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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 | // Geometric Tools, LLC
// Copyright (c) 1998-2014
// Distributed under the Boost Software License, Version 1.0.
// http://www.boost.org/LICENSE_1_0.txt
// http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
//
// File Version: 5.0.1 (2010/10/01)
#ifndef WM5APPRPOLYFIT2_H
#define WM5APPRPOLYFIT2_H
#include "Wm5MathematicsLIB.h"
namespace Wm5
{
// The samples are (x[i],w[i]) for 0 <= i < S. Think of w as a function of
// x, say w = f(x). The function fits the samples with a polynomial of
// degree d, say w = sum_{i=0}^d c[i]*x^i. The method is a least-squares
// fitting algorithm. The returned array stores the coefficients c[i] for
// 0 <= i <= d. The caller is responsible for deleting the input arrays if
// they were dynamically allocated. The caller is also responsible for
// deleting the returned array.
//
// WARNING. The fitting algorithm for polynomial terms
// (1,x,x^2,...,x^d)
// is known to be nonrobust for large degrees and for large magnitude data.
// One alternative is to use orthogonal polynomials
// (f[0](x),...,f[d](x))
// and apply the least-squares algorithm to these. Another alternative is to
// transform
// (x',w') = ((x-xcen)/rng, w/rng)
// where xmin = min(x[i]), xmax = max(x[i]), xcen = (xmin+xmax)/2, and
// rng = xmax-xmin. Fit the (x',w') points,
// w' = sum_{i=0}^d c'[i]*(x')^i.
// The original polynomial is evaluated as
// w = rng*sum_{i=0}^d c'[i]*((x-xcen)/rng)^i
template <typename Real> WM5_MATHEMATICS_ITEM
Real* PolyFit2 (int numSamples, const Real* xSamples, const Real* wSamples,
int xDegree);
}
#endif
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