提取numpy矩阵的上三角或下三角部分

I have a matrix A and I want 2 matrices U and L such that U contains the upper triangular elements of A (all elements above and not including diagonal) and similarly for L(all elements below and not including diagonal). Is there a numpy method to do this?

我有一个矩阵A，我想要2个矩阵U和L，使得U包含A的上三角形元素（上面的所有元素，不包括对角线），L类似（下面的所有元素，不包括对角线）。有一个numpy方法来做到这一点？

e.g

例如

A = array([[ 4.,  9., -3.],
           [ 2.,  4., -2.],
           [-2., -3.,  7.]])
U = array([[ 0.,  9., -3.],
           [ 0.,  0., -2.],
           [ 0.,  0.,  0.]])
L = array([[ 0.,  0.,  0.],
           [ 2.,  0.,  0.],
           [-2., -3.,  0.]])

3 个解决方案

#1

Try numpy.triu (triangle-upper) and numpy.tril (triangle-lower).

尝试numpy.triu（三角形 - 上部）和numpy.tril（三角形 - 下部）。

#2

To extract the upper triangle values to a flat vector, you can do something like the following:

要将上三角形值提取到平面矢量，您可以执行以下操作：

import numpy as np

a = np.array([[1,2,3],[4,5,6],[7,8,9]])
print(a)

array([[1, 2, 3],
       [4, 5, 6],
       [7, 8, 9]])

a[np.triu_indices(3)]
#or
list(a[np.triu_indices(3)])

---

Similarly, for the lower triangle, use

同样，对于下三角形，请使用

np.tril

np.tril

---

IMPORTANT

If you want to extract the values that are above the diagonal (or below) then use the k argument. This is usually used when the matrix is symmetric.

如果要提取对角线（或以下）以上的值，请使用k参数。这通常在矩阵对称时使用。

Example:

例：

import numpy as np

a = np.array([[1,2,3],[4,5,6],[7,8,9]])

a[np.triu_indices(3, k = 1)]

# this returns the following
array([2, 3, 6])

---

#3

Use the Array Creation Routines of numpy.triu and numpy.tril to return a copy of a matrix with the elements above or below the k-th diagonal zeroed.

使用numpy.triu和numpy.tril的Array Creation Routines返回矩阵的副本，其中第k个对角线上方或下方的元素归零。

    >>> a = np.array([[1,2,3],[4,5,6],[7,8,9]])
    >>> a
    array([[1, 2, 3],
           [4, 5, 6],
           [7, 8, 9]])

    >>> tri_upper_diag = np.triu(a, k=0)
    >>> tri_upper_diag
    array([[1, 2, 3],
           [0, 5, 6],
           [0, 0, 9]])

    >>> tri_upper_no_diag = np.triu(a, k=1)
    >>> tri_upper_no_diag
    array([[0, 2, 3],
           [0, 0, 6],
           [0, 0, 0]])

    >>> tri_lower_diag = np.tril(a, k=0)
    >>> tri_lower_diag
    array([[1, 0, 0],
           [4, 5, 0],
           [7, 8, 9]])

    >>> tri_lower_no_diag = np.tril(a, k=-1)
    >>> tri_lower_no_diag
    array([[0, 0, 0],
           [4, 0, 0],
           [7, 8, 0]])