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def geometric_transform(input, mapping, output_shape=None, output=None, order=3, mode='constant', cval=0.0, prefilter=True, extra_arguments=(), extra_keywords=None)
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 : array_like
The input array.
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 : array or dtype, optional
The array in which to place the output, or the dtype of the
returned array. By default an array of the same dtype as input
will be created.
order : int, optional
The order of the spline interpolation, default is 3.
The order has to be in the range 0-5.
mode : {'reflect', 'grid-mirror', 'constant', 'grid-constant', 'nearest', 'mirror', 'grid-wrap', 'wrap'}, optional
The `mode` parameter determines how the input array is extended
beyond its boundaries. Default is 'constant'. Behavior for each valid
value is as follows (see additional plots and details on
:ref:`boundary modes <ndimage-interpolation-modes>`):
'reflect' (`d c b a | a b c d | d c b a`)
The input is extended by reflecting about the edge of the last
pixel. This mode is also sometimes referred to as half-sample
symmetric.
'grid-mirror'
This is a synonym for 'reflect'.
'constant' (`k k k k | a b c d | k k k k`)
The input is extended by filling all values beyond the edge with
the same constant value, defined by the `cval` parameter. No
interpolation is performed beyond the edges of the input.
'grid-constant' (`k k k k | a b c d | k k k k`)
The input is extended by filling all values beyond the edge with
the same constant value, defined by the `cval` parameter. Interpolation
occurs for samples outside the input's extent as well.
'nearest' (`a a a a | a b c d | d d d d`)
The input is extended by replicating the last pixel.
'mirror' (`d c b | a b c d | c b a`)
The input is extended by reflecting about the center of the last
pixel. This mode is also sometimes referred to as whole-sample
symmetric.
'grid-wrap' (`a b c d | a b c d | a b c d`)
The input is extended by wrapping around to the opposite edge.
'wrap' (`d b c d | a b c d | b c a b`)
The input is extended by wrapping around to the opposite edge, but in a
way such that the last point and initial point exactly overlap. In this
case it is not well defined which sample will be chosen at the point of
overlap.
cval : scalar, optional
Value to fill past edges of input if `mode` is 'constant'. Default
is 0.0.
prefilter : bool, optional
Determines if the input array is prefiltered with `spline_filter`
before interpolation. The default is True, which will create a
temporary `float64` array of filtered values if ``order > 1``. If
setting this to False, the output will be slightly blurred if
``order > 1``, unless the input is prefiltered, i.e. it is the result
of calling `spline_filter` on the original input.
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])
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