使用置换向量重新排序矩阵但保持矩阵的原始大小
Reordering matrix with a permutation vector but keeping the original size of matrix
我有一个简单的问题，但无法解决。我有一个从另一个矩阵复制而来的 C_temp 16x16 矩阵 (size = 16)。
C_temp = np.zeros((size, size))
C_temp = np.copy(C_in)
然后，我有一个排列列表（或 numpy 数组，我不知道它是否重要）：
print('index_reorder =', index_reorder) 给出：
index_reorder = ', array([2, 4, 0, 5, 1, 3, 7, 8]))
我想根据 index_reorder 沿着 x axis 和 y axis 进行排列。
C_temp = np.copy(C_in)
C_temp = C_temp[:, index_reorder]
C_temp = C_temp[index_reorder, :]
C_new = np.copy(C_temp)
但不幸的是，新的矩阵 C_new 尺寸减小到 8x8。
这不是我想要的：我想为 C_new 矩阵 (16x16) 保持相同的大小，即在保持置换矩阵 [=15= 的整个大小的同时进行排列].
如何执行这个全局排列？
这叫做 "permutation in-place" 我相信，不是吗？
更新 1 : 这是 C_in 矩阵 16x16
的示例
C_in = ', array([[ 5.39607129e+06, 1.79979372e+06, -2.46370980e+06,
-1.12590397e+06, 2.54997996e+03, -3.48237530e+02,
1.77139942e+05, 2.10555125e+04, -2.24912032e+05,
-9.79292472e+01, -1.63415352e+05, -8.65388775e+01,
-8.10556705e+04, -6.40511456e+01, 1.31499502e+04,
-4.80973452e+01],
[ 1.79979372e+06, 1.85207497e+07, -5.97280544e+06,
-4.86527342e+05, -9.46833729e+05, -2.10321296e+05,
-7.71198259e+05, -8.88750203e+04, -1.66150873e+06,
-3.20782728e+02, -1.45257426e+06, -2.86060423e+02,
-1.10641471e+06, -2.17539743e+02, -9.34181143e+05,
-1.77667406e+02],
[-2.46370980e+06, -5.97280544e+06, 3.36326384e+06,
5.88733451e+05, 3.35606646e+05, 8.96417015e+04,
1.12240864e+05, 1.35483472e+04, 6.10023925e+05,
1.26679014e+02, 5.65166386e+05, 1.21455772e+02,
4.43234727e+05, 9.80424886e+01, 3.68206009e+05,
8.44106515e+01],
[-1.12590397e+06, -4.86527342e+05, 5.88733451e+05,
3.34731505e+05, -3.26665859e+04, -7.14038524e+03,
-7.25370986e+04, -8.44842826e+03, 4.40874561e+04,
2.82933253e+01, 2.77238713e+04, 2.47986977e+01,
7.27381187e+03, 1.80784440e+01, -1.87787106e+04,
1.31142301e+01],
[ 2.54997996e+03, -9.46833729e+05, 3.35606646e+05,
-3.26665859e+04, 7.90884228e+04, 1.92364617e+04,
5.66130910e+04, 6.70772964e+03, 1.07063410e+05,
1.46143888e+01, 9.53013920e+04, 1.33963997e+01,
7.42574771e+04, 1.04791841e+01, 6.58013341e+04,
8.95530786e+00],
[-3.48237530e+02, -2.10321296e+05, 8.96417015e+04,
-7.14038524e+03, 1.92364617e+04, 4.99000202e+03,
1.10082611e+04, 1.34941127e+03, 2.41927165e+04,
3.26733542e+00, 2.31011986e+04, 3.22432044e+00,
1.88491639e+04, 2.65297382e+00, 1.72802490e+04,
2.36016813e+00],
[ 1.77139942e+05, -7.71198259e+05, 1.12240864e+05,
