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# Source code for astropy.units.function.core

    # Licensed under a 3-clause BSD style license - see LICENSE.rst
    """Function Units and Quantities."""

    from abc import ABCMeta, abstractmethod
    from collections.abc import Collection
    from functools import cached_property
    from typing import Self

    import numpy as np
    from numpy._core import umath as np_umath

    from astropy.units import (
        Quantity,
        Unit,
        UnitBase,
        UnitConversionError,
        UnitsError,
        UnitTypeError,
        dimensionless_unscaled,
    )
    from astropy.units.typing import PhysicalTypeID

    __all__ = ["FunctionQuantity", "FunctionUnitBase"]

    SUPPORTED_UFUNCS = {
        getattr(np_umath, ufunc)
        for ufunc in (
            "isfinite",
            "isinf",
            "isnan",
            "sign",
            "signbit",
            "rint",
            "floor",
            "ceil",
            "trunc",
            "_ones_like",
            "ones_like",
            "positive",
        )
        if hasattr(np_umath, ufunc)
    }

    # TODO: the following could work if helper changed relative to Quantity:
    # - spacing should return dimensionless, not same unit
    # - negative should negate unit too,
    # - add, subtract, comparisons can work if units added/subtracted

    SUPPORTED_FUNCTIONS = {
        getattr(np, function)
        for function in ("clip", "trace", "mean", "min", "max", "round")
    }

    # subclassing UnitBase or CompositeUnit was found to be problematic, requiring
    # a large number of overrides. Hence, define new class.

    class FunctionUnitBase(metaclass=ABCMeta):
        """Abstract base class for function units.

        Function units are functions containing a physical unit, such as dB(mW).
        Most of the arithmetic operations on function units are defined in this
        base class.

        While instantiation is defined, this class should not be used directly.
        Rather, subclasses should be used that override the abstract properties
        `_default_function_unit` and `_quantity_class`, and the abstract methods
        `from_physical`, and `to_physical`.

        Parameters
        ----------
        physical_unit : `~astropy.units.Unit` or `string`
            Unit that is encapsulated within the function unit.
            If not given, dimensionless.

        function_unit :  `~astropy.units.Unit` or `string`
            By default, the same as the function unit set by the subclass.
        """

        # ↓↓↓ the following four need to be set by subclasses
        # Make this a property so we can ensure subclasses define it.
        @property
        @abstractmethod
        def _default_function_unit(self):
            """Default function unit corresponding to the function.

            This property should be overridden by subclasses, with, e.g.,
            `~astropy.unit.MagUnit` returning `~astropy.unit.mag`.
            """

        # This has to be a property because the function quantity will not be
        # known at unit definition time, as it gets defined after.
        @property
        @abstractmethod
        def _quantity_class(self):
            """Function quantity class corresponding to this function unit.

            This property should be overridden by subclasses, with, e.g.,
            `~astropy.unit.MagUnit` returning `~astropy.unit.Magnitude`.
            """

        @abstractmethod
        def from_physical(self, x):
            """Transformation from value in physical to value in function units.

            This method should be overridden by subclasses.  It is used to
            provide automatic transformations using an equivalency.
            """

        @abstractmethod
        def to_physical(self, x):
            """Transformation from value in function to value in physical units.

            This method should be overridden by subclasses.  It is used to
            provide automatic transformations using an equivalency.
            """

        # ↑↑↑ the above four need to be set by subclasses

        # have priority over arrays, regular units, and regular quantities
        __array_priority__ = 30000

        def __init__(self, physical_unit=None, function_unit=None):
            if physical_unit is None:
                physical_unit = dimensionless_unscaled
            else:
                physical_unit = Unit(physical_unit)
                if not isinstance(physical_unit, UnitBase) or physical_unit.is_equivalent(
                    self._default_function_unit
                ):
                    raise UnitConversionError(f"{physical_unit} is not a physical unit.")

