""" In this module, we define the coordinate representation classes, which are used to represent low-level cartesian, spherical, cylindrical, and other coordinates. """ import abc import functools import operator import inspect import warnings import numpy as np import astropy.units as u from erfa import ufunc as erfa_ufunc from .angles import Angle, Longitude, Latitude from .distances import Distance from .matrix_utilities import is_O3 from astropy.utils import ShapedLikeNDArray, classproperty from astropy.utils.data_info import MixinInfo from astropy.utils.exceptions import DuplicateRepresentationWarning __all__ = ["BaseRepresentationOrDifferential", "BaseRepresentation", "CartesianRepresentation", "SphericalRepresentation", "UnitSphericalRepresentation", "RadialRepresentation", "PhysicsSphericalRepresentation", "CylindricalRepresentation", "BaseDifferential", "CartesianDifferential", "BaseSphericalDifferential", "BaseSphericalCosLatDifferential", "SphericalDifferential", "SphericalCosLatDifferential", "UnitSphericalDifferential", "UnitSphericalCosLatDifferential", "RadialDifferential", "CylindricalDifferential", "PhysicsSphericalDifferential"] # Module-level dict mapping representation string alias names to classes. # This is populated by __init_subclass__ when called by Representation or # Differential classes so that they are all registered automatically. REPRESENTATION_CLASSES = {} DIFFERENTIAL_CLASSES = {} # set for tracking duplicates DUPLICATE_REPRESENTATIONS = set() # a hash for the content of the above two dicts, cached for speed. _REPRDIFF_HASH = None def _fqn_class(cls): ''' Get the fully qualified name of a class ''' return cls.__module__ + '.' + cls.__qualname__ def get_reprdiff_cls_hash(): """ Returns a hash value that should be invariable if the `REPRESENTATION_CLASSES` and `DIFFERENTIAL_CLASSES` dictionaries have not changed. """ global _REPRDIFF_HASH if _REPRDIFF_HASH is None: _REPRDIFF_HASH = (hash(tuple(REPRESENTATION_CLASSES.items())) + hash(tuple(DIFFERENTIAL_CLASSES.items()))) return _REPRDIFF_HASH def _invalidate_reprdiff_cls_hash(): global _REPRDIFF_HASH _REPRDIFF_HASH = None def _array2string(values, prefix=''): # Work around version differences for array2string. kwargs = {'separator': ', ', 'prefix': prefix} kwargs['formatter'] = {} return np.array2string(values, **kwargs) class BaseRepresentationOrDifferentialInfo(MixinInfo): """ Container for meta information like name, description, format. This is required when the object is used as a mixin column within a table, but can be used as a general way to store meta information. """ attrs_from_parent = {'unit'} # Indicates unit is read-only _supports_indexing = False @staticmethod def default_format(val): # Create numpy dtype so that numpy formatting will work. components = val.components values = tuple(getattr(val, component).value for component in components) a = np.empty(getattr(val, 'shape', ()), [(component, value.dtype) for component, value in zip(components, values)]) for component, value in zip(components, values): a[component] = value return str(a) @property def _represent_as_dict_attrs(self): return self._parent.components @property def unit(self): if self._parent is None: return None unit = self._parent._unitstr return unit[1:-1] if unit.startswith('(') else unit def new_like(self, reps, length, metadata_conflicts='warn', name=None): """ Return a new instance like ``reps`` with ``length`` rows. This is intended for creating an empty column object whose elements can be set in-place for table operations like join or vstack. Parameters ---------- reps : list List of input representations or differentials. length : int Length of the output column object metadata_conflicts : str ('warn'|'error'|'silent') How to handle metadata conflicts name : str Output column name Returns ------- col : `BaseRepresentation` or `BaseDifferential` subclass instance Empty instance of this class consistent with ``cols`` """ # Get merged info attributes like shape, dtype, format, description, etc. attrs = self.merge_cols_attributes(reps, metadata_conflicts, name, ('meta', 'description')) # Make a new representation or differential with the desired length # using the _apply / __getitem__ machinery to effectively return # rep0[[0, 0, ..., 0, 0]]. This will have the right shape, and # include possible differentials. indexes = np.zeros(length, dtype=np.int64) out = reps[0][indexes] # Use __setitem__ machinery to check whether all representations # can represent themselves as this one without loss of information. for rep in reps[1:]: try: out[0] = rep[0] except Exception as err: raise ValueError(f'input representations are inconsistent.') from err # Set (merged) info attributes. for attr in ('name', 'meta', 'description'): if attr in attrs: setattr(out.info, attr, attrs[attr]) return out class BaseRepresentationOrDifferential(ShapedLikeNDArray): """3D coordinate representations and differentials. Parameters ---------- comp1, comp2, comp3 : `~astropy.units.Quantity` or subclass The components of the 3D point or differential. The names are the keys and the subclasses the values of the ``attr_classes`` attribute. copy : bool, optional If `True` (default), arrays will be copied; if `False`, they will be broadcast together but not use new memory. """ # Ensure multiplication/division with ndarray or Quantity doesn't lead to # object arrays. __array_priority__ = 50000 info = BaseRepresentationOrDifferentialInfo() def __init__(self, *args, **kwargs): # make argument a list, so we can pop them off. args = list(args) components = self.components if (args and isinstance(args[0], self.__class__) and all(arg is None for arg in args[1:])): rep_or_diff = args[0] copy = kwargs.pop('copy', True) attrs = [getattr(rep_or_diff, component) for component in components] if 'info' in rep_or_diff.__dict__: self.info = rep_or_diff.info if kwargs: raise TypeError(f'unexpected keyword arguments for case ' f'where class instance is passed in: {kwargs}') else: attrs = [] for component in components: try: attr = args.pop(0) if args else kwargs.pop(component) except KeyError: raise TypeError(f'__init__() missing 1 required positional ' f'argument: {component!r}') from None if attr is None: raise TypeError(f'__init__() missing 1 required positional ' f'argument: {component!r} (or first ' f'argument should be an instance of ' f'{self.__class__.__name__}).') attrs.append(attr) copy = args.pop(0) if args else kwargs.pop('copy', True) if args: raise TypeError(f'unexpected arguments: {args}') if kwargs: for component in components: if component in kwargs: raise TypeError(f"__init__() got multiple values for " f"argument {component!r}") raise TypeError(f'unexpected keyword arguments: {kwargs}') # Pass attributes through the required initializing classes. attrs = [self.attr_classes[component](attr, copy=copy, subok=True) for component, attr in zip(components, attrs)] try: bc_attrs = np.broadcast_arrays(*attrs, subok=True) except ValueError as err: if len(components) <= 2: c_str = ' and '.join(components) else: c_str = ', '.join(components[:2]) + ', and ' + components[2] raise ValueError(f"Input parameters {c_str} cannot be broadcast") from err # The output of np.broadcast_arrays() has limitations on writeability, so we perform # additional handling to enable writeability in most situations. This is primarily # relevant for allowing the changing of the wrap angle of longitude components. # # If the shape has changed for a given component, broadcasting is needed: # If copy=True, we make a copy of the broadcasted array to ensure writeability. # Note that array had already been copied prior to the broadcasting. # TODO: Find a way to avoid the double copy. # If copy=False, we use the broadcasted array, and writeability may still be # limited. # If the shape has not changed for a given component, we can proceed with using the # non-broadcasted array, which avoids writeability issues from np.broadcast_arrays(). attrs = [(bc_attr.copy() if copy else bc_attr) if bc_attr.shape != attr.shape else attr for attr, bc_attr in zip(attrs, bc_attrs)] # Set private attributes for the attributes. (If not defined explicitly # on the class, the metaclass will define properties to access these.) for component, attr in zip(components, attrs): setattr(self, '_' + component, attr) @classmethod def get_name(cls): """Name of the representation or differential. In lower case, with any trailing 'representation' or 'differential' removed. (E.g., 'spherical' for `~astropy.coordinates.SphericalRepresentation` or `~astropy.coordinates.SphericalDifferential`.) """ name = cls.__name__.lower() if name.endswith('representation'): name = name[:-14] elif name.endswith('differential'): name = name[:-12] return name # The two methods that any subclass has to define. @classmethod @abc.abstractmethod def from_cartesian(cls, other): """Create a representation of this class from a supplied Cartesian one. Parameters ---------- other : `CartesianRepresentation` The representation to turn into this class Returns ------- representation : `BaseRepresentation` subclass instance A new representation of this class's type. """ # Note: the above docstring gets overridden for differentials. raise NotImplementedError() @abc.abstractmethod def to_cartesian(self): """Convert the representation to its Cartesian form. Note that any differentials get dropped. Also note that orientation information at the origin is *not* preserved by conversions through Cartesian coordinates. For example, transforming an angular position defined at distance=0 through cartesian coordinates and back will lose the original angular coordinates:: >>> import astropy.units as u >>> import astropy.coordinates as coord >>> rep = coord.SphericalRepresentation( ... lon=15*u.deg, ... lat=-11*u.deg, ... distance=0*u.pc) >>> rep.to_cartesian().represent_as(coord.SphericalRepresentation) Returns ------- cartrepr : `CartesianRepresentation` The representation in Cartesian form. """ # Note: the above docstring gets overridden for differentials. raise NotImplementedError() @property def components(self): """A tuple with the in-order names of the coordinate components.""" return tuple(self.attr_classes) def __eq__(self, value): """Equality operator This implements strict equality and requires that the representation classes are identical and that the representation data are exactly equal. """ if self.__class__ is not value.__class__: raise TypeError(f'cannot compare: objects must have same class: ' f'{self.__class__.__name__} vs. ' f'{value.__class__.__name__}') try: np.broadcast(self, value) except ValueError as exc: raise ValueError(f'cannot compare: {exc}') from exc out = True for comp in self.components: out &= (getattr(self, '_' + comp) == getattr(value, '_' + comp)) return out def __ne__(self, value): return np.logical_not(self == value) def _apply(self, method, *args, **kwargs): """Create a new representation or differential with ``method`` applied to the component data. In typical usage, the method is any of the shape-changing methods for `~numpy.ndarray` (``reshape``, ``swapaxes``, etc.), as well as those picking particular elements (``__getitem__``, ``take``, etc.), which are all defined in `~astropy.utils.shapes.ShapedLikeNDArray`. It will be applied to the underlying arrays (e.g., ``x``, ``y``, and ``z`` for `~astropy.coordinates.CartesianRepresentation`), with the results used to create a new instance. Internally, it is also used to apply functions to the components (in particular, `~numpy.broadcast_to`). Parameters ---------- method : str or callable If str, it is the name of a method that is applied to the internal ``components``. If callable, the function is applied. *args : tuple Any positional arguments for ``method``. **kwargs : dict Any keyword arguments for ``method``. """ if callable(method): apply_method = lambda array: method(array, *args, **kwargs) else: apply_method = operator.methodcaller(method, *args, **kwargs) new = super().__new__(self.__class__) for component in self.components: setattr(new, '_' + component, apply_method(getattr(self, component))) # Copy other 'info' attr only if it has actually been defined. # See PR #3898 for further explanation and justification, along # with Quantity.__array_finalize__ if 'info' in self.__dict__: new.info = self.info return new def __setitem__(self, item, value): if value.__class__ is not self.__class__: raise TypeError(f'can only set from object of same class: ' f'{self.__class__.__name__} vs. ' f'{value.__class__.__name__}') for component in self.components: getattr(self, '_' + component)[item] = getattr(value, '_' + component) @property def shape(self): """The shape of the instance and underlying arrays. Like `~numpy.ndarray.shape`, can be set to a new shape by assigning a tuple. Note that if different instances share some but not all underlying data, setting the shape of one instance can make the other instance unusable. Hence, it is strongly recommended to get new, reshaped instances with the ``reshape`` method. Raises ------ ValueError If the new shape has the wrong total number of elements. AttributeError If the shape of any of the components cannot be changed without the arrays being copied. For these cases, use the ``reshape`` method (which copies any arrays that cannot be reshaped in-place). """ return getattr(self, self.components[0]).shape @shape.setter def shape(self, shape): # We keep track of arrays that were already reshaped since we may have # to return those to their original shape if a later shape-setting # fails. (This can happen since coordinates are broadcast together.) reshaped = [] oldshape = self.shape for component in self.components: val = getattr(self, component) if val.size > 1: try: val.shape = shape except Exception: for val2 in reshaped: val2.shape = oldshape raise else: reshaped.append(val) # Required to support multiplication and division, and defined by the base # representation and differential classes. @abc.abstractmethod def _scale_operation(self, op, *args): raise NotImplementedError() def __mul__(self, other): return self._scale_operation(operator.mul, other) def __rmul__(self, other): return self.