/**
* Copyright (C) 2009 - present by OpenGamma Inc. and the OpenGamma group of companies
*
* Please see distribution for license.
*/
package com.opengamma.strata.math.impl.linearalgebra;
import com.opengamma.strata.collect.array.DoubleMatrix;
/**
* Contains the results of SV matrix decomposition.
*/
public interface SVDecompositionResult extends DecompositionResult {
/**
* Returns the matrix $\mathbf{U}$ of the decomposition.
* <p>
* $\mathbf{U}$ is an orthogonal matrix, i.e. its transpose is also its inverse.
* @return the $\mathbf{U}$ matrix
*/
DoubleMatrix getU();
/**
* Returns the transpose of the matrix $\mathbf{U}$ of the decomposition.
* <p>
* $\mathbf{U}$ is an orthogonal matrix, i.e. its transpose is also its inverse.
* @return the U matrix (or null if decomposed matrix is singular)
*/
DoubleMatrix getUT();
/**
* Returns the diagonal matrix $\mathbf{\Sigma}$ of the decomposition.
* <p>
* $\mathbf{\Sigma}$ is a diagonal matrix. The singular values are provided in
* non-increasing order.
* @return the $\mathbf{\Sigma}$ matrix
*/
DoubleMatrix getS();
/**
* Returns the diagonal elements of the matrix $\mathbf{\Sigma}$ of the decomposition.
* <p>
* The singular values are provided in non-increasing order.
* @return the diagonal elements of the $\mathbf{\Sigma}$ matrix
*/
double[] getSingularValues();
/**
* Returns the matrix $\mathbf{V}$ of the decomposition.
* <p>
* $\mathbf{V}$ is an orthogonal matrix, i.e. its transpose is also its inverse.
* @return the $\mathbf{V}$ matrix
*/
DoubleMatrix getV();
/**
* Returns the transpose of the matrix $\mathbf{V}$ of the decomposition.
* <p>
* $\mathbf{V}$ is an orthogonal matrix, i.e. its transpose is also its inverse.
* @return the $\mathbf{V}$ matrix
*/
DoubleMatrix getVT();
/**
* Returns the $L_2$ norm of the matrix.
* <p>
* The $L_2$ norm is $\max\left(\frac{|\mathbf{A} \times U|_2}{|U|_2}\right)$, where $|.|_2$ denotes the vectorial 2-norm
* (i.e. the traditional Euclidian norm).
* @return norm
*/
double getNorm();
/**
* Returns the condition number of the matrix.
* @return condition number of the matrix
*/
double getConditionNumber();
/**
* Returns the effective numerical matrix rank.
* <p>The effective numerical rank is the number of non-negligible
* singular values. The threshold used to identify non-negligible
* terms is $\max(m, n) \times \mathrm{ulp}(S_1)$, where $\mathrm{ulp}(S_1)$
* is the least significant bit of the largest singular value.
* @return effective numerical matrix rank
*/
int getRank();
}