Refactor LB exception mechanism

[jngrad]

Fixes #4354

Description of changes:

• complete rewrite of lb.pxd
• bugfix: C++ exception NoLBActive() now raises a Python exception

[reinaual]

why is this tolerance increased?

[jngrad]

The old lb.pyx file used to do unit conversions with grid and tau as Python floats, while now it is done with C++ doubles, which don't have the same precision. In very long simulations like this statistical tests, a tiny numerical error in the properties of the fluid can lead to large numerical fluctuations after 5000 steps. If we look at the current python branch, the diagonal of the pressure tensor deviates from the expectation value by 0.0600, and the absolute tolerance is c_s_lb**2 / 6 = 0.0555. The test still passes because the diagonal has a large value (50006.38), and thus the relative tolerance is 50006.38 * 1e-07 = 0.0050, which brings the total tolerance to 0.605, which is larger than the deviation, but not by much. In fact, this was an issue in the walberla branch, where I already had to adjust this tolerance a few weeks ago when the pressure tensor code was added. With the new absolute tolerance of c_s_lb**2 / 5 = 0.0666 we are no longer in the danger zone.

[reinaual]

I don't really see why Python floats in CPython should have a different precision than C++ doubles but since the relative tolerance is that large this should not matter.

[jngrad]

For example with the LB density setter, we have to calculate p_dens * agrid * agrid * agrid in the unit conversion. The original lb.pxd would do __pyx_PyFloat_AsFloat(__pyx_v_p_dens) and call PyNumber_Multiply(__pyx_t_5, __pyx_v_agrid) three times, the new lb.pxd simply does __pyx_v_dens * pow(__pyx_v_agrid, 3.0). This difference is probably enough to introduce an error of the order of std::numeric_limits<double>::epsilon.

Generated C++ code

Here is the original lb.pxd code:

/* "espressomd/lb.pxd":127
 *     # get pointers
 *     if isinstance(p_dens, float) or isinstance(p_dens, int):
 *         c_dens = <float > p_dens * agrid * agrid * agrid             # <<<<<<<<<<<<<<
 *     else:
 *         c_dens = p_dens * agrid * agrid * agrid
 */
    __pyx_t_4 = __pyx_PyFloat_AsFloat(__pyx_v_p_dens); if (unlikely((__pyx_t_4 == (float)-1) && PyErr_Occurred())) __PYX_ERR(0, 127, __pyx_L1_error)
    __pyx_t_5 = PyFloat_FromDouble(((float)__pyx_t_4)); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 127, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_5);
    __pyx_t_6 = PyNumber_Multiply(__pyx_t_5, __pyx_v_agrid); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 127, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_6);
    __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
    __pyx_t_5 = PyNumber_Multiply(__pyx_t_6, __pyx_v_agrid); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 127, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_5);
    __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
    __pyx_t_6 = PyNumber_Multiply(__pyx_t_5, __pyx_v_agrid); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 127, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_6);
    __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
    __pyx_t_7 = __pyx_PyFloat_AsDouble(__pyx_t_6); if (unlikely((__pyx_t_7 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 127, __pyx_L1_error)
    __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
    __pyx_v_c_dens = __pyx_t_7;

and here is the new lb.pxd code:

/* "espressomd/lb.pxd":125
 * 
 * cdef inline python_lbfluid_set_density(double dens, double agrid) except +:
 *     lb_lbfluid_set_density(dens * agrid**3)             # <<<<<<<<<<<<<<
 * 
 * cdef inline python_lbfluid_set_viscosity(double visc, double agrid, double tau) except +:
 */
  try {
    lb_lbfluid_set_density((__pyx_v_dens * pow(__pyx_v_agrid, 3.0)));
  } catch(...) {
    __Pyx_CppExn2PyErr();
    __PYX_ERR(3, 125, __pyx_L1_error)
  }

[jngrad]

Note: this mocked LB class was introduced to help testing exceptions thrown from core getters. This works around the function assert_agrid_tau_set() that intercepts some of the calls to core functions if agrid or tau is not set. Since this is a function from a compiled Cython file, it's not possible to redefine it from the Python interpreter. The mocked class solves the issue without too much code. In the walberla branch, we don't need this workaround.