Implement indexing operations for XTensorVariables

pytensor/xtensor/__init__.py

@@ -7,7 +7,6 @@
 )
 from pytensor.xtensor.shape import concat
 from pytensor.xtensor.type import (
-    XTensorType,
     as_xtensor,
     xtensor,
     xtensor_constant,

pytensor/xtensor/indexing.py

@@ -0,0 +1,186 @@
+# HERE LIE DRAGONS
+# Useful links to make sense of all the numpy/xarray complexity
+# https://numpy.org/devdocs//user/basics.indexing.html
+# https://numpy.org/neps/nep-0021-advanced-indexing.html
+# https://docs.xarray.dev/en/latest/user-guide/indexing.html
+# https://tutorial.xarray.dev/intermediate/indexing/advanced-indexing.html
+
+from pytensor.graph.basic import Apply, Constant, Variable
+from pytensor.scalar.basic import discrete_dtypes
+from pytensor.tensor.basic import as_tensor
+from pytensor.tensor.type_other import NoneTypeT, SliceType, make_slice
+from pytensor.xtensor.basic import XOp, xtensor_from_tensor
+from pytensor.xtensor.type import XTensorType, as_xtensor, xtensor
+
+
+def as_idx_variable(idx, indexed_dim: str):
+    if idx is None or (isinstance(idx, Variable) and isinstance(idx.type, NoneTypeT)):
+        raise TypeError(
+            "XTensors do not support indexing with None (np.newaxis), use expand_dims instead"
+        )
+    if isinstance(idx, slice):
+        idx = make_slice(idx)
+    elif isinstance(idx, Variable) and isinstance(idx.type, SliceType):
+        pass
+    elif (
+        isinstance(idx, tuple)
+        and len(idx) == 2
+        and (
+            isinstance(idx[0], str)
+            or (
+                isinstance(idx[0], tuple | list)
+                and all(isinstance(d, str) for d in idx[0])
+            )
+        )
+    ):
+        # Special case for ("x", array) that xarray supports
+        dim, idx = idx
+        if isinstance(idx, Variable) and isinstance(idx.type, XTensorType):
+            raise IndexError(
+                f"Giving a dimension name to an XTensorVariable indexer is not supported: {(dim, idx)}. "
+                "Use .rename() instead."
+            )
+        if isinstance(dim, str):
+            dims = (dim,)
+        else:
+            dims = tuple(dim)
+        idx = as_xtensor(as_tensor(idx), dims=dims)
+    else:
+        # Must be integer / boolean indices, we already counted for None and slices
+        try:
+            idx = as_xtensor(idx)
+        except TypeError:
+            idx = as_tensor(idx)
+            if idx.type.ndim > 1:
+                # Same error that xarray raises
+                raise IndexError(
+                    "Unlabeled multi-dimensional array cannot be used for indexing"
+                )
+            # This is implicitly an XTensorVariable with dim matching the indexed one
+            idx = xtensor_from_tensor(idx, dims=(indexed_dim,)[: idx.type.ndim])
+
+        if idx.type.dtype == "bool":
+            if idx.type.ndim != 1:
+                # xarray allaws `x[True]`, but I think it is a bug: https://github.com/pydata/xarray/issues/10379
+                # Otherwise, it is always restricted to 1d boolean indexing arrays
+                raise NotImplementedError(
+                    "Only 1d boolean indexing arrays are supported"
+                )
+            if idx.type.dims != (indexed_dim,):
+                raise IndexError(
+                    "Boolean indexer should be unlabeled or on the same dimension to the indexed array. "
+                    f"Indexer is on {idx.type.dims} but the target dimension is {indexed_dim}."
+                )
+
+            # Convert to nonzero indices
+            idx = as_xtensor(idx.values.nonzero()[0], dims=idx.type.dims)
+
+        elif idx.type.dtype not in discrete_dtypes:
+            raise TypeError("Numerical indices must be integers or boolean")
+    return idx
+
+
