mpv2
Class LUPDecomposition

java.lang.Object
  mpv2.LUPDecomposition

All Implemented Interfaces:

java.io.Serializable

public class LUPDecomposition
extends java.lang.Object
implements java.io.Serializable

LUP Decomposition, P*A = L*U A is N-by-K, P is N-by-N, M is Math.min(N,K), then L is N-by-M and U is M-by-K

See Also:

Serialized Form

Constructor Summary

LUPDecomposition(AllMatrices A)
LUP Decomposition, P*A = L*U Constructor returns a structure to access L, U and P.

LUPDecomposition(double[] vals)
LUP Decomposition, P*A = L*U.

LUPDecomposition(int N, int K, double[] vals)
LUP Decomposition, P*A = L*U Constructor returns a structure to access L, U and P.

Method Summary

double	det() Determinant
int	getK() Get number of columns in the original matrix A, i.e. length of each row vector.
double[]	getLArray() Return lower triangular factor as a column-ordered array of length N*M.
BandMatrix	getLMatrix() Return lower triangular factor as a BandMatrix object.
int	getM() Get number of columns in L and rows in U.
int	getN() Get number of rows in the original matrix A, i.e. length of each column vector.
int[]	getPivot() Return pivot permutation vector, P(n,k)=1 when p[n]=k.
PermutationMatrix	getPmatrix() Return the permutation matrix, P as a PermutationMatrix object.
double[]	getUArray() Return upper triangular factor as a column-ordered array of length M*K.
BandMatrix	getUMatrix() Return upper triangular factor as a BandMatrix object.
boolean	isNonsingular() Is the matrix nonsingular?
double[]	solveArray(AllMatrices B) Solve A*X = B, X is returned as an array.
double[]	solveArray(double[] b) Solve A*x = b
SimpleMatrix	solveMatrix(AllMatrices B) Solve A*X = B, X is returned as a SimpleMatrix object.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

LUPDecomposition

public LUPDecomposition(AllMatrices A)

LUP Decomposition, P*A = L*U Constructor returns a structure to access L, U and P.

Parameters:

A - Rectangular matrix of any AllMatrices type

LUPDecomposition

public LUPDecomposition(int N,
                        int K,
                        double[] vals)

LUP Decomposition, P*A = L*U Constructor returns a structure to access L, U and P.

Parameters:

N - Number of rows in the matrix

K - Number of columns in the matrix

vals - The (N*K) matrix elements ordered by columns in an array

Throws:

java.lang.IllegalArgumentException

LUPDecomposition

public LUPDecomposition(double[] vals)

LUP Decomposition, P*A = L*U. Constructor returns a structure to access L, U and P. The dimension of the matrix is assumed to be square and given by the length of the vals array.

Parameters:

vals - The (N*N) matrix elements ordered by columns in an array

Throws:

java.lang.IllegalArgumentException

Method Detail

getN

public int getN()

Get number of rows in the original matrix A, i.e. length of each column vector. LUP-decomposition is P*A = L*U, where A is N-by-K, P is N-by-N, M is Math.min(N,K), then L is N-by-M and U is M-by-K

Returns:

N, the number of rows in A

getK

public int getK()

Get number of columns in the original matrix A, i.e. length of each row vector. LUP-decomposition is P*A = L*U, where A is N-by-K, P is N-by-N, M is Math.min(N,K), then L is N-by-M and U is M-by-K

Returns:

K, the number of columns in A

getM

public int getM()

Get number of columns in L and rows in U. LUP-decomposition is P*A = L*U, where A is N-by-K, P is N-by-N, M is Math.min(N,K), then L is N-by-M and U is M-by-K

Returns:

M, the number of columns in L and rows in U

isNonsingular

public boolean isNonsingular()

Is the matrix nonsingular?

Returns:

true if U, and hence A, is nonsingular.

getLMatrix

public BandMatrix getLMatrix()

Return lower triangular factor as a BandMatrix object. LUP-decomposition is P*A = L*U, where A is N-by-K, P is N-by-N, M is Math.min(N,K), then L is N-by-M and U is M-by-K

Returns:

LMatrix

getLArray

public double[] getLArray()

Return lower triangular factor as a column-ordered array of length N*M. LUP-decomposition is P*A = L*U, where A is N-by-K, P is N-by-N, M is Math.min(N,K), then L is N-by-M and U is M-by-K

Returns:

Larray

getUMatrix

public BandMatrix getUMatrix()

Return upper triangular factor as a BandMatrix object. LUP-decomposition is P*A = L*U, where A is N-by-K, P is N-by-N, M is Math.min(N,K), then L is N-by-M and U is M-by-K

Returns:

UMatrix

getUArray

public double[] getUArray()

Return upper triangular factor as a column-ordered array of length M*K. LUP-decomposition is P*A = L*U, where A is N-by-K, P is N-by-N, M is Math.min(N,K), then L is N-by-M and U is M-by-K

Returns:

Uarray

getPivot

public int[] getPivot()

Return pivot permutation vector, P(n,k)=1 when p[n]=k. LUP-decomposition is P*A = L*U, where A is N-by-K, P is N-by-N, M is Math.min(N,K), then L is N-by-M and U is M-by-K

Returns:

p

getPmatrix

public PermutationMatrix getPmatrix()

Return the permutation matrix, P as a PermutationMatrix object. LUP-decomposition is P*A = L*U, where A is N-by-K, P is N-by-N, M is Math.min(N,K), then L is N-by-M and U is M-by-K

Returns:

P, the permutation matrix

det

public double det()

Determinant

Returns:

det(A)

Throws:

java.lang.IllegalArgumentException - Matrix must be square

solveArray

public double[] solveArray(double[] b)

Solve A*x = b

Parameters:

b - An array with as many elements as rows in A.

Returns:

The values in x, x so that L*U*x = P*b

Throws:

java.lang.IllegalArgumentException - Matrix row dimensions must agree.

java.lang.RuntimeException - Matrix is singular.

solveMatrix

public SimpleMatrix solveMatrix(AllMatrices B)

Solve A*X = B, X is returned as a SimpleMatrix object.

Parameters:

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

Returns:

A SimpleMatrix X so that L*U*X = P*B

Throws:

java.lang.IllegalArgumentException - Matrix row dimensions must agree.

java.lang.RuntimeException - Matrix is singular.

solveArray

public double[] solveArray(AllMatrices B)

Solve A*X = B, X is returned as an array. An array with the values of X is returned, but B can be any matrix, i.e. a descendant of AllMatrices. This is perhaps a little bit faster than the solveMatrix method which return a SimpleMatrix object.

Parameters:

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

Returns:

The values in X ordered by columns, X so that L*U*X = P*B

Throws:

java.lang.IllegalArgumentException - Matrix row dimensions must agree.

java.lang.RuntimeException - Matrix is singular.