Matrix.ElementwisePower(Z, 2));
// 6. Get the pre-image using z = -0.5*inv(Z')*(d2-d02)
double[,] inv = Matrix.PseudoInverse(Z.Transpose());
double[] w = (-0.5).Multiply(inv).Multiply(d2.Subtract(d02));
double[] z = w.Submatrix(U.GetLength(1));
// 8. Project the pre-image on the original basis
// using x = U*z + sum(X,2)/nn;
double[] x = (U.Multiply(z)).Add(Matrix.Sum(X.Transpose()).Multiply(1.0 / nn));
// 9. Store the computed pre-image.
for (int i = 0; i < reversion.GetLength(1); i++)
{
reversion[p, i] = x[i];
}
}
// if the data has been standardized or centered,
// we need to revert those operations as well
if (this.Method == AnalysisMethod.Standardize)
{
// multiply by standard deviation and add the mean
for (int i = 0; i < reversion.GetLength(0); i++)
{
for (int j = 0; j < reversion.GetLength(1); j++)
{
reversion[i, j] = (reversion[i, j] * StandardDeviations[j]) + Means[j];
}
}
}
else if (this.Method == AnalysisMethod.Center)
{
// only add the mean
for (int i = 0; i < reversion.GetLength(0); i++)
{
for (int j = 0; j < reversion.GetLength(1); j++)
{
reversion[i, j] = reversion[i, j] + Means[j];
}
}
}
return(reversion);
}
/// <summary>
/// Reverts a set of projected data into it's original form. Complete reverse
/// transformation is not always possible and is not even guaranteed to exist.
/// </summary>
/// <remarks>
/// This method works using a closed-form MDS approach as suggested by
/// Kwok and Tsang. It is currently a direct implementation of the algorithm
/// without any kind of optimization.
///
/// Reference:
/// - http://cmp.felk.cvut.cz/cmp/software/stprtool/manual/kernels/preimage/list/rbfpreimg3.html
/// </remarks>
/// <param name="data">The kpca-transformed data.</param>
/// <param name="neighbors">The number of nearest neighbors to use while constructing the pre-image.</param>
public double[,] Revert(double[,] data, int neighbors)
{
int rows = data.GetLength(0);
int cols = data.GetLength(1);
double[,] reversion = new double[rows, sourceCentered.GetLength(1)];
// number of neighbors cannot exceed the number of training vectors.
int nn = System.Math.Min(neighbors, sourceCentered.GetLength(0));
// For each point to be reversed
for (int p = 0; p < rows; p++)
{
// 1. Get the point in feature space
double[] y = data.GetRow(p);
// 2. Select nn nearest neighbors of the feature space
double[,] X = sourceCentered;
double[] d2 = new double[Result.GetLength(0)];
int[] inx = new int[Result.GetLength(0)];
// 2.1 Calculate distances
for (int i = 0; i < X.GetLength(0); i++)
{
inx[i] = i;
d2[i] = kernel.Distance(y, Result.GetRow(i).Submatrix(y.Length));
}
// 2.2 Order them
Array.Sort(d2, inx);
// 2.3 Select nn neighbors
inx = inx.Submatrix(nn);
X = X.Submatrix(inx).Transpose(); // X is in input space
d2 = d2.Submatrix(nn); // distances in input space
// 3. Create centering matrix
// H = eye(nn, nn) - 1 / nn * ones(nn, nn);
double[,] H = Matrix.Identity(nn).Subtract(Matrix.Create(nn, 1.0 / nn));
// 4. Perform SVD
// [U,L,V] = svd(X*H);
SingularValueDecomposition svd = new SingularValueDecomposition(X.Multiply(H));
double[,] U = svd.LeftSingularVectors;
double[,] L = Matrix.Diagonal(nn, svd.Diagonal);
double[,] V = svd.RightSingularVectors;
// 5. Compute projections
// Z = L*V';
double[,] Z = L.Multiply(V.Transpose());
// 6. Calculate distances
// d02 = sum(Z.^2)';
double[] d02 = Matrix.Sum(Matrix.DotPow(Z, 2));
// 7. Get the pre-image using z = -0.5*inv(Z')*(d2-d02)
double[,] inv = Matrix.PseudoInverse(Z.Transpose());
double[] z = (-0.5).Multiply(inv).Multiply(d2.Subtract(d02));
// 8. Project the pre-image on the original basis
// using x = U*z + sum(X,2)/nn;
double[] x = (U.Multiply(z)).Add(Matrix.Sum(X.Transpose()).Multiply(1.0 / nn));
// 9. Store the computed pre-image.
