# Copyright (C) 2003-2005 Peter J. Verveer
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import itertools
import warnings
import numpy
from numpy.core.multiarray import normalize_axis_index
from scipy import special
from . import _ni_support
from . import _nd_image
from ._ni_docstrings import docfiller
__all__ = ['spline_filter1d', 'spline_filter', 'geometric_transform',
'map_coordinates', 'affine_transform', 'shift', 'zoom', 'rotate']
@docfiller
def spline_filter1d(input, order=3, axis=-1, output=numpy.float64,
mode='mirror'):
"""
Calculate a 1-D spline filter along the given axis.
The lines of the array along the given axis are filtered by a
spline filter. The order of the spline must be >= 2 and <= 5.
Parameters
----------
%(input)s
order : int, optional
The order of the spline, default is 3.
axis : int, optional
The axis along which the spline filter is applied. Default is the last
axis.
output : ndarray or dtype, optional
The array in which to place the output, or the dtype of the returned
array. Default is ``numpy.float64``.
%(mode_interp_mirror)s
Returns
-------
spline_filter1d : ndarray
The filtered input.
Notes
-----
All functions in `ndimage.interpolation` do spline interpolation of
the input image. If using B-splines of `order > 1`, the input image
values have to be converted to B-spline coefficients first, which is
done by applying this 1-D filter sequentially along all
axes of the input. All functions that require B-spline coefficients
will automatically filter their inputs, a behavior controllable with
the `prefilter` keyword argument. For functions that accept a `mode`
parameter, the result will only be correct if it matches the `mode`
used when filtering.
For complex-valued `input`, this function processes the real and imaginary
components independently.
.. versionadded:: 1.6.0
Complex-valued support added.
See Also
--------
spline_filter : Multidimensional spline filter.
Examples
--------
We can filter an image using 1-D spline along the given axis:
>>> from scipy.ndimage import spline_filter1d
>>> import matplotlib.pyplot as plt
>>> orig_img = np.eye(20) # create an image
>>> orig_img[10, :] = 1.0
>>> sp_filter_axis_0 = spline_filter1d(orig_img, axis=0)
>>> sp_filter_axis_1 = spline_filter1d(orig_img, axis=1)
>>> f, ax = plt.subplots(1, 3, sharex=True)
>>> for ind, data in enumerate([[orig_img, "original image"],
... [sp_filter_axis_0, "spline filter (axis=0)"],
... [sp_filter_axis_1, "spline filter (axis=1)"]]):
... ax[ind].imshow(data[0], cmap='gray_r')
... ax[ind].set_title(data[1])
>>> plt.tight_layout()
>>> plt.show()
"""
if order < 0 or order > 5:
raise RuntimeError('spline order not supported')
input = numpy.asarray(input)
complex_output = numpy.iscomplexobj(input)
output = _ni_support._get_output(output, input,
complex_output=complex_output)
if complex_output:
spline_filter1d(input.real, order, axis, output.real, mode)
spline_filter1d(input.imag, order, axis, output.imag, mode)
return output
if order in [0, 1]:
output[...] = numpy.array(input)
else:
mode = _ni_support._extend_mode_to_code(mode)
axis = normalize_axis_index(axis, input.ndim)
_nd_image.spline_filter1d(input, order, axis, output, mode)
return output
def spline_filter(input, order=3, output=numpy.float64, mode='mirror'):
"""
Multidimensional spline filter.
For more details, see `spline_filter1d`.
See Also
--------
spline_filter1d : Calculate a 1-D spline filter along the given axis.
Notes
-----
The multidimensional filter is implemented as a sequence of
1-D spline filters. The intermediate arrays are stored
in the same data type as the output. Therefore, for output types
with a limited precision, the results may be imprecise because
intermediate results may be stored with insufficient precision.
For complex-valued `input`, this function processes the real and imaginary
components independently.
.. versionadded:: 1.6.0
Complex-valued support added.
