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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(), edmIntegrityCheck::d, VVIObjDetails::dzero(), MillePedeFileConverter_cfg::e, JetChargeProducer_cfi::exp, VVIObjDetails::expint(), sistripvvi::VVIObjDetails::f1(), sistripvvi::VVIObjDetails::f2(), gen::k, kappa, checklumidiff::l, cmsBatch::log, mode_, gen::n, omega_, lumiQueryAPI::q, q2, funct::sin(), VVIObjDetails::sincosint(), t0_, t1_, t_, x, and x0_.

48  : mode_(mode) {
49 
50  const double xp[9] = { 9.29,2.47,.89,.36,.15,.07,.03,.02,0.0 };
51  const double xq[7] = { .012,.03,.08,.26,.87,3.83,11.0 };
52  double h_[7];
53  double q, u, x, c1, c2, c3, c4, d1, h4, h5, h6, q2, x1, d, ll, ul, xf1, xf2, rv;
54  int lp, lq, k, l, n;
55 
56  // Make sure that the inputs are reasonable
57 
58  if(kappa < 0.01) kappa = 0.01;
59  if(kappa > 10.) kappa = 10.;
60  if(beta2 < 0.) beta2 = 0.;
61  if(beta2 > 1.) beta2 = 1.;
62 
63  h_[4] = 1. - beta2*0.42278433999999998 + 7.6/kappa;
64  h_[5] = beta2;
65  h_[6] = 1. - beta2;
66  h4 = -7.6/kappa - (beta2 * .57721566 + 1);
67  h5 = log(kappa);
68  h6 = 1./kappa;
69  t0_ = (h4 - h_[4]*h5 - (h_[4] + beta2)*(log(h_[4]) + VVIObjDetails::expint(h_[4])) + exp(-h_[4]))/h_[4];
70 
71  // Set up limits for the root search
72 
73  for (lp = 0; lp < 9; ++lp) {
74  if (kappa >= xp[lp]) break;
75  }
76  ll = -lp - 1.5;
77  for (lq = 0; lq < 7; ++lq) {
78  if (kappa <= xq[lq]) break;
79  }
80  ul = lq - 6.5;
81  auto f2 = [h_](double x) { return h_[4]-x+h_[5]*(std::log(std::abs(x))+VVIObjDetails::expint(x))-h_[6]*std::exp(-x);};
82  VVIObjDetails::dzero(ll, ul, u, rv, 1.e-5, 1000, f2);
83  q = 1./u;
84  t1_ = h4 * q - h5 - (beta2 * q + 1) * (log((fabs(u))) + VVIObjDetails::expint(u)) + exp(-u) * q;
85  t_ = t1_ - t0_;
86  omega_ = 6.2831853000000004/t_;
87  h_[0] = kappa * (beta2 * .57721566 + 2.) + 9.9166128600000008;
88  if (kappa >= .07) {h_[0] += 6.90775527;}
89  h_[1] = beta2 * kappa;
90  h_[2] = h6 * omega_;
91  h_[3] = omega_ * 1.5707963250000001;
92  auto f1 = [h_](double x){ return h_[0]+h_[1]*std::log(h_[2]*x)-h_[3]*x;};
93  VVIObjDetails::dzero(5., 155., x0_, rv, 1.e-5, 1000, f1);
94  n = x0_ + 1.;
95  d = exp(kappa * (beta2 * (.57721566 - h5) + 1.)) * .31830988654751274;
96  a_[n - 1] = 0.;
97  if (mode_ == 0) {
98  a_[n - 1] = omega_ * .31830988654751274;
99  }
100  q = -1.;
101  q2 = 2.;
102  for (k = 1; k < n; ++k) {
103  l = n - k;
104  x = omega_ * k;
105  x1 = h6 * x;
106  VVIObjDetails::sincosint(x1,c2,c1);
107  c1 = log(x) - c1;
108  c3 = sin(x1);
109  c4 = cos(x1);
110  xf1 = kappa * (beta2 * c1 - c4) - x * c2;
111  xf2 = x * c1 + kappa * (c3 + beta2 * c2) + t0_ * x;
112  if (mode_ == 0) {
113  d1 = q * d * omega_ * exp(xf1);
114  a_[l - 1] = d1 * cos(xf2);
115  b_[l - 1] = -d1 * sin(xf2);
116  } else {
117  d1 = q * d * exp(xf1)/k;
118  a_[l - 1] = d1 * sin(xf2);
119  b_[l - 1] = d1 * cos(xf2);
120  a_[n - 1] += q2 * a_[l - 1];
121  }
122  q = -q;
123  q2 = -q2;
124  }
125 
126 } // VVIObj
funct::sin
Sin< T >::type sin(const T &t)
Definition: Sin.h:22
VVIObj::a_
double a_[155]
Definition: VVIObj.h:43
VVIObj::t1_
double t1_
Definition: VVIObj.h:39
MillePedeFileConverter_cfg.e
e
Definition: MillePedeFileConverter_cfg.py:37
VVIObjDetails::dzero
int dzero(double a, double b, double &x0, double &rv, double eps, int mxf, F func)
Private version of the exponential integral.
Definition: VVIObj.cc:570
q2
double q2[4]
Definition: TauolaWrapper.h:88
VVIObj::b_
double b_[155]
Definition: VVIObj.h:44
ALCARECOPromptCalibProdSiPixelAli0T_cff.mode
mode
Definition: ALCARECOPromptCalibProdSiPixelAli0T_cff.py:96
funct::cos
Cos< T >::type cos(const T &t)
Definition: Cos.h:22
sistripvvi::VVIObjDetails::f1
double f1(double x, double const *h_)
Private version of the exponential integral.
Definition: VVIObj.cc:35
VVIObj::omega_
double omega_
Definition: VVIObj.h:41
funct::abs
Abs< T >::type abs(const T &t)
Definition: Abs.h:22
VVIObj::x0_
double x0_
Definition: VVIObj.h:42
sistripvvi::VVIObjDetails::f2
double f2(double x, double const *h_)
Definition: VVIObj.cc:36
gen::k
int k[5][pyjets_maxn]
Definition: Cascade2Hadronizer.cc:79
VVIObjDetails::sincosint
void sincosint(double x, double &sint, double &cint)
Definition: VVIObj.cc:345
VVIObj::t0_
double t0_
Definition: VVIObj.h:38
VVIObj::mode_
const int mode_
returns the limits on the non-zero (mode=0) or normalized region (mode=1)
Definition: VVIObj.h:37
VVIObj::t_
double t_
Definition: VVIObj.h:40
kappa
static const G4double kappa
Definition: UrbanMscModel93.cc:34
JetChargeProducer_cfi.exp
exp
Definition: JetChargeProducer_cfi.py:6
VVIObjDetails::expint
double expint(double x)
Private version of the sine integral.
Definition: VVIObj.cc:448

