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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11
votes
3answers
449 views

How to speed up Colorize

I have a list of about 500 images similar to the following: A = Import["http://i.stack.imgur.com/1bV4O.png"] ...
21
votes
4answers
702 views

How to reduce the InterpolatingFunction building overhead?

I want a linear interpolation from the following example list: ...
11
votes
1answer
120 views

Faster binary Hamming weight for big integers?

While working on an answer to Count the sequences in an array I found that DigitCount was the bottleneck in my code when used as ...
28
votes
1answer
906 views

Fast Spherical Harmonics radiative transfer

This is a rather specific question and I apologize for spamming you with some lengthy code. But it could be interesting for some reader and maybe you can help out, so please bear with me. I am using ...
2
votes
1answer
79 views

How to handle Indeterminate TimeConstrain

I have to use Timeconstrained[aux] first for avoid some bigs calculation that dont need and it use a lot of time of calculate, so i can't do this. ...
2
votes
2answers
90 views

How to Optimize Solution? (Project Euler #14) [duplicate]

Link to Question: https://projecteuler.net/problem=14 I began by defining the following functions below. ...
3
votes
0answers
41 views

Why is the Max function so slow when operating on lists of dates?

Example: dates = DateRange[DateObject[], DatePlus[DateObject[], 15]]; First[AbsoluteTiming[Max[dates]]] (* 21.364247 *) As a workaround, ...
14
votes
3answers
616 views

Nearest neighbor search in n-dimensions

Suppose a list of items such as: L1 = RandomReal[{0, 100}, 1000]; I need to find the position of each k-neighbor in the original list. And very quickly if ...
0
votes
0answers
165 views

Why does my calculation of a probability take too much time?

I am calculating the value of the following function for given argument values: ...
14
votes
3answers
360 views
+200

Solve a trig equation system

Background of the problem In the same plane, P is a fixed point, A,B,C are moving point, PA=a, PB=b, PC=c, find the maximize perimeter of △ABC. let ∠BPC=A, ∠CPA=B, ∠APB=2*Pi-A-B, then the ...
6
votes
0answers
204 views

Speed up MinimalPolynomial

My Mathematica code runs slowly MinimalPolynomial[Sqrt[2] + Sqrt[3]+ Sqrt[5]+ Sqrt[7]+ Sqrt[11]+ Sqrt[13], x] runs slowly, but the Maple version ...
5
votes
3answers
74 views

Conditional subset generation

I am trying to accomplish the following task: Given a list of coordinates of n points in the plane, I need to find subsets of all points that share the same ...
2
votes
1answer
63 views

Pros/Cons to updating in place

There are often times when I have to update a list. The following is an example: ...
6
votes
1answer
320 views

Speeding up the non-negativity algorithm for multilinear function with interval probabilities?

The algorithm is a branch-and-bound algorithm that calculates the non-negativity of a multilinear function with interval probabilities. The lines 9-11 has an optimization that is explained on the ...
10
votes
3answers
363 views

Riffle and Partition

At some point I noticed that I was using Riffle and Partition together a lot. I would do things like ...
15
votes
2answers
139 views

HDF5 importing large arrays

I have some computations that output a 300,000,000 element array of long unsigned ints, so about 2.4GB, in an h5 file. Mathematica handles files south of 2GB fine, albeit taking very long to import ...
3
votes
1answer
180 views

How can I understand this short example?

First launch kernels LaunchKernels[4] {KernelObject[5, "local"], KernelObject[6, "local"], KernelObject[7, "local"], KernelObject[8, "local"]} Then I calculate ...
5
votes
1answer
85 views

Slow-down encountered for RandomChoice in large lists

I was wondering if anyone could help me to speed up this code snippet which creates simple (sparse) networks by preferential attachment. The algorithm adds a vertex and an edge each time interval. ...
1
vote
1answer
80 views

Unexpected inefficiency when calculating matrix product by Dot

There is an unexpected inefficiency when I calculate matrix product by Dot. The only relevant part of my code is presented as follows: ...
2
votes
1answer
70 views

Memory usage optimization for a large Association/SparseArray

Reformulating my question in simpler terms. Take two lists list1 = RandomInteger[{1, 100000000}, 25000000]; list2 = RandomReal[{1, 10}, 25000000]; Make an ...
22
votes
7answers
2k views

How to improve the performance of solutions to Project Euler (#39)?

This is the problem 39 of Project Euler, which I asked in the chat room two days ago. My original code runs as slowly as snails, and finally I got two answers from JM and Rojo. Unfortunately, both of ...
3
votes
1answer
80 views

Solve an eigensystem faster and eliminate Root[…] from the solution

I have a symbolic, 2-parameter, 8x8 matrix to solve, but Mathematica takes something like 20 minutes to solve it and returns a very large output containing expressions of the form ...
4
votes
2answers
275 views

How can this DivisorSigma code be made fast?

Since Project Euler problems are now fair game for questions I have a question of my own. A certain problem* states: For a positive integer n, let σ2(n) be the sum of the squares of its ...
9
votes
2answers
298 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 ...
5
votes
2answers
134 views

Speed up image coloring with ReplaceImageValue

I have about 200000 rgb-images of such format (2160*577 pixels): I want to colorize in each image some parts in white color: ...
2
votes
0answers
84 views

When does Mathematica automatically use dispatch tables for function evaluation? [closed]

I've read the documentation for Dispatch, and it says: Lists of rules produced by assignments made with = and := are automatically optimized with dispatch ...
10
votes
1answer
660 views

Modular arithmetic - efficiently calculating the remainders of factorials

When working on this question regarding the divisibility of the sum of factorials, I decided to write some code to test "small values" of the problem using the following code. ...
2
votes
1answer
145 views

How to determine whether an expression can act as a “good” function?

It's not easy to see whether an expression can act as a "good" function. A good function refers to an operater that transforms symbolic entities like 1+x^2 or ...
11
votes
5answers
410 views

Most efficient way of making pair list from a list

I have a bunch of datasets which looks like: 3 7 1 6 5 8 2 4 1 2 8 1 5 2 5 ... and I need to make a list of pairs such that the first element makes a pair with ...
16
votes
2answers
287 views

How to improve performance of BesselJ to the level of GSL?

Consider the following code: zs = N /@ Range[0, 12, 10^-5]; AbsoluteTiming[bessels = BesselJ[1, #] & /@ zs;] Length@zs I've tried to measure only computation ...
1
vote
0answers
54 views

Efficient way for solving a matrix equation

I am looking for a more effcient method to perform the following analysis. I did my best, but running the following code on my machine takes 9.766s. I need to perform this analysis several times. ...
4
votes
3answers
2k views

Definite integral takes a very long time

I'm trying to integrate the following function: $$r_e=\int_0^z\frac{dz}{\sqrt{\Omega_m(1+z)^3+\Omega_\Lambda}}$$ where $\Omega_\Lambda=1-\Omega_M$ and both $\Omega_\Lambda$ and $\Omega_M$ are real ...
1
vote
2answers
119 views

Slow program- Mathematica shuts down

I've been trying to draw dynamic pictures of level sets of certain polynomials. The code right now looks like that : ...
6
votes
1answer
91 views

SameQ for unsorted lists

I have to compare two or more lists and check if they are the same, but their elements can be in different position. For instance ...
2
votes
1answer
64 views
2
votes
1answer
95 views

Compiling a summation

I have a sum over Legendre polynomials which I'm trying to speed up. I've come across the suggestion of using Compile to speed up code in previous answers around ...
6
votes
0answers
95 views

Using a Mathematica index as a DiscreteVariable in NDSolve when solving a coupled set of ordinary differential equations

Context Since the explanation below of the problem to be solved is lengthy, let me preamble this by saying that I have code that works to solve the problem, but I don't know whether (1) it's ...
5
votes
4answers
611 views

Distance between two line segments in 3-space

I need to compute the distance between two line segments in a project. After googling, I found this algorithm and used it to implement a Mathematica version: ...
2
votes
3answers
145 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 $N\times N$ ...
1
vote
1answer
79 views

Apply NonlinearModelFit to an image

I have several images (in FITS format), which I want to fit with a 2D-Gaussian distribution. The problem is that NonlinearModelFit expects data in the form of a ...
8
votes
2answers
219 views

How to read off coefficients of tensor-like expression in a speedy way?

I am considering identities involving t[a, b, c, d, ...], where number of indices is fixed. t has the cyclic property so that ...
5
votes
1answer
115 views

Reap, Sow with Parallelize: bad performance, why?

I have a question about the performance of Reap and Sow with Parallelize. I am aware of the following questions How to collect result continuously (interruptible calculation) when running parallel ...
4
votes
0answers
70 views

How to perform Bayesian optimization with Mathematica?

Does Mathematica have any Bayesian optimization methods for learning hyper-parameters? Practical Bayesian Optimization of Machine Learning Algorithms Jasper Snoek, Hugo Larochelle and Ryan P. ...
5
votes
1answer
106 views

Number of divisors visualized with the QPochhammer function, how improve performance of code?

I have this code that originally is Jeffrey Stopple's code for the Riemann zeta function in the complex plane. Because I discovered yesterday that the number of divisors can be generated with the ...
6
votes
3answers
169 views

Speed up derivative evaluation

I'm trying to calculate the normal vectors and the tangent vectors at the discrete points of a suface. For example: ...
16
votes
1answer
439 views

Speed up adding Poisson noise to an image

I'm simulating some images corrupted with Poisson noise, but I'm encountering a few problems with performance. According to the documentation on ImageEffect, one ...
4
votes
2answers
245 views

Why does having many Print statements slow down my code?

I have a code that I need to debug. I have put a Print[] into it that should give about 10^4 prints for table entries. I know that 10^4 is large, and this exposes ...
1
vote
1answer
129 views

Making ReplaceAll faster

I have a list of functions ncalc that is calculated by ...
10
votes
1answer
288 views

Drop selection of columns from a ragged array

I have an application where I need to drop some arbitrary list of columns from a ragged array (where of course the shortest array rows have at least all the specified columns). E.g., given a ragged ...