Class FirstOrderApproximation<N extends java.lang.Comparable<N>>

    • Field Detail

      • myDelegate

        private final AffineFunction<N extends java.lang.Comparable<N>> myDelegate
    • Method Detail

      • arity

        public int arity()
      • equals

        public boolean equals​(java.lang.Object obj)
        Overrides:
        equals in class ApproximateFunction<N extends java.lang.Comparable<N>>
      • getGradient

        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)

      • toString

        public java.lang.String toString()
        Overrides:
        toString in class java.lang.Object