Questions tagged [performance-tuning]
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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How to produce the following table faster?
Consider two data files, acc.m and distr.dat. They contain some functions that I need to multiply to obtain function ...
- 5,102
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2
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111
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How can I speed up calculation of the integral?
Is it possible to speed up the calculation of the Kx integral?
...
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Compiling a function that uses MapThread
I'm looking for tips on quickly applying the following update to $B$ pairs of $(w_i,x_i)$
$$\text{step}(w_i,x_i)=w_i-a x_i \langle w_i, x_i \rangle$$
Below is a readable but very slow version ...
- 6,767
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1
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Minimizing computational time for a quantum walk problem
Any suggestions as to how to speed up the computational time for this quantum walk problem which is coded using a normalized SparseArray coin operator as follows:
...
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Values of counting functions
I have a table of integers, say A, and consider the counting function C, which, for a given x, gives the number of elements in A which are less or equal to x. Next, I want to plot C(x) in some range, ...
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How to speedup integration of interpolated function with logarithmized data?
Consider some dataset corresponding to the grid x1, x2, function[x1,x2]:
...
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Why does Mathematica take so long to produce this sound?
Mathematica is behaving very slow, but it is not like I could compare, as the speed has always been like this. The following ran in 58.64 seconds. Is this normal? How can I speed it up?
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Efficient evaluation of vector inner products [closed]
I have a situation where I'm trying to quickly evaluate elements of some matrix products. Let $A, B$ be two Hermitian random matrices, and suppose that we have solved the eigenvalue problem for $A$. I ...
- 647
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Smoothening noisy distributions to learn eigenvalue statistics
I have a problem involving random matrices, in which I'm trying to learn properties of their spectral statistics. The problem I'm having can be boiled down to a list management issue, but I will begin ...
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4
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Speeding up Gaussian sampling
Edit Greg Hurst answers show how to independently get 3x speed-up using single-threaded MKL implementation and 4x speed-up by using native implementation with multi-threading, can they be combined?
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How to speedup calling the interpolation function? [duplicate]
Consider the following data:
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34
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Compile a code evaluating a condition only if another condition is positive
Consider the following three tables:
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How to assign a new value to the table inside Compile?
Consider some tables and function func:
phivals=RandomReal[{-Pi,Pi},10^5];
func[phi_]=phi^5*Exp[-phi];
acc=Table[0,10^5];
I ...
- 5,102
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Arrange 1-n^2 in n×n grid satisfy products of rows equal to products columns
For which $n\in\mathbb{N}$ is it possible to arrange $\{1,…,n^2\}$ in an $n\times n$ grid so that the set of products of columns equals the set of products of rows?
I can find solution for $3\times 3$ ...
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3
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1
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Why the ugly code is faster than the pretty code?
The task
Consider two tables, Tab1,Tab2, that include some real-number data. I need to evaluate the product of some boolean conditions on the value of some function ...
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How to generate points belonging to some region very fast?
Consider two variables Ex,th. th ranges within
thmin=10^-5;
thmax=Pi/2;
while ...
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Solving $\sum_i a_i p_i^k=b_0$ for $k$
Is there a fast way to find $k$ in the equation below for positive reals $a_i,p_i,b_0$?
$$\sum_i^d a_i p_i^k=b_0$$
Constraint of the problem means $p_i$ is very close to 1, so $p_i \approx \exp(p_i-1)$...
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How to keep lines on boundary or inside a region?
This post is related to one of my previous posts. My goal is to keep only the lines that fall on the boundary (2, 8) or inside the region ...
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3
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Compile code involving two matrix multiplications
Consider the following simple matrix operation ($a_j, b_j, z, w$ are matrices)
$$ w=\sum_j a_j\cdot z\cdot b_j$$
For performance reasons I am compiling the code
...
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70
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1
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2
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How to find the minimal and maximal polar angles covered by the following domain?
Consider some region in 3D space. Example is
reg = Cylinder[{{0, 24, 14}, {0, 42.7, 14}}, 9]
I want to find the minimal and maximal polar angle $\theta = \arccos\...
- 5,102
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3
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54
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Efficient and compact replacement for Association in the following case
Consider the following association:
...
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3
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272
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Efficient eigendecomposition of DPR1 matrices
I'm finding that the following bit is the bottleneck in my code
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Position command runs much slower for range containing numerically evaluated Bessel function
I have a long list (about 10000) of positive numbers (here simply denoted list), for which I want to find the positions of elements lying between 0.5 and the first ...
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How to minimize computational time in an if condition?
I have a code as below:
...
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Why do some functions, or at least, PowersRepresentations, run far faster on subsequent calls? What determines this behaviour?
Say I run the following:
PowersRepresentations[4782969,4,2]
and it takes about 2 minutes. If I call it again it takes only about 0.0005 seconds.
