gauss elimination determinant calculator, Python 3

gauss elimination determinant calculator

Language: Layout:

matrix = [[3, 1, 1, 1, 3, 3, 1, 2, 1, 2, 1, 1, 0, 3, 0, 3, 2, 0, 3, 3, 3, 2, 0, 0, 0, 1, 2, 0, 0, 2, 0, 1, 0, 0, 2, 0, 0, 1, 0, 3], [1, 1, 0, 1, 2, 1, 2, 2, 3, 3, 0, 2, 3, 2, 3, 0, 1, 0, 2, 3, 3, 1, 2, 1, 3, 3, 1, 0, 0, 0, 3, 2, 3, 3, 3, 0, 1, 3, 0, 0], [3, 1, 2, 0, 1, 1, 1, 1, 1, 0, 3, 1, 0, 1, 0, 0, 0, 0, 2, 2, 1, 2, 2, 2, 1, 0, 0, 3, 1, 2, 0, 1, 0, 3, 3, 0, 3, 2, 3, 3], [0, 1, 0, 3, 2, 3, 3, 3, 0, 2, 1, 2, 1, 0, 0, 2, 0, 2, 2, 2, 2, 3, 1, 0, 1, 3, 3, 2, 0, 2, 3, 2, 3, 3, 3, 3, 1, 2, 2, 2], [0, 1, 0, 0, 2, 3, 0, 2, 0, 1, 3, 1, 1, 0, 2, 1, 2, 1, 2, 3, 0, 2, 1, 0, 0, 3, 0, 2, 0, 0, 2, 2, 3, 3, 0, 2, 3, 3, 1, 3], [0, 0, 0, 0, 1, 2, 2, 0, 3, 1, 1, 3, 3, 0, 0, 1, 3, 1, 2, 0, 1, 3, 2, 1, 2, 1, 2, 3, 2, 3, 1, 1, 3, 3, 0, 2, 2, 1, 0, 0], [1, 2, 3, 1, 3, 2, 2, 3, 3, 0, 2, 2, 3, 1, 1, 2, 0, 0, 2, 0, 1, 3, 3, 1, 2, 1, 2, 3, 3, 2, 3, 3, 0, 1, 3, 2, 3, 0, 3, 2], [3, 0, 1, 0, 1, 1, 0, 3, 3, 3, 0, 2, 1, 1, 2, 2, 3, 3, 3, 0, 3, 2, 1, 0, 3, 1, 2, 3, 2, 1, 3, 3, 3, 1, 0, 0, 3, 2, 3, 1], [2, 0, 1, 3, 2, 2, 0, 2, 1, 2, 2, 1, 0, 1, 1, 0, 0, 2, 2, 3, 3, 3, 2, 3, 3, 1, 1, 1, 2, 2, 0, 0, 2, 2, 1, 0, 2, 0, 3, 1], [1, 0, 0, 0, 3, 2, 1, 1, 2, 1, 0, 3, 0, 3, 2, 0, 2, 3, 3, 1, 0, 2, 0, 0, 3, 3, 1, 3, 2, 2, 2, 2, 1, 2, 0, 3, 2, 0, 2, 1], [0, 0, 2, 3, 3, 2, 3, 3, 2, 3, 2, 2, 2, 0, 1, 3, 2, 1, 3, 3, 2, 1, 3, 0, 0, 0, 1, 1, 2, 0, 1, 3, 3, 2, 0, 3, 1, 1, 1, 2], [2, 1, 0, 2, 3, 3, 1, 1, 3, 3, 3, 1, 2, 1, 2, 0, 0, 3, 3, 2, 1, 3, 2, 3, 3, 1, 0, 3, 3, 3, 1, 1, 2, 3, 0, 0, 1, 2, 2, 0], [1, 3, 1, 2, 3, 2, 3, 3, 2, 3, 1, 2, 3, 0, 0, 0, 3, 0, 1, 0, 2, 3, 2, 3, 3, 3, 2, 2, 2, 0, 0, 3, 1, 1, 0, 3, 1, 1, 3, 2], [0, 1, 1, 2, 3, 1, 0, 0, 0, 1, 3, 0, 3, 2, 1, 2, 2, 1, 2, 1, 3, 1, 1, 1, 2, 2, 1, 2, 2, 0, 3, 3, 0, 2, 0, 2, 0, 1, 0, 0], [3, 0, 0, 1, 1, 3, 1, 3, 2, 3, 0, 1, 1, 3, 0, 3, 3, 2, 2, 2, 1, 2, 0, 3, 2, 2, 2, 0, 3, 3, 1, 1, 2, 0, 1, 3, 1, 0, 3, 0], [1, 1, 2, 3, 3, 0, 3, 3, 0, 0, 0, 2, 1, 1, 1, 3, 3, 1, 0, 0, 2, 0, 0, 1, 1, 3, 1, 1, 1, 0, 2, 2, 0, 1, 0, 3, 3, 3, 3, 3], [1, 3, 3, 0, 2, 2, 3, 3, 0, 0, 1, 0, 3, 1, 1, 3, 3, 0, 0, 3, 2, 1, 1, 1, 3, 2, 1, 3, 1, 0, 2, 3, 1, 3, 2, 1, 2, 3, 0, 1], [2, 2, 0, 1, 3, 2, 3, 0, 0, 0, 2, 2, 0, 2, 2, 3, 3, 3, 0, 3, 0, 1, 3, 2, 2, 0, 1, 3, 1, 0, 0, 0, 2, 2, 0, 2, 1, 0, 3, 3], [2, 0, 0, 3, 3, 2, 3, 2, 0, 0, 3, 1, 0, 2, 1, 1, 2, 2, 2, 0, 0, 0, 0, 3, 1, 1, 3, 3, 2, 2, 1, 0, 0, 2, 2, 1, 3, 1, 0, 0], [3, 2, 3, 0, 2, 1, 0, 2, 3, 0, 2, 3, 1, 1, 1, 3, 1, 1, 2, 1, 0, 2, 1, 3, 0, 3, 1, 3, 1, 3, 0, 2, 1, 1, 2, 1, 0, 3, 2, 1], [3, 2, 3, 1, 0, 3, 1, 1, 1, 2, 3, 3, 0, 3, 2, 3, 2, 0, 1, 3, 1, 3, 1, 3, 3, 1, 1, 1, 3, 1, 0, 3, 0, 3, 1, 3, 2, 0, 1, 3], [2, 0, 0, 1, 0, 0, 3, 0, 2, 1, 0, 2, 2, 1, 3, 0, 3, 1, 2, 3, 3, 1, 0, 1, 0, 3, 2, 3, 3, 1, 1, 3, 3, 1, 0, 0, 3, 0, 3, 3], [0, 3, 1, 0, 2, 2, 1, 1, 0, 3, 0, 1, 3, 2, 3, 0, 3, 0, 2, 2, 0, 2, 2, 1, 2, 3, 3, 2, 3, 2, 0, 2, 2, 3, 3, 1, 1, 0, 2, 3], [0, 1, 3, 2, 2, 3, 2, 0, 1, 3, 3, 3, 0, 1, 1, 3, 1, 0, 2, 1, 0, 1, 3, 1, 3, 0, 2, 3, 3, 2, 2, 2, 1, 3, 1, 0, 3, 1, 3, 1], [1, 1, 0, 0, 2, 2, 3, 3, 0, 1, 0, 2, 1, 2, 3, 3, 1, 1, 3, 1, 2, 0, 2, 1, 3, 2, 3, 2, 3, 0, 0, 3, 0, 1, 3, 0, 3, 3, 0, 1], [3, 0, 0, 1, 2, 0, 2, 1, 2, 2, 3, 0, 2, 0, 2, 1, 2, 0, 1, 1, 0, 2, 0, 1, 1, 2, 0, 3, 0, 3, 3, 1, 0, 0, 1, 1, 1, 2, 2, 3], [0, 1, 2, 0, 1, 0, 2, 0, 2, 3, 2, 1, 0, 3, 3, 3, 1, 0, 1, 2, 0, 3, 3, 2, 2, 0, 0, 2, 2, 3, 1, 3, 0, 3, 2, 3, 2, 2, 0, 1], [0, 0, 3, 2, 0, 1, 2, 0, 3, 0, 3, 0, 3, 2, 3, 1, 3, 2, 2, 3, 0, 2, 1, 2, 0, 2, 1, 0, 3, 0, 2, 2, 2, 3, 3, 0, 3, 2, 3, 0], [1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 3, 3, 3, 3, 2, 2, 1, 0, 3, 0, 2, 0, 0, 3, 3, 2, 1, 3, 0, 3, 1, 3, 2, 3, 2, 2, 2, 3, 2, 0], [1, 2, 2, 1, 1, 0, 3, 0, 3, 2, 3, 1, 3, 2, 2, 0, 1, 1, 1, 3, 0, 1, 0, 0, 0, 2, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0], [0, 2, 2, 2, 0, 0, 0, 2, 3, 1, 3, 1, 1, 0, 0, 1, 3, 1, 0, 0, 1, 2, 2, 3, 2, 0, 0, 2, 0, 2, 1, 1, 3, 3, 0, 0, 1, 2, 3, 0], [0, 3, 0, 3, 1, 1, 3, 0, 3, 3, 1, 0, 3, 2, 2, 1, 2, 0, 1, 3, 2, 2, 0, 3, 2, 2, 2, 2, 1, 0, 0, 2, 2, 2, 2, 1, 3, 0, 0, 2], [1, 1, 1, 1, 2, 0, 1, 2, 2, 3, 0, 0, 0, 2, 1, 1, 0, 3, 1, 1, 2, 2, 0, 3, 3, 1, 0, 0, 0, 1, 2, 1, 1, 2, 1, 0, 1, 2, 3, 1], [2, 0, 0, 1, 3, 0, 0, 0, 3, 3, 0, 2, 1, 0, 3, 1, 2, 1, 3, 0, 2, 0, 0, 1, 1, 3, 2, 1, 0, 0, 3, 1, 3, 3, 2, 1, 0, 3, 3, 2], [0, 0, 0, 3, 1, 1, 2, 2, 3, 1, 2, 0, 0, 2, 0, 2, 0, 3, 0, 1, 3, 0, 2, 1, 2, 0, 3, 3, 2, 2, 2, 0, 3, 1, 3, 3, 3, 3, 0, 0], [0, 1, 1, 2, 0, 0, 3, 1, 3, 2, 2, 0, 2, 2, 0, 3, 1, 1, 3, 1, 0, 1, 3, 0, 0, 0, 0, 0, 1, 1, 2, 2, 0, 3, 1, 0, 0, 1, 1, 2], [2, 3, 1, 1, 2, 1, 3, 1, 2, 2, 0, 2, 1, 0, 2, 0, 1, 1, 0, 0, 0, 3, 1, 2, 1, 1, 0, 0, 3, 3, 3, 3, 3, 3, 1, 2, 2, 1, 2, 3], [1, 3, 2, 3, 1, 1, 1, 3, 0, 2, 0, 0, 1, 1, 1, 0, 1, 3, 3, 1, 0, 1, 1, 0, 3, 2, 1, 2, 2, 2, 2, 0, 3, 1, 0, 1, 0, 2, 3, 2], [3, 1, 2, 0, 1, 3, 2, 1, 1, 2, 1, 2, 3, 2, 1, 2, 1, 3, 2, 2, 1, 2, 0, 0, 3, 1, 3, 1, 3, 3, 1, 1, 3, 0, 0, 3, 0, 2, 1, 0], [3, 3, 3, 3, 1, 1, 3, 1, 3, 1, 2, 1, 3, 1, 1, 2, 1, 0, 1, 0, 3, 3, 2, 1, 0, 1, 0, 2, 3, 3, 0, 1, 2, 0, 3, 3, 3, 0, 1, 1]]
#matrix = [[3,1,0,2,6],
