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3h
comment Differential equations with rational functions as solution
Difficult to say much without a specific Mathematica input.
4h
comment Symbolic expression for recursion
I put it in a community wiki response, but I'd not be surprised if the question gets closed anyway.
4h
answered Symbolic expression for recursion
5h
comment Symbolic expression for recursion
Check documentation for RSolve.
10h
comment Getting lengths of sublists that sum to more than one
@alancalvitti Sometimes Fortran-like code is the way to proceed. I mean, if it was good enough for Michaelangelo, then who am I to snub it?
10h
comment Is the “Custom Extension of C” that Mathematica is partially written in available for use or review?
It was around from the beginning.
1d
comment Table with List iterator return unpacked list
I do not recall the details but I believe it involves knowing there can be no dependency of inner iterator variables on outer ones (since there are no inner iterators in the 1-D case).
1d
comment Is the “Custom Extension of C” that Mathematica is partially written in available for use or review?
It's an in-house precompiler that primarily handles internal expression reference counting and some operator overloading.
1d
comment How to Minimize an NIntegral
(1) That's a comment, not the original question. (2) It's not formatted very well either; the code cannot be cut-and-pasted. (3) You are using a different minimization function, one that cannot handle these functions. Check documentation for NMinimize vs. Minimize. Very different animals, those.
1d
comment Is it possible to recover the efficiency of ListConvolve when generalizing the convolution?
This documentation might be helpful. Also this prior MSE thread has very good information. And here is a historic but probably still useful account.
1d
comment How to Minimize an NIntegral
Probably best to edit the extended problem into the original question.
1d
comment How to Minimize an NIntegral
I made a community wiki response since this is a common issue and was slightly subtle.
1d
answered How to Minimize an NIntegral
1d
comment Is this problem parametrically solvable or it can just be solved for specific $\sigma$ and $\theta$?
I don't think a formula will be easy to obtain. Another possible improvement in that difection might be to separate variables into real and imaginary parts (which will double the number for those that are complex-valued). Then replace Conjugate and Abs with explicit algebraic expressions and solve over the domain Reals. Still not likely to be tractable but it will have a better chance by virtue of being all algebraic
1d
comment Table with List iterator return unpacked list
Yes, if Table sees a non-explicit iterator range it will go to a general evaluator rather than auto-compile. So auto-compilation is a bit weak but Table gets to be very flexible..
1d
comment Is this problem parametrically solvable or it can just be solved for specific $\sigma$ and $\theta$?
(2) It is definitely going to be easier to handle the case of no parameters, wherein they are given specific numeric values. For one, it will avoid having to keep track of algebraic functions of the parameters that may cross paths, hence switching larger and smaller values.
1d
comment Is this problem parametrically solvable or it can just be solved for specific $\sigma$ and $\theta$?
(1) Might be easier to solve separately for where each of those determinants equals zero, then take the smallest solution for fv (this assumes that for all smaller values the determinants are all positive, else the question does not have an answer).
1d
comment Is it possible to recover the efficiency of ListConvolve when generalizing the convolution?
@MikeHoneychurch2I am not the developer although I have done some work on special cases, mostly involving integer inputs (and the usual convolution). After looking some more at where the non-default-heads case goes, I will revise my pessimism somewhat and speculate that possibly the bottleneck has to do with unpacking rather than asymptotically faster underlying methods. For a proof of concept you might try to code a handler using Compile, wherein the dimensions and nondefault heads are fixed e.g. to do LC2 above but maybe with default padding.
2d
comment Is it possible to recover the efficiency of ListConvolve when generalizing the convolution?
@MikeHoneychurch2 No, I mean in terms of coding. I have no idea how to attain such an improvement algorithmically, at least not in any general way. For some special cases where the operations are restricted to List and arithmetic, maybe some improvement could be made. Though I doubt it would compete with the speed of MKL code, as is used for the default case.
2d
comment How to Minimize an NIntegral
Also note NMinimize[fun2[2.5, a], a] will give a better result, albeit more slowly.