            if function_unit is None:
                function_unit = self._default_function_unit
            else:
                # any function unit should be equivalent to subclass default
                function_unit = Unit(getattr(function_unit, "function_unit", function_unit))
                if not function_unit.is_equivalent(self._default_function_unit):
                    raise UnitConversionError(
                        f"Cannot initialize '{self.__class__.__name__}' instance with "
                        f"function unit '{function_unit}', as it is not equivalent to "
                        f"default function unit '{self._default_function_unit}'."
                    )
            self._physical_unit = physical_unit
            self._function_unit = function_unit

        def _copy(self, physical_unit=None):
            """Copy oneself, possibly with a different physical unit."""
            if physical_unit is None:
                physical_unit = self.physical_unit
            return self.__class__(physical_unit, self.function_unit)

        @property
        def physical_unit(self):
            return self._physical_unit

        @property
        def function_unit(self):
            return self._function_unit

        @property
        def equivalencies(self):
            """List of equivalencies between function and physical units.

            Uses the `from_physical` and `to_physical` methods.
            """
            return [(self, self.physical_unit, self.to_physical, self.from_physical)]

        # ↓↓↓ properties/methods required to behave like a unit

        def decompose(self, bases: Collection[UnitBase] = ()) -> Self:
            """Copy the current unit with the physical unit decomposed.

            For details, see `~astropy.units.UnitBase.decompose`.
            """
            return self._copy(self.physical_unit.decompose(bases))

        @property
        def si(self):
            """Copy the current function unit with the physical unit in SI."""
            return self._copy(self.physical_unit.si)

        @property
        def cgs(self):
            """Copy the current function unit with the physical unit in CGS."""
            return self._copy(self.physical_unit.cgs)

        @cached_property
        def _physical_type_id(self) -> PhysicalTypeID:
            """Get physical type corresponding to physical unit."""
            return self.physical_unit._physical_type_id

        @property
        def physical_type(self):
            """Return the physical type of the physical unit (e.g., 'length')."""
            return self.physical_unit.physical_type

        def is_equivalent(self, other, equivalencies=[]):
            """
            Returns `True` if this unit is equivalent to ``other``.

            Parameters
            ----------
            other : `~astropy.units.Unit`, string, or tuple
                The unit to convert to. If a tuple of units is specified, this
                method returns true if the unit matches any of those in the tuple.

            equivalencies : list of tuple
                A list of equivalence pairs to try if the units are not
                directly convertible.  See :ref:`astropy:unit_equivalencies`.
                This list is in addition to the built-in equivalencies between the
                function unit and the physical one, as well as possible global
                defaults set by, e.g., `~astropy.units.set_enabled_equivalencies`.
                Use `None` to turn off any global equivalencies.

            Returns
            -------
            bool
            """
            if isinstance(other, tuple):
                return any(self.is_equivalent(u, equivalencies) for u in other)

            other_physical_unit = getattr(
                other,
                "physical_unit",
                (
                    dimensionless_unscaled
                    if self.function_unit.is_equivalent(other)
                    else other
                ),
            )

            return self.physical_unit.is_equivalent(other_physical_unit, equivalencies)

        def to(self, other, value=1.0, equivalencies=[]):
            """
            Return the converted values in the specified unit.

            Parameters
            ----------
            other : `~astropy.units.Unit`, `~astropy.units.FunctionUnitBase`, or str
                The unit to convert to.

            value : int, float, or scalar array-like, optional
                Value(s) in the current unit to be converted to the specified unit.
                If not provided, defaults to 1.0.

            equivalencies : list of tuple
                A list of equivalence pairs to try if the units are not
                directly convertible.  See :ref:`astropy:unit_equivalencies`.
                This list is in meant to treat only equivalencies between different
                physical units; the built-in equivalency between the function
                unit and the physical one is automatically taken into account.

            Returns
            -------
            values : scalar or array
                Converted value(s). Input value sequences are returned as
                numpy arrays.

