1.7 无悬浮功能设备和键盘操作的按钮直接显示，窄滚动条
1.5 增加作用于短信页
1.3 修复行高；设置 plaintext
1.2 限制最大高度
1.1 删去难绷的识别语言显示，修改为悬浮显示复制按钮

import numpy as np
import torch

def solve_block_tridiagonal(a, b, c, d):

    N = len(b)
    x = np.zeros_like(d)
   
    # Forward elimination with explicit C* and d* storage
    C_star = np.zeros_like(c)
    d_star = np.zeros_like(d)

    # Initial calculations for C_0* and d_0*
    C_star[0] = np.linalg.solve(b[0], c[0])
    d_star[0] = np.linalg.solve(b[0], d[0])

    # Forward elimination
    for i in range(1, N - 1):
        C_star[i] = np.linalg.solve(b[i] - a[i-1] @ C_star[i-1], c[i])
        d_star[i] = np.linalg.solve(b[i] - a[i-1] @ C_star[i-1], d[i] - a[i-1] @ d_star[i-1])

    # Last d_star update for the last block
    d_star[-1] = np.linalg.solve(b[-1] - a[-2] @ C_star[-2], d[-1] - a[-2] @ d_star[-2])

    # Backward substitution
    x[-1] = d_star[-1]
    for i in range(N-2, -1, -1):
        x[i] = d_star[i] - C_star[i] @ x[i+1]

    return x


def test_block_tridiagonal_solver():

    N = 4

    a = np.array([
        [[1, 0.5], [0.5, 1]],  
        [[1, 0.5], [0.5, 1]],
        [[1, 0.5], [0.5, 1]]
    ], dtype=np.float64)
   
    b = np.array([
        [[5, 0.5], [0.5, 5]],  
        [[5, 0.5], [0.5, 5]],
        [[5, 0.5], [0.5, 5]],
        [[5, 0.5], [0.5, 5]]
    ], dtype=np.float64)
   
    c = np.array([
        [[1, 0.5], [0.5, 1]],  
        [[1, 0.5], [0.5, 1]],
        [[1, 0.5], [0.5, 1]]
    ], dtype=np.float64)

    d = np.array([
        [1, 2],
        [2, 3],
        [3, 4],
        [4, 5]
    ], dtype=np.float64)
   
    x = solve_block_tridiagonal(a, b, c, d)

    # Construct the equivalent full matrix A_full and right-hand side d_full
    A_full = np.block([
        [b[0], c[0], np.zeros((2, 2)), np.zeros((2, 2))],
        [a[0], b[1], c[1], np.zeros((2, 2))],
        [np.zeros((2, 2)), a[1], b[2], c[2]],
        [np.zeros((2, 2)), np.zeros((2, 2)), a[2], b[3]]
    ])
   
    d_full = d.flatten()  # Flatten d for compatibility with the full system

    # Solve using numpy's direct solve for comparison
    x_np = np.linalg.solve(A_full, d_full).reshape((N, 2))
    # Print the solutions for comparison
    print("Solution x from block tridiagonal solver (TMDA):\n", x, "\nResidual:", torch.sum(torch.abs(torch.tensor(A_full)@torch.tensor(x).flatten() - torch.tensor(d).flatten())))
    print("Solution x from direct full matrix solver:\n", x_np, "\nResidual np:", torch.sum(torch.abs(torch.tensor(A_full)@torch.tensor(x_np).flatten() - torch.tensor(d).flatten())))
# Run the test function
test_block_tridiagonal_solver()