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# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""
Tabular models.
Tabular models of any dimension can be created using `tabular_model`.
For convenience `Tabular1D` and `Tabular2D` are provided.
Examples
--------
>>> table = np.array([[ 3., 0., 0.],
... [ 0., 2., 0.],
... [ 0., 0., 0.]])
>>> points = ([1, 2, 3], [1, 2, 3])
>>> t2 = Tabular2D(points, lookup_table=table, bounds_error=False, fill_value=None, method='nearest')
"""
from __future__ import (absolute_import, unicode_literals, division,
print_function)
import abc
import numpy as np
from .core import Model
from ..utils import minversion
from ..extern.six.moves import range
try:
import scipy
from scipy.interpolate import interpn
has_scipy = True
except ImportError:
has_scipy = False
has_scipy = has_scipy and minversion(scipy, "0.14")
__all__ = ['tabular_model', 'Tabular1D', 'Tabular2D']
__doctest_requires__ = {('tabular_model'): ['scipy']}
class _Tabular(Model):
"""
Returns an interpolated lookup table value.
Parameters
----------
points : tuple of ndarray of float, with shapes (m1, ), ..., (mn, ), optional
The points defining the regular grid in n dimensions.
lookup_table : array-like, shape (m1, ..., mn, ...)
The data on a regular grid in n dimensions.
method : str, optional
The method of interpolation to perform. Supported are "linear" and
"nearest", and "splinef2d". "splinef2d" is only supported for
2-dimensional data. Default is "linear".
bounds_error : bool, optional
If True, when interpolated values are requested outside of the
domain of the input data, a ValueError is raised.
If False, then ``fill_value`` is used.
fill_value : float, optional
If provided, the value to use for points outside of the
interpolation domain. If None, values outside
the domain are extrapolated. Extrapolation is not supported by method
"splinef2d".
Returns
-------
value : ndarray
Interpolated values at input coordinates.
Raises
------
ImportError
Scipy is not installed.
Notes
-----
Uses `scipy.interpolate.interpn`.
"""
linear = False
fittable = False
standard_broadcasting = False
outputs = ('y',)
lookup_table = abc.abstractproperty()
_is_dynamic = True
_id = 0
def __init__(self, points=None, lookup_table=None, method='linear',
bounds_error=True, fill_value=np.nan, **kwargs):
n_models = kwargs.get('n_models', 1)
if n_models > 1:
raise NotImplementedError('Only n_models=1 is supported.')
super(_Tabular, self).__init__(**kwargs)
if lookup_table is not None:
lookup_table = np.asarray(lookup_table)
if self.lookup_table.ndim != lookup_table.ndim:
raise ValueError("lookup_table should be an array with "
"{0} dimensions".format(self.lookup_table.ndim))
self.lookup_table = lookup_table
if points is None:
self.points = tuple(np.arange(x, dtype=np.float)
for x in self.lookup_table.shape)
else:
if self.lookup_table.ndim == 1 and not isinstance(points, tuple):
self.points = (points,)
else:
self.points = points
if len(self.points) != self.lookup_table.ndim:
raise ValueError("Expected grid points in "
"{0} directions, got {1}".format(self.lookup_table.ndim,
len(self.points)))
self.bounds_error = bounds_error
self.method = method
self.fill_value = fill_value
def __repr__(self):
fmt = "<{0}(points={1}, lookup_table={2})>".format(self.__class__.__name__,
self.points, self.lookup_table)
return fmt
def __str__(self):
default_keywords = [
('Model', self.__class__.__name__),
('Name', self.name),
('Inputs', self.inputs),
('Outputs', self.outputs),
('Parameters', ""),
(' points', self.points),
(' lookup_table', self.lookup_table),
(' method', self.method),
(' fill_value', self.fill_value),
(' bounds_error', self.bounds_error)
]
parts = ['{0}: {1}'.format(keyword, value)
for keyword, value in default_keywords
if value is not None]
return '\n'.join(parts)
@property
def bounding_box(self):
"""
Tuple defining the default ``bounding_box`` limits,
``(points_low, points_high)``.
Examples
--------
>>> from astropy.modeling.models import Tabular1D, Tabular2D
>>> t1 = Tabular1D(points=[1,2,3], lookup_table=[10, 20, 30])
>>> t1.bounding_box
(1, 3)
>>> t2 = Tabular2D(points=[[1,2,3],[2,3,4]], lookup_table=[[10,20,30],[20,30,40]])
>>> t2.bounding_box
((2, 4), (1, 3))
"""
bbox = [(min(p), max(p)) for p in self.points][::-1]
if len(bbox) == 1:
bbox = bbox[0]
return tuple(bbox)
def evaluate(self, *inputs):
"""
Return the interpolated values at the input coordinates.
Parameters
----------
inputs : list of scalars or ndarrays
Input coordinates. The number of inputs must be equal
to the dimensions of the lookup table.
"""
inputs = [inp.flatten() for inp in inputs[: self.n_inputs]]
inputs = np.array(inputs).T
if not has_scipy:
raise ImportError("This model requires scipy >= v0.14")
return interpn(self.points, self.lookup_table, inputs,
method=self.method, bounds_error=self.bounds_error,
fill_value=self.fill_value)
def tabular_model(dim, name=None):
"""
Make a ``Tabular`` model where ``n_inputs`` is
based on the dimension of the lookup_table.
This model has to be further initialized and when evaluated
returns the interpolated values.
Parameters
----------
dim : int
Dimensions of the lookup table.
name : str
Name for the class.
Examples
--------
>>> table = np.array([[ 3., 0., 0.],
... [ 0., 2., 0.],
... [ 0., 0., 0.]])
>>> tab = tabular_model(2, name='Tabular2D')
>>> print(tab)
<class 'abc.Tabular2D'>
Name: Tabular2D
Inputs: (u'x0', u'x1')
Outputs: (u'y',)
>>> points = ([1, 2, 3], [1, 2, 3])
Setting fill_value to None, allows extrapolation.
>>> m = tab(points, lookup_table=table, name='my_table', bounds_error=False, fill_value=None, method='nearest')
>>> xinterp = [0, 1, 1.5, 2.72, 3.14]
>>> m(xinterp, xinterp)
array([ 3., 3., 3., 0., 0.])
"""
table = np.zeros([2] * dim)
inputs = tuple('x{0}'.format(idx) for idx in range(table.ndim))
members = {'lookup_table': table, 'inputs': inputs}
if name is None:
model_id = _Tabular._id
_Tabular._id += 1
name = 'Tabular{0}'.format(model_id)
return type(str(name), (_Tabular,), members)
Tabular1D = tabular_model(1, name='Tabular1D')
Tabular2D = tabular_model(2, name='Tabular2D')
_tab_docs = """
method : str, optional
The method of interpolation to perform. Supported are "linear" and
"nearest", and "splinef2d". "splinef2d" is only supported for
2-dimensional data. Default is "linear".
bounds_error : bool, optional
If True, when interpolated values are requested outside of the
domain of the input data, a ValueError is raised.
If False, then ``fill_value`` is used.
fill_value : float, optional
If provided, the value to use for points outside of the
interpolation domain. If None, values outside
the domain are extrapolated. Extrapolation is not supported by method
"splinef2d".
Returns
-------
value : ndarray
Interpolated values at input coordinates.
Raises
------
ImportError
Scipy is not installed.
Notes
-----
Uses `scipy.interpolate.interpn`.
"""
Tabular1D.__doc__ = """
Tabular model in 1D.
Returns an interpolated lookup table value.
Parameters
----------
points : array-like of float of ndim=1.
The points defining the regular grid in n dimensions.
lookup_table : array-like, of ndim=1.
The data in one dimensions.
""" + _tab_docs
Tabular2D.__doc__ = """
Tabular model in 2D.
Returns an interpolated lookup table value.
Parameters
----------
points : tuple of ndarray of float, with shapes (m1, m2), optional
The points defining the regular grid in n dimensions.
lookup_table : array-like, shape (m1, m2)
The data on a regular grid in 2 dimensions.
""" + _tab_docs
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