import warnings
from collections.abc import Mapping, Sequence
from functools import singledispatch
from itertools import chain
from typing import Literal
from typing import cast as typing_cast

from pytensor import scalar as ps
from pytensor.graph import Apply, Op
from pytensor.graph.basic import Variable
from pytensor.graph.replace import _vectorize_node
from pytensor.graph.traversal import toposort, truncated_graph_inputs
from pytensor.graph.type import HasShape
from pytensor.scalar import discrete_dtypes
from pytensor.tensor import (
    TensorVariable,
    as_tensor,
    broadcast_shape,
    broadcast_to,
    tensor,
)
from pytensor.tensor.random.op import RNGConsumerOp
from pytensor.tensor.random.type import RandomType
from pytensor.tensor.utils import (
    get_static_shape_from_size_variables,
)
from pytensor.utils import unzip
from pytensor.xtensor.basic import XOp, XTypeCastOp
from pytensor.xtensor.type import XTensorType, XTensorVariable, as_xtensor, xtensor


def combine_dims_and_shape(
    inputs: Sequence[XTensorVariable], exclude: Sequence[str] | None = None
) -> dict[str, int | None]:
    """Combine information of static dimensions and shapes from multiple xtensor inputs.

    Parameters
    ----------
    inputs: Sequence of XTensorVariable
        Sequence of input XTensorVariables.
    exclude: Sequence of str, optional
        Dimensions to exclude from the result.
    """
    exclude_set: set[str] = set() if exclude is None else set(exclude)
    dims_and_shape: dict[str, int | None] = {}
    for inp in inputs:
        for dim, dim_length in zip(inp.type.dims, inp.type.shape):
            if dim in exclude_set:
                continue
            if dim not in dims_and_shape:
                dims_and_shape[dim] = dim_length
            elif dim_length is not None:
                # Check for conflicting shapes
                if (dims_and_shape[dim] is not None) and (
                    dims_and_shape[dim] != dim_length
                ):
                    raise ValueError(f"Dimension {dim} has conflicting shapes")
                # Keep the non-None shape
                dims_and_shape[dim] = dim_length
    return dims_and_shape


class XElemwise(XOp):
    __props__ = ("scalar_op",)

    def __init__(self, scalar_op):
        super().__init__()
        self.scalar_op = scalar_op

    def make_node(self, *inputs):
        inputs = [as_xtensor(inp) for inp in inputs]
        if (self.scalar_op.nin != -1) and (len(inputs) != self.scalar_op.nin):
            raise ValueError(
                f"Wrong number of inputs, expected {self.scalar_op.nin}, got {len(inputs)}"
            )

        output_dims, output_shape = unzip(combine_dims_and_shape(inputs).items(), n=2)
        dummy_scalars = [ps.get_scalar_type(inp.type.dtype)() for inp in inputs]
        output_dtypes = [
            out.type.dtype for out in self.scalar_op.make_node(*dummy_scalars).outputs
        ]
        outputs = [
            xtensor(dtype=output_dtype, dims=output_dims, shape=output_shape)
            for output_dtype in output_dtypes
        ]
        return Apply(self, inputs, outputs)

    def vectorize_node(self, node, *new_inputs, new_dim):
        return self(*new_inputs, return_list=True)


class XBlockwise(XOp):
    __props__ = ("core_op", "core_dims")

    def __init__(
        self,
        core_op: Op,
        core_dims: tuple[tuple[tuple[str, ...], ...], tuple[tuple[str, ...], ...]],
        signature: str | None = None,
    ):
        super().__init__()
        self.core_op = core_op
        self.core_dims = core_dims
        self.signature = signature  # Only used for lowering, not for validation

    def make_node(self, *inputs):
        inputs = [as_xtensor(i) for i in inputs]
        if len(inputs) != len(self.core_dims[0]):
            raise ValueError(
                f"Wrong number of inputs, expected {len(self.core_dims[0])}, got {len(inputs)}"
            )

        core_inputs_dims, core_outputs_dims = self.core_dims
        core_input_dims_set = set(chain.from_iterable(core_inputs_dims))