What determines ...
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Why does Module slow down StringMatchQ by 180 times?
I knew that Module is slower than With or Block, often by several times. But it surprises me ...
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37
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Why Names will search all subcontexts?
My version is 13.2. When debugging I came across this peculiar feature of Names.
Starting with a fresh kernel, define
Then ...
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8
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1
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232
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Troubleshooting Compile making things slower
I'm trying to speed up the following piece of code which runs in about 0.5 seconds on my machine.
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37
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How to plot a function efficiently without having to recalculate
I have to make a lot of graphs for two different functions Nzzp (which can be computed quickly without problem) and NzzG which requires three numerical integrations in a row so I'm using paralleltable ...
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Reduce max memory requriement for Kuramoto model code
I have some code for running the Kuramoto model on a random graph. Even with 128GB of virtual memory assigned, the routine sometimes exceeds its maximum allowance and is killed (I am running this on a ...
- 1,619
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Find all ways to split a list into k sublists (of different length)
I would like to write an efficient code for splitting a set into k disjoint subsets, whose union would be the input set. The input set is represented by sorted lists with no repetitions, and the ...
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Quickly summing matrix elements
I have a pair of rank-4 tensors, (T,V), where each index takes four values. I want to quickly contract these with the rank-4 antisymmetric tensor using the following operation:
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Efficient memory usage while building a large sparse matrix
I am sure the following problem has been solved already, but I am unable to find any solution... Any help appreciated!
So I am building a pretty huge matrix (or tensor, actually) using
...
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71
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Mathematica does not recognize all CPU kernels/cores [closed]
I am using Ubuntu 22 and Mathematica 13. According to the description of my laptop I should have four CPU cores, as seen in the following screenshot:
However, Mathematica only seems to recognize two ...
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Why does `MemoryInUse` keep increasing?
Consider MemoryInUse. After kernel initiation, I have noticed that its value keeps increasing, even when not evaluating any cell, as seen
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2
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Bugs with computational geometry: versions 12.2 vs 13.2
Updated
System Info: HONOR laptop AMD Ryzen 5 4600H 3Hz 6 cores 16GB Memory,
Windows 10 Pro 64 bit with updates.
Mathematica Info: Versions 12.2 and 13.2, both on the same laptop.
Examples:
...
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105
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How to gather functions which intersect at the same point?
How to gather functions which intersect at the same point (real solution)?
func = {2 x, x^2 + 1, (x^3 + 3)/2};
For example, with the list of functions above I ...
- 2,263
14
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432
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Memory leak with Mathematica Graph functions
I am running Mathematica 13.2 on a Mac OS Monterey. I have a large code that manipulates graphs both in graph form and as adjacency matrices, computes some graph properties, and returns a list. It has ...
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Slow performance of SequenceCases
While working on a solution to another question, I noticed some performance regression slow performance of SequenceCases and friends. Consider a problem of finding zeroes of a function, given a sorted ...
- 5,021
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1
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NIntegrate: slow convergence error and speed efficiency [closed]
I am trying to produce a plot but NIntegrate is very slow and making a number of warnings, I have used UnitStep[] to keep the ...
6
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2
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689
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NDSolve very slow on 2D heat equation
I am trying to solve the 2D heat equation
$$
\begin{cases}
u_{t}-u_{x x}-u_{y y}=f \\
u(0, x, y)=\sin (2 \pi x) \sin (2 \pi y) \\
u(t, 0, y)=0 \\
u(t, x, 1)=0 \\
u_{x}(t, 1, y)=2 \pi e^{-t} \sin (2 \...
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1
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RegionIntersection runs for a very long time and then aborts without returning a result
Is there a good strategy to speed up RegionIntersection computations like the one below:
...
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6
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0
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81
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3D region best way to create signed coastal distance?
As a test, I'm trying to create a signed coastal distance map of the world (assumed perfectly spherical), using the first 1800x900 image above, which I converted to the 2nd image above using ...
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How to refer to calling notebook instead of my personal include? / detector for high-memory-usage cells
Along the lines of a couple previous posts, I coded this function to show you where in your notebook your biggest space-wasters are. Useful for when your file is becoming huge and unmanageable for ...
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Optimize search for rational numbers on unit circle?
Crossposted: https://community.wolfram.com/groups/-/m/t/2763509
I'd like to classify rational numbers on a unit circle by the following property: number of digits in the denominator. It relates to an ...
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What is a good way to compute successive primorials with Mathematica?
Recall that the primorial of a positive integer $n$ is the product of the prime numbers smaller than $n$. One can define a primorial function in Mathematica quite easily:
...
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5
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Speed up replacement of very large alternatives expression
I'm doing a computation which effectively has the same issue as this code:
Range@1000000 /. (Alternatives@@RandomSample[Range@1000000,500000]) -> 0
i.e. ...
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