# [Maxima] Slowness of limit

Stefano Ferri ferriste at gmail.com
Thu Jul 23 11:29:13 CDT 2009

```I have to apply "limit" to a 42x42 matrix. Altough it is a very simple
operation (matrix is simple and also sparse) it takes a lot of time and memory
(on an athlon xp-m 2800+).

(%i15) limit(K,bk,inf)\$
Evaluation took 4.4963 seconds (4.5914 elapsed) using 29.406 MB.

and this:

(%i16) map(lambda([el],limit(el,bk,inf)),K)\$
Evaluation took 4.5323 seconds (4.6274 elapsed) using 29.417 MB.

I have do do a loop with thiis, so at the end it takes 100 seconds and 1000 Mb
of memory on my system.
Why is limit so slow?

This is the matrix, if you want to try...

K:matrix([1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],
[0,0,4*E*I/l,0,0,0,3*sqrt(3)*E*I/l^2,-3*E*I/l^2,2*E*I/l,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,A*E/l+bk,0,0,0,0,0,0,0,0,0,0,0,-A*E/l,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,12*E*I/l^3+bk,6*E*I/l^2,0,0,0,0,0,0,0,0,0,0,
-12*E*I/l^3,6*E*I/l^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0],
[0,0,0,0,6*E*I/l^2,4*E*I/l,0,0,0,0,0,0,0,0,0,0,-6*E*I/l^2,
2*E*I/l,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,3*sqrt(3)*E*I/l^2,0,0,0,9*E*I/l^3+A*E/(4*l)+bk,
sqrt(3)*A*E/(4*l)-3*sqrt(3)*E*I/l^3,3*sqrt(3)*E*I/l^2,-bk,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,-3*E*I/l^2,0,0,0,sqrt(3)*A*E/(4*l)-3*sqrt(3)*E*I/l^3,
3*E*I/l^3+3*A*E/(4*l)+bk,-3*E*I/l^2,0,-bk,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,2*E*I/l,0,0,0,3*sqrt(3)*E*I/l^2,-3*E*I/l^2,4*E*I/l,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,-bk,0,0,9*E*I/l^3+A*E/(4*l)+2*bk,
3*sqrt(3)*E*I/l^3-sqrt(3)*A*E/(4*l),3*sqrt(3)*E*I/l^2,-bk,0,0,
0,0,0,-9*E*I/l^3-A*E/(4*l),sqrt(3)*A*E/(4*l)-3*sqrt(3)*E*I/l^3,
3*sqrt(3)*E*I/l^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,-bk,0,3*sqrt(3)*E*I/l^3-sqrt(3)*A*E/(4*l),
3*E*I/l^3+3*A*E/(4*l)+2*bk,3*E*I/l^2,0,-bk,0,0,0,0,
sqrt(3)*A*E/(4*l)-3*sqrt(3)*E*I/l^3,-3*E*I/l^3-3*A*E/(4*l),
3*E*I/l^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,3*sqrt(3)*E*I/l^2,3*E*I/l^2,4*E*I/l,0,0,0,0,
0,0,-3*sqrt(3)*E*I/l^2,-3*E*I/l^2,2*E*I/l,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,-bk,0,0,A*E/l+bk,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-A*E/l,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,-bk,0,0,12*E*I/l^3+bk,6*E*I/l^2,0,0,0,0,0,
0,0,0,0,0,0,0,0,-12*E*I/l^3,6*E*I/l^2,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,6*E*I/l^2,4*E*I/l,0,0,0,0,0,0,0,0,0,
0,0,0,0,-6*E*I/l^2,2*E*I/l,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,-A*E/l,0,0,0,0,0,0,0,0,0,0,0,A*E/l+bk,0,0,-bk,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,-12*E*I/l^3,-6*E*I/l^2,0,0,0,0,0,0,0,0,0,0,
12*E*I/l^3+bk,-6*E*I/l^2,0,-bk,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0],
[0,0,0,0,6*E*I/l^2,2*E*I/l,0,0,0,0,0,0,0,0,0,0,-6*E*I/l^2,
4*E*I/l,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,-9*E*I/l^3-A*E/(4*l),
sqrt(3)*A*E/(4*l)-3*sqrt(3)*E*I/l^3,-3*sqrt(3)*E*I/l^2,0,0,0,
-bk,0,0,9*E*I/l^3+A*E/(4*l)+2*bk,
3*sqrt(3)*E*I/l^3-sqrt(3)*A*E/(4*l),-3*sqrt(3)*E*I/l^2,-bk,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,sqrt(3)*A*E/(4*l)-3*sqrt(3)*E*I/l^3,
