maspack.matrix

Class LUDecomposition

java.lang.Object

maspack.matrix.LUDecomposition

public class LUDecomposition
extends java.lang.Object

Constructs the LU decomposition of a square matrix. This takes the form
P M = L U
where P is a permutation matrix, M is the original matrix, L is unit-lower-triangular, and U is upper-triangular. Once an LU decomposition has been constructed, it can be used to perform various computations related to M, such as solving equations, computing the determinant, or estimating the condition number.

Providing a separate class for the LU decomposition allows an application to perform such decompositions repeatedly without having to reallocate temporary storage space.

Constructor Summary

Constructors

Constructor and Description
LUDecomposition() Creates an uninitialized LUDecomposition.
LUDecomposition(int n) Creates an uninitialized LUDecomposition with enough capacity to handle matrices of size n.
LUDecomposition(Matrix M) Creates an LUDecomposition for the Matrix specified by M.

Method Summary

Modifier and Type	Method and Description
double	conditionEstimate(Matrix M) Estimates the condition number of the original matrix M associated with this decomposition.
double	determinant() Compute the determinant of the original matrix M associated with this decomposition.
void	factor(Matrix M) Peforms an LU decomposition on the Matrix M.
void	get(MatrixNd L, MatrixNd U, int[] rperm) Gets the matrices associated with the LU decomposition.
boolean	inverse(DenseMatrix R) Computes the inverse of the original matrix M associated with this decomposition, and places the result in R.
boolean	solve(DenseMatrix X, Matrix B) Solves the linear equation M X = B where M is the original matrix associated with this decomposition, and X and B are matrices.
boolean	solve(Vector x, Vector b) Solves the linear equation M x = b where M is the original matrix associated with this decomposition, and x and b are vectors.

Methods inherited from class java.lang.Object

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

Constructor Detail

LUDecomposition

public LUDecomposition()

Creates an uninitialized LUDecomposition.

LUDecomposition

public LUDecomposition(int n)

Creates an uninitialized LUDecomposition with enough capacity to handle matrices of size n. This capacity will later be increased on demand.

Parameters:

n - initial maximum matrix size

LUDecomposition

public LUDecomposition(Matrix M)
                throws ImproperSizeException

Creates an LUDecomposition for the Matrix specified by M.

Parameters:

M - matrix to perform the LU decomposition on

Throws:

ImproperSizeException - if M is not square

Method Detail

factor

public void factor(Matrix M)
            throws ImproperSizeException

Peforms an LU decomposition on the Matrix M.

Parameters:

M - matrix to perform the LU decomposition on

Throws:

ImproperSizeException - if M is not square

get

public void get(MatrixNd L,
                MatrixNd U,
                int[] rperm)
         throws ImproperStateException,
                ImproperSizeException

Gets the matrices associated with the LU decomposition. Each argument is optional; values will be returned into them if they are present.

Parameters:

L - unit lower triangular matrix

U - upper triangular matrix

rperm - indices of the row permuation matrix P, such that the i-th row of P M is given by row perm[i] of M.

Throws:

ImproperStateException - if this LUDecomposition is uninitialized

ImproperSizeException - if L or U are not of the proper dimension and cannot be resized, or if the length of perm is less than the size of M.

solve

public boolean solve(Vector x,
                     Vector b)
              throws ImproperStateException,
                     ImproperSizeException

Solves the linear equation
M x = b
where M is the original matrix associated with this decomposition, and x and b are vectors.

Parameters:

x - unknown vector to solve for

b - constant vector

Returns:

false if M is singular (within working precision)

Throws:

ImproperStateException - if this decomposition is uninitialized

ImproperSizeException - if b does not have a size compatible with M, or if x does not have a size compatible with M and cannot be resized.

solve

public boolean solve(DenseMatrix X,
                     Matrix B)
              throws ImproperStateException,
                     ImproperSizeException

Solves the linear equation
M X = B
where M is the original matrix associated with this decomposition, and X and B are matrices.

Parameters:

X - unknown matrix to solve for

B - constant matrix

Returns:

false if M is singular (within working precision)

Throws:

ImproperStateException - if this decomposition is uninitialized

ImproperSizeException - if B has a different number of rows than M, or if X has a different number of rows than M or a different number of columns than B and cannot be resized.

conditionEstimate

public double conditionEstimate(Matrix M)
                         throws ImproperStateException,
                                ImproperSizeException

Estimates the condition number of the original matrix M associated with this decomposition. M must also be supplied as an argument. The algorithm for estimating the condition number is given in Section 3.5.4 of Golub and Van Loan, Matrix Computations (Second Edition).

Parameters:

M - original matrix

Returns:

condition number estimate

Throws:

ImproperStateException - if this LUDecomposition is uninitialized

ImproperSizeException - if the size of M does not match the size of the current LU decomposition

determinant

public double determinant()
                   throws ImproperStateException

Compute the determinant of the original matrix M associated with this decomposition.

Returns:

determinant

Throws:

ImproperStateException - if this decomposition is uninitialized

inverse

public boolean inverse(DenseMatrix R)
                throws ImproperStateException

Computes the inverse of the original matrix M associated with this decomposition, and places the result in R.

Parameters:

R - matrix in which the inverse is stored

Returns:

false if M is singular (within working precision)

Throws:

ImproperStateException - if this decomposition is uninitialized

ImproperSizeException - if R does not have the same size as M and cannot be resized.