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

    • 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

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