Class Hessian
- java.lang.Object
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- dev.nm.algebra.linear.matrix.doubles.matrixtype.dense.triangle.SymmetricMatrix
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- dev.nm.analysis.differentiation.multivariate.Hessian
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- All Implemented Interfaces:
Matrix
,MatrixAccess
,MatrixRing
,MatrixTable
,Densifiable
,AbelianGroup<Matrix>
,Monoid<Matrix>
,Ring<Matrix>
,Table
,DeepCopyable
public class Hessian extends SymmetricMatrix
The Hessian matrix is the square matrix of the second-order partial derivatives of a multivariate function. Mathematically, the Hessian of a scalar function is an \(n \times n\) matrix, where n is the domain dimension of f. For a scalar function f, we have \[ H(f) = \begin{bmatrix} \frac{\partial^2 f}{\partial x_1^2} & \frac{\partial^2 f}{\partial x_1\,\partial x_2} & \cdots & \frac{\partial^2 f}{\partial x_1\,\partial x_n} \\ \\ \frac{\partial^2 f}{\partial x_2\,\partial x_1} & \frac{\partial^2 f}{\partial x_2^2} & \cdots & \frac{\partial^2 f}{\partial x_2\,\partial x_n} \\ \\ \vdots & \vdots & \ddots & \vdots \\ \\ \frac{\partial^2 f}{\partial x_n\,\partial x_1} & \frac{\partial^2 f}{\partial x_n\,\partial x_2} & \cdots & \frac{\partial^2 f}{\partial x_n^2} \end{bmatrix} \] This implementation computes the Hessian matrix numerically using the finite difference method. We assume that the function f is continuous so the Hessian matrix is square and symmetric.- See Also:
- Wikipedia: Hessian matrix
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Constructor Summary
Constructors Constructor Description Hessian(RealScalarFunction f, Vector x)
Construct the Hessian matrix for a multivariate function f at point x.
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Method Summary
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Methods inherited from class dev.nm.algebra.linear.matrix.doubles.matrixtype.dense.triangle.SymmetricMatrix
add, deepCopy, equals, get, getColumn, getRow, hashCode, minus, multiply, multiply, nCols, nRows, ONE, opposite, scaled, set, t, toDense, toString, ZERO
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Constructor Detail
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Hessian
public Hessian(RealScalarFunction f, Vector x)
Construct the Hessian matrix for a multivariate function f at point x.- Parameters:
f
- a multivariate functionx
- the point to evaluate the Hessian of f at
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