def test_out_shape_from_meshgrid():
# 1d
x = np.zeros(2)
mg = sparse_meshgrid(x)
assert out_shape_from_meshgrid(mg) == (2, )
# 3d
x, y, z = np.zeros(2), np.zeros(3), np.zeros(4)
mg = sparse_meshgrid(x, y, z)
assert out_shape_from_meshgrid(mg) == (2, 3, 4)
# 3d, fleshed out meshgrids
x, y, z = np.zeros(2), np.zeros(3), np.zeros(4)
mg = np.meshgrid(x, y, z, sparse=False, indexing='ij', copy=True)
assert out_shape_from_meshgrid(mg) == (2, 3, 4)
mg = np.meshgrid(x, y, z, sparse=False, indexing='ij', copy=True)
mg = tuple(reversed([np.asfortranarray(arr) for arr in mg]))
assert out_shape_from_meshgrid(mg) == (2, 3, 4)
def test_out_shape_from_meshgrid():
# 1d
x = np.zeros(2)
mg = sparse_meshgrid(x)
assert out_shape_from_meshgrid(mg) == (2,)
# 3d
x, y, z = np.zeros(2), np.zeros(3), np.zeros(4)
mg = sparse_meshgrid(x, y, z)
assert out_shape_from_meshgrid(mg) == (2, 3, 4)
# 3d, fleshed out meshgrids
x, y, z = np.zeros(2), np.zeros(3), np.zeros(4)
mg = np.meshgrid(x, y, z, sparse=False, indexing='ij', copy=True)
assert out_shape_from_meshgrid(mg) == (2, 3, 4)
mg = np.meshgrid(x, y, z, sparse=False, indexing='ij', copy=True)
mg = tuple(reversed([np.asfortranarray(arr) for arr in mg]))
assert out_shape_from_meshgrid(mg) == (2, 3, 4)
def one_vec(x, out=None):
"""The one function, vectorized."""
if is_valid_input_meshgrid(x, self.domain.ndim):
order = meshgrid_input_order(x)
else:
order = 'C'
out_shape = out_shape_from_meshgrid(x)
if out is None:
return np.ones(out_shape, dtype=dtype, order=order)
else:
out.fill(1)
def one_vec(x, out=None):
"""The one function, vectorized."""
if is_valid_input_meshgrid(x, self.domain.ndim):
out_shape = out_shape_from_meshgrid(x)
elif is_valid_input_array(x, self.domain.ndim):
out_shape = out_shape_from_array(x)
else:
raise TypeError('invalid input type')
if out is None:
return np.ones(out_shape, dtype=self.out_dtype)
else:
out.fill(1)
def _default_out_of_place(func, dtype, x, **kwargs):
"""Default in-place evaluation method."""
if is_valid_input_array(x, func.domain.ndim):
out_shape = out_shape_from_array(x)
elif is_valid_input_meshgrid(x, func.domain.ndim):
out_shape = out_shape_from_meshgrid(x)
else:
raise TypeError('cannot use in-place method to implement '
'out-of-place non-vectorized evaluation.')
if dtype is None:
dtype = np.result_type(*x)
out = np.empty(out_shape, dtype=dtype)
func(x, out=out, **kwargs)
return out
def _default_out_of_place(func, x, **kwargs):
"""Default in-place evaluation method."""
if is_valid_input_array(x, func.domain.ndim):
out_shape = out_shape_from_array(x)
elif is_valid_input_meshgrid(x, func.domain.ndim):
out_shape = out_shape_from_meshgrid(x)
else:
raise TypeError('cannot use in-place method to implement '
'out-of-place non-vectorized evaluation')
dtype = func.space.out_dtype
if dtype is None:
dtype = np.result_type(*x)
out = np.empty(out_shape, dtype=dtype)
func(x, out=out, **kwargs)
return out
def __call__(self, x, out=None):
"""Do the interpolation.