Examples
--------
We can filter an image using multidimentional splines:
>>> from scipy.ndimage import spline_filter
>>> import matplotlib.pyplot as plt
>>> orig_img = np.eye(20) # create an image
>>> orig_img[10, :] = 1.0
>>> sp_filter = spline_filter(orig_img, order=3)
>>> f, ax = plt.subplots(1, 2, sharex=True)
>>> for ind, data in enumerate([[orig_img, "original image"],
... [sp_filter, "spline filter"]]):
... ax[ind].imshow(data[0], cmap='gray_r')
... ax[ind].set_title(data[1])
>>> plt.tight_layout()
>>> plt.show()
"""
if order < 2 or order > 5:
raise RuntimeError('spline order not supported')
input = numpy.asarray(input)
complex_output = numpy.iscomplexobj(input)
output = _ni_support._get_output(output, input,
complex_output=complex_output)
if complex_output:
spline_filter(input.real, order, output.real, mode)
spline_filter(input.imag, order, output.imag, mode)
return output
if order not in [0, 1] and input.ndim > 0:
for axis in range(input.ndim):
spline_filter1d(input, order, axis, output=output, mode=mode)
input = output
else:
output[...] = input[...]
return output
def _prepad_for_spline_filter(input, mode, cval):
if mode in ['nearest', 'grid-constant']:
npad = 12
if mode == 'grid-constant':
padded = numpy.pad(input, npad, mode='constant',
constant_values=cval)
elif mode == 'nearest':
padded = numpy.pad(input, npad, mode='edge')
else:
# other modes have exact boundary conditions implemented so
# no prepadding is needed
npad = 0
padded = input
return padded, npad
@docfiller
def geometric_transform(input, mapping, output_shape=None,
output=None, order=3,
mode='constant', cval=0.0, prefilter=True,
extra_arguments=(), extra_keywords={}):
"""
Apply an arbitrary geometric transform.
The given mapping function is used to find, for each point in the
output, the corresponding coordinates in the input. The value of the
input at those coordinates is determined by spline interpolation of
the requested order.
Parameters
----------
%(input)s
mapping : {callable, scipy.LowLevelCallable}
A callable object that accepts a tuple of length equal to the output
array rank, and returns the corresponding input coordinates as a tuple
of length equal to the input array rank.
output_shape : tuple of ints, optional
Shape tuple.
%(output)s
order : int, optional
The order of the spline interpolation, default is 3.
The order has to be in the range 0-5.
%(mode_interp_constant)s
%(cval)s
%(prefilter)s
extra_arguments : tuple, optional
Extra arguments passed to `mapping`.
extra_keywords : dict, optional
Extra keywords passed to `mapping`.
Returns
-------
output : ndarray
The filtered input.
See Also
--------
map_coordinates, affine_transform, spline_filter1d
Notes
-----
This function also accepts low-level callback functions with one
the following signatures and wrapped in `scipy.LowLevelCallable`:
.. code:: c
int mapping(npy_intp *output_coordinates, double *input_coordinates,
int output_rank, int input_rank, void *user_data)
int mapping(intptr_t *output_coordinates, double *input_coordinates,
int output_rank, int input_rank, void *user_data)
The calling function iterates over the elements of the output array,
calling the callback function at each element. The coordinates of the
current output element are passed through ``output_coordinates``. The
callback function must return the coordinates at which the input must
be interpolated in ``input_coordinates``. The rank of the input and
output arrays are given by ``input_rank`` and ``output_rank``
respectively. ``user_data`` is the data pointer provided
to `scipy.LowLevelCallable` as-is.
The callback function must return an integer error status that is zero
if something went wrong and one otherwise. If an error occurs, you should
normally set the Python error status with an informative message
before returning, otherwise a default error message is set by the
calling function.
In addition, some other low-level function pointer specifications
are accepted, but these are for backward compatibility only and should
not be used in new code.
For complex-valued `input`, this function transforms the real and imaginary
components independently.
.. versionadded:: 1.6.0
Complex-valued support added.
Examples
--------
>>> import numpy as np
>>> from scipy.ndimage import geometric_transform
>>> a = np.arange(12.).reshape((4, 3))
>>> def shift_func(output_coords):
... return (output_coords[0] - 0.5, output_coords[1] - 0.5)
...
>>> geometric_transform(a, shift_func)
array([[ 0. , 0. , 0. ],
[ 0. , 1.362, 2.738],
[ 0. , 4.812, 6.187],
[ 0. , 8.263, 9.637]])
>>> b = [1, 2, 3, 4, 5]
>>> def shift_func(output_coords):
... return (output_coords[0] - 3,)
...
