Error using command integral

Hi,

i have to valute this function

and plot the graphics for , i wrote:

u=linspace(0,4,1000);

q=integral(@(x)exp(-x.^2),0,u)-1/2;

and here i get:

'Error using integral (line 85)

A and B must be floating-point scalars.'

so i can't plot(u,q).. what can i do??

Thanks for the support and soryr for my bad english.

Answer 1

[John D'Errico]

Simplest is to just use cumtrapz. All you want is a plot anyway.

u = linspace(0,4,1000);
fun = @(x)exp(-x.^2);
plot(u,cumtrapz(u,fun(u)))

If all you want is the plot, then using a little bb-gun (cumtrapz) can be better than wielding a big gun like integral.

If you wanted to use integral, then you need to recognize that integral is not designed to solve a cumulative integral, so for an entire list of upper limits. You can't give it a vector of limits, and want it to work directly.

Simplest then could be to use a loop.

u = linspace(0,4,1000);
fun = @(x)exp(-x.^2);
uint = zeros(size(u));
for i = 2:numel(u)
  uint(i) = integral(fun,u(i-1),u(i));
end
uint = cumsum(uint);
plot(u,uint)

As you can see, I only integrate each segment, then I formed the cumulative sum. This will be more efficient than integrating from 0 to u(i), each pass through the loop, since there is no need to re-integrate the early parts each time.

Finally, if you ABSOLUTELY, POSITIVELY, DESPERATELY need to do the integral in a vectorized form, you could do it, but why? Writing "elegantly" vectorized code will often result in less readable, code, that is hard to debug. Unless there is a reason for efficiency, the vectorized form may be of little real value. But, CAN you? Sigh. Yes.

u = linspace(0,4,1000);
fun = @(x)exp(-x.^2);
intfun = @(upplim) integral(fun,0,upplim);
uint = arrayfun(intfun,u);
plot(u,uint)

The simplest code (the first) is the most efficient code. It is readable. Not always quite as accurate, but by use of a sufficiently fine grid spacing, it will be quite adequate. And the spacing used here? 1000 steps, from 0-4? Trapzezoidal rule is entirely adequate for such a fine spacing.