        # Check no input has a core_dim it shouldn't have
        for i, (inp, core_inp_dims) in enumerate(
            zip(inputs, core_inputs_dims, strict=True)
        ):
            if invalid_dims := (
                set(inp.dims) & (core_input_dims_set - set(core_inp_dims))
            ):
                raise ValueError(
                    f"Input {i} has invalid core dims {sorted(invalid_dims)}. Allowed: {core_inp_dims}"
                )

        dims_and_shape = combine_dims_and_shape(inputs)
        batch_dims, batch_shape = unzip(
            ((k, v) for k, v in dims_and_shape.items() if k not in core_input_dims_set),
            n=2,
        )

        dummy_core_inputs = []
        for inp, core_inp_dims in zip(inputs, core_inputs_dims):
            try:
                core_static_shape = [
                    inp.type.shape[inp.type.dims.index(d)] for d in core_inp_dims
                ]
            except IndexError:
                raise ValueError(
                    f"At least one core dim={core_inp_dims} missing from input {inp} with dims={inp.type.dims}"
                )
            dummy_core_inputs.append(
                tensor(dtype=inp.type.dtype, shape=core_static_shape)
            )
        core_node = self.core_op.make_node(*dummy_core_inputs)

        outputs = [
            xtensor(
                dtype=core_out.type.dtype,
                shape=batch_shape + core_out.type.shape,
                dims=batch_dims + core_out_dims,
            )
            for core_out, core_out_dims in zip(core_node.outputs, core_outputs_dims)
        ]
        return Apply(self, inputs, outputs)

    def vectorize_node(self, node, *new_inputs, new_dim):
        return self(*new_inputs, return_list=True)


class XRV(XOp, RNGConsumerOp):
    """Wrapper for RandomVariable operations that follows xarray-like broadcasting semantics.

    Xarray does not offer random generators, so this class implements a new API.

    It mostly works like a gufunc (or XBlockwise), which specifies core dimensions for inputs and output, and
    enforces dim-based broadcasting between inputs and output.

    It differs from XBlockwise in a couple of ways:
    1. It is restricted to one sample output
    2. It takes a random generator as the first input and returns the consumed generator as the first output.
    3. It has the concept of extra dimensions, which determine extra batch dimensions of the output, that are not
    implied by batch dimensions of the parameters.
    """

    default_output = 1
    __props__ = ("core_op", "core_dims", "extra_dims")

    def __init__(
        self,
        core_op,
        core_dims: tuple[tuple[tuple[str, ...], ...], tuple[str, ...]],
        extra_dims: tuple[str, ...],
        name: str | None = None,
    ):
        super().__init__()
        if name is None:
            name = getattr(core_op, "name", None)
        self.name = name
        self.core_op = core_op
        inps_core_dims, out_core_dims = core_dims
        for operand_dims in (*inps_core_dims, out_core_dims):
            if len(set(operand_dims)) != len(operand_dims):
                raise ValueError(f"Operand has repeated dims {operand_dims}")
        self.core_dims = (tuple(i for i in inps_core_dims), tuple(out_core_dims))
        if len(set(extra_dims)) != len(extra_dims):
            raise ValueError("size_dims must be unique")
        self.extra_dims = tuple(extra_dims)
        if print_name := getattr(core_op, "_print_name", None):
            self._print_name = print_name

    def __str__(self):
        if self.name is not None:
            name = self.name
            attrs = f"(core_dims={self.core_dims}, extra_dims={self.extra_dims})"
        else:
            name = self.__class__.__name__
            attrs = f"(core_op={self.core_op}, core_dims={self.core_dims}, extra_dims={self.extra_dims})"
        return f"{name}({attrs})"

    def rng_param(self, node):
        return node.inputs[0]

    def size_params(self, node):
        return node.inputs[1 : 1 + len(self.extra_dims)]

    def dist_params(self, node):
        return node.inputs[1 + len(self.extra_dims) :]

    def update(self, node):
        # RNG input and update are the first input and output respectively
        return {node.inputs[0]: node.outputs[0]}

    def make_node(self, rng, *extra_dim_lengths_and_params):
        if rng is None:
            from pytensor.tensor.random.variable import shared_rng

            warnings.warn(
                "Calling an XRV without an explicit rng is deprecated. "
                "Use xt.random.rng or xt.random.shared_rng.",
                DeprecationWarning,
                stacklevel=2,
            )
            rng = shared_rng(seed=None)
        elif not isinstance(rng.type, RandomType):
            raise TypeError(
                "The type of rng should be an instance of RandomGeneratorType "
            )

        rng.tag.used = True

        extra_dim_lengths = [
            as_tensor(dim_length, allow_xtensor_conversion=True)
            for dim_length in extra_dim_lengths_and_params[: len(self.extra_dims)]
        ]
        if not all(
            (dim_length.type.ndim == 0 and dim_length.type.dtype in discrete_dtypes)
            for dim_length in extra_dim_lengths
        ):
            raise TypeError("All dimension lengths should be scalar discrete dtype.")