>>> geometric_transform(b, shift_func, mode='constant')
array([0, 0, 0, 1, 2])
>>> geometric_transform(b, shift_func, mode='nearest')
array([1, 1, 1, 1, 2])
>>> geometric_transform(b, shift_func, mode='reflect')
array([3, 2, 1, 1, 2])
>>> geometric_transform(b, shift_func, mode='wrap')
array([2, 3, 4, 1, 2])
"""
if order < 0 or order > 5:
raise RuntimeError('spline order not supported')
input = numpy.asarray(input)
if output_shape is None:
output_shape = input.shape
if input.ndim < 1 or len(output_shape) < 1:
raise RuntimeError('input and output rank must be > 0')
complex_output = numpy.iscomplexobj(input)
output = _ni_support._get_output(output, input, shape=output_shape,
complex_output=complex_output)
if complex_output:
kwargs = dict(order=order, mode=mode, prefilter=prefilter,
output_shape=output_shape,
extra_arguments=extra_arguments,
extra_keywords=extra_keywords)
geometric_transform(input.real, mapping, output=output.real,
cval=numpy.real(cval), **kwargs)
geometric_transform(input.imag, mapping, output=output.imag,
cval=numpy.imag(cval), **kwargs)
return output
if prefilter and order > 1:
padded, npad = _prepad_for_spline_filter(input, mode, cval)
filtered = spline_filter(padded, order, output=numpy.float64,
mode=mode)
else:
npad = 0
filtered = input
mode = _ni_support._extend_mode_to_code(mode)
_nd_image.geometric_transform(filtered, mapping, None, None, None, output,
order, mode, cval, npad, extra_arguments,
extra_keywords)
return output
[docs]@docfiller
def map_coordinates(input, coordinates, output=None, order=3,
mode='constant', cval=0.0, prefilter=True):
"""
Map the input array to new coordinates by interpolation.
The array of coordinates is used to find, for each point in the output,
the corresponding coordinates in the input. The value of the input at
those coordinates is determined by spline interpolation of the
requested order.
The shape of the output is derived from that of the coordinate
array by dropping the first axis. The values of the array along
the first axis are the coordinates in the input array at which the
output value is found.
Parameters
----------
%(input)s
coordinates : array_like
The coordinates at which `input` is evaluated.
%(output)s
order : int, optional
The order of the spline interpolation, default is 3.
The order has to be in the range 0-5.
%(mode_interp_constant)s
%(cval)s
%(prefilter)s
Returns
-------
map_coordinates : ndarray
The result of transforming the input. The shape of the output is
derived from that of `coordinates` by dropping the first axis.
See Also
--------
spline_filter, geometric_transform, scipy.interpolate
Notes
-----
For complex-valued `input`, this function maps the real and imaginary
components independently.
.. versionadded:: 1.6.0
Complex-valued support added.
Examples
--------
>>> from scipy import ndimage
>>> a = np.arange(12.).reshape((4, 3))
>>> a
array([[ 0., 1., 2.],
[ 3., 4., 5.],
[ 6., 7., 8.],
[ 9., 10., 11.]])
>>> ndimage.map_coordinates(a, [[0.5, 2], [0.5, 1]], order=1)
array([ 2., 7.])
Above, the interpolated value of a[0.5, 0.5] gives output[0], while
a[2, 1] is output[1].
>>> inds = np.array([[0.5, 2], [0.5, 4]])
>>> ndimage.map_coordinates(a, inds, order=1, cval=-33.3)
array([ 2. , -33.3])
>>> ndimage.map_coordinates(a, inds, order=1, mode='nearest')
array([ 2., 8.])
