maspack.solvers

Class IncompleteLUDecomposition

java.lang.Object

maspack.solvers.IncompleteLUDecomposition

All Implemented Interfaces:

LinearTransformNd

public class IncompleteLUDecomposition
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	L
SparseMatrixNd	LU
SparseMatrixNd	U

Constructor Summary

Constructors

Constructor and Description
IncompleteLUDecomposition() Creates an uninitialized CholeskyDecomposition.
IncompleteLUDecomposition(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 droptol)
void	get(MatrixNd LU) Gets the lower and upper triangular matrices L and U associated with this 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	solveL(VectorNd x, VectorNd b) Solves L * x = b
boolean	solveU(VectorNd x, VectorNd b) Solves U * x = b

Methods inherited from class java.lang.Object

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

Field Detail

LU

public SparseMatrixNd LU

L

public SparseMatrixNd L

U

public SparseMatrixNd U

Constructor Detail

IncompleteLUDecomposition

public IncompleteLUDecomposition()

Creates an uninitialized CholeskyDecomposition.

IncompleteLUDecomposition

public IncompleteLUDecomposition(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

factor

public void factor(SparseMatrixNd A,
                   double droptol)

get

public void get(MatrixNd LU)

Gets the lower and upper triangular matrices L and U associated with this decomposition.

Parameters:

LU - lower and upper triangular matrices (sharing the same space)

Throws:

ImproperStateException - if this decomposition is uninitialized

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

solveL

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

Solves L * x = b

Throws:

ImproperStateException

ImproperSizeException

solveU

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

Solves U * 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