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, gen::k, mode_, gen::n, omega_, funct::sin(), t0_, t1_, t_, x0_, and y.

Referenced by SiPixelTemplateSplit::PixelTempSplit().

135  {
136 
137  // Local variables
138 
139  double f, u, y, a0, a1;
140  double a2 = 0.;
141  double b1, b0, b2, cof;
142  int k, n, n1;
143 
144  n = x0_;
145  if (x < t0_) {
146  f = 0.;
147  } else if (x <= t1_) {
148  y = x - t0_;
149  u = omega_ * y - 3.141592653589793;
150  cof = cos(u) * 2.;
151  a1 = 0.;
152  a0 = a_[0];
153  n1=n+1;
154  for (k = 2; k <= n1; ++k) {
155  a2 = a1;
156  a1 = a0;
157  a0 = a_[k - 1] + cof * a1 - a2;
158  }
159  b1 = 0.;
160  b0 = b_[0];
161  for (k = 2; k <= n; ++k) {
162  b2 = b1;
163  b1 = b0;
164  b0 = b_[k - 1] + cof * b1 - b2;
165  }
166  f = (a0 - a2) * .5 + b0 * sin(u);
167  if (mode_ != 0) {f += y / t_;}
168  } else {
169  f = 0.;
170  if (mode_ != 0) {f = 1.;}
171  }
172  return f;
173 } // fcn
funct::sin
Sin< T >::type sin(const T &t)
Definition: Sin.h:22
VVIObj::a_
double a_[155]
Definition: VVIObj.h:43
VVIObj::t1_
double t1_
Definition: VVIObj.h:39
VVIObj::b_
double b_[155]
Definition: VVIObj.h:44
funct::cos
Cos< T >::type cos(const T &t)
Definition: Cos.h:22
VVIObj::omega_
double omega_
Definition: VVIObj.h:41
f
double f[11][100]
Definition: MuScleFitUtils.cc:78
VVIObj::x0_
double x0_
Definition: VVIObj.h:42
gen::k
int k[5][pyjets_maxn]
Definition: Cascade2Hadronizer.cc:79
VVIObj::t0_
double t0_
Definition: VVIObj.h:38
VVIObj::mode_
const int mode_
returns the limits on the non-zero (mode=0) or normalized region (mode=1)
Definition: VVIObj.h:37
VVIObj::t_
double t_
Definition: VVIObj.h:40
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_.

184  {
185 
186  xl = t0_;
187  xu = t1_;
188  return;
189 } // limits
VVIObj::t1_
double t1_
Definition: VVIObj.h:39
VVIObj::t0_
double t0_
Definition: VVIObj.h:38

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().

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