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DSL and compiler framework for automated finite-differences and stencil computation

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This PR adds the ability to define `Function`'s on `SubDomain`'s, e.g. ``` f = Function(name='f', grid=grid, subdomain=grid.subdomains['middle']) ``` The shape of the `Data` allocated will then be `grid.subdomains['middle'].shape` (or `grid.subdomains['middle'].shape_local`...

WIP
testing

This is due to the way the DSE works at the moment -- detecting and hoisting expressions in a greedy fashion as a sequence of steps. Eg: ``` a =...

This is a non-trivial optimisation. Basically, the compiler, in doing data dependence analysis, abstracts away SubDimensions as pure Dimensions; so `yleft`, `yi`, `yright` they all become `y` to the eyes...

this code ``` from devito import * grid = Grid(shape=(3, 3)) t = grid.stepping_dim time = grid.time_dim x, y = grid.dimensions T = Dimension(name='T') x1 = Dimension(name='x1') x2 = Dimension(name='x2')...

Over time the work on resampling input data in time and the spatial interpolation of off-grid points seem to have a lot of overlap and this could be cleanly set...

An example below is provided for specifying derivative types. This issue is suggesting the second form bellow should throw an error, pehaps ```UnrecognizedParameterError```. **Correct, results in desired behavior** ``` from...

Take a look at: ``` @classmethod def left(cls, name, parent, thickness, local=True): lst, rst = cls._symbolic_thickness(name) return cls(name, parent, left=parent.symbolic_min, right=parent.symbolic_min+lst-1, thickness=((lst, thickness), (rst, 0)), local=local) @classmethod def right(cls, name,...

When looking at the dask tutorial, I noticed that `AcousticWaveSolver` takes a `model` and a `geometry` structure as input arguments. However, `geometry` already contains a `model` structure itself. Is it...

Current code generation with ``DSE=aggressive`` might break in some examples (e.g., TTI) if the backend compiler is not ICC, as GCC doesn't like ``#pragma omp simd`` if the following loop...

bug-py

[this map](https://github.com/devitocodes/devito/blob/master/devito/types/grid.py#L217) may actually be an `{expr: float}` map rather than a `{symbol: float}` map. Reproducer is `test_dimension.py::TestConditionalDimension::test_subsampled_fd`. The ConditionalDimension's spacing is a Mul between its factor and the parent's...

bug-py-minor