        params = [
            as_xtensor(param)
            for param in extra_dim_lengths_and_params[len(self.extra_dims) :]
        ]
        if len(params) != len(self.core_op.ndims_params):
            raise ValueError(
                f"Expected {len(self.core_op.ndims_params)} parameters + {len(self.extra_dims)} dim_lengths, "
                f"got {len(extra_dim_lengths_and_params)}"
            )

        param_core_dims, output_core_dims = self.core_dims
        input_core_dims_set = set(chain.from_iterable(param_core_dims))

        # Check parameters don't have core dimensions they shouldn't have
        for param, core_param_dims in zip(params, param_core_dims):
            if invalid_core_dims := (
                set(param.type.dims) - set(core_param_dims)
            ).intersection(input_core_dims_set):
                raise ValueError(
                    f"Parameter {param} has invalid core dimensions {sorted(invalid_core_dims)}"
                )

        extra_dims_and_shape = dict(
            zip(
                self.extra_dims, get_static_shape_from_size_variables(extra_dim_lengths)
            )
        )
        params_dims_and_shape = combine_dims_and_shape(params)

        # Check that no parameter dims conflict with size dims
        if conflict_dims := set(extra_dims_and_shape).intersection(
            params_dims_and_shape
        ):
            raise ValueError(
                f"Size dimensions {sorted(conflict_dims)} conflict with parameter dimensions. They should be unique."
            )

        batch_output_dims, batch_output_shape = unzip(
            (
                (dim, dim_length)
                for dim, dim_length in (
                    extra_dims_and_shape | params_dims_and_shape
                ).items()
                if dim not in input_core_dims_set
            ),
            n=2,
        )

        dummy_core_inputs = []
        for param, core_param_dims in zip(params, param_core_dims):
            try:
                core_static_shape = [
                    param.type.shape[param.type.dims.index(d)] for d in core_param_dims
                ]
            except ValueError:
                raise ValueError(
                    f"At least one core dim={core_param_dims} missing from input {param} with dims={param.type.dims}"
                )
            dummy_core_inputs.append(
                tensor(dtype=param.type.dtype, shape=core_static_shape)
            )
        # Use a dummy tensor rng for type inference (core_op expects RandomGeneratorType)
        from pytensor.tensor.random.type import random_generator_type

        dummy_rng = random_generator_type()
        core_node = self.core_op.make_node(dummy_rng, None, *dummy_core_inputs)

        if not len(core_node.outputs) == 2:
            raise NotImplementedError(
                "XRandomVariable only supports core ops with two outputs (rng, out)"
            )

        _, core_out = core_node.outputs
        out = xtensor(
            dtype=core_out.type.dtype,
            shape=batch_output_shape + core_out.type.shape,
            dims=batch_output_dims + output_core_dims,
        )

        return Apply(self, [rng, *extra_dim_lengths, *params], [rng.type(), out])

    def vectorize_node(self, node, *new_inputs, new_dim):
        new_rng, *new_extra_dim_lengths_and_params = new_inputs
        k = len(self.extra_dims)
        new_extra_dim_lengths, new_params = (
            new_extra_dim_lengths_and_params[:k],
            new_extra_dim_lengths_and_params[k:],
        )

        new_extra_dim_lengths = [dl.squeeze() for dl in new_extra_dim_lengths]
        if not all(dl.type.ndim == 0 for dl in new_extra_dim_lengths):
            raise NotImplementedError(
                f"Vectorization of {self} with batched extra_dim_lengths not implemented, "
            )

        return self.make_node(new_rng, *new_extra_dim_lengths, *new_params).outputs


@_vectorize_node.register(XOp)
@_vectorize_node.register(XTypeCastOp)
def vectorize_xop(op, node, *new_inputs) -> Sequence[Variable]:
    # This gets called by regular graph_replace, which isn't aware of xtensor and doesn't have a concept of `new_dim`
    return _vectorize_xnode(node.op, node, *new_inputs, new_dim=None)