+def get_static_slice_length(slc: Variable, dim_length: None | int) -> int | None:
+    if dim_length is None:
+        return None
+    if isinstance(slc, Constant):
+        d = slc.data
+        start, stop, step = d.start, d.stop, d.step
+    elif slc.owner is None:
+        # It's a root variable no way of knowing what we're getting
+        return None
+    else:
+        # It's a MakeSliceOp
+        start, stop, step = slc.owner.inputs
+        if isinstance(start, Constant):
+            start = start.data
+        else:
+            return None
+        if isinstance(stop, Constant):
+            stop = stop.data
+        else:
+            return None
+        if isinstance(step, Constant):
+            step = step.data
+        else:
+            return None
+    return len(range(*slice(start, stop, step).indices(dim_length)))
+
+
+class Index(XOp):
+    __props__ = ()
+
+    def make_node(self, x, *idxs):
+        x = as_xtensor(x)
+
+        if any(idx is Ellipsis for idx in idxs):
+            if idxs.count(Ellipsis) > 1:
+                raise IndexError("an index can only have a single ellipsis ('...')")
+            # Convert intermediate Ellipsis to slice(None)
+            ellipsis_loc = idxs.index(Ellipsis)
+            n_implied_none_slices = x.type.ndim - (len(idxs) - 1)
+            idxs = (
+                *idxs[:ellipsis_loc],
+                *((slice(None),) * n_implied_none_slices),
+                *idxs[ellipsis_loc + 1 :],
+            )
+
+        x_ndim = x.type.ndim
+        x_dims = x.type.dims
+        x_shape = x.type.shape
+        out_dims = []
+        out_shape = []
+
+        def combine_dim_info(idx_dim, idx_dim_shape):
+            if idx_dim not in out_dims:
+                # First information about the dimension length
+                out_dims.append(idx_dim)
+                out_shape.append(idx_dim_shape)
+            else:
+                # Dim already introduced in output by a previous index
+                # Update static shape or raise if incompatible
+                out_dim_pos = out_dims.index(idx_dim)
+                out_dim_shape = out_shape[out_dim_pos]
+                if out_dim_shape is None:
+                    # We don't know the size of the dimension yet
+                    out_shape[out_dim_pos] = idx_dim_shape
+                elif idx_dim_shape is not None and idx_dim_shape != out_dim_shape:
+                    raise IndexError(
+                        f"Dimension of indexers mismatch for dim {idx_dim}"
+                    )
+
+        if len(idxs) > x_ndim:
+            raise IndexError("Too many indices")
+
+        idxs = [
+            as_idx_variable(idx, dim) for idx, dim in zip(idxs, x_dims, strict=False)
+        ]
+
+        for i, idx in enumerate(idxs):
+            if isinstance(idx.type, SliceType):
+                idx_dim = x_dims[i]
+                idx_dim_shape = get_static_slice_length(idx, x_shape[i])
+                combine_dim_info(idx_dim, idx_dim_shape)
+            else:
+                if idx.type.ndim == 0:
+                    # Scalar index, dimension is dropped
+                    continue
+
+                assert isinstance(idx.type, XTensorType)
+
+                idx_dims = idx.type.dims
+                for idx_dim in idx_dims:
+                    idx_dim_shape = idx.type.shape[idx_dims.index(idx_dim)]
+                    combine_dim_info(idx_dim, idx_dim_shape)
+
+        for dim_i, shape_i in zip(x_dims[i + 1 :], x_shape[i + 1 :]):
+            # Add back any unindexed dimensions
+            if dim_i not in out_dims:
+                # If the dimension was not indexed, we keep it as is
+                combine_dim_info(dim_i, shape_i)
+
+        output = xtensor(dtype=x.type.dtype, shape=out_shape, dims=out_dims)
+        return Apply(self, [x, *idxs], [output])
+
+
+index = Index()

