Class SymmetricSchurDecomposition

Namespace

NanoQL.Numerics

Assembly

NanoQL.dll

The eigenvalues and eigenvectors of a real symmetric matrix, by the symmetric threshold Jacobi algorithm.

public sealed class SymmetricSchurDecomposition

Inheritance

object

SymmetricSchurDecomposition

Inherited Members

object.GetType()

object.ToString()

object.Equals(object)

object.Equals(object, object)

object.ReferenceEquals(object, object)

object.GetHashCode()

Remarks

Given a real symmetric matrix S, the Schur decomposition finds the eigenvalues and eigenvectors of S. If D is the diagonal matrix formed by the eigenvalues and U the unitarian matrix of the eigenvectors, S = U·D·Uᵀ. For details on the different Jacobi transformations see "Matrix computation", second edition, by Golub and Van Loan, The Johns Hopkins University Press.

The decomposition is computed in the constructor; Eigenvalues() and Eigenvectors() return copies. The eigenvalues are sorted in decreasing order, each eigenvector with its first component non-negative. A NaN eigenvalue, or a NaN in two equal eigenvalues' eigenvectors where their comparison reads it, is refused: QuantLib sorts the pairs with a comparison that NaN leaves undefined (a divergence).

Constructors

SymmetricSchurDecomposition(Matrix)

Initializes a new instance of the SymmetricSchurDecomposition class.

public SymmetricSchurDecomposition(Matrix s)

Parameters

s Matrix

The matrix, symmetric.

Exceptions

ArgumentException

s is empty or not square.

NanoQLException

The algorithm doesn't converge in 100 iterations, or the sort would read a NaN (a divergence).

Methods

Eigenvalues()

The eigenvalues, in decreasing order.

public Vector Eigenvalues()

Returns

Vector

A new vector.

Eigenvectors()

The eigenvectors, one per column in the eigenvalues' order, each with its first component non-negative.

public Matrix Eigenvectors()

Returns

Matrix

A new matrix.