Move all backend-agnostic assemble_lincomb logic to algorithms.lincomb

[sdrave]

This moves all assemble_lincomb methods for generic Operators into pymor.algorithms.lincomb. The RuleTable also takes care of eliminating ZeroOperators. ATM, the backends still need to handle IdentitiyOperators. Before merging, this issue should be resolved (e.g. by introducing a ShiftedOperator and apply_inverse_shifted interface methods or a separate argument to _assemble_lincomb).

This addresses #548.

[sdrave]

@pmli I am now quite satisfied with the state of this PR. What do you think?

[sdrave]

BTW, I decided against introducing a ShiftedOperator in this PR but added a shift parameter to _assemble_lincomb. I would propose to introduce ShiftedOperator in a separate PR if needed.

[pmli]

One of my favourite tests fails again.

>>> from pymor.basic import *
>>> I = IdentityOperator(NumpyVectorSpace(2))
>>> v = I.source.ones()
>>> (I + I).apply_inverse(v)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/path/pymor/src/pymor/operators/constructions.py", line 166, in apply_inverse
    return super().apply_inverse(V, mu=mu, least_squares=least_squares)
  File "/path/pymor/src/pymor/operators/basic.py", line 101, in apply_inverse
    assembled_op = self.assemble(mu)
  File "/path/pymor/src/pymor/operators/constructions.py", line 129, in assemble
    name=self.name + '_assembled')
  File "/path/pymor/src/pymor/algorithms/lincomb.py", line 48, in assemble_lincomb
    return AssembleLincombRules(tuple(coefficients), solver_options, name).apply(tuple(operators))
  File "/path/pymor/src/pymor/algorithms/rules.py", line 269, in apply
    result = r.action(self, obj)
  File "/path/pymor/src/pymor/algorithms/lincomb.py", line 168, in action_call_assemble_lincomb_method
    op = ops_without_id[0]._assemble_lincomb(ops_without_id, self.coefficients, shift=id_coeff,
IndexError: list index out of range

[renefritze]

Maybe add that as an actual test in https://github.com/pymor/pymor/blob/master/src/pymortests/operators.py ?

[sdrave]

That issue should be fixed. Anything else?

[pmli]

Technically, it looks ok to me. I'm a bit unsure about the name shift for the argument in _assemble_lincomb. An operator could be shifted by anything, not just IdentityOperator... How about renaming it to id_op_coef, or something similar?

[sdrave]

Aren't you guys usually speaking of solving shifted equation systems where you implicitly mean 'shifted by a multiple of the identity'. I have nothing against renaming the argument, but how abount 'identity_shift'?

[pmli]

Aren't you guys usually speaking of solving shifted equation systems where you implicitly mean 'shifted by a multiple of the identity'.

It can mean 'shifted by a multiple of the mass matrix' (s E - A in IRKA, A + p E in ADI) and the mass matrix can be almost anything.

I have nothing against renaming the argument, but how abount 'identity_shift'?

That also sounds good.

[sdrave]

Right, forgot about the mass matrix .. - I have renamed the parameter to identity_shift.