Mathematical constants

Small numbers
Small numbers used for cutoffs, integration accuracies, etc.
const double	apfel::eps2 = 1e-2
const double	apfel::eps3 = 1e-3
const double	apfel::eps4 = 1e-4
const double	apfel::eps5 = 1e-5
const double	apfel::eps6 = 1e-6
const double	apfel::eps7 = 1e-7
const double	apfel::eps8 = 1e-8
const double	apfel::eps9 = 1e-9
const double	apfel::eps10 = 1e-10
const double	apfel::eps11 = 1e-11
const double	apfel::eps12 = 1e-12
const double	apfel::eps13 = 1e-13
const double	apfel::eps14 = 1e-14
const double	apfel::eps15 = 1e-15
const double	apfel::eps25 = 1e-25

Gauss-Legendre quadrature
Coordinates and weights of the Gauss-Legendre quadrature with 8 and 16-point integration.
const std::array< std::vector< double >, 2 >	apfel::gl_x
const std::array< std::vector< double >, 2 >	apfel::gl_w

Gauss-Kronrod quadrature
Coordinates and weights of the Gauss-Kronrod quadrature with 7 and 15-point integration.
const std::array< std::vector< double >, 2 >	apfel::gk_x
const std::array< std::vector< double >, 2 >	apfel::gk_w

Numerical constants
Definitions for recurrent constants.
const double	apfel::Pi2 = M_PI * M_PI
const double	apfel::FourPi = 4 * M_PI
const double	apfel::emc = 0.5772156649015329
const double	apfel::zeta2 = 1.6449340668482264
const double	apfel::zeta3 = 1.2020569031595943
const double	apfel::zeta4 = 1.0823232337111382
const double	apfel::zeta5 = 1.0369277551433699
const double	apfel::zeta6 = 1.0173430619844491

QCD colour factors
The SU(3) Casimir's.
const double	apfel::TR = 0.5
const double	apfel::CF = 4. / 3.
const double	apfel::CA = 3.
const double	apfel::NC = 3.

Detailed Description

Collection of mathematical constants often used in the code.

Variable Documentation

CA

const double apfel::CA = 3.

CF

const double apfel::CF = 4. / 3.

Examples

distribution_test.cc, and operator_test.cc.

emc

const double apfel::emc = 0.5772156649015329

Examples

tmd_test.cc.

eps10

const double apfel::eps10 = 1e-10

eps11

const double apfel::eps11 = 1e-11

eps12

const double apfel::eps12 = 1e-12

eps13

const double apfel::eps13 = 1e-13

eps14

const double apfel::eps14 = 1e-14

eps15

const double apfel::eps15 = 1e-15

eps2

const double apfel::eps2 = 1e-2

eps25

const double apfel::eps25 = 1e-25

eps3

const double apfel::eps3 = 1e-3

eps4

const double apfel::eps4 = 1e-4

eps5

const double apfel::eps5 = 1e-5

Examples

massiveCF_test.cc, and principal_value_test.cc.

eps6

const double apfel::eps6 = 1e-6

eps7

const double apfel::eps7 = 1e-7

Examples

ogata_test.cc.

eps8

const double apfel::eps8 = 1e-8

eps9

const double apfel::eps9 = 1e-9

Examples

principal_value_test.cc.

FourPi

const double apfel::FourPi = 4 * M_PI

gk_w

const std::array<std::vector<double>, 2> apfel::gk_w

Initial value:

=
  {
    {
      std::vector<double>{4.1795918367346939e-01, 3.8183005050511894e-01, 2.7970539148927667e-01, 1.2948496616886969e-01},
      std::vector<double>{
        2.0948214108472783e-01, 2.0443294007529889e-01, 1.9035057806478541e-01, 1.6900472663926790e-01,
        1.4065325971552592e-01, 1.0479001032225018e-01, 6.3092092629978553e-02, 2.2935322010529225e-02
      }
    }
  }

gk_x

const std::array<std::vector<double>, 2> apfel::gk_x

Initial value:

=
  {
    {
      std::vector<double>{0.0000000000000000e+00, 4.0584515137739717e-01, 7.4153118559939444e-01, 9.4910791234275852e-01},
      std::vector<double>{
        0.0000000000000000e+00, 2.0778495500789847e-01, 4.0584515137739717e-01, 5.8608723546769113e-01,
        7.4153118559939444e-01, 8.6486442335976907e-01, 9.4910791234275852e-01, 9.9145537112081264e-01
      }
    }
  }

gl_w

const std::array<std::vector<double>, 2> apfel::gl_w

Initial value:

=
  {
    {
      std::vector<double>{0.3626837833783619, 0.3137066458778872, 0.2223810344533744, 0.1012285362903762},
      std::vector<double>{
        0.1894506104550684, 0.1826034150449235, 0.1691565193950025, 0.1495959888165767,
        0.1246289712555338, 0.0951585116824927, 0.0622535239386478, 0.0271524594117540
      }
    }
  }

gl_x

const std::array<std::vector<double>, 2> apfel::gl_x

Initial value:

=
  {
    {
      std::vector<double>{0.1834346424956498, 0.5255324099163289, 0.7966664774136267, 0.9602898564975362},
      std::vector<double>{
        0.0950125098376374, 0.2816035507792589, 0.4580167776572273, 0.6178762444026437,
        0.7554044083550030, 0.8656312023878317, 0.9445750230732325, 0.9894009349916499
      }
    }
  }

NC

const double apfel::NC = 3.

Pi2

const double apfel::Pi2 = M_PI * M_PI

TR

const double apfel::TR = 0.5

Examples

massiveCF_test.cc.

zeta2

const double apfel::zeta2 = 1.6449340668482264

zeta3

const double apfel::zeta3 = 1.2020569031595943

zeta4

const double apfel::zeta4 = 1.0823232337111382

zeta5

const double apfel::zeta5 = 1.0369277551433699

zeta6

const double apfel::zeta6 = 1.0173430619844491