05_binary_matrix_rank_test.py

import math
import copy
import gf2matrix

def test(input, n, M=32, Q=32):
    N = int(math.floor(n/(M*Q))) #Number of blocks
    
    if N < 38:
        print("  Number of blocks must be greater than 37")
        p = 0.0
        return [0]*9
        
    # Compute the reference probabilities for FM, FMM and remainder 
    r = M
    product = 1.0
    for i in range(r):
        upper1 = (1.0 - (2.0**(i-Q)))
        upper2 = (1.0 - (2.0**(i-M)))
        lower = 1-(2.0**(i-r))
        product = product * ((upper1*upper2)/lower)
    FR_prob = product * (2.0**((r*(Q+M-r)) - (M*Q)))
    
    r = M-1
    product = 1.0
    for i in range(r):
        upper1 = (1.0 - (2.0**(i-Q)))
        upper2 = (1.0 - (2.0**(i-M)))
        lower = 1-(2.0**(i-r))
        product = product * ((upper1*upper2)/lower)
    FRM1_prob = product * (2.0**((r*(Q+M-r)) - (M*Q)))
    
    LR_prob = 1.0 - (FR_prob + FRM1_prob)
    
    FM = 0      # Number of full rank matrices
    FMM = 0     # Number of rank -1 matrices
    remainder = 0
    for blknum in range(N):
        block = [None] * (M*Q)
        
        for i in range(M*Q):
            block[i] = int(input[blknum*M*Q + i],2)
            
        # Put in a matrix
        matrix = gf2matrix.matrix_from_bits(M,Q,block,blknum) 
        rank = gf2matrix.rank(M,Q,matrix,blknum)


        if rank == M: # count the result
            FM += 1
        elif rank == M-1:
            FMM += 1  
        else:
            remainder += 1

    chisq =  (((FM-(FR_prob*N))**2)/(FR_prob*N))
    chisq += (((FMM-(FRM1_prob*N))**2)/(FRM1_prob*N))
    chisq += (((remainder-(LR_prob*N))**2)/(LR_prob*N))
    
    p = math.e **(-chisq/2.0)

    success = (p >= 0.01)

    return [n, M, Q, N, FM, FMM, chisq, p, success]