# Source code for ufl.indexed

    """This module defines the Indexed class."""

    # Copyright (C) 2008-2016 Martin Sandve Alnæs
    #
    # This file is part of UFL (https://www.fenicsproject.org)
    #
    # SPDX-License-Identifier:    LGPL-3.0-or-later

    from ufl.constantvalue import Zero
    from ufl.core.expr import Expr, ufl_err_str
    from ufl.core.multiindex import FixedIndex, Index, MultiIndex
    from ufl.core.operator import Operator
    from ufl.core.ufl_type import ufl_type
    from ufl.index_combination_utils import unique_sorted_indices
    from ufl.precedence import parstr

    @ufl_type(is_shaping=True, num_ops=2, is_terminal_modifier=True)
    class Indexed(Operator):
        """Indexed expression."""

        __slots__ = (
            "_initialised",
            "ufl_free_indices",
            "ufl_index_dimensions",
        )

        def __new__(cls, expression, multiindex):
            """Create a new Indexed."""
            if len(multiindex) == 0:
                return expression
            if isinstance(expression, Zero):
                # Zero-simplify indexed Zero objects
                shape = expression.ufl_shape
                efi = expression.ufl_free_indices
                efid = expression.ufl_index_dimensions
                fi = list(zip(efi, efid))
                for pos, ind in enumerate(multiindex):
                    if isinstance(ind, Index):
                        fi.append((ind.count(), shape[pos]))
                fi = unique_sorted_indices(sorted(fi))
                if fi:
                    fi, fid = zip(*fi)
                else:
                    fi, fid = (), ()
                return Zero(shape=(), free_indices=fi, index_dimensions=fid)

            try:
                # Simplify if possible
                return expression._simplify_indexed(multiindex)
            except NotImplementedError:
                # Construct a new instance to be initialised
                self = Operator.__new__(cls)
                self._initialised = False
                return self

        def __init__(self, expression, multiindex):
            """Initialise."""
            if self._initialised:
                return
            # Store operands
            Operator.__init__(self, (expression, multiindex))

            # Error checking
            if not isinstance(expression, Expr):
                raise ValueError(f"Expecting Expr instance, not {ufl_err_str(expression)}.")
            if not isinstance(multiindex, MultiIndex):
                raise ValueError(f"Expecting MultiIndex instance, not {ufl_err_str(multiindex)}.")

            shape = expression.ufl_shape

            # Error checking
            if len(shape) != len(multiindex):
                raise ValueError(
                    f"Invalid number of indices ({len(multiindex)}) for tensor "
                    f"expression of rank {len(expression.ufl_shape)}:\n    {ufl_err_str(expression)}"
                )
            if any(
                int(di) >= int(si) or int(di) < 0
                for si, di in zip(shape, multiindex)
                if isinstance(di, FixedIndex)
            ):
                raise ValueError("Fixed index out of range!")

            # Build tuples of free index ids and dimensions
            efi = expression.ufl_free_indices
            efid = expression.ufl_index_dimensions
            fi = list(zip(efi, efid))
            for pos, ind in enumerate(multiindex):
                if isinstance(ind, Index):
                    fi.append((ind.count(), shape[pos]))
            fi = unique_sorted_indices(sorted(fi))
            if fi:
                fi, fid = zip(*fi)
            else:
                fi, fid = (), ()

            # Cache free index and dimensions
            self.ufl_free_indices = fi
            self.ufl_index_dimensions = fid
            self._initialised = True

        ufl_shape = ()

        def evaluate(self, x, mapping, component, index_values, derivatives=()):
            """Evaluate."""
            A, ii = self.ufl_operands
            component = ii.evaluate(x, mapping, None, index_values)
            if derivatives:
                return A.evaluate(x, mapping, component, index_values, derivatives)
            else:
                return A.evaluate(x, mapping, component, index_values)

        def __str__(self):
            """Format as a string."""
            return f"{parstr(self.ufl_operands[0], self)}[{self.ufl_operands[1]}]"

        def __getitem__(self, key):
            """Get an item."""
            if key == ():
                # So that one doesn't have to special case indexing of
                # expressions without shape.
                return self
            raise ValueError(
                f"Attempting to index with {ufl_err_str(key)}, "
                f"but object is already indexed: {ufl_err_str(self)}"
            )