@singledispatch
def _vectorize_xnode(
    op: XOp | XTypeCastOp,
    node: Apply,
    *batched_inputs: Variable,
    new_dim: str | None = None,
) -> Sequence[Variable]:
    """Returns vectorized version of node with new batched inputs."""

    all_old_dims_set = set(
        chain.from_iterable(
            x.type.dims
            for x in (*node.inputs, *node.outputs)
            if isinstance(x.type, XTensorType)
        )
    )
    for new_inp, old_inp in zip(batched_inputs, node.inputs, strict=True):
        if not (
            isinstance(new_inp.type, XTensorType)
            and isinstance(old_inp.type, XTensorType)
        ):
            continue

        old_dims_set = set(old_inp.type.dims)
        new_dims_set = set(new_inp.type.dims)

        # Validate that new inputs didn't drop pre-existing dims
        if missing_dims := old_dims_set - new_dims_set:
            raise ValueError(
                f"Vectorized input {new_inp} is missing pre-existing dims: {sorted(missing_dims)}"
            )
        # Or have new dimensions that were already in the graph
        if new_core_dims := ((new_dims_set - old_dims_set) & all_old_dims_set):
            raise ValueError(
                f"Vectorized input {new_inp} has new dimensions that were present in the original graph: {new_core_dims}"
            )

    return op.vectorize_node(node, *batched_inputs, new_dim=new_dim)


def _vectorize_single_dim(outputs, replace, new_dim: str):
    inputs = truncated_graph_inputs(outputs, ancestors_to_include=replace.keys())
    new_inputs = [replace.get(inp, inp) for inp in inputs]

    vect_vars = dict(zip(inputs, new_inputs, strict=True))
    for node in toposort(outputs, blockers=inputs):
        vect_inputs = [vect_vars.get(inp, inp) for inp in node.inputs]

        if isinstance(node.op, XOp | XTypeCastOp):
            node_vect_outs = _vectorize_xnode(
                node.op, node, *vect_inputs, new_dim=new_dim
            )
        else:
            node_vect_outs_or_apply = _vectorize_node(node.op, node, *vect_inputs)
            # Old API compatibility
            node_vect_outs = (
                node_vect_outs_or_apply.outputs
                if isinstance(node_vect_outs_or_apply, Apply)
                else node_vect_outs_or_apply
            )

        for output, vect_output in zip(node.outputs, node_vect_outs, strict=True):
            if output in vect_vars:
                # This can happen when some outputs of a multi-output node are given a replacement,
                # while some of the remaining outputs are still needed in the graph.
                # We make sure we don't overwrite the provided replacement with the newly vectorized output
                continue
            vect_vars[output] = vect_output

    return [vect_vars[out] for out in outputs]


def vectorize_graph(
    outputs: Variable | Sequence[Variable],
    replace: Mapping[Variable, Variable],
    *,
    new_tensor_dims: Sequence[str] = (),
):
    """Dimension-aware vectorize_graph.

    This is an extension to :func:`pytensor.graph.replace.vectorize_graph` that correctly handles
    mixed XTensor/TensorVariable graphs.

    Vectorization rule for batch TensorVariables works like regular ``vectorize_graph``,
    with batched axes assumed to be aligned positionally and present on the left of the new inputs.
    They must be given labels with ``new_tensor_dims`` argument (left to right),
    for correct interaction with XTensorVariables (and even if there are no XTensorVariables in the graph).

    Batched XTensorVariables may contain new dimensions anywhere.
    These can include dimensions in ``new_tensor_dims``, as well as other new dimensions
    implied by the variable's ``dims``. New dimensions for a given input should not have
    existed in the original graph.

    The vectorized outputs will have the new dimensions on the left.
    The order of new dimensions is:
    1. New dimensions introduced by XTensorVariables (that are not in ``new_tensor_dims``).
    2. Dimensions specified in ``new_tensor_dims``.

    Parameters
    ----------
    outputs: Variable or Sequence of Variable
        The output variable(s) of the graph to be vectorized.
    replace: Mapping of Variable to Variable
        A dictionary mapping original variables to their vectorized counterparts.
    new_tensor_dims: Sequence of str, optional
        A sequence of string labels for the new batch dimensions introduced by ``TensorVariable``
        replacements. These dimensions correspond to the leading axes of the new tensor variables.
        This argument is required if any ``TensorVariable`` replacements introduce new dimensions.

    Returns
    -------
    vectorized_outputs: Variable or Sequence of Variable
        Vectorized output variable(s).

