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src/integrals/three_point/func_he [ Modules ]

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NAME

  Module func_he

USAGE

  use func_he

DESCRIPTION

  This module contains several functions for the computation of
  int^1_0 dy y^(n-1)/(y*z1+(1-y)*z3) where z1 and z3 are complex numbers

OUTPUT

  This modules exports three functions:
  * he -- a function
  * he_gen -- a function
  * he_c -- a function

USES

  * precision (src/module/precision_golem.f90)
  * numerical_evaluation (src/numerical/mod_numeric.f90)
  * sortie_erreur (src/module/sortie_erreur.f90)
  * parametre (src/module/parametre.f90)
  * logarithme (src/module/z_log.f90)
  * constante (src/module/constante.f90)

src/integrals/three_point/func_he/he [ Functions ]

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NAME

  Function he
  Note that this function is an interface for two other functions
  he_rarg and he_carg

USAGE

  real_dim2 = he(n,a1,a3)

DESCRIPTION

  This function computes:
  - int^1_0 dy y^(n-1)/(y*z1+(1-y)*z3)
  where z1 = -a1 -i lambda and z3 = -a3 - i lambda
  For n=1, it is equal to: - (ln(z1)-ln(z3))/(z1-z3)
  compatible with the definition of HnE
  It switches to numerical evaluation if 
  |a1-a3|/max(|a1|,|a3|) < coupure_3p2m

INPUTS

  * n -- an integer, the power of y in the integrand
  * a1 -- a real/complex (type ki), z1 (time -1)
  * a3 -- a real/complex (type ki), z3 (time -1)
  or
  * n -- an integer, the power of y in the integrand
  * a1 -- a complex (type ki), z1 (time -1)
  * a3 -- a complex (type ki), z3 (time -1)

SIDE EFFECTS

  No side effect, the returned value depends on the global variables
  rat_or_tot_par, coupure_3p2m

RETURN VALUE

  It returns a real (type ki) array of rank 1 and shape 2

EXAMPLE


src/integrals/three_point/func_he/he_c [ Functions ]

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NAME

  Function he_c

USAGE

  complex = he_c(n,a1,a3)

DESCRIPTION

 This function computes the same thing as he
 but it returns a complex instead of a real array of rank 1 and shape 2

INPUTS

  * n -- an integer, the power of y in the integrand
  * a1 -- a real (type ki), the real part of z1 (time -1)
  * a3 -- a real (type ki), the real part of z3 (time -1)

SIDE EFFECTS

  No side effect

RETURN VALUE

  It returns a complex (type ki)

EXAMPLE


src/integrals/three_point/func_he/he_gen [ Functions ]

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NAME

  Function he_gen

USAGE

  real_dim2 = he_gen(n,a1,b1,a3,b3)

DESCRIPTION

  This function computes:
  int^1_0 dy y^n/(y*z1+(1-y)*z3)
  where z1 = a1 + i b1 and z3 = a3 + i b3
  For n=1, it is equal to: (ln(z1)-ln(z3))/(z1-z3)
  It switches to numerical evaluation if 
  |a1-a3|/max(|a1|,|a3|) < coupure_3p2m

INPUTS

  * n -- an integer, the power of y in the integrand
  * a1 -- a real (type ki), the real part of z1 
  * b1 -- a real (type ki), the imaginary part of z1 
  * a3 -- a real (type ki), the real part of z3 
  * b3 -- a real (type ki), the imaginary part of z3 

SIDE EFFECTS

  No side effect, the returned value depends on the global variables
  rat_or_tot_par, coupure_3p2m

RETURN VALUE

  It returns a real (type ki) array of rank 1 and shape 2

EXAMPLE