com.opengamma.strata.math.impl.linearalgebra

Interface SVDecompositionResult

All Superinterfaces:

DecompositionResult

All Known Implementing Classes:

SVDecompositionCommonsResult

public interface SVDecompositionResult
extends DecompositionResult

Contains the results of SV matrix decomposition.

Method Summary

Modifier and Type	Method and Description
double	getConditionNumber() Returns the condition number of the matrix.
double	getNorm() Returns the $L_2$ norm of the matrix.
int	getRank() Returns the effective numerical matrix rank.
DoubleMatrix	getS() Returns the diagonal matrix $\mathbf{\Sigma}$ of the decomposition.
double[]	getSingularValues() Returns the diagonal elements of the matrix $\mathbf{\Sigma}$ of the decomposition.
DoubleMatrix	getU() Returns the matrix $\mathbf{U}$ of the decomposition.
DoubleMatrix	getUT() Returns the transpose of the matrix $\mathbf{U}$ of the decomposition.
DoubleMatrix	getV() Returns the matrix $\mathbf{V}$ of the decomposition.
DoubleMatrix	getVT() Returns the transpose of the matrix $\mathbf{V}$ of the decomposition.

Methods inherited from interface com.opengamma.strata.math.linearalgebra.DecompositionResult

solve, solve, solve

Method Detail

getU

DoubleMatrix getU()

Returns the matrix $\mathbf{U}$ of the decomposition.

$\mathbf{U}$ is an orthogonal matrix, i.e. its transpose is also its inverse.

Returns:

the $\mathbf{U}$ matrix

getUT

DoubleMatrix getUT()

Returns the transpose of the matrix $\mathbf{U}$ of the decomposition.

$\mathbf{U}$ is an orthogonal matrix, i.e. its transpose is also its inverse.

Returns:

the U matrix (or null if decomposed matrix is singular)

getS

DoubleMatrix getS()

Returns the diagonal matrix $\mathbf{\Sigma}$ of the decomposition.

$\mathbf{\Sigma}$ is a diagonal matrix. The singular values are provided in non-increasing order.

Returns:

the $\mathbf{\Sigma}$ matrix

getSingularValues

double[] getSingularValues()

Returns the diagonal elements of the matrix $\mathbf{\Sigma}$ of the decomposition.

The singular values are provided in non-increasing order.

Returns:

the diagonal elements of the $\mathbf{\Sigma}$ matrix

getV

DoubleMatrix getV()

Returns the matrix $\mathbf{V}$ of the decomposition.

$\mathbf{V}$ is an orthogonal matrix, i.e. its transpose is also its inverse.

Returns:

the $\mathbf{V}$ matrix

getVT

DoubleMatrix getVT()

Returns the transpose of the matrix $\mathbf{V}$ of the decomposition.

$\mathbf{V}$ is an orthogonal matrix, i.e. its transpose is also its inverse.

Returns:

the $\mathbf{V}$ matrix

getNorm

double getNorm()

Returns the $L_2$ norm of the matrix.

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).

Returns:

norm

getConditionNumber

double getConditionNumber()

Returns the condition number of the matrix.

Returns:

condition number of the matrix

getRank

int getRank()

Returns the effective numerical matrix rank.

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.

Returns:

effective numerical matrix rank