Parameters
----------
x : `meshgrid` or `numpy.ndarray`
Evaluation points of the interpolator
out : `numpy.ndarray`, optional
Array to which the results are written. Needs to have
correct shape according to input ``x``.
Returns
-------
out : `numpy.ndarray`
Interpolated values. If ``out`` was given, the returned
object is a reference to it.
"""
ndim = len(self.coord_vecs)
if self.input_type == 'array':
# Make a (1, n) array from one with shape (n,)
x = x.reshape([ndim, -1])
out_shape = out_shape_from_array(x)
else:
if len(x) != ndim:
raise ValueError('number of vectors in x is {} instead of '
'the grid dimension {}'
''.format(len(x), ndim))
out_shape = out_shape_from_meshgrid(x)
if out is not None:
if not isinstance(out, np.ndarray):
raise TypeError('`out` {!r} not a `numpy.ndarray` '
'instance'.format(out))
if out.shape != out_shape:
raise ValueError('output shape {} not equal to expected '
'shape {}'.format(out.shape, out_shape))
if out.dtype != self.values.dtype:
raise ValueError('output dtype {} not equal to expected '
'dtype {}'
''.format(out.dtype, self.values.dtype))
indices, norm_distances = self._find_indices(x)
return self._evaluate(indices, norm_distances, out)
def _evaluate(self, indices, norm_distances, out=None):
"""Evaluate linear interpolation.
Modified for in-place evaluation and treatment of out-of-bounds
points by implicitly assuming 0 at the next node."""
# slice for broadcasting over trailing dimensions in self.values
vslice = (slice(None),) + (None,) * (self.values.ndim - len(indices))
out_shape = out_shape_from_meshgrid(norm_distances)
out_dtype = norm_distances[0].dtype
if out is None:
out = np.zeros(out_shape, dtype=out_dtype)
else:
out[:] = 0.0
# Weights and indices (per axis)
low_weights, high_weights, edge_indices = _create_weight_edge_lists(
indices, norm_distances, self.schemes, self.nn_variants)
# Iterate over all possible combinations of [i, i+1] for each
# axis, resulting in a loop of length 2**ndim
for lo_hi, edge in zip(product(*([['l', 'h']] * len(indices))),
product(*edge_indices)):
weight = 1.0
# TODO: determine best summation order from array strides
for lh, w_lo, w_hi in zip(lo_hi, low_weights, high_weights):
# We don't multiply in place to exploit the cheap operations
# in the beginning: sizes grow gradually as following:
# (n, 1, 1, ...) -> (n, m, 1, ...) -> ...
# Hence, it is faster to build up the weight array instead
# of doing full-size operations from the beginning.
if lh == 'l':
weight = weight * w_lo
else:
weight = weight * w_hi
out += np.asarray(self.values[edge]) * weight[vslice]
return np.array(out, copy=False, ndmin=1)
def __call__(self, x, out=None, **kwargs):
"""Evaluate the function at one or multiple values ``x``.
Parameters
----------
x : object
Input argument for the function evaluation. Conditions
on ``x`` depend on vectorization:
`False` : ``x`` must be a domain element
`True` : ``x`` must be a `numpy.ndarray` with shape
``(d, N)``, where ``d`` is the number of dimensions of
the function domain
OR
``x`` is a sequence of `numpy.ndarray` with length
``space.ndim``, and the arrays can be broadcast
against each other.
out : `numpy.ndarray`, optional
Output argument holding the result of the function
evaluation, can only be used for vectorized
functions. Its shape must be equal to
``np.broadcast(*x).shape``.
bounds_check : bool
Whether or not to check if all input points lie in
the function domain. For vectorized evaluation,
this requires the domain to implement
`Set.contains_all`.
Default: `True`
Returns
-------
out : range element or array of elements
Result of the function evaluation. If ``out`` was provided,
the returned object is a reference to it.
