Can I just calculate the amplitudes for a (sub)process and check them point-by-point in phase space points using MadGraph ?

The easiest way to do this is to create a Standalone package:

   generate p p > e+ e-
   output standalone PATH

You can then easily choose which diagrams to include in the matrix.f files of the SubProcesses/P_xx_xxxx directories. There is also an example program (check_sa.f) in the SubProcesses directory which shows how to calculate the amplitude at specific phase space points or by using PS configurations from RAMBO.

You can also returns a valid c++ standalon code by running

   generate p p > e+ e-
   output standalone_cpp PATH

Pythton

If you want to have acces to the matrix-element via python. The easiest is to have the fortran code wrapped into python (evaluating a matrix element in python is just too slow to be usable). Each of the SubProcesses/P_xx_xxxx of the standalone directory can be compiled to be python linkable (note this require f2py part of numpy and to have python-devel package installed):

make matrix2py.so

Then you can link this from your python code. Here is an example:

import matrix2py

def invert_momenta(p):
        """ fortran/C-python do not order table in the same order"""
        new_p = []
        for i in range(len(p[0])):  new_p.append([0]*len(p))
        for i, onep in enumerate(p):
            for j, x in enumerate(onep):
                new_p[j][i] = x
        return new_p

matrix2py.initialisemodel('../../Cards/param_card.dat')
p = [[   0.5000000E+03,  0.0000000E+00,  0.0000000E+00,  0.5000000E+03],
     [   0.5000000E+03,  0.0000000E+00,  0.0000000E+00, -0.5000000E+03],
     [   0.5000000E+03,  0.1109243E+03,  0.4448308E+03, -0.1995529E+03],
     [   0.5000000E+03, -0.1109243E+03, -0.4448308E+03,  0.1995529E+03]]

P =invert_momenta(p)
alphas = 0.13
nhel = -1 # means sum over all helicity                                                                                                                                                                   
me2 = matrix2py.get_value(P, alphas, nhel)
print me2

Full library of process in python

If you are interested to have a single python library for a set of matrix-element. This is also possible in fortran/python. This is possible both for loop output ([sqr=virt]) and for tree level.

   generate p p > t t~
   output standalone PATH --prefix=int

then you can compile the library by going to the SubProcesses directory and

make allmatrix2py.so

Here is one example in that case

import allmatrix2py
allmatrix2py.initialise('../Cards/param_card.dat')

def invert_momenta(p):
        """ fortran/C-python do not order table in the same order"""
        new_p = []
        for i in range(len(p[0])):  new_p.append([0]*len(p))
        for i, onep in enumerate(p):
            for j, x in enumerate(onep):
                new_p[j][i] = x
        return new_p
p =[[  0.5000000E+03,  0.0000000E+00,  0.0000000E+00,  0.5000000E+03],
    [0.5000000E+03,  0.0000000E+00,  0.0000000E+00, -0.5000000E+03],
    [ 0.5000000E+03,  0.1040730E+03,  0.4173556E+03, -0.1872274E+03],
    [ 0.5000000E+03, -0.1040730E+03, -0.4173556E+03,  0.1872274E+03]
    ]

p =invert_momenta(p)
nhel = -1 # means sum over all helicity
pdgs = [21,21,6,-6] #which pdg is requested
scale2 = 0.  #only used for loop matrix element. should be set to 0 for tree-level
alphas=0.13

ans = allmatrix2py.smatrixhel(pdgs,p,alphas,scale2,nhel)
print ans

Python for version MG5_aMC version 2.5.x

For version of the code older than 2.6.0, the syntax was:

import matrix2py

def invert_momenta(p):
        """ fortran/C-python do not order table in the same order"""
        new_p = []
        for i in range(len(p[0])):  new_p.append([0]*len(p))
        for i, onep in enumerate(p):
            for j, x in enumerate(onep):
                new_p[j][i] = x
        return new_p

matrix2py.initialise('../../Cards/param_card.dat')
p = [[   0.5000000E+03,  0.0000000E+00,  0.0000000E+00,  0.5000000E+03],
     [   0.5000000E+03,  0.0000000E+00,  0.0000000E+00, -0.5000000E+03],
     [   0.5000000E+03,  0.1109243E+03,  0.4448308E+03, -0.1995529E+03],
     [   0.5000000E+03, -0.1109243E+03, -0.4448308E+03,  0.1995529E+03]]

P =invert_momenta(p)
alphas = 0.13
nhel = 0 # means sum over all helicity                                                                                                                                                                   
me2 = matrix2py.get_me(P, alphas, nhel)
print me2