__mul__(other) def __truediv__(self, other): return self._scale_operation(operator.truediv, other) def __neg__(self): return self._scale_operation(operator.neg) # Follow numpy convention and make an independent copy. def __pos__(self): return self.copy() # Required to support addition and subtraction, and defined by the base # representation and differential classes. @abc.abstractmethod def _combine_operation(self, op, other, reverse=False): raise NotImplementedError() def __add__(self, other): return self._combine_operation(operator.add, other) def __radd__(self, other): return self._combine_operation(operator.add, other, reverse=True) def __sub__(self, other): return self._combine_operation(operator.sub, other) def __rsub__(self, other): return self._combine_operation(operator.sub, other, reverse=True) # The following are used for repr and str @property def _values(self): """Turn the coordinates into a record array with the coordinate values. The record array fields will have the component names. """ coo_items = [(c, getattr(self, c)) for c in self.components] result = np.empty(self.shape, [(c, coo.dtype) for c, coo in coo_items]) for c, coo in coo_items: result[c] = coo.value return result @property def _units(self): """Return a dictionary with the units of the coordinate components.""" return dict([(component, getattr(self, component).unit) for component in self.components]) @property def _unitstr(self): units_set = set(self._units.values()) if len(units_set) == 1: unitstr = units_set.pop().to_string() else: unitstr = '({})'.format( ', '.join([self._units[component].to_string() for component in self.components])) return unitstr def __str__(self): return f'{_array2string(self._values)} {self._unitstr:s}' def __repr__(self): prefixstr = ' ' arrstr = _array2string(self._values, prefix=prefixstr) diffstr = '' if getattr(self, 'differentials', None): diffstr = '\n (has differentials w.r.t.: {})'.format( ', '.join([repr(key) for key in self.differentials.keys()])) unitstr = ('in ' + self._unitstr) if self._unitstr else '[dimensionless]' return '<{} ({}) {:s}\n{}{}{}>'.format( self.__class__.__name__, ', '.join(self.components), unitstr, prefixstr, arrstr, diffstr) def _make_getter(component): """Make an attribute getter for use in a property. Parameters ---------- component : str The name of the component that should be accessed. This assumes the actual value is stored in an attribute of that name prefixed by '_'. """ # This has to be done in a function to ensure the reference to component # is not lost/redirected. component = '_' + component def get_component(self): return getattr(self, component) return get_component class RepresentationInfo(BaseRepresentationOrDifferentialInfo): @property def _represent_as_dict_attrs(self): attrs = super()._represent_as_dict_attrs if self._parent._differentials: attrs += ('differentials',) return attrs def _represent_as_dict(self, attrs=None): out = super()._represent_as_dict(attrs) for key, value in out.pop('differentials', {}).items(): out[f'differentials.{key}'] = value return out def _construct_from_dict(self, map): differentials = {} for key in list(map.keys()): if key.startswith('differentials.'): differentials[key[14:]] = map.pop(key) map['differentials'] = differentials return super()._construct_from_dict(map) class BaseRepresentation(BaseRepresentationOrDifferential): """Base for representing a point in a 3D coordinate system. Parameters ---------- comp1, comp2, comp3 : `~astropy.units.Quantity` or subclass The components of the 3D points. The names are the keys and the subclasses the values of the ``attr_classes`` attribute. differentials : dict, `~astropy.coordinates.BaseDifferential`, optional Any differential classes that should be associated with this representation. The input must either be a single `~astropy.coordinates.BaseDifferential` subclass instance, or a dictionary with keys set to a string representation of the SI unit with which the differential (derivative) is taken. For example, for a velocity differential on a positional representation, the key would be ``'s'`` for seconds, indicating that the derivative is a time derivative. copy : bool, optional If `True` (default), arrays will be copied. If `False`, arrays will be references, though possibly broadcast to ensure matching shapes. Notes ----- All representation classes should subclass this base representation class, and define an ``attr_classes`` attribute, a `dict` which maps component names to the class that creates them. They must also define a ``to_cartesian`` method and a ``from_cartesian`` class method. By default, transformations are done via the cartesian system, but classes that want to define a smarter transformation path can overload the ``represent_as`` method. If one wants to use an associated differential class, one should also define ``unit_vectors`` and ``scale_factors`` methods (see those methods for details). """ info = RepresentationInfo() def __init_subclass__(cls, **kwargs): # Register representation name (except for BaseRepresentation) if cls.__name__ == 'BaseRepresentation': return if not hasattr(cls, 'attr_classes'): raise NotImplementedError('Representations must have an ' '"attr_classes" class attribute.') repr_name = cls.get_name() # first time a duplicate is added # remove first entry and add both using their qualnames if repr_name in REPRESENTATION_CLASSES: DUPLICATE_REPRESENTATIONS.add(repr_name) fqn_cls = _fqn_class(cls) existing = REPRESENTATION_CLASSES[repr_name] fqn_existing = _fqn_class(existing) if fqn_cls == fqn_existing: raise ValueError(f'Representation "{fqn_cls}" already defined') msg = ( f'Representation "{repr_name}" already defined, removing it to avoid confusion.' f'Use qualnames "{fqn_cls}" and "{fqn_existing}" or class instances directly' ) warnings.warn(msg, DuplicateRepresentationWarning) del REPRESENTATION_CLASSES[repr_name] REPRESENTATION_CLASSES[fqn_existing] = existing repr_name = fqn_cls # further definitions with the same name, just add qualname elif repr_name in DUPLICATE_REPRESENTATIONS: fqn_cls = _fqn_class(cls) warnings.warn(f'Representation "{repr_name}" already defined, using qualname ' f'"{fqn_cls}".') repr_name = fqn_cls if repr_name in REPRESENTATION_CLASSES: raise ValueError( f'Representation "{repr_name}" already defined' ) REPRESENTATION_CLASSES[repr_name] = cls _invalidate_reprdiff_cls_hash() # define getters for any component that does not yet have one. for component in cls.attr_classes: if not hasattr(cls, component): setattr(cls, component, property(_make_getter(component), doc=f"The '{component}' component of the points(s).")) super().__init_subclass__(**kwargs) def __init__(self, *args, differentials=None, **kwargs): # Handle any differentials passed in. super().__init__(*args, **kwargs) if (differentials is None and args and isinstance(args[0], self.__class__)): differentials = args[0]._differentials self._differentials = self._validate_differentials(differentials) def _validate_differentials(self, differentials): """ Validate that the provided differentials are appropriate for this representation and recast/reshape as necessary and then return. Note that this does *not* set the differentials on ``self._differentials``, but rather leaves that for the caller. """ # Now handle the actual validation of any specified differential classes if differentials is None: differentials = dict() elif isinstance(differentials, BaseDifferential): # We can't handle auto-determining the key for this combo if (isinstance(differentials, RadialDifferential) and isinstance(self, UnitSphericalRepresentation)): raise ValueError("To attach a RadialDifferential to a " "UnitSphericalRepresentation, you must supply " "a dictionary with an appropriate key.") key = differentials._get_deriv_key(self) differentials = {key: differentials} for key in differentials: try: diff = differentials[key] except TypeError as err: raise TypeError("'differentials' argument must be a " "dictionary-like object") from err diff._check_base(self) if (isinstance(diff, RadialDifferential) and isinstance(self, UnitSphericalRepresentation)): # We trust the passing of a key for a RadialDifferential # attached to a UnitSphericalRepresentation because it will not # have a paired component name (UnitSphericalRepresentation has # no .distance) to automatically determine the expected key pass else: expected_key = diff._get_deriv_key(self) if key != expected_key: raise ValueError("For differential object '{}', expected " "unit key = '{}' but received key = '{}'" .format(repr(diff), expected_key, key)) # For now, we are very rigid: differentials must have the same shape # as the representation. This makes it easier to handle __getitem__ # and any other shape-changing operations on representations that # have associated differentials if diff.shape != self.shape: # TODO: message of IncompatibleShapeError is not customizable, # so use a valueerror instead? raise ValueError("Shape of differentials must be the same " "as the shape of the representation ({} vs " "{})".format(diff.shape, self.shape)) return differentials def _raise_if_has_differentials(self, op_name): """ Used to raise a consistent exception for any operation that is not supported when a representation has differentials attached. """ if self.differentials: raise TypeError("Operation '{}' is not supported when " "differentials are attached to a {}." .format(op_name, self.__class__.__name__)) @classproperty def _compatible_differentials(cls): return [DIFFERENTIAL_CLASSES[cls.get_name()]] @property def differentials(self): """A dictionary of differential class instances. The keys of this dictionary must be a string representation of the SI unit with which the differential (derivative) is taken. For example, for a velocity differential on a positional representation, the key would be ``'s'`` for seconds, indicating that the derivative is a time derivative. """ return self._differentials # We do not make unit_vectors and scale_factors abstract methods, since # they are only necessary if one also defines an associated Differential. # Also, doing so would break pre-differential representation subclasses. def unit_vectors(self): r"""Cartesian unit vectors in the direction of each component. Given unit vectors :math:`\hat{e}_c` and scale factors :math:`f_c`, a change in one component of :math:`\delta c` corresponds to a change in representation of :math:`\delta c \times f_c \times \hat{e}_c`. Returns ------- unit_vectors : dict of `CartesianRepresentation` The keys are the component names. """ raise NotImplementedError(f"{type(self)} has not implemented unit vectors") def scale_factors(self): r"""Scale factors for each component's direction. Given unit vectors :math:`\hat{e}_c` and scale factors :math:`f_c`, a change in one component of :math:`\delta c` corresponds to a change in representation of :math:`\delta c \times f_c \times \hat{e}_c`. Returns ------- scale_factors : dict of `~astropy.units.Quantity` The keys are the component names. """ raise NotImplementedError(f"{type(self)} has not implemented scale factors.") def _re_represent_differentials(self, new_rep, differential_class): """Re-represent the differentials to the specified classes. This returns a new dictionary with the same keys but with the attached differentials converted to the new differential classes. """ if differential_class is None: return dict() if not self.differentials and differential_class: raise ValueError("No differentials associated with this " "representation!") elif (len(self.differentials) == 1 and inspect.isclass(differential_class) and issubclass(differential_class, BaseDifferential)): # TODO: is there a better way to do this? differential_class = { list(self.differentials.keys())[0]: differential_class } elif differential_class.keys() != self.differentials.keys(): raise ValueError("Desired differential classes must be passed in " "as a dictionary with keys equal to a string " "representation of the unit of the derivative " "for each differential stored with this " "representation object ({0})" .format(self.differentials)) new_diffs = dict() for k in self.differentials: diff = self.differentials[k] try: new_diffs[k] = diff.represent_as(differential_class[k], base=self) except Exception as err: if (differential_class[k] not in new_rep._compatible_differentials): raise TypeError("Desired differential class {} is not " "compatible with the desired " "representation class {}" .format(differential_class[k], new_rep.__class__)) from err else: raise return new_diffs def represent_as(self, other_class, differential_class=None): """Convert coordinates to another representation. If the instance is of the requested class, it is returned unmodified. By default, conversion is done via Cartesian coordinates. Also note that orientation information at the origin is *not* preserved by conversions through Cartesian coordinates. See the docstring for :meth:`~astropy.coordinates.BaseRepresentationOrDifferential.to_cartesian` for an example. Parameters ---------- other_class : `~astropy.coordinates.BaseRepresentation` subclass The type of representation to turn the coordinates into. differential_class : dict of `~astropy.coordinates.BaseDifferential`, optional Classes in which the differentials should be represented. Can be a single class if only a single differential is attached, otherwise it should be a `dict` keyed by the same keys as the differentials. """ if other_class is self.__class__ and not differential_class: return self.without_differentials() else: if isinstance(other_class, str): raise ValueError("Input to a representation's represent_as " "must be a class, not a string. For " "strings, use frame objects") if other_class is not self.