    Examples
    --------
    Vectorize a graph with XTensor variables:

    .. testcode:: python

        from pytensor.xtensor import xtensor
        from pytensor.xtensor.vectorization import vectorize_graph

        x = xtensor("x", dims=("a",))
        y = xtensor("y", dims=("a",))
        out = x + y

        # We want to vectorize over new dimensions "c" and "b"
        # For XTensor, new dimensions can be anywhere
        x_new = xtensor("x_new", dims=("c", "a"))
        y_new = xtensor("y_new", dims=("a", "b"))
        out_vec = vectorize_graph(out, {x: x_new, y: y_new})

        # Output batch dimensions are always on the left
        assert out_vec.type.dims == ("c", "b", "a")

    Vectorize a graph with standard Tensor variables:

    .. testcode:: python

        from pytensor.tensor import tensor, TensorVariable
        from pytensor.xtensor.vectorization import vectorize_graph

        x = tensor("x", shape=(3,))
        y = tensor("y", shape=(3,))
        out = x + y

        # We vectorize over new dimension of "a", and "b".
        # These must be on the left and broadcast correctly
        x_new = tensor("x_new", shape=(5, 3))
        y_new = tensor("y_new", shape=(7, 1, 3))
        out_vec = vectorize_graph(out, {x: x_new, y: y_new}, new_tensor_dims=["a", "b"])

        assert isinstance(out_vec, TensorVariable)
        assert out_vec.type.shape == (7, 5, 3)

    Vectorize a mixed graph:

    .. testcode:: python

        from pytensor.tensor import tensor
        from pytensor.xtensor import as_xtensor, xtensor
        from pytensor.xtensor.vectorization import vectorize_graph

        x = xtensor("x", shape=(5,), dims=("a",))
        y = tensor("y", shape=(5,))
        out = x + as_xtensor(y, dims=("a",))

        # Vectorize over a new dimension "c"
        x_new = xtensor("x_new", dims=("a", "c"), shape=(5, 3))
        y_new = tensor("y_new", shape=(3, 5)) # Leading dim corresponds to "c" (size 3)

        out_vec = vectorize_graph(out, {x: x_new, y: y_new}, new_tensor_dims=["c"])
        assert out_vec.type.dims == ("c", "a")

        # Treat the new dimension of y_new as being "b" (size 3)
        # x_new introduces "c" (size 3)
        # Result has XTensor-only new dims first ("c"), then new_tensor_dims ("b")
        out_vec = vectorize_graph(out, {x: x_new, y: y_new}, new_tensor_dims=["b"])
        assert out_vec.type.dims == ("c", "b", "a")

    """
    seq_outputs = outputs if isinstance(outputs, Sequence) else (outputs,)

    if not all(
        isinstance(key, Variable) and isinstance(value, Variable)
        for key, value in replace.items()
    ):
        raise ValueError(f"Some of the replaced items are not Variables: {replace}")

    # Collect new dimensions and sizes, and validate
    new_xtensor_sizes: dict[str, TensorVariable] = {}
    new_tensor_dim_lengths: list[tuple[TensorVariable | Literal[1], ...]] = []
    for old, new in replace.items():
        if isinstance(new, XTensorVariable):
            old_var_dims_set = set(old.type.dims)
            new_var_dims_set = set(new.type.dims)
            if missing_dims := old_var_dims_set - new_var_dims_set:
                raise ValueError(
                    f"Vectorized input {new} is missing pre-existing dims: {sorted(missing_dims)}"
                )
            new_xtensor_sizes.update(
                {d: s for d, s in new.sizes.items() if d not in old_var_dims_set}
            )
        elif isinstance(new, TensorVariable):
            n_new_dims = new.type.ndim - old.type.ndim
            if n_new_dims < 0:
                raise ValueError(
                    f"Vectorized input {new} is missing pre-existing dims {new.type.ndim=}, {old.type.ndim=}"
                )
            if n_new_dims > len(new_tensor_dims):
                if not new_tensor_dims:
                    raise ValueError(
                        f"TensorVariable replacement {new} has {n_new_dims} batch dimensions. "
                        f"You must specify `new_tensor_dims` to label these."
                    )
                else:
                    raise ValueError(
                        f"TensorVariable replacement {new} has {n_new_dims} batch dimensions "
                        f"but only {new_tensor_dims=} were specified. "
                    )
            new_tensor_dim_lengths.append(
                tuple(
                    1 if b else s
                    for s, b in zip(
                        tuple(new.shape)[:n_new_dims],
                        new.type.broadcastable[:n_new_dims],
                    )
                )
            )

        elif isinstance(new.type, HasShape) and new.type.ndim != old.type.ndim:
            raise NotImplementedError(
                f"vectorize_graph does not know how to handle batched input {new} of type {new.type}"
            )

