矩阵数据画彩色图以及二维拟合问题

背景：我现在有从comsol中导出的电场图的数据，可以处理成三个矩阵，分别为x（横坐标，如1000*1的矩阵），y（纵坐标，如1000*1的矩阵），F（需要最终展示的数据，如1000*1的矩阵），其中x,y,F一一对应，也就是说，（x(1),y(1)）对应的数据就是F（1）。另外x矩阵以及y矩阵内元素的顺序不是从小到大或者从大到小，而是乱序的，且不具备等差数列等规律

问题：（1）我想在matlab中画出这个矩阵对应的图，但是用我常用的imagesc、pcolor等方式没有用，并且实际矩阵是比较大的，大概1*17189，所以处理起来也比较麻烦，所以想问问各位有什么更好的办法可以处理这个问题

（2）图画好之后，需要对既有的数据做固定间隔的x以及y方向的插值拟合，想了一下，这种数据貌似传统的interp2也不是很好用，像请教下看有没有什么更好的办法

附件附上了具体的数据

附图截了一小部分的数据：第一列为x，第二列为y，第四列为F，第三列忽略掉就行

Answer 1

[Suraj Kumar]

Hi feng,

From what I gather, your goal is to visualize a large matrix and subsequently execute interpolation fitting at consistent intervals. To achieve the desired results, you can go through the following steps along with the code snippets:

1. The data consists of three matrices: `x`, `y`, and `F`. These scattered data points are interpolated onto a regular grid for visualization. Grid points are defined using `linspace` and a meshgrid is created with the function `meshgrid`.

xq = linspace(min(x), max(x), 500);  
yq = linspace(min(y), max(y), 500);  
[Xq, Yq] = meshgrid(xq, yq); % meshgrid for grid points 

2. The `griddata` function interpolates the scattered data (`x`, `y`, `F`) onto the grid using the 'cubic' method. The data is then visualized with `imagesc`, including axis adjustments.

figure; 
imagesc(xq, yq, Fq);   
axis xy;   
colorbar;   
xlabel('X'); 
ylabel('Y'); 
title('Interpolated Data Plot'); 

3. To perform interpolation fitting, you can create an interpolant object from the scattered data using `scatteredInterpolant`. Then define grid points using `linspace` and create a meshgrid with `meshgrid`.

F_interpolant = scatteredInterpolant(x, y, F, 'linear',       'none');  

% Define the grid for interpolation 
xq = linspace(min(x), max(x), 500);  
yq = linspace(min(y), max(y), 500);  
[Xq, Yq] = meshgrid(xq, yq); %meshgrid for grid points 

4. Then evaluate the interpolant at these grid points (`Xq`, `Yq`) and finally, visualize the interpolated data using `imagesc`, adjusting the axis with `axis xy’.

Fq = F_interpolant(Xq, Yq); % Evaluate the interpolant at the grid points 
figure; 
imagesc(xq, yq, Fq);  
axis xy;  
colorbar; 
xlabel('X'); 
ylabel('Y'); 
title('Interpolated Data Plot from Interpolant'); 

You may refer the attached output for better understanding:

Kindly refer to the documentation links as mentioned below:

• Meshgrid : https://www.mathworks.com/help/matlab/ref/meshgrid.html
• Griddata : https://www.mathworks.com/help/matlab/ref/griddata.html
• Imagesc : https://www.mathworks.com/help/matlab/ref/imagesc.html
• scatteredInterpolant : https://www.mathworks.com/help/matlab/ref/scatteredinterpolant.html

Happy Coding!