com.numericalmethod.suanshu.matrix.doubles.operation.positivedefinite

Class MatthewsDavies

java.lang.Object

com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.DenseMatrix

com.numericalmethod.suanshu.matrix.doubles.operation.positivedefinite.MatthewsDavies

All Implemented Interfaces:

Table, DeepCopyable, AbelianGroup<Matrix>, Monoid<Matrix>, Ring<Matrix>, Matrix, MatrixAccess, MatrixRing, MatrixTable, Densifiable, java.io.Serializable

public class MatthewsDavies
extends DenseMatrix

Matthews and Davies propose the following way to coerce a non-positive definite Hessian matrix to become symmetric, positive definite. An LDL decomposition is performed on the non-positive definite matrix. The zero and negative entries are then replaced by the smallest positive entry in the diagonal matrix.

See Also:

"Andreas Antoniou and Wu-Sheng Lu, "Algorithm 5.4," Practical Optimization: Algorithms and Engineering Applications.", Serialized Form

Constructor Summary

Constructors

Constructor and Description
MatthewsDavies(Matrix H) Construct a symmetric, positive definite matrix using the Matthews-Davies algorithm.

Method Summary

Modifier and Type	Method and Description
DiagonalMatrix	D() Get the diagonal matrix D in the LDL decomposition.
DiagonalMatrix	Dhat() Get the modified diagonal matrix which is positive definite.
LowerTriangularMatrix	L() Get the lower triangular matrix L in the LDL decomposition.
UpperTriangularMatrix	Lt() Get the transpose of the lower triangular matrix L in the LDL decomposition.

Methods inherited from class com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.DenseMatrix

add, deepCopy, equals, get, getColumn, getColumn, getRow, getRow, hashCode, minus, multiply, multiply, nCols, nRows, ONE, opposite, scaled, set, setColumn, setRow, t, toDense, toString, ZERO

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Constructor Detail

MatthewsDavies

public MatthewsDavies(Matrix H)

Construct a symmetric, positive definite matrix using the Matthews-Davies algorithm. This implementation replaces all zero or negative entries on the diagonal by the smallest positive entry on the diagonal. If all entries in the diagonal are negative, D becomes an identity matrix.

Parameters:

H - a non-positive definite matrix

Method Detail

L

public LowerTriangularMatrix L()

Get the lower triangular matrix L in the LDL decomposition.

Returns:

L

Lt

public UpperTriangularMatrix Lt()

Get the transpose of the lower triangular matrix L in the LDL decomposition. The transpose is upper triangular.

Returns:

L^t

D

public DiagonalMatrix D()

Get the diagonal matrix D in the LDL decomposition.

Returns:

D

Dhat

public DiagonalMatrix Dhat()

Get the modified diagonal matrix which is positive definite.

Returns:

D^