for (int i = 0; i < reversion.GetLength(1); i++)
{
reversion[p, i] = x[i];
}
}
// if the data has been standardized or centered,
// we need to revert those operations as well
if (this.Method == AnalysisMethod.Correlation)
{
// multiply by standard deviation and add the mean
for (int i = 0; i < reversion.GetLength(0); i++)
{
for (int j = 0; j < reversion.GetLength(1); j++)
{
reversion[i, j] = (reversion[i, j] * StandardDeviations[j]) + Means[j];
}
}
}
else
{
// only add the mean
for (int i = 0; i < reversion.GetLength(0); i++)
{
for (int j = 0; j < reversion.GetLength(1); j++)
{
reversion[i, j] = reversion[i, j] + Means[j];
}
}
}
return(reversion);
}
public void PC()
{
Random rng = new Random(1);
double s = 1.0 / Math.Sqrt(2.0);
MultivariateSample MS = new MultivariateSample(2);
RectangularMatrix R = new RectangularMatrix(1000, 2);
for (int i = 0; i < 1000; i++)
{
double r1 = 2.0 * rng.NextDouble() - 1.0;
double r2 = 2.0 * rng.NextDouble() - 1.0;
double x = r1 * 4.0 * s - r2 * 9.0 * s;
double y = r1 * 4.0 * s + r2 * 9.0 * s;
R[i, 0] = x; R[i, 1] = y;
MS.Add(x, y);
}
Console.WriteLine("x {0} {1}", MS.Column(0).Mean, MS.Column(0).Variance);
Console.WriteLine("y {0} {1}", MS.Column(1).Mean, MS.Column(1).Variance);
Console.WriteLine("SVD");
SingularValueDecomposition SVD = R.SingularValueDecomposition();
for (int i = 0; i < SVD.Dimension; i++)
{
Console.WriteLine("{0} {1}", i, SVD.SingularValue(i));
ColumnVector v = SVD.RightSingularVector(i);
Console.WriteLine(" {0} {1}", v[0], v[1]);
}
Console.WriteLine("PCA");
PrincipalComponentAnalysis PCA = MS.PrincipalComponentAnalysis();
Console.WriteLine("Dimension = {0} Count = {1}", PCA.Dimension, PCA.Count);
for (int i = 0; i < PCA.Dimension; i++)
{
PrincipalComponent PC = PCA.Component(i);
Console.WriteLine(" {0} {1} {2} {3}", PC.Index, PC.Weight, PC.VarianceFraction, PC.CumulativeVarianceFraction);
RowVector v = PC.NormalizedVector();
Console.WriteLine(" {0} {1}", v[0], v[1]);
}
// reconstruct
SquareMatrix U = SVD.LeftTransformMatrix();
SquareMatrix V = SVD.RightTransformMatrix();
double x1 = U[0, 0] * SVD.SingularValue(0) * V[0, 0] + U[0, 1] * SVD.SingularValue(1) * V[0, 1];
Console.WriteLine("x1 = {0} {1}", x1, R[0, 0]);
double y1 = U[0, 0] * SVD.SingularValue(0) * V[1, 0] + U[0, 1] * SVD.SingularValue(1) * V[1, 1];
Console.WriteLine("y1 = {0} {1}", y1, R[0, 1]);
double x100 = U[100, 0] * SVD.SingularValue(0) * V[0, 0] + U[100, 1] * SVD.SingularValue(1) * V[0, 1];
Console.WriteLine("x100 = {0} {1}", x100, R[100, 0]);
double y100 = U[100, 0] * SVD.SingularValue(0) * V[1, 0] + U[100, 1] * SVD.SingularValue(1) * V[1, 1];
Console.WriteLine("y100 = {0} {1}", y100, R[100, 1]);
ColumnVector d1 = U[0, 0] * SVD.SingularValue(0) * SVD.RightSingularVector(0) +
U[0, 1] * SVD.SingularValue(1) * SVD.RightSingularVector(1);
Console.WriteLine("d1 = ({0} {1})", d1[0], d1[1]);
ColumnVector d100 = U[100, 0] * SVD.SingularValue(0) * SVD.RightSingularVector(0) +
U[100, 1] * SVD.SingularValue(1) * SVD.RightSingularVector(1);
Console.WriteLine("d100 = ({0} {1})", d100[0], d100[1]);
Console.WriteLine("compare");
MultivariateSample RS = PCA.TransformedSample();
IEnumerator <double[]> RSE = RS.GetEnumerator();
RSE.MoveNext();
double[] dv1 = RSE.Current;
Console.WriteLine("{0} {1}", dv1[0], dv1[1]);
Console.WriteLine("{0} {1}", U[0, 0], U[0, 1]);
RSE.Dispose();
}
public void AllTests()
{
Matrix A, B, C, Z, O, I, R, S, X, SUB, M, T, SQ, DEF, SOL;
double tmp;
double[] columnwise = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 };
double[] rowwise = { 1.0, 4.0, 7.0, 10.0, 2.0, 5.0, 8.0, 11.0, 3.0, 6.0, 9.0, 12.0 };
double[][] avals = { new double[] { 1.0, 4.0, 7.0, 10.0 }, new double[] { 2.0, 5.0, 8.0, 11.0 }, new double[] { 3.0, 6.0, 9.0, 12.0 } };
double[][] rankdef = avals;
double[][] tvals = { new double[] { 1.0, 2.0, 3.0 }, new double[] { 4.0, 5.0, 6.0 }, new double[] { 7.0, 8.0, 9.0 }, new double[] { 10.0, 11.0, 12.0 } };
double[][] subavals = { new double[] { 5.0, 8.0, 11.0 }, new double[] { 6.0, 9.0, 12.0 } };
double[][] pvals = { new double[] { 25, -5, 10 }, new double[] { -5, 17, 10 }, new double[] { 10, 10, 62 } };
double[][] ivals = { new double[] { 1.0, 0.0, 0.0, 0.0 }, new double[] { 0.0, 1.0, 0.0, 0.0 }, new double[] { 0.0, 0.0, 1.0, 0.0 } };
double[][] evals = { new double[] { 0.0, 1.0, 0.0, 0.0 }, new double[] { 1.0, 0.0, 2e-7, 0.0 }, new double[] { 0.0, -2e-7, 0.0, 1.0 }, new double[] { 0.0, 0.0, 1.0, 0.0 } };
double[][] square = { new double[] { 166.0, 188.0, 210.0 }, new double[] { 188.0, 214.0, 240.0 }, new double[] { 210.0, 240.0, 270.0 } };
double[][] sqSolution = { new double[] { 13.0 }, new double[] { 15.0 } };
