Matlab / Octave：如何在指定网格线间距的同时显示矩阵？

Question

I would like to display a 2D array named C under MATLAB/Octave; I would normally use imagesc , but this time I would like to specify multiple cell sizes.

imagesc does not allow me to do this: if I set x and y as two elements vectors, imagesc(x,y,C) simply specifies the image location, but does not give me control over the grid spacing.

I was thinking of using pcolor , but it creates a pseudocolor plot using each set of four adjacent points in C to define a surface rectangle. Therefore a 4x4 matrix will appear as a 3x3 grid!

QUESTION: do you know about any built-in function that would allow me to display a 2D array while specifying grid lines spacing?

Thanks a lot for your answer!

EXAMPLE

Here is an example of what I would like to achieve.
Let's say I want to display the matrix C=magic(4)

imagesc(C) will return:

Now let's define two arrays X and Y containing the pixel's width and height (or length):

X=[1, 1, 2, 1]
Y=[1, 1, 1, 1]

I am looking for a function of X , Y and C that would return the following image:

Please note that I created the image above using paint!

Answer 1

Disclaimer: this solution is simple, and close to the intended result, but it will distort the data due to the way pcolor creates the plot. For a more cumbersome but precise solution, see the answer by Tasos Papastylianou .

You could kludge your way with pcolor , you just have to use cumsum to turn your pixel widths into coordinates. The kludgy bit is adding zero-padding that is later thrown away by pcolor :

C = magic(4);
X = [1, 1, 2, 1];
Y = [1, 1, 1, 1];
Xt = [0, cumsum(X)];
Yt = [0, cumsum(Y)];
Ct = C;
Ct(end+1,end+1) = 0; % or more nicely: pre-allocate and overwrite with C

pcolor(Xt,Yt,Ct);
%optionally flip y axis to reconstruct imagesc() output
axis ij;

Answer 2

tl;dr : control aspect ratio with daspect and draw custom gridlines

---

Explanation : Find below several examples which will give you an understanding of what's going on.

Here is the solution I mentioned in the comments. It involves drawing an image with imagesc and coordinates, as you hinted, and also controlling the pixel aspect ratio using daspect . For complete control, it's best to draw your gridlines separately.

Run each cell separately to see what it does.

%%%% In file LookAtMeHacker.m
[Shodan,M] = imread('http://vignette2.wikia.nocookie.net/shodan/images/0/09/SHODAN_1.jpg');

%% Aspect ratios for normal imagesc
% Default aspect ratio, automatically calculated from image size
imagesc(Shodan); 
ImageSize   = size(Shodan)
AspectRatio = daspect()
title(sprintf('Default view. Aspect Ratio= %d:%d', ...
              AspectRatio(2), AspectRatio(1)));
%% Isotropic pixels
axis equal; AspectRatio = daspect();
title(sprintf('Axis ''equal''. Aspect Radio= %d:%d', ...
              AspectRatio(2), AspectRatio(1)));

%% Custom aspect ratio: 16:9
daspect([9,16,1]); AspectRatio = daspect();
title(sprintf('Custom Aspect Radio= %d:%d', ...
              AspectRatio(2), AspectRatio(1)));

%% Aspect ratios for imagesc with coordinates
% Default view
imagesc([0,40], [10, 30], Shodan)
AspectRatio = daspect()
title(sprintf('Default view.with coordinates; Aspect Ratio= %d:%d', ...
              AspectRatio(2), AspectRatio(1)));

%% Isotropic pixels IN TERMS OF COORDINATES
axis equal; AspectRatio = daspect();
title(sprintf('Axis ''equal''. Aspect Radio= %d:%d', ...
              AspectRatio(2), AspectRatio(1)));

%% Custom VISUAL aspect ratio: 16:9
daspect([9/20,16/40,1]); AspectRatio = daspect();
title('Custom Aspect Radio= 16:9')

%% Custom gridlines:
for i = 10:5:30; line(xlim, i, 'linestyle',':','color','w', 'linewidth',3); end;
for i = 0:5:40; line(i, ylim, 'linestyle',':','color','w', 'linewidth',3); end;

End result:

Answer 3

This adds on Andras' nice cumsum approach; however, the problem with pcolor is that the values you get in the faces are not the values / colours you expect in your matrix, but interpolations from the values applied at the vertices of the pcolor graph.

Here's an approach that works around this. It's slow, because we're essentially plotting an area for each patch, and manually assigning colour, but you'll get the idea.

C = magic(4);
X = [1, 1, 2, 1];
Y = [1, 1, 1, 1];
Xt = [0, cumsum(X)];
Yt = [0, cumsum(Y)];

Ct = round(1 + (255 * mat2gray(C))); % convert to 256 colourmap indices
Cmap = permute(jet(256),[1,3,2]);
Ct = Cmap(Ct,1,:);
Ct = reshape(Ct, size(C,1), size(C,2), []);

LimX = Xt(end);
for i = size(C,1):-1:1
  for j = 1:size(C,2);
    area([Xt(j),LimX],[Yt(i+1),Yt(i+1)], 'edgecolor','none','facecolor', squeeze(Ct(i,j,:))); hold on;
  end
end
hold off;
axis ij; daspect([1,1,1]);

Result / Comparisons: