maspack.matrix

Class CholeskyDecomposition

java.lang.Object

maspack.matrix.CholeskyDecomposition

public class CholeskyDecomposition
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
CholeskyDecomposition() Creates an uninitialized CholeskyDecomposition.
CholeskyDecomposition(int n) Creates an uninitialized CholeskyDecomposition with enough capacity to handle matrices of size n.
CholeskyDecomposition(Matrix M) Creates a CholeskyDecomposition for the Matrix specified by M.

Method Summary

Modifier and Type	Method and Description
void	addRowAndColumn(VectorNd col)
boolean	addRowAndColumn(VectorNd col, double tol)
void	clear()
double	conditionEstimate(Matrix M) Estimates the condition number of the original matrix M associated with this decomposition.
void	deleteRowAndColumn(int idx)
double	determinant() Compute the determinant of the original matrix M associated with this decomposition.
void	factor(Matrix M) Peforms a Cholesky decomposition on the Matrix M.
void	get(MatrixNd L) Gets the lower-triangular matrix L associated with the Cholesky decomposition.
double[]	getBuffer()
int	getBufferWidth()
boolean	inverse(DenseMatrix R) Computes the inverse of the original matrix M associated with this decomposition, and places the result in R.
boolean	leftSolveL(DenseMatrix X, Matrix B) Solves the linear equation X L = B for X, where L is the lower triangular factor associated with this decomposition, and X and B are matrices.
boolean	leftSolveL(Vector x, Vector b) Solves the linear equation x L = b for x, where L is the lower triangular factor associated this decomposition, and x and b are vectors.
void	setCapacity(int n)
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.
boolean	solveL(DenseMatrix X, Matrix B) Solves the linear equation L X = B for X, where L is the lower triangular factor associated with this decomposition, and X and B are matrices.
boolean	solveL(Vector x, Vector b) Solves the linear equation L x = b for x, where L is the lower triangular factor associated 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

CholeskyDecomposition

public CholeskyDecomposition()

Creates an uninitialized CholeskyDecomposition.

CholeskyDecomposition

public CholeskyDecomposition(int n)

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

Parameters:

n - initial maximum matrix size

CholeskyDecomposition

public CholeskyDecomposition(Matrix M)
                      throws ImproperSizeException

Creates a CholeskyDecomposition for the Matrix specified by M.

Parameters:

M - matrix to perform the Cholesky decomposition on

Throws:

ImproperSizeException - if M is not square

Method Detail

setCapacity

public void setCapacity(int n)

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)
         throws ImproperStateException,
                ImproperSizeException

Gets the lower-triangular matrix L associated with the Cholesky decomposition.

Parameters:

L - lower triangular matrix

Throws:

ImproperStateException - if this CholeskyDecomposition is uninitialized

ImproperSizeException - if L is not of the proper dimension and cannot be resized

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.

solveL

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

Solves the linear equation
L x = b
for x, where L is the lower triangular factor associated 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 L, or if x does not have a size compatible with L and cannot be resized.

solveL

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

Solves the linear equation
L X = B
for X, where L is the lower triangular factor 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 does not have a size compatible with L, or if X does not have a size compatible with L or B and cannot be resized.

leftSolveL

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

Solves the linear equation
x L = b
for x, where L is the lower triangular factor associated 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 L, or if x does not have a size compatible with L and cannot be resized.

leftSolveL

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

Solves the linear equation
X L = B
for X, where L is the lower triangular factor 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 does not have a size compatible with L, or if X does not have a size compatible with L or 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 CholeskyDecomposition 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()

addRowAndColumn

public void addRowAndColumn(VectorNd col)

addRowAndColumn

public boolean addRowAndColumn(VectorNd col,
                               double tol)

deleteRowAndColumn

public void deleteRowAndColumn(int idx)