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+--- Thread: WP-34S Integration speed (/thread-731.html)
WP-34S Integration speed - lrdheat - 02-21-2014 03:08 AM
Is there a way to balance accuracy with speed of integration on the 34S as with HP's that can integrate? The HP's give the user the ability to require, say, 4 significant digits of accuracy vs. the full 12 digits in order to arrive at a result in a significantly shorter amount of time. Can this be accomplished on the wonderful 34S?
RE: WP-34S Integration speed - Marcus von Cube - 02-22-2014 11:44 AM
The integration routine is modeled after the IG routine from the HP 41 PPC ROM. It uses the display accuracy to determine the number of iterations by means of the x≈ Y comparison command. You can improve the integration speed by setting a different display mode such as FIX 4 or SCI 4.
RE: WP-34S Integration speed - Paul Dale - 02-22-2014 12:35 PM
However, an integral that is approximately zero will hit a snag and will continue iterating long after it should.
Nobody like the Gauss-Kronrod quadrature I initially implemented which was fast and good for smooth functions but in no way adaptive.
- Pauli
RE: WP-34S Integration speed - Dieter - 02-23-2014 02:02 PM
(02-22-2014 12:35 PM)Paul Dale Wrote: However, an integral that is approximately zero will hit a snag and will continue iterating long after it should.
Pauli, I remember we had a discussion on this very topic some time ago, and I suggested a possible fix: compare the current value of \(\int f(x)\) with an approximation of \(\int |f(x)|\). It worked well with the examples we discussed then. Details can be found here, cf. message 6 ff.
This change was supposed to get implemented in v. 3460 resp. 3462. So I thought this issue had been resolved.
Dieter
RE: WP-34S Integration speed - Paul Dale - 02-23-2014 09:42 PM
Sorry, Dieter is correct. We implemented a fix for the integral approaching zero. I'd just forgotten about it.
- Pauli
RE: WP-34S Integration speed - Dave Hicks - 02-27-2014 12:14 AM
This thread was moved from the General forum by request.
RE: WP-34S Integration speed - walter b - 02-27-2014 06:43 AM
χαιρε, Δρακων. Now it's where ο δημος will look for it.
d:-)
RE: WP-34S Integration speed - Dieter - 02-27-2014 02:28 PM
(02-23-2014 09:42 PM)Paul Dale Wrote: We implemented a fix for the integral approaching zero.
I see the fix got implemented, but one final improvement I posted back then still is missing (cf. last message in the mentioned thread). It's one single line that should be added:
Code:
...
FC?C f_final /* final iteration done? */
x[approx]? Y /* or convergence? */
JMP int_done
RCL/ r_SkAbs
RCL/ r_deltau
RCL/ r_ba4 <== add this line
ABS
...Maybe it can be added with the next update.
Dieter
RE: WP-34S Integration speed - Paul Dale - 02-27-2014 09:28 PM
Dieter, I must have missed that final improvement. Added now but not built.
- Pauli
RE: WP-34S Integration speed - Marcus von Cube - 03-02-2014 01:15 PM
(02-27-2014 09:28 PM)Paul Dale Wrote: Dieter, I must have missed that final improvement. Added now but not built.My Job! Build 3530 is Committed to SVN...
