Sparse matrices

[majosm]

Adds CSRMatmul array type for multiplication by sparse matrices in compressed sparse row format.

cc @lukeolson

[majosm]

@inducer I started looking through the loopy codegen code to try to figure out how to generate temporaries for the reduction bounds to avoid islpy errors (as is done in the loopy example), but I'm having some trouble figuring out how best to do that. Seems like I need to create the temporaries inside InlinedExpressionGenMapper.map_reduce() before adding the reduction domain to the kernel, but I'm not sure how to make sure the temporaries get the right scope, dependencies, inames, etc. Any suggestions on how I could approach this? Should I maybe be doing it inside CodeGenMapper.map_index_lambda by collecting the reduction info ahead of time and creating temporaries before calling the exprgen_mapper?

[inducer]

Yes, working inside of CodeGenMapper.map_index_lambda seems like a possibly promising route. I'm not sur what info you would need to collect ahead of time though.

[majosm]

@inducer I think this is ready for a look. I'm not sure how to fix the lingering doc build errors.

Here's what the results are looking like. Code:

A_pl = pt.make_csr_matrix(  # noqa: N806
    shape=(n-2, n),
    elem_values=pt.make_placeholder("A_elem_values", (3*(n-2),)),
    elem_col_indices=pt.make_placeholder("A_elem_col_indices", (3*(n-2),)),
    row_starts=pt.make_placeholder("A_row_starts", (n-1,)))
u_pl = pt.make_placeholder("u", n)
prog = pt.generate_loopy(A_pl @ u_pl)

Kernel:

---------------------------------------------------------------------------
KERNEL: _pt_kernel
---------------------------------------------------------------------------
ARGUMENTS:
A_elem_values: type: np:dtype('float64'), shape: (54), dim_tags: (N0:stride:1), offset: <class 'loopy.typing.auto'> in aspace: global
A_elem_col_indices: type: np:dtype('float64'), shape: (54), dim_tags: (N0:stride:1), offset: <class 'loopy.typing.auto'> in aspace: global
A_row_starts: type: np:dtype('float64'), shape: (19), dim_tags: (N0:stride:1), offset: <class 'loopy.typing.auto'> in aspace: global
u: type: np:dtype('float64'), shape: (20), dim_tags: (N0:stride:1), offset: <class 'loopy.typing.auto'> in aspace: global
_pt_out: type: np:dtype('float64'), shape: (18), dim_tags: (N0:stride:1) out aspace: global
---------------------------------------------------------------------------
DOMAINS:
{  :  }
{ [_pt_temp_dim0] : 0 <= _pt_temp_dim0 <= 17 }
  [_pt_sum_r0_lbound, _pt_sum_r0_ubound] -> { [_pt_sum_r0] : _pt_sum_r0_lbound <= _pt_sum_r0 < _pt_sum_r0_ubound }
{ [_pt_out_dim0] : 0 <= _pt_out_dim0 <= 17 }
---------------------------------------------------------------------------
INAME TAGS:
_pt_out_dim0: None
_pt_sum_r0: None
_pt_temp_dim0: None
---------------------------------------------------------------------------
TEMPORARIES:
_pt_sum_r0_lbound: type: np:dtype('int64'), shape: () aspace: global
_pt_sum_r0_ubound: type: np:dtype('int64'), shape: () aspace: global
_pt_temp: type: np:dtype('float64'), shape: (18), dim_tags: (N0:stride:1) aspace: global
---------------------------------------------------------------------------
INSTRUCTIONS:
    for _pt_temp_dim0
↱     _pt_sum_r0_lbound = A_row_starts[_pt_temp_dim0]  {id=_pt_sum_r0_lbound_store}
│↱    _pt_sum_r0_ubound = A_row_starts[_pt_temp_dim0 + 1]  {id=_pt_sum_r0_ubound_store}
└└↱   _pt_temp[_pt_temp_dim0] = reduce(sum, [_pt_sum_r0], A_elem_values[_pt_sum_r0]*u[A_elem_col_indices[_pt_sum_r0]])  {id=_pt_temp_store}
  │ end _pt_temp_dim0
  │ for _pt_out_dim0
  └   _pt_out[_pt_out_dim0] = _pt_temp[_pt_out_dim0]  {id=_pt_out_store}
    end _pt_out_dim0
---------------------------------------------------------------------------

[majosm]

FWIW, while experimenting with containers in inducer/arraycontext#349, I tried seeing what this PR would look like if sparse matrix objects were treated as arrays. The changes are here. (Basically, matrices are treated as any other array except in codegen-related mappers, which refuse to process matrices that aren't reached through matmul arrays.)