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.

learn more… | top users | synonyms (2)

4
votes
2answers
204 views

About auto-compiling and performance between Do and Fold

I was investigating how Fold could improve performance vs Do. I tested the code ...
6
votes
0answers
285 views

Poor CUDALink performance, when calling a kernel multiple times

When working on a project of mine I noticed that CUDALink shows very poor performance when calling CUDA kernels multiple times in a loop-construct. To demonstrate this I put together this little ...
70
votes
2answers
876 views

Why are numeric division and subtraction not handled better in Mathematica?

There is something that has been troubling me for a while. At least in version 7, the performance of a / b and a - b is not ...
5
votes
1answer
113 views

Finer granularity with ParallelDo

ParallelDo only parallelizes by the innermost variable. Is it possible to distribute the calculation over all the points (all the variable) separately? let me ...
7
votes
6answers
233 views

Faster list duplicate 'limiter'

Given some list, e.g., {5, 3, 2, 3, 1, 0, 1, 3, 5, 5, 4, 5, 1, 2, 5, 2, 2, 0, 1, 4}, I need to limit the duplicates, if any, to an arbitrarily chosen number. The ...
21
votes
5answers
589 views

More efficient way of generating list of occurrence counts?

Given a list, e.g., target = {a, b, c, b, c, d, c, d, e, f, a, h, g}, I want to generate a list containing the occurrence count of the corresponding element of the ...
4
votes
4answers
268 views

Using Locators in a non-standard Manipulate code

I'm trying to adapt Nasser's method for using a control variable inside Manipulate to selectively choose what part of the code should be recalculated depending on the controls changed (see this ...
1
vote
1answer
166 views

Using Manipulate with a control variable for selective recalculation

I'm trying to adapt Nasser's method for using a control variable inside Manipulate to selectively choose what part of the code should be recalculated depending on the controls changed. I've also read ...
9
votes
2answers
241 views

How to avoid an expensive subset of a Manipulate computation when dependent variables have not changed?

I have a Manipulate where a portion of the calculation that ends up displayed is dependent on a subset of the Manipulate control ...
16
votes
1answer
471 views

Fast DensityPlot

Is it possible to increase the perforamce the DensityPlot? For example, let's try to plot this "flower" ...
33
votes
1answer
1k views

Benchmarking Mathematica performance on the Raspberry Pi

It is not surprising that Mathematica on the Raspberry Pi is slow and clunky. In Stephen Wolfram's words, the command line is "quite zippy" but the notebook interface is "a trifle sluggish by modern ...
5
votes
1answer
93 views
2
votes
1answer
304 views

Speeding up solving a system of simultaneous equations

I am trying to solve the following system of equations. Solve takes a very long time to solve the following system of equations. Is there any way to speed it up? ...
26
votes
1answer
296 views

Exporting extremely large images; arrays generated via TensorProduct use 5 times as much RAM as expected?

I am generating plots of the roots of certain classes of polynomials, in the spirit of the multicolored visuals on the Wiki page on algebraic numbers. I've thus far been able to make some extremely ...
1
vote
0answers
355 views

Solve[] unexpectedly giving empty solution sets for extremely large problems

I was calculating the set of lattice vectors in $\mathbb{Z}^4$ which have taxicab norm $r$. For example, executing ...
10
votes
3answers
241 views

Can I return lists with different dimensions from a compiled function?

Sometimes I'll need several lists with different dimensions to be returned by a compiled function, but compiled function will fail if an irregular list contained: ...
5
votes
1answer
353 views

Functional programming Style & Performance

Hello i have been spending time to convert my R tools into Mathematica Packages mainly because i like the functional programming style in Mathematica. In doing so it seems that i run into one ...
3
votes
1answer
169 views

Faster Solve for Fermat 4n+1 conjecture

Assuming that Fermat 4n+1 conjecture (each prime of the form 4n+1 is the sum of two squares) is true then I like to solve the ...
0
votes
0answers
147 views

Code performance problem

Could anyone help me with the attached code? How would you speed up my attached code in some degree? Your comments are highly welcome. ...
5
votes
1answer
176 views

MapThread over large graph

I am trying to build a very large graph with approximately $16\,000\,000$ edges, each being a two-dimensional integer vector. I have a list of edges in the form $\{\{e_{11}, e_{12}\}, \{e_{21}, ...
1
vote
0answers
105 views

Sum slowing down computations

I am trying to compute higher order Casimir invariants for some representations of certain groups. I can get the quadratic, cubic and quartic but beyond that things are taking too long to the point I ...
4
votes
3answers
195 views

How to compile a diagonal array efficiently?

For example, if we use some functions defined prior to Compile, we usually have the main evaluators in the compiled codes, pointing to the definition of the ...
6
votes
2answers
320 views

Memory management and speed for Fast GCD

Let's say that we have some $300\,\text{K}$ digits (arbitrary function) and want to trial factor with $100{,}000{,}000$ first prime numbers. ...
1
vote
2answers
246 views

What's the best way to generate all the upper triangular matrix whose singular values are given?

For example, given $\lambda_1 = 1, \lambda_2 = 2, \lambda_3 = 3$, what's the best way to generate all the upper triangular matrix ($3\times 3$) whose singular values are $\lambda_i$? Note:Given a ...
10
votes
4answers
270 views

Efficient way of identifying the indices of first occurrences

It seems to me like identifying the first occurrence of unique elements should take about the same amount of time as it takes to delete duplicates. My data sets are much larger than this (...
0
votes
1answer
181 views

speed up for computing MatrixExp

My code use two method to computing MatrixExp, I expected the second snippet code will faster than the first one, but in fact it a bit slower than that. How can I ...
4
votes
1answer
136 views

Selecting expressions from a sequence that are not subexpressions of earlier elements

I have a While loop that generates and prints an expression on each iteration (there can be thousands of iterations). UPDATE: Some expressions are generated in ...
0
votes
1answer
189 views

How to improve the performance of this code

I have implemented a code in Mathematica 9 to simulate a scattering problem, and I got really disappointed about its performance when compared to Matlab. Since I am a newbie in Mathematica, would ...
0
votes
0answers
57 views

Can you set up a remote kernel for computation and a local kernel for predictive interface?

I am able to launch remote kernels from my Windows box to our Linux cluster that has the data I need and the capacity to run analysis (numerous & speedy cores, spacious memory, etc.). Works ...
22
votes
1answer
218 views

Why is multidimensional Reverse slow?

I have found that multidimensional Reverse is ~10 times slower than exact -1 ;; 1 ;; -1: ...
6
votes
2answers
123 views

Integrate perfomance

I have a notebook in Mathematica 4. I'm trying to convert it to use in Mathematica 9. One of the problem is the long computation of definite integral in the new version of Mathematica. Here's the ...
5
votes
2answers
145 views

Reading non-tabular data with NaN-s from file

A NaN stands for an entry that is not a number/undefined/missing/infinite/etc. On my machine the C code printf("%f", 0/0.) produces ...
4
votes
1answer
153 views

Calculate the covariance of a large matrix

I have to compute the covariance of 50 very large integer matrices (2500x2000 elements). However, according to my estimation this will take around 10 days. Do you have any ideas how to speed things ...
2
votes
2answers
118 views

Definite Integral. Perfomance problem

I have a notebook in Mathematica 4. I'm trying to convert it to use in Mathematica 9. One of the problem is the long computation of definite integral. In Mathematica 4 the result of the following code ...
3
votes
2answers
193 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
102 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
177 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
90 views

Slow NIntegrate over complicated domains (sometimes)

Overview I have a very large matrix I need to calculate where each element requires the integration of a product of two functions over some complicated domain. I would like to find a set of options ...
4
votes
5answers
249 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
votes
1answer
435 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 ...
4
votes
1answer
220 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
157 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 ...
6
votes
1answer
382 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
84 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
268 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 ...
9
votes
2answers
316 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
378 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
173 views

How to optimize computing a product?

Problem description Write a function to caculate the formula My solutions Solution 1: ...
6
votes
1answer
700 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 ...
5
votes
1answer
197 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: ...