>>> ndimage.map_coordinates(a, inds, order=1, cval=0, output=bool)
array([ True, False], dtype=bool)
"""
if order < 0 or order > 5:
raise RuntimeError('spline order not supported')
input = numpy.asarray(input)
coordinates = numpy.asarray(coordinates)
if numpy.iscomplexobj(coordinates):
raise TypeError('Complex type not supported')
output_shape = coordinates.shape[1:]
if input.ndim < 1 or len(output_shape) < 1:
raise RuntimeError('input and output rank must be > 0')
if coordinates.shape[0] != input.ndim:
raise RuntimeError('invalid shape for coordinate array')
complex_output = numpy.iscomplexobj(input)
output = _ni_support._get_output(output, input, shape=output_shape,
complex_output=complex_output)
if complex_output:
kwargs = dict(order=order, mode=mode, prefilter=prefilter)
map_coordinates(input.real, coordinates, output=output.real,
cval=numpy.real(cval), **kwargs)
map_coordinates(input.imag, coordinates, output=output.imag,
cval=numpy.imag(cval), **kwargs)
return output
if prefilter and order > 1:
padded, npad = _prepad_for_spline_filter(input, mode, cval)
filtered = spline_filter(padded, order, output=numpy.float64,
mode=mode)
else:
npad = 0
filtered = input
mode = _ni_support._extend_mode_to_code(mode)
_nd_image.geometric_transform(filtered, None, coordinates, None, None,
output, order, mode, cval, npad, None, None)
return output
@docfiller
def affine_transform(input, matrix, offset=0.0, output_shape=None,
output=None, order=3,
mode='constant', cval=0.0, prefilter=True):
"""
Apply an affine transformation.
Given an output image pixel index vector ``o``, the pixel value
is determined from the input image at position
``np.dot(matrix, o) + offset``.
This does 'pull' (or 'backward') resampling, transforming the output space
to the input to locate data. Affine transformations are often described in
the 'push' (or 'forward') direction, transforming input to output. If you
have a matrix for the 'push' transformation, use its inverse
(:func:`numpy.linalg.inv`) in this function.
Parameters
----------
%(input)s
matrix : ndarray
The inverse coordinate transformation matrix, mapping output
coordinates to input coordinates. If ``ndim`` is the number of
dimensions of ``input``, the given matrix must have one of the
following shapes:
- ``(ndim, ndim)``: the linear transformation matrix for each
output coordinate.
- ``(ndim,)``: assume that the 2-D transformation matrix is
diagonal, with the diagonal specified by the given value. A more
efficient algorithm is then used that exploits the separability
of the problem.
- ``(ndim + 1, ndim + 1)``: assume that the transformation is
specified using homogeneous coordinates [1]_. In this case, any
value passed to ``offset`` is ignored.
- ``(ndim, ndim + 1)``: as above, but the bottom row of a
homogeneous transformation matrix is always ``[0, 0, ..., 1]``,
and may be omitted.
offset : float or sequence, optional
The offset into the array where the transform is applied. If a float,
`offset` is the same for each axis. If a sequence, `offset` should
contain one value for each axis.
output_shape : tuple of ints, optional
Shape tuple.
%(output)s
order : int, optional
The order of the spline interpolation, default is 3.
The order has to be in the range 0-5.
%(mode_interp_constant)s
%(cval)s
%(prefilter)s
Returns
-------
affine_transform : ndarray
The transformed input.
Notes
-----
The given matrix and offset are used to find for each point in the
output the corresponding coordinates in the input by an affine
transformation. The value of the input at those coordinates is
determined by spline interpolation of the requested order. Points
outside the boundaries of the input are filled according to the given
mode.
.. versionchanged:: 0.18.0
Previously, the exact interpretation of the affine transformation
depended on whether the matrix was supplied as a 1-D or a
2-D array. If a 1-D array was supplied
to the matrix parameter, the output pixel value at index ``o``
was determined from the input image at position
``matrix * (o + offset)``.
For complex-valued `input`, this function transforms the real and imaginary
components independently.
.. versionadded:: 1.6.0
Complex-valued support added.
