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## cern.colt.matrix.linalg
Class SingularValueDecomposition

    java.lang.Object
      cern.colt.matrix.linalg.SingularValueDecomposition

All Implemented Interfaces:
  Serializable

public class SingularValueDecomposition
extends Object
implements 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

Constructor Summary
`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.

Method Summary
`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 values
`DoubleMatrix2D` | `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.
`String` | `toString()` Returns a String with (propertyName, propertyValue) pairs.

Methods inherited from class java.lang.Object
`equals, getClass, hashCode, notify, notifyAll, wait, wait, wait`

Constructor Detail

### 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.

Throws:
  `IllegalArgumentException` - if `A.rows() < A.columns()`.

Method Detail

### cond

    public double cond()

  Returns the two norm condition number, which is `max(S) / min(S)`.

### getS

    public DoubleMatrix2D getS()

  Returns the diagonal matrix of singular values.

  Returns:
    S

### getSingularValues

    public double[] getSingularValues()

  Returns the diagonal of `S`, which is a one-dimensional array of singular values

  Returns:
    diagonal of `S`.

### getU

    public DoubleMatrix2D getU()

  Returns the left singular vectors `U`.

  Returns:
    `U`

### getV

    public DoubleMatrix2D getV()

  Returns the right singular vectors `V`.

  Returns:
    `V`

### norm2

    public double norm2()

  Returns the two norm, which is `max(S)`.

### rank

    public int rank()

  Returns the effective numerical matrix rank, which is the number of nonnegligible singular values.

### toString

    public 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

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