Raises
------
TypeError
If ``x`` is not a valid vectorized evaluation argument
If ``out`` is not a range element or a `numpy.ndarray`
of range elements
ValueError
If evaluation points fall outside the valid domain
"""
bounds_check = kwargs.pop('bounds_check', True)
if bounds_check and not hasattr(self.domain, 'contains_all'):
raise AttributeError('bounds check not possible for '
'domain {}, missing `contains_all()` '
'method.'.format(self.domain))
# Check for input type and determine output shape
if is_valid_input_array(x, self.domain.ndim):
out_shape = out_shape_from_array(x)
scalar_out = False
# For 1d, squeeze the array
if self.domain.ndim == 1 and x.ndim == 2:
x = x.squeeze()
elif is_valid_input_meshgrid(x, self.domain.ndim):
out_shape = out_shape_from_meshgrid(x)
scalar_out = False
# For 1d, fish out the vector from the tuple
if self.domain.ndim == 1:
x = x[0]
elif x in self.domain:
x = np.atleast_2d(x).T # make a (d, 1) array
out_shape = (1,)
scalar_out = (out is None)
else:
# Unknown input
raise TypeError('argument {!r} not a valid vectorized '
'input. Expected an element of the domain '
'{dom}, a ({dom.ndim}, n) array '
'or a length-{dom.ndim} meshgrid sequence.'
''.format(x, dom=self.domain))
# Check bounds if specified
if bounds_check:
if not self.domain.contains_all(x):
raise ValueError('input contains points outside '
'the domain {}.'.format(self.domain))
# Call the function and check out shape, before or after
if out is None:
out = self._call(x, **kwargs)
if out_shape != (1,) and out.shape != out_shape:
raise ValueError('output shape {} not equal to shape '
'{} expected from input.'
''.format(out.shape, out_shape))
else:
if not isinstance(out, np.ndarray):
raise TypeError('output {!r} not a `numpy.ndarray` '
'instance.')
if out_shape != (1,) and out.shape != out_shape:
raise ValueError('output shape {} not equal to shape '
'{} expected from input.'
''.format(out.shape, out_shape))
self._call(x, out=out, **kwargs)
# Check output values
if bounds_check:
if not self.range.contains_all(out):
raise ValueError('output contains points outside '
'the range {}.'
''.format(self.domain))
# Numpy does not implement __complex__ for arrays (in contrast to
# __float__), so we have to fish out the scalar ourselves.
return self.range.element(out.ravel()[0]) if scalar_out else out
def __call__(self, x, out=None, **kwargs):
"""Return ``self(x[, out, **kwargs])``.
Parameters
----------
x : domain `element-like`, `meshgrid` or `numpy.ndarray`
Input argument for the function evaluation. Conditions
on ``x`` depend on its type:
element-like: must be a castable to a domain element
meshgrid: length must be ``space.ndim``, and the arrays must
be broadcastable against each other.
array: shape must be ``(d, N)``, where ``d`` is the number
of dimensions of the function domain
out : `numpy.ndarray`, optional
Output argument holding the result of the function
evaluation, can only be used for vectorized
functions. Its shape must be equal to
``np.broadcast(*x).shape``.
Other Parameters
----------------
bounds_check : `bool`
If `True`, check if all input points lie in the function
domain in the case of vectorized evaluation. This requires
the domain to implement `Set.contains_all`.
Default: `True`
Returns
-------
out : range element or array of elements
Result of the function evaluation. If ``out`` was provided,
the returned object is a reference to it.
Raises
------
TypeError
If ``x`` is not a valid vectorized evaluation argument
If ``out`` is not a range element or a `numpy.ndarray`
of range elements
ValueError
If evaluation points fall outside the valid domain
"""
bounds_check = kwargs.pop('bounds_check', True)
if bounds_check and not hasattr(self.domain, 'contains_all'):
raise AttributeError('bounds check not possible for '
'domain {}, missing `contains_all()` '
'method'.format(self.domain))
if bounds_check and not hasattr(self.range, 'contains_all'):
raise AttributeError('bounds check not possible for '
'range {}, missing `contains_all()` '
'method'.format(self.range))
ndim = getattr(self.domain, 'ndim', None)
# Check for input type and determine output shape
if is_valid_input_meshgrid(x, ndim):
out_shape = out_shape_from_meshgrid(x)
scalar_out = False
# Avoid operations on tuples like x * 2 by casting to array
if ndim == 1:
x = x[0][None, ...]
