Python中的三对角矩阵

三对角矩阵是仅在主对角线、其下方和上方的对角线处具有非零元素的矩阵。所有其他元素都为零。因此，维数小于或等于 3 的三对角矩阵似乎毫无意义。

Example 1:

[a11,  a22,  0  ,  0  ,  0  ,  0  ]   

[a21,  a22,  a23,  0  ,  0  ,  0  ]

[0  ,  a32,  a33,  a34,  0  ,  0  ]

[0  ,  0  ,  a43,  a44,  a55,  0  ]

[0  ,  0  ,  0  ,  a54,  a55,  a56]

[0  ,  0  ,  0  ,  0  ,  a65,  a66]

Example 2:

[1,  1,  0,  0,  0,  0]   

[1,  1,  1,  0,  0,  0]

[0,  1,  1,  1,  0,  0]

[0,  0,  1,  1,  1,  0]

[0,  0,  0,  1,  1,  1]

[0,  0,  0,  0,  1,  1]

方法

• 将矩阵的大小作为输入
• 检查是否大于 3
  • 如果没有，退出
  • 如果是，继续进行
• 将矩阵的元素作为输入
• 现在在除主对角线和主对角线下方和上方的对角线之外的任何地方都设置零。

程序：

Python3

# if you enter number n it will automatically 
# be considered as a square matrix of size n by n
size_of_a_matrix = int(input("Enter size the matrix that you want : "))
   
if size_of_a_matrix <= 3:
      
    # since size should be greater than 3
    print("Please enter the size that is greater than 3")
    exit()
  
diagonal = []
numbers1 = [[0 for j in range(0, size_of_a_matrix)]
            for i in range(0, size_of_a_matrix)]
   
# created a loop to enter numbers
for a in range(size_of_a_matrix):
    numbers1 = int(input(f"Enter the numbers for the main diagonal for position[{a}][{a}] : "))
       
    # appending the values to the list
    diagonal.append(numbers1)
  
diagonalAbove = []
print("*********")
   
# created a loop to enter numbers
for k in range(size_of_a_matrix-1):
    numbers2 = int(input(f"Enter the numbers for diagonal above the main diagonal for position[{k}][{k+1}]: "))
      
    # appending the values to the list
    diagonalAbove.append(numbers2)
  
diagonalBelow = []
print("*********")
   
# created a loop to enter numbers
for z in range(size_of_a_matrix-1):
    numbers3 = int(input(f"Enter the numbers for diagonal below the main diagonal for position[{z+1}][{z}]: "))
      
    # appending the values to the list
    diagonalBelow.append(numbers3)
print("*********")
   
   
def tridiagonal(size_of_a_matrix, diagonal, diagonalAbove, diagonalBelow):
   
    matrix = [[0 for j in range(size_of_a_matrix)]
              for i in range(size_of_a_matrix)]
      
    for k in range(size_of_a_matrix-1):
        matrix[k][k] = diagonal[k]
        matrix[k][k+1] = diagonalAbove[k]
        matrix[k+1][k] = diagonalBelow[k]
      
    matrix[size_of_a_matrix-1][size_of_a_matrix - 1] = diagonal[size_of_a_matrix-1]
   
    # so that the values will print row by row
    for row in matrix:
        print(row)
  
    return "this is the tridiagonal matrix"
  
# printing final values
print(tridiagonal(size_of_a_matrix, diagonal, diagonalAbove, diagonalBelow))

输出：

我们程序的输出