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  1. # Name : Ananda Das;
  2. # ID : 230241053;
  3. # Lab : 3 , problem : 02;
  4. def lu_decomposition(A, n):
  5.     L = [[0.0] * n for _ in range(n)]
  6.     U = [[0.0] * n for _ in range(n)]
  7.  
  8.     for i in range(n):
  9.         L[i][i] = 1.0
  10.  
  11.     for j in range(n):
  12.         for i in range(n):
  13.             if i <= j:
  14.                 U[i][j] = A[i][j] - sum(L[i][k] * U[k][j] for k in range(i))
  15.             else:
  16.                 if abs(U[j][j]) < 1e-10:
  17.                     print("Matrix is singular or nearly singular. Cannot proceed with LU Decomposition.")
  18.                     exit()
  19.                 L[i][j] = (A[i][j] - sum(L[i][k] * U[k][j] for k in range(j))) / U[j][j]
  20.     return L, U
  21.  
  22. def forward_substitution(L, B, n):
  23.     Y = [0.0] * n
  24.     for i in range(n):
  25.         Y[i] = B[i] - sum(L[i][j] * Y[j] for j in range(i))
  26.     return Y
  27.  
  28. def backward_substitution(U, Y, n):
  29.     X = [0.0] * n
  30.     for i in reversed(range(n)):
  31.         if abs(U[i][i]) < 1e-10:
  32.             print("Zero on diagonal during backward substitution. No unique solution.")
  33.             exit()
  34.         X[i] = (Y[i] - sum(U[i][j] * X[j] for j in range(i + 1, n))) / U[i][i]
  35.     return X
  36.  
  37. def print_matrix(name, matrix):
  38.     print(f"[{name}]:")
  39.     for row in matrix:
  40.         print(" ".join(f"{val:.3f}" for val in row))
  41.     print()
  42.  
  43. def print_vector(name, vector):
  44.     print(f"[{name}]:", " ".join(f"{val:.3f}" for val in vector))
  45.     print()
  46.  
  47. # Main program
  48. n = int(input("Enter the order of square matrix: "))
  49. print("Enter matrix elements row-wise:")
  50. A = [list(map(float, input().split())) for _ in range(n)]
  51. B = list(map(float, input("Enter the constant terms: ").split()))
  52.  
  53. L, U = lu_decomposition(A, n)
  54. Y = forward_substitution(L, B, n)
  55. X = backward_substitution(U, Y, n)
  56.  
  57. print_matrix("L", L)
  58. print_matrix("U", U)
  59. print_vector("Y", Y)
  60. print_vector("X", X)
  61.  
Success #stdin #stdout 0.09s 14116KB
comments (?)
stdin
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3
2 4 -2
4 9 -3
-2 -3 -7
2 8 10
stdout
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Enter the order of square matrix: Enter matrix elements row-wise:
Enter the constant terms: [L]:
1.000 0.000 0.000
2.000 1.000 0.000
-1.000 1.000 1.000

[U]:
2.000 4.000 -2.000
0.000 1.000 1.000
0.000 0.000 -10.000

[Y]: 2.000 4.000 8.000

[X]: -9.400 4.800 -0.800
https://ideone.com/b4PNp5
language:
Python 3 (python  3.12)
created:
8 days ago
visibility:
public

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