Interface MultiaryFunction.TwiceDifferentiable<N extends Comparable<N>>

All Superinterfaces:
BasicFunction, BasicFunction.PlainUnary<Access1D<N>, N>, MultiaryFunction<N>
All Known Implementing Classes:
AffineFunction, ApproximateFunction, ConstantFunction, ConvexObjectiveFunction, FirstOrderApproximation, LinearFunction, PureQuadraticFunction, QuadraticFunction, SecondOrderApproximation
Enclosing interface:
MultiaryFunction<N extends Comparable<N>>
public static interface MultiaryFunction.TwiceDifferentiable<N extends Comparable<N>> extends MultiaryFunction<N>
Twice (Continuously) Differentiable Multiary Function

  • Method Details

    • 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

      MatrixStore<N> getLinearFactors(boolean negated)
      Returns:
      The gradient at origin (0-vector), negated or not

    • toFirstOrderApproximation

      default MultiaryFunction.TwiceDifferentiable<N> toFirstOrderApproximation(Access1D<N> arg)

    • toSecondOrderApproximation

      default MultiaryFunction.TwiceDifferentiable<N> toSecondOrderApproximation(Access1D<N> arg)