def test_resizing_op_call(odl_tspace_impl):
impl = odl_tspace_impl
dtypes = [
dt for dt in tensor_space_impl(impl).available_dtypes()
if is_numeric_dtype(dt)
]
for dtype in dtypes:
# Minimal test since this operator only wraps resize_array
space = odl.uniform_discr([0, -1], [1, 1], (4, 5), impl=impl)
res_space = odl.uniform_discr([0, -0.6], [2, 0.2], (8, 2), impl=impl)
res_op = odl.ResizingOperator(space, res_space)
out = res_op(space.one())
true_res = np.zeros((8, 2))
true_res[:4, :] = 1
assert np.array_equal(out, true_res)
out = res_space.element()
res_op(space.one(), out=out)
assert np.array_equal(out, true_res)
# Test also mapping to default impl for other 'impl'
if impl != 'numpy':
space = odl.uniform_discr([0, -1], [1, 1], (4, 5), impl=impl)
res_space = odl.uniform_discr([0, -0.6], [2, 0.2], (8, 2))
res_op = odl.ResizingOperator(space, res_space)
out = res_op(space.one())
true_res = np.zeros((8, 2))
true_res[:4, :] = 1
assert np.array_equal(out, true_res)
out = res_space.element()
res_op(space.one(), out=out)
assert np.array_equal(out, true_res)
def examples(self):
"""Return example random vectors."""
# Always return the same numbers
rand_state = np.random.get_state()
np.random.seed(1337)
if is_numeric_dtype(self.dtype):
yield ('Linearly spaced samples',
self.element(
np.linspace(0, 1, self.size).reshape(self.shape)))
yield ('Normally distributed noise',
self.element(np.random.standard_normal(self.shape)))
if self.is_real:
yield ('Uniformly distributed noise',
self.element(np.random.uniform(size=self.shape)))
elif self.is_complex:
yield ('Uniformly distributed noise',
self.element(
np.random.uniform(size=self.shape) +
np.random.uniform(size=self.shape) * 1j))
else:
# TODO: return something that always works, like zeros or ones?
raise NotImplementedError('no examples available for non-numeric'
'data type')
np.random.set_state(rand_state)
def complex_space(self):
"""The space corresponding to this space's `complex_dtype`.
Raises
------
ValueError
If `dtype` is not a numeric data type.
"""
if not is_numeric_dtype(self.dtype):
raise ValueError(
'`complex_space` not defined for non-numeric `dtype`')
return self.astype(self.complex_dtype)
def complex_dtype(self):
"""The complex dtype corresponding to this space's `dtype`.
Raises
------
NotImplementedError
If `dtype` is not a numeric data type.
"""
if not is_numeric_dtype(self.dtype):
raise NotImplementedError(
'`complex_dtype` not defined for non-numeric `dtype`')
return self.__complex_dtype
def real_space(self):
"""The space corresponding to this space's `real_dtype`.
Raises
------
NotImplementedError
If `dtype` is not a numeric data type.
"""
if not is_numeric_dtype(self.dtype):
raise NotImplementedError(
'`real_space` not defined for non-numeric `dtype`')
return self.astype(self.real_dtype)
def tspace_type(space, impl, dtype=None):
"""Select the correct corresponding tensor space.
Parameters
----------
space : `LinearSpace`
Template space from which to infer an adequate tensor space. If
it has a `LinearSpace.field` attribute, ``dtype`` must be
consistent with it.
impl : string
Implementation backend for the tensor space.
dtype : optional
Data type which the space is supposed to use. If ``None`` is
given, the space type is purely determined from ``space`` and
``impl``. Otherwise, it must be compatible with the
field of ``space``.
Returns
-------
stype : type
Space type selected after the space's field, the backend and
the data type.