double[][] condmat = { new double[] { 1.0, 3.0 }, new double[] { 7.0, 9.0 } };
int rows = 3, cols = 4;
int invalidld = 5; /* should trigger bad shape for construction with val */
int validld = 3; /* leading dimension of intended test Matrices */
int nonconformld = 4; /* leading dimension which is valid, but nonconforming */
int ib = 1, ie = 2, jb = 1, je = 3; /* index ranges for sub Matrix */
int[] rowindexset = new int[] { 1, 2 };
int[] badrowindexset = new int[] { 1, 3 };
int[] columnindexset = new int[] { 1, 2, 3 };
int[] badcolumnindexset = new int[] { 1, 2, 4 };
double columnsummax = 33.0;
double rowsummax = 30.0;
double sumofdiagonals = 15;
double sumofsquares = 650;
#region Testing constructors and constructor-like methods
// Constructors and constructor-like methods:
// double[], int
// double[,]
// int, int
// int, int, double
// int, int, double[,]
// Create(double[,])
// Random(int,int)
// Identity(int)
try
{
// check that exception is thrown in packed constructor with invalid length
A = new Matrix(columnwise, invalidld);
Assert.Fail("Catch invalid length in packed constructor: exception not thrown for invalid input");
}
catch (ArgumentException) { }
A = new Matrix(columnwise, validld);
B = new Matrix(avals);
tmp = B[0, 0];
avals[0][0] = 0.0;
C = B - A;
avals[0][0] = tmp;
B = Matrix.Create(avals);
tmp = B[0, 0];
avals[0][0] = 0.0;
Assert.AreEqual((tmp - B[0, 0]), 0.0, "Create");
avals[0][0] = columnwise[0];
I = new Matrix(ivals);
NumericAssert.AreAlmostEqual(I, Matrix.Identity(3, 4), "Identity");
#endregion
#region Testing access methods
// Access Methods:
// getColumnDimension()
// getRowDimension()
// getArray()
// getArrayCopy()
// getColumnPackedCopy()
// getRowPackedCopy()
// get(int,int)
// GetMatrix(int,int,int,int)
// GetMatrix(int,int,int[])
// GetMatrix(int[],int,int)
// GetMatrix(int[],int[])
// set(int,int,double)
// SetMatrix(int,int,int,int,Matrix)
// SetMatrix(int,int,int[],Matrix)
// SetMatrix(int[],int,int,Matrix)
// SetMatrix(int[],int[],Matrix)
// Various get methods
B = new Matrix(avals);
Assert.AreEqual(B.RowCount, rows, "getRowDimension");
Assert.AreEqual(B.ColumnCount, cols, "getColumnDimension");
B = new Matrix(avals);
double[][] barray = (Matrix)B;
Assert.AreSame(barray, avals, "getArray");
barray = B.Clone();
Assert.AreNotSame(barray, avals, "getArrayCopy");
NumericAssert.AreAlmostEqual(new Matrix(barray), B, "getArrayCopy II");
// double[] bpacked = B.ColumnPackedCopy;
// try
// {
// check(bpacked, columnwise);
// try_success("getColumnPackedCopy... ", "");
// }
// catch (System.SystemException e)
// {
// errorCount = try_failure(errorCount, "getColumnPackedCopy... ", "data not successfully (deep) copied by columns");
// System.Console.Out.WriteLine(e.Message);
// }
// bpacked = B.RowPackedCopy;
// try
// {
// check(bpacked, rowwise);
// try_success("getRowPackedCopy... ", "");
// }
// catch (System.SystemException e)
// {
// errorCount = try_failure(errorCount, "getRowPackedCopy... ", "data not successfully (deep) copied by rows");
// System.Console.Out.WriteLine(e.Message);
// }
try
{
tmp = B[B.RowCount, B.ColumnCount - 1];
Assert.Fail("get(int,int): OutOfBoundsException expected but not thrown");
}
catch (IndexOutOfRangeException) { }
try
{
tmp = B[B.RowCount - 1, B.ColumnCount];
Assert.Fail("get(int,int): OutOfBoundsException expected but not thrown II");
}
catch (IndexOutOfRangeException) { }
Assert.AreEqual(B[B.RowCount - 1, B.ColumnCount - 1], avals[B.RowCount - 1][B.ColumnCount - 1], "get(int,int)");
SUB = new Matrix(subavals);
try
{
M = B.GetMatrix(ib, ie + B.RowCount + 1, jb, je);
Assert.Fail("GetMatrix(int,int,int,int): IndexOutOfBoundsException expected but not thrown");
}
catch (IndexOutOfRangeException) { }
try
{
M = B.GetMatrix(ib, ie, jb, je + B.ColumnCount + 1);
Assert.Fail("GetMatrix(int,int,int,int): IndexOutOfBoundsException expected but not thrown II");
}
catch (IndexOutOfRangeException) { }
M = B.GetMatrix(ib, ie, jb, je);
NumericAssert.AreAlmostEqual(SUB, M, "GetMatrix(int,int,int,int)");
try
{
M = B.GetMatrix(ib, ie, badcolumnindexset);
Assert.Fail("GetMatrix(int,int,int[]): IndexOutOfBoundsException expected but not thrown");
}
catch (IndexOutOfRangeException) { }
try
{
M = B.GetMatrix(ib, ie + B.RowCount + 1, columnindexset);
Assert.Fail("GetMatrix(int,int,int[]): IndexOutOfBoundsException expected but not thrown II");
}
catch (IndexOutOfRangeException) { }
M = B.GetMatrix(ib, ie, columnindexset);
NumericAssert.AreAlmostEqual(SUB, M, "GetMatrix(int,int,int[])");
try
{
M = B.GetMatrix(badrowindexset, jb, je);