-7.25370986e+04, 5.66130910e+04, 1.10082611e+04,
9.36434428e+04, 1.07348807e+04, 6.09534507e+04,
3.44072173e+00, 5.90764148e+04, 4.26292063e+00,
5.10904441e+04, 4.37089791e+00, 5.24285786e+04,
5.06825219e+00],
[ 2.10555125e+04, -8.88750203e+04, 1.35483472e+04,
-8.44842826e+03, 6.70772964e+03, 1.34941127e+03,
1.07348807e+04, 1.48215248e+03, 2.49002654e+03,
1.40557890e-01, 5.84713359e+03, 4.21925848e-01,
7.21719030e+03, 6.17446227e-01, 9.39064037e+03,
9.07789891e-01],
[-2.24912032e+05, -1.66150873e+06, 6.10023925e+05,
4.40874561e+04, 1.07063410e+05, 2.41927165e+04,
6.09534507e+04, 2.49002654e+03, 5.91760033e+05,
9.77850970e+01, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00],
[-9.79292472e+01, -3.20782728e+02, 1.26679014e+02,
2.82933253e+01, 1.46143888e+01, 3.26733542e+00,
3.44072173e+00, 1.40557890e-01, 9.77850970e+01,
2.42137019e-02, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00],
[-1.63415352e+05, -1.45257426e+06, 5.65166386e+05,
2.77238713e+04, 9.53013920e+04, 2.31011986e+04,
5.90764148e+04, 5.84713359e+03, 0.00000000e+00,
0.00000000e+00, 4.84422452e+05, 8.24104281e+01,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00],
[-8.65388775e+01, -2.86060423e+02, 1.21455772e+02,
2.47986977e+01, 1.33963997e+01, 3.22432044e+00,
4.26292063e+00, 4.21925848e-01, 0.00000000e+00,
0.00000000e+00, 8.24104281e+01, 2.11226210e-02,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00],
[-8.10556705e+04, -1.10641471e+06, 4.43234727e+05,
7.27381187e+03, 7.42574771e+04, 1.88491639e+04,
5.10904441e+04, 7.21719030e+03, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
3.50093152e+05, 6.00111232e+01, 0.00000000e+00,
0.00000000e+00],
[-6.40511456e+01, -2.17539743e+02, 9.80424886e+01,
1.80784440e+01, 1.04791841e+01, 2.65297382e+00,
4.37089791e+00, 6.17446227e-01, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
6.00111232e+01, 1.57248915e-02, 0.00000000e+00,
0.00000000e+00],
[ 1.31499502e+04, -9.34181143e+05, 3.68206009e+05,
-1.87787106e+04, 6.58013341e+04, 1.72802490e+04,
5.24285786e+04, 9.39064037e+03, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 2.83150690e+05,
4.74239664e+01],
[-4.80973452e+01, -1.77667406e+02, 8.44106515e+01,
1.31142301e+01, 8.95530786e+00, 2.36016813e+00,
5.06825219e+00, 9.07789891e-01, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 4.74239664e+01,
1.26116519e-02]]))
和输出 C_new 矩阵：
