Question

Can you explain this line by line, especially the for loop
this function solve Ly = b for y

Forward solve a unit lower triangular system Ly = b for y

b = L @ y

def Lsolve(L, b):

  m, n = L.shape

assert m == n

assert np.all(np.tril(L) == L)

   assert np.all(np.diag(L) == 1)

y = b.astype(np.float64).copy()

for col in range(n):

  y[col+1:] -= y[col] * L[col+1:, col]

  return y

Answer 1

m, n = L.shape , so basically here getting the matrix size , after this assert m == n , here checking basically if this square matrix and if its not then show error , after this in next line (np.tril(L) == L) here checking basically if this lower triangular or something else and after this ,(np.diag(L) == 1), here checking that basically unit diagonal , after this basically in next line  copying b to y, in next line basically solving here if we say for each y's element , for equation see below after solving y , return it.

21 dr