在python中创建上下三角矩阵

Question

I want to create a python program that computes a matrix from a vector with some coefficients. This matrix is some kind of an Lower and Upper triangular. So lets say we have the following vector of coefficients a = [a0, a1, a2, a3, a4, a5], then I want to compute the matrix:

I need to go from vector a to creating a lower/upper triangular matrix A. I know how to index it manually, but I need a program that can do it instead.

I was maybe thinking about a loop inside another loop but I struggle with how it is done in python, what do you think should be done here?

Answer 1

You can try the following:

import numpy as np

c = [1, 2, 3, 4, 5, 6]
n = len(c)
m = 3
a = np.zeros((n,n))
for i in range(n):
    np.fill_diagonal(a[i:, :m], c[i])

np.fill_diagonal(a[:, m:], -1)    
print(a)

It gives:

[[ 1.  0.  0. -1.  0.  0.]
 [ 2.  1.  0.  0. -1.  0.]
 [ 3.  2.  1.  0.  0. -1.]
 [ 4.  3.  2.  0.  0.  0.]
 [ 5.  4.  3.  0.  0.  0.]
 [ 6.  5.  4.  0.  0.  0.]]

Answer 2

Here is an approach using np.roll , np.stack , np.tril and np.diag .

coeff = [1,2,3,4,5,6]
m = 3

nums = [np.roll(coeff,i) for i in range(m)] #get rolling ranges
a = np.tril(np.stack(nums).T) #stack -> transpose -> lower triangular
b = np.diag([-1]*m, m) #create matrix with offset diagonal
b[:,:m] = a  #update offset matrix
print(b)

[[ 1  0  0 -1  0  0]
 [ 2  1  0  0 -1  0]
 [ 3  2  1  0  0 -1]
 [ 4  3  2  0  0  0]
 [ 5  4  3  0  0  0]
 [ 6  5  4  0  0  0]]