Package elki.math.linearalgebra
Class SingularValueDecomposition
- java.lang.Object
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- elki.math.linearalgebra.SingularValueDecomposition
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public class SingularValueDecomposition extends java.lang.Object
Singular Value Decomposition.For an m-by-n matrix A with m >= n, the singular value decomposition is an m-by-n orthogonal matrix U, an n-by-n diagonal matrix S, and an n-by-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.
- Since:
- 0.1
- Author:
- Arthur Zimek
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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.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(double[][] Arg)
Constructor.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description double
cond()
Two norm condition numberprivate int
convergence(int k, int pp, boolean wantu, boolean wantv)
private void
deflate(double[] e, int p, int k, boolean wantv)
private void
generateU(int nu, int nct)
private void
generateV(int nu, double[] e, int nrt)
double[][]
getS()
Return the diagonal matrix of singular valuesdouble[]
getSingularValues()
Return the one-dimensional array of singular valuesdouble[][]
getU()
Return the left singular vectorsdouble[][]
getV()
Return the right singular vectorsdouble
norm2()
Two normprivate void
qrStep(double[] e, int p, int k, boolean wantu, boolean wantv)
int
rank()
Effective numerical matrix rankprivate void
split(double[] e, int p, int k, boolean wantu)
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Method Detail
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generateU
private void generateU(int nu, int nct)
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generateV
private void generateV(int nu, double[] e, int nrt)
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deflate
private void deflate(double[] e, int p, int k, boolean wantv)
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split
private void split(double[] e, int p, int k, boolean wantu)
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qrStep
private void qrStep(double[] e, int p, int k, boolean wantu, boolean wantv)
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convergence
private int convergence(int k, int pp, boolean wantu, boolean wantv)
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getU
public double[][] getU()
Return the left singular vectors- Returns:
- U
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getV
public double[][] getV()
Return the right singular vectors- Returns:
- V
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getSingularValues
public double[] getSingularValues()
Return the one-dimensional array of singular values- Returns:
- diagonal of S.
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getS
public double[][] getS()
Return the diagonal matrix of singular values- Returns:
- S
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norm2
public double norm2()
Two norm- Returns:
- max(S)
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cond
public double cond()
Two norm condition number- Returns:
- max(S)/min(S)
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rank
public int rank()
Effective numerical matrix rank- Returns:
- Number of non-negligible singular values.
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