# Licensed under a 3-clause BSD style license - see LICENSE.rst """Spline models and fitters.""" # pylint: disable=line-too-long, too-many-lines, too-many-arguments, invalid-name import abc import functools import warnings import numpy as np from astropy.utils import isiterable from astropy.utils.exceptions import AstropyUserWarning from .core import FittableModel, ModelDefinitionError from .parameters import Parameter __all__ = ['Spline1D', 'SplineInterpolateFitter', 'SplineSmoothingFitter', 'SplineExactKnotsFitter', 'SplineSplrepFitter'] __doctest_requires__ = {('Spline1D'): ['scipy']} class _Spline(FittableModel): """Base class for spline models""" _knot_names = () _coeff_names = () optional_inputs = {} def __init__(self, knots=None, coeffs=None, degree=None, bounds=None, n_models=None, model_set_axis=None, name=None, meta=None): super().__init__( n_models=n_models, model_set_axis=model_set_axis, name=name, meta=meta) self._user_knots = False self._init_tck(degree) # Hack to allow an optional model argument self._create_optional_inputs() if knots is not None: self._init_spline(knots, coeffs, bounds) elif coeffs is not None: raise ValueError("If one passes a coeffs vector one needs to also pass knots!") @property def param_names(self): """ Coefficient names generated based on the spline's degree and number of knots. """ return tuple(list(self._knot_names) + list(self._coeff_names)) @staticmethod def _optional_arg(arg): return f'_{arg}' def _create_optional_inputs(self): for arg in self.optional_inputs: attribute = self._optional_arg(arg) if hasattr(self, attribute): raise ValueError(f'Optional argument {arg} already exists in this class!') else: setattr(self, attribute, None) def _intercept_optional_inputs(self, **kwargs): new_kwargs = kwargs for arg in self.optional_inputs: if (arg in kwargs): attribute = self._optional_arg(arg) if getattr(self, attribute) is None: setattr(self, attribute, kwargs[arg]) del new_kwargs[arg] else: raise RuntimeError(f'{arg} has already been set, something has gone wrong!') return new_kwargs def evaluate(self, *args, **kwargs): """ Extract the optional kwargs passed to call """ optional_inputs = kwargs for arg in self.optional_inputs: attribute = self._optional_arg(arg) if arg in kwargs: # Options passed in optional_inputs[arg] = kwargs[arg] elif getattr(self, attribute) is not None: # No options passed in and Options set optional_inputs[arg] = getattr(self, attribute) setattr(self, attribute, None) else: # No options passed in and No options set optional_inputs[arg] = self.optional_inputs[arg] return optional_inputs def __call__(self, *args, **kwargs): """ Make model callable to model evaluation """ # Hack to allow an optional model argument kwargs = self._intercept_optional_inputs(**kwargs) return super().__call__(*args, **kwargs) def _create_parameter(self, name: str, index: int, attr: str, fixed=False): """ Create a spline parameter linked to an attribute array. Parameters ---------- name : str Name for the parameter index : int The index of the parameter in the array attr : str The name for the attribute array fixed : optional, bool If the parameter should be fixed or not """ # Hack to allow parameters and attribute array to freely exchange values # _getter forces reading value from attribute array # _setter forces setting value to attribute array def _getter(value, model: "_Spline", index: int, attr: str): return getattr(model, attr)[index] def _setter(value, model: "_Spline", index: int, attr: str): getattr(model, attr)[index] = value return value getter = functools.partial(_getter, index=index, attr=attr) setter = functools.partial(_setter, index=index, attr=attr) default = getattr(self, attr) param = Parameter(name=name, default=default[index], fixed=fixed, getter=getter, setter=setter) # setter/getter wrapper for parameters in this case require the # parameter to have a reference back to its parent model param.model = self param.value = default[index] # Add parameter to model self.