Linked Questions

549
votes
19answers
139k views

Where can I find examples of good Mathematica programming practice?

I consider myself a pretty good Mathematica programmer, but I'm always looking out for ways to either improve my way of doing things in Mathematica, or to see if there's something nifty that I haven't ...
33
votes
2answers
4k views

Determining which rule NIntegrate selects automatically

I need to numerically integrate a highly oscillatory function over the semi-infinite domain $(0,\infty)$: $$\int_0^\infty \frac{\sin^2(x) \sin^2(1000 x)}{x^{5/2}}\mathrm dx$$ Since the Levin rule (...
19
votes
4answers
1k views

the winding number for the circle map (Arnold tongue)

I want to perform an iterative calculation and visualize the results: f[n_, a_, b_] := Nest[# + a - b Sin[2 π #] &, 0, n]/n; If I use machine precision, it ...
24
votes
2answers
1k views

Obtain approximate Hessian using FindMinimum

According to the documentation, when FindMinimum is told to use the method "QuasiNewton" on a unconstrained problem, it uses the ...
21
votes
2answers
774 views

How to create internally optimized expression for computing with high WorkingPrecision?

I have large dataset and need to fit rather complicated function on it with different values of one of its parameters (this parameter must be fixed in every fit). I use the ...
9
votes
3answers
1k views

NIntegrate-ing a compiled function

I'm trying to integrate numerically in 6 dimensions a very long expression and I read about the option to NIntegrate a compiled function which should be faster. ...
11
votes
1answer
821 views

Is there a way to see the result of NIntegrate's symbolic preprocessing?

NIntegrate can do a number of different types of symbolic preprocessing on the integrand before starting the numerical calculations, including changes of variables. ...
67
votes
1answer
2k views

Is this the most effective and efficient programming style for prototyping (a ray tracer) in Mathematica?

I am trying out Mathematica as a prototyping tool. As an initial exercise I have put together a brute force ray tracer, with a view to using Mathematica's built in probability distribution functions ...
11
votes
2answers
725 views

Using StepMonitor/EvaluationMonitor with DifferentialEvolution in NMinimize

My question about tracking the progress of a minimisation/fitting process is two-fold: 1. The first part of my question can be considered a slight duplicate/follow-up of this question. There the OP ...
14
votes
1answer
650 views

Jacobian of ParametricNDSolve and FindRoot for the Three Body Problem

The main problem I took the time to reformulate the question in a more appealing and concise way. I want to find bifurcations of solutions to the three body problem. In order to do that, I define ...
11
votes
1answer
379 views

Experimental`NumericalFunction in NMinimize solution

I try to make a number of optimizations using this code: ...
6
votes
1answer
756 views

Preconditioning the objective function of NIntegrate for higher PrecisionGoal

By default, NIntegrate works with MachinePrecision and its PrecisionGoal is set to ...
3
votes
1answer
241 views

Is there any way to use compile and still maintain high precision in Mathematica? [duplicate]

Is there any way to use compile and still maintain Arbitrary-precision like 50 in Mathematica?
14
votes
1answer
197 views

How is the Hessian computed using ``Experimental`NumericalFunction``?

Here and here it was explained how to use Experimental`NumericalFunction to compute the Hessian of a numerical function. I would like to know how this undocumented ...
6
votes
1answer
111 views

Is it possible to make listable Experimental`NumericalFunction?

I have been playing a bit with the undocumented function Experimental`CreateNumericalFunction and I wanted to know if somebody found a way to make generated ...

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