            Raises
            ------
            `~astropy.units.UnitsError`
                If units are inconsistent.
            """
            # conversion to one's own physical unit should be fastest
            if other is self.physical_unit:
                return self.to_physical(value)

            other_function_unit = getattr(other, "function_unit", other)
            if self.function_unit.is_equivalent(other_function_unit):
                # when other is an equivalent function unit:
                # first convert physical units to other's physical units
                other_physical_unit = getattr(
                    other, "physical_unit", dimensionless_unscaled
                )
                if self.physical_unit != other_physical_unit:
                    value_other_physical = self.physical_unit.to(
                        other_physical_unit, self.to_physical(value), equivalencies
                    )
                    # make function unit again, in own system
                    value = self.from_physical(value_other_physical)

                # convert possible difference in function unit (e.g., dex->dB)
                return self.function_unit.to(other_function_unit, value)

            else:
                try:
                    # when other is not a function unit
                    return self.physical_unit.to(
                        other, self.to_physical(value), equivalencies
                    )
                except UnitConversionError as e:
                    if self.function_unit == Unit("mag"):
                        # One can get to raw magnitudes via math that strips the dimensions off.
                        # Include extra information in the exception to remind users of this.
                        msg = "Did you perhaps subtract magnitudes so the unit got lost?"
                        e.args += (msg,)
                        raise e
                    else:
                        raise

        def is_unity(self):
            return False

        def __eq__(self, other):
            return self.physical_unit == getattr(
                other, "physical_unit", dimensionless_unscaled
            ) and self.function_unit == getattr(other, "function_unit", other)

        def __ne__(self, other):
            return not self.__eq__(other)

        def __rlshift__(self, other):
            """Unit conversion operator ``<<``."""
            try:
                return self._quantity_class(other, self, copy=None, subok=True)
            except Exception:
                return NotImplemented

        def __mul__(self, other):
            if isinstance(other, (str, UnitBase, FunctionUnitBase)):
                if self.physical_unit == dimensionless_unscaled:
                    # If dimensionless, drop back to normal unit and retry.
                    return self.function_unit * other
                else:
                    raise UnitsError(
                        "Cannot multiply a function unit with a physical dimension "
                        "with any unit."
                    )
            else:
                # Anything not like a unit, try initialising as a function quantity.
                try:
                    return self._quantity_class(other, unit=self)
                except Exception:
                    return NotImplemented

        def __rmul__(self, other):
            return self.__mul__(other)

        def __truediv__(self, other):
            if isinstance(other, (str, UnitBase, FunctionUnitBase)):
                if self.physical_unit == dimensionless_unscaled:
                    # If dimensionless, drop back to normal unit and retry.
                    return self.function_unit / other
                else:
                    raise UnitsError(
                        "Cannot divide a function unit with a physical dimension "
                        "by any unit."
                    )
            else:
                # Anything not like a unit, try initialising as a function quantity.
                try:
                    return self._quantity_class(1.0 / other, unit=self)
                except Exception:
                    return NotImplemented

        def __rtruediv__(self, other):
            if isinstance(other, (str, UnitBase, FunctionUnitBase)):
                if self.physical_unit == dimensionless_unscaled:
                    # If dimensionless, drop back to normal unit and retry.
                    return other / self.function_unit
                else:
                    raise UnitsError(
                        "Cannot divide a function unit with a physical dimension "
                        "into any unit"
                    )
            else:
                # Don't know what to do with anything not like a unit.
                return NotImplemented

        def __pow__(self, power):
            if power == 0:
                return dimensionless_unscaled
            elif power == 1:
                return self._copy()

            if self.physical_unit == dimensionless_unscaled:
                return self.function_unit**power

            raise UnitsError(
                "Cannot raise a function unit with a physical dimension "
                "to any power but 0 or 1."
            )

        def __pos__(self):
            return self._copy()

        def to_string(self, format="generic", **kwargs):
            """
            Output the unit in the given format as a string.

            The physical unit is appended, within parentheses, to the function
            unit, as in "dB(mW)", with both units set using the given format