__class__: # The default is to convert via cartesian coordinates new_rep = other_class.from_cartesian(self.to_cartesian()) else: new_rep = self new_rep._differentials = self._re_represent_differentials( new_rep, differential_class) return new_rep def transform(self, matrix): """Transform coordinates using a 3x3 matrix in a Cartesian basis. This returns a new representation and does not modify the original one. Any differentials attached to this representation will also be transformed. Parameters ---------- matrix : (3,3) array-like A 3x3 (or stack thereof) matrix, such as a rotation matrix. """ # route transformation through Cartesian difs_cls = {k: CartesianDifferential for k in self.differentials.keys()} crep = self.represent_as(CartesianRepresentation, differential_class=difs_cls ).transform(matrix) # move back to original representation difs_cls = {k: diff.__class__ for k, diff in self.differentials.items()} rep = crep.represent_as(self.__class__, difs_cls) return rep def with_differentials(self, differentials): """ Create a new representation with the same positions as this representation, but with these new differentials. Differential keys that already exist in this object's differential dict are overwritten. Parameters ---------- differentials : sequence of `~astropy.coordinates.BaseDifferential` subclass instance The differentials for the new representation to have. Returns ------- `~astropy.coordinates.BaseRepresentation` subclass instance A copy of this representation, but with the ``differentials`` as its differentials. """ if not differentials: return self args = [getattr(self, component) for component in self.components] # We shallow copy the differentials dictionary so we don't update the # current object's dictionary when adding new keys new_rep = self.__class__(*args, differentials=self.differentials.copy(), copy=False) new_rep._differentials.update( new_rep._validate_differentials(differentials)) return new_rep def without_differentials(self): """Return a copy of the representation without attached differentials. Returns ------- `~astropy.coordinates.BaseRepresentation` subclass instance A shallow copy of this representation, without any differentials. If no differentials were present, no copy is made. """ if not self._differentials: return self args = [getattr(self, component) for component in self.components] return self.__class__(*args, copy=False) @classmethod def from_representation(cls, representation): """Create a new instance of this representation from another one. Parameters ---------- representation : `~astropy.coordinates.BaseRepresentation` instance The presentation that should be converted to this class. """ return representation.represent_as(cls) def __eq__(self, value): """Equality operator for BaseRepresentation This implements strict equality and requires that the representation classes are identical, the differentials are identical, and that the representation data are exactly equal. """ # BaseRepresentationOrDifferental (checks classes and compares components) out = super().__eq__(value) # super() checks that the class is identical so can this even happen? # (same class, different differentials ?) if self._differentials.keys() != value._differentials.keys(): raise ValueError(f'cannot compare: objects must have same differentials') for self_diff, value_diff in zip(self._differentials.values(), value._differentials.values()): out &= (self_diff == value_diff) return out def __ne__(self, value): return np.logical_not(self == value) def _apply(self, method, *args, **kwargs): """Create a new representation with ``method`` applied to the component data. This is not a simple inherit from ``BaseRepresentationOrDifferential`` because we need to call ``._apply()`` on any associated differential classes. See docstring for `BaseRepresentationOrDifferential._apply`. Parameters ---------- method : str or callable If str, it is the name of a method that is applied to the internal ``components``. If callable, the function is applied. *args : tuple Any positional arguments for ``method``. **kwargs : dict Any keyword arguments for ``method``. """ rep = super()._apply(method, *args, **kwargs) rep._differentials = dict( [(k, diff._apply(method, *args, **kwargs)) for k, diff in self._differentials.items()]) return rep def __setitem__(self, item, value): if not isinstance(value, BaseRepresentation): raise TypeError(f'value must be a representation instance, ' f'not {type(value)}.') if not (isinstance(value, self.__class__) or len(value.attr_classes) == len(self.attr_classes)): raise ValueError( f'value must be representable as {self.__class__.__name__} ' f'without loss of information.') diff_classes = {} if self._differentials: if self._differentials.keys() != value._differentials.keys(): raise ValueError('value must have the same differentials.') for key, self_diff in self._differentials.items(): diff_classes[key] = self_diff_cls = self_diff.__class__ value_diff_cls = value._differentials[key].__class__ if not (isinstance(value_diff_cls, self_diff_cls) or (len(value_diff_cls.attr_classes) == len(self_diff_cls.attr_classes))): raise ValueError( f'value differential {key!r} must be representable as ' f'{self_diff.__class__.__name__} without loss of information.') value = value.represent_as(self.__class__, diff_classes) super().__setitem__(item, value) for key, differential in self._differentials.items(): differential[item] = value._differentials[key] def _scale_operation(self, op, *args): """Scale all non-angular components, leaving angular ones unchanged. Parameters ---------- op : `~operator` callable Operator to apply (e.g., `~operator.mul`, `~operator.neg`, etc. *args Any arguments required for the operator (typically, what is to be multiplied with, divided by). """ results = [] for component, cls in self.attr_classes.items(): value = getattr(self, component) if issubclass(cls, Angle): results.append(value) else: results.append(op(value, *args)) # try/except catches anything that cannot initialize the class, such # as operations that returned NotImplemented or a representation # instead of a quantity (as would happen for, e.g., rep * rep). try: result = self.__class__(*results) except Exception: return NotImplemented for key, differential in self.differentials.items(): diff_result = differential._scale_operation(op, *args, scaled_base=True) result.differentials[key] = diff_result return result def _combine_operation(self, op, other, reverse=False): """Combine two representation. By default, operate on the cartesian representations of both. Parameters ---------- op : `~operator` callable Operator to apply (e.g., `~operator.add`, `~operator.sub`, etc. other : `~astropy.coordinates.BaseRepresentation` subclass instance The other representation. reverse : bool Whether the operands should be reversed (e.g., as we got here via ``self.__rsub__`` because ``self`` is a subclass of ``other``). """ self._raise_if_has_differentials(op.__name__) result = self.to_cartesian()._combine_operation(op, other, reverse) if result is NotImplemented: return NotImplemented else: return self.from_cartesian(result) # We need to override this setter to support differentials @BaseRepresentationOrDifferential.shape.setter def shape(self, shape): orig_shape = self.shape # See: https://stackoverflow.com/questions/3336767/ for an example BaseRepresentationOrDifferential.shape.fset(self, shape) # also try to perform shape-setting on any associated differentials try: for k in self.differentials: self.differentials[k].shape = shape except Exception: BaseRepresentationOrDifferential.shape.fset(self, orig_shape) for k in self.differentials: self.differentials[k].shape = orig_shape raise def norm(self): """Vector norm. The norm is the standard Frobenius norm, i.e., the square root of the sum of the squares of all components with non-angular units. Note that any associated differentials will be dropped during this operation. Returns ------- norm : `astropy.units.Quantity` Vector norm, with the same shape as the representation. """ return np.sqrt(functools.reduce( operator.add, (getattr(self, component)**2 for component, cls in self.attr_classes.items() if not issubclass(cls, Angle)))) def mean(self, *args, **kwargs): """Vector mean. Averaging is done by converting the representation to cartesian, and taking the mean of the x, y, and z components. The result is converted back to the same representation as the input. Refer to `~numpy.mean` for full documentation of the arguments, noting that ``axis`` is the entry in the ``shape`` of the representation, and that the ``out`` argument cannot be used. Returns ------- mean : `~astropy.coordinates.BaseRepresentation` subclass instance Vector mean, in the same representation as that of the input. """ self._raise_if_has_differentials('mean') return self.from_cartesian(self.to_cartesian().mean(*args, **kwargs)) def sum(self, *args, **kwargs): """Vector sum. Adding is done by converting the representation to cartesian, and summing the x, y, and z components. The result is converted back to the same representation as the input. Refer to `~numpy.sum` for full documentation of the arguments, noting that ``axis`` is the entry in the ``shape`` of the representation, and that the ``out`` argument cannot be used. Returns ------- sum : `~astropy.coordinates.BaseRepresentation` subclass instance Vector sum, in the same representation as that of the input. """ self._raise_if_has_differentials('sum') return self.from_cartesian(self.to_cartesian().sum(*args, **kwargs)) def dot(self, other): """Dot product of two representations. The calculation is done by converting both ``self`` and ``other`` to `~astropy.coordinates.CartesianRepresentation`. Note that any associated differentials will be dropped during this operation. Parameters ---------- other : `~astropy.coordinates.BaseRepresentation` The representation to take the dot product with. Returns ------- dot_product : `~astropy.units.Quantity` The sum of the product of the x, y, and z components of the cartesian representations of ``self`` and ``other``. """ return self.to_cartesian().dot(other) def cross(self, other): """Vector cross product of two representations. The calculation is done by converting both ``self`` and ``other`` to `~astropy.coordinates.CartesianRepresentation`, and converting the result back to the type of representation of ``self``. Parameters ---------- other : `~astropy.coordinates.BaseRepresentation` subclass instance The representation to take the cross product with. Returns ------- cross_product : `~astropy.coordinates.BaseRepresentation` subclass instance With vectors perpendicular to both ``self`` and ``other``, in the same type of representation as ``self``. """ self._raise_if_has_differentials('cross') return self.from_cartesian(self.to_cartesian().cross(other)) class CartesianRepresentation(BaseRepresentation): """ Representation of points in 3D cartesian coordinates. Parameters ---------- x, y, z : `~astropy.units.Quantity` or array The x, y, and z coordinates of the point(s). If ``x``, ``y``, and ``z`` have different shapes, they should be broadcastable. If not quantity, ``unit`` should be set. If only ``x`` is given, it is assumed that it contains an array with the 3 coordinates stored along ``xyz_axis``. unit : unit-like If given, the coordinates will be converted to this unit (or taken to be in this unit if not given. xyz_axis : int, optional The axis along which the coordinates are stored when a single array is provided rather than distinct ``x``, ``y``, and ``z`` (default: 0). differentials : dict, `CartesianDifferential`, optional Any differential classes that should be associated with this representation. The input must either be a single `CartesianDifferential` instance, or a dictionary of `CartesianDifferential` s with keys set to a string representation of the SI unit with which the differential (derivative) is taken. For example, for a velocity differential on a positional representation, the key would be ``'s'`` for seconds, indicating that the derivative is a time derivative. copy : bool, optional If `True` (default), arrays will be copied. If `False`, arrays will be references, though possibly broadcast to ensure matching shapes. """ attr_classes = {'x': u.Quantity, 'y': u.Quantity, 'z': u.Quantity} _xyz = None def __init__(self, x, y=None, z=None, unit=None, xyz_axis=None, differentials=None, copy=True): if y is None and z is None: if isinstance(x, np.ndarray) and x.dtype.kind not in 'OV': # Short-cut for 3-D array input. x = u.Quantity(x, unit, copy=copy, subok=True) # Keep a link to the array with all three coordinates # so that we can return it quickly if needed in get_xyz. self._xyz = x if xyz_axis: x = np.moveaxis(x, xyz_axis, 0) self._xyz_axis = xyz_axis else: self._xyz_axis = 0 self._x, self._y, self._z = x self._differentials = self._validate_differentials(differentials) return elif (isinstance(x, CartesianRepresentation) and unit is None and xyz_axis is None): if differentials is None: differentials = x._differentials return super().__init__(x, differentials=differentials, copy=copy) else: x, y, z = x if xyz_axis is not None: raise ValueError("xyz_axis should only be set if x, y, and z are " "in a single array passed in through x, " "i.e., y and z should not be not given.") if y is None or z is None: raise ValueError("x, y, and z are required to instantiate {}" .format(self.__class__.__name__)) if unit is not None: x = u.Quantity(x, unit, copy=copy, subok=True) y = u.Quantity(y, unit, copy=copy, subok=True) z = u.Quantity(z, unit, copy=copy, subok=True) copy = False super().__init__(x, y, z, copy=copy, differentials=differentials) if not (self._x.unit.is_equivalent(self._y.unit) and self._x.unit.is_equivalent(self._z.unit)): raise u.UnitsError("x, y, and z should have matching physical types") def unit_vectors(self): l = np.broadcast_to(1.*u.one, self.shape, subok=True) o = np.broadcast_to(0.*u.one, self.shape, subok=True) return { 'x': CartesianRepresentation(l, o, o, copy=False), 'y': CartesianRepresentation(o, l, o, copy=False), 'z': CartesianRepresentation(o, o, l, copy=False)} def scale_factors(self): l = np.broadcast_to(1.