maspack.matrix

Class LDLTDecomposition

java.lang.Object

maspack.matrix.LDLTDecomposition

public class LDLTDecomposition
extends java.lang.Object

Constructs the Cholesky decomposition of a symmetric positive definite matrix. This takes the form
M = L L'
where M is the original matrix, L is a lower-triangular matrix and L' denotes its transpose. Once this 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 Cholesky decomposition allows an application to perform such decompositions repeatedly without having to reallocate temporary storage space.

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and Description
void	clear()
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	ensureCapacity(int cap)
void	factor(Matrix M) Peforms a Cholesky decomposition on the Matrix M.
void	get(MatrixNd L, VectorNd D) Gets the components associated with this signed Cholesky decomposition.
double[]	getBuffer()
int	getBufferWidth()
int	getSize()
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 for X, where M is the original matrix associated with this decomposition, and X and B are matrices.
boolean	solve(double[] x, int xoff, double[] b, int boff) Solves the linear equation M x = b for x, where M is the original matrix associated with this decomposition, and x and b are vectors.
boolean	solve(Vector x, Vector b) Solves the linear equation M x = b for x, 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

LDLTDecomposition

public LDLTDecomposition()

Creates an uninitialized LDLTDecomposition.

LDLTDecomposition

public LDLTDecomposition(int n)

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

Parameters:

n - initial maximum matrix size

LDLTDecomposition

public LDLTDecomposition(Matrix M)
                  throws ImproperSizeException

Creates a LDLTDecomposition for the Matrix specified by M.

Parameters:

M - matrix to perform the Cholesky decomposition on

Throws:

ImproperSizeException - if M is not square

Method Detail

ensureCapacity

public void ensureCapacity(int cap)

getSize

public int getSize()

factor

public void factor(Matrix M)
            throws ImproperSizeException

Peforms a Cholesky decomposition on the Matrix M.

Parameters:

M - matrix to perform the Cholesky decomposition on

Throws:

ImproperSizeException - if M is not square

java.lang.IllegalArgumentException - if M is detected to be not symmetric positive definite

get

public void get(MatrixNd L,
                VectorNd D)
         throws ImproperStateException

Gets the components associated with this signed Cholesky decomposition.

Parameters:

L - if non-null, returns the lower triangular matrix

D - if non-null, returns the diagonal

Throws:

ImproperStateException - if this LDLTDecomposition is uninitialized

solve

public boolean solve(double[] x,
                     int xoff,
                     double[] b,
                     int boff)

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

Parameters:

x - unknown vector to solve for

xoff - starting offset into x

b - constant vector

boff - starting offset into b

Returns:

false if M is singular (within working precision)

Throws:

ImproperStateException - if this decomposition is uninitialized

ImproperSizeException - if x or b do not have a length compatible with M

solve

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

Solves the linear equation
M x = b
for x, 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
for X, 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 numberis based on 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 LDLTDecomposition is uninitialized

ImproperSizeException - if the size of M does not match the size of the current Cholesky 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.

getBuffer

public double[] getBuffer()

getBufferWidth

public int getBufferWidth()

clear

public void clear()