仅使用广播从矩阵的指定列向量中减去列向量 [英] Subtract a column vector from matrix at specified vector of columns using only broadcast

问题描述

我想使用另一个向量从numpy矩阵中减去列向量，该向量是需要从主矩阵中减去第一个列向量的列的索引.例如.

I want to subtract a column vector from a numpy matrix using another vector which is index of columns where the first column vector needs to be subtracted from the main matrix. For eg.

M = array([[  1,   2,   1,   1],
           [  2,   1,   1,   1],
           [  1,   1,   2,   1],
           [  2,   1,   1,   1],
           [  1,   1,   1,   2]])  # An example matrix

V = array([1, 1, 1, 1, 1]) # An example column vector

I = array([0, 3, 2, 3, 1, 3, 3]) # The index maxtrix

现在我想在I中给定的列号上从M中减去V. 例如. I [0]为0，因此从矩阵M的第一列(零索引)中减去V.

Now I want to subtract V from M at column numbers given in I. For eg. I[0] is 0, so subtract V from first column (zero index) of matrix M.

类似地，I [1] = 3，从矩阵M的第四列(三个索引)中减去V.

Similarly I[1] = 3, subtract V from fourth column (three index) of matrix M.

操作结束时，由于3在I中出现4次，因此将从第三列中减去V，即M-4的最后一列.

At the end of operation, since 3 occurs 4 times in I, so V will be subtracted from third column i.e. last column of M- 4 times.

我只需要广播，不循环就可以做到这一点.

I need to do this using only broadcast, no loops.

我尝试了以下操作:

M[:, I] - V[np.newaxis, :].T

但是它最终广播的结果矩阵的列数比M中的列数还要多.

but it ends up broadcasting resultant matrix to have more columns than there are in M.

推荐答案

一个人可以使用bincount和outer

>>> M - np.outer(V, np.bincount(I, None, M.shape[1]))
array([[ 0,  1,  0, -3],
       [ 1,  0,  0, -3],
       [ 0,  0,  1, -3],
       [ 1,  0,  0, -3],
       [ 0,  0,  0, -2]])

或subtract.at

>>> out = M.copy()
>>> np.subtract.at(out, (np.s_[:], I), V[:, None])
>>> out
array([[ 0,  1,  0, -3],
       [ 1,  0,  0, -3],
       [ 0,  0,  1, -3],
       [ 1,  0,  0, -3],
       [ 0,  0,  0, -2]])

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