Matlab网格生成器

Question

下面是我从我的数值分析教材中得到的Matlab代码。它被用来离散一个拉普拉斯，并建立一个基于所选区域的矩阵(在本例中是单位平方)。我想知道如何修改这段代码以更改域的维度。即4x5矩形。我并不经常使用Matlab，但我很想看到不同领域的结果。

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

看起来您可以通过设置nx和ny来更改大小。

Answer 2

我不知道如何修改上面的代码，但我认为您可以得到一个表示mxn的单位方格点的网格，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));

这将产生一个单位正方形，m+1点在x方向，n+1点在y方向.