import shutil
from pySecDec import make_package
if __name__ == "__main__":
make_package(
name='thetafunction',
integration_variables=['z%i' % i for i in range(3)],
# the order here defines the order of the expansion
regulators=['eps'],
real_parameters=['delta'],
functions=['cut1'],
polynomials_to_decompose=['(z0+z1)**(-2-2*eps)', 'z2**(-1-4*eps)'],
remainder_expression='cut1(z1,delta)',
# the highest orders of the final regulator expansion
# the order here matches the order of ``regulators``
requested_orders=[1],
# the optimization level to use in FORM (can be 0, 1, 2, 3, 4)
form_optimization_level=2,
# the WorkSpace parameter for FORM
form_work_space='500M',
)
# copy 'functions.hpp' (predefined for this example) to required directory
shutil.copy('functions_thetafunction.hpp',
'thetafunction/thetafunction_integral/src/functions.hpp')
name = 'userdefined_cpp'
make_package(
name=name,
integration_variables = ['x','y','z'],
# use integration by parts rather than subtraction for ``x`` and ``y``
# generate subtraction term for ``z`` to avoid derivative of HeavisideTheta
ibp_power_goal = [0,0,-1],
# the order here defines the order of the expansion
regulators = ['eps'],
functions = ['HeavisideTheta','func'],
polynomials_to_decompose = ['(x+y)**(-2+eps)','z**(-1+eps)'],
remainder_expression = 'HeavisideTheta(1/4-z)*func(y)',
# full analytic result for func(y)=1:
# (4^-eps (-2 + 2^eps))/((-1 + eps) eps^2)
# = 1/eps^2 + (1 - Log[2] - Log[4])/eps + 1/2 (2 - 2 Log[2] - Log[2]^2 - 2 Log[4] + 2 Log[2] Log[4] + Log[4]^2) + O[eps]
# = 1.0000000000000000000/eps^2 - 1.0794415416798359283/eps + 0.60214400703386905808 + O[eps]
# the highest orders of the final regulator expansion
# the order here matches the order of ``regulators``
requested_orders = [0],
)
# check the generated "functions.hpp"
cpp_function_declarations = (
name = 'userdefined_cpp'
make_package(
name=name,
integration_variables = ['z%i' % i for i in range(4)],
# the order here defines the order of the expansion
regulators = ['eps'],
real_parameters = ['alpha'],
functions = ['dum1', 'dum2'],
#
polynomials_to_decompose = ['(z0+z1)**(-2-2*eps)', 'z2**(-1-4*eps)'],
remainder_expression = '(dum1(z0,z1,z2,z3) + 5*eps*z0)**(1+eps) * dum2(z0,z1,alpha)**(2-6*eps)',
#remainder_expression = '(z0**2+z1**3+z2**4+z3**5 + 4*z0*z1*z2*z3+2-z0**2*z1**3*z2**4*z3**5 + 5*eps*z0)**(1+eps) * (z0**2 + z1**2 +alpha**2 + 4*z0*z1+3*z0**2*z1**2 - sqrt(z0*z1*alpha))**(2-6*eps)',
# the highest orders of the final regulator expansion
# the order here matches the order of ``regulators``
requested_orders = [1],
# the optimization level to use in FORM (can be 0, 1, 2, 3, 4)
form_optimization_level = 2,
# the WorkSpace parameter for FORM
form_work_space = '500M',
)
# check the generated "functions.hpp"
with open(name + '/' + name + '_integral/src/functions.hpp') as generated_header_file:
make_package(
name='two_regulators',
integration_variables=['z%i' % i for i in range(2)],
# the order here defines the order of the expansion
regulators=['alpha', 'eps'],
#complex_parameters = ['A'],
#functions = ['F1', 'F2'],
prefactor='''exp(-EulerGamma*(2*eps+alpha))''',
polynomials_to_decompose=[
'z0**(-1-2*eps-alpha)', '(1-z0)**(-1+2*eps+alpha)',
'z1**(-1+alpha/2)'
],
remainder_expression='exp(-z0/(1-z0))',
# the highest orders of the final regulator expansion
# the order here matches the order of ``regulators``
requested_orders=[0, 0],
