Class SingularValueDecompositionImpl
- All Implemented Interfaces:
SingularValueDecomposition
The Singular Value Decomposition of matrix A is a set of three matrices: U, Σ and V such that A = U × Σ × VT. Let A be a m × n matrix, then U is a m × p orthogonal matrix, Σ is a p × p diagonal matrix with positive or null elements, V is a p × n orthogonal matrix (hence VT is also orthogonal) where p=min(m,n).
- Since:
- 2.0
- Version:
- $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 août 2010) $
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Constructor Summary
ConstructorsConstructorDescriptionCalculates the compact Singular Value Decomposition of the given matrix. -
Method Summary
Modifier and TypeMethodDescriptiondouble
Return the condition number of the matrix.getCovariance
(double minSingularValue) Returns the n × n covariance matrix.double
getNorm()
Returns the L2 norm of the matrix.int
getRank()
Return the effective numerical matrix rank.getS()
Returns the diagonal matrix Σ of the decomposition.double[]
Returns the diagonal elements of the matrix Σ of the decomposition.Get a solver for finding the A × X = B solution in least square sense.getU()
Returns the matrix U of the decomposition.getUT()
Returns the transpose of the matrix U of the decomposition.getV()
Returns the matrix V of the decomposition.getVT()
Returns the transpose of the matrix V of the decomposition.
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Constructor Details
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SingularValueDecompositionImpl
Calculates the compact Singular Value Decomposition of the given matrix.- Parameters:
matrix
- The matrix to decompose.- Throws:
InvalidMatrixException
- (wrapping aConvergenceException
if algorithm fails to converge
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Method Details
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getU
Returns the matrix U of the decomposition.U is an orthogonal matrix, i.e. its transpose is also its inverse.
- Specified by:
getU
in interfaceSingularValueDecomposition
- Returns:
- the U matrix
- Throws:
InvalidMatrixException
- See Also:
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getUT
Returns the transpose of the matrix U of the decomposition.U is an orthogonal matrix, i.e. its transpose is also its inverse.
- Specified by:
getUT
in interfaceSingularValueDecomposition
- Returns:
- the U matrix (or null if decomposed matrix is singular)
- Throws:
InvalidMatrixException
- See Also:
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getS
Returns the diagonal matrix Σ of the decomposition.Σ is a diagonal matrix. The singular values are provided in non-increasing order, for compatibility with Jama.
- Specified by:
getS
in interfaceSingularValueDecomposition
- Returns:
- the Σ matrix
- Throws:
InvalidMatrixException
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getSingularValues
Returns the diagonal elements of the matrix Σ of the decomposition.The singular values are provided in non-increasing order, for compatibility with Jama.
- Specified by:
getSingularValues
in interfaceSingularValueDecomposition
- Returns:
- the diagonal elements of the Σ matrix
- Throws:
InvalidMatrixException
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getV
Returns the matrix V of the decomposition.V is an orthogonal matrix, i.e. its transpose is also its inverse.
- Specified by:
getV
in interfaceSingularValueDecomposition
- Returns:
- the V matrix (or null if decomposed matrix is singular)
- Throws:
InvalidMatrixException
- See Also:
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getVT
Returns the transpose of the matrix V of the decomposition.V is an orthogonal matrix, i.e. its transpose is also its inverse.
- Specified by:
getVT
in interfaceSingularValueDecomposition
- Returns:
- the V matrix (or null if decomposed matrix is singular)
- Throws:
InvalidMatrixException
- See Also:
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getCovariance
Returns the n × n covariance matrix.The covariance matrix is V × J × VT where J is the diagonal matrix of the inverse of the squares of the singular values.
- Specified by:
getCovariance
in interfaceSingularValueDecomposition
- Parameters:
minSingularValue
- value below which singular values are ignored (a 0 or negative value implies all singular value will be used)- Returns:
- covariance matrix
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getNorm
Returns the L2 norm of the matrix.The L2 norm is max(|A × u|2 / |u|2), where |.|2 denotes the vectorial 2-norm (i.e. the traditional euclidian norm).
- Specified by:
getNorm
in interfaceSingularValueDecomposition
- Returns:
- norm
- Throws:
InvalidMatrixException
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getConditionNumber
Return the condition number of the matrix.- Specified by:
getConditionNumber
in interfaceSingularValueDecomposition
- Returns:
- condition number of the matrix
- Throws:
InvalidMatrixException
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getRank
Return 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) × ulp(s1) where ulp(s1) is the least significant bit of the largest singular value.
- Specified by:
getRank
in interfaceSingularValueDecomposition
- Returns:
- effective numerical matrix rank
- Throws:
IllegalStateException
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getSolver
Get a solver for finding the A × X = B solution in least square sense.- Specified by:
getSolver
in interfaceSingularValueDecomposition
- Returns:
- a solver
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