import scipy.io as sio
import scipy.linalg as la
import scipy.sparse.linalg as sla
import numpy as np
import matplotlib.pyplot as plt
import time


#dict = sio.loadmat('MFDLapl_primal.mat')
#A = dict['A1']
dict = sio.loadmat('MFDLapl.mat')
A = dict['A']

N,M=A.shape

nelement = N*M
nnz = A.nnz

print('Number of elements,      A: %e' % nelement)
print('Number of non-zeros,     A: %e' % nnz)
print('Percentage of non-zeros, A: %e%%' % (100*float(nnz)/nelement))
plt.spy(A, markersize=1)
plt.show()

# Sparse LU, reorder to minimize fill-in
start1 = time.time()
lu1    = sla.splu(A,permc_spec='COLAMD')
end1   = time.time()

print('Time elapsed,          lu1: %e' % (end1-start1))
print('Number of non-zeros,   lu1: %e' % (lu1.L.nnz+lu1.U.nnz))


# Sparse LU, no reordering to minimize fill-in
start2 = time.time()
lu2    = sla.splu(A,permc_spec='natural')
end2   = time.time()

print('Time elapsed,          lu2: %e' % (end2-start2))
print('Number of non-zeros,   lu2: %e' % (lu2.L.nnz+lu2.U.nnz))



# Dense LU, takes a while
start3 = time.time()
[P,L,U]= la.lu(A.todense())
end3   = time.time()

print('Time elapsed,          lu3: %e' % (end3-start3))
print('Number of non-zeros,   lu3: %e' % (nelement))