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## cern.colt.matrix.linalg
Class CholeskyDecomposition

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

All Implemented Interfaces:
  Serializable

public class CholeskyDecomposition
extends Object
implements Serializable

For a symmetric, positive definite matrix `A`, the Cholesky decomposition is a lower triangular matrix `L` so that `A = L*L'`; If the matrix is not symmetric or positive definite, the constructor returns a partial decomposition and sets an internal flag that may be queried by the `isSymmetricPositiveDefinite()` method.

See Also:
  Serialized Form

Constructor Summary
`CholeskyDecomposition(DoubleMatrix2D A)` Constructs and returns a new Cholesky decomposition object for a symmetric and positive definite matrix; The decomposed matrices can be retrieved via instance methods of the returned decomposition object.

Method Summary
`DoubleMatrix2D` | `getL()` Returns the triangular factor, `L`.
`boolean` | `isSymmetricPositiveDefinite()` Returns whether the matrix `A` is symmetric and positive definite.
`DoubleMatrix2D` | `solve(DoubleMatrix2D B)` Solves `A*X = B`; returns `X`.
`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

### CholeskyDecomposition

    public CholeskyDecomposition(DoubleMatrix2D A)

  Constructs and returns a new Cholesky decomposition object for a symmetric and positive definite matrix; The decomposed matrices can be retrieved via instance methods of the returned decomposition object.

Parameters:
  `A` - Square, symmetric matrix.
Throws:
  `IllegalArgumentException` - if `A` is not square.

Method Detail

### getL

    public DoubleMatrix2D getL()

  Returns the triangular factor, `L`.

  Returns:
    `L`

### isSymmetricPositiveDefinite

    public boolean isSymmetricPositiveDefinite()

  Returns whether the matrix `A` is symmetric and positive definite.

  Returns:
    true if `A` is symmetric and positive definite; false otherwise

### solve

    public DoubleMatrix2D solve(DoubleMatrix2D B)

  Solves `A*X = B`; returns `X`.

  Parameters:
    `B` - A Matrix with as many rows as `A` and any number of columns.
  Returns:
    `X` so that `L*L'*X = B`.
  Throws:
    `IllegalArgumentException` - if `B.rows() != A.rows()`.
    `IllegalArgumentException` - if `!isSymmetricPositiveDefinite()`.

### 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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