## Interface SVDecompositionResult

• All Superinterfaces:
DecompositionResult
All Known Implementing Classes:
SVDecompositionCommonsResult

public interface SVDecompositionResult
extends DecompositionResult
Contains the results of SV matrix decomposition.
• ### Method Summary

All Methods
Modifier and Type Method 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