cern.colt.matrix.tfloat.algo.decomposition

Class DenseFloatLUDecomposition

java.lang.Object

cern.colt.matrix.tfloat.algo.decomposition.DenseFloatLUDecomposition

All Implemented Interfaces:

Serializable

public class DenseFloatLUDecomposition
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

Constructor Summary

Constructors

Constructor and Description
DenseFloatLUDecomposition(FloatMatrix2D A) Constructs and returns a new LU Decomposition object; The decomposed matrices can be retrieved via instance methods of the returned decomposition object.

Method Summary

Methods

Modifier and Type	Method and Description
float	det() Returns the determinant, det(A).
FloatMatrix2D	getL() Returns the lower triangular factor, L.
int[]	getPivot() Returns a copy of the pivot permutation vector.
FloatMatrix2D	getU() Returns the upper triangular factor, U.
boolean	isNonsingular() Returns whether the matrix is nonsingular (has an inverse).
FloatMatrix1D	solve(FloatMatrix1D b) Solves A*x = b.
FloatMatrix2D	solve(FloatMatrix2D B) Solves A*X = B.
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

DenseFloatLUDecomposition

public DenseFloatLUDecomposition(FloatMatrix2D 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

Method Detail

det

public float det()

Returns the determinant, det(A).

Throws:

IllegalArgumentException - Matrix must be square

getL

public FloatMatrix2D 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 FloatMatrix2D 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 FloatMatrix2D solve(FloatMatrix2D 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().

solve

public FloatMatrix1D solve(FloatMatrix1D b)

Solves A*x = b.

Parameters:

b - A vector of size A.rows()

Returns:

x so that L*U*x = b(piv).

Throws:

IllegalArgumentException - if b.size() != 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
 
 

Overrides:

toString in class Object