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Questions tagged [performance]

Questions about the execution speed and memory usage of algorithms, data structures, languages and libraries.

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4 votes
1 answer
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Does it make sense to build ATLAS from source on a cloud machine?

ATLAS is an extremely popular linear algebra library. When you install ATLAS from source, it tries to automatically tune a number of parameters to give you the fastest code. Does it make sense to do ...
Thomas Johnson's user avatar
10 votes
1 answer
3k views

Fortran 90/95: Deallocating variables

I understand the crucial importance of freeing memory when certain variables or arrays need to be reused later in the program, or may not be in use for a while. However, in my experience with ...
Salim's user avatar
  • 165
1 vote
2 answers
97 views

Performance metrics to compare initial-boundary value problem solutions

I am comparing the performance several finite difference methods of solving an initial-boundary value problem. There are several dimensions to this comparison: Number of cells Number of timesteps ...
Neal Kruis's user avatar
4 votes
1 answer
403 views

Fast way to repeatedly solve a small nonlinear equation system

A small nonlinear equation system (sizes around 12 ✕ 12) needs to be solved repeatedly (millions of times); each time with some variation in parameters/coefficients (although the equation set is ...
e.tadeu's user avatar
  • 149
4 votes
2 answers
761 views

Finding the minimum hamming distance between a bit vector and any pairwise intersection of multiple bit vectors

I'm looking for a way to optimize this procedure. This is the problem: I have a list of bit vectors $\mathbf{A} = [ a_1, a_2, a_3, ..., a_n ]$ I have a list of bit vectors $\mathbf{B} = [ b_1, b_2, ...
dktyph's user avatar
  • 41
4 votes
2 answers
559 views

Why is computational cost measured in Floating Pt. Ops. in times of parallel computing?

In times of parallel computing, it seems to me that algorithms (also basic ones, like matrix-vector multiplication) should be measured by their dependent steps (that use results from steps before) ...
Bananach's user avatar
  • 799
9 votes
10 answers
5k views

Is it possible to optimise this integration code so that it runs faster?

...
user2970116's user avatar
4 votes
1 answer
664 views

Increasing thread number degrades performance

I have a problem with parallelization and the brownian dynamics (molecular dynamics) code that I am using. We have our own home-grown framework at the university, and recently we've made the change ...
NuclearAlchemist's user avatar
8 votes
1 answer
510 views

WELL pseudo-random number generations

I've used MT19937 in a test harness to generate uniformly (unsigned) 32-bit [0, $2^{32}$- 1] values, based on the original Authors' mt19937.c implementation, to ...
Brett Hale's user avatar
8 votes
1 answer
3k views

What is the best way to multiply a diagonal matrix (in fortran)

What is the best way to compute: $$ Y = D X $$ where $D \in \mathbb{R}^{m\times m}$ is diagonal and $X \in \mathbb{C}^{m \times n}$ is general. I am mostly interested in these two cases: $m >> ...
Max Hutchinson's user avatar
2 votes
2 answers
189 views

Ways to speed up the computations

OK, I have a FORTRAN code which numerically integrates equations of motion for large data sets of initial conditions. I run this program in my PC and it requires about 1 day of computations per data ...
Vaggelis_Z's user avatar
5 votes
1 answer
210 views

What is the correct way of performing numerical experiments on desktops?

Suppose I want to set up an experiment to measure the performance of some numerical code on a desktop machine running Linux/Windows/MacOS. What kind of environment should I arrange in order to get ...
faleichik's user avatar
  • 1,832
4 votes
1 answer
116 views

What is the added cost of generalizing an eigensystem?

Problem Let's say I can write a model as the Hermitian eigensystem: $$ A x = \lambda x $$ where $A \in \mathbb{C}^{n\times n}$ is Hermitian, or as the generalized Hermitian eigensystem: $$ \tilde A \...
Max Hutchinson's user avatar
4 votes
1 answer
185 views

Using PAPI in PETSc code

I am trying to count the number of cache misses, total cycles, etc. per iteration of a for loop inside MatMult_SeqSBAIJ_2() . I'...
i8086's user avatar
  • 61
6 votes
2 answers
644 views

Why performance is given in Gflop/s rather than actual time in seconds

While reading many research-papers comparing parallel implementations of algorithms on different machines/architectures, I have noticed that the performance comparison is always listed in terms of ...
gdawg's user avatar
  • 61
10 votes
2 answers
368 views

What is the underlying structure of scientific code performance?

