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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1
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3answers
99 views

Efficient matrix multiplication

I have a list of vectors vecs={vec1,vec2,...,vecN} where veci is a list with length N. Now I have a matrix N*N called mat. I would like to efficiently get all the numbers veci.mat.veci for i=1 to N in ...
3
votes
2answers
207 views

My code for solving n queens problem Compile Failed

I want to make my code for solving n-queens problem faster, but it seems that MapIndexed can't be compiled. Mathematica return CompiledFunction::cfse: Compiled ...
2
votes
1answer
115 views

Putting values into a grid after iteration process

I'm developing a model of thermodynamic cycle in Mathematica. I wrote several functions, applied them to a list containing starting values and iterated, for the model to converge. ...
3
votes
1answer
216 views

How could I improve this Central Limit Theorem demonstration speed- and content-wise?

My purpose is to demonstrate the Central Limit theorem by assuming two custom distributions, taking some random samples, calculating their means and ploting the results. Ideally, the histograms should ...
6
votes
0answers
110 views

Slow NIntegrate over complicated domains (sometimes)

This is no longer a problem with Mathematica 10.* where I can use regions to do the integrations Overview I have a very large matrix I need to calculate where each element requires the integration ...
4
votes
5answers
263 views

Can I generate a “piecewise” list from a list in a fast and elegant way?

Suppose we have a number list a: n = 1000000; a = RandomReal[{0, 1}, {n}]; We want to generate a list ...
2
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0answers
130 views
2
votes
1answer
525 views

Simulated Annealing InitialPoints option

I have a cost function that depends on 4 parameters: CostFunction[{tx,ty,tz,ox}]. I used NMinimize[] function with ...
6
votes
1answer
279 views

Efficiently searching a list for the position of the closest number to a specified number

Searching by closest and position I wasn't able to find an answer—but found Nearest by guessing. Nearest, however, returns ...
4
votes
1answer
235 views

MapThread Alternatives

I want to add two matrices, the first one containing a 2D vector at each position the other one a list of 2D vectors. The 2D vector from the first matrix should be added to each of the 2D vectors at ...
4
votes
1answer
166 views

MapThread and Compile

After discovering that MapIndexed cannot be used with compile (see MapIndexed and Compile) I am now trying do implement similar functionality using a combination of ...
8
votes
1answer
512 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 ...
3
votes
0answers
333 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 ...
10
votes
2answers
387 views

Why is ParallelMap way slower than Map

I recently tried to use ParallelMap instead of Map and to my surprise encountered that ...
4
votes
3answers
407 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
175 views

How to optimize computing a product?

Problem description Write a function to caculate the formula My solutions Solution 1: ...
6
votes
1answer
833 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
130 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
238 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: ...
24
votes
5answers
607 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 ...
0
votes
1answer
156 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};` ...
2
votes
2answers
205 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 ...
8
votes
2answers
210 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
367 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
236 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
402 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
281 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
261 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
289 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
179 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
183 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 : ...
12
votes
2answers
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
210 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
198 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 ...
3
votes
2answers
335 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
162 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
81 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: ...
9
votes
1answer
96 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? ...
4
votes
1answer
201 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
311 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 ...
7
votes
2answers
273 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
408 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
94 views

Speed improvement in string distance function

I'm using this distance function to compare distance between strings: ...
5
votes
1answer
466 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: ...
4
votes
2answers
162 views

Replace function call with expression resulting from the symbolic evaluation of the function when defining a second function?

Suppose the evaluation of a function f[x_, y_] := ... takes a very long time, but the output is a not-so-complicated polynomial in ...
3
votes
2answers
582 views
3
votes
0answers
132 views

Force Dispatch to generate dispatch tables

Dispatch creates hash tables only for lists of length larger than 3. Is there any way to force MMA to create hash tables even for lists of length smaller than 4? ...