-3*E*I/l^3-3*A*E/(4*l),-3*E*I/l^2,0,0,0,0,-bk,0,
3*sqrt(3)*E*I/l^3-sqrt(3)*A*E/(4*l),3*E*I/l^3+3*A*E/(4*l)+2*bk,
-3*E*I/l^2,0,-bk,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,3*sqrt(3)*E*I/l^2,3*E*I/l^2,2*E*I/l,0,0,0,0,
0,0,-3*sqrt(3)*E*I/l^2,-3*E*I/l^2,4*E*I/l,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-bk,0,0,
9*E*I/l^3+A*E/(4*l)+2*bk,sqrt(3)*A*E/(4*l)-3*sqrt(3)*E*I/l^3,
-3*sqrt(3)*E*I/l^2,-bk,0,0,0,0,0,-9*E*I/l^3-A*E/(4*l),
3*sqrt(3)*E*I/l^3-sqrt(3)*A*E/(4*l),-3*sqrt(3)*E*I/l^2,0,0,0,0,
0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-bk,0,
sqrt(3)*A*E/(4*l)-3*sqrt(3)*E*I/l^3,3*E*I/l^3+3*A*E/(4*l)+2*bk,
3*E*I/l^2,0,-bk,0,0,0,0,3*sqrt(3)*E*I/l^3-sqrt(3)*A*E/(4*l),
-3*E*I/l^3-3*A*E/(4*l),3*E*I/l^2,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3*sqrt(3)*E*I/l^2,
3*E*I/l^2,4*E*I/l,0,0,0,0,0,0,3*sqrt(3)*E*I/l^2,-3*E*I/l^2,
2*E*I/l,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-bk,0,0,A*E/l+bk,0,0,
0,0,0,0,0,0,0,0,0,-A*E/l,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-bk,0,0,
12*E*I/l^3+bk,6*E*I/l^2,0,0,0,0,0,0,0,0,0,0,-12*E*I/l^3,
6*E*I/l^2,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6*E*I/l^2,
4*E*I/l,0,0,0,0,0,0,0,0,0,0,-6*E*I/l^2,2*E*I/l,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,-A*E/l,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
A*E/l+bk,0,0,-bk,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,-12*E*I/l^3,-6*E*I/l^2,0,0,0,0,0,0,0,
0,0,0,0,0,0,12*E*I/l^3+bk,-6*E*I/l^2,0,-bk,0,0,0,0,0,0,0,0,0,
0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,6*E*I/l^2,2*E*I/l,0,0,0,0,0,0,0,0,0,
0,0,0,0,-6*E*I/l^2,4*E*I/l,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-9*E*I/l^3-A*E/(4*l),
3*sqrt(3)*E*I/l^3-sqrt(3)*A*E/(4*l),3*sqrt(3)*E*I/l^2,0,0,0,
-bk,0,0,9*E*I/l^3+A*E/(4*l)+2*bk,
sqrt(3)*A*E/(4*l)-3*sqrt(3)*E*I/l^3,3*sqrt(3)*E*I/l^2,-bk,0,0,
0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
3*sqrt(3)*E*I/l^3-sqrt(3)*A*E/(4*l),-3*E*I/l^3-3*A*E/(4*l),
-3*E*I/l^2,0,0,0,0,-bk,0,sqrt(3)*A*E/(4*l)-3*sqrt(3)*E*I/l^3,
3*E*I/l^3+3*A*E/(4*l)+2*bk,-3*E*I/l^2,0,-bk,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3*sqrt(3)*E*I/l^2,
3*E*I/l^2,2*E*I/l,0,0,0,0,0,0,3*sqrt(3)*E*I/l^2,-3*E*I/l^2,
4*E*I/l,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-bk,0,0,9*E*I/l^3+A*E/(4*l)+bk,
3*sqrt(3)*E*I/l^3-sqrt(3)*A*E/(4*l),3*sqrt(3)*E*I/l^2,0,0,0,0,
0,3*sqrt(3)*E*I/l^2],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-bk,0,3*sqrt(3)*E*I/l^3-sqrt(3)*A*E/(4*l),
3*E*I/l^3+3*A*E/(4*l)+bk,3*E*I/l^2,0,0,0,0,0,3*E*I/l^2],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,3*sqrt(3)*E*I/l^2,3*E*I/l^2,4*E*I/l,0,0,0,0,0,2*E*I/l],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-A*E/l,0,0,0,0,
0,0,0,0,0,0,0,A*E/l+bk,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-12*E*I/l^3,
-6*E*I/l^2,0,0,0,0,0,0,0,0,0,0,12*E*I/l^3+bk,-6*E*I/l^2,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6*E*I/l^2,
2*E*I/l,0,0,0,0,0,0,0,0,0,0,-6*E*I/l^2,4*E*I/l,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,3*sqrt(3)*E*I/l^2,3*E*I/l^2,2*E*I/l,0,0,0,0,0,4*E*I/l])\$

Thanks
Stefano
```