Join quad calls

[alecandido]

In order to have a consistent treatment of the integration error we should have only one integral per kinematic point, producing directly the whole result on its own.

Alternatives

There are two alternatives that make sense:

1. joining all the integrands in a single one
2. joining the integrands and the addends

Second alternative

The second looks good because the result is fully provided by scipy.integrate.quad method, that in this way is able to deal properly with the error.

Pro - Integration error

In this way it makes meaningful to call it setting a target error, otherwise keeping anything apart (as the addend that are a main contribution to the result) will make useless to set a relative error.

Note: maybe we can use the same an absolute error, since addends are not providing any integration error to the result

Contra - Domain measure

In order to join also the addends they should be divided by the domain measure, that it is a small number in large x region.

Report of run against APFEL with setup 2.

---F2---
    x   Q2     APFEL    yadism  yadism_error  rel_err[%]

0   0.005   90  0.423601  0.421183  1.639359e-09   -0.570732

1   0.010   90  0.408118  0.407460  1.656415e-08   -0.161155

2   0.050   90  0.406260  0.409613  2.110029e-09    0.825171

3   0.100   90  0.415573  0.419292  1.088329e-08    0.894909

4   0.200   90  0.398328  0.400737  3.673791e-09    0.604670

5   0.400   90  0.270478  0.270922  4.579316e-10    0.164007

6   0.600   90  0.118117  0.118232  2.012938e-09    0.097045

7   0.800   90  0.021769  0.021760  3.067386e-10   -0.042198

8   0.900   90  0.003521  0.003519  6.400343e-11   -0.049224

9   0.990   90  0.000006  0.000003  1.671909e-11  -59.032912

10  0.100  100  0.415969  0.419604  1.182132e-08    0.873961

11  0.100  200  0.418463  0.421459  1.722654e-08    0.716092

12  0.100  400  0.421075  0.423022  2.339947e-08    0.462387

13  0.100  800  0.424712  0.424356  2.169060e-08   -0.083774

---FL---
    x   Q2         APFEL        yadism  yadism_error  rel_err[%]

0   0.005   90  5.039327e-02  5.035929e-02  5.211968e-15   -0.067441

1   0.010   90  4.599659e-02  4.596613e-02  2.568837e-15   -0.066239

2   0.050   90  3.278713e-02  3.276761e-02  5.607194e-16   -0.059512

3   0.100   90  2.480442e-02  2.478631e-02  3.873131e-16   -0.073047

4   0.200   90  1.519444e-02  1.518592e-02  2.476151e-16   -0.056124

5   0.400   90  5.113912e-03  5.114357e-03  8.828225e-17    0.008714

6   0.600   90  1.083225e-03  1.085742e-03  2.346203e-17    0.232361

7   0.800   90  7.136434e-05  7.128380e-05  1.201232e-18   -0.112852

8   0.900   90  4.547322e-06  4.535800e-06  1.941100e-19   -0.253384

9   0.990   90  4.526005e-10 -3.375707e-10  1.276474e-20 -174.584683

10  0.100  100  2.445356e-02  2.443396e-02  3.818074e-16   -0.080156

11  0.100  200  2.237996e-02  2.234433e-02  3.491546e-16   -0.159177

12  0.100  400  2.065771e-02  2.058396e-02  3.216469e-16   -0.356989

13  0.100  800  1.925086e-02  1.908071e-02  2.981570e-16   -0.883839

[alecandido]

Task linked: CU-8junnp Heavy Quark Mass Scheme

[felixhekhorn]

discontinued for now due to very old code base - the idea got transformed in #85