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Spline.cc

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// -*- C++ -*-
//
// Package:     MVAComputer
// Class  :     Spline
// 

// Implementation:
//     Simple cubic spline implementation for equidistant points in x.
//
// Author:      Christophe Saout
// Created:     Sat Apr 24 15:18 CEST 2007
// $Id: Spline.cc,v 1.3 2007/12/07 15:04:44 saout Exp $
//

#include <cstring>
#include <cmath>

#include "PhysicsTools/MVAComputer/interface/Spline.h"

namespace PhysicsTools {

double Spline::Segment::eval(double x) const
{
        double tmp;
        double y = 0.0;
        y += coeffs[0];         tmp = x;
        y += coeffs[1] * tmp;   tmp *= x;
        y += coeffs[2] * tmp;   tmp *= x;
        y += coeffs[3] * tmp;
        return y;
}

double Spline::Segment::integral(double x) const
{
        double tmp = x;
        double area = this->area;
        area += coeffs[0] * tmp;               tmp *= x;
        area += coeffs[1] * tmp * (1.0 / 2.0); tmp *= x;
        area += coeffs[2] * tmp * (1.0 / 3.0); tmp *= x;
        area += coeffs[3] * tmp * (1.0 / 4.0);
        return area;
}

Spline::Spline() : n(0), segments(0), area(0.0)
{}

Spline::Spline(const Spline &orig) : n(orig.n), area(orig.area)
{
        segments = new Segment[n];
        std::memcpy(segments, orig.segments, sizeof(Segment) * n);
}

Spline::Spline(unsigned int n_, const double *vals) :
        n(0), segments(0), area(0.0)
{ set(n_, vals); }

void Spline::set(unsigned int n_, const double *vals)
{
        n = n_ - 1;
        area = 0.0;

        delete[] segments;
        segments = new Segment[n];

        if (n == 1) {
                Segment *seg = &segments[0];
                seg->coeffs[0] = vals[0];
                seg->coeffs[1] = vals[1] - vals[0];
                seg->coeffs[2] = 0.0;
                seg->coeffs[3] = 0.0;
                seg->area = 0.0;
                area = seg->integral(1.0);
                return;
        }

        double m0, m1;
        Segment *seg = &segments[0];
        m0 = 0.0, m1 = 0.5 * (vals[2] - vals[0]);
        seg->coeffs[0] = vals[0];
        seg->coeffs[1] = -2.0 * vals[0] + 2.0 * vals[1] - m1;
        seg->coeffs[2] = vals[0] - vals[1] + m1;
        seg->coeffs[3] = 0.0;
        seg->area = 0.0;
        area = seg->integral(1.0);
        m0 = m1;
        seg++, vals++;

        for(unsigned int i = 1; i < n - 1; i++, seg++, vals++) {
                m1 = 0.5 * (vals[2] - vals[0]);
                seg->coeffs[0] = vals[0];
                seg->coeffs[1] = m0;
                seg->coeffs[2] = -3.0 * vals[0] - 2.0 * m0 + 3.0 * vals[1] - m1;
                seg->coeffs[3] = 2.0 * vals[0] + m0 - 2.0 * vals[1] + m1;
                seg->area = area;
                area = seg->integral(1.0);
                m0 = m1;
        }

        seg->coeffs[0] = vals[0];
        seg->coeffs[1] = m0;
        seg->coeffs[2] = - vals[0] - m0 + vals[1];
        seg->coeffs[3] = 0.0;
        seg->area = area;
        area = seg->integral(1.0);
}

Spline::~Spline()
{
        delete[] segments;
}

Spline &Spline::operator = (const Spline &orig)
{
        delete[] segments;
        n = orig.n;
        segments = new Segment[n];
        std::memcpy(segments, orig.segments, sizeof(Segment) * n);
        area = orig.area;
        return *this;
}

double Spline::eval(double x) const
{
        if (x <= 0.0)
                return segments[0].eval(0.0);
        if (x >= 1.0)
                return segments[n - 1].eval(1.0);

        double total;
        double rest = std::modf(x * n, &total);

        return segments[(unsigned int)total].eval(rest);
}

double Spline::integral(double x) const
{
        if (x <= 0.0)
                return 0.0;
        if (x >= 1.0)
                return 1.0;

        if (area < 1.0e-9)
                return 0.0;

        double total;
        double rest = std::modf(x * n, &total);

        return segments[(unsigned int)total].integral(rest) / area;
}

} // namespace PhysicsTools

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