plotting separate parts of a column on different figures

I have a large matrix. In the 3rd column, I have my "eta" values. In my 4th column, I have "r" values. In my 8th column, I have "g" values.

Eta is the same as you go down column for a while. How can I plot g vs. r as long as eta is the same, then make a new plot with g vs r anytime eta changes?

Maybe the matrix needs to be reshaped first? Note that the number of eta values that are the same can change.

[Stephen23]

"Maybe the matrix needs to be reshaped first?"

That would only work if the number of eta elements was the same for each group. The simplest solution is to use diff on the third column to detect the indices of the changes, and then plot in a simple loop.

But the specifics depend on your data: are identical eta values always contiguous? If not, do you want to plot discontinuous groups with the same eta value as one plot or mulutple plots?

[Benjamin]

I basically want multiple plots. For the same eta, I want to plot r vs g. Currently I am loading in the data like this:

eta_104720=xlsread('C:example.xlsx','0.20','A2:H1000');
eta_130900=xlsread('C:example.xlsx','0.25','A2:H1000');
eta_157080=xlsread('C:example.xlsx','0.30','A2:H1000');
eta_183260=xlsread('C:example.xlsx','0.35','A2:H1000');
eta_209440=xlsread('C:example.xlsx','0.40','A2:H1000');
eta_235620=xlsread('C:example.xlsx','0.45','A2:H1000');
eta_261799=xlsread('C:example.xlsx','0.50','A2:H1000');
eta_287979=xlsread('C:example.xlsx','0.55','A2:H1000');
eta_314159=xlsread('C:example.xlsx','0.60','A2:H1000');
eta_340339=xlsread('C:example.xlsx','0.65','A2:H1000');
eta_366519=xlsread('C:example.xlsx','0.70','A2:H1000');
eta_392699=xlsread('C:example.xlsx','0.75','A2:H1000');
eta_408407=xlsread('C:example.xlsx','0.78','A2:H1000');
eta_418879=xlsread('C:example.xlsx','0.80','A2:H1000');
eta_434597=xlsread('C:example.xlsx','0.83','A2:H1000');
eta_445059=xlsread('C:example.xlsx','0.85','A2:H1000');
eta_460767=xlsread('C:example.xlsx','0.88','A2:H1000');
eta_471239=xlsread('C:example.xlsx','0.90','A2:H1000');
eta_476475=xlsread('C:example.xlsx','0.91','A2:H1000');
eta_481711=xlsread('C:example.xlsx','0.92','A2:H1000');
eta_486947=xlsread('C:example.xlsx','0.93','A2:H1000');
eta_492183=xlsread('C:example.xlsx','0.94','A2:H1000');
eta_497419=xlsread('C:example.xlsx','0.95','A2:H1000');
eta_502655=xlsread('C:example.xlsx','0.96','A2:H1000');
eta_507891=xlsread('C:example.xlsx','0.97','A2:H1000');
eta_513127=xlsread('C:example.xlsx','0.98','A2:H1000');
eta_518363=xlsread('C:example.xlsx','0.99','A2:H1000');
eta_523599=xlsread('C:example.xlsx','1.00','A2:H1000');
eta_528835=xlsread('C:example.xlsx','1.01','A2:H1000');
eta_534071=xlsread('C:example.xlsx','1.02','A2:H1000');

[Stephen23]

"Currently I am loading in the data like this:"

Numbering variables is a sign that you are doing something wrong in your code.

Copy-and-pasting code is a sign that you are doing something wrong in your code.

Think of it this way: computers are really very stupid but are particularly good at doing simple repetitive tasks very quickly. So when you sit and copy-and-paste code like that you are actually just doing the computer's job for it.

Instead of repeating code you need to use a loop and indexing into one array (which could be numeric, cell, structure, etc., whatever suits your data). First fix the data importing, then worry about how to plot it.

[Benjamin]

But all of them are different sizes though, they can't easily go into an array. I'm not sure how to better import the data. How could I load all of this in a struct?

The alternative is I just import the sheet name "Master" and then I have all the data. Then I have the problem that I initially asked in this question. By loading them in separately, I don't have to separate them in MATLAB.

You can see the sheet names. Can I load these in a better way? How do I load all of them to avoid this mess of a code?

[Stephen23]

"But all of them are different sizes though, they can't easily go into an array"

That is exactly what cell arrays are for.

"The alternative is I just import the sheet name "Master" and then I have all the data."

That would likely be the best solution.

"Then I have the problem that I initially asked in this question. By loading them in separately, I don't have to separate them in MATLAB."

Processing the data within MATLAB is much more efficient than importing data from file multiple times (hard-drives are very slow!). Simply import that data all at once, use diff to detect where eta changes, then loop over those indices and plot the data.

[Benjamin]

I am not sure how to use diff to detect eta changes and plot appropriately. Any chance you could show me what you mean?

Answer 1

[Stephen23]

Following your description "I have a large matrix. In the 3rd column, I have my "eta" values. In my 4th column, I have "r" values. In my 8th column, I have "g" values", here is one simple loop:

% Random fake data with contiguous eta groups:
mat = rand(32,8);
mat(:,3) = sort(randi(9,32,1));
% Detect eta groups (i.e. changes in eta):
bnd = find([true;diff(mat(:,3));true]);
% Plot data for each eta group:
for k = 1:numel(bnd)-1
	figure() % using ONE figure is usually simpler.
	idx = bnd(k):bnd(k+1)-1;
	G = mat(idx,8);
	R = mat(idx,4);
	plot(R,G) % or plot(G,R), whatever you want
	title(sprintf('eta = %d',mat(bnd(k),3)))
end

[Benjamin]

Ok it works, but I need to plot something else over each figure.

I have an equation with all of my coefficients.

Is there a way to plot this equation over each plot?

The equation is:

g(count) =    C00*r^0*rpf^0 + C10*r^1*rpf^0 + C20*r^2*rpf^0 + C30*r^3*rpf^0 + ...
                    + C40*r^4*rpf^0 + C50*r^5*rpf^0 + C60*r^6*rpf^0 + C01*r^0*rpf^1 + ...
                    + C11*r^1*rpf^1 + C21*r^2*rpf^1 + C31*r^3*rpf^1 + C41*r^4*rpf^1 + ...
                    + C51*r^5*rpf^1 + C61*r^6*rpf^1 + C02*r^0*rpf^2 + C12*r^1*rpf^2 + ...
                    + C22*r^2*rpf^2 + C32*r^3*rpf^2 + C42*r^4*rpf^2 + C52*r^5*rpf^2 + ...
                    + C62*r^6*rpf^2 + C03*r^0*rpf^3 + C13*r^1*rpf^3 + C23*r^2*rpf^3 + ...
                    + C33*r^3*rpf^3 + C43*r^4*rpf^3 + C53*r^5*rpf^3 + C63*r^6*rpf^3 + ...
                    + C04*r^0*rpf^4 + C14*r^1*rpf^4 + C24*r^2*rpf^4 + C34*r^3*rpf^4 + ...
                    + C44*r^4*rpf^4 + C54*r^5*rpf^4 + C64*r^6*rpf^4 + C05*r^0*rpf^5 + ...
                    + C15*r^1*rpf^5 + C25*r^2*rpf^5 + C35*r^3*rpf^5 + C45*r^4*rpf^5 + ...
                    + C55*r^5*rpf^5 + C65*r^6*rpf^5 + C06*r^0*rpf^6 + C16*r^1*rpf^6 + ...
                    + C26*r^2*rpf^6 + C36*r^3*rpf^6 + C46*r^4*rpf^6 + C56*r^5*rpf^6 + ...
                    + C66*r^6*rpf^6;

How can I plot the results of this equation on each graph? Note that each eta from before needs to be divided by 0.6452 which equals the rpf in the equation. Then the r values is the same. I know this is asking a lot, but any chance this can be done? Your code looks so much nicer than mine, and runs so much more quickly.

Do I just create a list of the etas?

eta =[0.104 ... ]/eta_c then loop over them somehow? Also, can the figures be concatenated some, maybe 4 lines per figure?

Here are the coeffs and the excel file is attached.

     C00 =           1
       C10 =           0
       C20 =           0
       C30 =           0
       C40 =           0
       C50 =           0
       C60 =           0
       C21 =           0
       C41 =           0
       C51 =           0
       C61 =           0

       C01	=	3.852524207
C02	=	23.53599039
C03	=	0.118526083
C04	=	-43.41332658
C05	=	948.0535831
C06	=	3776.25898
C11	=	-4.237794684
C12	=	-49.91457825
C13	=	2.035107487
C14	=	-0.043239356
C15	=	-2349.036448
C16	=	-18933.62303
C22	=	29.81614236
C23	=	0.950554481
C24	=	212.7205481
C25	=	1704.289707
C26	=	38209.91607
C31	=	0.40010662
C32	=	-0.315528868
C33	=	-0.100534241
C34	=	-240.1274163
C35	=	0.503405195
C36	=	-39973.94603
C42	=	-3.280392297
C43	=	-1.124766435
C44	=	0.142346294
C45	=	-340.6795507
C46	=	22948.25649
C52	=	-0.196586982
C53	=	-4.005541175
C54	=	107.7802926
C55	=	0.408800522
C56	=	-6867.596077
C62	=	0.219277449
C63	=	2.818808315
C64	=	-38.91546551
C65	=	40.40684041
C66	=	837.4581623

[Stephen23]

"Also, I'm not sure what ... does"_

You definitely should NOT use that line on your actual data!

Because you did not upload any sample data for us to use, I had to create some fake data for my code to run on . That line is part of the fake data creation, it defines the eta values (which you can tell by looking at the indexing). That is why I put that line under the title "Random fake data...", so that you would know that it is random fake data unrelated to your own data.

[Benjamin]

Sorry, yeah I figured that out. My bad. I have a new question about plotting an equation over each figure in my comment above. Is this possible? It might help if a cell array or something is created with all the data separated out right so that I can easily access it?

I also attached the excel file. Basically, I want to plot the results of each equation to see how close the data and the fit are to each other.

I guess, somehow we could get all the unique etas from column 3, create a list, divide by eta_c then loop over these values (rpf) along with the r values to plot the equation over each data set?

[Stephen23]

" Your code looks so much nicer than mine, and runs so much more quickly."

As I wrote earlier, always get computers to do the looping for you, it is what they are good for.

"but I need to plot something else over each figure."

You can certainly plot more data on those figures: you might find hold on to be useful.

"Do I just create a list of the etas?"

MATLAB does not have a "list" data type. It has many numeric array classes, cell arrays, structure arrays, and several other classes of data:

https://www.mathworks.com/help/matlab/matlab_prog/fundamental-matlab-classes.html

"...then loop over them somehow?"

You already have a loop, I doubt that you need another one. You can easily get the eta value within each loop iteration (look at the title command in my answer to see how). Just use that eta value with your big coefficient calculation, and then plot it.

You can also simplify your coefficients into one vector/array: I recommend that you read about vectorized code:

https://www.mathworks.com/help/matlab/matlab_prog/vectorization.html

"Also, can the figures be concatenated some, maybe 4 lines per figure?"

Sure, get rid of the figure call (or move it before the loop), plot inside the loop, and use mod of the loop iterator with an if statement to select between hold on and hold off, something like this (this should get you started, experiment and adjust to suit your needs...):

for k = 1:numel(...)
    ...
    plot(...)
    if mod(k,4)
        hold off
    else
        hold on
    end
end

"Ok it works"

I'm glad! You can show your appreciation by accepting my answer.

[Benjamin]

I accomplished what I want using this below. It seems to work. Are there any bad programming things in this code? I had to create another loop I think for the r's.

clear; clc; close all;
mat =xlsread('C:\example.xlsx','Master','A2:H100000');

%Fitted coefficients
C01	=	3.948865057;
C02	=	14.25897353;
C03	=	-0.147408847;
C04	=	-67.12239818;
C05	=	957.6898398;
C06	=	3594.695699;
C11	=	-4.356067276;
C12	=	-22.9612674;
C13	=	2.338700784;
C14	=	127.3297068;
C15	=	-2409.417912;
C16	=	-17986.34369;
C22	=	1.524174204;
C23	=	2.04273652;
C24	=	0.723024469;
C25	=	1776.750914;
C26	=	36178.57305;
C31	=	0.426666375;
C32	=	10.02732415;
C33	=	1.804441828;
C34	=	-114.8945779;
C35	=	5.074533729;
C36	=	-37646.86952;
C42	=	-0.893431697;
C43	=	-7.007982809;
C44	=	-0.026982216;
C45	=	-372.7572177;
C46	=	21426.71162;
C52	=	-2.848536942;
C53	=	-0.69536636;
C54	=	87.39447636;
C55	=	-0.194479016;
C56	=	-6324.324548;
C62	=	0.703997366;
C63	=	2.493413196;
C64	=	-35.3331676;
C65	=	46.6948293;
C66	=	754.3778141;


