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Josh Reuben

 

 
 
Overview
·        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 Curve class
·        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
 
The GeneralCurve class
·        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)
private double f(double x)
{
    return 1 / (1 + x*x);
}
 
// Its derivative is -2x/(1+x^2)^2
private double df(double x)
{
    double y = 1 + x*x;
    return -2*x* / (y*y);
}
 
// The integral of f is Arctan(x), which is available from the Math class.
var c1 = new GeneralCurve (new RealFunction(f), new RealFunction(df), new RealFunction(System.Math.Atan));
// Find the tangent to this curve at x=1 (the Line class is derived from Curve)
Line l1 = c1.TangentAt(1);
Posted on Friday, January 28, 2011 11:46 AM Numerical Computing | Back to top


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

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