*u.one, self.shape, subok=True) return {'x': l, 'y': l, 'z': l} def get_xyz(self, xyz_axis=0): """Return a vector array of the x, y, and z coordinates. Parameters ---------- xyz_axis : int, optional The axis in the final array along which the x, y, z components should be stored (default: 0). Returns ------- xyz : `~astropy.units.Quantity` With dimension 3 along ``xyz_axis``. Note that, if possible, this will be a view. """ if self._xyz is not None: if self._xyz_axis == xyz_axis: return self._xyz else: return np.moveaxis(self._xyz, self._xyz_axis, xyz_axis) # Create combined array. TO DO: keep it in _xyz for repeated use? # But then in-place changes have to cancel it. Likely best to # also update components. return np.stack([self._x, self._y, self._z], axis=xyz_axis) xyz = property(get_xyz) @classmethod def from_cartesian(cls, other): return other def to_cartesian(self): return self def transform(self, matrix): """ Transform the cartesian coordinates using a 3x3 matrix. This returns a new representation and does not modify the original one. Any differentials attached to this representation will also be transformed. Parameters ---------- matrix : ndarray A 3x3 transformation matrix, such as a rotation matrix. Examples -------- We can start off by creating a cartesian representation object: >>> from astropy import units as u >>> from astropy.coordinates import CartesianRepresentation >>> rep = CartesianRepresentation([1, 2] * u.pc, ... [2, 3] * u.pc, ... [3, 4] * u.pc) We now create a rotation matrix around the z axis: >>> from astropy.coordinates.matrix_utilities import rotation_matrix >>> rotation = rotation_matrix(30 * u.deg, axis='z') Finally, we can apply this transformation: >>> rep_new = rep.transform(rotation) >>> rep_new.xyz # doctest: +FLOAT_CMP """ # erfa rxp: Multiply a p-vector by an r-matrix. p = erfa_ufunc.rxp(matrix, self.get_xyz(xyz_axis=-1)) # transformed representation rep = self.__class__(p, xyz_axis=-1, copy=False) # Handle differentials attached to this representation new_diffs = dict((k, d.transform(matrix, self, rep)) for k, d in self.differentials.items()) return rep.with_differentials(new_diffs) def _combine_operation(self, op, other, reverse=False): self._raise_if_has_differentials(op.__name__) try: other_c = other.to_cartesian() except Exception: return NotImplemented first, second = ((self, other_c) if not reverse else (other_c, self)) return self.__class__(*(op(getattr(first, component), getattr(second, component)) for component in first.components)) def norm(self): """Vector norm. The norm is the standard Frobenius norm, i.e., the square root of the sum of the squares of all components with non-angular units. Note that any associated differentials will be dropped during this operation. Returns ------- norm : `astropy.units.Quantity` Vector norm, with the same shape as the representation. """ # erfa pm: Modulus of p-vector. return erfa_ufunc.pm(self.get_xyz(xyz_axis=-1)) def mean(self, *args, **kwargs): """Vector mean. Returns a new CartesianRepresentation instance with the means of the x, y, and z components. Refer to `~numpy.mean` for full documentation of the arguments, noting that ``axis`` is the entry in the ``shape`` of the representation, and that the ``out`` argument cannot be used. """ self._raise_if_has_differentials('mean') return self._apply('mean', *args, **kwargs) def sum(self, *args, **kwargs): """Vector sum. Returns a new CartesianRepresentation instance with the sums of the x, y, and z components. Refer to `~numpy.sum` for full documentation of the arguments, noting that ``axis`` is the entry in the ``shape`` of the representation, and that the ``out`` argument cannot be used. """ self._raise_if_has_differentials('sum') return self._apply('sum', *args, **kwargs) def dot(self, other): """Dot product of two representations. Note that any associated differentials will be dropped during this operation. Parameters ---------- other : `~astropy.coordinates.BaseRepresentation` subclass instance If not already cartesian, it is converted. Returns ------- dot_product : `~astropy.units.Quantity` The sum of the product of the x, y, and z components of ``self`` and ``other``. """ try: other_c = other.to_cartesian() except Exception as err: raise TypeError("cannot only take dot product with another " "representation, not a {} instance." .format(type(other))) from err # erfa pdp: p-vector inner (=scalar=dot) product. return erfa_ufunc.pdp(self.get_xyz(xyz_axis=-1), other_c.get_xyz(xyz_axis=-1)) def cross(self, other): """Cross product of two representations. Parameters ---------- other : `~astropy.coordinates.BaseRepresentation` subclass instance If not already cartesian, it is converted. Returns ------- cross_product : `~astropy.coordinates.CartesianRepresentation` With vectors perpendicular to both ``self`` and ``other``. """ self._raise_if_has_differentials('cross') try: other_c = other.to_cartesian() except Exception as err: raise TypeError("cannot only take cross product with another " "representation, not a {} instance." .format(type(other))) from err # erfa pxp: p-vector outer (=vector=cross) product. sxo = erfa_ufunc.pxp(self.get_xyz(xyz_axis=-1), other_c.get_xyz(xyz_axis=-1)) return self.__class__(sxo, xyz_axis=-1) class UnitSphericalRepresentation(BaseRepresentation): """ Representation of points on a unit sphere. Parameters ---------- lon, lat : `~astropy.units.Quantity` ['angle'] or str The longitude and latitude of the point(s), in angular units. The latitude should be between -90 and 90 degrees, and the longitude will be wrapped to an angle between 0 and 360 degrees. These can also be instances of `~astropy.coordinates.Angle`, `~astropy.coordinates.Longitude`, or `~astropy.coordinates.Latitude`. differentials : dict, `~astropy.coordinates.BaseDifferential`, optional Any differential classes that should be associated with this representation. The input must either be a single `~astropy.coordinates.BaseDifferential` instance (see `._compatible_differentials` for valid types), or a dictionary of of differential instances with keys set to a string representation of the SI unit with which the differential (derivative) is taken. For example, for a velocity differential on a positional representation, the key would be ``'s'`` for seconds, indicating that the derivative is a time derivative. copy : bool, optional If `True` (default), arrays will be copied. If `False`, arrays will be references, though possibly broadcast to ensure matching shapes. """ attr_classes = {'lon': Longitude, 'lat': Latitude} @classproperty def _dimensional_representation(cls): return SphericalRepresentation def __init__(self, lon, lat=None, differentials=None, copy=True): super().__init__(lon, lat, differentials=differentials, copy=copy) @classproperty def _compatible_differentials(cls): return [UnitSphericalDifferential, UnitSphericalCosLatDifferential, SphericalDifferential, SphericalCosLatDifferential, RadialDifferential] # Could let the metaclass define these automatically, but good to have # a bit clearer docstrings. @property def lon(self): """ The longitude of the point(s). """ return self._lon @property def lat(self): """ The latitude of the point(s). """ return self._lat def unit_vectors(self): sinlon, coslon = np.sin(self.lon), np.cos(self.lon) sinlat, coslat = np.sin(self.lat), np.cos(self.lat) return { 'lon': CartesianRepresentation(-sinlon, coslon, 0., copy=False), 'lat': CartesianRepresentation(-sinlat*coslon, -sinlat*sinlon, coslat, copy=False)} def scale_factors(self, omit_coslat=False): sf_lat = np.broadcast_to(1./u.radian, self.shape, subok=True) sf_lon = sf_lat if omit_coslat else np.cos(self.lat) / u.radian return {'lon': sf_lon, 'lat': sf_lat} def to_cartesian(self): """ Converts spherical polar coordinates to 3D rectangular cartesian coordinates. """ # erfa s2c: Convert [unit]spherical coordinates to Cartesian. p = erfa_ufunc.s2c(self.lon, self.lat) return CartesianRepresentation(p, xyz_axis=-1, copy=False) @classmethod def from_cartesian(cls, cart): """ Converts 3D rectangular cartesian coordinates to spherical polar coordinates. """ p = cart.get_xyz(xyz_axis=-1) # erfa c2s: P-vector to [unit]spherical coordinates. return cls(*erfa_ufunc.c2s(p), copy=False) def represent_as(self, other_class, differential_class=None): # Take a short cut if the other class is a spherical representation # TODO! for differential_class. This cannot (currently) be implemented # like in the other Representations since `_re_represent_differentials` # keeps differentials' unit keys, but this can result in a mismatch # between the UnitSpherical expected key (e.g. "s") and that expected # in the other class (here "s / m"). For more info, see PR #11467 if inspect.isclass(other_class) and not differential_class: if issubclass(other_class, PhysicsSphericalRepresentation): return other_class(phi=self.lon, theta=90 * u.deg - self.lat, r=1.0, copy=False) elif issubclass(other_class, SphericalRepresentation): return other_class(lon=self.lon, lat=self.lat, distance=1.0, copy=False) return super().represent_as(other_class, differential_class) def transform(self, matrix): r"""Transform the unit-spherical coordinates using a 3x3 matrix. This returns a new representation and does not modify the original one. Any differentials attached to this representation will also be transformed. Parameters ---------- matrix : (3,3) array-like A 3x3 matrix, such as a rotation matrix (or a stack of matrices). Returns ------- `UnitSphericalRepresentation` or `SphericalRepresentation` If ``matrix`` is O(3) -- :math:`M \dot M^T = I` -- like a rotation, then the result is a `UnitSphericalRepresentation`. All other matrices will change the distance, so the dimensional representation is used instead. """ # the transformation matrix does not need to be a rotation matrix, # so the unit-distance is not guaranteed. For speed, we check if the # matrix is in O(3) and preserves lengths. if np.all(is_O3(matrix)): # remain in unit-rep xyz = erfa_ufunc.s2c(self.lon, self.lat) p = erfa_ufunc.rxp(matrix, xyz) lon, lat = erfa_ufunc.c2s(p) rep = self.__class__(lon=lon, lat=lat) # handle differentials new_diffs = dict((k, d.transform(matrix, self, rep)) for k, d in self.differentials.items()) rep = rep.with_differentials(new_diffs) else: # switch to dimensional representation rep = self._dimensional_representation( lon=self.lon, lat=self.lat, distance=1, differentials=self.differentials ).transform(matrix) return rep def _scale_operation(self, op, *args): return self._dimensional_representation( lon=self.lon, lat=self.lat, distance=1., differentials=self.differentials)._scale_operation(op, *args) def __neg__(self): if any(differential.base_representation is not self.__class__ for differential in self.differentials.values()): return super().__neg__() result = self.__class__(self.lon + 180. * u.deg, -self.lat, copy=False) for key, differential in self.differentials.items(): new_comps = (op(getattr(differential, comp)) for op, comp in zip((operator.pos, operator.neg), differential.components)) result.differentials[key] = differential.__class__(*new_comps, copy=False) return result def norm(self): """Vector norm. The norm is the standard Frobenius norm, i.e., the square root of the sum of the squares of all components with non-angular units, which is always unity for vectors on the unit sphere. Returns ------- norm : `~astropy.units.Quantity` ['dimensionless'] Dimensionless ones, with the same shape as the representation. """ return u.Quantity(np.ones(self.shape), u.dimensionless_unscaled, copy=False) def _combine_operation(self, op, other, reverse=False): self._raise_if_has_differentials(op.__name__) result = self.to_cartesian()._combine_operation(op, other, reverse) if result is NotImplemented: return NotImplemented else: return self._dimensional_representation.from_cartesian(result) def mean(self, *args, **kwargs): """Vector mean. The representation is converted to cartesian, the means of the x, y, and z components are calculated, and the result is converted to a `~astropy.coordinates.SphericalRepresentation`. Refer to `~numpy.mean` for full documentation of the arguments, noting that ``axis`` is the entry in the ``shape`` of the representation, and that the ``out`` argument cannot be used. """ self._raise_if_has_differentials('mean') return self._dimensional_representation.from_cartesian( self.to_cartesian().mean(*args, **kwargs)) def sum(self, *args, **kwargs): """Vector sum. The representation is converted to cartesian, the sums of the x, y, and z components are calculated, and the result is converted to a `~astropy.coordinates.SphericalRepresentation`. Refer to `~numpy.sum` for full documentation of the arguments, noting that ``axis`` is the entry in the ``shape`` of the representation, and that the ``out`` argument cannot be used. """ self._raise_if_has_differentials('sum') return self._dimensional_representation.from_cartesian( self.to_cartesian().sum(*args, **kwargs)) def cross(self, other): """Cross product of two representations. The calculation is done by converting both ``self`` and ``other`` to `~astropy.coordinates.CartesianRepresentation`, and converting the result back to `~astropy.coordinates.SphericalRepresentation`. Parameters ---------- other : `~astropy.coordinates.BaseRepresentation` subclass instance The representation to take the cross product with. Returns ------- cross_product : `~astropy.coordinates.SphericalRepresentation` With vectors perpendicular to both ``self`` and ``other``. """ self._raise_if_has_differentials('cross') return self._dimensional_representation.from_cartesian( self.to_cartesian().cross(other)) class RadialRepresentation(BaseRepresentation): """ Representation of the distance of points from the origin. Note that this is mostly intended as an internal helper representation. It can do little else but being used as a scale in multiplication. Parameters ---------- distance : `~astropy.units.Quantity` ['length'] The distance of the point(s) from the origin. differentials : dict, `~astropy.coordinates.BaseDifferential`, optional Any differential classes that should be associated with this representation. The input must either be a single `~astropy.coordinates.BaseDifferential` instance (see `._compatible_differentials` for valid types), or a dictionary of of differential instances with keys set to a string representation of the SI unit with which the differential (derivative) is taken. For example, for a velocity differential on a positional representation, the key would be ``'s'`` for seconds, indicating that the derivative is a time derivative. copy : bool, optional If `True` (default), arrays will be copied. If `False`, arrays will be references, though possibly broadcast to ensure matching shapes. """ attr_classes = {'distance': u.Quantity} def __init__(self, distance, differentials=None, copy=True): super().