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问题:
I need to get a diagonal stripe of the matrix (not sure about the terminology here, diagonal matrix stripe seems to describe it best).
Say, I have a matrix of size KxN, where K and N are arbitrary sizes and K>N. Say, I have a matrix:
[[ 0 1 2] [ 3 4 5] [ 6 7 8] [ 9 10 11]]
From it I would need to extract a diagonal stripe, in this case, a matrix MxV size that is created by truncating the original one:
[[ 0 x x] [ 3 4 x] [ x 7 8] [ x x 11]]
So the result matrix is:
[[ 0 4 8] [ 3 7 11]]
Here is a small example code using masking for the matrices, to strip out the masked positions:
import numpy as np X=np.arange(12).reshape(4,3) mask=np.asarray([ [ True, False, False], [ True, True, False], [ False, True, True], [ False, False, True] ]) >>> mask array([[ True, False, False], [ True, True, False], [False, True, True], [False, False, True]], dtype=bool) >>> X array([[ 0, 1, 2], [ 3, 4, 5], [ 6, 7, 8], [ 9, 10, 11]]) >>> X.T[mask.T].reshape(3,2).T array([[ 0, 4, 8], [ 3, 7, 11]])
But I don't see how such a mask could be automatically generated to any K and N sizes, e.i. 39x9 or 360x96
Any help is appreciated. Maybe there is some function that does this automatically either in numpy, scipy or pytorch?
回答1:
Extending Paul's answer. You can do the same in PyTorch using diag multiple times (I do not think there is any direct function to do strides in PyTorch)
In [1]: import torch In [2]: def stripe(a): ...: i, j = a.size() ...: assert(i>=j) ...: out = torch.zeros((i-j+1, j)) ...: for diag in range(0, i-j+1): ...: out[diag] = torch.diag(a, -diag) ...: return out ...: In [3]: a = torch.randn((6, 3)) In [4]: a Out[4]: 0.7669 0.6808 -0.6102 -1.0624 -1.2016 -0.7308 1.4054 -1.0621 0.2618 -0.9505 -0.9322 -0.4321 -0.0134 -1.3684 0.1883 -0.8499 0.2533 -0.3976 [torch.FloatTensor of size 6x3] In [5]: stripe(a) Out[5]: 0.7669 -1.2016 0.2618 -1.0624 -1.0621 -0.4321 1.4054 -0.9322 0.1883 -0.9505 -1.3684 -0.3976 [torch.FloatTensor of size 4x3]
回答2:
stride_tricks do the trick:
>>> import numpy as np >>> >>> def stripe(a): ... a = np.asanyarray(a) ... i, j = a.shape ... assert i >= j ... k, l = a.strides ... return np.lib.stride_tricks.as_strided(a, (i-j+1, j), (k, k+l)) ... >>> a = np.arange(24).reshape(6, 4) >>> a array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11], [12, 13, 14, 15], [16, 17, 18, 19], [20, 21, 22, 23]]) >>> stripe(a) array([[ 0, 5, 10, 15], [ 4, 9, 14, 19], [ 8, 13, 18, 23]])
If a is an array this creates a writable view, meaning that if you feel so inclined you can do things like
>>> stripe(a)[...] *= 10 >>> a array([[ 0, 1, 2, 3], [ 40, 50, 6, 7], [ 80, 90, 100, 11], [ 12, 130, 140, 150], [ 16, 17, 180, 190], [ 20, 21, 22, 230]])
