功能: 求解对称7带宽带状矩阵方程

格式: SparseSolveSym7(A, B)

A : 一个列数为3的矩阵变量,且行数不少于7的矩阵变量
B : 一个与A行数一致的矩阵变量

说明:
1. 本函数主要求解如下线性方程组里的X
$$
AX = B
$$
这里A具有如下对称且带宽为5的形式
$$
A=\begin{bmatrix}
a_1 & b_1 & c_1 &d_1
\\
b_1 & a_2 & b_2 & c_2&d_2
\\
c_1 & b_2 & a_3 & b_3 & c_3&d_3
\\
d_1&c_2 & b_3 & a_4 & b_4 & c_4&d_4
\\
&d_2&c_3 & b_4 & a_5 & b_5 & c_5&d_5
\\
&&d_3&c_4 & b_5 & a_6 & b_6 & c_6&d_6
\\
...
\\
&&&&d_{n-6}&c_{n-5} & b_{n-4} & a_{n-3} & b_{n-3} & c_{n-3} & d_{n-3}
\\
&&&&&d_{n-5}&c_{n-4} & b_{n-3} & a_{n-2} & b_{n-2} & c_{n-2}
\\
&&&&&&d_{n-4}&c_{n-3} & b_{n-2} & a_{n-1} & b_{n-1}
\\
&&&&&&&d_{n-3}&c_{n-2} & b_{n-1} & a_n
\end{bmatrix}
$$
由于A对称，因此函数里的A约定按如下方式存储
$$
A=\begin{bmatrix}
a_1 &b_1&c_1&d_1
\\
a_2 &b_2&c_2&d_2
\\
a_3 &b_3&c_3&d_3
\\
...
\\
a_{n-3} &b_{n-3}&c_{n-3}&d_{n-3}
\\
a_{n-2} &b_{n-2}&c_{n-2}&0
\\
a_{n-1} &b_{n-1}&0&0
\\
a_n &0&0&0
\end{bmatrix}
$$

2. B参数如果有多列，每一列单独进行求解

3. 当矩阵A分解失败时,本函数内部会采用拟牛顿法进行求解。

例子:
已知如下A,b
$$
\begin{cases}
A&=\begin{bmatrix}
10.886&-0.452059&-9.67399&0.258648
\\
-0.452059&4.12387&-5.14226&6.78224&5.39828
\\
-9.67399&-5.14226&-11.6086&2.2528&-1.99543&-6.15572
\\
0.258648&6.78224&2.2528&-6.52699&7.83059&3.26454&7.0184
\\
&5.39828&-1.99543&7.83059&-6.93393&7.80465&-4.66669&8.6162
\\
&&-6.15572&3.26454&7.80465&-4.83543&0.795207&4.41905&-3.39326
\\
&&&7.0184&-4.66669&0.795207&-3.99338&-4.31413&-5.42064&-2.03127
\\
&&&&8.6162&4.41905&-4.31413&7.6331&7.86745&6.29534
\\
&&&&&-3.39326&-5.42064&7.86745&-4.78847&3.68437
\\
&&&&&&-2.03127&6.29534&3.68437&13.1511
\end{bmatrix}
\\
\\
\mathbf{b}&=\begin{bmatrix}-0.350187&-5.6835&9.00505&8.40257&-7.0468&7.62124&2.82161&-1.36093&2.39193&-4.37881\end{bmatrix}^T
\end{cases}
$$

a = [ 10.8860000000000   -0.45205900000000   -9.67399000000000    0.25864800000000
      4.12387000000000   -5.14226000000000    6.78224000000000    5.39828000000000
     -11.6086000000000    2.25280000000000   -1.99543000000000   -6.15572000000000
     -6.52699000000000    7.83059000000000    3.26454000000000    7.01840000000000
     -6.93393000000000    7.80465000000000   -4.66669000000000    8.61620000000000
     -4.83543000000000    0.79520700000000    4.41905000000000   -3.39326000000000
     -3.99338000000000   -4.31413000000000   -5.42064000000000   -2.03127000000000
      7.63310000000000    7.86745000000000    6.29534000000000    0.00000000000000
     -4.78847000000000    3.68437000000000    0.00000000000000    0.00000000000000
      13.1511000000000    0.00000000000000    0.00000000000000    0.00000000000000 ];
b = [-0.35018700000000
     -5.68350000000000
      9.00505000000000
      8.40257000000000
     -7.04680000000000
      7.62124000000000
      2.82161000000000
     -1.36093000000000
      2.39193000000000
     -4.37881000000000 ];

x = SparseSolveSym7(a, b)//执行得到如下结果
x =
[-0.78325403301987
 -2.50997556908470
 -0.74728267254360
 -0.72510030501137
  0.99815467373212
  2.68510272356934
  0.85452588993510
  0.07453621548374
 -2.82111309259713
  0.55369941910844 ]