Package cern.colt.matrix.linalg
Class SingularValueDecomposition
- java.lang.Object
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- cern.colt.matrix.linalg.SingularValueDecomposition
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- All Implemented Interfaces:
java.io.Serializable
public class SingularValueDecomposition extends java.lang.Object implements java.io.Serializable
For an m x n matrix A with m >= n, the singular value decomposition is an m x n orthogonal matrix U, an n x n diagonal matrix S, and an n x n orthogonal matrix V so that A = U*S*V'.The singular values, sigma[k] = S[k][k], are ordered so that sigma[0] >= sigma[1] >= ... >= sigma[n-1].
The singular value decomposition always exists, so the constructor will never fail. The matrix condition number and the effective numerical rank can be computed from this decomposition.
- See Also:
- Serialized Form
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Field Summary
Fields Modifier and Type Field Description private int
m
Row and column dimensions.private int
n
Row and column dimensions.private double[]
s
Array for internal storage of singular values.(package private) static long
serialVersionUID
private double[][]
U
Arrays for internal storage of U and V.private double[][]
V
Arrays for internal storage of U and V.
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Constructor Summary
Constructors Constructor Description SingularValueDecomposition(DoubleMatrix2D Arg)
Constructs and returns a new singular value decomposition object; The decomposed matrices can be retrieved via instance methods of the returned decomposition object.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description double
cond()
Returns the two norm condition number, which is max(S) / min(S).DoubleMatrix2D
getS()
Returns the diagonal matrix of singular values.double[]
getSingularValues()
Returns the diagonal of S, which is a one-dimensional array of singular valuesDoubleMatrix2D
getU()
Returns the left singular vectors U.DoubleMatrix2D
getV()
Returns the right singular vectors V.double
norm2()
Returns the two norm, which is max(S).int
rank()
Returns the effective numerical matrix rank, which is the number of nonnegligible singular values.java.lang.String
toString()
Returns a String with (propertyName, propertyValue) pairs.
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Field Detail
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serialVersionUID
static final long serialVersionUID
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- Constant Field Values
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U
private double[][] U
Arrays for internal storage of U and V.
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V
private double[][] V
Arrays for internal storage of U and V.
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s
private double[] s
Array for internal storage of singular values.
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m
private int m
Row and column dimensions.
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n
private int n
Row and column dimensions.
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Constructor Detail
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SingularValueDecomposition
public SingularValueDecomposition(DoubleMatrix2D Arg)
Constructs and returns a new singular value decomposition object; The decomposed matrices can be retrieved via instance methods of the returned decomposition object.- Parameters:
A
- A rectangular matrix.- Throws:
java.lang.IllegalArgumentException
- if A.rows() < A.columns().
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Method Detail
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cond
public double cond()
Returns the two norm condition number, which is max(S) / min(S).
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getS
public DoubleMatrix2D getS()
Returns the diagonal matrix of singular values.- Returns:
- S
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getSingularValues
public double[] getSingularValues()
Returns the diagonal of S, which is a one-dimensional array of singular values- Returns:
- diagonal of S.
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getU
public DoubleMatrix2D getU()
Returns the left singular vectors U.- Returns:
- U
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getV
public DoubleMatrix2D getV()
Returns the right singular vectors V.- Returns:
- V
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norm2
public double norm2()
Returns the two norm, which is max(S).
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rank
public int rank()
Returns the effective numerical matrix rank, which is the number of nonnegligible singular values.
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toString
public java.lang.String toString()
Returns a String with (propertyName, propertyValue) pairs. Useful for debugging or to quickly get the rough picture. For example,rank : 3 trace : 0
- Overrides:
toString
in classjava.lang.Object
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