Assert.Fail("GetMatrix(int[],int,int): IndexOutOfBoundsException expected but not thrown");
}
catch (IndexOutOfRangeException) { }
try
{
M = B.GetMatrix(rowindexset, jb, je + B.ColumnCount + 1);
Assert.Fail("GetMatrix(int[],int,int): IndexOutOfBoundsException expected but not thrown II");
}
catch (IndexOutOfRangeException) { }
M = B.GetMatrix(rowindexset, jb, je);
NumericAssert.AreAlmostEqual(SUB, M, "GetMatrix(int[],int,int)");
try
{
M = B.GetMatrix(badrowindexset, columnindexset);
Assert.Fail("GetMatrix(int[],int[]): IndexOutOfBoundsException expected but not thrown");
}
catch (IndexOutOfRangeException) { }
try
{
M = B.GetMatrix(rowindexset, badcolumnindexset);
Assert.Fail("GetMatrix(int[],int[]): IndexOutOfBoundsException expected but not thrown II");
}
catch (IndexOutOfRangeException) { }
M = B.GetMatrix(rowindexset, columnindexset);
NumericAssert.AreAlmostEqual(SUB, M, "GetMatrix(int[],int[])");
// Various set methods:
try
{
B[B.RowCount, B.ColumnCount - 1] = 0.0;
Assert.Fail("set(int,int,double): IndexOutOfBoundsException expected but not thrown");
}
catch (IndexOutOfRangeException) { }
try
{
B[B.RowCount - 1, B.ColumnCount] = 0.0;
Assert.Fail("set(int,int,double): IndexOutOfBoundsException expected but not thrown II");
}
catch (IndexOutOfRangeException) { }
B[ib, jb] = 0.0;
tmp = B[ib, jb];
NumericAssert.AreAlmostEqual(tmp, 0.0, "set(int,int,double)");
M = new Matrix(2, 3, 0.0);
try
{
B.SetMatrix(ib, ie + B.RowCount + 1, jb, je, M);
Assert.Fail("SetMatrix(int,int,int,int,Matrix): IndexOutOfBoundsException expected but not thrown");
}
catch (IndexOutOfRangeException) { }
try
{
B.SetMatrix(ib, ie, jb, je + B.ColumnCount + 1, M);
Assert.Fail("SetMatrix(int,int,int,int,Matrix): IndexOutOfBoundsException expected but not thrown II");
}
catch (IndexOutOfRangeException) { }
B.SetMatrix(ib, ie, jb, je, M);
NumericAssert.AreAlmostEqual(M - B.GetMatrix(ib, ie, jb, je), M, "SetMatrix(int,int,int,int,Matrix)");
B.SetMatrix(ib, ie, jb, je, SUB);
try
{
B.SetMatrix(ib, ie + B.RowCount + 1, columnindexset, M);
Assert.Fail("SetMatrix(int,int,int[],Matrix): IndexOutOfBoundsException expected but not thrown");
}
catch (IndexOutOfRangeException) { }
try
{
B.SetMatrix(ib, ie, badcolumnindexset, M);
Assert.Fail("SetMatrix(int,int,int[],Matrix): IndexOutOfBoundsException expected but not thrown II");
}
catch (IndexOutOfRangeException) { }
B.SetMatrix(ib, ie, columnindexset, M);
NumericAssert.AreAlmostEqual(M - B.GetMatrix(ib, ie, columnindexset), M, "SetMatrix(int,int,int[],Matrix)");
B.SetMatrix(ib, ie, jb, je, SUB);
try
{
B.SetMatrix(rowindexset, jb, je + B.ColumnCount + 1, M);
Assert.Fail("SetMatrix(int[],int,int,Matrix): IndexOutOfBoundsException expected but not thrown");
}
catch (IndexOutOfRangeException) { }
try
{
B.SetMatrix(badrowindexset, jb, je, M);
Assert.Fail("SetMatrix(int[],int,int,Matrix): IndexOutOfBoundsException expected but not thrown II");
}
catch (IndexOutOfRangeException) { }
B.SetMatrix(rowindexset, jb, je, M);
NumericAssert.AreAlmostEqual(M - B.GetMatrix(rowindexset, jb, je), M, "SetMatrix(int[],int,int,Matrix)");
B.SetMatrix(ib, ie, jb, je, SUB);
try
{
B.SetMatrix(rowindexset, badcolumnindexset, M);
Assert.Fail("SetMatrix(int[],int[],Matrix): IndexOutOfBoundsException expected but not thrown");
}
catch (IndexOutOfRangeException) { }
try
{
B.SetMatrix(badrowindexset, columnindexset, M);
Assert.Fail("SetMatrix(int[],int[],Matrix): IndexOutOfBoundsException expected but not thrown");
}
catch (IndexOutOfRangeException) { }
B.SetMatrix(rowindexset, columnindexset, M);
NumericAssert.AreAlmostEqual(M - B.GetMatrix(rowindexset, columnindexset), M, "SetMatrix(int[],int[],Matrix)");
#endregion
#region Testing array-like methods
// Array-like methods:
// Subtract
// SubtractEquals
// Add
// AddEquals
// ArrayLeftDivide
// ArrayLeftDivideEquals
// ArrayRightDivide
// ArrayRightDivideEquals
// arrayTimes
// ArrayMultiplyEquals
// uminus
S = new Matrix(columnwise, nonconformld);
R = Matrix.Random(A.RowCount, A.ColumnCount);
A = R;
try
{
S = A - S;
Assert.Fail("Subtract conformance check: nonconformance not raised");
}
catch (ArgumentException) { }
Assert.AreEqual((A - R).Norm1(), 0.0, "Subtract: difference of identical Matrices is nonzero,\nSubsequent use of Subtract should be suspect");
A = R.Clone();
A.Subtract(R);
Z = new Matrix(A.RowCount, A.ColumnCount);
try
{
A.Subtract(S);
Assert.Fail("SubtractEquals conformance check: nonconformance not raised");
}
catch (ArgumentException) { }
Assert.AreEqual((A - Z).Norm1(), 0.0, "SubtractEquals: difference of identical Matrices is nonzero,\nSubsequent use of Subtract should be suspect");
A = R.Clone();
