在 Python 中从数组中向量化压缩的稀疏矩阵

Question

我正在尝试将图论方法应用于图像处理问题。我想从包含我要绘制的点的数组中生成一个邻接矩阵。我想生成数组中点的完整图。如果我需要绘制数组中有 N 个点，我将需要一个 NxN 矩阵。权重应该是点之间的距离，所以这是我的代码：

''' vertexarray is an array where the points that are to be 
    included in the complete graph are True and all others False.'''

import numpy as np
def array_to_complete_graph(vertexarray):

    vertcoords = np.transpose(np.where(vertexarray == True))

    cg_array = np.eye(len(vertcoords))

    for idx, vals in enumerate(vertcoords):
        x_val_1, y_val_1 = vals
        for jdx, wals in enumerate(vertcoords):
            x_diff = wals[0] - vals[0]
            y_diff = wals[1] - vals[1]
            cg_array[idx,jdx] = np.sqrt(x_diff**2 + y_diff**2)
    return cg_array

这当然可行，但我的问题是：可以在没有嵌套 for 循环的情况下生成相同的数组吗？

Answer 1

使用函数scipy.spatial.distance.cdist()：

import numpy as np

def array_to_complete_graph(vertexarray):

    vertcoords = np.transpose(np.where(vertexarray == True))

    cg_array = np.eye(len(vertcoords))

    for idx, vals in enumerate(vertcoords):
        x_val_1, y_val_1 = vals
        for jdx, wals in enumerate(vertcoords):
            x_diff = wals[0] - vals[0]
            y_diff = wals[1] - vals[1]
            cg_array[idx,jdx] = np.sqrt(x_diff**2 + y_diff**2)
    return cg_array

arr = np.random.rand(10, 20) > 0.75

from scipy.spatial.distance import cdist
y, x = np.where(arr)
p = np.c_[x, y]
dist = cdist(p, p)
np.allclose(array_to_complete_graph(arr), dist)