列为Matlab中的索引 [英] List as index in matlab
问题描述
有一种我想转换为Python的用Matlab编写的方法.但是，我不明白如何解释用矩阵faces的一行索引稀疏矩阵M的表示法. Python中的等价物是什么?
There is this method written in Matlab that I want to translate into Python. However, I don't understand how to interpret the notation of indexing the sparse matrix M with a row of the matrix faces. What would be the equivalent in Python?
M = spalloc(size(template,1), size(template,1), 10*size(template,1));
for i = 1:size(faces,1)
v = faces(i,:); % faces is a Nx3 matrix
...
M(v, v) = M(v, v) + WIJ; % WIJ is some 3x3 matrix
推荐答案
@Eric Yu`使用密集的numpy数组:
@Eric Yu` uses a dense numpy array:
In [239]: A=np.array([[1,2,3],[3,4,5],[5,6,7]])
In [240]: A
Out[240]:
array([[1, 2, 3],
[3, 4, 5],
[5, 6, 7]])
In [241]: v=[0,1]
此索引选择行:
In [242]: A[v]
Out[242]:
array([[1, 2, 3],
[3, 4, 5]])
，然后从选择的列中进行
and from that select columns:
In [243]: A[v][:,v]
Out[243]:
array([[1, 2],
[3, 4]])
但是A[v]是副本，而不是视图，因此分配将失败:
But A[v] is a copy, not a view, so assignment will fail:
In [244]: A[v][:,v] = 0
In [245]: A
Out[245]:
array([[1, 2, 3],
[3, 4, 5],
[5, 6, 7]])
===
要正确索引numpy数组的一个块，请使用ix_(或等效方法)创建相互广播以定义该块的索引数组:
To properly index a block of a numpy array, use ix_ (or equivalent) to create indexing arrays that broadcast against each other to define the block:
In [247]: np.ix_(v,v)
Out[247]:
(array([[0],
[1]]), array([[0, 1]]))
In [248]: A[np.ix_(v,v)]
Out[248]:
array([[1, 2],
[3, 4]])
In [249]: A[np.ix_(v,v)]=0
In [250]: A
Out[250]:
array([[0, 0, 3],
[0, 0, 5],
[5, 6, 7]])
在没有ix_变换的情况下，使用[v,v]进行索引会选择对角线:
Without the ix_ transform, indexing with [v,v] selects a diagonal:
In [251]: A[v,v]
Out[251]: array([0, 0])
MATLAB M(v,v)对块进行索引.另一方面，索引对角线需要使用sub2idx(或类似的东西).在这种情况下，MATLAB的索引符号使一项任务变得容易，而另一项任务变得更加复杂. numpy进行相反的操作.
MATLAB M(v,v) indexes the block. Indexing the diagonal on the other hand requires use of sub2idx (or something like that). This is a case where MATLAB's indexing notation makes one task easy, and the other more complex. numpy does the reverse.
===
我写的内容也适用于稀疏矩阵
What I wrote is applicable to sparse matrices as well
In [253]: M=sparse.lil_matrix(np.array([[1,2,3],[3,4,5],[5,6,7]]))
In [254]: M
Out[254]:
<3x3 sparse matrix of type '<class 'numpy.int64'>'
with 9 stored elements in LInked List format>
对角线选择:
In [255]: M[v,v]
Out[255]:
<1x2 sparse matrix of type '<class 'numpy.int64'>'
with 2 stored elements in LInked List format>
In [256]: _.A
Out[256]: array([[1, 4]], dtype=int64)
请注意，按照MATLAB矩阵的样式，此矩阵为(1,2)，仍为2d.
Note that this matrix is (1,2), still 2d, in the style of MATLAB matrices.
块选择:
In [258]: M[np.ix_(v,v)]
Out[258]:
<2x2 sparse matrix of type '<class 'numpy.int64'>'
with 4 stored elements in LInked List format>
In [259]: _.A
Out[259]:
array([[1, 2],
[3, 4]], dtype=int64)
In [260]: M[np.ix_(v,v)]=0
In [261]: M.A
Out[261]:
array([[0, 0, 3],
[0, 0, 5],
[5, 6, 7]], dtype=int64)
sparse.csr_matrix将以相同的方式编制索引(在分配步骤中有所不同).
sparse.csr_matrix will index in the same way (with some differences in the assignment step).
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