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java.lang.Object edu.northwestern.at.utils.math.matrix.SingularValueDecomposition
public class SingularValueDecomposition
Singular Value Decomposition of a matrix.
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 decompostion always exists, so the constructor will never fail. The matrix condition number and the effective numerical rank can be computed from this decomposition.
This code is a slight modification of the JAMA code, which in turn is based on the Linpack code.
Constructor Summary | |
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SingularValueDecomposition(Matrix matrix)
Construct the singular value decomposition. |
Method Summary | |
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double |
cond()
Return two norm condition number. |
Matrix |
getS()
Return diagonal matrix of singular values. |
double[] |
getSingularValues()
Return singular values. |
Matrix |
getU()
Return the left singular vectors |
Matrix |
getV()
Return the right singular vectors |
double |
norm2()
Return two norm. |
int |
rank()
Return effective numerical matrix rank. |
Methods inherited from class java.lang.Object |
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clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Constructor Detail |
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public SingularValueDecomposition(Matrix matrix)
matrix
- Rectangular matrix to decompose. Method Detail |
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public Matrix getU()
public Matrix getV()
public double[] getSingularValues()
public Matrix getS()
public double norm2()
public double cond()
public int rank()
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