VVIObj Class Reference

#include <VVIObj.h>

Public Member Functions
double	fcn (double x) const
void	limits (double &xl, double &xu) const
	density (mode=0) or distribution (mode=1) function More...
	VVIObj (double kappa=0.01, double beta2=1., int mode=0)
	Constructor. More...

Private Attributes
double	a_ [155]
double	b_ [155]
const int	mode_
	returns the limits on the non-zero (mode=0) or normalized region (mode=1) More...
double	omega_
double	t0_
double	t1_
double	t_
double	x0_

Detailed Description

Port of CERNLIB routines vvidis/vviden (G116) to calculate higher quality Vavilov density and distribution functions

Definition at line 24 of file VVIObj.h.

Constructor & Destructor Documentation

VVIObj::VVIObj	(	double	kappa = 0.01,
		double	beta2 = 1.,
		int	mode = 0
	)

Constructor.

Constructor Set Vavilov parameters kappa and beta2 and define whether to calculate density fcn or distribution fcn

Parameters

kappa	- (input) Vavilov kappa parameter [0.01 (Landau-like) < kappa < 10. (Gaussian-like)]
beta2	- (input) Vavilov beta2 parameter (square of particle speed in v/c units)
mode	- (input) set to 0 to calculate the density function and to 1 to calculate the distribution function

Definition at line 48 of file VVIObj.cc.

References a_, funct::abs(), b_, alignmentValidation::c1, funct::cos(), ztail::d, VVIObjDetails::dzero(), alignCSCRings::e, create_public_lumi_plots::exp, VVIObjDetails::expint(), validate-o2o-wbm::f1, validate-o2o-wbm::f2, relval_2017::k, kappa, cmsLHEtoEOSManager::l, dqm-mbProfile::log, mode_, gen::n, omega_, lumiQueryAPI::q, q2, funct::sin(), VVIObjDetails::sincosint(), t0_, t1_, t_, x, and x0_.

                                                   : mode_(mode) {
  
  const double xp[9] = { 9.29,2.47,.89,.36,.15,.07,.03,.02,0.0 };
  const double xq[7] = { .012,.03,.08,.26,.87,3.83,11.0 };
  double h_[7];
  double  q, u, x, c1, c2, c3, c4, d1, h4, h5, h6, q2, x1, d, ll, ul, xf1, xf2, rv;
  int lp, lq, k, l, n;
  
  // Make sure that the inputs are reasonable
  
  if(kappa < 0.01) kappa = 0.01;
  if(kappa > 10.) kappa = 10.;
  if(beta2 < 0.) beta2 = 0.;
  if(beta2 > 1.) beta2 = 1.;
  
  h_[4] = 1. - beta2*0.42278433999999998 + 7.6/kappa;
  h_[5] = beta2;
  h_[6] = 1. - beta2;
  h4 = -7.6/kappa - (beta2 * .57721566 + 1);
  h5 = log(kappa);
  h6 = 1./kappa;
  t0_ = (h4 - h_[4]*h5 - (h_[4] + beta2)*(log(h_[4]) + VVIObjDetails::expint(h_[4])) + exp(-h_[4]))/h_[4];
  
  // Set up limits for the root search
  
  for (lp = 0; lp < 9; ++lp) {
    if (kappa >= xp[lp]) break;
  }
  ll = -lp - 1.5;
  for (lq = 0; lq < 7; ++lq) {
    if (kappa <= xq[lq]) break;
  }
  ul = lq - 6.5;
  auto f2 = [h_](double x) { return h_[4]-x+h_[5]*(std::log(std::abs(x))+VVIObjDetails::expint(x))-h_[6]*std::exp(-x);};
  VVIObjDetails::dzero(ll, ul, u, rv, 1.e-5, 1000, f2);
  q = 1./u;
  t1_ = h4 * q - h5 - (beta2 * q + 1) * (log((fabs(u))) + VVIObjDetails::expint(u)) + exp(-u) * q;
  t_ = t1_ - t0_;
  omega_ = 6.2831853000000004/t_;
  h_[0] = kappa * (beta2 * .57721566 + 2.) + 9.9166128600000008;
  if (kappa >= .07) {h_[0] += 6.90775527;}
  h_[1] = beta2 * kappa;
  h_[2] = h6 * omega_;
  h_[3] = omega_ * 1.5707963250000001;
  auto f1 = [h_](double x){ return h_[0]+h_[1]*std::log(h_[2]*x)-h_[3]*x;};
  VVIObjDetails::dzero(5., 155., x0_, rv, 1.e-5, 1000, f1);
  n = x0_ + 1.;
  d = exp(kappa * (beta2 * (.57721566 - h5) + 1.)) * .31830988654751274;
  a_[n - 1] = 0.;
  if (mode_ == 0) {
    a_[n - 1] = omega_ * .31830988654751274;
  }
  q = -1.;
  q2 = 2.;
  for (k = 1; k < n; ++k) {
    l = n - k;
    x = omega_ * k;
    x1 = h6 * x;
    VVIObjDetails::sincosint(x1,c2,c1);
    c1 = log(x) - c1;
    c3 = sin(x1);
    c4 = cos(x1);
    xf1 = kappa * (beta2 * c1 - c4) - x * c2;
    xf2 = x * c1 + kappa * (c3 + beta2 * c2) + t0_ * x;
    if (mode_ == 0) {
      d1 = q * d * omega_ * exp(xf1);
      a_[l - 1] = d1 * cos(xf2);
      b_[l - 1] = -d1 * sin(xf2);
    } else {
      d1 = q * d * exp(xf1)/k;
      a_[l - 1] = d1 * sin(xf2);
      b_[l - 1] = d1 * cos(xf2);
      a_[n - 1] += q2 * a_[l - 1];
    }
    q = -q;
    q2 = -q2;
  }
  
