com.numericalmethod.suanshu.optimization.unconstrained.hessian
Class MatthewsDavies

java.lang.Object
  com.numericalmethod.suanshu.matrix.doubles.matrixtype.MatrixMathImpl<T>
      com.numericalmethod.suanshu.matrix.doubles.matrixtype.MatrixStorageImpl<DenseMatrix>
          com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.DenseMatrix
              com.numericalmethod.suanshu.optimization.unconstrained.hessian.MatthewsDavies

All Implemented Interfaces:

DeepCopyable, AbelianGroup<Matrix>, Monoid<Matrix>, Ring<Matrix>, Matrix, MatrixAccessor, MatrixRing, Densifiable, MatrixDimension

public class MatthewsDavies
extends DenseMatrix

Matthews and Davies propose the following way to coerce a non-positive definite Hessian matrix to become positive definite.

The 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:

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

Constructor Summary

MatthewsDavies(Matrix H)
Construct a MatthewsDavies instance.

Method Summary

DiagonalMatrix	D() Get a copy of the diagonal matrix D in the LDL decomposition.
DiagonalMatrix	Dhat() Get a copy of the modified diagonal matrix which is positive definite.
LowerTriangularMatrix	L() Get a copy of 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, getColumn, getColumn, getMatrixData, getRow, getRow, getSample, minus, multiply, multiply, ONE, overwrite, scaled, t, toDense, ZERO

Methods inherited from class com.numericalmethod.suanshu.matrix.doubles.matrixtype.MatrixStorageImpl

equals, get, hashCode, set, setMatrixData

Methods inherited from class com.numericalmethod.suanshu.matrix.doubles.matrixtype.MatrixMathImpl

add, call, minus, multiply, nCols, nRows, opposite, setColumn, setColumn, setRow, setRow, toString

Methods inherited from class java.lang.Object

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

Constructor Detail

MatthewsDavies

public MatthewsDavies(Matrix H)

Construct a MatthewsDavies instance. In this particular implementation, any zero or negative element is replaced by the smallest positive entry in D.

If all entries in D is < 0, D is replaced by an identity matrix.

Parameters:

H - a non-positive definite matrix

Method Detail

L

public LowerTriangularMatrix L()

Get a copy of the lower triangular matrix L in the LDL decomposition.

Returns:

a copy of L

Lt

public UpperTriangularMatrix Lt()

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

The transpose is upper triangular.

Returns:

a copy of Lt

D

public DiagonalMatrix D()

Get a copy of the diagonal matrix D in the LDL decomposition.

Returns:

a copy of D

Dhat

public DiagonalMatrix Dhat()

Get a copy of the modified diagonal matrix which is positive definite.

Returns:

a copy of D^