/// <summary>
/// Computes the singular value decomposition of the matrix.
/// </summary>
/// <returns>The SVD of the matrix.</returns>
public SingularValueDecomposition SingularValueDecomposition()
{
if (rows >= cols)
{
// copy the matrix so as not to distrub the original
double[] copy = MatrixAlgorithms.Copy(store, offset, rowStride, colStride, rows, cols);
// bidiagonalize it
double[] a, b;
MatrixAlgorithms.Bidiagonalize(copy, rows, cols, out a, out b);
// form the U and V matrices
double[] left = MatrixAlgorithms.AccumulateBidiagonalU(copy, rows, cols);
double[] right = MatrixAlgorithms.AccumulateBidiagonalV(copy, rows, cols);
// find the singular values of the bidiagonal matrix
MatrixAlgorithms.ExtractSingularValues(a, b, left, right, rows, cols);
// sort them
MatrixAlgorithms.SortValues(a, left, right, rows, cols);
// package it all up
return(new SingularValueDecomposition(left, a, right, rows, cols));
}
else
{
double[] scratch = MatrixAlgorithms.Transpose(store, rows, cols);
double[] a, b;
MatrixAlgorithms.Bidiagonalize(scratch, cols, rows, out a, out b);
double[] left = MatrixAlgorithms.AccumulateBidiagonalU(scratch, cols, rows);
double[] right = MatrixAlgorithms.AccumulateBidiagonalV(scratch, cols, rows);
MatrixAlgorithms.ExtractSingularValues(a, b, left, right, cols, rows);
MatrixAlgorithms.SortValues(a, left, right, cols, rows);
left = MatrixAlgorithms.Transpose(left, cols, cols);
right = MatrixAlgorithms.Transpose(right, rows, rows);
return(new SingularValueDecomposition(right, a, left, rows, cols));
}
}
/// <summary>
/// Returns the transpose of the matrix.
/// </summary>
/// <returns>M<sup>T</sup></returns>
public RectangularMatrix Transpose()
{
double[] tStore = MatrixAlgorithms.Transpose(store, rows, cols);
return(new RectangularMatrix(tStore, cols, rows));
}
/*
* IMatrix IMatrix.Clone () {
* return (Clone());
* }
*/
/// <summary>
/// Creates a transpose of the matrix.
/// </summary>
/// <returns>The matrix transpose M<sup>T</sup>.</returns>
public SquareMatrix Transpose()
{
double[] tStore = MatrixAlgorithms.Transpose(store, dimension, dimension);
return(new SquareMatrix(tStore, dimension));
}
/// <summary>
/// The orthogonal matrix Q.
/// </summary>
/// <returns>The orthogonal matrix Q.</returns>
public SquareMatrix QMatrix()
{
double[] qStore = MatrixAlgorithms.Transpose(qtStore, dimension, dimension);
return(new SquareMatrix(qStore, dimension));
}
/// <summary>
/// Returns the left transform matrix.
/// </summary>
/// <returns>The matrix U, such that A = U S V<sup>T</sup>.</returns>
public SquareMatrix LeftTransformMatrix()
{
double[] left = MatrixAlgorithms.Transpose(utStore, rows, rows);
return(new SquareMatrix(left, rows));
}
