/// <summary>
/// Example program that illustrates how to determine the condition number of a matrix
/// to find its largest and smallest singular values.
/// </summary>
/// <remarks>
/// MODULE LSVD.cc
///
/// In this example, Arpack++ is called to solve the symmetric problem:
///
/// (A'*A)*v = sigma*v
///
/// where A is an m by n real matrix. This formulation is appropriate when m >= n.
/// The roles of A and A' must be reversed in the case that m < n.
/// </remarks>
private static void LSVDcond()
{
// Number of columns in A.
int n = 100;
// Creating a rectangular matrix with m = 200 and n = 100.
var A = Generate.RectangularMatrix(n);
int m = A.RowCount; // Number of rows in A.
// Defining what we need: eigenvalues from both ends of the spectrum.
var prob = new Arpack(A)
{
ArnoldiCount = 20
};
// Finding eigenvalues.
var result = prob.SingularValues(6, true, Spectrum.BothEnds);
Solution.Condition(A, (ArpackResult)result);
}
/// <summary>
/// Example program that illustrates how to determine the truncated SVD of a matrix.
/// </summary>
/// <remarks>
/// MODULE LSVD.cc
///
/// In this example, Arpack++ is called to solve the symmetric problem:
///
/// | 0 A |*y = sigma*y,
/// | A' 0 |
///
/// where A is an m by n real matrix.
///
/// This problem can be used to obtain the decomposition A = U*S*V'. The positive
/// eigenvalues of this problem are the singular values of A (the eigenvalues come
/// in pairs, the negative eigenvalues have the same magnitude of the positive ones
/// and can be discarded). The columns of U can be extracted from the first m
/// components of the eigenvectors y, while the columns of V can be extracted from
/// the the remaining n components.
/// </remarks>
private static void LSVDpart()
{
// Number of columns in A.
int n = 100;
// Creating a rectangular matrix with m = 200 and n = 100.
var A = Generate.RectangularMatrix(n);
int m = A.RowCount; // Number of rows in A.
// Defining what we need: the four eigenvalues with largest algebraic value.
var prob = new Arpack(A)
{
ArnoldiCount = 20, ComputeEigenVectors = true
};
// Finding eigenvalues.
var result = prob.SingularValues(5, false, Spectrum.LargestAlgebraic);
// Printing the solution.
Solution.SVD(A, (ArpackResult)result);
}