# Tagged Questions

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.

405 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 ...
191 views

### Wiggly and imprecise animated gif output

Trying to make animated gif of zooming into famous Ford circles. With the code ...
96 views

### Why are so many built-in numerical function doesn't check its argument is packed array or not? [on hold]

This question is brought by this one. Outer[Times, RandomReal[1., 1000000], {1., 2.}]; is much slower than ...
421 views

### Creating a fast random array generator

I want to create N x N array of random numbers. (N is an integer). The constraints are, each element should be between 0 to l(integer) ( here 0<= l <= N) and the sum of elements in each row ...
128 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 ...
47 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 ...
70 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 ,...}} ...
79 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 $n$ ...
430 views

### A quicker than outer

I need to get a matrix $\{a(x_i-x_j)\}$, where $x_i$ form a partition of an interval, $a(x)$ is a given function. I use ...
89 views

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55 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 ...
188 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 ...
88 views

### Manipulate gets stuck when ConvexHullMesh is made transparent

Version 10.3 The followinng Manipulate is a bit slow, but quite OK ...
120 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 ...
132 views

### strange timing result of LinearAlgebraBLAS in mathematica? [on hold]

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 ...
29 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 ...
63 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 ...
147 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: ...
77 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 ...
109 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 ...
45 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 ...
39 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 ...
284 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 ...
156 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 ...
64 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 $F(x)=0$, ...
81 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 ...
669 views

### Terrifying performance decrease for contour/density plots in v10.1 -> 10.3

I setup for download a test dataset at http://www.inrim.it/~magni/cm.dat.gz (a set of 64800 triplets x,y,z). The behavior can be reproduced with the following code: ...
69 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]]; ...
96 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 ...
87 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 ...
178 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 ...
135 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 ...
139 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. ...
301 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 ...
51 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 ...
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: ...
91 views

### Efficient and fastest way to execute 4 nested loops

I have a question regarding the use of ParallelDo. I tried to parallelize the following code involving four nested do loops by using paralleldo to make it as fast ...
308 views

### Why is multidimensional Reverse slow?

Bug introduced in 6.0 or earlier and persisting through 10.3 I have found that multidimensional Reverse is ~10 times slower than exact ...
126 views

### can this code be faster?

Below is a lattice point generation code I write ...
81 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 ...
366 views

### Highlighting pattern strings in a large text

I would like to apply Style to strings that are matched, for example, with one or more specified patterns or regular expressions, a string or a list of both, ...
60 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 ...
37 views

### NMinimize error

I want to use NMinimize in the following way: ...
55 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 ...
937 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 ...
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 ...
485 views

### Riffle and Partition

At some point I noticed that I was using Riffle and Partition together a lot. I would do things like ...
87 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 ...