Whilst playing around trying to write a function to remove text rows from a mixed string/numeric matrix (*), I discovered that the undocumented (but very useful) function fold doesn't just work on vectors but also works on matrices, scanning down each column in turn, in the normal Mathcad fashion.
This behaviour opens up the possibility of some straightforward implementations of useful functions, such as converting a (potentially arbitrarily nested) array into a vector and summing the elements of an array.
Here are some Mathcad Express 7 functions.
Or we could define matsum to sum just the numeric elements of an array.
Alternatively, we could shift the burden of removing non-numbers to a specialized version of vec.
We can even count the elements in nested arrays.
The full version of Mathcad Prime allows the user to write programs to create functions. This facility opens up the possibility of writing a more generic filter function using fold by creating functions containing tailored boolean predicates.
Stuart
(*) https://community.ptc.com/t5/PTC-Mathcad/READ-FILE-RANGE-OF-ROWS-AND-COLUMNS/m-p/760410#M198424
I found a few more undocumented Prime functions. Not sure about their value, though.
update1 and update2 can be used to add values at arbitrary positions in vectors or matrices and the function is not ORIGIN-aware.
mapvector seems to allow us to avoid vectorization, but then, I may not be able to see its potential right now. Just playing around with the functions for a few minutes so far.
I found those function by looking for "mc_fold" in all files in the PTC program directory and found it in some dll's (not surprising). I looked at those files with a simple text editor and noticed other mc_*** mentioned which I wasn't aware of.
OK, I also was not aware of the functions "foldover" and "fullfact2", but they are documented functions 😉
But I guess that further digging into the dll's may bring up a few more undocumented functions as well.
@Werner_E wrote:
I found a few more undocumented Prime functions. Not sure about their value, though.
update1 and update2 can be used to add values at arbitrary positions in vectors or matrices and the function is not ORIGIN-aware.
mapvector seems to allow us to avoid vectorization, but then, I may not be able to see its potential right now. Just playing around with the functions for a few minutes so far.
I found those function by looking for "mc_fold" in all files in the PTC program directory and found it in some dll's (not surprising). I looked at those files with a simple text editor and noticed other mc_*** mentioned which I wasn't aware of.
OK, I also was not aware of the functions "foldover" and "fullfact2", but they are documented functions 😉
But I guess that further digging into the dll's may bring up a few more undocumented functions as well.
Nice work, Werner!
update potentially solve a problem I commonly encounter.
One of the problems with passing arrays around in Express is that there's no simple way to set an array element's value without going through some hoops. Yes, it can be done, but it can be awkward (I have a function, but ... ). update looks like it might be a neater, and more efficient, solution to the problem.
mapvector could be useful for those odd occasions when I want to pass an operator as an argument to another function.
Stuart
All these undocumented functions work as from Prime 2, Express. Can't check Prime 1, but expect it will work there as well.
Update1 and 2 will (also) help in creating vectors and matrices with constant data:
update1(0,5,0) creates a 6 element vector of zero's, what otherwise matrix(6,1,max)*0 would do.
Prime 2 file attached.
Success!
Luc
Found just a few more undocumented Prime stuff.
The most interesting is the contradictio in terminis constant undefined, which isn't undefined:
Then there is the function sleep(t) that wastes computer time by calculating for t seconds and then returning the value of t.
Very useful if Prime is too fast.
Then there are functions ceilMc11, floorMc11, truncMc11, CeilMc11, FloorMc11 and TruncMc11, which appear to do nothing else then ceil, floor, trunc, Ceil Floor and Trunc respectively.
Finally there are getmaxthreads() and setnumthreads(), which give (so far) unpredictable results:
Success!
Luc
@LucMeekes wrote:
Found just a few more undocumented Prime stuff.
The most interesting is the contradictio in terminis constant undefined, which isn't undefined:
Then there are functions ceilMc11, floorMc11, truncMc11, CeilMc11, FloorMc11 and TruncMc11, which appear to do nothing else then ceil, floor, trunc, Ceil Floor and Trunc respectively.
I was aware of undefined, but the Mc11 functions are interesting, Playing around ...
Stuart
@Werner_E wrote:
mapvector seems to allow us to avoid vectorization, but then, I may not be able to see its potential right now.
Naturally, having scratched my head in vain doing likewise, I thought of several cases where I'd needed to avoid the blunt tool of vectorization (sometimes a sledgehammer is what you need). mapvector is useful when creating an array argument in situ.
Most of the time, I need a polyadic map, though.
where
Stuart
@Werner_E wrote:
I found a few more undocumented Prime functions. Not sure about their value, though.
update1 and update2 can be used to add values at arbitrary positions in vectors or matrices and the function is not ORIGIN-aware.
And here's a demo for update1. I sometimes need to use a list of indices to either get or set values from a vector. This is, of course, a good cat-skinning exercise, but this version demonstrates the advantage of being able to directly update and return an array.
Stuart
@VladimirN wrote:
@StuartBruff wrote:
Umm. I knew you'd ask me that.
😀
I thought that might amuse you. 🙂
Anyway, please find attached a quickly edited worksheet. It's probably full of errors, so caveat emptor.
Could you also please tell me why I'm doing work on a weekend evening when I'm not even getting paid for it, let alone at time and a half?
A brief summary of some of the highlights:
Have you mastered the new Arduino plate again 🤔?
Нет!! It appears as if there was poor contact inside one of the header sockets. I suspect that this might have induced a hardware failure on either the (SAM-based) Feather RP2040 or the RGB Matrix. Just to show I haven't lost my magical effect on physical equipment, the Feather's no longer working as a CircuitPython device. I guess I'm going to have to try the Arduino IDE and C++, or take the road to eternal damnation and try using the debug facility. ☹️
Stuart