B = Matrix.Random(A.RowCount, A.ColumnCount);
C = A - B;
try
{
S = A + S;
Assert.Fail("Add conformance check: nonconformance not raised");
}
catch (ArgumentException) { }
NumericAssert.AreAlmostEqual(C + B, A, "Add");
C = A - B;
C.Add(B);
try
{
A.Add(S);
Assert.Fail("AddEquals conformance check: nonconformance not raised");
}
catch (ArgumentException) { }
NumericAssert.AreAlmostEqual(C, A, "AddEquals");
A = ((Matrix)R.Clone());
A.UnaryMinus();
NumericAssert.AreAlmostEqual(A + R, Z, "UnaryMinus");
A = (Matrix)R.Clone();
O = new Matrix(A.RowCount, A.ColumnCount, 1.0);
try
{
Matrix.ArrayDivide(A, S);
Assert.Fail("ArrayRightDivide conformance check: nonconformance not raised");
}
catch (ArgumentException) { }
C = Matrix.ArrayDivide(A, R);
NumericAssert.AreAlmostEqual(C, O, "ArrayRightDivide");
try
{
A.ArrayDivide(S);
Assert.Fail("ArrayRightDivideEquals conformance check: nonconformance not raised");
}
catch (ArgumentException) { }
A.ArrayDivide(R);
NumericAssert.AreAlmostEqual(A, O, "ArrayRightDivideEquals");
A = (Matrix)R.Clone();
B = Matrix.Random(A.RowCount, A.ColumnCount);
try
{
S = Matrix.ArrayMultiply(A, S);
Assert.Fail("arrayTimes conformance check: nonconformance not raised");
}
catch (ArgumentException) { }
C = Matrix.ArrayMultiply(A, B);
C.ArrayDivide(B);
NumericAssert.AreAlmostEqual(C, A, "arrayTimes");
try
{
A.ArrayMultiply(S);
Assert.Fail("ArrayMultiplyEquals conformance check: nonconformance not raised");
}
catch (ArgumentException) { }
A.ArrayMultiply(B);
A.ArrayDivide(B);
NumericAssert.AreAlmostEqual(A, R, "ArrayMultiplyEquals");
#endregion
#region Testing linear algebra methods
// LA methods:
// Transpose
// Multiply
// Condition
// Rank
// Determinant
// trace
// Norm1
// norm2
// normF
// normInf
// Solve
// solveTranspose
// Inverse
// chol
// Eigen
// lu
// qr
// svd
A = new Matrix(columnwise, 3);
T = new Matrix(tvals);
T = Matrix.Transpose(A);
NumericAssert.AreAlmostEqual(Matrix.Transpose(A), T, "Transpose");
NumericAssert.AreAlmostEqual(A.Norm1(), columnsummax, "Norm1");
NumericAssert.AreAlmostEqual(A.NormInf(), rowsummax, "NormInf");
NumericAssert.AreAlmostEqual(A.NormF(), Math.Sqrt(sumofsquares), "NormF");
NumericAssert.AreAlmostEqual(A.Trace(), sumofdiagonals, "Trace");
NumericAssert.AreAlmostEqual(A.GetMatrix(0, A.RowCount - 1, 0, A.RowCount - 1).Determinant(), 0.0, "Determinant");
SQ = new Matrix(square);
NumericAssert.AreAlmostEqual(A * Matrix.Transpose(A), SQ, "Multiply(Matrix)");
NumericAssert.AreAlmostEqual(0.0 * A, Z, "Multiply(double)");
A = new Matrix(columnwise, 4);
QRDecomposition QR = A.QRDecomposition;
R = QR.R;
NumericAssert.AreAlmostEqual(A, QR.Q * R, "QRDecomposition");
SingularValueDecomposition SVD = A.SingularValueDecomposition;
NumericAssert.AreAlmostEqual(A, SVD.LeftSingularVectors * (SVD.S * Matrix.Transpose(SVD.RightSingularVectors)), "SingularValueDecomposition");
DEF = new Matrix(rankdef);
NumericAssert.AreAlmostEqual(DEF.Rank(), Math.Min(DEF.RowCount, DEF.ColumnCount) - 1, "Rank");
B = new Matrix(condmat);
SVD = B.SingularValueDecomposition;
double[] singularvalues = SVD.SingularValues;
NumericAssert.AreAlmostEqual(B.Condition(), singularvalues[0] / singularvalues[Math.Min(B.RowCount, B.ColumnCount) - 1], "Condition");
int n = A.ColumnCount;
A = A.GetMatrix(0, n - 1, 0, n - 1);
A[0, 0] = 0.0;
LUDecomposition LU = A.LUDecomposition;
NumericAssert.AreAlmostEqual(A.GetMatrix(LU.Pivot, 0, n - 1), LU.L * LU.U, "LUDecomposition");
X = A.Inverse();
NumericAssert.AreAlmostEqual(A * X, Matrix.Identity(3, 3), "Inverse");
O = new Matrix(SUB.RowCount, 1, 1.0);
SOL = new Matrix(sqSolution);
SQ = SUB.GetMatrix(0, SUB.RowCount - 1, 0, SUB.RowCount - 1);
NumericAssert.AreAlmostEqual(SQ.Solve(SOL), O, "Solve");
A = new Matrix(pvals);
CholeskyDecomposition Chol = A.CholeskyDecomposition;
Matrix L = Chol.TriangularFactor;
NumericAssert.AreAlmostEqual(A, L * Matrix.Transpose(L), "CholeskyDecomposition");
X = Chol.Solve(Matrix.Identity(3, 3));
NumericAssert.AreAlmostEqual(A * X, Matrix.Identity(3, 3), "CholeskyDecomposition Solve");
EigenvalueDecomposition Eig = A.EigenvalueDecomposition;
Matrix D = Eig.BlockDiagonal;
Matrix V = Eig.EigenVectors;
NumericAssert.AreAlmostEqual(A * V, V * D, "EigenvalueDecomposition (symmetric)");
A = new Matrix(evals);
Eig = A.EigenvalueDecomposition;
D = Eig.BlockDiagonal;
V = Eig.EigenVectors;
NumericAssert.AreAlmostEqual(A * V, V * D, "EigenvalueDecomposition (nonsymmetric)");
#endregion
}
/// <summary>
/// Parallel (symmetric) iterative algorithm.
/// </summary>
/// <returns>
/// Returns a matrix in which each row contains
/// the mixing coefficients for each component.
