Question

我正在尝试使用涉及方程组的FDE（有限差分法）在Matlab中解决问题。

所以我有

[A] {T} = {C} - ＆gt; [A] ^（ - 1）{C} = {T}

我“知道”[A]和{C}的所有值。因为矩阵大多是零，所以我使用稀疏矩阵。

但Matlab在向矩阵填充已知值时给出了警告。

这种稀疏索引表达式可能很慢。

以下是一个例子：

clear;clc;
% Number of nodes.
nodes = 5000;

% My 
A = sparse(nodes,nodes);    % Known parameters.
C = sparse(nodes,1);        % Known parameters.
T = sparse(nodes,1);        % Trying to find.

% Solving equation: [A]{T}={C} -> [A]^(-1){C}={T}

% I'm trying to fill my known values to [A]

% I have 40+ 'sections' with different values. For this example I use one
% section with all values equals to 1.

Section1 = [1, 30, 50, 60, 100, 430, 4500];  % Nodes in section 1.

% Random numbers for the example. (I generate them for each node.)
q = 10;
w = 400;
e = 1000;
r = 3500;

for i = 1:nodes
    if any(Section1(:)==i)
        A(i,q) = 1;                   % Error on this line
        A(i,w) = 1;                   % Error on this line
        A(i,e) = 1;                   % Error on this line
        A(i,r) = 1;                   % Error on this line
    end
end

Answer 1

您可以使用行，列和值列表构建稀疏矩阵。

E.G。

>> i = [1,2,3];
>> j = [2,3,4];
>> s = [10, 20, 30];
>> A = sparse(i,j,s,5,5)

A =

   (1,2)       10
   (2,3)       20
   (3,4)       30

>> full(A)

ans =

     0    10     0     0     0
     0     0    20     0     0
     0     0     0    30     0
     0     0     0     0     0
     0     0     0     0     0

如果您无法提前构建i，j和s，则可以使用spalloc来预先分配稀疏空间矩阵，这应该加快分配。

将已知值填充到稀疏矩阵

1 个答案: