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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6
votes
1answer
153 views

Strange performance of Outer

The following takes 0.07 seconds on my laptop. list1 = RandomReal[1.,1000000]; (Outer[Times, list1, RandomReal[1., 2]];) // AbsoluteTiming But this takes 1.2 ...
1
vote
1answer
58 views

Improving strategy to solve this constrained root-finding problem

I am looking for roots of the function eqs defined below. It has $2k$ unknowns and returns a vector of $2k-1$ components. The sole purpose of the following block ...
3
votes
2answers
75 views

union several arrays of same flag(date for example) efficiently

Suppose I have several arrays from data files which look like: arrayi = {{datei1, xi11, xi21, ...}, {datei2, xi12, xi22, ...}, ..., {datein, xi1n, xi2n ,...}} ...
2
votes
0answers
85 views

Solving this system of nonlinear equations

Edit Interestingly, I realized solving my problem with $2n$ equations appeared to be more efficient than using mathematical results on the solutions to reduce the problem to $n$ equations (the $n$ ...
4
votes
1answer
67 views

More efficient method to implement knots instertion algorithm

Knots instertion algorithm of B-spline About the definition of B-spline, please see here. Suppose $\overline u \in [u_{k},u_{k+1})$initially has multiplicity $s$, and suppose it is to be inserted ...
7
votes
1answer
201 views

How to terminate early a functional computation

Problem description: Given a list $A=\{1,2,0,7,0,-1,2,6,\ldots\}$ and a list $B=\{0,7,0\}$ write a program that determines whether $B$ appears in $A$ or not. Note: the order of $B$'s items does ...
2
votes
1answer
98 views
3
votes
1answer
135 views

default RGB coloring

I am playing with some basic genetic algorithms to recreate input images by transparent plane figures (similar like here:). Everything would work great but the speed is terrible. I was looking for a ...
4
votes
0answers
144 views

strange timing result of LinearAlgebra`BLAS` in mathematica? [closed]

BLAS is short for "Basic Linear Algebra Subprograms". It is a famous collection of routines for doing linear algebra. I just know from Oleksandr R. that mma can directly call BLAS under the context ...
0
votes
0answers
34 views

Multivariate remainder of polynomial in respect to a set of polynomials

I would like to have a really fast routine that computes the so called Normal Form of a multivariate polynomial f in respect to a set of other multivariate ...
1
vote
0answers
92 views

Exceeding time constraint of 300 seconds when taking coefficients of some expressions from schur polynomial [closed]

I have written a code that takes coefficients of some expressions from schur function, but it seems to take a lot of time, and Mathematica will stop after 300 seconds saying that it's over the time ...
5
votes
1answer
182 views

My introduction to Compile

I am reading Fractals from the Newton-Raphson method from Peter Young's page [http://young.physics.ucsc.edu/115/]{http://young.physics.ucsc.edu/115/}. I've tried: ...
1
vote
2answers
91 views

Finding matrix given null space

Suppose I input a very large $n$ integer vectors and I wish to compute the matrix whose nullspace is spanned uniquely by these vectors. Is there an appropriate command/module to do this using ...
4
votes
2answers
123 views

How to be more efficient/faster with this MatrixExp-vector multiplication?

I am looking for expertise that helps to improve speed of the code below. First, a little bit of background: There is some system of differential equations $\dot{\vec{m}}(t)=S(t)\vec{m}(t)$. In order ...
0
votes
1answer
56 views

Minimization of linear combination of vectors

Suppose I have a vectors in $\mathbb{R}^{6}$. For example, take the vector $v = k(-2,2,4,6,2,2)$. I would like to find some $k$ with the constraint that the last two components are necessarily ...
2
votes
0answers
43 views

Performance of different Count patterns

The two pieces of code below are functionally equivalent, and I would have expected similar performance. (The only difference between the two is the form of the pattern used.) But the second piece of ...
5
votes
2answers
336 views

Efficient way to perform local Otsu thresholding on image

I have images of cell nuclei that have locally varying intensity distributions. Therefore, I need a robust local threshold algorithm. LocalAdaptiveBinarize works ...
17
votes
2answers
182 views

Speeding up generation of block diagonal matrix

I'm struggling with the following problem. I have $48$ square matrices (full, filled with real machine precision numbers, thus are packed, all different) of size $128$. I wolud like to place them on a ...
9
votes
0answers
83 views

Efficient solution of huge sparse linear system

I'm trying to improve efficiency of my code in which main task is a solution to huge (~$10^4\times 10^4$) but sparse linear system $$Ax=b$$ (In fact my aim is to solve nonlinear equations $F(x)=0$, ...
5
votes
1answer
102 views

How to increase speed of iterations with nonlinear functions

Let me ask about part of a problem which I have in solving of a nonlinear DE (numerically). I am working with vectors of length $xN$. I have an initial vector $v$, a given $xN\times xN$ matrix $A$ and ...
2
votes
1answer
73 views

Deleting isomorphic graphs efficiently

I'm trying to delete isomorphic graphs from a large list. My solution is as follows: DeleteIsoG1[gl_List]:= Module[{}, DeleteDuplicates[gl,IsomorphicGraphQ]]; ...
2
votes
1answer
104 views

Is there a good way to check, whether a small value produced numerically is a symbolic zero?

