Class GoldfeldQuandtTrotter
- java.lang.Object
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- dev.nm.algebra.linear.matrix.doubles.matrixtype.dense.DenseMatrix
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- dev.nm.algebra.linear.matrix.doubles.operation.positivedefinite.GoldfeldQuandtTrotter
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- All Implemented Interfaces:
Matrix,MatrixAccess,MatrixRing,MatrixTable,Densifiable,AbelianGroup<Matrix>,Monoid<Matrix>,Ring<Matrix>,Table,DeepCopyable
public class GoldfeldQuandtTrotter extends DenseMatrix
Goldfeld, Quandt and Trotter propose the following way to coerce a non-positive definite Hessian matrix to become symmetric, positive definite. For a non-positive definite Hessian matrix H, we compute \[ \widehat{H} = \frac{H + \beta I}{1 + \beta} \]
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Constructor Summary
Constructors Constructor Description GoldfeldQuandtTrotter(Matrix H, double beta)Constructs a symmetric, positive definite matrix using the Goldfeld-Quandt-Trotter algorithm.
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Method Summary
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Methods inherited from class dev.nm.algebra.linear.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
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Constructor Detail
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GoldfeldQuandtTrotter
public GoldfeldQuandtTrotter(Matrix H, double beta)
Constructs a symmetric, positive definite matrix using the Goldfeld-Quandt-Trotter algorithm.- Parameters:
H- a non-positive definite matrixbeta- a positive number. The bigger beta is, the closer H^ is to I. Ifbeta == Double.POSITIVE_INFINITY, then H^ = I.
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