vector gives 0 integral
Show older comments
Hello
I have plotted a vector which has 3 planes.. When I integrate the integral is 0. There are negative regions, yet I expect a number. I us
sd = trapz((z),0,20)
sd =
0
will someone tell me if there is an error with my use of trapz?
sr
Accepted Answer
Star Strider
on 28 Jul 2021
There quite definitely is!
In your call to it:
sd = trapz((z),0,20)
the function interprets ‘z’ (the parentheses aren’t necessary) as the indepdent variable ‘x’, 0 as the dependent variable ‘y’, and 20 as the dimension. Integrating 0 produces 0 as the result.
.
30 Comments
John D'Errico
on 28 Jul 2021
My guess is, @Gavin Seddon was thinking the 0 and 20 were the limits of integration. Of course that is not how trapz works.
If you want to define a range of integration with trapz (or cumtrapz), do something like this:
x = linspace(-50, 50, 250);
z = sin(2*pi*x).^2; % 'z' Is A Vector
intRange = (x>=0) & (x<=20);
int_y = trapz(x(intRange), z(intRange))
or something similar.
int_y = integral(@(x)sin(2*pi*x).^2, 0, 20) % 'z' Is A Function
.
Gavin Seddon
on 22 Aug 2021
Star Strider
on 22 Aug 2021
I have no idea.
Another possibility is that there were no values in that range.
Gavin Seddon
on 23 Aug 2021
Star Strider
on 23 Aug 2021
I have no idea what ‘y’ is, or what ‘z’ is.
In any event, trapz integrates vectors, and int integrates symbolic functions.
A bit more information would be helpful.
.
Gavin Seddon
on 24 Aug 2021
Star Strider
on 24 Aug 2021
Thank you!
.
Gavin Seddon
on 19 Oct 2021
Try this —
int_y = integral(@(x)(x*6.4985e-4-x.^2*2.8208e-7+x.^3*3.9742e-11+2.4178), 0, 5000)
Note — All the (^) are now (.^). No other element-wise operations are necessary. See Array vs. MAtrix Operations for an extended discussion.
.
Gavin Seddon
on 20 Oct 2021
As always, my pleasure!
You can use syms if you wish, however I see no significant advantage to doing that.
syms x
int_y = int((x*6.4985e-4-x^2*2.8208e-7+x^3*3.9742e-11+2.4178), x, 0, 5000)
int_y = vpa(int_y, 42)
int_y = vpaintegral((x*6.4985e-4-x^2*2.8208e-7+x^3*3.9742e-11+2.4178), x, 0, 5000)
.
Gavin Seddon
on 21 Oct 2021
Gavin Seddon
on 21 Oct 2021
Star Strider
on 21 Oct 2021
The integrand must be different from what was originally posted.
The integral should not also be a function of ‘x’, if it was integrated with respect to ‘x’.
What changed, and what is the objective?
Should this be a double integral, and if so, with respect to what variables?
Details — and the code that created those results — are important.
I cannot go farther with this until I have more information about it.
.
Gavin Seddon
on 22 Oct 2021
Star Strider
on 22 Oct 2021
I still do not understand this Comment. I have no idea how those results were calculated, so I cannot help with the code to get the desired result.
What integrand produced that integrated result? What were the limits of integration?
Post that code and I will see if I can produce the desired result. Note that the elements of that vector are all functions of ‘x’ so the integral must have been with respect to a different variable.
.
Gavin Seddon
on 23 Oct 2021
I’m sorry, however I still don’t understand.
It would appear that it is only necessary to provide values for whatever ‘x’ is to create numerical data from the ‘int_v’ and ‘int_y’ expressions. I have no idea what those ‘x’ values would be, however creating them as symbolic functions would make this straightforward (and avoids the use of the subs function) —
syms x
int_y(x) = 0.00000000000993550000000000022516417793009971867052021*x^4-0.000000094026666666666665122288924957597016979586*x^3 + 0.000324924999999999996810884361764237837633118*x^2 + 2.4178*x;
x = sym(0:10:100);
int_y_val = vpa(int_y(x), 5)
figure
fplot(int_y, [0 100])
grid
I have no idea if this is the desired direction for this problem, however it is the only one I can think of.
.
Gavin Seddon
on 24 Oct 2021
It is not possible to make it an integer as long as it has symbolic variables in it. They have to be evaluated first.
x=30;
% >> diff(y)
%
% ans =
%
% (4612332472619961*x^2)/38685626227668133590597632 - (2664170274975739*x)/4722366482869645213696 + 1498452079537519/2305843009213693952
%
% >> v0=diff(y)
v0 = (4612332472619961*x^2)/38685626227668133590597632 - (2664170274975739*x)/4722366482869645213696 + 1498452079537519/2305843009213693952
Result = vpa(v0) % Substitution For 'x' Is Implied, So Is Done Automatically
% ans =
%
% 0.0000000001192260000000000027019701351612*x^2 - 0.00000056415999999999999073372735497456*x + 0.00064984999999999999362176872352848
This produces both double and symbolic results.
.
Gavin Seddon
on 25 Oct 2021
Gavin Seddon
on 25 Oct 2021
That value of ‘v0’ exists in the workspace.
x=30;
v0 = (4612332472619961*x^2)/38685626227668133590597632 - (2664170274975739*x)/4722366482869645213696 + 1498452079537519/2305843009213693952
To print it using the largest available precision, use —
fprintf('%23.15E',v0)
There are any number of ways to write it to a file. Please refer to the appropriate parts of the documentation for that.
.
Gavin Seddon
on 26 Oct 2021
Star Strider
on 26 Oct 2021
Thank you!
Gavin Seddon
on 3 Nov 2021
Star Strider
on 3 Nov 2021
I’m not certain what argument to fprintf is throuwing that error. One possible fix is to use the double funciton, however that won’t work if there are any symbolic variables in the expression to be printed. In that evernt, evaluate the expression first, with numeric values of all the variables previously defined.
.
Gavin Seddon
on 3 Nov 2021
Star Strider
on 3 Nov 2021
That expression is a function of ‘x’, so provide a value for it (scalar, vector, using subs if necessary), evaluate it, then print the double result as a funciton of the values of ‘x’.
.
More Answers (3)
Gavin Seddon
on 29 Jul 2021
0 votes
4 Comments
Gavin Seddon
on 29 Jul 2021
Star Strider
on 29 Jul 2021
As always, my pleasure!
I am not certain what function you are integrating. The difference in the values in my example is due to the trapz function using trapezoidal integration on a finite-resolution vector, and the integral call doing a much finer adaptive numerical integration of the function provided to it.
.
Gavin Seddon
on 29 Jul 2021
Star Strider
on 29 Jul 2021
Thank you!
Just curious as to what you are integrating.
.
Gavin Seddon
on 29 Jul 2021
0 votes
Categories
Find more on Numerical Integration and Differentiation in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!
