NumPy - 将向量乘以标量添加到矩阵

Question

I'm new to NumPy and try to do the following thing without using loops.

I have a (n, n) square matrix A and a vector x with size (1,n), and I would like to add the vector to each row of the matrix, while multiplying the vector by the index of the row.
That is, adding the vector * 1 to the first line, the vector * 2 to the second line and so on.
Again, loops are not allowed, only NumPy functions.

For example, given the matrix:
[[0, 0, 0]
[0, 0, 0]
[0, 0, 0]]

and the vector [[1,1,1]]

I would like to get:
[[1, 1, 1]
[2, 2, 2]
[3, 3, 3]]

I tried to use repeat in order to create a matrix with the shape of A from x, but couldn't manage the scalar multiplication. Is there any helpful function / effective method?

Answer 1

You can use broadcasting to achieve this.

A = np.ones((5,5))
x = np.arange(5)
indices = np.arange(5)[None,:].T
A * x + indices

array([[0., 1., 2., 3., 4.],
       [1., 2., 3., 4., 5.],
       [2., 3., 4., 5., 6.],
       [3., 4., 5., 6., 7.],
       [4., 5., 6., 7., 8.]])