References
----------
.. [1] https://en.wikipedia.org/wiki/Homogeneous_coordinates
"""
if order < 0 or order > 5:
raise RuntimeError('spline order not supported')
input = numpy.asarray(input)
if output_shape is None:
output_shape = input.shape
if input.ndim < 1 or len(output_shape) < 1:
raise RuntimeError('input and output rank must be > 0')
complex_output = numpy.iscomplexobj(input)
output = _ni_support._get_output(output, input, shape=output_shape,
complex_output=complex_output)
if complex_output:
kwargs = dict(offset=offset, output_shape=output_shape, order=order,
mode=mode, prefilter=prefilter)
affine_transform(input.real, matrix, output=output.real,
cval=numpy.real(cval), **kwargs)
affine_transform(input.imag, matrix, output=output.imag,
cval=numpy.imag(cval), **kwargs)
return output
if prefilter and order > 1:
padded, npad = _prepad_for_spline_filter(input, mode, cval)
filtered = spline_filter(padded, order, output=numpy.float64,
mode=mode)
else:
npad = 0
filtered = input
mode = _ni_support._extend_mode_to_code(mode)
matrix = numpy.asarray(matrix, dtype=numpy.float64)
if matrix.ndim not in [1, 2] or matrix.shape[0] < 1:
raise RuntimeError('no proper affine matrix provided')
if (matrix.ndim == 2 and matrix.shape[1] == input.ndim + 1 and
(matrix.shape[0] in [input.ndim, input.ndim + 1])):
if matrix.shape[0] == input.ndim + 1:
exptd = [0] * input.ndim + [1]
if not numpy.all(matrix[input.ndim] == exptd):
msg = ('Expected homogeneous transformation matrix with '
'shape %s for image shape %s, but bottom row was '
'not equal to %s' % (matrix.shape, input.shape, exptd))
raise ValueError(msg)
# assume input is homogeneous coordinate transformation matrix
offset = matrix[:input.ndim, input.ndim]
matrix = matrix[:input.ndim, :input.ndim]
if matrix.shape[0] != input.ndim:
raise RuntimeError('affine matrix has wrong number of rows')
if matrix.ndim == 2 and matrix.shape[1] != output.ndim:
raise RuntimeError('affine matrix has wrong number of columns')
if not matrix.flags.contiguous:
matrix = matrix.copy()
offset = _ni_support._normalize_sequence(offset, input.ndim)
offset = numpy.asarray(offset, dtype=numpy.float64)
if offset.ndim != 1 or offset.shape[0] < 1:
raise RuntimeError('no proper offset provided')
if not offset.flags.contiguous:
offset = offset.copy()
if matrix.ndim == 1:
warnings.warn(
"The behavior of affine_transform with a 1-D "
"array supplied for the matrix parameter has changed in "
"SciPy 0.18.0."
)
_nd_image.zoom_shift(filtered, matrix, offset/matrix, output, order,
mode, cval, npad, False)
else:
_nd_image.geometric_transform(filtered, None, None, matrix, offset,
output, order, mode, cval, npad, None,
None)
return output
@docfiller
def shift(input, shift, output=None, order=3, mode='constant', cval=0.0,
prefilter=True):
"""
Shift an array.
The array is shifted using spline interpolation of the requested order.
Points outside the boundaries of the input are filled according to the
given mode.
Parameters
----------
%(input)s
shift : float or sequence
The shift along the axes. If a float, `shift` is the same for each
axis. If a sequence, `shift` should contain one value for each axis.
%(output)s
order : int, optional
The order of the spline interpolation, default is 3.
The order has to be in the range 0-5.
%(mode_interp_constant)s
%(cval)s
%(prefilter)s
Returns
-------
shift : ndarray
The shifted input.
Notes
-----
For complex-valued `input`, this function shifts the real and imaginary
components independently.
.. versionadded:: 1.6.0
Complex-valued support added.
"""
if order < 0 or order > 5:
raise RuntimeError('spline order not supported')
input = numpy.asarray(input)
if input.ndim < 1:
raise RuntimeError('input and output rank must be > 0')
complex_output = numpy.iscomplexobj(input)
output = _ni_support._get_output(output, input,
complex_output=complex_output)
if complex_output:
# import under different name to avoid confusion with shift parameter
from scipy.ndimage.interpolation import shift as _shift
kwargs = dict(order=order, mode=mode, prefilter=prefilter)
_shift(input.real, shift, output=output.real, cval=numpy.real(cval),
**kwargs)
_shift(input.imag, shift, output=output.imag, cval=numpy.imag(cval),
**kwargs)
return output
if prefilter and order > 1:
padded, npad = _prepad_for_spline_filter(input, mode, cval)
filtered = spline_filter(padded, order, output=numpy.float64,
mode=mode)
else:
npad = 0
filtered = input
mode = _ni_support._extend_mode_to_code(mode)
shift = _ni_support._normalize_sequence(shift, input.ndim)
shift = [-ii for ii in shift]
shift = numpy.asarray(shift, dtype=numpy.float64)
if not shift.flags.contiguous:
shift = shift.copy()
_nd_image.zoom_shift(filtered, None, shift, output, order, mode, cval,
npad, False)
return output
@docfiller
def zoom(input, zoom, output=None, order=3, mode='constant', cval=0.0,
prefilter=True, *, grid_mode=False):
"""
Zoom an array.