pytensor/xtensor/math.py

@@ -1,8 +1,13 @@
 import inspect
 import sys
 
+import numpy as np
+
 import pytensor.scalar as ps
+from pytensor import config
 from pytensor.scalar import ScalarOp
+from pytensor.scalar.basic import _cast_mapping
+from pytensor.xtensor.basic import as_xtensor
 from pytensor.xtensor.vectorization import XElemwise
 
 
@@ -29,3 +34,26 @@ def get_all_scalar_ops():
 
 for name, op in get_all_scalar_ops().items():
     setattr(this_module, name, op)
+
+
+_xelemwise_cast_op: dict[str, XElemwise] = {}
+
+
+def cast(x, dtype):
+    if dtype == "floatX":
+        dtype = config.floatX
+    else:
+        dtype = np.dtype(dtype).name
+
+    x = as_xtensor(x)
+    if x.type.dtype == dtype:
+        return x
+    if x.type.dtype.startswith("complex") and not dtype.startswith("complex"):
+        raise TypeError(
+            "Casting from complex to real is ambiguous: consider"
+            " real(), imag(), angle() or abs()"
+        )
+
+    if dtype not in _xelemwise_cast_op:
+        _xelemwise_cast_op[dtype] = XElemwise(scalar_op=_cast_mapping[dtype])
+    return _xelemwise_cast_op[dtype](x)

pytensor/xtensor/rewriting/__init__.py

@@ -1,4 +1,5 @@
 import pytensor.xtensor.rewriting.basic
+import pytensor.xtensor.rewriting.indexing
 import pytensor.xtensor.rewriting.reduction
 import pytensor.xtensor.rewriting.shape
 import pytensor.xtensor.rewriting.vectorization