__init__(distance, differentials=differentials, copy=copy) @property def distance(self): """ The distance from the origin to the point(s). """ return self._distance def unit_vectors(self): """Cartesian unit vectors are undefined for radial representation.""" raise NotImplementedError('Cartesian unit vectors are undefined for ' '{} instances'.format(self.__class__)) def scale_factors(self): l = np.broadcast_to(1.*u.one, self.shape, subok=True) return {'distance': l} def to_cartesian(self): """Cannot convert radial representation to cartesian.""" raise NotImplementedError('cannot convert {} instance to cartesian.' .format(self.__class__)) @classmethod def from_cartesian(cls, cart): """ Converts 3D rectangular cartesian coordinates to radial coordinate. """ return cls(distance=cart.norm(), copy=False) def __mul__(self, other): if isinstance(other, BaseRepresentation): return self.distance * other else: return super().__mul__(other) def norm(self): """Vector norm. Just the distance itself. Returns ------- norm : `~astropy.units.Quantity` ['dimensionless'] Dimensionless ones, with the same shape as the representation. """ return self.distance def _combine_operation(self, op, other, reverse=False): return NotImplemented def transform(self, matrix): """Radial representations cannot be transformed by a Cartesian matrix. Parameters ---------- matrix : array-like The transformation matrix in a Cartesian basis. Must be a multiplication: a diagonal matrix with identical elements. Must have shape (..., 3, 3), where the last 2 indices are for the matrix on each other axis. Make sure that the matrix shape is compatible with the shape of this representation. Raises ------ ValueError If the matrix is not a multiplication. """ scl = matrix[..., 0, 0] # check that the matrix is a scaled identity matrix on the last 2 axes. if np.any(matrix != scl[..., np.newaxis, np.newaxis] * np.identity(3)): raise ValueError("Radial representations can only be " "transformed by a scaled identity matrix") return self * scl def _spherical_op_funcs(op, *args): """For given operator, return functions that adjust lon, lat, distance.""" if op is operator.neg: return lambda x: x+180*u.deg, operator.neg, operator.pos try: scale_sign = np.sign(args[0]) except Exception: # This should always work, even if perhaps we get a negative distance. return operator.pos, operator.pos, lambda x: op(x, *args) scale = abs(args[0]) return (lambda x: x + 180*u.deg*np.signbit(scale_sign), lambda x: x * scale_sign, lambda x: op(x, scale)) class SphericalRepresentation(BaseRepresentation): """ Representation of points in 3D spherical coordinates. Parameters ---------- lon, lat : `~astropy.units.Quantity` ['angle'] The longitude and latitude of the point(s), in angular units. The latitude should be between -90 and 90 degrees, and the longitude will be wrapped to an angle between 0 and 360 degrees. These can also be instances of `~astropy.coordinates.Angle`, `~astropy.coordinates.Longitude`, or `~astropy.coordinates.Latitude`. distance : `~astropy.units.Quantity` ['length'] The distance to the point(s). If the distance is a length, it is passed to the :class:`~astropy.coordinates.Distance` class, otherwise it is passed to the :class:`~astropy.units.Quantity` class. differentials : dict, `~astropy.coordinates.BaseDifferential`, optional Any differential classes that should be associated with this representation. The input must either be a single `~astropy.coordinates.BaseDifferential` instance (see `._compatible_differentials` for valid types), or a dictionary of of differential instances with keys set to a string representation of the SI unit with which the differential (derivative) is taken. For example, for a velocity differential on a positional representation, the key would be ``'s'`` for seconds, indicating that the derivative is a time derivative. copy : bool, optional If `True` (default), arrays will be copied. If `False`, arrays will be references, though possibly broadcast to ensure matching shapes. """ attr_classes = {'lon': Longitude, 'lat': Latitude, 'distance': u.Quantity} _unit_representation = UnitSphericalRepresentation def __init__(self, lon, lat=None, distance=None, differentials=None, copy=True): super().__init__(lon, lat, distance, copy=copy, differentials=differentials) if (not isinstance(self._distance, Distance) and self._distance.unit.physical_type == 'length'): try: self._distance = Distance(self._distance, copy=False) except ValueError as e: if e.args[0].startswith('distance must be >= 0'): raise ValueError("Distance must be >= 0. To allow negative " "distance values, you must explicitly pass" " in a `Distance` object with the the " "argument 'allow_negative=True'.") from e else: raise @classproperty def _compatible_differentials(cls): return [UnitSphericalDifferential, UnitSphericalCosLatDifferential, SphericalDifferential, SphericalCosLatDifferential, RadialDifferential] @property def lon(self): """ The longitude of the point(s). """ return self._lon @property def lat(self): """ The latitude of the point(s). """ return self._lat @property def distance(self): """ The distance from the origin to the point(s). """ return self._distance def unit_vectors(self): sinlon, coslon = np.sin(self.lon), np.cos(self.lon) sinlat, coslat = np.sin(self.lat), np.cos(self.lat) return { 'lon': CartesianRepresentation(-sinlon, coslon, 0., copy=False), 'lat': CartesianRepresentation(-sinlat*coslon, -sinlat*sinlon, coslat, copy=False), 'distance': CartesianRepresentation(coslat*coslon, coslat*sinlon, sinlat, copy=False)} def scale_factors(self, omit_coslat=False): sf_lat = self.distance / u.radian sf_lon = sf_lat if omit_coslat else sf_lat * np.cos(self.lat) sf_distance = np.broadcast_to(1.*u.one, self.shape, subok=True) return {'lon': sf_lon, 'lat': sf_lat, 'distance': sf_distance} def represent_as(self, other_class, differential_class=None): # Take a short cut if the other class is a spherical representation if inspect.isclass(other_class): if issubclass(other_class, PhysicsSphericalRepresentation): diffs = self._re_represent_differentials(other_class, differential_class) return other_class(phi=self.lon, theta=90 * u.deg - self.lat, r=self.distance, differentials=diffs, copy=False) elif issubclass(other_class, UnitSphericalRepresentation): diffs = self._re_represent_differentials(other_class, differential_class) return other_class(lon=self.lon, lat=self.lat, differentials=diffs, copy=False) return super().represent_as(other_class, differential_class) def to_cartesian(self): """ Converts spherical polar coordinates to 3D rectangular cartesian coordinates. """ # We need to convert Distance to Quantity to allow negative values. if isinstance(self.distance, Distance): d = self.distance.view(u.Quantity) else: d = self.distance # erfa s2p: Convert spherical polar coordinates to p-vector. p = erfa_ufunc.s2p(self.lon, self.lat, d) return CartesianRepresentation(p, xyz_axis=-1, copy=False) @classmethod def from_cartesian(cls, cart): """ Converts 3D rectangular cartesian coordinates to spherical polar coordinates. """ p = cart.get_xyz(xyz_axis=-1) # erfa p2s: P-vector to spherical polar coordinates. return cls(*erfa_ufunc.p2s(p), copy=False) def transform(self, matrix): """Transform the spherical coordinates using a 3x3 matrix. This returns a new representation and does not modify the original one. Any differentials attached to this representation will also be transformed. Parameters ---------- matrix : (3,3) array-like A 3x3 matrix, such as a rotation matrix (or a stack of matrices). """ xyz = erfa_ufunc.s2c(self.lon, self.lat) p = erfa_ufunc.rxp(matrix, xyz) lon, lat, ur = erfa_ufunc.p2s(p) rep = self.__class__(lon=lon, lat=lat, distance=self.distance * ur) # handle differentials new_diffs = dict((k, d.transform(matrix, self, rep)) for k, d in self.differentials.items()) return rep.with_differentials(new_diffs) def norm(self): """Vector norm. The norm is the standard Frobenius norm, i.e., the square root of the sum of the squares of all components with non-angular units. For spherical coordinates, this is just the absolute value of the distance. Returns ------- norm : `astropy.units.Quantity` Vector norm, with the same shape as the representation. """ return np.abs(self.distance) def _scale_operation(self, op, *args): # TODO: expand special-casing to UnitSpherical and RadialDifferential. if any(differential.base_representation is not self.__class__ for differential in self.differentials.values()): return super()._scale_operation(op, *args) lon_op, lat_op, distance_op = _spherical_op_funcs(op, *args) result = self.__class__(lon_op(self.lon), lat_op(self.lat), distance_op(self.distance), copy=False) for key, differential in self.differentials.items(): new_comps = (op(getattr(differential, comp)) for op, comp in zip( (operator.pos, lat_op, distance_op), differential.components)) result.differentials[key] = differential.__class__(*new_comps, copy=False) return result class PhysicsSphericalRepresentation(BaseRepresentation): """ Representation of points in 3D spherical coordinates (using the physics convention of using ``phi`` and ``theta`` for azimuth and inclination from the pole). Parameters ---------- phi, theta : `~astropy.units.Quantity` or str The azimuth and inclination of the point(s), in angular units. The inclination should be between 0 and 180 degrees, and the azimuth will be wrapped to an angle between 0 and 360 degrees. These can also be instances of `~astropy.coordinates.Angle`. If ``copy`` is False, `phi` will be changed inplace if it is not between 0 and 360 degrees. r : `~astropy.units.Quantity` The distance to the point(s). If the distance is a length, it is passed to the :class:`~astropy.coordinates.Distance` class, otherwise it is passed to the :class:`~astropy.units.Quantity` class. differentials : dict, `PhysicsSphericalDifferential`, optional Any differential classes that should be associated with this representation. The input must either be a single `PhysicsSphericalDifferential` instance, or a dictionary of of differential instances with keys set to a string representation of the SI unit with which the differential (derivative) is taken. For example, for a velocity differential on a positional representation, the key would be ``'s'`` for seconds, indicating that the derivative is a time derivative. copy : bool, optional If `True` (default), arrays will be copied. If `False`, arrays will be references, though possibly broadcast to ensure matching shapes. """ attr_classes = {'phi': Angle, 'theta': Angle, 'r': u.Quantity} def __init__(self, phi, theta=None, r=None, differentials=None, copy=True): super().__init__(phi, theta, r, copy=copy, differentials=differentials) # Wrap/validate phi/theta # Note that _phi already holds our own copy if copy=True. self._phi.wrap_at(360 * u.deg, inplace=True) # This invalid catch block can be removed when the minimum numpy # version is >= 1.19 (NUMPY_LT_1_19) with np.errstate(invalid='ignore'): if np.any(self._theta < 0.*u.deg) or np.any(self._theta > 180.*u.deg): raise ValueError('Inclination angle(s) must be within ' '0 deg <= angle <= 180 deg, ' 'got {}'.format(theta.to(u.degree))) if self._r.unit.physical_type == 'length': self._r = self._r.view(Distance) @property def phi(self): """ The azimuth of the point(s). """ return self._phi @property def theta(self): """ The elevation of the point(s). """ return self._theta @property def r(self): """ The distance from the origin to the point(s). """ return self._r def unit_vectors(self): sinphi, cosphi = np.sin(self.phi), np.cos(self.phi) sintheta, costheta = np.sin(self.theta), np.cos(self.theta) return { 'phi': CartesianRepresentation(-sinphi, cosphi, 0., copy=False), 'theta': CartesianRepresentation(costheta*cosphi, costheta*sinphi, -sintheta, copy=False), 'r': CartesianRepresentation(sintheta*cosphi, sintheta*sinphi, costheta, copy=False)} def scale_factors(self): r = self.r / u.radian sintheta = np.sin(self.theta) l = np.broadcast_to(1.*u.one, self.shape, subok=True) return {'phi': r * sintheta, 'theta': r, 'r': l} def represent_as(self, other_class, differential_class=None): # Take a short cut if the other class is a spherical representation if inspect.isclass(other_class): if issubclass(other_class, SphericalRepresentation): diffs = self._re_represent_differentials(other_class, differential_class) return other_class(lon=self.phi, lat=90 * u.deg - self.theta, distance=self.r, differentials=diffs, copy=False) elif issubclass(other_class, UnitSphericalRepresentation): diffs = self._re_represent_differentials(other_class, differential_class) return other_class(lon=self.phi, lat=90 * u.deg - self.theta, differentials=diffs, copy=False) return super().represent_as(other_class, differential_class) def to_cartesian(self): """ Converts spherical polar coordinates to 3D rectangular cartesian coordinates. """ # We need to convert Distance to Quantity to allow negative values. if isinstance(self.r, Distance): d = self.r.view(u.Quantity) else: d = self.r x = d * np.sin(self.theta) * np.cos(self.phi) y = d * np.sin(self.theta) * np.sin(self.phi) z = d * np.cos(self.theta) return CartesianRepresentation(x=x, y=y, z=z, copy=False) @classmethod def from_cartesian(cls, cart): """ Converts 3D rectangular cartesian coordinates to spherical polar coordinates. """ s = np.hypot(cart.x, cart.y) r = np.hypot(s, cart.z) phi = np.arctan2(cart.y, cart.x) theta = np.arctan2(s, cart.z) return cls(phi=phi, theta=theta, r=r, copy=False) def transform(self, matrix): """Transform the spherical coordinates using a 3x3 matrix. This returns a new representation and does not modify the original one. Any differentials attached to this representation will also be transformed. Parameters ---------- matrix : (3,3) array-like A 3x3 matrix, such as a rotation matrix (or a stack of matrices). """ # apply transformation in unit-spherical coordinates xyz = erfa_ufunc.s2c(self.phi, 90*u.deg-self.theta) p = erfa_ufunc.rxp(matrix, xyz) lon, lat, ur = erfa_ufunc.p2s(p) # `ur` is transformed unit-`r` # create transformed physics-spherical representation, # reapplying the distance scaling rep = self.