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  1. from sympy import *
  2. import numpy as np
  3. import string
  4.  
  5.  
  6. # this code implement Gauss_elimination to solve
  7. # set of equation
  8.  
  9. # edit in line 119
  10.  
  11. def isZero(_vect):
  12.     n = _vect.shape[0]
  13.  
  14.     result = True
  15.     for i in range(n):
  16.         if _vect[i] != 0:
  17.             result = False
  18.             break
  19.  
  20.     return result
  21.  
  22.  
  23. def swap(a, b):
  24.     temp = a[0:].copy()
  25.     a[0:] = b[0:]
  26.     b[0:] = temp
  27.  
  28.  
  29. def rank(A):
  30.     rows = A.shape[0]
  31.  
  32.     result = 0
  33.     for i in range(rows):
  34.         if (isZero(A[i]) == False):
  35.             result += 1
  36.     return result
  37.  
  38.  
  39. def getMatrix(A):
  40.     return (A.T)[0:-1].copy().T
  41.  
  42.  
  43. def isAllBelowZero(A, index):
  44.     rows = A.shape[0]
  45.  
  46.     result = True
  47.     for i in range(index + 1, rows):
  48.         if A[i][index] != 0:
  49.             result = False
  50.             break
  51.  
  52.     return result
  53.  
  54.  
  55. def Gauss_elimination(A):
  56.     rows, cols = A.shape
  57.     loop_epoch = cols if cols < rows else rows
  58.     i = 0
  59.  
  60.     while i < loop_epoch:
  61.         if A[i][i] != 0:
  62.             for j in range(i + 1, rows):
  63.                 scaling_value = A[j][i] / A[i][i]
  64.                 A[j] = A[j] - scaling_value * A[i]
  65.         else:
  66.             for index in range(i + 1, rows):
  67.                 if A[index][i] != 0:
  68.                     swap(A[i], A[index])
  69.                     i -= 1
  70.                     break
  71.         i += 1
  72.  
  73.     for i in range(rows - 1):
  74.         if (isZero(A[i])):
  75.             for j in range(i + 1, rows):
  76.                 if (isZero(A[j]) == False):
  77.                     swap(A[i], A[j])
  78.                     break
  79.  
  80.  
  81. def back_substitution(A):
  82.     Gauss_elimination(A)
  83.     rows,  cols = A.shape
  84.     cols -= 1
  85.     rA = rank(getMatrix(A))
  86.     rAB = rank(A)
  87.  
  88.     x = np.zeros(cols)
  89.  
  90.     if (rA + 1 == rAB):
  91.         print(f"Setequation have no solution")
  92.     elif (rA == rAB and rA == cols):
  93.         print(f"Setequation have one solution: ")
  94.         # back substitution
  95.         i = cols - 1
  96.         while i >= 0:
  97.             x[i] = (A[i][cols] - x.dot(getMatrix(A)[i])) / A[i][i]
  98.             i -= 1
  99.     else:
  100.         alphabet = symbols(list(string.ascii_lowercase))
  101.         print(f"Setequation have infinity solution with {cols - rA} ")
  102.         n_iter = 0
  103.         pivot_row = 0
  104.         y = []
  105.         for i in range(cols):
  106.             if A[i + pivot_row][i] == 0:
  107.                 pivot_row -= 1
  108.                 y.append(alphabet[n_iter])
  109.                 n_iter += 1
  110.             else:
  111.                 zero = symbols('0')
  112.                 y.append(zero)
  113.  
  114.         i = cols - 1
  115.         while i >= 0:
  116.             s = (getMatrix(A)[i]).dot(y)
  117.             if A[i][i] != 0:
  118.             	# simplify right this expression
  119.                 y[i] = (((A[i][cols] - s) / A[i][i]))
  120.  
  121.             i -= 1
  122.         x = y
  123.  
  124.     return x
  125.  
  126.  
  127. def main():
  128.     # matrix = np.array([[1, 2, 2, 9], [3, 4, 4, 1], [5, 6, 7, 0]])
  129.     matrix = np.array([[1, 2, 3, 0],
  130.                        [3, 2, 3, 2],
  131.                        [2, 2, 3, 1]])
  132.     print(matrix)
  133.     Gauss_elimination(matrix)
  134.     print(matrix)
  135.     print((back_substitution(matrix)))
  136.  
  137.  
  138. main()
  139.  
Compilation error #stdin compilation error #stdout 0s 0KB
comments (?)
stdin 
Standard input is empty
compilation info 
Traceback (most recent call last):
  File "<string>", line 1, in <module>
  File "/usr/lib/python2.7/py_compile.py", line 117, in compile
    raise py_exc
py_compile.PyCompileError:   File "prog.py", line 91
    print(f"Setequation have no solution")
                                        ^
SyntaxError: invalid syntax
stdout 
Standard output is empty
https://ideone.com/RuS8u6
language:
Python (cpython 2.7.16)
created:
3 years ago
visibility:
secret

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