C_new = ', array([[ 3.36326384e+06, 3.35606646e+05, -2.46370980e+06,
8.96417015e+04, -5.97280544e+06, 5.88733451e+05,
1.35483472e+04, 6.10023925e+05],
[ 3.35606646e+05, 7.90884228e+04, 2.54997996e+03,
1.92364617e+04, -9.46833729e+05, -3.26665859e+04,
6.70772964e+03, 1.07063410e+05],
[-2.46370980e+06, 2.54997996e+03, 5.39607129e+06,
-3.48237530e+02, 1.79979372e+06, -1.12590397e+06,
2.10555125e+04, -2.24912032e+05],
[ 8.96417015e+04, 1.92364617e+04, -3.48237530e+02,
4.99000202e+03, -2.10321296e+05, -7.14038524e+03,
1.34941127e+03, 2.41927165e+04],
[-5.97280544e+06, -9.46833729e+05, 1.79979372e+06,
-2.10321296e+05, 1.85207497e+07, -4.86527342e+05,
-8.88750203e+04, -1.66150873e+06],
[ 5.88733451e+05, -3.26665859e+04, -1.12590397e+06,
-7.14038524e+03, -4.86527342e+05, 3.34731505e+05,
-8.44842826e+03, 4.40874561e+04],
[ 1.35483472e+04, 6.70772964e+03, 2.10555125e+04,
1.34941127e+03, -8.88750203e+04, -8.44842826e+03,
1.48215248e+03, 2.49002654e+03],
[ 6.10023925e+05, 1.07063410e+05, -2.24912032e+05,
2.41927165e+04, -1.66150873e+06, 4.40874561e+04,
2.49002654e+03, 5.91760033e+05]]))
我只想交换 rows/columns（即看起来像排列？）作为 rows/columns 向量的函数 index_reorder。
正如您自己发现的那样，问题是 index_reorder 只包含重新排序的元素。
解决方案是，将其扩展为所有元素的完整排列。如果元素应该保留在原位，只需将它们的索引写在它们原来的位置，这样它们就会保留。
例如：
index_reorder = [2, 4, 0, 5, 1, 3, 7, 8]
应转换为：
full_reorder = [2, 4, 0, 5, 1, 3, 7, 8, 6, 9, 10, 11, 12, 13, 14, 15]
注意，9->9, 10->10, 11->11.... 这样，它们就不会移动，也不会丢失。还有其他 full_reorders 可以想到的，他们的选择仅取决于您的喜好。第一，您可能更喜欢 [2, 4, 0, 5, 1, 3, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]。这里 6->6 并且原始排列围绕它展开。
第一个示例中给出的更改后的重新排序可以如下实现：
all_indices = np.array(range(16))
other_indices = np.setdiff1d(all_indices, index_reorder)
full_reorder = np.concatenate([index_reorder, other_indices])
然后按照你所做的继续：
C_temp = np.copy(C_in)
C_temp = C_temp[:, full_reorder]
C_temp = C_temp[full_reorder, :]
我有一个简单的问题，但无法解决。我有一个从另一个矩阵复制而来的 C_temp 16x16 矩阵 (size = 16)。
C_temp = np.zeros((size, size))
C_temp = np.copy(C_in)
然后，我有一个排列列表（或 numpy 数组，我不知道它是否重要）：
print('index_reorder =', index_reorder) 给出：
index_reorder = ', array([2, 4, 0, 5, 1, 3, 7, 8]))
我想根据 index_reorder 沿着 x axis 和 y axis 进行排列。
C_temp = np.copy(C_in)
C_temp = C_temp[:, index_reorder]
C_temp = C_temp[index_reorder, :]
C_new = np.copy(C_temp)
但不幸的是，新的矩阵 C_new 尺寸减小到 8x8。
这不是我想要的：我想为 C_new 矩阵 (16x16) 保持相同的大小，即在保持置换矩阵 [=15= 的整个大小的同时进行排列].
