MATLAB: How to use trapz and cumtrapz

cumtrapzquadtrapz

I'm having problems understanding how to use trapz. Lets say I have this code:

quad(@(x)myfun,-2,2)

Were myfun is a function in a different .m-file. But I want to solve it using trapz instead of quad. With quad its simple. You just write your function and then the limits of the integral. But with trapz I'm not at all sure how to do even when having read the help about it several times.

Another question on the same topic is about cumtrapz. I wonder what the difference between trapz and cumtrapz are and when to use which?

EDIT:

Let me specify some further questions. First in trapz(X,Y) what doest X and Y signify? Is Y the function that trapz solves? If it is so what does X do? My problem is bigger than one small integral and to better understand how to solve it I will show a more complicated example which is part of what I have to do. I got a function that looks like this:

function Wiz = Wizfun(y,T,TM,TMO,G2,A,b,x,Epsi,ny,Vc,c2,D2,Q,z,sigma)
G = G2.*(1+((T-300)./TM).*TMO);
Ei = -(1/2.*pi).*((1+ny)./(1-ny)).*G.*A.*Epsi;
Wiz = -(2/3).*b.*x.*Ei.*(1./(x.^2+z.^2));

I know I'm not using all the in-data in the function but I have many functions who calls each other and some of them uses all those parameters. In my main window I then write like this:

syms y
T = 1273;
TM = 2163;
TMO = -0.5;
G2 = 126000;
A = 1.2E-29;
b = 0.000000000258;
x = 2/3*b;
Epsi = 0.00487903650119246;
ny = 0.3;
Vc = 1E-9;
c2 = 18.07551;
D2 = 0.0000169;
Q = 263900;
syms z;
sigma = 170;
intg = quad(@(z) Wizfun(y,T,TM,TMO,G2,A,b,x,Epsi,ny,Vc,c2,D2,Q,z,sigma),-250*b,250*b)

And I get this answer:

intg =
1.3118e-034

If I write trapz as Matt suggest:

Edit 2, changing from x = -2:.01:2; to the right numbers:

x = -250*b:0.1*b:250*b;
intg = trapz(x,Wizfun(y,T,TM,TMO,G2,A,b,x,Epsi,ny,Vc,c2,D2,Q,z,sigma))

I get this answer:

intg =
0

Why does this value differ from quad? Is it because the quad value is too small? If I write like Jan suggest:

X = linspace(-2, 2, 1000)
Y = Wizfun(y,T,TM,TMO,G2,A,b,x,Epsi,ny,Vc,c2,D2,Q,z,sigma);  % Or a loop, if myfun cannot handle vectors
Int = trapz(X, Y)

I get this error:

??? Undefined function or method 'max' for input arguments of type 'sym'.
Error in ==> trapz at 43
perm = [dim:max(ndims(y),dim) 1:dim-1];
Error in ==> test at 30
Int = trapz(X, Y)

This might be because of that loop thing you wrote about but I'm not sure what you meant by that and how to do a loop.

Best Answer

x = -2:.01:2;
intg = trapz(x,myfun(x));

Jan beat me to it! But CUMTRAPZ is the cumulative integral on your data, not a function. So it is like doing this (explicitly with a loop):

x = 0:.1:2;
cum_int = zeros(size(x));
cnt = 1;
for ii = 0:.1:2
    cum_int(cnt) = quadl(@sin,0,ii);
    cnt = cnt+1;
end
cum_int2 = cumtrapz(x,sin(x));
plot(x,cum_int,'b',x,cum_int2,'r')

EDIT In response to your further questions.

You need to think a little bit about what you are doing! You were given examples of what TRAPZ does. TRAPS doesn't work on functions, but data... Look again at the examples. You get different numbers because you are doing different things. When using quad you are integrating from:

>> b = 0.000000000258;LH = -250*b
LH =
   -6.45e-008

LH to abs(LH). When using TRAPZ you are integrating from -2 to 2 (as you showed in your first question) with a much larger spacing than used from LH to abs(LH). Remember TRAPZ operates on data (look again at the examples given to you), not functions. QUAD operates on functions so it can evaluate a function on arbitrary (well, not quite, but for all intents and purposes...) spacing while determining the integral - TRAPZ is stuck with the spacing in the data. Thus if the spacing in the data misses some important features of the underlying function, TRAPZ won't see it.

Since you have a function, you should stick with QUAD or QUADL.

Related Solutions

MATLAB: Improper integral

I don't think quad ever allowed infinite limits. quadgk does. The answer you need depends on how old your MATLAB version is. I am going to express an answer in more recent syntax. If you try

a=0; b=1; 
fun = @(u) exp(-a.* exp(2.*u)).*exp(-(u + b.^2).^2./2.*b.^2)/...
  (sqrt(2.*pi.*b.^2));
quad(fun,-Inf,Inf)

then you get this message:

Warning: Infinite or Not-a-Number function value encountered.

and the answer is NaN. The likely reason is that there is underflow in these exponential expressions:

>> fun(1000)
ans =
   NaN

However, if you plot this function, you can see that this function approaches zero very rapidly. For example,

>> fun(0)
ans = 
    0

Therefore, you can do this calculation:

quadl(fun,-100,100)
ans = 
    1.0000

This is 1 to an accuracy of about 10^-8.

Note: the fun = ... line is an anonymous function.

MATLAB: Sending parameters to a function

Of course, "But it don't work" is very vague.

http://www.mathworks.com/matlabcentral/answers/6200-tutorial-how-to-ask-a-question-on-answers-and-get-a-fast-asnwer

Now, even though you don't say what happens, I am guessing that your input variables are immediately overwritten in the function by your declarations. When a value is passed in, you don't then re-declare it inside the function, because then whatever you passed in is lost. For example, if you pass in a value for T of 1273, as you show, the first thing that happens (on the first line!) in your function is that the value you passed in is overwritten and T is declared as a symbolic variable.

Try this simple function as an example. It simply takes a number and doubles it. First try to double any number using the function as I have written it, then try it again with the first line of the function erased. See if you get a different answer!

function B = mydouble(A)
A = rand;  % Erase this line after you try to call, say:  mydouble(3)
B = 2*A;

EDIT In response to your 'answer' below...

The first error is because you have declared your function to take 14 argument with this line:

function ci = cifun(y,T,TM,TMO,G2,A,b,x,Epsi,ny,Vc,c2,D2,Q)

But then on this line,

ci = cifun(T,TM,TMO,G2,A,b,x,Epsi,ny,Vc,c2,D2,Q)

You only pass in 13. MATLAB doesn't care about the names, just the number and order. When you call your function as above, MATLAB goes through and assigns the first passed argument to the first declared parameter. So it gives the value you passed in as T to the parameter y inside the function. Then it assigns the second passed argument to the second declared parameter. So it gives the value you passed in as TM to the parameter T inside the function... and so on until you see that the value you passed in as Q goes to the parameter D2 inside the function, leaving Q inside the function undefined.

So if your function declaration says it takes N arguments and you only pass N-1, the Nth parameter will be undeclared inside the function. If you try to then use this parameter, you will see the same error you saw.

Since you declare y as syms inside the function, you are back to the first problem you had. That you are overwriting the value as soon as it is passed in. So take the y out of the function declaration line!

Best Answer

Related Solutions

MATLAB: Improper integral

MATLAB: Sending parameters to a function

Related Question