__class__(phi=lon, theta=90*u.deg-lat, r=self.r * ur) new_diffs = dict((k, d.transform(matrix, self, rep)) for k, d in self.differentials.items()) return rep.with_differentials(new_diffs) def norm(self): """Vector norm. The norm is the standard Frobenius norm, i.e., the square root of the sum of the squares of all components with non-angular units. For spherical coordinates, this is just the absolute value of the radius. Returns ------- norm : `astropy.units.Quantity` Vector norm, with the same shape as the representation. """ return np.abs(self.r) def _scale_operation(self, op, *args): if any(differential.base_representation is not self.__class__ for differential in self.differentials.values()): return super()._scale_operation(op, *args) phi_op, adjust_theta_sign, r_op = _spherical_op_funcs(op, *args) # Also run phi_op on theta to ensure theta remains between 0 and 180: # any time the scale is negative, we do -theta + 180 degrees. result = self.__class__(phi_op(self.phi), phi_op(adjust_theta_sign(self.theta)), r_op(self.r), copy=False) for key, differential in self.differentials.items(): new_comps = (op(getattr(differential, comp)) for op, comp in zip( (operator.pos, adjust_theta_sign, r_op), differential.components)) result.differentials[key] = differential.__class__(*new_comps, copy=False) return result class CylindricalRepresentation(BaseRepresentation): """ Representation of points in 3D cylindrical coordinates. Parameters ---------- rho : `~astropy.units.Quantity` The distance from the z axis to the point(s). phi : `~astropy.units.Quantity` or str The azimuth of the point(s), in angular units, which will be wrapped to an angle between 0 and 360 degrees. This can also be instances of `~astropy.coordinates.Angle`, z : `~astropy.units.Quantity` The z coordinate(s) of the point(s) differentials : dict, `CylindricalDifferential`, optional Any differential classes that should be associated with this representation. The input must either be a single `CylindricalDifferential` instance, or a dictionary of of differential instances with keys set to a string representation of the SI unit with which the differential (derivative) is taken. For example, for a velocity differential on a positional representation, the key would be ``'s'`` for seconds, indicating that the derivative is a time derivative. copy : bool, optional If `True` (default), arrays will be copied. If `False`, arrays will be references, though possibly broadcast to ensure matching shapes. """ attr_classes = {'rho': u.Quantity, 'phi': Angle, 'z': u.Quantity} def __init__(self, rho, phi=None, z=None, differentials=None, copy=True): super().__init__(rho, phi, z, copy=copy, differentials=differentials) if not self._rho.unit.is_equivalent(self._z.unit): raise u.UnitsError("rho and z should have matching physical types") @property def rho(self): """ The distance of the point(s) from the z-axis. """ return self._rho @property def phi(self): """ The azimuth of the point(s). """ return self._phi @property def z(self): """ The height of the point(s). """ return self._z def unit_vectors(self): sinphi, cosphi = np.sin(self.phi), np.cos(self.phi) l = np.broadcast_to(1., self.shape) return { 'rho': CartesianRepresentation(cosphi, sinphi, 0, copy=False), 'phi': CartesianRepresentation(-sinphi, cosphi, 0, copy=False), 'z': CartesianRepresentation(0, 0, l, unit=u.one, copy=False)} def scale_factors(self): rho = self.rho / u.radian l = np.broadcast_to(1.*u.one, self.shape, subok=True) return {'rho': l, 'phi': rho, 'z': l} @classmethod def from_cartesian(cls, cart): """ Converts 3D rectangular cartesian coordinates to cylindrical polar coordinates. """ rho = np.hypot(cart.x, cart.y) phi = np.arctan2(cart.y, cart.x) z = cart.z return cls(rho=rho, phi=phi, z=z, copy=False) def to_cartesian(self): """ Converts cylindrical polar coordinates to 3D rectangular cartesian coordinates. """ x = self.rho * np.cos(self.phi) y = self.rho * np.sin(self.phi) z = self.z return CartesianRepresentation(x=x, y=y, z=z, copy=False) def _scale_operation(self, op, *args): if any(differential.base_representation is not self.__class__ for differential in self.differentials.values()): return super()._scale_operation(op, *args) phi_op, _, rho_op = _spherical_op_funcs(op, *args) z_op = lambda x: op(x, *args) result = self.__class__(rho_op(self.rho), phi_op(self.phi), z_op(self.z), copy=False) for key, differential in self.differentials.items(): new_comps = (op(getattr(differential, comp)) for op, comp in zip( (rho_op, operator.pos, z_op), differential.components)) result.differentials[key] = differential.__class__(*new_comps, copy=False) return result class BaseDifferential(BaseRepresentationOrDifferential): r"""A base class representing differentials of representations. These represent differences or derivatives along each component. E.g., for physics spherical coordinates, these would be :math:`\delta r, \delta \theta, \delta \phi`. Parameters ---------- d_comp1, d_comp2, d_comp3 : `~astropy.units.Quantity` or subclass The components of the 3D differentials. The names are the keys and the subclasses the values of the ``attr_classes`` attribute. copy : bool, optional If `True` (default), arrays will be copied. If `False`, arrays will be references, though possibly broadcast to ensure matching shapes. Notes ----- All differential representation classes should subclass this base class, and define an ``base_representation`` attribute with the class of the regular `~astropy.coordinates.BaseRepresentation` for which differential coordinates are provided. This will set up a default ``attr_classes`` instance with names equal to the base component names prefixed by ``d_``, and all classes set to `~astropy.units.Quantity`, plus properties to access those, and a default ``__init__`` for initialization. """ def __init_subclass__(cls, **kwargs): """Set default ``attr_classes`` and component getters on a Differential. class BaseDifferential(BaseRepresentationOrDifferential): For these, the components are those of the base representation prefixed by 'd_', and the class is `~astropy.units.Quantity`. """ # Don't do anything for base helper classes. if cls.__name__ in ('BaseDifferential', 'BaseSphericalDifferential', 'BaseSphericalCosLatDifferential'): return if not hasattr(cls, 'base_representation'): raise NotImplementedError('Differential representations must have a' '"base_representation" class attribute.') # If not defined explicitly, create attr_classes. if not hasattr(cls, 'attr_classes'): base_attr_classes = cls.base_representation.attr_classes cls.attr_classes = {'d_' + c: u.Quantity for c in base_attr_classes} repr_name = cls.get_name() if repr_name in DIFFERENTIAL_CLASSES: raise ValueError(f"Differential class {repr_name} already defined") DIFFERENTIAL_CLASSES[repr_name] = cls _invalidate_reprdiff_cls_hash() # If not defined explicitly, create properties for the components. for component in cls.attr_classes: if not hasattr(cls, component): setattr(cls, component, property(_make_getter(component), doc=f"Component '{component}' of the Differential.")) super().__init_subclass__(**kwargs) @classmethod def _check_base(cls, base): if cls not in base._compatible_differentials: raise TypeError(f"Differential class {cls} is not compatible with the " f"base (representation) class {base.__class__}") def _get_deriv_key(self, base): """Given a base (representation instance), determine the unit of the derivative by removing the representation unit from the component units of this differential. """ # This check is just a last resort so we don't return a strange unit key # from accidentally passing in the wrong base. self._check_base(base) for name in base.components: comp = getattr(base, name) d_comp = getattr(self, f'd_{name}', None) if d_comp is not None: d_unit = comp.unit / d_comp.unit # This is quite a bit faster than using to_system() or going # through Quantity() d_unit_si = d_unit.decompose(u.si.bases) d_unit_si._scale = 1 # remove the scale from the unit return str(d_unit_si) else: raise RuntimeError("Invalid representation-differential units! This" " likely happened because either the " "representation or the associated differential " "have non-standard units. Check that the input " "positional data have positional units, and the " "input velocity data have velocity units, or " "are both dimensionless.") @classmethod def _get_base_vectors(cls, base): """Get unit vectors and scale factors from base. Parameters ---------- base : instance of ``self.base_representation`` The points for which the unit vectors and scale factors should be retrieved. Returns ------- unit_vectors : dict of `CartesianRepresentation` In the directions of the coordinates of base. scale_factors : dict of `~astropy.units.Quantity` Scale factors for each of the coordinates Raises ------ TypeError : if the base is not of the correct type """ cls._check_base(base) return base.unit_vectors(), base.scale_factors() def to_cartesian(self, base): """Convert the differential to 3D rectangular cartesian coordinates. Parameters ---------- base : instance of ``self.base_representation`` The points for which the differentials are to be converted: each of the components is multiplied by its unit vectors and scale factors. Returns ------- `CartesianDifferential` This object, converted. """ base_e, base_sf = self._get_base_vectors(base) return functools.reduce( operator.add, (getattr(self, d_c) * base_sf[c] * base_e[c] for d_c, c in zip(self.components, base.components))) @classmethod def from_cartesian(cls, other, base): """Convert the differential from 3D rectangular cartesian coordinates to the desired class. Parameters ---------- other The object to convert into this differential. base : `BaseRepresentation` The points for which the differentials are to be converted: each of the components is multiplied by its unit vectors and scale factors. Will be converted to ``cls.base_representation`` if needed. Returns ------- `BaseDifferential` subclass instance A new differential object that is this class' type. """ base = base.represent_as(cls.base_representation) base_e, base_sf = cls._get_base_vectors(base) return cls(*(other.dot(e / base_sf[component]) for component, e in base_e.items()), copy=False) def represent_as(self, other_class, base): """Convert coordinates to another representation. If the instance is of the requested class, it is returned unmodified. By default, conversion is done via cartesian coordinates. Parameters ---------- other_class : `~astropy.coordinates.BaseRepresentation` subclass The type of representation to turn the coordinates into. base : instance of ``self.base_representation`` Base relative to which the differentials are defined. If the other class is a differential representation, the base will be converted to its ``base_representation``. """ if other_class is self.__class__: return self # The default is to convert via cartesian coordinates. self_cartesian = self.to_cartesian(base) if issubclass(other_class, BaseDifferential): return other_class.from_cartesian(self_cartesian, base) else: return other_class.from_cartesian(self_cartesian) @classmethod def from_representation(cls, representation, base): """Create a new instance of this representation from another one. Parameters ---------- representation : `~astropy.coordinates.BaseRepresentation` instance The presentation that should be converted to this class. base : instance of ``cls.base_representation`` The base relative to which the differentials will be defined. If the representation is a differential itself, the base will be converted to its ``base_representation`` to help convert it. """ if isinstance(representation, BaseDifferential): cartesian = representation.to_cartesian( base.represent_as(representation.base_representation)) else: cartesian = representation.to_cartesian() return cls.from_cartesian(cartesian, base) def transform(self, matrix, base, transformed_base): """Transform differential using a 3x3 matrix in a Cartesian basis. This returns a new differential and does not modify the original one. Parameters ---------- matrix : (3,3) array-like A 3x3 (or stack thereof) matrix, such as a rotation matrix. base : instance of ``cls.base_representation`` Base relative to which the differentials are defined. If the other class is a differential representation, the base will be converted to its ``base_representation``. transformed_base : instance of ``cls.base_representation`` Base relative to which the transformed differentials are defined. If the other class is a differential representation, the base will be converted to its ``base_representation``. """ # route transformation through Cartesian cdiff = self.represent_as(CartesianDifferential, base=base ).transform(matrix) # move back to original representation diff = cdiff.represent_as(self.__class__, transformed_base) return diff def _scale_operation(self, op, *args, scaled_base=False): """Scale all components. Parameters ---------- op : `~operator` callable Operator to apply (e.g., `~operator.mul`, `~operator.neg`, etc. *args Any arguments required for the operator (typically, what is to be multiplied with, divided by). scaled_base : bool, optional Whether the base was scaled the same way. This affects whether differential components should be scaled. For instance, a differential in longitude should not be scaled if its spherical base is scaled in radius. """ scaled_attrs = [op(getattr(self, c), *args) for c in self.components] return self.__class__(*scaled_attrs, copy=False) def _combine_operation(self, op, other, reverse=False): """Combine two differentials, or a differential with a representation. If ``other`` is of the same differential type as ``self``, the components will simply be combined. If ``other`` is a representation, it will be used as a base for which to evaluate the differential, and the result is a new representation. Parameters ---------- op : `~operator` callable Operator to apply (e.g., `~operator.add`, `~operator.sub`, etc. other : `~astropy.coordinates.BaseRepresentation` subclass instance The other differential or representation. reverse : bool Whether the operands should be reversed (e.g., as we got here via ``self.