org.ojalgo.function.multiary

## Class FirstOrderApproximation<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>`
• ### Constructor Summary

Constructors
Constructor and Description
```FirstOrderApproximation(MultiaryFunction.TwiceDifferentiable<N> function, Access1D<N> point)```
• ### Method Summary

All Methods
Modifier and Type Method and Description
`int` `arity()`
`boolean` `equals(Object obj)`
`protected PhysicalStore.Factory<N,?>` `factory()`
`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()`
`int` `hashCode()`
`N` `invoke(Access1D<N> arg)`
`PhysicalStore<N>` `linear()`
`protected PhysicalStore<N>` `shift(Access1D<?> arg)`
`FirstOrderApproximation<N>` `toFirstOrderApproximation(Access1D<N> arg)`
`SecondOrderApproximation<N>` `toSecondOrderApproximation(Access1D<N> arg)`
`String` `toString()`
• ### Methods inherited from class java.lang.Object

`clone, finalize, getClass, notify, notifyAll, wait, wait, wait`
• ### Methods inherited from interface org.ojalgo.function.multiary.MultiaryFunction

`andThen`
• ### Constructor Detail

• #### FirstOrderApproximation

```public FirstOrderApproximation(MultiaryFunction.TwiceDifferentiable<N> function,
Access1D<N> point)```
• ### Method Detail

• #### arity

`public int arity()`
• #### equals

`public boolean equals(Object obj)`

`public MatrixStore<N> getGradient(Access1D<N> point)`
Description copied from interface: `MultiaryFunction.TwiceDifferentiable`

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

`public MatrixStore<N> getHessian(Access1D<N> point)`
Description copied from interface: `MultiaryFunction.TwiceDifferentiable`

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)

• #### hashCode

`public int hashCode()`
• #### invoke

`public N invoke(Access1D<N> arg)`
• #### linear

`public PhysicalStore<N> linear()`
• #### toString

`public String toString()`
Overrides:
`toString` in class `Object`
• #### factory

`protected PhysicalStore.Factory<N,?> factory()`
• #### getLinearFactors

`public Access1D<N> getLinearFactors()`
Specified by:
`getLinearFactors` in interface `MultiaryFunction.TwiceDifferentiable<N extends Number>`
Returns:
• #### toFirstOrderApproximation

`public final FirstOrderApproximation<N> toFirstOrderApproximation(Access1D<N> arg)`
Specified by:
`toFirstOrderApproximation` in interface `MultiaryFunction.TwiceDifferentiable<N extends Number>`
• #### toSecondOrderApproximation

`public final SecondOrderApproximation<N> toSecondOrderApproximation(Access1D<N> arg)`
Specified by:
`toSecondOrderApproximation` in interface `MultiaryFunction.TwiceDifferentiable<N extends Number>`
• #### shift

`protected PhysicalStore<N> shift(Access1D<?> arg)`