"""
field_type = type(getattr(space, 'field', None))
if dtype is None:
pass
elif is_real_floating_dtype(dtype):
if field_type is None or field_type == ComplexNumbers:
raise TypeError('real floating data type {!r} requires space '
'field to be of type RealNumbers, got {}'
''.format(dtype, field_type))
elif is_complex_floating_dtype(dtype):
if field_type is None or field_type == RealNumbers:
raise TypeError('complex floating data type {!r} requires space '
'field to be of type ComplexNumbers, got {!r}'
''.format(dtype, field_type))
elif is_numeric_dtype(dtype):
if field_type == ComplexNumbers:
raise TypeError('non-floating data type {!r} requires space field '
'to be of type RealNumbers, got {!r}'.format(
dtype, field_type))
try:
return tensor_space_impl(impl)
except ValueError:
raise NotImplementedError('no corresponding tensor space available '
'for space {!r} and implementation {!r}'
''.format(space, impl))
def test_resizing_op_properties(odl_tspace_impl, padding):
impl = odl_tspace_impl
dtypes = [
dt for dt in tensor_space_impl(impl).available_dtypes()
if is_numeric_dtype(dt)
]
pad_mode, pad_const = padding
for dtype in dtypes:
# Explicit range
space = odl.uniform_discr([0, -1], [1, 1], (10, 5), dtype=dtype)
res_space = odl.uniform_discr([0, -3], [2, 3], (20, 15), dtype=dtype)
res_op = odl.ResizingOperator(space,
res_space,
pad_mode=pad_mode,
pad_const=pad_const)
assert res_op.domain == space
assert res_op.range == res_space
assert res_op.offset == (0, 5)
assert res_op.pad_mode == pad_mode
assert res_op.pad_const == pad_const
if pad_mode == 'constant' and pad_const != 0:
assert not res_op.is_linear
else:
assert res_op.is_linear
# Implicit range via ran_shp and offset
res_op = odl.ResizingOperator(space,
ran_shp=(20, 15),
offset=[0, 5],
pad_mode=pad_mode,
pad_const=pad_const)
assert np.allclose(res_op.range.min_pt, res_space.min_pt)
assert np.allclose(res_op.range.max_pt, res_space.max_pt)
assert np.allclose(res_op.range.cell_sides, res_space.cell_sides)
assert res_op.range.dtype == res_space.dtype
assert res_op.offset == (0, 5)
assert res_op.pad_mode == pad_mode
assert res_op.pad_const == pad_const
if pad_mode == 'constant' and pad_const != 0:
assert not res_op.is_linear
else:
assert res_op.is_linear
def test_resizing_op_inverse(padding, odl_tspace_impl):
impl = odl_tspace_impl
pad_mode, pad_const = padding
dtypes = [dt for dt in tensor_space_impl(impl).available_dtypes()
if is_numeric_dtype(dt)]
for dtype in dtypes:
space = odl.uniform_discr([0, -1], [1, 1], (4, 5), dtype=dtype,
impl=impl)
res_space = odl.uniform_discr([0, -1.4], [1.5, 1.4], (6, 7),
dtype=dtype, impl=impl)
res_op = odl.ResizingOperator(space, res_space, pad_mode=pad_mode,
pad_const=pad_const)
# Only left inverse if the operator extends in all axes
x = noise_element(space)
assert res_op.inverse(res_op(x)) == x
def astype(self, dtype):
"""Return a copy of this space with new ``dtype``.
Parameters
----------
dtype :
Scalar data type of the returned space. Can be provided
in any way the `numpy.dtype` constructor understands, e.g.
as built-in type or as a string. Data types with non-trivial
shapes are not allowed.
Returns
-------
newspace : `TensorSpace`
Version of this space with given data type.
"""
if dtype is None:
# Need to filter this out since Numpy iterprets it as 'float'
raise ValueError('`None` is not a valid data type')
dtype = np.dtype(dtype)
if dtype == self.dtype:
return self
if is_numeric_dtype(self.dtype):
# Caching for real and complex versions (exact dtype mappings)
if dtype == self.__real_dtype:
if self.__real_space is None:
self.__real_space = self._astype(dtype)
return self.__real_space
elif dtype == self.__complex_dtype:
if self.__complex_space is None:
self.__complex_space = self._astype(dtype)
return self.__complex_space
else:
return self._astype(dtype)
else:
return self._astype(dtype)
def contains_all(self, other):
"""Return ``True`` if ``other`` is a sequence of complex numbers."""
dtype = getattr(other, 'dtype', None)
if dtype is None:
dtype = np.result_type(*other)
return is_numeric_dtype(dtype)
def dft_preprocess_data(arr, shift=True, axes=None, sign='-', out=None):
"""Pre-process the real-space data before DFT.
This function multiplies the given data with the separable
function::
p(x) = exp(+- 1j * dot(x - x[0], xi[0]))
where ``x[0]`` and ``xi[0]`` are the minimum coodinates of
the real-space and reciprocal grids, respectively. The sign of
the exponent depends on the choice of ``sign``. In discretized
form, this function becomes an array::
p[k] = exp(+- 1j * k * s * xi[0])
If the reciprocal grid is not shifted, i.e. symmetric around 0,
it is ``xi[0] = pi/s * (-1 + 1/N)``, hence::
p[k] = exp(-+ 1j * pi * k * (1 - 1/N))
For a shifted grid, we have :math:``xi[0] = -pi/s``, thus the
array is given by::
p[k] = (-1)**k
Parameters
----------
arr : `array-like`
Array to be pre-processed. If its data type is a real
non-floating type, it is converted to 'float64'.
shift : bool or or sequence of bools, optional
If ``True``, the grid is shifted by half a stride in the negative
direction. With a sequence, this option is applied separately on
each axis.
axes : int or sequence of ints, optional
Dimensions in which to calculate the reciprocal. The sequence
must have the same length as ``shift`` if the latter is given
as a sequence.
