一维numpy数组，该数组在新2D数组中的每个连续行向右移动 [英] 1D numpy array which is shifted to the right for each consecutive row in a new 2D array

问题描述

我正在尝试通过删除循环并仅在处理大型数据集时使用numpy数组来优化某些代码.

I am trying to optimise some code by removing for loops and using numpy arrays only as I am working with large data sets.

我想使用一维numpy数组，例如:

I would like to take a 1D numpy array, for example:

a = [1, 2, 3, 4, 5]

并生成一个二维numpy数组，其中每列中的值沿一个位置移动，例如，在上面的情况中，对于I，我希望有一个返回以下函数的函数:

and produce a 2D numpy array whereby the value in each column shifts along a place, for example in the case above for a I wish to have a function which returns:

[[1 2 3 4 5]
 [0 1 2 3 4]
 [0 0 1 2 3]
 [0 0 0 1 2]
 [0 0 0 0 1]]

我发现了一些使用strides函数执行类似于生产的示例，例如:

I have found examples which use the strides function to do something similar to produce, for example:

[[1 2 3]
 [2 3 4]
 [3 4 5]]

但是，我试图将我的每列向另一个方向移动.或者，可以将问题视为将a的第一个元素放在第一个对角线上，将第二个元素放在第二个对角线上，依此类推.但是，我想再次强调如何避免完全使用for，while或if循环.任何帮助将不胜感激.

However I am trying to shift each of my columns in the other direction. Alternatively, one can view the problem as putting the first element of a on the first diagonal, the second element on the second diagonal and so on. However, I would like to stress again how I would like to avoid using a for, while or if loop entirely. Any help would be greatly appreciated.

推荐答案

此类矩阵是 Toeplitz矩阵.您可以使用 scipy.linalg.toeplitz 来创建它:

Such a matrix is an example of a Toeplitz matrix. You could use scipy.linalg.toeplitz to create it:

In [32]: from scipy.linalg import toeplitz

In [33]: a = range(1,6)

In [34]: toeplitz(a, np.zeros_like(a)).T
Out[34]: 
array([[1, 2, 3, 4, 5],
       [0, 1, 2, 3, 4],
       [0, 0, 1, 2, 3],
       [0, 0, 0, 1, 2],
       [0, 0, 0, 0, 1]])

---

受@EelcoHoogendoorn的回答启发，这是一种变体，其使用的内存不及scipy.linalg.toeplitz:

In [47]: from numpy.lib.stride_tricks import as_strided

In [48]: a
Out[48]: array([1, 2, 3, 4, 5])

In [49]: t = as_strided(np.r_[a[::-1], np.zeros_like(a)], shape=(a.size,a.size), strides=(a.itemsize, a.itemsize))[:,::-1]

In [50]: t
Out[50]: 
array([[1, 2, 3, 4, 5],
       [0, 1, 2, 3, 4],
       [0, 0, 1, 2, 3],
       [0, 0, 0, 1, 2],
       [0, 0, 0, 0, 1]])

结果应被视为只读"数组.否则，当您更改元素时，您会感到有些惊讶.例如:

The result should be treated as a "read only" array. Otherwise, you'll be in for some surprises when you change an element. For example:

In [51]: t[0,2] = 99

In [52]: t
Out[52]: 
array([[ 1,  2, 99,  4,  5],
       [ 0,  1,  2, 99,  4],
       [ 0,  0,  1,  2, 99],
       [ 0,  0,  0,  1,  2],
       [ 0,  0,  0,  0,  1]])

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