            Parameters
            ----------
            format : `astropy.units.format.Base` subclass or str
                The name of a format or a formatter class.  If not
                provided, defaults to the generic format.
            """
            supported_formats = (
                "generic",
                "latex",
                "latex_inline",
                "unicode",
                "console",
            )
            if format not in supported_formats:
                raise ValueError(
                    f"Function units cannot be written in {format} "
                    f"format. Only {', '.join(supported_formats)} are supported."
                )
            self_str = self.function_unit.to_string(format, **kwargs)
            pu_str = self.physical_unit.to_string(format, **kwargs)
            if pu_str == "":
                pu_str = "1"
            if format.startswith("latex"):
                # Add the physical unit with parentheses, removing its latex
                # initialization stuff ("$\mathrm{" and "}$").
                # For self_str, remove trailing "}$" and put it back at the end.
                self_str = rf"{self_str[:-2]}\left({pu_str[9:-2]}\right)}}$"
            else:
                pu_lines = pu_str.splitlines()
                if len(pu_lines) == 1:
                    self_str += f"({pu_str})"
                else:
                    # If the physical unit is formatted into a multiline
                    # string, the lines need to be adjusted so that the
                    # functional string is aligned with the fraction line
                    # (second one), and all other lines are indented
                    # accordingly.
                    f = f"{{0:^{len(self_str) + 1}s}}{{1:s}}"
                    lines = [
                        f.format("", pu_lines[0]),
                        f.format(f"{self_str}(", f"{pu_lines[1]})"),
                    ] + [f.format("", line) for line in pu_lines[2:]]
                    self_str = "\n".join(lines)
            return self_str

        def __format__(self, format_spec):
            """Try to format units using a formatter."""
            try:
                return self.to_string(format=format_spec)
            except ValueError:
                return format(str(self), format_spec)

        def __str__(self):
            """Return string representation for unit."""
            self_str = str(self.function_unit)
            pu_str = str(self.physical_unit)
            if pu_str:
                self_str += f"({pu_str})"
            return self_str

        def __repr__(self):
            # By default, try to give a representation using `Unit(<string>)`,
            # with string such that parsing it would give the correct FunctionUnit.
            if callable(self.function_unit):
                return f'Unit("{self.to_string()}")'

            else:
                return '{}("{}"{})'.format(
                    self.__class__.__name__,
                    self.physical_unit,
                    ""
                    if self.function_unit is self._default_function_unit
                    else f', unit="{self.function_unit}"',
                )

        def _repr_latex_(self):
            """
            Generate latex representation of unit name.  This is used by
            the IPython notebook to print a unit with a nice layout.

            Returns
            -------
            Latex string
            """
            return self.to_string("latex")

        def __hash__(self):
            return hash((self.function_unit, self.physical_unit))

    class FunctionQuantity(Quantity):
        """A representation of a (scaled) function of a number with a unit.

        Function quantities are quantities whose units are functions containing a
        physical unit, such as dB(mW).  Most of the arithmetic operations on
        function quantities are defined in this base class.

        While instantiation is also defined here, this class should not be
        instantiated directly.  Rather, subclasses should be made which have
        ``_unit_class`` pointing back to the corresponding function unit class.

        Parameters
        ----------
        value : number, quantity-like, or sequence thereof
            The numerical value of the function quantity. If a number or
            a `~astropy.units.Quantity` with a function unit, it will be converted
            to ``unit`` and the physical unit will be inferred from ``unit``.
            If a `~astropy.units.Quantity` with just a physical unit, it will
            converted to the function unit, after, if necessary, converting it to
            the physical unit inferred from ``unit``.

        unit : str, `~astropy.units.UnitBase`, or `~astropy.units.FunctionUnitBase`, optional
            For an `~astropy.units.FunctionUnitBase` instance, the
            physical unit will be taken from it; for other input, it will be
            inferred from ``value``. By default, ``unit`` is set by the subclass.

        dtype : `~numpy.dtype`, optional
            The dtype of the resulting Numpy array or scalar that will
            hold the value.  If not provided, it is determined from the input,
            except that any input that cannot represent float (integer and bool)
            is converted to float.

        copy : bool, optional
            If `True` (default), then the value is copied.  Otherwise, a copy will
            only be made if ``__array__`` returns a copy, if value is a nested
            sequence, or if a copy is needed to satisfy an explicitly given
            ``dtype``.  (The `False` option is intended mostly for internal use,
            to speed up initialization where a copy is known to have been made.
            Use with care.)

        order : {'C', 'F', 'A'}, optional
            Specify the order of the array.  As in `~numpy.array`.  Ignored
            if the input does not need to be converted and ``copy=False``.

        subok : bool, optional
            If `False` (default), the returned array will be forced to be of the
            class used.  Otherwise, subclasses will be passed through.

        ndmin : int, optional
            Specifies the minimum number of dimensions that the resulting array
            should have.  Ones will be prepended to the shape as needed to meet
            this requirement.  This parameter is ignored if the input is a
            `~astropy.units.Quantity` and ``copy=False``.