pytensor/xtensor/rewriting/indexing.py

@@ -0,0 +1,150 @@
+from itertools import zip_longest
+
+from pytensor import as_symbolic
+from pytensor.graph import Constant, node_rewriter
+from pytensor.tensor import TensorType, arange, specify_shape
+from pytensor.tensor.subtensor import _non_consecutive_adv_indexing
+from pytensor.tensor.type_other import NoneTypeT, SliceType
+from pytensor.xtensor.basic import tensor_from_xtensor, xtensor_from_tensor
+from pytensor.xtensor.indexing import Index
+from pytensor.xtensor.rewriting.utils import register_xcanonicalize
+from pytensor.xtensor.type import XTensorType
+
+
+def to_basic_idx(idx):
+    if isinstance(idx.type, SliceType):
+        if isinstance(idx, Constant):
+            return idx.data
+        elif idx.owner:
+            # MakeSlice Op
+            # We transform NoneConsts to regular None so that basic Subtensor can be used if possible
+            return slice(
+                *[
+                    None if isinstance(i.type, NoneTypeT) else i
+                    for i in idx.owner.inputs
+                ]
+            )
+        else:
+            return idx
+    if (
+        isinstance(idx.type, XTensorType)
+        and idx.type.ndim == 0
+        and idx.type.dtype != bool
+    ):
+        return idx.values
+    raise TypeError("Cannot convert idx to basic idx")
+
+
+@register_xcanonicalize
+@node_rewriter(tracks=[Index])
+def lower_index(fgraph, node):
+    """Lower XTensorVariable indexing to regular TensorVariable indexing.
+
+    xarray-like indexing has two modes:
+    1. Orthogonal indexing: Indices of different output labeled dimensions are combined to produce all combinations of indices.
+    2. Vectorized indexing: Indices of the same output labeled dimension are combined point-wise like in regular numpy advanced indexing.
+
+    An Index Op can combine both modes.
+    To achieve orthogonal indexing using numpy semantics we must use multidimensional advanced indexing.
+    We expand the dims of each index so they are as large as the number of output dimensions, place the indices that
+    belong to the same output dimension in the same axis, and those that belong to different output dimensions in different axes.
+
+    For instance to do an outer 2x2 indexing we can select x[arange(x.shape[0])[:, None], arange(x.shape[1])[None, :]],
+    This is a generalization of `np.ix_` that allows combining some dimensions, and not others, as well as have
+    indices that have more than one dimension at the start.
+
+    In addition, xarray basic index (slices), can be vectorized with other advanced indices (if they act on the same output dimension).
+    However, in numpy, basic indices are always orthogonal to advanced indices. To make them behave like vectorized indices
+    we have to convert the slices to equivalent advanced indices.
+    We do this by creating an `arange` tensor that matches the shape of the dimension being indexed,
+    and then indexing it with the original slice. This index is then handled as a regular advanced index.
+
+    Note: The IndexOp has only 2 types of indices: Slices and XTensorVariables. Regular array indices
+    are converted to the appropriate XTensorVariable by `Index.make_node`
+    """
+
+    x, *idxs = node.inputs
+    [out] = node.outputs
+    x_tensor = tensor_from_xtensor(x)
+
+    if all(
+        (
+            isinstance(idx.type, SliceType)
+            or (isinstance(idx.type, XTensorType) and idx.type.ndim == 0)
+        )
+        for idx in idxs
+    ):
+        # Special case having just basic indexing
+        x_tensor_indexed = x_tensor[tuple(to_basic_idx(idx) for idx in idxs)]
+
+    else:
+        # General case, we have to align the indices positionally to achieve vectorized or orthogonal indexing
+        # May need to convert basic indexing to advanced indexing if it acts on a dimension that is also indexed by an advanced index
+        x_dims = x.type.dims
+        x_shape = tuple(x.shape)
+        out_ndim = out.type.ndim
+        out_dims = out.type.dims
+        aligned_idxs = []
+        basic_idx_axis = []
+        # zip_longest adds the implicit slice(None)
+        for i, (idx, x_dim) in enumerate(
+            zip_longest(idxs, x_dims, fillvalue=as_symbolic(slice(None)))
+        ):
+            if isinstance(idx.type, SliceType):
+                if not any(
+                    (
+                        isinstance(other_idx.type, XTensorType)
+                        and x_dim in other_idx.dims
+                    )
+                    for j, other_idx in enumerate(idxs)
+                    if j != i
+                ):
+                    # We can use basic indexing directly if no other index acts on this dimension
+                    # This is an optimization that avoids creating an unnecessary arange tensor
+                    # and facilitates the use of the specialized AdvancedSubtensor1 when possible
+                    aligned_idxs.append(idx)
+                    basic_idx_axis.append(out_dims.index(x_dim))
+                else:
+                    # Otherwise we need to convert the basic index into an equivalent advanced indexing
+                    # And align it so it interacts correctly with the other advanced indices
+                    adv_idx_equivalent = arange(x_shape[i])[to_basic_idx(idx)]
+                    ds_order = ["x"] * out_ndim
+                    ds_order[out_dims.index(x_dim)] = 0
+                    aligned_idxs.append(adv_idx_equivalent.dimshuffle(ds_order))
+            else:
+                assert isinstance(idx.type, XTensorType)
+                if idx.type.ndim == 0:
+                    # Scalar index, we can use it directly
+                    aligned_idxs.append(idx.values)
+                else:
+                    # Vector index, we need to align the indexing dimensions with the base_dims
+                    ds_order = ["x"] * out_ndim
+                    for j, idx_dim in enumerate(idx.dims):
+                        ds_order[out_dims.index(idx_dim)] = j
+                    aligned_idxs.append(idx.values.dimshuffle(ds_order))
+
+        # Squeeze indexing dimensions that were not used because we kept basic indexing slices
+        if basic_idx_axis:
+            aligned_idxs = [
+                idx.squeeze(axis=basic_idx_axis)
+                if (isinstance(idx.type, TensorType) and idx.type.ndim > 0)
+                else idx
+                for idx in aligned_idxs
+            ]
+
+        x_tensor_indexed = x_tensor[tuple(aligned_idxs)]
+
+        if basic_idx_axis and _non_consecutive_adv_indexing(aligned_idxs):
+            # Numpy moves advanced indexing dimensions to the front when they are not consecutive
+            # We need to transpose them back to the expected output order
+            x_tensor_indexed_basic_dims = [out_dims[axis] for axis in basic_idx_axis]
+            x_tensor_indexed_dims = [
+                dim for dim in out_dims if dim not in x_tensor_indexed_basic_dims
+            ] + x_tensor_indexed_basic_dims
+            transpose_order = [x_tensor_indexed_dims.index(dim) for dim in out_dims]
+            x_tensor_indexed = x_tensor_indexed.transpose(transpose_order)
+
+    # Add lost shape information
+    x_tensor_indexed = specify_shape(x_tensor_indexed, out.type.shape)
+    new_out = xtensor_from_tensor(x_tensor_indexed, dims=out.type.dims)
+    return [new_out]