#          [4,0,2,1,3],
#          [2,1,0,1,2],
#          [4,3,2,5,1],
#          [0,2,1,0,3]]
def find_upper_triangular_matrix(matrix):
    i, j, k, n = 0, -1, 0, 40        # i timi tou "n" prepei na allazei me ti diastasi tou pinaka 
    while i < n - 1:
        k = i
        while k < n - 1:
              j = -1
              var = matrix[k + 1][i]
              for e in matrix[i]:
#                  var = matrix[k + 1][i]
#                  print ("var =", var)
                  j = j + 1
                  if e == 0:
                      matrix[k + 1][j] = matrix[k + 1][j] - e  # (6)
#                      continue   (2)
                  else:
#                      e = var * e / matrix[i][i]
                      e = e / matrix[i][i] * var
                      matrix[k + 1][j] = matrix[k + 1][j] - e 
#                      print ("k =", k, "", "j =", j, "", "matrix[k + 1][j] = ", matrix[k + 1][j])
#                      j = j + 1  (1)
              if i == 0:
                 j = -1  #(5)
              else:
                  j = i
              k = k + 1
        j = j + 1  #  (4)
        i = i + 1
#        print ('matrix =', matrix)
    i, product = 1, matrix[0][0]
    while i < n:
#        print ("matrix[0:7] =", matrix[0:7])
        product = product * matrix[i][i]
#        print ("matrix[i][i] =", matrix[i][i], "", "product =", product)
        i = i + 1
    return matrix, product

print (find_upper_triangular_matrix(matrix))

[ + ] Show input
Absolute running time: 0.51 sec, cpu time: 0.41 sec, memory peak: 7 Mb, absolute service time: 0,52 sec

([[3, 1, 1, 1, 3, 3, 1, 2, 1, 2, 1, 1, 0, 3, 0, 3, 2, 0, 3, 3, 3, 2, 0, 0, 0, 1, 2, 0, 0, 2, 0, 1, 0, 0, 2, 0, 0, 1, 0, 3], [0.0, 0.6666666666666667, -0.3333333333333333, 0.6666666666666667, 1.0, 0.0, 1.6666666666666667, 1.3333333333333335, 2.6666666666666665, 2.3333333333333335, -0.3333333333333333, 1.6666666666666667, 3, 1.0, 3, -1.0, 0.33333333333333337, 0, 1.0, 2.0, 2.0, 0.33333333333333337, 2, 1, 3, 2.6666666666666665, 0.33333333333333337, 0, 0, -0.6666666666666666, 3, 1.6666666666666667, 3, 3, 2.3333333333333335, 0, 1, 2.6666666666666665, 0, -1.0], [0.0, 0.0, 1.0, -1.0, -2.0, -2.0, 0.0, -1.0, 0.0, -2.0, 2.0, 0.0, 0.0, -2.0, 0.0, -3.0, -2.0, 0, -1.0, -1.0, -2.0, 0.0, 2.0, 2.0, 1.0, -1.0, -2.0, 3, 1, 0.0, 0.0, 0.0, 0.0, 3.0, 1.0, 0, 3.0, 1.0, 3, 0.0], [0.0, 0.0, 0.0, 2.5, 1.5, 4.0, 0.5, 1.5, -3.9999999999999996, -0.5000000000000001, 0.5000000000000001, -0.5, -3.499999999999999, -0.4999999999999999, -4.499999999999999, 5.0, 0.4999999999999999, 2, 1.0000000000000002, -0.4999999999999996, 3.3306690738754696e-16, 2.5, -2.9999999999999996, -2.4999999999999996, -3.999999999999999, -0.4999999999999996, 3.5, 0.5000000000000002, -0.49999999999999994, 3.0, -1.4999999999999991, -0.5, -1.4999999999999991, -2.999999999999999, -1.0, 3, -1.9999999999999996, -2.4999999999999996, 0.5000000000000002, 3.5], [0.0, 0.0, 0.0, 0.0, 1.8, 4.8, -2.4, 0.7999999999999999, -4.8, -1.6, 2.6, -1.6, -4.199999999999999, -0.5999999999999999, -3.399999999999999, 5.0, 2.6, 1.4, 1.2000000000000002, 0.4000000000000005, -1.9999999999999996, 2.0, -3.5999999999999996, -2.9999999999999996, -5.799999999999999, -0.5999999999999995, 1.1999999999999997, 0.6000000000000003, -0.6, 1.5999999999999999, -2.799999999999999, -0.6, -1.799999999999999, -3.5999999999999988, -4.2, 2.6, -0.39999999999999947, -1.9999999999999996, -0.39999999999999974, 5.2], [0.0, 0.0, 0.0, 0.0, 0.0, -0.6666666666666665, 3.333333333333333, -0.4444444444444444, 5.666666666666666, 1.8888888888888888, -0.4444444444444444, 3.888888888888889, 5.333333333333333, 0.33333333333333326, 1.8888888888888884, -1.7777777777777777, 1.5555555555555556, 0.22222222222222232, 1.3333333333333333, -0.22222222222222252, 2.1111111111111107, 1.8888888888888888, 4.0, 2.666666666666666, 5.222222222222221, 1.333333333333333, 1.3333333333333335, 2.6666666666666665, 2.3333333333333335, 2.111111111111111, 2.555555555555555, 1.3333333333333333, 3.999999999999999, 4.999999999999999, 2.3333333333333335, 0.5555555555555556, 2.222222222222222, 2.1111111111111107, 0.22222222222222207, -2.888888888888889], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -43.00000000000001, 5.0, -66.00000000000001, -21.000000000000004, -5.999999999999999, -52.00000000000001, -64.0, 2.0, -18.999999999999996, 20.0, -24.000000000000004, -9.0, -21.0, 3.552713678800501e-15, -22.0, -33.0, -52.00000000000001, -35.0, -62.00000000000001, -19.0, -18.000000000000004, -47.0, -31.000000000000004, -34.0, -30.999999999999996, -18.0, -57.0, -73.99999999999999, -27.000000000000004, -16.0, -38.0, -32.0, -9.999999999999998, 26.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 3.2480620155038755, 2.825581395348837, 2.7248062015503876, -0.031007751937984218, 2.12015503875969, 2.558139534883721, -1.267441860465116, 3.9573643410852712, -0.007751937984495694, 1.8759689922480627, 3.62015503875969, 1.558139534883721, -0.6666666666666667, 1.275193798449612, 1.3294573643410863, 1.953488372093024, -0.06976744186046524, 3.957364341085272, 2.7906976744186043, 0.9069767441860468, 3.5348837209302326, 