__rsub__`` because ``self`` is a subclass of ``other``). """ if isinstance(self, type(other)): first, second = (self, other) if not reverse else (other, self) return self.__class__(*[op(getattr(first, c), getattr(second, c)) for c in self.components]) else: try: self_cartesian = self.to_cartesian(other) except TypeError: return NotImplemented return other._combine_operation(op, self_cartesian, not reverse) def __sub__(self, other): # avoid "differential - representation". if isinstance(other, BaseRepresentation): return NotImplemented return super().__sub__(other) def norm(self, base=None): """Vector norm. The norm is the standard Frobenius norm, i.e., the square root of the sum of the squares of all components with non-angular units. Parameters ---------- base : instance of ``self.base_representation`` Base relative to which the differentials are defined. This is required to calculate the physical size of the differential for all but Cartesian differentials or radial differentials. Returns ------- norm : `astropy.units.Quantity` Vector norm, with the same shape as the representation. """ # RadialDifferential overrides this function, so there is no handling here if not isinstance(self, CartesianDifferential) and base is None: raise ValueError("`base` must be provided to calculate the norm of a" f" {type(self).__name__}") return self.to_cartesian(base).norm() class CartesianDifferential(BaseDifferential): """Differentials in of points in 3D cartesian coordinates. Parameters ---------- d_x, d_y, d_z : `~astropy.units.Quantity` or array The x, y, and z coordinates of the differentials. If ``d_x``, ``d_y``, and ``d_z`` have different shapes, they should be broadcastable. If not quantities, ``unit`` should be set. If only ``d_x`` is given, it is assumed that it contains an array with the 3 coordinates stored along ``xyz_axis``. unit : `~astropy.units.Unit` or str If given, the differentials will be converted to this unit (or taken to be in this unit if not given. xyz_axis : int, optional The axis along which the coordinates are stored when a single array is provided instead of distinct ``d_x``, ``d_y``, and ``d_z`` (default: 0). copy : bool, optional If `True` (default), arrays will be copied. If `False`, arrays will be references, though possibly broadcast to ensure matching shapes. """ base_representation = CartesianRepresentation _d_xyz = None def __init__(self, d_x, d_y=None, d_z=None, unit=None, xyz_axis=None, copy=True): if d_y is None and d_z is None: if isinstance(d_x, np.ndarray) and d_x.dtype.kind not in 'OV': # Short-cut for 3-D array input. d_x = u.Quantity(d_x, unit, copy=copy, subok=True) # Keep a link to the array with all three coordinates # so that we can return it quickly if needed in get_xyz. self._d_xyz = d_x if xyz_axis: d_x = np.moveaxis(d_x, xyz_axis, 0) self._xyz_axis = xyz_axis else: self._xyz_axis = 0 self._d_x, self._d_y, self._d_z = d_x return else: d_x, d_y, d_z = d_x if xyz_axis is not None: raise ValueError("xyz_axis should only be set if d_x, d_y, and d_z " "are in a single array passed in through d_x, " "i.e., d_y and d_z should not be not given.") if d_y is None or d_z is None: raise ValueError("d_x, d_y, and d_z are required to instantiate {}" .format(self.__class__.__name__)) if unit is not None: d_x = u.Quantity(d_x, unit, copy=copy, subok=True) d_y = u.Quantity(d_y, unit, copy=copy, subok=True) d_z = u.Quantity(d_z, unit, copy=copy, subok=True) copy = False super().__init__(d_x, d_y, d_z, copy=copy) if not (self._d_x.unit.is_equivalent(self._d_y.unit) and self._d_x.unit.is_equivalent(self._d_z.unit)): raise u.UnitsError('d_x, d_y and d_z should have equivalent units.') def to_cartesian(self, base=None): return CartesianRepresentation(*[getattr(self, c) for c in self.components]) @classmethod def from_cartesian(cls, other, base=None): return cls(*[getattr(other, c) for c in other.components]) def transform(self, matrix, base=None, transformed_base=None): """Transform differentials using a 3x3 matrix in a Cartesian basis. This returns a new differential and does not modify the original one. Parameters ---------- matrix : (3,3) array-like A 3x3 (or stack thereof) matrix, such as a rotation matrix. base, transformed_base : `~astropy.coordinates.CartesianRepresentation` or None, optional Not used in the Cartesian transformation. """ # erfa rxp: Multiply a p-vector by an r-matrix. p = erfa_ufunc.rxp(matrix, self.get_d_xyz(xyz_axis=-1)) return self.__class__(p, xyz_axis=-1, copy=False) def get_d_xyz(self, xyz_axis=0): """Return a vector array of the x, y, and z coordinates. Parameters ---------- xyz_axis : int, optional The axis in the final array along which the x, y, z components should be stored (default: 0). Returns ------- d_xyz : `~astropy.units.Quantity` With dimension 3 along ``xyz_axis``. Note that, if possible, this will be a view. """ if self._d_xyz is not None: if self._xyz_axis == xyz_axis: return self._d_xyz else: return np.moveaxis(self._d_xyz, self._xyz_axis, xyz_axis) # Create combined array. TO DO: keep it in _d_xyz for repeated use? # But then in-place changes have to cancel it. Likely best to # also update components. return np.stack([self._d_x, self._d_y, self._d_z], axis=xyz_axis) d_xyz = property(get_d_xyz) class BaseSphericalDifferential(BaseDifferential): def _d_lon_coslat(self, base): """Convert longitude differential d_lon to d_lon_coslat. Parameters ---------- base : instance of ``cls.base_representation`` The base from which the latitude will be taken. """ self._check_base(base) return self.d_lon * np.cos(base.lat) @classmethod def _get_d_lon(cls, d_lon_coslat, base): """Convert longitude differential d_lon_coslat to d_lon. Parameters ---------- d_lon_coslat : `~astropy.units.Quantity` Longitude differential that includes ``cos(lat)``. base : instance of ``cls.base_representation`` The base from which the latitude will be taken. """ cls._check_base(base) return d_lon_coslat / np.cos(base.lat) def _combine_operation(self, op, other, reverse=False): """Combine two differentials, or a differential with a representation. If ``other`` is of the same differential type as ``self``, the components will simply be combined. If both are different parts of a `~astropy.coordinates.SphericalDifferential` (e.g., a `~astropy.coordinates.UnitSphericalDifferential` and a `~astropy.coordinates.RadialDifferential`), they will combined appropriately. If ``other`` is a representation, it will be used as a base for which to evaluate the differential, and the result is a new representation. Parameters ---------- op : `~operator` callable Operator to apply (e.g., `~operator.add`, `~operator.sub`, etc. other : `~astropy.coordinates.BaseRepresentation` subclass instance The other differential or representation. reverse : bool Whether the operands should be reversed (e.g., as we got here via ``self.__rsub__`` because ``self`` is a subclass of ``other``). """ if (isinstance(other, BaseSphericalDifferential) and not isinstance(self, type(other)) or isinstance(other, RadialDifferential)): all_components = set(self.components) | set(other.components) first, second = (self, other) if not reverse else (other, self) result_args = {c: op(getattr(first, c, 0.), getattr(second, c, 0.)) for c in all_components} return SphericalDifferential(**result_args) return super()._combine_operation(op, other, reverse) class UnitSphericalDifferential(BaseSphericalDifferential): """Differential(s) of points on a unit sphere. Parameters ---------- d_lon, d_lat : `~astropy.units.Quantity` The longitude and latitude of the differentials. copy : bool, optional If `True` (default), arrays will be copied. If `False`, arrays will be references, though possibly broadcast to ensure matching shapes. """ base_representation = UnitSphericalRepresentation @classproperty def _dimensional_differential(cls): return SphericalDifferential def __init__(self, d_lon, d_lat=None, copy=True): super().__init__(d_lon, d_lat, copy=copy) if not self._d_lon.unit.is_equivalent(self._d_lat.unit): raise u.UnitsError('d_lon and d_lat should have equivalent units.') @classmethod def from_cartesian(cls, other, base): # Go via the dimensional equivalent, so that the longitude and latitude # differentials correctly take into account the norm of the base. dimensional = cls._dimensional_differential.from_cartesian(other, base) return dimensional.represent_as(cls) def to_cartesian(self, base): if isinstance(base, SphericalRepresentation): scale = base.distance elif isinstance(base, PhysicsSphericalRepresentation): scale = base.r else: return super().to_cartesian(base) base = base.represent_as(UnitSphericalRepresentation) return scale * super().to_cartesian(base) def represent_as(self, other_class, base=None): # Only have enough information to represent other unit-spherical. if issubclass(other_class, UnitSphericalCosLatDifferential): return other_class(self._d_lon_coslat(base), self.d_lat) return super().represent_as(other_class, base) @classmethod def from_representation(cls, representation, base=None): # All spherical differentials can be done without going to Cartesian, # though CosLat needs base for the latitude. if isinstance(representation, SphericalDifferential): return cls(representation.d_lon, representation.d_lat) elif isinstance(representation, (SphericalCosLatDifferential, UnitSphericalCosLatDifferential)): d_lon = cls._get_d_lon(representation.d_lon_coslat, base) return cls(d_lon, representation.d_lat) elif isinstance(representation, PhysicsSphericalDifferential): return cls(representation.d_phi, -representation.d_theta) return super().from_representation(representation, base) def transform(self, matrix, base, transformed_base): """Transform differential using a 3x3 matrix in a Cartesian basis. This returns a new differential and does not modify the original one. Parameters ---------- matrix : (3,3) array-like A 3x3 (or stack thereof) matrix, such as a rotation matrix. base : instance of ``cls.base_representation`` Base relative to which the differentials are defined. If the other class is a differential representation, the base will be converted to its ``base_representation``. transformed_base : instance of ``cls.base_representation`` Base relative to which the transformed differentials are defined. If the other class is a differential representation, the base will be converted to its ``base_representation``. """ # the transformation matrix does not need to be a rotation matrix, # so the unit-distance is not guaranteed. For speed, we check if the # matrix is in O(3) and preserves lengths. if np.all(is_O3(matrix)): # remain in unit-rep # TODO! implement without Cartesian intermediate step. # some of this can be moved to the parent class. diff = super().transform(matrix, base, transformed_base) else: # switch to dimensional representation du = self.d_lon.unit / base.lon.unit # derivative unit diff = self._dimensional_differential( d_lon=self.d_lon, d_lat=self.d_lat, d_distance=0 * du ).transform(matrix, base, transformed_base) return diff def _scale_operation(self, op, *args, scaled_base=False): if scaled_base: return self.copy() else: return super()._scale_operation(op, *args) class SphericalDifferential(BaseSphericalDifferential): """Differential(s) of points in 3D spherical coordinates. Parameters ---------- d_lon, d_lat : `~astropy.units.Quantity` The differential longitude and latitude. d_distance : `~astropy.units.Quantity` The differential distance. copy : bool, optional If `True` (default), arrays will be copied. If `False`, arrays will be references, though possibly broadcast to ensure matching shapes. """ base_representation = SphericalRepresentation _unit_differential = UnitSphericalDifferential def __init__(self, d_lon, d_lat=None, d_distance=None, copy=True): super().__init__(d_lon, d_lat, d_distance, copy=copy) if not self._d_lon.unit.is_equivalent(self._d_lat.unit): raise u.UnitsError('d_lon and d_lat should have equivalent units.') def represent_as(self, other_class, base=None): # All spherical differentials can be done without going to Cartesian, # though CosLat needs base for the latitude. if issubclass(other_class, UnitSphericalDifferential): return other_class(self.d_lon, self.d_lat) elif issubclass(other_class, RadialDifferential): return other_class(self.d_distance) elif issubclass(other_class, SphericalCosLatDifferential): return other_class(self._d_lon_coslat(base), self.d_lat, self.d_distance) elif issubclass(other_class, UnitSphericalCosLatDifferential): return other_class(self._d_lon_coslat(base), self.d_lat) elif issubclass(other_class, PhysicsSphericalDifferential): return other_class(self.d_lon, -self.d_lat, self.d_distance) else: return super().represent_as(other_class, base) @classmethod def from_representation(cls, representation, base=None): # Other spherical differentials can be done without going to Cartesian, # though CosLat needs base for the latitude. if isinstance(representation, SphericalCosLatDifferential): d_lon = cls._get_d_lon(representation.d_lon_coslat, base) return cls(d_lon, representation.d_lat, representation.d_distance) elif isinstance(representation, PhysicsSphericalDifferential): return cls(representation.d_phi, -representation.d_theta, representation.d_r) return super().from_representation(representation, base) def _scale_operation(self, op, *args, scaled_base=False): if scaled_base: return self.