/// </returns>
private double[,] parallel(double[,] X, int components, double[,] winit)
{
int n = X.GetLength(0);
int m = X.GetLength(1);
// Algorithm initialization
double[,] W0 = winit;
double[,] W = winit;
double[,] K = new double[components, components];
bool stop = false;
int iterations = 0;
do // until convergence
{
// Perform simultaneous decorrelation of all components at once
var svd = new SingularValueDecomposition(W, true, false, true);
var S = svd.Diagonal;
var U = svd.LeftSingularVectors;
// Normalize
for (int i = 0; i < components; i++)
{
for (int j = 0; j < components; j++)
{
double s = 0;
for (int k = 0; k < components; k++)
if (S[k] != 0.0)
s += U[i, k] * U[j, k] / S[k];
K[i, j] = s;
}
}
// Decorrelate
W = K.Multiply(W);
// Gets the maximum absolute change in the parameters
double delta = Matrix.Max(Matrix.Abs(Matrix.Abs(Matrix.Diagonal(W0.Multiply(W.Transpose()))).Subtract(1.0)));
// Check for convergence
if (delta < tolerance || iterations >= maxIterations)
{
stop = true;
}
else
{
// Advance to the next iteration
W0 = W; W = new double[components,m];
iterations++;
#if DEBUG // For each component (in parallel)
for (int i = 0; i < components; i++)
#else
GABIZ.Base.Parallel.For(0, components, i =>
#endif
{
double[] wx = new double[n];
double[] dgwx = new double[n];
double[] gwx = new double[n];
double[] means = new double[m];
// Compute wx = w*x
for (int j = 0; j < n; j++)
{
double s = 0;
for (int k = 0; k < m; k++)
s += W0[i, k] * X[j, k];
wx[j] = s;
}
// Compute g(wx) and g'(wx)
contrast.Evaluate(wx, gwx, dgwx);
// Compute E{ x*g(w*x) }
for (int j = 0; j < m; j++)
{
for (int k = 0; k < n; k++)
means[j] += X[k, j] * gwx[k];
means[j] /= n;
}
// Compute E{ g'(w*x) }
double mean = GABIZ.Base.Statistics.Tools.Mean(dgwx);
// Compute next update for w
for (int j = 0; j < m; j++)
W[i, j] = means[j] - W0[i, j] * mean;
}
#if !DEBUG
);
#endif
}
} while (!stop);
// Return the component basis matrix
return W; // vectors stored as rows.
}
protected static void svd(double[,] m, out double[,] U)
{
var svd = new SingularValueDecomposition(m, true, false, true);
U = svd.LeftSingularVectors;
}
/// <summary>
/// Perform the Singular Value Decomposition and identify the rank of the embedding subspace
/// Characteristic of projection: the proportion of variance captured in the subspace
/// </summary>
public void Decompose()
{
//transformation of the embedded matrix
var XT = _xCom.Transpose();
//embedding (trajectory) matrix helper var
var X = _xCom;
//S matrix calculation
double[,] S = _xCom.Dot(XT);
/*Single Value Decomposition
* For an m-by-n matrix A with m >= n, the singular value decomposition is
*
* an m-by-n orthogonal matrix U,
* an n-by-n diagonal matrix S,
* and an n-by-n orthogonal matrix V
* so that A = U * S * V'.
*
* The singular values, sigma[k] = S[k,k], are ordered so that sigma[0] >= sigma[1] >= ... >= sigma[n-1].
*/
var svd = new SingularValueDecomposition(S);
//summary of the SVD calculation
//left eigenvector
double[,] U = svd.LeftSingularVectors;
double[] s = svd.Diagonal.Sqrt();
//right eigenvector
double[,] V = svd.RightSingularVectors;
int d = svd.Rank;
//helper variable to calculate characteristics of projection
double[][] Ys = new double[d][];
double[][] Zs = new double[d][];
var Vs = new double[d][];
//SVD trajectory matrix written as Xs = X1 + X2 + X3 + ... + Xd
_Xs = new Dictionary <int, double[, ]>();
//calculation of the eigen-triple of the SVD
for (int i = 0; i < d; i++)
{
//
Zs[i] = V.GetColumn(i).Multiply(s[i]);
//
Vs[i] = XT.Dot(U.GetColumn(i).Divide(s[i]));
//
Ys[i] = U.GetColumn(i).Multiply(s[i]);
//vector of Ys[i] to matrix d x 1
var y = Ys[i].ToMatrix(asColumnVector: true);
//vector of Vs[i] to matrix 1 x n
var v = Vs[i].ToMatrix(asColumnVector: false);
//matrix multiplication
var x = y.Dot(v);
_Xs.Add(i, x);
}
//calculate contributions
_sContributions = getControbutions(X, s);
int r = _sContributions.Length;
var firstRValues = s.Take(r).ToArray();
var _rCharacteristic = Math.Round(firstRValues.Multiply(firstRValues).Sum() / s.Multiply(s).Sum(), 4);
//
var orthonormalBase = new double[r][];
foreach (var ind in Enumerable.Range(0, r))
{
orthonormalBase[ind] = U.GetColumn(ind);
}
//set final value of the orthonormal matrix
_orthonormalBase = orthonormalBase;
}
private static void decompose(NormalOptions options, double[,] cov, out CholeskyDecomposition chol, out SingularValueDecomposition svd)
{
svd = null;
chol = null;
if (options == null)
{
// We don't have options. Just attempt a standard fitting. If
// the matrix is not positive semi-definite, throw an exception.
chol = new CholeskyDecomposition(cov);
if (!chol.IsPositiveDefinite)
{
throw new NonPositiveDefiniteMatrixException("Covariance matrix is not positive "
+ "definite. Try specifying a regularization constant in the fitting options "
+ "(there is an example in the Multivariate Normal Distribution documentation).");
}
return;
}
else
{
// We have options. In this case, we will either be using the SVD
// or we can add a regularization constant until the covariance
// matrix becomes positive semi-definite.