    # Align xtensor batch dimensions on the left, and broadcast tensor batch dimensions
    new_dims = (
        *(dim for dim in new_xtensor_sizes if dim not in new_tensor_dims),
        *new_tensor_dims,
    )

    # Create a mapping from new_tensor_dims -> broadcasted shape from tensors
    new_tensor_sizes: dict[str, Variable] = {}
    if new_tensor_dims:
        new_tensor_bcast_dim_lengths = broadcast_shape(
            *new_tensor_dim_lengths, arrays_are_shapes=True
        )
        del new_tensor_dim_lengths
        if len(new_tensor_bcast_dim_lengths) != len(new_tensor_dims):
            raise ValueError(
                f"{len(new_tensor_dims)} tensor dims were specified, but only {len(new_tensor_bcast_dim_lengths)} were found in the new inputs"
            )
        new_tensor_sizes = dict(zip(new_tensor_dims, new_tensor_bcast_dim_lengths))

    # Give preference to tensor sizes to avoid unnecessary broadcasting (Alloc)
    # XTensor sizes are implicitly handled by transpose and dim names, so they don't need strict size equality
    new_sizes = tuple(
        new_xtensor_sizes.get(dim, new_tensor_sizes.get(dim, 1)) for dim in new_dims
    )
    # Align batch dimensions on the left (*xtensor_unique_batch_dims, *tensor_batch_dims, ...)
    # We broadcast tensor batch dims as they may have been length 1
    aligned_replace = {}
    for old, new in replace.items():
        if isinstance(new, XTensorVariable):
            new = new.transpose(*new_dims, ..., missing_dims="ignore")
        elif isinstance(new, TensorVariable):
            n_existing_batch_dims = new.type.ndim - old.type.ndim
            if n_existing_batch_dims < len(new_dims) or any(
                new.type.broadcastable[: len(new_dims)]
            ):
                new = broadcast_to(
                    new,
                    shape=(*new_sizes, *tuple(new.shape)[n_existing_batch_dims:]),
                )
        aligned_replace[old] = new
    del replace

    seq_vect_outputs = seq_outputs
    remaining_new_dims = list(new_dims)
    while remaining_new_dims:
        new_dim = remaining_new_dims.pop()

        if remaining_new_dims:
            # We need to use a dummy inputs to batch graph once at a time
            # We drop all the dims that are still in `remaining_new_dims`
            # Create a mapping: original -> intermediate_batched
            single_dim_replace = {}
            for old, new in aligned_replace.items():
                n_remaining_dims = len(remaining_new_dims)
                if isinstance(new, XTensorVariable):
                    intermediate_dims, intermediate_shape = unzip(
                        (
                            (d, s)
                            for d, s in zip(new.type.dims, new.type.shape)
                            if d not in remaining_new_dims
                        ),
                        n=2,
                    )
                    intermediate_type = new.type.clone(
                        dims=intermediate_dims, shape=intermediate_shape
                    )
                elif isinstance(new, TensorVariable):
                    intermediate_type = new.type.clone(
                        shape=new.type.shape[n_remaining_dims:]
                    )
                else:
                    intermediate_type = new.type
                single_dim_replace[old] = intermediate_type()
            # Updated aligned replace mapping: intermediate_batched -> final_batched
            aligned_replace = dict(
                zip(single_dim_replace.values(), aligned_replace.values())
            )
        else:
            single_dim_replace = aligned_replace
        seq_vect_outputs = _vectorize_single_dim(
            seq_vect_outputs, single_dim_replace, new_dim
        )

    aligned_seq_vect_outputs = [
        new.transpose(*new_dims, *typing_cast(XTensorVariable, old).dims)
        if isinstance(new, XTensorVariable)
        else new
        for new, old in zip(seq_vect_outputs, seq_outputs)
    ]

    return (
        aligned_seq_vect_outputs
        if isinstance(outputs, Sequence)
        else aligned_seq_vect_outputs[0]
    )
