def spline_filter(input, order=3, output=numpy.float64):
"""
Multi-dimensional spline filter.
For more details, see `spline_filter1d`.
See Also
--------
spline_filter1d
Notes
-----
The multi-dimensional filter is implemented as a sequence of
one-dimensional 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.
"""
if order < 2 or order > 5:
raise RuntimeError('spline order not supported')
input = numpy.asarray(input)
if numpy.iscomplexobj(input):
raise TypeError('Complex type not supported')
output, return_value = _ni_support._get_output(output, input)
if order not in [0, 1] and input.ndim > 0:
for axis in range(input.ndim):
spline_filter1d(input, order, axis, output=output)
input = output
else:
output[...] = input[...]
return return_value
def correlate1d(input,
weights,
axis=-1,
output=None,
mode="reflect",
cval=0.0,
origin=0):
"""Calculate a one-dimensional correlation along the given axis.
The lines of the array along the given axis are correlated with the
given weights.
Parameters
----------
%(input)s
weights : array
One-dimensional sequence of numbers.
%(axis)s
%(output)s
%(mode)s
%(cval)s
%(origin)s
"""
input = numpy.asarray(input)
if numpy.iscomplexobj(input):
raise TypeError('Complex type not supported')
output, return_value = _ni_support._get_output(output, input)
weights = numpy.asarray(weights, dtype=numpy.float64)
if weights.ndim != 1 or weights.shape[0] < 1:
raise RuntimeError('no filter weights given')
if not weights.flags.contiguous:
weights = weights.copy()
axis = _ni_support._check_axis(axis, input.ndim)
if (len(weights) // 2 + origin < 0) or (len(weights) // 2 + origin >
len(weights)):
raise ValueError('invalid origin')
mode = _ni_support._extend_mode_to_code(mode)
_nd_image.correlate1d(input, weights, axis, output, mode, cval, origin)
return return_value
def spline_filter1d(input, order=3, axis=-1, output=numpy.float64):
"""
Calculates a one-dimensional 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 : array_like
The input array.
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`.
Returns
-------
spline_filter1d : ndarray or None
The filtered input. If `output` is given as a parameter, None is
returned.
"""
if order < 0 or order > 5:
raise RuntimeError('spline order not supported')
input = numpy.asarray(input)
if numpy.iscomplexobj(input):
raise TypeError('Complex type not supported')
output, return_value = _ni_support._get_output(output, input)
if order in [0, 1]:
output[...] = numpy.array(input)
else:
axis = _ni_support._check_axis(axis, input.ndim)
_nd_image.spline_filter1d(input, order, axis, output)
return return_value
def gaussian_filter(input,
sigma,
order=0,
output=None,
mode="reflect",
cval=0.0,
truncate=4.0):
"""Multidimensional Gaussian filter.
Parameters
----------
%(input)s
sigma : scalar or sequence of scalars
Standard deviation for Gaussian kernel. The standard
deviations of the Gaussian filter are given for each axis as a
sequence, or as a single number, in which case it is equal for
all axes.
order : {0, 1, 2, 3} or sequence from same set, optional
The order of the filter along each axis is given as a sequence
of integers, or as a single number. An order of 0 corresponds
to convolution with a Gaussian kernel. An order of 1, 2, or 3
corresponds to convolution with the first, second or third
derivatives of a Gaussian. Higher order derivatives are not
implemented
%(output)s
%(mode)s
%(cval)s
truncate : float
Truncate the filter at this many standard deviations.
Default is 4.0.
Returns
-------
gaussian_filter : ndarray
Returned array of same shape as `input`.
Notes
-----
The multidimensional filter is implemented as a sequence of
one-dimensional convolution 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.
Examples
--------
>>> from scipy.ndimage import gaussian_filter
>>> a = np.arange(50, step=2).reshape((5,5))
>>> a
array([[ 0, 2, 4, 6, 8],
[10, 12, 14, 16, 18],
[20, 22, 24, 26, 28],
[30, 32, 34, 36, 38],
[40, 42, 44, 46, 48]])
>>> gaussian_filter(a, sigma=1)
array([[ 4, 6, 8, 9, 11],
[10, 12, 14, 15, 17],
[20, 22, 24, 25, 27],
[29, 31, 33, 34, 36],
[35, 37, 39, 40, 42]])
"""
input = numpy.asarray(input)
output, return_value = _ni_support._get_output(output, input)
orders = _ni_support._normalize_sequence(order, input.ndim)
if not set(orders).issubset(set(range(4))):
raise ValueError('Order outside 0..4 not implemented')
sigmas = _ni_support._normalize_sequence(sigma, input.ndim)
axes = list(range(input.ndim))
axes = [(axes[ii], sigmas[ii], orders[ii]) for ii in range(len(axes))
if sigmas[ii] > 1e-15]
if len(axes) > 0:
for axis, sigma, order in axes:
gaussian_filter1d(input, sigma, axis, order, output, mode, cval,
truncate)
input = output
else:
output[...] = input[...]
return return_value
def zoom(input,
zoom,
output=None,
order=3,
mode='constant',
cval=0.0,
prefilter=True):
"""
Zoom an array.
The array is zoomed using spline interpolation of the requested order.
Parameters
----------
input : ndarray
The input array.
zoom : float or sequence, optional
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 : ndarray or dtype, optional
The array in which to place the output, or the dtype of the returned
array.
order : int, optional
The order of the spline interpolation, default is 3.
The order has to be in the range 0-5.
mode : str, optional
Points outside the boundaries of the input are filled according
to the given mode ('constant', 'nearest', 'reflect' or 'wrap').
Default is 'constant'.
cval : scalar, optional
Value used for points outside the boundaries of the input if
``mode='constant'``. Default is 0.0
prefilter : bool, optional
The parameter prefilter determines if the input is pre-filtered with
`spline_filter` before interpolation (necessary for spline
interpolation of order > 1). If False, it is assumed that the input is
already filtered. Default is True.
Returns
-------
zoom : ndarray or None
The zoomed input. If `output` is given as a parameter, None is
returned.
"""
if order < 0 or order > 5:
raise RuntimeError('spline order not supported')
input = numpy.asarray(input)
if numpy.iscomplexobj(input):
raise TypeError('Complex type not supported')
if input.ndim < 1:
raise RuntimeError('input and output rank must be > 0')
mode = _extend_mode_to_code(mode)
if prefilter and order > 1:
filtered = spline_filter(input, order, output=numpy.float64)
else:
filtered = input
zoom = _ni_support._normalize_sequence(zoom, input.ndim)
output_shape = tuple(
[int(round(ii * jj)) for ii, jj in zip(input.shape, zoom)])
zoom_div = numpy.array(output_shape, float) - 1
zoom = (numpy.array(input.shape) - 1) / zoom_div
# Zooming to non-finite values is unpredictable, so just choose
# zoom factor 1 instead
zoom[~numpy.isfinite(zoom)] = 1
output, return_value = _ni_support._get_output(output,
input,
shape=output_shape)
zoom = numpy.asarray(zoom, dtype=numpy.float64)
zoom = numpy.ascontiguousarray(zoom)
_nd_image.zoom_shift(filtered, zoom, None, output, order, mode, cval)
return return_value