@Hullzie16 I apologize if my message's tone came off as harsh. I'm feeling quite under the weather. You should never have to worry about being new to Maple programming. We all have things to learn, and we all started off at some time.

By the way, there are several other ways to construct the second Array, B.

For example, if you have already constructed Array A, then either of these can work:

Array([seq(F,t=A)]);

Ffun := unapply(F,t);
Ffun~(A);

Which unhelpful person keeps vandalizing this Question and stripping off the tags?

@mmcdara Using the preformed Sample Vectors made it about ten times faster (at L=50000, and more as L increased I suspect), if I recall.

Having the loop code operate under fast evalhf mode made that about 10 times faster again, if I recall.

I used subs on a template for the helper procedure so that evalhf would not baulk (lexical scoping not supported) at evaluation of the beta_pdf procedure. Thus I shoe-horned the piecewise result from a call to beta_pdf (with appropriate symbolic name as argument) into a "template" for the helper procedure.

@mmcdara With some edits your mcmc procedure can be made faster, in the hardware floats case.

The following is done with L = 50000 which is ten times as many as you had above. On my machine it takes 0.15 sec using Maple 2015.2.

For L = 10^6 it took my machine 1.97 sec.

Below the Sample(proposal,...) is computed up front for 5*Length values. Hopefully that is enough, since each "early" acceptance keeps more guesses for the later tries. This total supply can be adjusted.

And similarly Sample(Uniform(0,1),...) is computed up front for Length values. The looping code can then be run under evalhf.

I also increased the Histogram's bin count, for fun. And randomize() can be added to the top of the worksheet if you want a different first run for each complete re-execution.

Download MCMC_ac2.mw

There are several possible causes, eg. as shown here.

If you upload and attach your worksheet (green up-arrow in the Mapleprimes editor) then someone might be able to tell you where the mistake is, and how to correct it.

@JAMET Please don't create multiple Question threads for this topic.

Please put your followup queries and discussion here, instead of in a new and wholly separate Question thread.

@richinex Here is a shorter version of what I had above, with less exposition but still following the idea of your document.

Download maple_attempt_ac3.mw

Replace colon statement terminators with semicolons to see the intermediate results.

Inspired by Axel's clever use of implicit RootOf, I reworked some of the above...

(I have no idea whether the OP wants such an implicit result. But it's fun.)

Download some_trig_opt_2.mw

Your Question is lacking key details.

For example, you have not shown explicitly how f and fproc were constructed. There is no code in your original Question like, say, a call to any export of the Interpolate package. You mention "an interpolation object, f(x)" but did not show or clearly describe what you did to create that. There are several ways to do such things in Maple, with several different commands from several different packages. You might be using commands from the CurveFitting, Statistics, or ArrayTools packages.

Also, your Question did not originally contain a sentence like, "The name "fproc" is not something I have in my  code, just the name, "f"." You may have edited your Question, and added that, since I first replied.

Quite a bit of what else you've written makes little to no sense without context. Even a clear sentence that stated that you were trying to perform numeric integration using an object returned by command X from the Interpolate package (where X is an actual command name). would have been useful and more clear. The word "object" can be used as a technical Maple term (jargon) or as a general English word, and without your mentioning the Interpolate package it becomes a matter of guessing here.

Why haven't you bothered to upload and attach a worksheet so that we could see what you have actually done, what Maple version you're using, with code to reproduce the problems? (Green up-arrow in the Mapleprimes editor)

@WA573 You can use any valid value that you want for the pointplot3d command's symbol, symbolsize, and color options.

p3dopt2.mw

@Ronan It's slightly bewildering, because I already mentioned using LibraryTools in your previous Question thread.

Saving/exporting your procedures from a worksheet to external files is a methodology that you yourself described, and was not proposed by responders to recent Question threads. It's not necessary.

Personally I think that authoring source in directly plaintext files has benefits, that especially manifest themselves if it's used and re-used over the years. But authoring in the GUI and then saving to external files is a backwards and unnecessary process.

@Ronan In this latest scenario (saving as .m format) there's no reason to even export/save at all.

In that situation you could just as easily use LibraryTools to Save the procedure or module directly to a .mla archive file.

See my earlier Reply above, for various benefits of having/authoring your code in plaintext files. Using the mint Maple syntax checker (at full strength, not the less flexible/weakened maplemint or CodeEdit/Startup facilities in the GUI) is yet another motivation.

I'm not the only person who sees benefits to using plaintext files for packages/procedures that you might utilize into the future; see also here for a comment by someone else in a related and recent discussion thread.

If none of that rationale interests you then you don't need to export/save your procedures/modules to external source files.

@nmacsai It wasn't clear to me from your original Question whether you wanted just the number of base b digits, or the actual conversion as well.

I guessed that it was just the number of base b digits.

@Carl Love I was shooting for speed, especially as n gets very large.

Are the numbers you want to handle only positive integers? Or floats?

How large are the numbers you want to handle?

How many number do you want to handle? How fast do you need it?