__dict__[name] = param def _create_parameters(self, base_name: str, attr: str, fixed=False): """ Create a spline parameters linked to an attribute array for all elements in that array Parameters ---------- base_name : str Base name for the parameters attr : str The name for the attribute array fixed : optional, bool If the parameters should be fixed or not """ names = [] for index in range(len(getattr(self, attr))): name = f"{base_name}{index}" names.append(name) self._create_parameter(name, index, attr, fixed) return tuple(names) @abc.abstractmethod def _init_parameters(self): raise NotImplementedError("This needs to be implemented") @abc.abstractmethod def _init_data(self, knots, coeffs, bounds=None): raise NotImplementedError("This needs to be implemented") def _init_spline(self, knots, coeffs, bounds=None): self._init_data(knots, coeffs, bounds) self._init_parameters() # fill _parameters and related attributes self._initialize_parameters((), {}) self._initialize_slices() # Calling this will properly fill the _parameter vector, which is # used directly sometimes without being properly filled. _ = self.parameters def _init_tck(self, degree): self._c = None self._t = None self._degree = degree class Spline1D(_Spline): """ One dimensional Spline Model Parameters ---------- knots : optional Define the knots for the spline. Can be 1) the number of interior knots for the spline, 2) the array of all knots for the spline, or 3) If both bounds are defined, the interior knots for the spline coeffs : optional The array of knot coefficients for the spline degree : optional The degree of the spline. It must be 1 <= degree <= 5, default is 3. bounds : optional The upper and lower bounds of the spline. Notes ----- Much of the functionality of this model is provided by `scipy.interpolate.BSpline` which can be directly accessed via the bspline property. Fitting for this model is provided by wrappers for: `scipy.interpolate.UnivariateSpline`, `scipy.interpolate.InterpolatedUnivariateSpline`, and `scipy.interpolate.LSQUnivariateSpline`. If one fails to define any knots/coefficients, no parameters will be added to this model until a fitter is called. This is because some of the fitters for splines vary the number of parameters and so we cannot define the parameter set until after fitting in these cases. Since parameters are not necessarily known at model initialization, setting model parameters directly via the model interface has been disabled. Direct constructors are provided for this model which incorporate the fitting to data directly into model construction. Knot parameters are declared as "fixed" parameters by default to enable the use of other `astropy.modeling` fitters to be used to fit this model. Examples -------- >>> import numpy as np >>> from astropy.modeling.models import Spline1D >>> from astropy.modeling import fitting >>> np.random.seed(42) >>> x = np.linspace(-3, 3, 50) >>> y = np.exp(-x**2) + 0.1 * np.random.randn(50) >>> xs = np.linspace(-3, 3, 1000) A 1D interpolating spline can be fit to data: >>> fitter = fitting.SplineInterpolateFitter() >>> spl = fitter(Spline1D(), x, y) Similarly, a smoothing spline can be fit to data: >>> fitter = fitting.SplineSmoothingFitter() >>> spl = fitter(Spline1D(), x, y, s=0.5) Similarly, a spline can be fit to data using an exact set of interior knots: >>> t = [-1, 0, 1] >>> fitter = fitting.SplineExactKnotsFitter() >>> spl = fitter(Spline1D(), x, y, t=t) """ n_inputs = 1 n_outputs = 1 _separable = True optional_inputs = {'nu': 0} def __init__(self, knots=None, coeffs=None, degree=3, bounds=None, n_models=None, model_set_axis=None, name=None, meta=None): super().__init__( knots=knots, coeffs=coeffs, degree=degree, bounds=bounds, n_models=n_models, model_set_axis=model_set_axis, name=name, meta=meta ) @property def t(self): """ The knots vector """ if self._t is None: return np.concatenate((np.zeros(self._degree + 1), np.ones(self._degree + 1))) else: return self._t @t.setter def t(self, value): if self._t is None: raise ValueError("The model parameters must be initialized before setting knots.") elif len(value) == len(self._t): self._t = value else: raise ValueError("There must be exactly as many knots as previously defined.") @property def t_interior(self): """ The interior knots """ return self.t[self.degree + 1: -(self.degree + 1)] @property def c(self): """ The coefficients vector """ if self._c is None: return np.zeros(len(self.t)) else: return self._c @c.setter def c(self, value): if self._c is None: raise ValueError("The model parameters must be initialized before setting coeffs.") elif len(value) == len(self._c): self._c = value else: raise ValueError("There must be exactly as many coeffs as previously defined.") @property def degree(self): """ The degree of the spline polynomials """ return self._degree @property def _initialized(self): return self._t is not None and self._c is not None @property def tck(self): """ Scipy 'tck' tuple representation """ return (self.t, self.c, self.degree) @tck.setter def tck(self, value): if self._initialized: if value[2] != self.degree: raise ValueError("tck has incompatible degree!") self.t = value[0] self.c = value[1] else: self._init_spline(value[0], value[1]) # Calling this will properly fill the _parameter vector, which is # used directly sometimes without being properly filled. _ = self.parameters @property def bspline(self): """ Scipy bspline object representation """ from scipy.interpolate import BSpline return BSpline(*self.tck) @bspline.setter def bspline(self, value): from scipy.interpolate import BSpline if isinstance(value, BSpline): self.tck = value.tck else: self.tck = value @property def knots(self): """ Dictionary of knot parameters """ return [getattr(self, knot) for knot in self._knot_names] @property def user_knots(self): """If the knots have been supplied by the user""" return self._user_knots @user_knots.setter def user_knots(self, value): self._user_knots = value @property def coeffs(self): """ Dictionary of coefficient parameters """ return [getattr(self, coeff) for coeff in self._coeff_names] def _init_parameters(self): self._knot_names = self._create_parameters("knot", "t", fixed=True) self._coeff_names = self._create_parameters("coeff", "c") def _init_bounds(self, bounds=None): if bounds is None: bounds = [None, None] if bounds[0] is None: lower = np.zeros(self._degree + 1) else: lower = np.array([bounds[0]] * (self._degree + 1)) if bounds[1] is None: upper = np.ones(self._degree + 1) else: upper = np.array([bounds[1]] * (self._degree + 1)) if bounds[0] is not None and bounds[1] is not None: self.bounding_box = bounds has_bounds = True else: has_bounds = False return has_bounds, lower, upper def _init_knots(self, knots, has_bounds, lower, upper): if np.issubdtype(type(knots), np.integer): self._t = np.concatenate( (lower, np.zeros(knots), upper) ) elif isiterable(knots): self._user_knots = True if has_bounds: self._t = np.concatenate( (lower, np.array(knots), upper) ) else: if len(knots) < 2*(self._degree + 1): raise ValueError(f"Must have at least {2*(self._degree + 1)} knots.") self._t = np.array(knots) else: raise ValueError(f"Knots: {knots} must be iterable or value") # check that knots form a viable spline self.bspline def _init_coeffs(self, coeffs=None): if coeffs is None: self._c = np.zeros(len(self._t)) else: self._c = np.array(coeffs) # check that coeffs form a viable spline self.bspline def _init_data(self, knots, coeffs, bounds=None): self._init_knots(knots, *self._init_bounds(bounds)) self._init_coeffs(coeffs) def evaluate(self, *args, **kwargs): """ Evaluate the spline. Parameters ---------- x : (positional) The points where the model is evaluating the spline at nu : optional (kwarg) The derivative of the spline for evaluation, 0 <= nu <= degree + 1. Default: 0. """ kwargs = super().evaluate(*args, **kwargs) x = args[0] if 'nu' in kwargs: if kwargs['nu'] > self.degree + 1: raise RuntimeError("Cannot evaluate a derivative of " f"order higher than {self.degree + 1}") return self.bspline(x, **kwargs) def derivative(self, nu=1): """ Create a spline that is the derivative of this one Parameters ---------- nu : int, optional Derivative order, default is 1. """ if nu <= self.degree: bspline = self.bspline.derivative(nu=nu) derivative = Spline1D(degree=bspline.k) derivative.bspline = bspline return derivative else: raise ValueError(f'Must have nu <= {self.degree}') def antiderivative(self, nu=1): """ Create a spline