PhysicsTools::Spline Class Reference

A simple class for cubic splines. More...

#include <Spline.h>

Classes
struct	Segment
	internal class describing a "segment" (between two x points) More...

Public Member Functions
float	deriv (float x) const
	compute the derivate at x coordinate x More...
float	eval (float x) const
	compute y coordinate at x coordinate x More...
float	getArea () const
	total area (integral between 0 and 1) under curve More...
float	integral (float x) const
	compute integral under curve between 0 and x More...
unsigned int	numberOfEntries () const
	return the number of entries More...
Spline &	operator= (const Spline &orig)
void	set (unsigned int n, const double *vals)
	initialize spline from n y coordinates in array vals More...
	Spline ()
	Spline (const Spline &orig)
	Spline (unsigned int n, const double *vals)
	construct spline from n y coordinates in array vals More...
	~Spline ()

Private Attributes
float	area
unsigned int	n
Segment *	segments

Detailed Description

A simple class for cubic splines.

This class implements cubic splines for n equidistant points in x between 0 and 1. It is constructed from an array of n y coordinates and can compute the interpolated y coordinate for a given x.

Definition at line 25 of file Spline.h.

Constructor & Destructor Documentation

PhysicsTools::Spline::Spline

(

)

Definition at line 58 of file Spline.cc.

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

PhysicsTools::Spline::Spline

(

const Spline &

orig

)

Definition at line 60 of file Spline.cc.

References n, and segments.

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

PhysicsTools::Spline::Spline	(	unsigned int	n,
		const double *	vals
	)

construct spline from n y coordinates in array vals

Definition at line 65 of file Spline.cc.

: n(0), segments(nullptr), area(0.0) { set(n_, vals); }

PhysicsTools::Spline::~Spline

(

)

Definition at line 116 of file Spline.cc.

References segments.

{ delete[] segments; }

Member Function Documentation

float PhysicsTools::Spline::deriv

(

float

x

)

const

compute the derivate at x coordinate x

Definition at line 139 of file Spline.cc.

References PhysicsTools::Spline::Segment::deriv(), createfilelist::int, n, mergeAndRegister::rest, segments, and dqmMemoryStats::total.

                                   {
    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 PhysicsTools::Spline::eval

(

float

x

)

const

compute y coordinate at x coordinate x

Definition at line 127 of file Spline.cc.

References PhysicsTools::Spline::Segment::eval(), createfilelist::int, n, mergeAndRegister::rest, segments, and dqmMemoryStats::total.

                                  {
    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 PhysicsTools::Spline::getArea ( ) const

inline

total area (integral between 0 and 1) under curve

Definition at line 49 of file Spline.h.

References area.

{ return area; }

float PhysicsTools::Spline::integral

(

float

x

)

const

compute integral under curve between 0 and x

Definition at line 153 of file Spline.cc.

References area, MillePedeFileConverter_cfg::e, createfilelist::int, n, mergeAndRegister::rest, segments, and dqmMemoryStats::total.

                                      {
    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;
  }

unsigned int PhysicsTools::Spline::numberOfEntries ( ) const

inline

return the number of entries

Definition at line 52 of file Spline.h.

{ return n + 1; }

Spline & PhysicsTools::Spline::operator=

(

const Spline &

orig

)

Definition at line 118 of file Spline.cc.

References area, n, and segments.

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

void PhysicsTools::Spline::set	(	unsigned int	n,
		const double *	vals
	)

initialize spline from n y coordinates in array vals

Definition at line 67 of file Spline.cc.

References PhysicsTools::Spline::Segment::area, area, PhysicsTools::Spline::Segment::coeffs, mps_fire::i, PhysicsTools::Spline::Segment::integral(), n, and segments.

                                                      {
    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);
  }

Member Data Documentation

float PhysicsTools::Spline::area

private

Definition at line 67 of file Spline.h.

Referenced by getArea(), integral(), operator=(), and set().

unsigned int PhysicsTools::Spline::n

private

Definition at line 65 of file Spline.h.

Referenced by deriv(), eval(), integral(), operator=(), set(), and Spline().

Segment* PhysicsTools::Spline::segments

private

Definition at line 66 of file Spline.h.

Referenced by deriv(), eval(), integral(), operator=(), set(), Spline(), and ~Spline().