        Raises
        ------
        TypeError
            If the value provided is not a Python numeric type.
        TypeError
            If the unit provided is not a `~astropy.units.FunctionUnitBase`
            or `~astropy.units.Unit` object, or a parseable string unit.
        """

        _unit_class = None
        """Default `~astropy.units.FunctionUnitBase` subclass.

        This should be overridden by subclasses.
        """

        # Ensure priority over ndarray, regular Unit & Quantity, and FunctionUnit.
        __array_priority__ = 40000

        # Define functions that work on FunctionQuantity.
        _supported_ufuncs = SUPPORTED_UFUNCS
        _supported_functions = SUPPORTED_FUNCTIONS

        def __new__(
            cls,
            value,
            unit=None,
            dtype=np.inexact,
            copy=True,
            order=None,
            subok=False,
            ndmin=0,
        ):
            if unit is not None:
                # Convert possible string input to a (function) unit.
                unit = Unit(unit)

            if not isinstance(unit, FunctionUnitBase):
                # By default, use value's physical unit.
                value_unit = getattr(value, "unit", None)
                if value_unit is None:
                    # if iterable, see if first item has a unit
                    # (mixed lists fail in super call below).
                    try:
                        value_unit = value[0].unit
                    except Exception:
                        pass
                physical_unit = getattr(value_unit, "physical_unit", value_unit)
                unit = cls._unit_class(physical_unit, function_unit=unit)

            # initialise!
            return super().__new__(
                cls,
                value,
                unit,
                dtype=dtype,
                copy=copy,
                order=order,
                subok=subok,
                ndmin=ndmin,
            )

        # ↓↓↓ properties not found in Quantity
        @property
        def physical(self):
            """The physical quantity corresponding the function one."""
            return self.to(self.unit.physical_unit)

        @property
        def _function_view(self):
            """View as Quantity with function unit, dropping the physical unit.

            Use `~astropy.units.quantity.Quantity.value` for just the value.
            """
            return self._new_view(unit=self.unit.function_unit)

        # ↓↓↓ methods overridden to change the behavior
        @property
        def si(self):
            """Return a copy with the physical unit in SI units."""
            return self.__class__(self.physical.si)

        @property
        def cgs(self):
            """Return a copy with the physical unit in CGS units."""
            return self.__class__(self.physical.cgs)

        def decompose(self, bases: Collection[UnitBase] = ()) -> Self:
            """Generate a new instance with the physical unit decomposed.

            For details, see `~astropy.units.Quantity.decompose`.
            """
            return self.__class__(self.physical.decompose(bases))

        # ↓↓↓ methods overridden to add additional behavior
        def __quantity_subclass__(self, unit):
            if isinstance(unit, FunctionUnitBase):
                return self.__class__, True
            else:
                return super().__quantity_subclass__(unit)[0], False

        def _set_unit(self, unit):
            if not isinstance(unit, self._unit_class):
                # Have to take care of, e.g., (10*u.mag).view(u.Magnitude)
                try:
                    # "or 'nonsense'" ensures `None` breaks, just in case.
                    unit = self._unit_class(function_unit=unit or "nonsense")
                except Exception:
                    raise UnitTypeError(
                        f"{type(self).__name__} instances require"
                        f" {self._unit_class.__name__} function units, so cannot set it to"
                        f" '{unit}'."
                    )

            self._unit = unit

        def __array_ufunc__(self, function, method, *inputs, **kwargs):
            # TODO: it would be more logical to have this in Quantity already,
            # instead of in UFUNC_HELPERS, where it cannot be overridden.
            # And really it should just return NotImplemented, since possibly
            # another argument might know what to do.
            if function not in self._supported_ufuncs:
                raise UnitTypeError(
                    f"Cannot use ufunc '{function.__name__}' with function quantities"
                )

            return super().__array_ufunc__(function, method, *inputs, **kwargs)

        def _maybe_new_view(self, result):
            """View as function quantity if the unit is unchanged.