1.895348837209303, -1.1201550387596892, 5.562015503875969, 3.906976744186047, 5.372093023255815, 2.895348837209305, -0.6395348837209309, 1.3062015503875972, 4.248062015503876, 3.1124031007751944, 3.5038759689922476, -0.643410852713179], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 3.87470167064439, 1.5787589498806662, 5.293556085918855, 2.8031026252983278, 4.281622911694504, -1.3758949880668265, 5.659904534606203, -6.176610978520286, 0.7398568019093068, 1.4773269689737456, 1.4988066825775643, 4.81145584725537, 0.5525059665871099, 2.7887828162291157, 6.505966587112168, 6.410501193317422, 6.6599045346062, 3.579952267303101, -3.336515513126492, 4.5346062052505935, 2.681384248210022, -0.020286396181386473, 2.2183770883054867, 1.0119331742243411, 7.39140811455847, 10.464200477326962, 0.9295942720763721, 0.2589498806682576, 7.782816229116944, 5.409307875894987, 3.828162291169451, -0.6587112171837667], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.9149984601170338, 7.201108715737604, 2.763165999384042, -0.34770557437635663, -1.5457345241761624, 5.3455497382198915, -8.78380043116723, -2.268555589775179, 4.315368032029562, 1.643055127810284, 5.40190945488143, -3.348937480751464, 2.8780412688635635, 5.141669233138276, 6.240837696335079, 6.156760086233445, 5.28118263012011, -5.2340622112719455, 8.289497998152132, 2.23960578995996, 0.2460732984293157, 2.6205728364644267, 1.5488142901139477, 5.871881736987987, 13.304896827841073, 1.9593470896211889, 3.5060055435786865, 10.06529103788112, 5.855866954111486, 8.623344625808437, 2.2842623960579047], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 30.363850555368572, 8.335577246718266, 0.9683608212722549, -6.851901716593742, 22.06125883540895, -32.050824638168976, -5.709525412319087, 11.408616627398168, 6.750925614271277, 27.55974419387413, -10.22147425109391, 7.406260518343986, 21.804442948502185, 23.81588690676542, 18.94109727364524, 18.43184113093235, -23.392123864018863, 26.006731740154795, 5.0053853921238565, -4.014809828340649, 6.888589700437558, 5.671491080444275, 25.62908111746887, 52.20801077078421, 6.422753281723326, 10.020531807472215, 36.58195893638507, 27.367216425445974, 26.850218781555025, 10.389431167956932], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.9781955637339097, -1.1262373768165745, -1.5822682377980501, -0.8582212812184746, 1.2053186418507682, -1.4475618272716204, 3.608684085089407, 0.3264014366318968, -4.365421068384125, -3.180543392712642, -0.3930230237997532, 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