Questions on optimizing Mathematica code for higher performance. This may mean faster execution, lower memory usage or both. Not to be confused with mathematical optimization.

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8
votes
1answer
579 views

Imposing a Periodic Boundary Condition in Nearest Neighbour Search

I am trying to find first nearest neighbour distributions of randomly dispersed point-like objects in an infinite system. To do this I make a finite sized box unit cell with a chosen concentration of ...
5
votes
0answers
86 views

Is there something like MaxProcessorUsed?

For standard procedures it is easy to test if the implementation is better or worse than other by using Timing etc. It does not help us with creating ...
0
votes
0answers
144 views
3
votes
0answers
354 views

Taking real and imaginary parts of indexed functions and speeding up ComplexExpand

I am setting up a large system of ODEs and in order to use the IDA method (which is sig. faster for my system and thus attractive), I must split my equations into real and imaginary parts. I am ...
5
votes
1answer
136 views
10
votes
2answers
427 views

Why is ParallelMap way slower than Map

I recently tried to use ParallelMap instead of Map and to my surprise encountered that ...
0
votes
1answer
154 views

Better way to evaluate integral containing Boolean function

I am trying to compute the integral ...
0
votes
1answer
225 views

How to combine two usages of # into one and speed up the code?

I have a function num with two variables, matf and matg. How can I combine the last two lines of code below into one? The code is aimed to find out the maxiaml count bel when we give each $i3 = ...
4
votes
3answers
418 views

Improve the performance of solutions to Project Euler (#14)

Problem I have following code, when n<=10^5 it's not slow, but n>2*10^5 it's became very slow. I think maybe some temp value greater than 2^31-1, so make compile invalid. Could you give any idea ...
5
votes
2answers
179 views

How to optimize computing a product?

Problem description Write a function to caculate the formula My solutions Solution 1: ...
6
votes
1answer
895 views

Fastest way to do vector / matrix multiplication with constant matrix

Suppose we have a fixed n x n matrix, call it $B$. What is fastest way to evaluate $v^t B\;v$ over many different vectors $v$? Since $B$ is a constant matrix, does this allow the number of operations ...
0
votes
1answer
140 views

Efficiency problem with least square algorithm (Error in both variables)

I was informing myself about the least square algorithms with errors in x and y. I found this post and the top answer wasn't ...
5
votes
1answer
259 views

How to speed up multi-curve plotting?

The following example is a very simplified version of the problem I'm working with, though I hope it still captures the essentials. First, the definitions: ...
3
votes
1answer
163 views

Any way to speed up evaluation in an Animate?

I have a self-defined function which is fairly complicated and gives the analytical form. The result contains two independent variables. I use Animate to plot the ...
25
votes
5answers
636 views

Compiling ColorFunction for faster complex phase-amplitude plots

I have gotten into the habit of plotting complex-valued functions on a plane using a color-function along the lines of ...
7
votes
1answer
106 views

Why does Rescale performance vary significantly based on the real number values in a list?

I have a list of the form: testList = Table[{Flatten[RandomReal[{-200, 200}, {1, 2}], 1], RandomReal[{-200, 200}, {69, 2}]}, {i, 1, 100}]; And I would like to ...
0
votes
1answer
163 views

johansen test error in code

Cross-posted at the Wolfram community forum I have found this code on a forum, apparently it worked in a previous version of mathematica. Now when I run it, it keeps running for ages. I am not able ...
1
vote
1answer
85 views

Insert glyphs into a string using functional code

I asked this question few days ago: Replace For-loop with functional code Suppose I use strings instead of lists; for example a = ToString /@ {123123, 112233};` ...
5
votes
2answers
211 views

Parallelizing or optimizing a script for calculating the size of all pairwise intersections between collections of sets

I need to speed up or parallelize an operation that looks essentially like this: ...
4
votes
2answers
372 views

Quickly reducing the number of decimal digits for a set of real numbers

How can I quickly convert a number with $n$ decimal points to a number of with $m$ decimal points? Round works, however, it is slower than I would like. This ...
2
votes
2answers
217 views

Reducing quality of Graphics3D scene to improve performance?

ProteinData["SERPINA1", "MoleculePlot"] gives the detailed Graphics3D plot below. I'd like to make many small copies of this ...
6
votes
1answer
144 views

Why LinearModelFit is slower than NonlinearModelFit?

Why LinearModelFit is slower than NonlinearModelFit? ...
8
votes
2answers
218 views

How to reduce the number of operations needed to evaluate an expression? [duplicate]

For some numerical calculations in C++ I have, for example, this complicated expression to evaluate. Given as Mathematica input, in its original form it is ...
4
votes
3answers
407 views

SparseArray row operations

Given a large (very) sparse matrix, A, how can I efficiently "operate" on only the nonzeros in a given row? For example: For each row in A, generate a list of column indices that have a magnitude ...
2
votes
1answer
254 views

Manipulate executes expressions multiple times

I am using Manipulate for a rather intricate front end for data visualization. I was getting very sluggish performance and was able to boil the problem down to a ...
5
votes
2answers
452 views

Faster Eigenvalues with lower precision goal

I compute all eigenvalues of a large matrix, and I decide that the speed is more important than the precision. Then the question is, can I speed up Eigenvalues[] by ...
5
votes
1answer
304 views

How to speed up calculations with large number of replacement rules?

