## Class SVDecompositionCommonsResult

• java.lang.Object
• com.opengamma.strata.math.impl.linearalgebra.SVDecompositionCommonsResult
• ### Constructor Summary

Constructors
Constructor Description
SVDecompositionCommonsResult​(org.apache.commons.math3.linear.SingularValueDecomposition svd)
Creates an instance.
• ### 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.
double[] solve​(double[] b)
Solves $\mathbf{A}x = b$ where $\mathbf{A}$ is a (decomposed) matrix and $b$ is a vector.
DoubleArray solve​(DoubleArray b)
Solves $\mathbf{A}x = b$ where $\mathbf{A}$ is a (decomposed) matrix and $b$ is a vector.
DoubleMatrix solve​(DoubleMatrix b)
Solves $\mathbf{A}x = \mathbf{B}$ where $\mathbf{A}$ is a (decomposed) matrix and $\mathbf{B}$ is a matrix.
• ### Constructor Detail

• #### SVDecompositionCommonsResult

public SVDecompositionCommonsResult​(org.apache.commons.math3.linear.SingularValueDecomposition svd)
Creates an instance.
Parameters:
svd - The result of the SV decomposition, not null
• ### Method Detail

• #### getConditionNumber

public double getConditionNumber()
Returns the condition number of the matrix.
Specified by:
getConditionNumber in interface SVDecompositionResult
Returns:
condition number of the matrix
• #### getNorm

public 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).

Specified by:
getNorm in interface SVDecompositionResult
Returns:
norm
• #### getRank

public 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.

Specified by:
getRank in interface SVDecompositionResult
Returns:
effective numerical matrix rank
• #### getS

public 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.

Specified by:
getS in interface SVDecompositionResult
Returns:
the $\mathbf{\Sigma}$ matrix
• #### getSingularValues

public double[] getSingularValues()
Returns the diagonal elements of the matrix $\mathbf{\Sigma}$ of the decomposition.

The singular values are provided in non-increasing order.

Specified by:
getSingularValues in interface SVDecompositionResult
Returns:
the diagonal elements of the $\mathbf{\Sigma}$ matrix
• #### getU

public DoubleMatrix getU()
Returns the matrix $\mathbf{U}$ of the decomposition.

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

Specified by:
getU in interface SVDecompositionResult
Returns:
the $\mathbf{U}$ matrix
• #### getUT

public 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.

Specified by:
getUT in interface SVDecompositionResult
Returns:
the U matrix (or null if decomposed matrix is singular)
• #### getV

public DoubleMatrix getV()
Returns the matrix $\mathbf{V}$ of the decomposition.

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

Specified by:
getV in interface SVDecompositionResult
Returns:
the $\mathbf{V}$ matrix
• #### getVT

public 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.

Specified by:
getVT in interface SVDecompositionResult
Returns:
the $\mathbf{V}$ matrix
• #### solve

public DoubleArray solve​(DoubleArray b)
Solves $\mathbf{A}x = b$ where $\mathbf{A}$ is a (decomposed) matrix and $b$ is a vector.
Specified by:
solve in interface DecompositionResult
Parameters:
b - the vector to calculate with
Returns:
the vector x
• #### solve

public double[] solve​(double[] b)
Solves $\mathbf{A}x = b$ where $\mathbf{A}$ is a (decomposed) matrix and $b$ is a vector.
Specified by:
solve in interface DecompositionResult
Parameters:
b - the vector to calculate with
Returns:
the vector x
• #### solve

public DoubleMatrix solve​(DoubleMatrix b)
Solves $\mathbf{A}x = \mathbf{B}$ where $\mathbf{A}$ is a (decomposed) matrix and $\mathbf{B}$ is a matrix.
Specified by:
solve in interface DecompositionResult
Parameters:
b - the matrix to calculate with
Returns:
the matrix x