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>>
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Nested Class Summary
Nested classes/interfaces inherited from interface org.ojalgo.function.BasicFunction
BasicFunction.Differentiable<N extends Comparable<N>,
F extends BasicFunction>, BasicFunction.Integratable<N extends Comparable<N>, F extends BasicFunction>, BasicFunction.PlainUnary<T, R> Nested classes/interfaces inherited from interface org.ojalgo.function.multiary.MultiaryFunction
MultiaryFunction.Affine<N extends Comparable<N>>, MultiaryFunction.Constant<N extends Comparable<N>>, MultiaryFunction.Convex<N extends Comparable<N>>, MultiaryFunction.Linear<N extends Comparable<N>>, MultiaryFunction.PureQuadratic<N extends Comparable<N>>, MultiaryFunction.Quadratic<N extends Comparable<N>>, MultiaryFunction.TwiceDifferentiable<N extends Comparable<N>>
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Method Summary
Modifier and TypeMethodDescriptiongetGradient
(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.getHessian
(Access1D<N> point) The Hessian matrix or Hessian is a square matrix of second-order partial derivatives of a function.getLinearFactors
(boolean negated) default MultiaryFunction.TwiceDifferentiable
<N> default MultiaryFunction.TwiceDifferentiable
<N> Methods inherited from interface org.ojalgo.function.multiary.MultiaryFunction
andThen, arity, invoke
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Method Details
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getGradient
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).
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getHessian
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)
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getLinearFactors
- Returns:
- The gradient at origin (0-vector), negated or not
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toFirstOrderApproximation
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toSecondOrderApproximation
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