In my program I have an expression which looks like: ...
5
votes
1answer
279 views

How to avoid unpacking from Language`ExtendedFullDefinition

Consider this code: LaunchKernels[]; On["Packing"] a = RandomReal[{0., 1.}, {64, 30000}]; ParallelMap[Fourier, a]; // AbsoluteTiming Developer...
9
votes
1answer
293 views

Why I only get 2X speedup when parallelized with 16 kernels

I'm trying to parallelize a function by ParallelTable, and it seems the speedup is not very good. I have 16 parallel kernels on my computer node: ...
4
votes
2answers
195 views

How can I speed up my compiled RBF interpolating function?

Overview I have a function that acts like the Interpolation on sparse $n$-dimensional data using a simple implementation of RBF interpolation method. I want my ...
3
votes
1answer
186 views

Optimization of power tower fractal generator [closed]

I tried to optimize the code for generating power tower fractals from here. As the author suggested, I tried to memorize the points already tested in a list. Here is my code : ...
17
votes
3answers
1k views

How can I efficiently “remap” an image?

Many image processing libraries like OpenCV, Intel Performance Primitives or Octave have a useful function called "remap", that takes an image, an array with X coordinates and an array with Y ...
8
votes
1answer
228 views

Why is building a table of function values so much slower than just plotting the function?

Here is a function that take some time to evaluate: n = 1000; coeffs = RandomVariate[NormalDistribution[], n]; f[x_] := Sum[coeffs[[k]] Sin[k x]/k, {k, 1, n}]; ...
8
votes
0answers
205 views

Improving the performance of a package for working with rational functions

As Mathematica gets slow for large symbolic calculations, the cost of putting terms over a common denominator (Together), in particular, gets too high. It occurred ...
1
vote
0answers
193 views

Is there a way to speed up Simplify and/or PolynomialReduce Modulus-> 2?

I'm trying to simplify a series of equations with at most 64 input terms. As the number of terms involved in the equations increase, the runtime seems to grow exponentially. Does anyone know of ways ...
4
votes
5answers
341 views

How to generalize and speed up this program?

There is a vector whose length is $n*m$, we can part it into $n$ sections in order. I want to define a function to compare the $i$-th and $i+1$-th section and find the minimum. The program for $n=m=3$ ...
3
votes
2answers
371 views

How can I track the execution time of an evaluating Manipulate cell?

In Wolfram's tutorial on Advanced Manipulate Functionality, a nice example of a continually evaluating Manipulate cell is presented: ...
6
votes
2answers
179 views

Consecutive Print to target same output Cell

Is it possible to conveniently direct the output of consecutive Print statements to the same output without actually accumulating the output in a temporary string/variable. This would be useful in ...
6
votes
0answers
86 views

Does one need to be careful about loading multiple (many) contexts or packages in the same session?

I have a number of large pieces of precomputed data which I am considering putting into individual packages in order to load them (via DeclarePackage) and unload ...
7
votes
3answers
2k views

Simulate MATLAB's meshgrid function

Here is MATLAB's meshgrid. I came up with these implementations in Mathematica: ...
2
votes
2answers
195 views

Time differences between code using user-defined probability distribution and code using built-in distribution

Why is the reponse time of of kernel significantly different when I use the first code rather than the second? Shouldn it not be the same? Is there any way that the response time can be made smaller ...
9
votes
1answer
97 views

IntegerDigits has Listable attributes, but not fast

See this example, a function has Listable attributes often more efficient than Map,but why is this one is an exception? ...
2
votes
1answer
120 views

What is the best way to produce a symmetric semi-definite matrix using as few variables as possible?

As we know, there are only $\frac{n(n+1)}{2}$ variables in a symmetric $n$-dimensional semi-definite matrix. Is it possible to produce a $n$-dimensional semi-definite matrix whose trace is $1$ using ...
4
votes
1answer
208 views

How do I put a Monitor into CDF?

I would like to keep track of progress of a database request in an Enterprise CDF, but it won't allow PrintTemporary or ...
10
votes
1answer
327 views

Mathematica9: NDSolve slows down after repeated calls

I have noted that in Mathematica 9 my code, which involves a lot of calls to NDSolve, slows down considerably after some time. Apparently, the problem is NDSolve itself and it seems to be related to ...
9
votes
2answers
305 views

Complement on pre-sorted lists

Is there any way to instruct Complement to skip the sorting part? If the answer is no (likely), the next question would be: how can I remove from a sorted list ...
18
votes
1answer
423 views

Underlying Algorithms for List Manipulation Functions

Does anyone know, or know of a link for the underlying algorithms used for list manipulation functions? Specifically: Union with and without the ...
2
votes
0answers
99 views

Speed improvement in string distance function

I'm using this distance function to compare distance between strings: ...
5
votes
1answer
506 views

Efficiently generating histograms with large numbers of bins

I'm trying to generate a histogram for a large data set with the following lines of code: ...