create a square array in matlab

tommyers

Hi,

I realise this is a physics forum, but thought someone may be able to help!

I would like to create a square array i.e 4x4 and then plot a vector of data (16 elements) over this 4x4 array.

I have created the following code, it doesnt work but thats what I am ideally aiming after:

[X,Y] = meshgrid([1:1:4]);

z = [30 20 20 30 20 10 10 20 20 10 10 20 30 20 20 30];

mesh(X,Y,z)

The reason that I believe that it doesnt work is that my z variable is not a funtion of X or Y. But it isn't in real life so how do I get around this?

Regards

Tom

Claude Bile

You need some way for the program to assign an X and Y coordinate to each z value. I guess the easiest way to do this would be to make z a 4x4 matrix. Then you could have something like -

z = z(x,y)

Claude.

Hash

You must plot the same sized variables, ie :
size(X)=size(Y)=size(Z)

so you must have z in 4x4 form.

By example, maybe you can (it depends of your problem) just reshape your z :
>> Z = reshape(z,4,4)

Z =

30 20 20 30
20 10 10 20
20 10 10 20
30 20 20 30

then
mesh(X,Y,Z)
and maybe mesh isn't adapted to what you want. Try pcolor instead for a 2D visualisation.

J77

Specifically, you need to specify the value of z at each point (x,y).

I see you have 16 z values.

Therefore, you may want a 4x4 grid with the z values in a corresponding 4x4 matrix.

My little bit: I always use surf(x,y,z) with "shading interp" for best results.

tommyers

Thanks guys - I have now got the following code, so near yet so far:

x = [1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4];
y = [1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4];

x = reshape(x,4,4)
y = reshape(y,4,4)

z = [30 20 20 30 20 10 10 20 20 10 10 20 30 20 20 30];

z = reshape(z,4,4)

z = (z.*x + z.*y);

surf(x,y,z)
colormap hsv
axis([0 4 0 4 0 250])

to generate the attached plot (see below)

The plot is not what I want! I want 16 squares the 4 corners to be the same value, the 4 middle ones to be the same value and the rest a third value - as indicated by the z matrix. I am not bothered about the actual values i.e the 4 corners do not have to be 30 I am more interested in the weighting between each of the 3 values.

Regards

Tom

Attached Thumbnails

 

Claude Bile

You are getting a distorted curve because of this line.

z = (z.*x + z.*y);

Take out this line and the code should work. Don't get hung up on making z a function of x and y. It wont work because z has no analytic dependance on x and y, thus you need to manually specify the values of z at each coordinate (which you have already done).

Claude.

tommyers

Thanks Claude,

I have now chnaged my code to:

x = [1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4];
y = [1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4];

x = reshape(x,4,4)
y = reshape(y,4,4)

z = [30 20 20 30 20 10 10 20 20 10 10 20 30 20 20 30];

z = reshape(z,4,4)

surf(x,y,z)
colormap hsv
axis([0 4 0 4 0 250])

Although my matrix (coloured part) is still 3 x 3!

I am trying to achieve something like the following:

30 20 20 30
20 10 10 20
20 10 10 20
30 20 20 30

in mesh / surf representation..................

Regards

Tom

J77

It's 3x3 squares, but 4x4 coordinate points - as you specify.

tommyers

Further .... this is what I want.

4
30 20 20 30
3
20 10 10 20
2
20 10 10 20
1
30 20 20 30
0
0 1 2 3 4

where green represent the axis 'ticks' and the purple represent the values between these 'ticks'.

Regards

Tom

tommyers

J77,

I NOW realise this - but any suggestions how to change this?

... and keep my matrices the same length?

Tom

J77

Use bar3 ?

Though you won't get a 'smooth' surface anymore.

tommyers

Thats not what I am really looking for!

Tom

J77

The only other way I see is representing your values at the bisection of two tick marks, ie. at (0.5,0.5)=30, (0.5,1.5)=20, (0.5,2.5)=20, (0.5,3.5)=30 etc.

You don't have enough data to do anything more...

(And there aren't enough points to accurately extrapulate away from the data you have)

tommyers

J77,

There is no more data - thats all there is....

I want a 4x4 mesh i.e. 16 squares, with a z term in each!

Have would you do as you suggested in an automated way?

Regards

Tom

J77

tommyers

WOW J77,

That looks amazing!

Although when I turn the shading interp off I still only see 3x3 and the coloring isn't symmetrical - why is this?

The pattern is symmetrical when the shading is one!

Regards

Tom

J77

Colours in Matlab are quite hard (numerous) to explain... read up on the various colormaps in the helpdesk.