Démonstration animée du stockage compressé d'une matrice tridiagonale

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

示例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]

示例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，请进一步进行
将矩阵的元素作为输入
现在，除了主对角线以及主对角线下方和上方的对角线之外，所有地方都置零。

程序：

Python3

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