如何执行这个全局排列？
这叫做 "permutation in-place" 我相信，不是吗？
更新 1 : 这是 C_in 矩阵 16x16
C_in = ', array([[ 5.39607129e+06, 1.79979372e+06, -2.46370980e+06,
-1.12590397e+06, 2.54997996e+03, -3.48237530e+02,
1.77139942e+05, 2.10555125e+04, -2.24912032e+05,
-9.79292472e+01, -1.63415352e+05, -8.65388775e+01,
-8.10556705e+04, -6.40511456e+01, 1.31499502e+04,
-4.80973452e+01],
[ 1.79979372e+06, 1.85207497e+07, -5.97280544e+06,
-4.86527342e+05, -9.46833729e+05, -2.10321296e+05,
-7.71198259e+05, -8.88750203e+04, -1.66150873e+06,
-3.20782728e+02, -1.45257426e+06, -2.86060423e+02,
-1.10641471e+06, -2.17539743e+02, -9.34181143e+05,
-1.77667406e+02],
[-2.46370980e+06, -5.97280544e+06, 3.36326384e+06,
5.88733451e+05, 3.35606646e+05, 8.96417015e+04,
1.12240864e+05, 1.35483472e+04, 6.10023925e+05,
1.26679014e+02, 5.65166386e+05, 1.21455772e+02,
4.43234727e+05, 9.80424886e+01, 3.68206009e+05,
8.44106515e+01],
[-1.12590397e+06, -4.86527342e+05, 5.88733451e+05,
3.34731505e+05, -3.26665859e+04, -7.14038524e+03,
-7.25370986e+04, -8.44842826e+03, 4.40874561e+04,
2.82933253e+01, 2.77238713e+04, 2.47986977e+01,
7.27381187e+03, 1.80784440e+01, -1.87787106e+04,
1.31142301e+01],
[ 2.54997996e+03, -9.46833729e+05, 3.35606646e+05,
-3.26665859e+04, 7.90884228e+04, 1.92364617e+04,
5.66130910e+04, 6.70772964e+03, 1.07063410e+05,
1.46143888e+01, 9.53013920e+04, 1.33963997e+01,
7.42574771e+04, 1.04791841e+01, 6.58013341e+04,
8.95530786e+00],
[-3.48237530e+02, -2.10321296e+05, 8.96417015e+04,
-7.14038524e+03, 1.92364617e+04, 4.99000202e+03,
1.10082611e+04, 1.34941127e+03, 2.41927165e+04,
3.26733542e+00, 2.31011986e+04, 3.22432044e+00,
1.88491639e+04, 2.65297382e+00, 1.72802490e+04,
2.36016813e+00],
[ 1.77139942e+05, -7.71198259e+05, 1.12240864e+05,
-7.25370986e+04, 5.66130910e+04, 1.10082611e+04,
9.36434428e+04, 1.07348807e+04, 6.09534507e+04,
3.44072173e+00, 5.90764148e+04, 4.26292063e+00,
5.10904441e+04, 4.37089791e+00, 5.24285786e+04,
5.06825219e+00],
[ 2.10555125e+04, -8.88750203e+04, 1.35483472e+04,
-8.44842826e+03, 6.70772964e+03, 1.34941127e+03,
1.07348807e+04, 1.48215248e+03, 2.49002654e+03,
1.40557890e-01, 5.84713359e+03, 4.21925848e-01,
7.21719030e+03, 6.17446227e-01, 9.39064037e+03,
9.07789891e-01],
[-2.24912032e+05, -1.66150873e+06, 6.10023925e+05,
4.40874561e+04, 1.07063410e+05, 2.41927165e+04,
6.09534507e+04, 2.49002654e+03, 5.91760033e+05,
9.77850970e+01, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00],
[-9.79292472e+01, -3.20782728e+02, 1.26679014e+02,
2.82933253e+01, 1.46143888e+01, 3.26733542e+00,
3.44072173e+00, 1.40557890e-01, 9.77850970e+01,
2.42137019e-02, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00],
[-1.63415352e+05, -1.45257426e+06, 5.65166386e+05,
2.77238713e+04, 9.53013920e+04, 2.31011986e+04,
5.90764148e+04, 5.84713359e+03, 0.00000000e+00,
0.00000000e+00, 4.84422452e+05, 8.24104281e+01,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00],
[-8.65388775e+01, -2.86060423e+02, 1.21455772e+02,
2.47986977e+01, 1.33963997e+01, 3.22432044e+00,
4.26292063e+00, 4.21925848e-01, 0.00000000e+00,
0.00000000e+00, 8.24104281e+01, 2.11226210e-02,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00],
[-8.10556705e+04, -1.10641471e+06, 4.43234727e+05,
7.27381187e+03, 7.42574771e+04, 1.88491639e+04,
5.10904441e+04, 7.21719030e+03, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
3.50093152e+05, 6.00111232e+01, 0.00000000e+00,
0.00000000e+00],
[-6.40511456e+01, -2.17539743e+02, 9.80424886e+01,
1.80784440e+01, 1.04791841e+01, 2.65297382e+00,
4.37089791e+00, 6.17446227e-01, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
6.00111232e+01, 1.57248915e-02, 0.00000000e+00,
0.00000000e+00],
[ 1.31499502e+04, -9.34181143e+05, 3.68206009e+05,
-1.87787106e+04, 6.58013341e+04, 1.72802490e+04,
5.24285786e+04, 9.39064037e+03, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 2.83150690e+05,
4.74239664e+01],
[-4.80973452e+01, -1.77667406e+02, 8.44106515e+01,
1.31142301e+01, 8.95530786e+00, 2.36016813e+00,
5.06825219e+00, 9.07789891e-01, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 4.74239664e+01,
1.26116519e-02]]))
和输出 C_new 矩阵：
C_new = ', array([[ 3.36326384e+06, 3.35606646e+05, -2.46370980e+06,
8.96417015e+04, -5.97280544e+06, 5.88733451e+05,
1.35483472e+04, 6.10023925e+05],
[ 3.35606646e+05, 7.90884228e+04, 2.54997996e+03,
1.92364617e+04, -9.46833729e+05, -3.26665859e+04,
6.70772964e+03, 1.07063410e+05],
[-2.46370980e+06, 2.54997996e+03, 5.39607129e+06,
-3.48237530e+02, 1.79979372e+06, -1.12590397e+06,
2.10555125e+04, -2.24912032e+05],
[ 8.96417015e+04, 1.92364617e+04, -3.48237530e+02,
4.99000202e+03, -2.10321296e+05, -7.14038524e+03,
1.34941127e+03, 2.41927165e+04],
[-5.97280544e+06, -9.46833729e+05, 1.79979372e+06,
-2.10321296e+05, 1.85207497e+07, -4.86527342e+05,
-8.88750203e+04, -1.66150873e+06],
[ 5.88733451e+05, -3.26665859e+04, -1.12590397e+06,
-7.14038524e+03, -4.86527342e+05, 3.34731505e+05,
-8.44842826e+03, 4.40874561e+04],
[ 1.35483472e+04, 6.70772964e+03, 2.10555125e+04,
1.34941127e+03, -8.88750203e+04, -8.44842826e+03,
1.48215248e+03, 2.49002654e+03],
[ 6.10023925e+05, 1.07063410e+05, -2.24912032e+05,
2.41927165e+04, -1.66150873e+06, 4.40874561e+04,
2.49002654e+03, 5.91760033e+05]]))
我只想交换 rows/columns（即看起来像排列？）作为 rows/columns 向量的函数 index_reorder。
正如您自己发现的那样，问题是 index_reorder 只包含重新排序的元素。
解决方案是，将其扩展为所有元素的完整排列。如果元素应该保留在原位，只需将它们的索引写在它们原来的位置，这样它们就会保留。
例如：
index_reorder = [2, 4, 0, 5, 1, 3, 7, 8]
应转换为：
full_reorder = [2, 4, 0, 5, 1, 3, 7, 8, 6, 9, 10, 11, 12, 13, 14, 15]
注意，9->9, 10->10, 11->11.... 这样，它们就不会移动，也不会丢失。还有其他 full_reorders 可以想到的，他们的选择仅取决于您的喜好。第一，您可能更喜欢 [2, 4, 0, 5, 1, 3, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]。这里 6->6 并且原始排列围绕它展开。
第一个示例中给出的更改后的重新排序可以如下实现：
all_indices = np.array(range(16))
other_indices = np.setdiff1d(all_indices, index_reorder)
full_reorder = np.concatenate([index_reorder, other_indices])
然后按照你所做的继续：
C_temp = np.copy(C_in)
C_temp = C_temp[:, full_reorder]
C_temp = C_temp[full_reorder, :]