org.ojalgo.function.multiary

## Interface MultiaryFunction.TwiceDifferentiable<N extends Number>

• ### Nested classes/interfaces inherited from interface org.ojalgo.function.multiary.MultiaryFunction

`MultiaryFunction.Constant<N extends Number,F extends MultiaryFunction.Constant<N,?>>, MultiaryFunction.Convex<N extends Number>, MultiaryFunction.Linear<N extends Number>, MultiaryFunction.Quadratic<N extends Number>, MultiaryFunction.TwiceDifferentiable<N extends Number>`
• ### Nested classes/interfaces inherited from interface org.ojalgo.function.BasicFunction

`BasicFunction.Differentiable<N extends Number,F extends BasicFunction>, BasicFunction.Integratable<N extends Number,F extends BasicFunction>, BasicFunction.PlainUnary<T,R>`
• ### Method Summary

All Methods
Modifier and Type Method and Description
`MatrixStore<N>` `getGradient(Access1D<N> point)`
The gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is that rate of increase.
`MatrixStore<N>` `getHessian(Access1D<N> point)`
The Hessian matrix or Hessian is a square matrix of second-order partial derivatives of a function.
`Access1D<N>` `getLinearFactors()`
`FirstOrderApproximation<N>` `toFirstOrderApproximation(Access1D<N> point)`
`SecondOrderApproximation<N>` `toSecondOrderApproximation(Access1D<N> point)`
• ### Methods inherited from interface org.ojalgo.function.multiary.MultiaryFunction

`andThen, arity, invoke`
• ### Method Detail

• #### getGradient

`MatrixStore<N> getGradient(Access1D<N> point)`

The gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is that rate of increase.

The Jacobian is a generalization of the gradient. Gradients are only defined on scalar-valued functions, but Jacobians are defined on vector- valued functions. When f is real-valued (i.e., f : Rn → R) the derivative Df(x) is a 1 × n matrix, i.e., it is a row vector. Its transpose is called the gradient of the function: ∇f(x) = Df(x)T , which is a (column) vector, i.e., in Rn. Its components are the partial derivatives of f:

The first-order approximation of f at a point x ∈ int dom f can be expressed as (the affine function of z) f(z) = f(x) + ∇f(x)T (z − x).

• #### getHessian

`MatrixStore<N> getHessian(Access1D<N> point)`

The Hessian matrix or Hessian is a square matrix of second-order partial derivatives of a function. It describes the local curvature of a function of many variables. The Hessian is the Jacobian of the gradient.

The second-order approximation of f, at or near x, is the quadratic function of z defined by f(z) = f(x) + ∇f(x)T (z − x) + (1/2)(z − x)T ∇2f(x)(z − x)

• #### getLinearFactors

`Access1D<N> getLinearFactors()`
Returns:
The gradient at 0 (0-vector)
• #### toFirstOrderApproximation

`FirstOrderApproximation<N> toFirstOrderApproximation(Access1D<N> point)`
• #### toSecondOrderApproximation

`SecondOrderApproximation<N> toSecondOrderApproximation(Access1D<N> point)`

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