Skip to content

Instantly share code, notes, and snippets.

Embed
What would you like to do?
Convolution Matrix
# Author: Jake VanderPlas
# LICENSE: MIT
from __future__ import division
import numpy as np
def convolution_matrix(x, N=None, mode='full'):
"""Compute the Convolution Matrix
This function computes a convolution matrix that encodes
the computation equivalent to ``numpy.convolve(x, y, mode)``
Parameters
----------
x : array_like
One-dimensional input array
N : integer (optional)
Size of the array to be convolved. Default is len(x).
mode : {'full', 'valid', 'same'}, optional
The type of convolution to perform. Default is 'full'.
See ``np.convolve`` documentation for details.
Returns
-------
C : ndarray
Matrix operator encoding the convolution. The matrix is of shape
[Nout x N], where Nout depends on ``mode`` and the size of ``x``.
Example
-------
>>> x = np.random.rand(10)
>>> y = np.random.rand(20)
>>> xy = np.convolve(x, y, mode='full')
>>> C = convolution_matrix(x, len(y), mode='full')
>>> np.allclose(xy, np.dot(C, y))
True
See Also
--------
numpy.convolve : direct convolution operation
scipy.signal.fftconvolve : direct convolution via the
fast Fourier transform
scipy.linalg.toeplitz : construct the Toeplitz matrix
"""
x = np.asarray(x)
if x.ndim != 1:
raise ValueError("x should be 1-dimensional")
M = len(x)
N = M if N is None else N
if mode == 'full':
Nout = M + N - 1
offset = 0
elif mode == 'valid':
Nout = max(M, N) - min(M, N) + 1
offset = min(M, N) - 1
elif mode == 'same':
Nout = max(N, M)
offset = (min(N, M) - 1) // 2
else:
raise ValueError("mode='{0}' not recognized".format(mode))
xpad = np.hstack([x, np.zeros(Nout)])
n = np.arange(Nout)[:, np.newaxis]
m = np.arange(N)
return xpad[n - m + offset]
# Author: Jake VanderPlas
# LICENSE: MIT
import pytest
from numpy.testing import assert_allclose
import numpy as np
from convolution_matrix import convolution_matrix
@pytest.mark.parametrize('M', [10, 15, 20, 25])
@pytest.mark.parametrize('N', [10, 15, 20, 25])
@pytest.mark.parametrize('dtype', ['float', 'complex'])
@pytest.mark.parametrize('mode', ['full', 'same', 'valid'])
def test_convolution_matrix(M, N, dtype, mode):
rand = np.random.RandomState(42)
x = rand.rand(M)
y = rand.rand(N)
if dtype == 'complex':
x = x * np.exp(2j * np.pi * rand.rand(M))
y = y * np.exp(2j * np.pi * rand.rand(N))
result1 = np.dot(convolution_matrix(x, len(y), mode), y)
result2 = np.convolve(x, y, mode)
assert_allclose(result1, result2)
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment