VVIObjF Class Reference

#include <VVIObjF.h>

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

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

Constructor & Destructor Documentation

VVIObjF::VVIObjF	(	float	kappa = 0.01,
		float	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 45 of file VVIObjF.cc.

References a_, funct::abs(), b_, EnergyCorrector::c, alignmentValidation::c1, ztail::d, VVIObjFDetails::dzero(), alignCSCRings::e, VVIObjFDetails::expint(), f, python.connectstrParser::f1, python.connectstrParser::f2, myMath::fast_expf(), myMath::fast_logf(), relval_steps::k, kappa, prof2calltree::l, mode_, gen::n, omega_, lumiQueryAPI::q, q2, alignCSCRings::s, VVIObjFDetails::sincosint(), t0_, t1_, t_, x, and x0_.

                                                   : mode_(mode) {
  
  const float xp[9] = { 9.29,2.47,.89,.36,.15,.07,.03,.02,0.0 };
  const float xq[7] = { .012,.03,.08,.26,.87,3.83,11.0 };
  float h_[7];
  float  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 < 0.01f) kappa = 0.01f;
  if(kappa > 10.f) kappa = 10.f;
  if(beta2 < 0.f) beta2 = 0.f;
  if(beta2 > 1.f) beta2 = 1.f;
  
  float invKappa = 1.f/kappa;
  h_[4] = 1.f - beta2*0.42278433999999998f + (7.6f*invKappa);
  h_[5] = beta2;
  h_[6] = 1.f - beta2;
  h4 = - (7.6f*invKappa) - (beta2 * .57721566f + 1.f);
  h5 = vdt::fast_logf(kappa);
  h6 = invKappa;
  t0_ = (h4 - h_[4]*h5 - (h_[4] + beta2)*(vdt::fast_logf(h_[4]) + VVIObjFDetails::expint(h_[4])) + vdt::fast_expf(-h_[4]))/h_[4];
  
  // Set up limits for the root search
  
  for (lp = 0; lp < 9; ++lp) {
    if (kappa >= xp[lp]) break;
  }
  ll = -float(lp) - 1.5f;
  for (lq = 0; lq < 7; ++lq) {
    if (kappa <= xq[lq]) break;
  }
  ul = lq - 6.5f;
  auto f2 = [h_](float x) { return h_[4]-x+h_[5]*(vdt::fast_logf(std::abs(x))+VVIObjFDetails::expint(x))-h_[6]*vdt::fast_expf(-x);};
  VVIObjFDetails::dzero(ll, ul, u, rv, 1.e-3f, 100, f2);
  q = 1./u;
  t1_ = h4 * q - h5 - (beta2 * q + 1.f) * (vdt::fast_logf((fabs(u))) + VVIObjFDetails::expint(u)) + vdt::fast_expf(-u) * q;
  t_ = t1_ - t0_;
  omega_ = 6.2831853000000004f/t_;
  h_[0] = kappa * (beta2 * .57721566f + 2.f) + 9.9166128600000008f;
  if (kappa >= .07) {h_[0] += 6.90775527f;}
  h_[1] = beta2 * kappa;
  h_[2] = h6 * omega_;
  h_[3] = omega_ * 1.5707963250000001f;
  auto f1 = [h_](float x){ return h_[0]+h_[1]*vdt::fast_logf(h_[2]*x)-h_[3]*x;};
  VVIObjFDetails::dzero(5.f, 155.f, x0_, rv, 1.e-3f, 100, f1);
  n = x0_ + 1.;
  d = vdt::fast_expf(kappa * (beta2 * (.57721566f - h5) + 1.f)) * .31830988654751274f;
  a_[n - 1] = 0.f;
  if (mode_ == 0) {
    a_[n - 1] = omega_ * .31830988654751274f;
  }
  q = -1.;
  q2 = 2.;
  for (k = 1; k < n; ++k) {
    l = n - k;
    x = omega_ * k;
    x1 = h6 * x;
    VVIObjFDetails::sincosint(x1,c2,c1);
    c1 = vdt::fast_logf(x) - c1;
    vdt::fast_sincosf(x1,c3,c4);
    xf1 = kappa * (beta2 * c1 - c4) - x * c2;
    xf2 = x * c1 + kappa * (c3 + beta2 * c2) + t0_ * x;
    float s,c; vdt::fast_sincosf(xf2,s,c);
    if (mode_ == 0) {
      d1 = q * d * omega_ * vdt::fast_expf(xf1);
      a_[l - 1] = d1 * c;
      b_[l - 1] = -d1 * s;
    } else {
      d1 = q * d * vdt::fast_expf(xf1)/k;
      a_[l - 1] = d1 * s;
      b_[l - 1] = d1 * c;
      a_[n - 1] += q2 * a_[l - 1];
    }
    q = -q;
    q2 = -q2;
  }
  
} // VVIObjF

Member Function Documentation

float VVIObjF::fcn

(

float

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 133 of file VVIObjF.cc.

References a_, b_, f, relval_steps::k, mode_, gen::n, omega_, t0_, t1_, t_, x0_, and y.

Referenced by SiPixelTemplateReco::PixelTempReco2D().

                                {
    
    // Local variables
    
    float f, u, y, a0, a1;
    float a2 = 0.;
    float b1, b0, b2, cof;
    int k, n, n1;
    
    n = x0_;
    if (x < t0_) {
        f = 0.f;
    } else if (x <= t1_) {
      y = x - t0_;
      u = omega_ * y - 3.141592653589793f;
      float su,cu; vdt::fast_sincosf(u,su,cu);
      cof = cu * 2.f;
      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) * .5f + b0 * su;
      if (mode_ != 0) {f += y / t_;}
    } else {
      f = 0.f;
      if (mode_ != 0) {f = 1.f;}
    }
    return f;
} // fcn

void VVIObjF::limits	(	float &	xl,
		float &	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 183 of file VVIObjF.cc.

References t0_, and t1_.

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

Member Data Documentation

float VVIObjF::a_[155]

private

Definition at line 43 of file VVIObjF.h.

Referenced by fcn(), and VVIObjF().

float VVIObjF::b_[155]

private

Definition at line 44 of file VVIObjF.h.

Referenced by fcn(), and VVIObjF().

const int VVIObjF::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 VVIObjF.h.

Referenced by fcn(), and VVIObjF().

float VVIObjF::omega_

private

Definition at line 41 of file VVIObjF.h.

Referenced by fcn(), and VVIObjF().

float VVIObjF::t0_

private

Definition at line 38 of file VVIObjF.h.

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

float VVIObjF::t1_

private

Definition at line 39 of file VVIObjF.h.

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

float VVIObjF::t_

private

Definition at line 40 of file VVIObjF.h.

Referenced by fcn(), and VVIObjF().

float VVIObjF::x0_

private

Definition at line 42 of file VVIObjF.h.

Referenced by fcn(), and VVIObjF().