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#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 | |
| VVIObj (double kappa=0.01, double beta2=1., double mode=0) | |
| Constructor. | |
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) | |
| double | omega_ |
| double | t0_ |
| double | t1_ |
| double | t_ |
| double | x0_ |
Port of CERNLIB routines vvidis/vviden (G116) to calculate higher quality Vavilov density and distribution functions
| VVIObj::VVIObj | ( | double | kappa = 0.01, |
| double | beta2 = 1., |
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| double | mode = 0 |
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| ) |
Constructor.
Constructor Set Vavilov parameters kappa and beta2 amd define whether to calculate density fcn or distribution fcn
| 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 49 of file VVIObj.cc.
References a_, b_, alignmentValidation::c1, funct::cos(), debug_cff::d1, VVIObjDetails::dzero(), funct::exp(), VVIObjDetails::expint(), VVIObjDetails::f1(), VVIObjDetails::f2(), gen::k, prof2calltree::l, funct::log(), mode_, 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; // double (*fp2)(double) = reinterpret_cast<double(*)(double)>(&VVIObj::f2); VVIObjDetails::dzero(ll, ul, u, rv, 1.e-5, 1000, boost::bind(&VVIObjDetails::f2, _1,h_)); 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; // double (*fp1)(double) = reinterpret_cast<double(*)(double)>(&VVIObj::f1); VVIObjDetails::dzero(5., 155., x0_, rv, 1.e-5, 1000, boost::bind(&VVIObjDetails::f1, _1,h_)); 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
| double VVIObj::fcn | ( | double | x | ) | const |
Vavilov function method Returns density fcn (mode=0) or distribution fcn (mode=1)
| x | - (input) Argument of function [typically defined as (Q-mpv)/sigma] |
Definition at line 136 of file VVIObj.cc.
References a_, b_, funct::cos(), f, gen::k, mode_, n, omega_, funct::sin(), t0_, t1_, t_, x0_, and detailsBasic3DVector::y.
Referenced by SiPixelTemplateReco::PixelTempReco2D().
{
// 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
| 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 |
double VVIObj::a_[155] [private] |
double VVIObj::b_[155] [private] |
const int VVIObj::mode_ [private] |
double VVIObj::omega_ [private] |
double VVIObj::t0_ [private] |
double VVIObj::t1_ [private] |
double VVIObj::t_ [private] |
double VVIObj::x0_ [private] |
1.7.3