# the optimization level to use in FORM (can be 0, 1, 2, 3, 4)
form_optimization_level=2,
# the WorkSpace parameter for FORM
form_work_space='500M',
# Note:
# * this integral is numerically regulated for z0->1 (see remainder_expression)
# * default korobov3x3 transforms the integrand strongly close to z0->1
# * applying korobov3x3 makes the integrand too numerically unstable to integrate (often get nan)
# We instead use the asymmetric korobov3x1 to avoid introducing too much noise for z0->1
pylink_qmc_transforms=['korobov3x1'])
make_package(
name='hypergeo5F4',
integration_variables = ['z%i' % i for i in range(4)],
# the order here defines the order of the expansion
regulators = ['eps'],
real_parameters = ['b'],
#functions = [],
prefactor = '''
gamma(2*eps)*gamma(4*eps)*gamma(6*eps)*gamma(8*eps)/
(gamma(-eps)*gamma(-3*eps)*gamma(-5*eps)*gamma(-7*eps))/
gamma(3*eps)/gamma(7*eps)/gamma(11*eps)/gamma(15*eps)
''',
#prefactor = '947.4609375*eps**4 - 286765.9822507143*eps**6 + 1.4350164700988792*^6*eps**7 + 2.668449372562483*^7*eps**8',
polynomials_to_decompose = ['z0**(-1-7*eps)','z1**(-1-5*eps)','z2**(-1-3*eps)','z3**(-1-eps)', '(1-z0)**(-1+15*eps)','(1-z1)**(-1+11*eps)','(1-z2)**(-1+7*eps)','(1-z3)**(-1+3*eps)','(1-b*z0*z1*z2*z3)**(-eps)'],
#remainder_expression = '',
# the highest orders of the final regulator expansion
# the order here matches the order of ``regulators``
requested_orders = [4],
# the optimization level to use in FORM (can be 0, 1, 2, 3, 4)
form_optimization_level = 2,
# the WorkSpace parameter for FORM
form_work_space = '500M',
split = True,
)
#!/usr/bin/env python3
import shutil
from pySecDec import make_package
if __name__ == "__main__":
name = 'no_default_transform'
make_package(
name=name,
integration_variables=['x'],
# the order here defines the order of the expansion
regulators=['eps'],
# the highest orders of the final regulator expansion
# the order here matches the order of ``regulators``
requested_orders=[1],
polynomials_to_decompose=['(x)**(-1+eps)'],
polynomial_names=['p'],
other_polynomials=['p**-2'],
pylink_qmc_transforms=['korobov2x1', 'sidi3'])
#!/usr/bin/env python3
from pySecDec import make_package
if __name__ == "__main__":
make_package(
name='difference',
integration_variables=['z1', 'z2', 'z3'],
regulators=['eps'],
polynomials_to_decompose=['(z1-z2*z3)**(-1+eps)'],
# the contour deformation adds a "-i * delta" prescription to the polynomial above
polynomial_names=['P'],
contour_deformation_polynomial='P',
# we want to compute up to order "eps**2"
requested_orders=[2],
# split the integration region at 1/2 to remap singularities
# at one to zero
split=True,
)
# analytic result:
# ( 1.64493406684822643647241516664602518923 + 3.1415926535897932384626433832795028842 * I) * eps ** 0
# ( 2.08781123053685858754509217178101012328 - 6.2831853071795864769252867665590057684 * I) * eps ** 1
# (-5.94029019737039970544633397517750766917 + 4.2570651807194096861418776386549427857 * I) * eps ** 2
# ( 5.77945251635494087034720012662916969501 - 2.2309450542592328953584685107508798034 * I) * eps ** 3 # set ``requested_orders = [3]`` to compute up to order "eps**3"
#!/usr/bin/env python3
from pySecDec import make_package
if __name__ == "__main__":
make_package(
name='easy',
integration_variables=['x', 'y'],
regulators=['eps'],
requested_orders=[0],
polynomials_to_decompose=['(x+y)^(-2+eps)'],
)