__class__(self.d_lon, self.d_lat, op(self.d_distance, *args)) else: return super()._scale_operation(op, *args) class BaseSphericalCosLatDifferential(BaseDifferential): """Differentials from points on a spherical base representation. With cos(lat) assumed to be included in the longitude differential. """ @classmethod def _get_base_vectors(cls, base): """Get unit vectors and scale factors from (unit)spherical base. Parameters ---------- base : instance of ``self.base_representation`` The points for which the unit vectors and scale factors should be retrieved. Returns ------- unit_vectors : dict of `CartesianRepresentation` In the directions of the coordinates of base. scale_factors : dict of `~astropy.units.Quantity` Scale factors for each of the coordinates. The scale factor for longitude does not include the cos(lat) factor. Raises ------ TypeError : if the base is not of the correct type """ cls._check_base(base) return base.unit_vectors(), base.scale_factors(omit_coslat=True) def _d_lon(self, base): """Convert longitude differential with cos(lat) to one without. Parameters ---------- base : instance of ``cls.base_representation`` The base from which the latitude will be taken. """ self._check_base(base) return self.d_lon_coslat / np.cos(base.lat) @classmethod def _get_d_lon_coslat(cls, d_lon, base): """Convert longitude differential d_lon to d_lon_coslat. Parameters ---------- d_lon : `~astropy.units.Quantity` Value of the longitude differential without ``cos(lat)``. base : instance of ``cls.base_representation`` The base from which the latitude will be taken. """ cls._check_base(base) return d_lon * np.cos(base.lat) def _combine_operation(self, op, other, reverse=False): """Combine two differentials, or a differential with a representation. If ``other`` is of the same differential type as ``self``, the components will simply be combined. If both are different parts of a `~astropy.coordinates.SphericalDifferential` (e.g., a `~astropy.coordinates.UnitSphericalDifferential` and a `~astropy.coordinates.RadialDifferential`), they will combined appropriately. If ``other`` is a representation, it will be used as a base for which to evaluate the differential, and the result is a new representation. Parameters ---------- op : `~operator` callable Operator to apply (e.g., `~operator.add`, `~operator.sub`, etc. other : `~astropy.coordinates.BaseRepresentation` subclass instance The other differential or representation. reverse : bool Whether the operands should be reversed (e.g., as we got here via ``self.__rsub__`` because ``self`` is a subclass of ``other``). """ if (isinstance(other, BaseSphericalCosLatDifferential) and not isinstance(self, type(other)) or isinstance(other, RadialDifferential)): all_components = set(self.components) | set(other.components) first, second = (self, other) if not reverse else (other, self) result_args = {c: op(getattr(first, c, 0.), getattr(second, c, 0.)) for c in all_components} return SphericalCosLatDifferential(**result_args) return super()._combine_operation(op, other, reverse) class UnitSphericalCosLatDifferential(BaseSphericalCosLatDifferential): """Differential(s) of points on a unit sphere. Parameters ---------- d_lon_coslat, d_lat : `~astropy.units.Quantity` The longitude and latitude of the differentials. copy : bool, optional If `True` (default), arrays will be copied. If `False`, arrays will be references, though possibly broadcast to ensure matching shapes. """ base_representation = UnitSphericalRepresentation attr_classes = {'d_lon_coslat': u.Quantity, 'd_lat': u.Quantity} @classproperty def _dimensional_differential(cls): return SphericalCosLatDifferential def __init__(self, d_lon_coslat, d_lat=None, copy=True): super().__init__(d_lon_coslat, d_lat, copy=copy) if not self._d_lon_coslat.unit.is_equivalent(self._d_lat.unit): raise u.UnitsError('d_lon_coslat and d_lat should have equivalent ' 'units.') @classmethod def from_cartesian(cls, other, base): # Go via the dimensional equivalent, so that the longitude and latitude # differentials correctly take into account the norm of the base. dimensional = cls._dimensional_differential.from_cartesian(other, base) return dimensional.represent_as(cls) def to_cartesian(self, base): if isinstance(base, SphericalRepresentation): scale = base.distance elif isinstance(base, PhysicsSphericalRepresentation): scale = base.r else: return super().to_cartesian(base) base = base.represent_as(UnitSphericalRepresentation) return scale * super().to_cartesian(base) def represent_as(self, other_class, base=None): # Only have enough information to represent other unit-spherical. if issubclass(other_class, UnitSphericalDifferential): return other_class(self._d_lon(base), self.d_lat) return super().represent_as(other_class, base) @classmethod def from_representation(cls, representation, base=None): # All spherical differentials can be done without going to Cartesian, # though w/o CosLat needs base for the latitude. if isinstance(representation, SphericalCosLatDifferential): return cls(representation.d_lon_coslat, representation.d_lat) elif isinstance(representation, (SphericalDifferential, UnitSphericalDifferential)): d_lon_coslat = cls._get_d_lon_coslat(representation.d_lon, base) return cls(d_lon_coslat, representation.d_lat) elif isinstance(representation, PhysicsSphericalDifferential): d_lon_coslat = cls._get_d_lon_coslat(representation.d_phi, base) return cls(d_lon_coslat, -representation.d_theta) return super().from_representation(representation, base) def transform(self, matrix, base, transformed_base): """Transform differential using a 3x3 matrix in a Cartesian basis. This returns a new differential and does not modify the original one. Parameters ---------- matrix : (3,3) array-like A 3x3 (or stack thereof) matrix, such as a rotation matrix. base : instance of ``cls.base_representation`` Base relative to which the differentials are defined. If the other class is a differential representation, the base will be converted to its ``base_representation``. transformed_base : instance of ``cls.base_representation`` Base relative to which the transformed differentials are defined. If the other class is a differential representation, the base will be converted to its ``base_representation``. """ # the transformation matrix does not need to be a rotation matrix, # so the unit-distance is not guaranteed. For speed, we check if the # matrix is in O(3) and preserves lengths. if np.all(is_O3(matrix)): # remain in unit-rep # TODO! implement without Cartesian intermediate step. diff = super().transform(matrix, base, transformed_base) else: # switch to dimensional representation du = self.d_lat.unit / base.lat.unit # derivative unit diff = self._dimensional_differential( d_lon_coslat=self.d_lon_coslat, d_lat=self.d_lat, d_distance=0 * du ).transform(matrix, base, transformed_base) return diff def _scale_operation(self, op, *args, scaled_base=False): if scaled_base: return self.copy() else: return super()._scale_operation(op, *args) class SphericalCosLatDifferential(BaseSphericalCosLatDifferential): """Differential(s) of points in 3D spherical coordinates. Parameters ---------- d_lon_coslat, d_lat : `~astropy.units.Quantity` The differential longitude (with cos(lat) included) and latitude. d_distance : `~astropy.units.Quantity` The differential distance. copy : bool, optional If `True` (default), arrays will be copied. If `False`, arrays will be references, though possibly broadcast to ensure matching shapes. """ base_representation = SphericalRepresentation _unit_differential = UnitSphericalCosLatDifferential attr_classes = {'d_lon_coslat': u.Quantity, 'd_lat': u.Quantity, 'd_distance': u.Quantity} def __init__(self, d_lon_coslat, d_lat=None, d_distance=None, copy=True): super().__init__(d_lon_coslat, d_lat, d_distance, copy=copy) if not self._d_lon_coslat.unit.is_equivalent(self._d_lat.unit): raise u.UnitsError('d_lon_coslat and d_lat should have equivalent ' 'units.') def represent_as(self, other_class, base=None): # All spherical differentials can be done without going to Cartesian, # though some need base for the latitude to remove cos(lat). if issubclass(other_class, UnitSphericalCosLatDifferential): return other_class(self.d_lon_coslat, self.d_lat) elif issubclass(other_class, RadialDifferential): return other_class(self.d_distance) elif issubclass(other_class, SphericalDifferential): return other_class(self._d_lon(base), self.d_lat, self.d_distance) elif issubclass(other_class, UnitSphericalDifferential): return other_class(self._d_lon(base), self.d_lat) elif issubclass(other_class, PhysicsSphericalDifferential): return other_class(self._d_lon(base), -self.d_lat, self.d_distance) return super().represent_as(other_class, base) @classmethod def from_representation(cls, representation, base=None): # Other spherical differentials can be done without going to Cartesian, # though we need base for the latitude to remove coslat. if isinstance(representation, SphericalDifferential): d_lon_coslat = cls._get_d_lon_coslat(representation.d_lon, base) return cls(d_lon_coslat, representation.d_lat, representation.d_distance) elif isinstance(representation, PhysicsSphericalDifferential): d_lon_coslat = cls._get_d_lon_coslat(representation.d_phi, base) return cls(d_lon_coslat, -representation.d_theta, representation.d_r) return super().from_representation(representation, base) def _scale_operation(self, op, *args, scaled_base=False): if scaled_base: return self.__class__(self.d_lon_coslat, self.d_lat, op(self.d_distance, *args)) else: return super()._scale_operation(op, *args) class RadialDifferential(BaseDifferential): """Differential(s) of radial distances. Parameters ---------- d_distance : `~astropy.units.Quantity` The differential distance. copy : bool, optional If `True` (default), arrays will be copied. If `False`, arrays will be references, though possibly broadcast to ensure matching shapes. """ base_representation = RadialRepresentation def to_cartesian(self, base): return self.d_distance * base.represent_as( UnitSphericalRepresentation).to_cartesian() def norm(self, base=None): return self.d_distance @classmethod def from_cartesian(cls, other, base): return cls(other.dot(base.represent_as(UnitSphericalRepresentation)), copy=False) @classmethod def from_representation(cls, representation, base=None): if isinstance(representation, (SphericalDifferential, SphericalCosLatDifferential)): return cls(representation.d_distance) elif isinstance(representation, PhysicsSphericalDifferential): return cls(representation.d_r) else: return super().from_representation(representation, base) def _combine_operation(self, op, other, reverse=False): if isinstance(other, self.base_representation): if reverse: first, second = other.distance, self.d_distance else: first, second = self.d_distance, other.distance return other.__class__(op(first, second), copy=False) elif isinstance(other, (BaseSphericalDifferential, BaseSphericalCosLatDifferential)): all_components = set(self.components) | set(other.components) first, second = (self, other) if not reverse else (other, self) result_args = {c: op(getattr(first, c, 0.), getattr(second, c, 0.)) for c in all_components} return SphericalDifferential(**result_args) else: return super()._combine_operation(op, other, reverse) class PhysicsSphericalDifferential(BaseDifferential): """Differential(s) of 3D spherical coordinates using physics convention. Parameters ---------- d_phi, d_theta : `~astropy.units.Quantity` The differential azimuth and inclination. d_r : `~astropy.units.Quantity` The differential radial distance. copy : bool, optional If `True` (default), arrays will be copied. If `False`, arrays will be references, though possibly broadcast to ensure matching shapes. """ base_representation = PhysicsSphericalRepresentation def __init__(self, d_phi, d_theta=None, d_r=None, copy=True): super().__init__(d_phi, d_theta, d_r, copy=copy) if not self._d_phi.unit.is_equivalent(self._d_theta.unit): raise u.UnitsError('d_phi and d_theta should have equivalent ' 'units.') def represent_as(self, other_class, base=None): # All spherical differentials can be done without going to Cartesian, # though CosLat needs base for the latitude. For those, explicitly # do the equivalent of self._d_lon_coslat in SphericalDifferential. if issubclass(other_class, SphericalDifferential): return other_class(self.d_phi, -self.d_theta, self.d_r) elif issubclass(other_class, UnitSphericalDifferential): return other_class(self.d_phi, -self.d_theta) elif issubclass(other_class, SphericalCosLatDifferential): self._check_base(base) d_lon_coslat = self.d_phi * np.sin(base.theta) return other_class(d_lon_coslat, -self.d_theta, self.d_r) elif issubclass(other_class, UnitSphericalCosLatDifferential): self._check_base(base) d_lon_coslat = self.d_phi * np.sin(base.theta) return other_class(d_lon_coslat, -self.d_theta) elif issubclass(other_class, RadialDifferential): return other_class(self.d_r) return super().represent_as(other_class, base) @classmethod def from_representation(cls, representation, base=None): # Other spherical differentials can be done without going to Cartesian, # though we need base for the latitude to remove coslat. For that case, # do the equivalent of cls._d_lon in SphericalDifferential. if isinstance(representation, SphericalDifferential): return cls(representation.d_lon, -representation.d_lat, representation.d_distance) elif isinstance(representation, SphericalCosLatDifferential): cls._check_base(base) d_phi = representation.d_lon_coslat / np.sin(base.theta) return cls(d_phi, -representation.d_lat, representation.d_distance) return super().from_representation(representation, base) def _scale_operation(self, op, *args, scaled_base=False): if scaled_base: return self.__class__(self.d_phi, self.d_theta, op(self.d_r, *args)) else: return super()._scale_operation(op, *args) class CylindricalDifferential(BaseDifferential): """Differential(s) of points in cylindrical coordinates. Parameters ---------- d_rho : `~astropy.units.Quantity` ['speed'] The differential cylindrical radius. d_phi : `~astropy.units.Quantity` ['angular speed'] The differential azimuth. d_z : `~astropy.units.Quantity` ['speed'] The differential height. copy : bool, optional If `True` (default), arrays will be copied. If `False`, arrays will be references, though possibly broadcast to ensure matching shapes. """ base_representation = CylindricalRepresentation def __init__(self, d_rho, d_phi=None, d_z=None, copy=False): super().__init__(d_rho, d_phi, d_z, copy=copy) if not self._d_rho.unit.is_equivalent(self._d_z.unit): raise u.UnitsError("d_rho and d_z should have equivalent units.")