if (options.Robust)
{
// No need to apply a regularization constant in this case
svd = new SingularValueDecomposition(cov, true, true, true);
}
else
{
// Apply a regularization constant until covariance becomes positive
chol = new CholeskyDecomposition(cov);
// Check if need to add a regularization constant
double regularization = options.Regularization;
if (regularization > 0)
{
int dimension = cov.Rows();
while (!chol.IsPositiveDefinite)
{
for (int i = 0; i < dimension; i++)
{
for (int j = 0; j < dimension; j++)
{
if (Double.IsNaN(cov[i, j]) || Double.IsInfinity(cov[i, j]))
{
cov[i, j] = 0.0;
}
}
cov[i, i] += regularization;
}
chol = new CholeskyDecomposition(cov, false, true);
}
}
if (!chol.IsPositiveDefinite)
{
throw new NonPositiveDefiniteMatrixException("Covariance matrix is not positive "
+ "definite. Try specifying a regularization constant in the fitting options "
+ "(there is an example in the Multivariate Normal Distribution documentation).");
}
}
}
}
/// <summary>
/// Fits the underlying distribution to a given set of observations.
/// </summary>
///
/// <param name="observations">The array of observations to fit the model against. The array
/// elements can be either of type double (for univariate data) or
/// type double[] (for multivariate data).</param>
/// <param name="weights">The weight vector containing the weight for each of the samples.</param>
/// <param name="options">Optional arguments which may be used during fitting, such
/// as regularization constants and additional parameters.</param>
///
/// <example>
/// Please see <see cref="MultivariateNormalDistribution"/>.
/// </example>
///
public void Fit(double[][] observations, double[] weights, NormalOptions options)
{
double[] means;
double[,] cov;
if (weights != null)
{
#if DEBUG
for (int i = 0; i < weights.Length; i++)
{
if (Double.IsNaN(weights[i]) || Double.IsInfinity(weights[i]))
{
throw new ArgumentException("Invalid numbers in the weight vector.", "weights");
}
}
#endif
// Compute weighted mean vector
means = Measures.WeightedMean(observations, weights);
// Compute weighted covariance matrix
if (options != null && options.Diagonal)
{
cov = Matrix.Diagonal(Measures.WeightedVariance(observations, weights, means));
}
else
{
cov = Measures.WeightedCovariance(observations, weights, means);
}
}
else
{
// Compute mean vector
means = Measures.Mean(observations);
// Compute covariance matrix
if (options != null && options.Diagonal)
{
cov = Matrix.Diagonal(Measures.Variance(observations, means));
}
cov = Measures.Covariance(observations, means);
}
CholeskyDecomposition chol = null;
SingularValueDecomposition svd = null;
if (options == null)
{
// We don't have further options. Just attempt a standard
// fitting. If the matrix is not positive semi-definite,
// throw an exception.
chol = new CholeskyDecomposition(cov,
robust: false, lowerTriangular: true);
if (!chol.PositiveDefinite)
{
throw new NonPositiveDefiniteMatrixException("Covariance matrix is not positive "
+ "definite. Try specifying a regularization constant in the fitting options "
+ "(there is an example in the Multivariate Normal Distribution documentation).");
}
// Become the newly fitted distribution.
initialize(means, cov, chol, svd: null);
return;
}
// We have options. In this case, we will either be using the SVD
// or we can add a regularization constant until the covariance
// matrix becomes positive semi-definite.
if (options.Robust)
{
svd = new SingularValueDecomposition(cov, true, true, true);
// No need to apply a regularization constant in this case
// Become the newly fitted distribution.
initialize(means, cov, null, svd);
return;
}
chol = new CholeskyDecomposition(cov,
robust: false, lowerTriangular: true);
// Check if need to add a regularization constant
double regularization = options.Regularization;
if (regularization > 0)
{
int dimension = observations[0].Length;
while (!chol.PositiveDefinite)
{
for (int i = 0; i < dimension; i++)
{
for (int j = 0; j < dimension; j++)
{
if (Double.IsNaN(cov[i, j]) || Double.IsInfinity(cov[i, j]))
{
cov[i, j] = 0.0;
}
}
cov[i, i] += regularization;
}
chol = new CholeskyDecomposition(cov, false, true);
}
}
if (!chol.PositiveDefinite)
{
throw new NonPositiveDefiniteMatrixException("Covariance matrix is not positive "
+ "definite. Try specifying a regularization constant in the fitting options "
+ "(there is an example in the Multivariate Normal Distribution documentation).");
}
// Become the newly fitted distribution.
initialize(means, cov, chol, svd: null);
}
public virtual void Compute()
{
if (!onlyCovarianceMatrixAvailable)
{
int rows;
if (this.array != null)
{
rows = array.Length;
// Center and standardize the source matrix
double[][] matrix = Adjust(array, Overwrite);
// Perform the Singular Value Decomposition (SVD) of the matrix
var svd = new JaggedSingularValueDecomposition(matrix,
computeLeftSingularVectors: true,
computeRightSingularVectors: true,
autoTranspose: true,
inPlace: true);
SingularValues = svd.Diagonal;
// 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.
// The right singular vectors contains the principal components of the data matrix
ComponentVectors = svd.RightSingularVectors.Transpose();
}
else
{
rows = source.GetLength(0);
// Center and standardize the source matrix
#pragma warning disable 612, 618
double[,] matrix = Adjust(source, Overwrite);
#pragma warning restore 612, 618
// Perform the Singular Value Decomposition (SVD) of the matrix
var svd = new SingularValueDecomposition(matrix,
computeLeftSingularVectors: true,
computeRightSingularVectors: true,
autoTranspose: true,
inPlace: true);
SingularValues = svd.Diagonal;
// 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.
