· a curve is a functional map relationship between two factors (i.e. a *function -* However, the word function is a reserved word).

· You can use the EO API to create common types of functions, find zeroes and calculate derivatives - currently supports constants, lines, quadratic curves, polynomials and Chebyshev approximations.

· A function basis is a set of functions that can be combined to form a particular class of functions.

· the abstract base class from which all other curve classes are derived – it provides the following methods:

· **ValueAt(Double)** - evaluates the curve at a specific point.

· **SlopeAt(Double)** - evaluates the derivative

· **Integral(Double, Double)** - evaluates the definite integral over a specified interval.

· **TangentAt(Double)** - returns a **Line** curve that is the tangent to the curve at a specific point.

· **FindRoots() **- attempts to find all the roots or zeroes of the curve.

· A particular type of curve is defined by a **Parameters** property, of type **ParameterCollection**

· defines a curve whose value and, optionally, derivative and integrals, are calculated using arbitrary methods. A general curve has no parameters.

· Constructor params: **RealFunction** delegates – 1 for the function, and optionally another 2 for the derivative and integral

· If no derivative or integral function is supplied, they are calculated via the **NumericalDifferentiation** and **AdaptiveIntegrator**__ __classes in the **Extreme.Mathematics.Calculus** namespace.

// the function is 1/(1+x^2)

// Its derivative is -2x/(1+x^2)^2

// The integral of f is Arctan(x), which is available from the Math class.

// Find the tangent to this curve at x=1 (the **Line** class is derived from **Curve**)

Comments on this post: Extreme Optimization – Curves (Function Mapping) Part 1

# re: Extreme Optimization – Curves (Function Mapping) Part 1

Easy to follow and it really works well. - Dr. Thomas G. Devlin MD, PhD

Left by Robert Jacob
on
Dec 28, 2016 2:00 PM

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