that is an antiderivative of this one Parameters ---------- nu : int, optional Antiderivative order, default is 1. Notes ----- Assumes constant of integration is 0 """ if (nu + self.degree) <= 5: bspline = self.bspline.antiderivative(nu=nu) antiderivative = Spline1D(degree=bspline.k) antiderivative.bspline = bspline return antiderivative else: raise ValueError("Supported splines can have max degree 5, " f"antiderivative degree will be {nu + self.degree}") class _SplineFitter(abc.ABC): """ Base Spline Fitter """ def __init__(self): self.fit_info = { 'resid': None, 'spline': None } def _set_fit_info(self, spline): self.fit_info['resid'] = spline.get_residual() self.fit_info['spline'] = spline @abc.abstractmethod def _fit_method(self, model, x, y, **kwargs): raise NotImplementedError("This has not been implemented for _SplineFitter.") def __call__(self, model, x, y, z=None, **kwargs): model_copy = model.copy() if isinstance(model_copy, Spline1D): if z is not None: raise ValueError("1D model can only have 2 data points.") spline = self._fit_method(model_copy, x, y, **kwargs) else: raise ModelDefinitionError("Only spline models are compatible with this fitter.") self._set_fit_info(spline) return model_copy class SplineInterpolateFitter(_SplineFitter): """ Fit an interpolating spline """ def _fit_method(self, model, x, y, **kwargs): weights = kwargs.pop('weights', None) bbox = kwargs.pop('bbox', [None, None]) if model.user_knots: warnings.warn("The current user specified knots maybe ignored for interpolating data", AstropyUserWarning) model.user_knots = False if bbox != [None, None]: model.bounding_box = bbox from scipy.interpolate import InterpolatedUnivariateSpline spline = InterpolatedUnivariateSpline(x, y, w=weights, bbox=bbox, k=model.degree) model.tck = spline._eval_args return spline class SplineSmoothingFitter(_SplineFitter): """ Fit a smoothing spline """ def _fit_method(self, model, x, y, **kwargs): s = kwargs.pop('s', None) weights = kwargs.pop('weights', None) bbox = kwargs.pop('bbox', [None, None]) if model.user_knots: warnings.warn("The current user specified knots maybe ignored for smoothing data", AstropyUserWarning) model.user_knots = False if bbox != [None, None]: model.bounding_box = bbox from scipy.interpolate import UnivariateSpline spline = UnivariateSpline(x, y, w=weights, bbox=bbox, k=model.degree, s=s) model.tck = spline._eval_args return spline class SplineExactKnotsFitter(_SplineFitter): """ Fit a spline using least-squares regression. """ def _fit_method(self, model, x, y, **kwargs): t = kwargs.pop('t', None) weights = kwargs.pop('weights', None) bbox = kwargs.pop('bbox', [None, None]) if t is not None: if model.user_knots: warnings.warn("The current user specified knots will be " "overwritten for by knots passed into this function", AstropyUserWarning) else: if model.user_knots: t = model.t_interior else: raise RuntimeError("No knots have been provided") if bbox != [None, None]: model.bounding_box = bbox from scipy.interpolate import LSQUnivariateSpline spline = LSQUnivariateSpline(x, y, t, w=weights, bbox=bbox, k=model.degree) model.tck = spline._eval_args return spline class SplineSplrepFitter(_SplineFitter): """ Fit a spline using the `scipy.interpolate.splrep` function interface. """ def __init__(self): super().__init__() self.fit_info = { 'fp': None, 'ier': None, 'msg': None } def _fit_method(self, model, x, y, **kwargs): t = kwargs.pop('t', None) s = kwargs.pop('s', None) task = kwargs.pop('task', 0) weights = kwargs.pop('weights', None) bbox = kwargs.pop('bbox', [None, None]) if t is not None: if model.user_knots: warnings.warn("The current user specified knots will be " "overwritten for by knots passed into this function", AstropyUserWarning) else: if model.user_knots: t = model.t_interior if bbox != [None, None]: model.bounding_box = bbox from scipy.interpolate import splrep tck, fp, ier, msg = splrep(x, y, w=weights, xb=bbox[0], xe=bbox[1], k=model.degree, s=s, t=t, task=task, full_output=1) model.tck = tck return fp, ier, msg def _set_fit_info(self, spline): self.fit_info['fp'] = spline[0] self.fit_info['ier'] = spline[1] self.fit_info['msg'] = spline[2]