The array is zoomed using spline interpolation of the requested order.
Parameters
----------
%(input)s
zoom : float or sequence
The zoom factor along the axes. If a float, `zoom` is the same for each
axis. If a sequence, `zoom` should contain one value for each axis.
%(output)s
order : int, optional
The order of the spline interpolation, default is 3.
The order has to be in the range 0-5.
%(mode_interp_constant)s
%(cval)s
%(prefilter)s
grid_mode : bool, optional
If False, the distance from the pixel centers is zoomed. Otherwise, the
distance including the full pixel extent is used. For example, a 1d
signal of length 5 is considered to have length 4 when `grid_mode` is
False, but length 5 when `grid_mode` is True. See the following
visual illustration:
.. code-block:: text
| pixel 1 | pixel 2 | pixel 3 | pixel 4 | pixel 5 |
|<-------------------------------------->|
vs.
|<----------------------------------------------->|
The starting point of the arrow in the diagram above corresponds to
coordinate location 0 in each mode.
Returns
-------
zoom : ndarray
The zoomed input.
Notes
-----
For complex-valued `input`, this function zooms the real and imaginary
components independently.
.. versionadded:: 1.6.0
Complex-valued support added.
Examples
--------
>>> from scipy import ndimage, misc
>>> import matplotlib.pyplot as plt
>>> fig = plt.figure()
>>> ax1 = fig.add_subplot(121) # left side
>>> ax2 = fig.add_subplot(122) # right side
>>> ascent = misc.ascent()
>>> result = ndimage.zoom(ascent, 3.0)
>>> ax1.imshow(ascent, vmin=0, vmax=255)
>>> ax2.imshow(result, vmin=0, vmax=255)
>>> plt.show()
>>> print(ascent.shape)
(512, 512)
>>> print(result.shape)
(1536, 1536)
"""
if order < 0 or order > 5:
raise RuntimeError('spline order not supported')
input = numpy.asarray(input)
if input.ndim < 1:
raise RuntimeError('input and output rank must be > 0')
zoom = _ni_support._normalize_sequence(zoom, input.ndim)
output_shape = tuple(
[int(round(ii * jj)) for ii, jj in zip(input.shape, zoom)])
complex_output = numpy.iscomplexobj(input)
output = _ni_support._get_output(output, input, shape=output_shape,
complex_output=complex_output)
if complex_output:
# import under different name to avoid confusion with zoom parameter
from scipy.ndimage.interpolation import zoom as _zoom
kwargs = dict(order=order, mode=mode, prefilter=prefilter)
_zoom(input.real, zoom, output=output.real, cval=numpy.real(cval),
**kwargs)
_zoom(input.imag, zoom, output=output.imag, cval=numpy.imag(cval),
**kwargs)
return output
if prefilter and order > 1:
padded, npad = _prepad_for_spline_filter(input, mode, cval)
filtered = spline_filter(padded, order, output=numpy.float64,
mode=mode)
else:
npad = 0
filtered = input
if grid_mode:
# warn about modes that may have surprising behavior
suggest_mode = None
if mode == 'constant':
suggest_mode = 'grid-constant'
elif mode == 'wrap':
suggest_mode = 'grid-wrap'
if suggest_mode is not None:
warnings.warn(
("It is recommended to use mode = {} instead of {} when "
"grid_mode is True."
).format(suggest_mode, mode)
)
mode = _ni_support._extend_mode_to_code(mode)
zoom_div = numpy.array(output_shape)
zoom_nominator = numpy.array(input.shape)
if not grid_mode:
zoom_div -= 1
zoom_nominator -= 1
# Zooming to infinite values is unpredictable, so just choose
# zoom factor 1 instead
zoom = numpy.divide(zoom_nominator, zoom_div,
out=numpy.ones_like(input.shape, dtype=numpy.float64),
where=zoom_div != 0)
zoom = numpy.ascontiguousarray(zoom)
_nd_image.zoom_shift(filtered, zoom, None, output, order, mode, cval, npad,
grid_mode)
return output
@docfiller
def rotate(input, angle, axes=(1, 0), reshape=True, output=None, order=3,
mode='constant', cval=0.0, prefilter=True):
"""
Rotate an array.
