Question

以下是我从数字分析教科书中获得的Matlab代码。它用于离散拉普拉斯算子并基于所选域（在这种情况下为单位平方）设置矩阵。我想知道如何修改此代码以更改域的维度。即一个4 x 5的矩形。我并没有真正使用Matlab，但我很想看到不同域的结果。

N = nx * ny;  
N5 = 5 * N;
irow = zeros(N5, 1);
icol = irow; 
NZA = irow;

index = 0;
row = 0;

for j = 1:ny
   for k = 1:nx

      row = row + 1;

      if j > 1
         index = index + 1;
         NZA (index) = -1.0;
         irow(index) = row;
         icol(index) = row - nx;   % South
      end

      if k > 1
         index = index + 1;
         NZA (index) = -1.0;
         irow(index) = row;
         icol(index) = row - 1;    % West
      end

      index = index + 1;
      NZA (index) = 4.0;
      irow(index) = row;
      icol(index) = row;           % P (self)

      if k < nx
         index = index + 1;
         NZA (index) = -1.0;
         irow(index) = row;
         icol(index) = row + 1;    % East
      end

      if j < ny 
         index = index + 1;
         NZA (index) = -1.0;
         irow(index) = row;
         icol(index) = row + nx;   % North
      end
   end
end            

icol = icol(1:index); 
irow = irow(1:index);
NZA = NZA(1:index);

A = sparse (irow, icol, NZA, N, N);

Answer 1

看起来你可以通过设置nx和ny来改变大小。

Answer 2

我不知道修改上面的代码，但我认为你可以得到一个代表unit square的mxn点网格，如下所示：

%user input
m=4; % points in x-direction
n=5; %points in y-direction

%code
[x,y]=meshgrid(0:1/m:1,0:1/n:1);

%visualization
allPointsOnGrid=[x(:) y(:)];
scatter(allPointsOnGrid(:,1),allPointsOnGrid(:,2));

这将生成一个单位正方形，在x方向上有m+1个点，在y方向上有n+1个点。

Matlab网格生成器

2 个答案: