maspack.solvers

Class IncompleteCholeskyDecomposition

java.lang.Object

maspack.solvers.IncompleteCholeskyDecomposition

All Implemented Interfaces:

LinearTransformNd

public class IncompleteCholeskyDecomposition
extends java.lang.Object
implements LinearTransformNd

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.

Field Summary

Fields

Modifier and Type	Field and Description
SparseMatrixNd	C

Constructor Summary

Constructors

Constructor and Description
IncompleteCholeskyDecomposition() Creates an uninitialized CholeskyDecomposition.
IncompleteCholeskyDecomposition(SparseMatrixNd M) Creates a CholeskyDecomposition for the Matrix specified by M.

Method Summary

Modifier and Type	Method and Description
int	colSize() Number of columns in the matrix associated with this transformation.
void	factor(SparseMatrixNd A) Peforms an Cholesky decomposition on the Matrix M.
void	factor(SparseMatrixNd A, double tol)
void	get(MatrixNd L) Gets the lower-triangular matrix L associated with the Cholesky decomposition.
void	mul(VectorNd vr, VectorNd v1) Applies this transformation to vector v1 and returns the result in vr.
int	rowSize() Number of rows in the matrix associated with this transformation.
boolean	solve(VectorNd x, VectorNd b) Solves L * x = b
boolean	solveTranspose(VectorNd x, VectorNd b) Solves L' * x = b

Methods inherited from class java.lang.Object

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

Field Detail

C

public SparseMatrixNd C

Constructor Detail

IncompleteCholeskyDecomposition

public IncompleteCholeskyDecomposition()

Creates an uninitialized CholeskyDecomposition.

IncompleteCholeskyDecomposition

public IncompleteCholeskyDecomposition(SparseMatrixNd 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

factor

public void factor(SparseMatrixNd A)

Peforms an Cholesky decomposition on the Matrix M.

Parameters:

A - matrix on which to perform the Cholesky decomposition

Throws:

ImproperSizeException - if M is not square

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

factor

public void factor(SparseMatrixNd A,
                   double tol)

get

public void get(MatrixNd L)

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(VectorNd x,
                     VectorNd b)
              throws ImproperStateException,
                     ImproperSizeException

Solves L * x = b

Throws:

ImproperStateException

ImproperSizeException

solveTranspose

public boolean solveTranspose(VectorNd x,
                              VectorNd b)
                       throws ImproperStateException,
                              ImproperSizeException

Solves L' * x = b

Throws:

ImproperStateException

ImproperSizeException

colSize

public int colSize()

Description copied from interface: LinearTransformNd

Number of columns in the matrix associated with this transformation. This will equal the size of the input vector in mul.

Specified by:

colSize in interface LinearTransformNd

Returns:

number of columns

rowSize

public int rowSize()

Description copied from interface: LinearTransformNd

Number of rows in the matrix associated with this transformation. This will equal the size of the output vector in mul.

Specified by:

rowSize in interface LinearTransformNd

Returns:

number of rows

mul

public void mul(VectorNd vr,
                VectorNd v1)

Description copied from interface: LinearTransformNd

Applies this transformation to vector v1 and returns the result in vr.

Specified by:

mul in interface LinearTransformNd

Parameters:

vr - vector in which result is returned

v1 - vector to transform