elif is_valid_input_array(x, ndim):
x = np.asarray(x)
out_shape = out_shape_from_array(x)
scalar_out = False
# For 1d, squeeze the array
if ndim == 1 and x.ndim == 2:
x = x.squeeze()
elif x in self.domain:
x = np.atleast_2d(x).T # make a (d, 1) array
out_shape = (1,)
scalar_out = (out is None)
else:
# Unknown input
txt_1d = ' or (n,)' if ndim == 1 else ''
raise TypeError('Argument {!r} not a valid vectorized '
'input. Expected an element of the domain '
'{domain}, an array-like with shape '
'({domain.ndim}, n){} or a length-{domain.ndim} '
'meshgrid tuple.'
''.format(x, txt_1d, domain=self.domain))
# Check bounds if specified
if bounds_check:
if not self.domain.contains_all(x):
raise ValueError('input contains points outside '
'the domain {}'.format(self.domain))
# Call the function and check out shape, before or after
if out is None:
if ndim == 1:
try:
out = self._call(x, **kwargs)
if np.ndim(out) == 0 and not scalar_out:
# Don't accept scalar result. A typical situation where
# this occurs is with comparison operators, e.g.
# "return x > 0" which simply gives 'True' for a
# non-empty tuple (in Python 2). We raise TypeError
# to trigger the call with x[0].
raise TypeError
out = np.atleast_1d(np.squeeze(out))
except (TypeError, IndexError):
# TypeError is raised if a meshgrid was used but the
# function expected an array (1d only). In this case we try
# again with the first meshgrid vector.
# IndexError is raised in expressions like x[x > 0] since
# "x > 0" evaluates to 'True', i.e. 1, and that index is
# out of range for a meshgrid tuple of length 1 :-). To get
# the real errors with indexing, we check again for the
# same scenario (scalar output when not valid) as in the
# first case.
out = self._call(x[0], **kwargs)
if np.ndim(out) == 0 and not scalar_out:
raise ValueError('invalid scalar output')
out = np.atleast_1d(np.squeeze(out))
else:
out = self._call(x, **kwargs)
if self.out_dtype is not None:
# Cast to proper dtype if needed
out = out.astype(self.out_dtype)
if out_shape != (1,) and out.shape != out_shape:
# Try to broadcast the returned element if possible
try:
out = np.broadcast_to(out, out_shape)
except AttributeError:
# The above requires numpy 1.10, fallback impl else
shape = [m if n == 1 and m != 1 else 1
for n, m in zip(out.shape, out_shape)]
out = out + np.zeros(shape, dtype=out.dtype)
else:
if not isinstance(out, np.ndarray):
raise TypeError('output {!r} not a `numpy.ndarray` '
'instance')
if out_shape != (1,) and out.shape != out_shape:
raise ValueError('output shape {} not equal to shape '
'{} expected from input'
''.format(out.shape, out_shape))
if self.out_dtype is not None and out.dtype != self.out_dtype:
raise ValueError('`out.dtype` ({}) does not match out_dtype '
'({})'.format(out.dtype, self.out_dtype))
if ndim == 1:
# TypeError for meshgrid in 1d, but expected array (see above)
try:
self._call(x, out=out, **kwargs)
except TypeError:
self._call(x[0], out=out, **kwargs)
else:
self._call(x, out=out, **kwargs)
# Check output values
if bounds_check:
if not self.range.contains_all(out):
raise ValueError('output contains points outside '
'the range {}'
''.format(self.range))
# Numpy does not implement __complex__ for arrays (in contrast to
# __float__), so we have to fish out the scalar ourselves.
return self.range.element(out.ravel()[0]) if scalar_out else out