            Used for the case that self.unit.physical_unit is dimensionless,
            where multiplication and division is done using the Quantity
            equivalent, to transform them back to a FunctionQuantity if possible.
            """
            if isinstance(result, Quantity) and result.unit == self.unit:
                return self._new_view(result)
            else:
                return result

        # ↓↓↓ methods overridden to change behavior
        def __mul__(self, other):
            if self.unit.physical_unit == dimensionless_unscaled:
                return self._maybe_new_view(self._function_view * other)

            raise UnitTypeError(
                "Cannot multiply function quantities which are not dimensionless "
                "with anything."
            )

        def __truediv__(self, other):
            if self.unit.physical_unit == dimensionless_unscaled:
                return self._maybe_new_view(self._function_view / other)

            raise UnitTypeError(
                "Cannot divide function quantities which are not dimensionless by anything."
            )

        def __rtruediv__(self, other):
            if self.unit.physical_unit == dimensionless_unscaled:
                return self._maybe_new_view(self._function_view.__rtruediv__(other))

            raise UnitTypeError(
                "Cannot divide function quantities which are not dimensionless "
                "into anything."
            )

        def _comparison(self, other, comparison_func):
            """Do a comparison between self and other, raising UnitsError when
            other cannot be converted to self because it has different physical
            unit, and returning NotImplemented when there are other errors.
            """
            try:
                # will raise a UnitsError if physical units not equivalent
                other_in_own_unit = self._to_own_unit(other, check_precision=False)
            except UnitsError as exc:
                if self.unit.physical_unit != dimensionless_unscaled:
                    raise exc

                try:
                    other_in_own_unit = self._function_view._to_own_unit(
                        other, check_precision=False
                    )
                except Exception:
                    raise exc

            except Exception:
                return NotImplemented

            return comparison_func(other_in_own_unit)

        def __eq__(self, other):
            try:
                return self._comparison(other, self.value.__eq__)
            except UnitsError:
                return False

        def __ne__(self, other):
            try:
                return self._comparison(other, self.value.__ne__)
            except UnitsError:
                return True

        def __gt__(self, other):
            return self._comparison(other, self.value.__gt__)

        def __ge__(self, other):
            return self._comparison(other, self.value.__ge__)

        def __lt__(self, other):
            return self._comparison(other, self.value.__lt__)

        def __le__(self, other):
            return self._comparison(other, self.value.__le__)

        def __lshift__(self, other):
            """Unit conversion operator `<<`."""
            try:
                other = Unit(other, parse_strict="silent")
            except UnitTypeError:
                return NotImplemented

            return self.__class__(self, other, copy=False, subok=True)

        # Ensure Quantity methods are used only if they make sense.
        def _wrap_function(self, function, *args, **kwargs):
            if function in self._supported_functions:
                return super()._wrap_function(function, *args, **kwargs)

            # For dimensionless, we can convert to regular quantities.
            if all(
                arg.unit.physical_unit == dimensionless_unscaled
                for arg in (self,) + args
                if (hasattr(arg, "unit") and hasattr(arg.unit, "physical_unit"))
            ):
                args = tuple(getattr(arg, "_function_view", arg) for arg in args)
                return self._function_view._wrap_function(function, *args, **kwargs)

            raise TypeError(
                f"Cannot use method that uses function '{function.__name__}' with "
                "function quantities that are not dimensionless."
            )

        # Override functions that are supported but do not use _wrap_function
        # in Quantity.

        def max(self, axis=None, out=None, keepdims=False):
            return self._wrap_function(np.max, axis, out=out, keepdims=keepdims)

        def min(self, axis=None, out=None, keepdims=False):
            return self._wrap_function(np.min, axis, out=out, keepdims=keepdims)

        def sum(self, axis=None, dtype=None, out=None, keepdims=False):
            return self._wrap_function(np.sum, axis, dtype, out=out, keepdims=keepdims)

        def cumsum(self, axis=None, dtype=None, out=None):
            return self._wrap_function(np.cumsum, axis, dtype, out=out)

        def clip(self, a_min, a_max, out=None):
            return self._wrap_function(
                np.clip, self._to_own_unit(a_min), self._to_own_unit(a_max), out=out
            )