MaplePrimes - answers and comments on Question, Integration of piecewise is so slow

Cutting the Gordian knot by MonteCarlo method

Markiyan Hirnyk — Wed, 07 Nov 2012 22:53:23 Z

I found out that the best way to solve the

nerdpole — Thu, 08 Nov 2012 18:18:51 Z

I found out that the best way to solve the problem was to store the piecewise function in an array and modify the integralfunction. I wrote a script which now integrates the entries of the matrix piecewise.

like this:

int(int(int(T1[11], x1 = -x2+1 .. x2), x2 = (1/2)*1 .. -x3+1), x3 = 0 .. (1/2)*1)+
int(int(int(T1[12], x2 = x1 .. -x1+1), x1 = x3 .. (1/2)*1), x3 = 0 .. (1/2)*1)+
int(int(int(T1[9], x1 = x2 .. -x2+1), x2 = x3 .. (1/2)*1), x3 = 0 .. (1/2)*1)+
int(int(int(T1[10], x2 = -x1+1 .. x1), x1 = (1/2)*1 .. -x3+1), x3 = 0 .. (1/2)*1)+

Hopefully my comment helps users having the same problem.

Cheerio,

Nerdpole

integrate w.r.t. to what?

Axel Vogt — Thu, 08 Nov 2012 02:06:45 Z

The function also depends on h, no clear what you want, Markiyan gave an example
(and silently did some more).

I do not even see that the 'rules' exhaust a domain.

Best would be to post the integral you want. And talk about h a bit as well.

Criticism should be constructive

Markiyan Hirnyk — Thu, 08 Nov 2012 09:18:09 Z

Can somebody suppose a better thing than a numerical calculation after evaluating h and A1[j], j=1..21?

PS. The question is correct under the assumptions that h > 0 and A1[j],j=1..21 are symbolic constants.

Handwork

Markiyan Hirnyk — Thu, 08 Nov 2012 20:44:18 Z

This works well. Here is a part of the output:

> int(int(int(T1[11], x1 = -x2+1 .. x2), x2 = 1/2 .. -x3+1), x3 = 0 .. 1/2)+int(int(int(T1[12], x2 = x1 .. -x1+1), x1 = x3 .. 1/2), x3 = 0 .. 1/2)+int(int(int(T1[9], x1 = x2 .. -x2+1), x2 = x3 .. 1/2), x3 = 0 .. 1/2);

Everything has its advantages and disadvantages. Your approach is a handwork.