import numpy as np
import laff
import flame

m = 8
n = 8
k = 3

# Random matrix of size mxn
B = np.matrix( np.random.rand( m, n ) )

# A is k columns of B taken at even intervals
if 2*k <= n: #k is less than half of n
    interval = np.ceil( n/k ) 
    A = B[ :, ::interval ] # These are slices in python. 
                           # This says take all rows of B, and columns 
                           # from 0 to the end at interval steps
else:
    A = B[ :, :k] #If k is greater than half of n, then just take the first k columns

print( 'A = ' )
print( A )

print( 'B = ' )
print( B )


C = np.transpose( A ) * A 

print( 'C = ' )
print( C )

V = np.transpose( A ) * B

# Insert your LU_unb_var5 method here

LU_unb_var5( C )

# Insert Code Here...
# Use laff.trsm(uplo, transpose, diag, A, B) to solve A X = B overwriting B with X

def RankKApprox( B, k ):
    
    m,n = B.shape
    
    # A is k columns of B taken at even intervals
    if 2*k <= n: #k is less than half of n
        interval = np.ceil( n/k ) 
        A = B[ :, ::interval ] # These are slices in python. 
                               # This says take all rows of B, and columns 
                               # from 0 to the end at interval steps
    else:
        A = B[ :, :k] #If k is greater than half of n, then just take the first k columns

    #------------------------------------------------------------#
    
    # Replace the comments below with their respective operations from the notebook
    
    # C = A^T A
    # W = A^T B
    # Overwrite C with its LU factorization
    # Solve L(UX) = W, overwriting W with X
    
    #------------------------------------------------------------#
    
    # Return A * W
    return A * W

 %pylab inline

from im_approx import *

# Try varying the number of columns used for the approximation 
numCols = 40

# Load an image
filename = 'building.png'

img = np.matrix(read_image( filename ))

# Make the approximations using normal equations and the SVD
# This step might take a while as it is a lot of computation.
normalApprox, SVDApprox = create_approximations( img, k=numCols, approximator=RankKApprox )

#Now plot the approximations that we have created

# Note that we're having some issues with our 
# approximations being somewhat darker than the 
# real image and are investigating.
plot_approximations( img, normalApprox, SVDApprox, k=numCols )