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Please describe the purpose of the new feature or describe the problem to solve.
I would be great to have support for ND convolution of sparse arrays. Basically an implementation of scipy.signal.convolve, with support for sparse arrays.
Suggest a solution if possible.
I have played around a bit with implementing a convolution via sparse matrix multiplication:
import sparse as sp
import numpy as np
import matplotlib.pyplot as plt
from scipy.signal import convolve2d
from scipy.linalg import circulant
random_state = np.random.RandomState(7236)
coords = random_state.randint(0, 100, size=(2, 100))
data = random_state.gamma(10, size=100)
data_sparse = sp.COO(coords, data, shape=(100, 100))
def gaussian_kernel(sigma, size=None):
"""Get 2d Gaussian kernel"""
if size is None:
size = int(3 * sigma) * 2 + 1
x = np.linspace(-size, size, 2*size+1)
y = np.linspace(-size, size, 2*size+1)
x, y = np.meshgrid(x, y)
kernel = np.exp(-(x**2 + y**2) / (2 * sigma**2))
return kernel / kernel.sum()
def convolve2d_sparse(data, kernel):
"""Convolve sparse 2d data with 2d kernel"""
shape_diff = np.array(data.shape) - np.array(kernel.shape)
kernel_pad = np.pad(kernel, pad_width=((shape_diff[0], 0), (shape_diff[1], 0)), mode='constant', constant_values=0)
kernel_matrix = sp.COO.from_numpy(circulant(kernel_pad))
result = (kernel_matrix @ data.flatten()).reshape(data.shape)
return sp.roll(result, shift=(kernel.shape[0]//2, kernel.shape[1]//2 + 1), axis=(0, 1))
kernel = gaussian_kernel(1.5)
result_sparse = convolve2d_sparse(data_sparse, kernel)
result_dense = convolve2d(data_sparse.todense(), kernel, mode='same', boundary='wrap')
fig, axes = plt.subplots(1, 3, figsize=(12, 4))
diff = result_dense - result_sparse.todense()
axes[0].imshow(result_sparse.todense(), cmap='viridis')
axes[0].set_title('Sparse convolution')
axes[1].imshow(result_dense, cmap='viridis')
axes[1].set_title('Dense convolution')
axes[2].imshow(diff, vmin=-0.5, vmax=0.5, cmap="RdBu")
axes[2].set_title('Diff')
But performance wise this is really bad:
Also boundary handling becomes really complex. And I am sure the experts have much better ideas on how to implement this.
If you have tried alternatives, please describe them below.
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