Create a new large matrix by stacking in its diagonal K matrices - python-3.x

Question

l have K (let K here be 7) distincts matrices of dimension (50,50).
I would like to create a new matrix L by filling it in diagonal with the K matrices. Hence L is of dimension (50*K,50*K).
What l have tried ?
K1=np.random.random((50,50))
N,N=K1.shape
K=7
out=np.zeros((K,N,K,N),K1.dtype)
np.einsum('ijik->ijk', out)[...] = K1
L=out.reshape(K*N, K*N) # L is of dimension (50*7,50*7)=(350,350)
Its indeed creating a new matrix L by stacking K1 seven times within its diagonal. However, l would like to stack respectively K1,K2,K3,K5,K6,K7 rather than K1 seven times.
Inputs :
K1=np.random.random((50,50))
K2=np.random.random((50,50))
K3=np.random.random((50,50))
K4=np.random.random((50,50))
K5=np.random.random((50,50))
K6=np.random.random((50,50))
K7=np.random.random((50,50))
L=np.zeros((50*7,50*7))#
Expected outputs :
L[:50,:50]=K1
L[50:100,50:100]=K2
L[100:150,100:50]=K3
L[150:200,150:200]=K4
L[200:250,200:250]=K5
L[250:300,250:300]=K6
L[300:350,300:350]=K7

Answer 1

You could try scipy.linalg.block_diag. If you look at the source, this function basically just loops over the given blocks the way you have written as your output. It can be used like:
K1=np.random.random((50,50))
K2=np.random.random((50,50))
K3=np.random.random((50,50))
K4=np.random.random((50,50))
K5=np.random.random((50,50))
K6=np.random.random((50,50))
K7=np.random.random((50,50))
L=sp.linalg.block_diag(K1,K2,K3,K4,K5,K6,K7)
If you have your K as a ndarray of shape (7,50,50) you can unpack it directly like:
K=np.random.random((7,50,50))
L=sp.linalg.block_diag(*K)
If you don't want to import scipy, you can always just write a simple loop to do what you have written for the expected output.

Answer 2

Here is a way to do that with NumPy:
import numpy as np
def put_in_diagonals(a):
n, rows, cols = a.shape
b = np.zeros((n * rows, n * cols), dtype=a.dtype)
a2 = a.reshape(-1, cols)
ii, jj = np.indices(a2.shape)
jj += (ii // rows) * cols
b[ii, jj] = a2
return b
# Test
a = np.arange(24).reshape(4, 2, 3)
print(put_in_diagonals(a))
Output:
[[ 0 1 2 0 0 0 0 0 0 0 0 0]
[ 3 4 5 0 0 0 0 0 0 0 0 0]
[ 0 0 0 6 7 8 0 0 0 0 0 0]
[ 0 0 0 9 10 11 0 0 0 0 0 0]
[ 0 0 0 0 0 0 12 13 14 0 0 0]
[ 0 0 0 0 0 0 15 16 17 0 0 0]
[ 0 0 0 0 0 0 0 0 0 18 19 20]
[ 0 0 0 0 0 0 0 0 0 21 22 23]]