cern.colt.matrix.linalg
Class LUDecomposition

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

All Implemented Interfaces:

Serializable

public class LUDecomposition

extends Object

implements Serializable

For an m x n matrix A with m >= n, the LU decomposition is an m x n unit lower triangular matrix L, an n x n upper triangular matrix U, and a permutation vector piv of length m so that A(piv,:) = L*U; If m < n, then L is m x m and U is m x n.

The LU decomposition with pivoting always exists, even if the matrix is singular, so the constructor will never fail. The primary use of the LU decomposition is in the solution of square systems of simultaneous linear equations. This will fail if isNonsingular() returns false.

See Also:

Serialized Form

LUDecomposition

public LUDecomposition(DoubleMatrix2D A)

Constructs and returns a new LU Decomposition object; The decomposed matrices can be retrieved via instance methods of the returned decomposition object.

Parameters:

A - Rectangular matrix

det

public double det()

Returns the determinant, det(A).

Throws:

IllegalArgumentException - Matrix must be square

getL

public DoubleMatrix2D getL()

Returns the lower triangular factor, L.

Returns:

L

getPivot

public int[] getPivot()

Returns a copy of the pivot permutation vector.

Returns:

piv

getU

public DoubleMatrix2D getU()

Returns the upper triangular factor, U.

Returns:

U

isNonsingular

public boolean isNonsingular()

Returns whether the matrix is nonsingular (has an inverse).

Returns:

true if U, and hence A, is nonsingular; false otherwise.

solve

public DoubleMatrix2D solve(DoubleMatrix2D B)

Solves A*X = B.

Parameters:

B - A matrix with as many rows as A and any number of columns.

Returns:

X so that L*U*X = B(piv,:).

Throws:

IllegalArgumentException - if B.rows() != A.rows().

IllegalArgumentException - if A is singular, that is, if !this.isNonsingular().

IllegalArgumentException - if A.rows() < A.columns().

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