} // VVIObj

Member Function Documentation

double VVIObj::fcn

(

double

x

)

const

Vavilov function method Returns density fcn (mode=0) or distribution fcn (mode=1)

Parameters

x	- (input) Argument of function [typically defined as (Q-mpv)/sigma]

Definition at line 135 of file VVIObj.cc.

References a_, b_, funct::cos(), f, relval_2017::k, mode_, gen::n, omega_, funct::sin(), t0_, t1_, t_, x0_, and y.

Referenced by SiPixelTemplateSplit::PixelTempSplit().

                                 {
    
    // Local variables
    
    double f, u, y, a0, a1;
    double a2 = 0.;
    double b1, b0, b2, cof;
    int k, n, n1;
    
    n = x0_;
    if (x < t0_) {
        f = 0.;
    } else if (x <= t1_) {
      y = x - t0_;
      u = omega_ * y - 3.141592653589793;
      cof = cos(u) * 2.;
      a1 = 0.;
      a0 = a_[0];
      n1=n+1;
      for (k = 2; k <= n1; ++k) {
        a2 = a1;
        a1 = a0;
        a0 = a_[k - 1] + cof * a1 - a2;
      }
      b1 = 0.;
      b0 = b_[0];
      for (k = 2; k <= n; ++k) {
        b2 = b1;
        b1 = b0;
        b0 = b_[k - 1] + cof * b1 - b2;
      }
      f = (a0 - a2) * .5 + b0 * sin(u);
      if (mode_ != 0) {f += y / t_;}
    } else {
      f = 0.;
      if (mode_ != 0) {f = 1.;}
    }
    return f;
} // fcn

void VVIObj::limits	(	double &	xl,
		double &	xu
	)		const

density (mode=0) or distribution (mode=1) function

Vavilov limits method

Parameters

xl	- (output) Smallest value of the argument for the density and the beginning of the normalized region for the distribution
xu	- (output) Largest value of the argument for the density and the end of the normalized region for the distribution

Definition at line 184 of file VVIObj.cc.

References t0_, and t1_.

                                                {
    
   xl = t0_;
   xu = t1_;
    return;
} // limits

Member Data Documentation

double VVIObj::a_[155]

private

Definition at line 43 of file VVIObj.h.

Referenced by fcn(), and VVIObj().

double VVIObj::b_[155]

private

Definition at line 44 of file VVIObj.h.

Referenced by fcn(), and VVIObj().

const int VVIObj::mode_

private

returns the limits on the non-zero (mode=0) or normalized region (mode=1)

set to 0 to calculate the density function and to 1 to calculate the distribution function

Definition at line 37 of file VVIObj.h.

Referenced by fcn(), and VVIObj().

double VVIObj::omega_

private

Definition at line 41 of file VVIObj.h.

Referenced by fcn(), and VVIObj().

double VVIObj::t0_

private

Definition at line 38 of file VVIObj.h.

Referenced by fcn(), limits(), and VVIObj().

double VVIObj::t1_

private

Definition at line 39 of file VVIObj.h.

Referenced by fcn(), limits(), and VVIObj().

double VVIObj::t_

private

Definition at line 40 of file VVIObj.h.

Referenced by fcn(), and VVIObj().

double VVIObj::x0_

private

Definition at line 42 of file VVIObj.h.

Referenced by fcn(), and VVIObj().