To draw an intensity curve with Matlab

I have a function :

And I want to draw the intensity curve :

where T has values : 600, 800, 1000, 1100 And λ:(0,10*^-5] I have to use max function with two values and the solution must not consist of repeating four times of similar snippets of code, one for each curve.The image should be stylish. For example. so the texts may not cut curves, but neatly placed just above the maximum point.

Can somebody please help me how I can start ?! I must say I'm a beginner too

Answer 1

[Star Strider]

This should get you started.

Since this seems to be a homework problem, I will let you determine how to locate and plot the peaks. See the documentation for the various functions and the section on Anonymous Functions in Function Basics.

The Code —

f = @(L,T) 3.7E-16 ./ (L.^5 .* (exp(0.014 ./ (L .* T)) -1));

T = [600, 800, 1000, 1100];
L =  linspace(0, 1E-5);
[Tm,Lm] = meshgrid(T, L);

fm = f(Lm,Tm);

figure(1)
plot(L, fm)
grid
xlabel('\lambda')
ylabel('\itF\rm(\it\lambda,T\rm)')
lgndcell = regexp(sprintf('T = %d\n',T), '\n', 'split')
legend(lgndcell(1:end-1), 'Location','NE')

Also see the documentation for the text function. You will need that to label the peaks. Specifically note the name-value pair arguments so you can position the labels correctly with respect to the points you plotted at the peaks.

The Plot —

EDIT — Added plot my code produces.

[Pouyan Msgn]

Thank you very much for your help but if I will use max function, how should I do that ?!

[Pouyan Msgn]

I have another question too, why did you use meshgrid ?! I saw the help meshgrid on Matlab but I don't get it.

[Star Strider]

My pleasure.

The meshgrid call creates a matching matrix of values for each argument vector. The function then calculates a resulting matrix for both argument matrices, making it easier to calculate and plot them.

The plot function automatically chooses the correct dimension of the ‘fm’ matrix to plot, depending on the x-vector.

The meshgrid call eliminates an explicit loop, although there are likely implicit loops in the way the ‘f’ function is evaluated.

You could also plot the function as:

figure(2)
surfc(Tm, Lm, fm)
grid on

if you want to see what it looks like in 3D.

Answer 2

[Pouyan Msgn]

Thank you! I get this after your help and using max function but I don't know how should I use text function to write the value of T for correspond curve....

Answer 3

[Pouyan Msgn]

This how I could develop the code but I fail with one thing !

clear all

clc

F=@(L,T) 3.7415E-16 ./((L.^5).*(exp(0.014 ./(L.*T))-1));

T=[600 800 1000 1100];

L=0:10^-7:10^-5;

[Tm Lm]=meshgrid(T,L);

fm=F(Lm,Tm);

plot(L,fm)

grid on

[Y I]=max(fm);

hold on

plot(L(I),Y,'*')

%text(L(I),Y,'T= ')

hold on

for i=1:1:4

S=['T= ',num2str(T(i))]

N = L(I)-1.E-7;

     G = Y+5.E8;

     text(N,G, S)

end

I get this image as result :

I see number 6000 everywhere and I don't like it !

[Star Strider]

You have every reason not to like it!

You have to create separate strings for each temperature curve in a cell array of strings. You can do that easily enough in a loop, but a much more efficient way is to use a regexp call (or the strsplit function) with sprintf.

The New Revised Code —

f = @(L,T) 3.7E-16 ./ (L.^5 .* (exp(0.014 ./ (L .* T)) -1));

T = [600, 800, 1000, 1100];
L =  linspace(0, 1E-5);
[Tm,Lm] = meshgrid(T, L);

fm = f(Lm,Tm);
[fm_max, idx] = max(fm,[],1);                               % Find ‘fm’ Column Maxima & Indices

figure(1)
plot(L, fm)
hold on
plot(L(idx), fm_max, 'pr', 'MarkerFaceColor','g')           % Plot Markers
hold off
grid
xlabel('\lambda')
ylabel('\itF\rm(\it\lambda,T\rm)')
Tcell = regexp(sprintf('T = %4d\n', T), '\n', 'split');     % You Can Also Use The ‘strsplit’ Function
text(L(idx), fm_max, Tcell(1:end-1), 'HorizontalAlignment','left', 'VerticalAlignment','bottom', 'FontSize',8)

The New Revised Plot —

[Pouyan Msgn]

Thank you very much!

[Star Strider]

As always, my pleasure!

[Pouyan Msgn]

Ok , so far thanks for youre help, but I hade some questions and would be happy if you help me with them if you have time.

1) When I used the meshgrid function, I notised something different. If I use:

[Tm,Lm]=meshgrid(T,L)

I get just the result as you got. But When I use [L1,T1]=meshgrid(L,T) fm=F(L1,T1)

and cm=F(Lm,Tm) well if I plot just this :

plot(L,fm)

I get the same plot as plot(L,cm)

But if I use [Y I]=max(fm) and plot it I get a different plot compared with [Y I]=max(cm)

I have passed Linear Algebra but I have trouble understanding vectors as functions in 2D. I know that size of max(fm) and max(cm) is different but I can not perceive it why we should use [Tm,Lm]=meshgrid(T,L)

[Star Strider]

I use

[Tm,Lm]=meshgrid(T,L);

because it is easier for me to understand in the context of the arguments to ‘fm’.

The function expects the arguments to be in the order I defined them. Entering them in the opposite order can produce unexpected results.

With respect to:

[Y I]=max(fm);

and

[Y I]=max(cm);

check the sizes (row and column dimensions) of ‘fm’ and ‘cm’, then check the documentation for max with respect to the dimensions it uses for its default dimensions.

Compare:

[Y I]=max(fm);

with:

[Y I]=max(cm);

and with:

[Y I]=max(cm');

Note the transpose operator (').

You will see and understand the differences.

[Pouyan Msgn]

OK, for sprintf('T = %4d\n', T), why must we use %4d\n?! what is the philosophy and logic behind that ?! I see if I delete %4d\n and just write sprintf('T = ', T), it gives me just 'T= ' without any number. But why is this so ?!

[Star Strider]

You need to specify a format descriptor to tell sprintf to print a numerical value. Your largest temperature values are 4 digits, so I chose '%4d' to output a 4-digit integer for all of them (using leading spaces for the values with less than 4 digits). See the documentation for sprintf for details on specifying format descriptors.

The '\n' is a ‘newline’ character that would normally produce a carriage return and linefeed sequence with, for example, fprintf. Here, I use it as a separator that regexp will recognise as the end-of-string indicator to do the split. See the documentation on regexp for details.