I have a complicated 4x4 matrix and need to know the eigenvalues. I expect a zero eigenvalue for physical reasons. Giving numerical values first gives me an eigenvalue of $\mathcal O(10^{-15})$. Now ...
6
votes
1answer
88 views

Count degrees of freedom of a polynomial

I want to count the independent degrees of freedom of a polynomial in three variables $(z_0,z_1,z_2)$. Therefore I take the coefficients of $f$ and compute the rank Jacobian with respect to the ...
4
votes
2answers
201 views

Finding large Collatz Sequences, trying to improve speed

Background: I am already very much in love with Mathematica but I am also a novice. So far I have only gathered experience in procedural programming in Python. Generally speaking I am trying to ...
1
vote
1answer
157 views

precision and speed inefficiency issues of Nearest function with sqrt expression [closed]

Recently, Nearest has been attacked for many bugs. Some are already fixed. I am going to show some issues when Nearest applied ...
2
votes
1answer
142 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. ...
5
votes
2answers
314 views

Smallest element distance between two lists

I have a problem, where I generate two lists of points, and I want to see which points are the closest. If I just want to find which ones are exactly the same, I can use ...
2
votes
0answers
64 views

MySQL insert statement over remote server is extremely slow. How can I speed it up?

I need to insert values to a remote MySQL server. However it is extremely slow compared to a local MySQL server. This is my timing for the local MySQL server ...
21
votes
2answers
2k views

Difference between AbsoluteTiming and Timing

I need to evaluate the efficiency of my code. Therefore I would like to evaluate the time the code need for some calculations. Mathematica gives me two possibilities for this kind of evaluation: ...
6
votes
1answer
87 views

Expensive MeshRefinementFunction

I want to discretize a region using DiscretizeRegion. Now, I want the mesh to be more refined, when the curvature of a certain function ...
5
votes
1answer
61 views

Can not understand this timing result

I set a=1. tmptmp = Tuples[Range /@ {1000, 100}].{{3 a, 0}, {0, Sqrt[3] a}} And then run ...
1
vote
1answer
44 views
2
votes
0answers
60 views

Long delays before showing the result in a notebook

I'm new to Mathematica. I have Version 10.3.0 running under Windows 10, 64-bit. If I open the 10.3.0 kernel and type 2 + 2 Shift Return I get an immediate answer. If I open the main program and ...
28
votes
3answers
955 views

DeleteDuplicatesBy is not performing as I'd hoped. Am I missing something?

Déjà vu: a new-in-v10 function should provide a better solution to an old problem, but my enthusiasm is curbed when I run timings. This time the function is ...
20
votes
3answers
2k views

Fastest way to measure Hamming distance of integers

I am looking for a fast and robust way to calculate the Hamming distance of integers. The Hamming distance of two integers is the number of matching bits in their binary representations. I expect that ...
11
votes
3answers
515 views

Riffle and Partition

At some point I noticed that I was using Riffle and Partition together a lot. I would do things like ...
1
vote
0answers
101 views

integration of a list of gaussian type orbitals (GTO)

I am currently trying to integrate various components of a current density (j={jx,jy,jz}) over space. The problem is that the current j is extracted from a quantum chemical computation and is a sum of ...
8
votes
2answers
221 views

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

I have this code that is originally 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 ...
1
vote
0answers
124 views

Speed matrix multiplications

I am trying to run this function ...
6
votes
2answers
212 views

Gamma function computation efficiency?

I wonder what kind of algorithm is used to compute the values for the gamma function. Specifically, I am interested in how the computational load increases when the complexity of the input grows. So, ...
4
votes
1answer
85 views

Efficiently traversing a list

Suppose I have a large list of algebraic expressions, sorted by their equivalent numerical value (under a certain set of assumptions). Some of these expressions are identical, but commands like ...
4
votes
2answers
88 views

Parallel function evaluation for minimal value

I am asking myself, if the evaluation of a function f looking for a minimal value over a discrete set of values can be parallelize (brute scan for a potential ...
3
votes
1answer
116 views

Efficiently generating plots from lists of differing lengths

I guess this is more of an informatic question. A quite complicated function of mine generates me a list of valid points, depending on a parameter, like this: ...
1
vote
1answer
81 views

Why does Timing return different times for the same calculation?

I did an experiment in which I calculated the same quantity two different ways to see which method was faster. To my surprise, the kernel time was different in different runs. In fact, which method ...
70
votes
3answers
3k views

What is a Mathematica packed array?

A simple sounding question with a few sub questions: What is the difference between unpacked vs packed array? Are packed arrays more space efficent, how much so? Are packed arrays more time ...
3
votes
1answer
82 views

Speeding up constrained optimization problem solving

I have a problem on my homework with Lagrangian multipliers that Mathematica has now been bashing at fruitlessly for 10 minutes. I'm not sure whether I did something horribly wrong codewise, but it's ...
4
votes
2answers
310 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 ...
15
votes
3answers
494 views

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 ...