Default: all axes.
sign : {'-', '+'}, optional
Sign of the complex exponent.
out : `numpy.ndarray`, optional
Array in which the result is stored. If ``out is arr``,
an in-place modification is performed. For real data type,
this is only possible for ``shift=True`` since the factors are
complex otherwise.
Returns
-------
out : `numpy.ndarray`
Result of the pre-processing. If ``out`` was given, the returned
object is a reference to it.
Notes
-----
If ``out`` is not specified, the data type of the returned array
is the same as that of ``arr`` except when ``arr`` has real data
type and ``shift`` is not ``True``. In this case, the return type
is the complex counterpart of ``arr.dtype``.
"""
arr = np.asarray(arr)
if not is_numeric_dtype(arr.dtype):
raise ValueError('array has non-numeric data type {}'
''.format(dtype_repr(arr.dtype)))
elif is_real_dtype(arr.dtype) and not is_real_floating_dtype(arr.dtype):
arr = arr.astype('float64')
if axes is None:
axes = list(range(arr.ndim))
else:
try:
axes = [int(axes)]
except TypeError:
axes = list(axes)
shape = arr.shape
shift_list = normalized_scalar_param_list(shift,
length=len(axes),
param_conv=bool)
# Make a copy of arr with correct data type if necessary, or copy values.
if out is None:
if is_real_dtype(arr.dtype) and not all(shift_list):
out = np.array(arr, dtype=complex_dtype(arr.dtype), copy=True)
else:
out = arr.copy()
else:
out[:] = arr
if is_real_dtype(out.dtype) and not shift:
raise ValueError('cannot pre-process real input in-place without '
'shift')
if sign == '-':
imag = -1j
elif sign == '+':
imag = 1j
else:
raise ValueError("`sign` '{}' not understood".format(sign))
def _onedim_arr(length, shift):
if shift:
# (-1)^indices
factor = np.ones(length, dtype=out.dtype)
factor[1::2] = -1
else:
factor = np.arange(length, dtype=out.dtype)
factor *= -imag * np.pi * (1 - 1.0 / length)
np.exp(factor, out=factor)
return factor.astype(out.dtype, copy=False)
onedim_arrs = []
for axis, shift in zip(axes, shift_list):
length = shape[axis]
onedim_arrs.append(_onedim_arr(length, shift))
fast_1d_tensor_mult(out, onedim_arrs, axes=axes, out=out)
return out
def __init__(self, map_type, fspace, partition, tspace, linear=False):
"""Initialize a new instance.
Parameters
----------
map_type : {'sampling', 'interpolation'}
The type of operator
fspace : `FunctionSpace`
The non-discretized (abstract) set of functions to be
discretized
partition : `RectPartition`
Partition of (a subset of) ``fspace.domain`` based on a
`RectGrid`.
tspace : `TensorSpace`
Space providing containers for the values/coefficients of a
discretized object. Its `TensorSpace.shape` must be equal
to ``partition.shape``.
linear : bool, optional
Create a linear operator if ``True``, otherwise a non-linear
operator.
"""
map_type, map_type_in = str(map_type).lower(), map_type
if map_type not in ('sampling', 'interpolation'):
raise ValueError('`map_type` {!r} not understood'
''.format(map_type_in))
if not isinstance(fspace, FunctionSpace):
raise TypeError('`fspace` {!r} is not a `FunctionSpace` '
'instance'.format(fspace))
if not isinstance(partition, RectPartition):
raise TypeError('`partition` {!r} is not a `RectPartition` '
'instance'.format(partition))
if not isinstance(tspace, TensorSpace):
raise TypeError('`tspace` {!r} is not a `TensorSpace` instance'
''.format(tspace))
if not fspace.domain.contains_set(partition):
raise ValueError('{} not contained in the domain {} '
'of the function set {}'
''.format(partition, fspace.domain, fspace))
if tspace.shape != partition.shape:
raise ValueError('`tspace.shape` not equal to `partition.shape`: '
'{} != {}'
''.format(tspace.shape, partition.shape))
domain = fspace if map_type == 'sampling' else tspace
range = tspace if map_type == 'sampling' else fspace
super(FunctionSpaceMapping, self).__init__(domain,
range,
linear=linear)
self.__partition = partition
if self.is_linear:
if self.domain.field is None:
raise TypeError('`fspace.field` cannot be `None` for '
'`linear=True`')
if not is_numeric_dtype(tspace.dtype):
raise TypeError('`tspace.dtype` must be a numeric data type '
'for `linear=True`, got {}'
''.format(dtype_repr(tspace)))
if fspace.field != tspace.field:
raise ValueError('`fspace.field` not equal to `tspace.field`: '
'{} != {}'
''.format(fspace.field, tspace.field))