C00	=	1;
C10	=	0;
C20	=	0;
C30	=	0;
C40	=	0;
C50	=	0;
C60	=	0;
C21	=	0;
C41	=	0;
C51	=	0;
C61	=	0;

% Detect eta groups (i.e. changes in eta):
bnd = find([true;diff(mat(:,3));true]);
% Plot data for each eta group:
for k = 1:numel(bnd)-1
	figure() % using ONE figure is usually simpler.
	idx = bnd(k):bnd(k+1)-1;
	G = mat(idx,8);
	R = mat(idx,4);
	plot(R,G)
	title(sprintf('eta = %d',mat(bnd(k),3)))
    xlim([1 2]);
    ylim([0 1]);
    grid on;
    hold on;
    eta = mat(bnd(k),3);
    eta_c = 0.6452;
    rpf = eta/eta_c;
    
    count = 0;
    for r = 1:0.01:2
        count = count + 1;
     g_fit(count) = C00*r^0*rpf^0 + C10*r^1*rpf^0 + C20*r^2*rpf^0 + C30*r^3*rpf^0 + ...
                    + C40*r^4*rpf^0 + C50*r^5*rpf^0 + C60*r^6*rpf^0 + C01*r^0*rpf^1 + ...
                    + C11*r^1*rpf^1 + C21*r^2*rpf^1 + C31*r^3*rpf^1 + C41*r^4*rpf^1 + ...
                    + C51*r^5*rpf^1 + C61*r^6*rpf^1 + C02*r^0*rpf^2 + C12*r^1*rpf^2 + ...
                    + C22*r^2*rpf^2 + C32*r^3*rpf^2 + C42*r^4*rpf^2 + C52*r^5*rpf^2 + ...
                    + C62*r^6*rpf^2 + C03*r^0*rpf^3 + C13*r^1*rpf^3 + C23*r^2*rpf^3 + ...
                    + C33*r^3*rpf^3 + C43*r^4*rpf^3 + C53*r^5*rpf^3 + C63*r^6*rpf^3 + ...
                    + C04*r^0*rpf^4 + C14*r^1*rpf^4 + C24*r^2*rpf^4 + C34*r^3*rpf^4 + ...
                    + C44*r^4*rpf^4 + C54*r^5*rpf^4 + C64*r^6*rpf^4 + C05*r^0*rpf^5 + ...
                    + C15*r^1*rpf^5 + C25*r^2*rpf^5 + C35*r^3*rpf^5 + C45*r^4*rpf^5 + ...
                    + C55*r^5*rpf^5 + C65*r^6*rpf^5 + C06*r^0*rpf^6 + C16*r^1*rpf^6 + ...
                    + C26*r^2*rpf^6 + C36*r^3*rpf^6 + C46*r^4*rpf^6 + C56*r^5*rpf^6 + ...
                    + C66*r^6*rpf^6;
    
    end
    r = 1:0.01:2;
    plot(r,g_fit,'o');
end

[Stephen23]

"How do I plot this equation without looping through the r's?"

Why not just use the R values, which are defined on this line:

R = mat(idx,4);

You do NOT need a loop, read the link I gave you earlier about vectorized code (and make the appropriate changes to your formula, e.g. replace

^

with

.^

As I wrote before, most likely you could simplify the entire "formula" by vectorizing the coefficients as well. But for a start atleast vectorize it for the R values.

[Benjamin]

So I took your advice, removed the loop and vectorized it with r.^. Seems to work well. One issue that I get when I replace r with R is that the vectors must be the same length. The number of R values changes on each eta value. Is there a way to circumvent this?

[Stephen23]

"The number of R values changes on each eta value."

It is not clear to me what this means.

"Is there a way to circumvent this?"

As far a I can tell you could use the dimensions of your arrays. For example, if R is a column vector and eta a row vector, then they can be different lengths and you wll get all values at the output:

>> eta = [1,2,3]; % row
>> R = [4;5;6;7]; % column
>> R.^eta
ans =
  4  16   64
  5  25  125
  6  36  216
  7  49  343

Use higher dimensions if required: e.g. if R is an MxN matrix that you do not want to reshape, then reshape eta to a 1x1xP vector, it works in exactly the same way.

Using the dimensions ot arrays is one of MATLAB's most powerful features.

For MATLAB versions prior to R2016b you will need to use bsxfun.