// The right singular vectors contains the principal components of the data matrix
ComponentVectors = svd.RightSingularVectors.ToArray().Transpose();
// The left singular vectors contains the factor scores for the principal components
}
// Eigenvalues are the square of the singular values
Eigenvalues = new double[SingularValues.Length];
for (int i = 0; i < SingularValues.Length; i++)
{
Eigenvalues[i] = SingularValues[i] * SingularValues[i] / (rows - 1);
}
}
else
{
// We only have the covariance matrix. Compute the Eigenvalue decomposition
var evd = new EigenvalueDecomposition(covarianceMatrix,
assumeSymmetric: true,
sort: true);
// Gets the Eigenvalues and corresponding Eigenvectors
Eigenvalues = evd.RealEigenvalues;
var eigenvectors = evd.Eigenvectors.ToJagged();
SingularValues = Eigenvalues.Sqrt();
ComponentVectors = eigenvectors.Transpose();
}
if (Whiten)
{
ComponentVectors = ComponentVectors.Transpose().Divide(Eigenvalues, dimension: 0).Transpose();
}
CreateComponents();
if (!onlyCovarianceMatrixAvailable)
{
if (array != null)
{
result = Transform(array).ToMatrix();
}
else if (source != null)
{
result = Transform(source.ToJagged()).ToMatrix();
}
}
}
public ArgumentsValue Function(MatrixValue M)
{
var svd = new SingularValueDecomposition(M);
return(new ArgumentsValue(svd.S, svd.GetU(), svd.GetV()));
}
private void computeMagCalButton_Click(object sender, EventArgs e)
{
int i, j;
calStatusText.Text = "Computing Calibration...";
// Construct D matrix
// D = [x.^2, y.^2, z.^2, x.*y, x.*z, y.*z, x, y, z, ones(N,1)];
for (i = 0; i < SAMPLES; i++)
{
// x^2 term
D.SetElement(i, 0, loggedData[i, 0] * loggedData[i, 0]);
// y^2 term
D.SetElement(i, 1, loggedData[i, 1] * loggedData[i, 1]);
// z^2 term
D.SetElement(i, 2, loggedData[i, 2] * loggedData[i, 2]);
// x*y term
D.SetElement(i, 3, loggedData[i, 0] * loggedData[i, 1]);
// x*z term
D.SetElement(i, 4, loggedData[i, 0] * loggedData[i, 2]);
// y*z term
D.SetElement(i, 5, loggedData[i, 1] * loggedData[i, 2]);
// x term
D.SetElement(i, 6, loggedData[i, 0]);
// y term
D.SetElement(i, 7, loggedData[i, 1]);
// z term
D.SetElement(i, 8, loggedData[i, 2]);
// Constant term
D.SetElement(i, 9, 1);
}
// QR=triu(qr(D))
QRDecomposition QR = new QRDecomposition(D);
// [U,S,V] = svd(D)
SingularValueDecomposition SVD = new SingularValueDecomposition(QR.R);
GeneralMatrix V = SVD.GetV();
GeneralMatrix A = new GeneralMatrix(3, 3);
double[] p = new double[V.RowDimension];
for (i = 0; i < V.RowDimension; i++)
{
p[i] = V.GetElement(i, V.ColumnDimension - 1);
}
/*
* A = [p(1) p(4)/2 p(5)/2;
* p(4)/2 p(2) p(6)/2;
* p(5)/2 p(6)/2 p(3)];
*/
if (p[0] < 0)
{
for (i = 0; i < V.RowDimension; i++)
{
p[i] = -p[i];
}
}
A.SetElement(0, 0, p[0]);
A.SetElement(0, 1, p[3] / 2);
A.SetElement(1, 2, p[4] / 2);
A.SetElement(1, 0, p[3] / 2);
A.SetElement(1, 1, p[1]);
A.SetElement(1, 2, p[5] / 2);
A.SetElement(2, 0, p[4] / 2);
A.SetElement(2, 1, p[5] / 2);
A.SetElement(2, 2, p[2]);
CholeskyDecomposition Chol = new CholeskyDecomposition(A);
GeneralMatrix Ut = Chol.GetL();
GeneralMatrix U = Ut.Transpose();
double[] bvect = { p[6] / 2, p[7] / 2, p[8] / 2 };
double d = p[9];
GeneralMatrix b = new GeneralMatrix(bvect, 3);
GeneralMatrix v = Ut.Solve(b);
double vnorm_sqrd = v.GetElement(0, 0) * v.GetElement(0, 0) + v.GetElement(1, 0) * v.GetElement(1, 0) + v.GetElement(2, 0) * v.GetElement(2, 0);
double s = 1 / Math.Sqrt(vnorm_sqrd - d);
GeneralMatrix c = U.Solve(v);
for (i = 0; i < 3; i++)
{
c.SetElement(i, 0, -c.GetElement(i, 0));
}
U = U.Multiply(s);
for (i = 0; i < 3; i++)
{
for (j = 0; j < 3; j++)
{
calMat[i, j] = U.GetElement(i, j);
}
}
for (i = 0; i < 3; i++)
{
bias[i] = c.GetElement(i, 0);
}
magAlignment00.Text = calMat[0, 0].ToString();
magAlignment01.Text = calMat[0, 1].ToString();
magAlignment02.Text = calMat[0, 2].ToString();
magAlignment10.Text = calMat[1, 0].ToString();
magAlignment11.Text = calMat[1, 1].ToString();
magAlignment12.Text = calMat[1, 2].ToString();
magAlignment20.Text = calMat[2, 0].ToString();
magAlignment21.Text = calMat[2, 1].ToString();
magAlignment22.Text = calMat[2, 2].ToString();
biasX.Text = bias[0].ToString();
biasY.Text = bias[1].ToString();
biasZ.Text = bias[2].ToString();
calStatusText.Text = "Done";
flashCommitButton.Enabled = true;
magAlignmentCommitButton.Enabled = true;
}
public SingularValueDecompositionWrapper(SingularValueDecomposition svd)
{
_svd = svd;
}
