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
//

#include <cstring>
#include <cmath>

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

namespace PhysicsTools {

float Spline::Segment::eval(float x) const
{
    float tmp;
    float 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;
}

float Spline::Segment::deriv(float x) const
{
    float tmp;
    float d = 0.0;
    d += coeffs[1];         tmp = x;
    d += coeffs[2] * tmp * 2.0; tmp *= x;
    d += coeffs[3] * tmp * 3.0;
    return d;
}

float Spline::Segment::integral(float x) const
{
    float tmp = x;
    float 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(nullptr), 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(nullptr), 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;
    }

    float 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;
}

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

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

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

float Spline::deriv(float x) const
{
    if (x < 0.0 || x > 1.0)
        return 0.0;
    else if (x == 0.0)
        return segments[0].deriv(0.0);
    else if (x == 1.0)
        return segments[n - 1].deriv(1.0);

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

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

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

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

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

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

} // namespace PhysicsTools