The array is rotated in the plane defined by the two axes given by the
`axes` parameter using spline interpolation of the requested order.
Parameters
----------
%(input)s
angle : float
The rotation angle in degrees.
axes : tuple of 2 ints, optional
The two axes that define the plane of rotation. Default is the first
two axes.
reshape : bool, optional
If `reshape` is true, the output shape is adapted so that the input
array is contained completely in the output. Default is True.
%(output)s
order : int, optional
The order of the spline interpolation, default is 3.
The order has to be in the range 0-5.
%(mode_interp_constant)s
%(cval)s
%(prefilter)s
Returns
-------
rotate : ndarray
The rotated input.
Notes
-----
For complex-valued `input`, this function rotates the real and imaginary
components independently.
.. versionadded:: 1.6.0
Complex-valued support added.
Examples
--------
>>> from scipy import ndimage, misc
>>> import matplotlib.pyplot as plt
>>> fig = plt.figure(figsize=(10, 3))
>>> ax1, ax2, ax3 = fig.subplots(1, 3)
>>> img = misc.ascent()
>>> img_45 = ndimage.rotate(img, 45, reshape=False)
>>> full_img_45 = ndimage.rotate(img, 45, reshape=True)
>>> ax1.imshow(img, cmap='gray')
>>> ax1.set_axis_off()
>>> ax2.imshow(img_45, cmap='gray')
>>> ax2.set_axis_off()
>>> ax3.imshow(full_img_45, cmap='gray')
>>> ax3.set_axis_off()
>>> fig.set_tight_layout(True)
>>> plt.show()
>>> print(img.shape)
(512, 512)
>>> print(img_45.shape)
(512, 512)
>>> print(full_img_45.shape)
(724, 724)
"""
input_arr = numpy.asarray(input)
ndim = input_arr.ndim
if ndim < 2:
raise ValueError('input array should be at least 2D')
axes = list(axes)
if len(axes) != 2:
raise ValueError('axes should contain exactly two values')
if not all([float(ax).is_integer() for ax in axes]):
raise ValueError('axes should contain only integer values')
if axes[0] < 0:
axes[0] += ndim
if axes[1] < 0:
axes[1] += ndim
if axes[0] < 0 or axes[1] < 0 or axes[0] >= ndim or axes[1] >= ndim:
raise ValueError('invalid rotation plane specified')
axes.sort()
c, s = special.cosdg(angle), special.sindg(angle)
rot_matrix = numpy.array([[c, s],
[-s, c]])
img_shape = numpy.asarray(input_arr.shape)
in_plane_shape = img_shape[axes]
if reshape:
# Compute transformed input bounds
iy, ix = in_plane_shape
out_bounds = rot_matrix @ [[0, 0, iy, iy],
[0, ix, 0, ix]]
# Compute the shape of the transformed input plane
out_plane_shape = (out_bounds.ptp(axis=1) + 0.5).astype(int)
else:
out_plane_shape = img_shape[axes]
out_center = rot_matrix @ ((out_plane_shape - 1) / 2)
in_center = (in_plane_shape - 1) / 2
offset = in_center - out_center
output_shape = img_shape
output_shape[axes] = out_plane_shape
output_shape = tuple(output_shape)
complex_output = numpy.iscomplexobj(input_arr)
output = _ni_support._get_output(output, input_arr, shape=output_shape,
complex_output=complex_output)
if ndim <= 2:
affine_transform(input_arr, rot_matrix, offset, output_shape, output,
order, mode, cval, prefilter)
else:
# If ndim > 2, the rotation is applied over all the planes
# parallel to axes
planes_coord = itertools.product(
*[[slice(None)] if ax in axes else range(img_shape[ax])
for ax in range(ndim)])
out_plane_shape = tuple(out_plane_shape)
for coordinates in planes_coord:
ia = input_arr[coordinates]
oa = output[coordinates]
affine_transform(ia, rot_matrix, offset, out_plane_shape,
oa, order, mode, cval, prefilter)
return output