Re: Re: Compute once question
- To: mathgroup at smc.vnet.net
- Subject: [mg105675] Re: [mg105640] Re: Compute once question
- From: Michael Greene <mgreene at csumb.edu>
- Date: Tue, 15 Dec 2009 07:25:46 -0500 (EST)
- References: <hg00d9$j98$1@smc.vnet.net> <200912131038.FAA21060@smc.vnet.net>
Thanks David. I think I'm 'zeroing' all the variables before I use them. Got
some nasty displays early on that I've cleaned out so I think I know what
you're referring to.
Here's the code- I've tried to clean it up somewhat so it's clearer what's
going on.
I expect the transition from step 8 to step 9 to be immediate as I've
already computed what I need to display. Yet the delay for the 9th step
message to appear is as long as the delay for the 8th step graphic. It's as
if Mathematica isn't evaluating the code in the If statement as much as it's
treating the code as a function definition that will be evaluated when it's
referred to in the Graphic[] call.
Manipulate[
(*Do some initial work *)
msg = {{"A circle has a circumference of 2\[Pi]r..."}, {"...so \
halfway around a circle is \[Pi]r"}, {"We can re-arrange the slices \
without changing the area..."}, {"...or the distance halfway around \
the circle."}, {"Slice the circle into more pieces & the right shape \
morphs..."}, {"...into a rectangle"}, {"The rectangle is r units high \
and 2\[Pi]r units wide..."}};
Slices = {4, 8, 16, 100};
(* Figure out which message and what pieces we're going to show next based
on which step \
we're on*)
If[Step == 1, {n = 1; ms = 1; showSlice = 0; showSlice2 = 0;
showPerim = 0;
showPerim2 = 0;}, If[Step == 2, showPerim = 1; ms = 2;];
If[Step == 3, showSlice = 1; showSlice2 = 1; ms = 3;];
If[Step == 4, showPerim2 = 1; ms = 4; showSlice = .5];
If[Step == 5, ms = 5; n = 2;];
If[Step > 5 && Step < 9, n = Part[Slices, Step - 4];];
If[n == 100, ms = 6];];
If[Step == 9, ms = 7];
nm = Text[Style[Take[msg, {ms, ms}], Bold, 24], {3.25, 2.7}];
(*Computation begins here. Slice a circle, rotate the slices and \
translate them
Only do this up through step 8, reuse results after step 8*)
If[Step <= 8, \[Theta] = Pi/(n + 1); bottom = Red; top = Gray;
ef = If[n < 15, White, If[n < 30, LightBlue, None]];
cn = Table[
Circle[{1, 1}, 1, {s \[Theta], s \[Theta] + \[Theta]}], {s, 0,
n}];
ct = Table[
Rotate[Take[cn, {s1}],
Pi/2 - (s1 - 1) \[Theta] - \[Theta]/2, {1, 1}], {s1, 1,
n + 1}];
ctt = Table[
Translate[
Take[ct, {s2}], {2 (s2 - 1) Sin[\[Theta]/2] +
2, -Cos[\[Theta]/2]/2}], {s2, 1, n + 1}];
p = {3, 1 - Cos[\[Theta]/2]/2};
p2 = p + {Cos[Pi/2 + \[Theta]/2], Sin[Pi/2 + \[Theta]/2]};
ra = Line[{{1, 1}, {0, 1}}];
ra2 = Line[{p, p2}];
ral = Text[Style["r", Bold, 36], {.5, 1.1}];
ral2 = Translate[ral, {1.3 + Cos[\[Theta]/2], -.10}];
cir = Text[Style["\[Pi]r", Bold, 36], {1, 2.2}];
cir2 = Translate[cir, {2 + Cos[\[Theta]/2], -.5}];
dn = Table[
Disk[{1, 1}, 1, {s \[Theta], s \[Theta] + \[Theta]}], {s, 0,
n}];
dt = Table[
Rotate[Take[dn, {s1}],
Pi/2 - (s1 - 1) \[Theta] - \[Theta]/2, {1, 1}], {s1, 1,
n + 1}];
dtt = Table[
Translate[
Take[dt, {s2}], {2 (s2 - 1) Sin[\[Theta]/2] +
2, -Cos[\[Theta]/2]/2}], {s2, 1, n + 1}];
dnn = Table[
Disk[{1, 1},
1, {s \[Theta] + Pi, Pi + s \[Theta] + \[Theta]}], {s, 0, n}];
dtn = Table[
Rotate[Take[dnn, {s1}],
3 Pi/2 - (s1 - 1) \[Theta] - \[Theta]/2 + Pi, {1, 1}], {s1, 1,
n + 1}];
dttn =
Table[Translate[
Take[dtn, {s2}], {2 (s2 - 1) Sin[\[Theta]/2] +
2*Sin[\[Theta]/2]/2 + 2, Cos[\[Theta]/2]/2}], {s2, 1,
n + 1}];
](* Computation should end here and not repeat at step 9 *)
(* Display computation results *)
Graphics[{EdgeForm[ef],
nm, {FaceForm[top], dn}, {FaceForm[bottom], dnn}, {FaceForm[top],
Opacity[showSlice], dtt}, {FaceForm[bottom], Opacity[showSlice2],
dttn, {Thick,
Blue, {{Opacity[showPerim], cn, ra, cir,
ral}, {Opacity[showPerim2], ctt, cir2, ra2, ral2}}}}},
PlotRange -> {{-.50, 6.5}, {0, 3}}, Axes -> True,
ImageSize -> {800, 470}],
{Step, Table[ii, {ii, 9}], ControlType -> SetterBar}]
Thanks again,
Michael
On Sun, Dec 13, 2009 at 2:38 AM, David Bailey <dave at removedbailey.co.uk>wrote:
> Michael Greene wrote:
> > I'm having trouble getting Mathematica not to repeatedly compute values
> in a
> > Manipulate Window. I'm not sure if it's a bug in my code or if it's a
> > fundamental disconnect between what I think is going on and what
> Mathematica
> > is actually doing.
> >
> > What my code is doing is slicing a circle into segments, rotating the
> slices
> > and then translating them. When the process first starts out, I'm
> dealing
> > with a small number of slices so the response is immediate. The process
> > eventually works up to around 20 slices and the user begins to see a
> slight
> > delay between manipulating the controller and seeing the result. At 100
> > slices, we're talking about a 3 or 4 second lag which isn't OK.
> >
> > When I first started the process, I was allowing the user to directly
> > manipulate the slice count. When I saw the lags starting to kick in, I
> > thought I'd just let the user control a step counter instead and based on
> > which step the user was on, compute the graphic, store the graphic and
> reuse
> > the stored graphic as we moved further into the process. That is:
> >
> > If[Step<=8, <do intensive computation and store graphic in G>];
> > Graphics[G];
> >
> > So when Step gets to 9, I expect G to pop up on the screen right away but
> it
> > doesn't. The program still takes several seconds as if it's recomputing
> G.
> > Am I wrong to expect Mathematica to only compute G when Step is less than
> 9?
> > I'd post the actual code but it's rather hoary. Hopefully my question
> still
> > makes sense sans code.
> >
> > What I'd really like to be able to do is timeslice G's computation in
> the
> > earlier steps when the user is spending time assimilating the earlier
> > information so by the time he/she gets to the computationally expensive
> > step, the work is done and G just pops onto the screen as if it's no big
> > deal. But first things first...
> >
> > Thanks,
> > Michael
> >
> >
> It is awfully hard to comment in detail without some actual code, but it
> may be worth adding counters to your code, such as
>
> Global`couter1++;
>
> If you zeroise all the counters before use (otherwise you will get nasty
> recursion errors) and move the Manipulate controls, you will be able to
> inspect the counters to determine how many times things got executed. I
> specified the Global` context just in case your code was nested in
> another context for one reason or another.
>
> David Bailey
> http://www.dbaileyconsultancy.co.uk
>
>
--
Michael Greene - Programmer Analyst
Information Systems, mgreene at csumb.edu
California State University, Monterey Bay
Corporation Bldg - RM 201 - 100 Campus Center, Seaside, CA 93955-8001
831.582.3567 Fax 831.582.4796
- References:
- Re: Compute once question
- From: David Bailey <dave@removedbailey.co.uk>
- Re: Compute once question