bundles / scipy latest / scipy / ndimage / _filters / convolve

function

`scipy.ndimage._filters:convolve`

source: /scipy/ndimage/_filters.py :1379

Signature

   def     convolve (    input    ,    weights    ,    output    =  None   ,    mode    =  reflect   ,    cval    =  0.0   ,    origin    =  0   ,  * ,     axes    =  None     )

Summary

Multidimensional convolution.

Extended Summary

The array is convolved with the given kernel.

Parameters

input : array_like

The input array.

weights : array_like

Array of weights, same number of dimensions as input

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.

mode : {'reflect', 'constant', 'nearest', 'mirror', 'wrap'}, optional

The mode parameter determines how the input array is extended beyond its boundaries. Default is 'reflect'. Behavior for each valid value is as follows:

'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.
'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.
'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.
'wrap' (a b c d | a b c d | a b c d): The input is extended by wrapping around to the opposite edge.

For consistency with the interpolation functions, the following mode names can also be used:

'grid-mirror': This is a synonym for 'reflect'.
'grid-constant': This is a synonym for 'constant'.
'grid-wrap': This is a synonym for 'wrap'.

cval : scalar, optional

Value to fill past edges of input if mode is 'constant'. Default is 0.0

origin : int or sequence, optional

Controls the placement of the filter on the input array's pixels. A value of 0 (the default) centers the filter over the pixel, with positive values shifting the filter to the right, and negative ones to the left. By passing a sequence of origins with length equal to the number of dimensions of the input array, different shifts can be specified along each axis.

axes : tuple of int or None, optional

If None, input is filtered along all axes. Otherwise, input is filtered along the specified axes. When axes is specified, any tuples used for mode or origin must match the length of axes. The ith entry in any of these tuples corresponds to the ith entry in axes.

Returns

result : ndarray: The result of convolution of input with weights.

Notes

Each value in result is $C_{i} = \sum_{j} I_{i + k - j} W_{j}$ , where W is the weights kernel, j is the N-D spatial index over $W$ , I is the input and k is the coordinate of the center of W, specified by origin in the input parameters.

Array API Standard Support

convolve has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ✅                   
PyTorch               ✅                     ⛔                   
JAX                   ⚠️ no JIT             ⛔                   
Dask                  ⚠️ computes graph     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

Examples

Perhaps the simplest case to understand is ``mode='constant', cval=0.0``, because in this case borders (i.e., where the `weights` kernel, centered on any one value, extends beyond an edge of `input`) are treated as zeros.

import numpy as np
a = np.array([[1, 2, 0, 0],
              [5, 3, 0, 4],
              [0, 0, 0, 7],
              [9, 3, 0, 0]])
k = np.array([[1,1,1],[1,1,0],[1,0,0]])
from scipy import ndimage
ndimage.convolve(a, k, mode='constant', cval=0.0)

✓

Setting ``cval=1.0`` is equivalent to padding the outer edge of `input` with 1.0's (and then extracting only the original region of the result).

ndimage.convolve(a, k, mode='constant', cval=1.0)

✓

With ``mode='reflect'`` (the default), outer values are reflected at the edge of `input` to fill in missing values.

b = np.array([[2, 0, 0],
              [1, 0, 0],
              [0, 0, 0]])
k = np.array([[0,1,0], [0,1,0], [0,1,0]])
ndimage.convolve(b, k, mode='reflect')

✓

This includes diagonally at the corners.

k = np.array([[1,0,0],[0,1,0],[0,0,1]])
ndimage.convolve(b, k)

✓

With ``mode='nearest'``, the single nearest value in to an edge in `input` is repeated as many times as needed to match the overlapping `weights`.

c = np.array([[2, 0, 1],
              [1, 0, 0],
              [0, 0, 0]])
k = np.array([[0, 1, 0],
              [0, 1, 0],
              [0, 1, 0],
              [0, 1, 0],
              [0, 1, 0]])
ndimage.convolve(c, k, mode='nearest')

✓

Aliases

scipy.ndimage.convolve

Referenced by

This package

release:1.6.0-notes