Consider two computers with different hardware and software configurations. When running the exact same serial Navier-Stokes code on each platform it takes x and y time to execute one iteration for ...
Isopycnal Oscillation's user avatar
6 votes
1 answer
118 views

Measures of parsimony for numerical models?

There are hundreds of different types of performance measures for numerical models, many of which are applicable to many different types of models. But a good model doesn't just perform well, it ...
naught101's user avatar
  • 373
10 votes
3 answers
8k views

Nvidia K20X vs GeForce Titan for GPGPU acceleration

Im trying to understand the difference between these two graphics cards for academic computing, specifically for the DGEMM component. If we look at the raw statistics, both have the same GK110 chip, ...
Ophion's user avatar
  • 153
14 votes
3 answers
2k views

Comparison of iteration methods: number of iterations vs. cpu time

I am comparing two iterative methods for inverting random square matrices. Since the matrices are random, every test case takes both different amounts of iterations and different elapsed times. My ...
Srijan's user avatar
  • 365
13 votes
3 answers
1k views

Is there any benefit to compiling LAPACK from source versus installing the prebuilt package from Ubuntu?

I know that ATLAS is able to optimize itself for the machine it is compiled on and thus maximum benefits are found by compiling from source. Is there any benefit to compiling LAPACK from source? It ...
OSE's user avatar
  • 397
16 votes
3 answers
17k views

What is the fastest way to compute all eigenvalues of a very big and sparse adjacency matrix in python?

I'm trying to figure out if there is a faster way to compute all the eigenvalues and eigenvectors of a very big and sparse adjacency matrix than using scipy.sparse.linalg.eigsh As far as I know, this ...
Noam Peled's user avatar
6 votes
1 answer
550 views

Reference BLAS/LAPACK from NETLIB is twice as fast as MKL for complex numbers

I'm solving the Helmholtz equation using PETSc. I found with the PETSc configure option --download-f-blas-lapack my program runs twice as fast over running it with ...
Hui Zhang's user avatar
  • 1,319
2 votes
0 answers
476 views

Prediction model on GPU [closed]

I am doing a small project at school. I have done my code implementations in CUDA and did some performance measurements with real values, i.e. running the program with different number of threads, ...
BRabbit27's user avatar
  • 1,029
2 votes
2 answers
249 views

Speedup prediction of rotating mask filter

I am trying to do the speed up analysis of the rotating mask filter (section 4.2.3). Let $N^2$ be the pixels in the image and let $m^2$ be the neighborhood of a given pixel, what I have for my ...
BRabbit27's user avatar
  • 1,029
9 votes
2 answers
473 views

How do Volkov and Demmel experimentally determine the latencies, line sizes, and page sizes of a GPU?

In "LU, QR and Cholesky Factorizations using Vector Capabilities of GPUs", by Vasily Volkov and James Demmel, there is an interesting way to interpret the latencies, line sizes, and page sizes of a ...
John Hoffman's user avatar
2 votes
2 answers
4k views

Matlab element within ranges and distance between two points

I have a $53534\times 3$ matrix with $x$, $y$, and $z$ coordinates. I want to find the element of matrix within ranges as follows: ...
user avatar
3 votes
3 answers
311 views

How do I get reliable timing data for time spent in function calls in my code?

This question is a follow-up to Fortran: Best way to time sections of your code?. If I want to time functions in my code, I know I could use gprof or kcachegrind. I also know that the results from ...
Geoff Oxberry's user avatar
4 votes
1 answer
1k views

Effecient CFD programming techniques

I'm trying to make highly efficient CFD programming complex for solving combustion problems. I've finished writing core which realises mathematical model, and now I'm concerned about code performance. ...
Yakovenko Ivan's user avatar
10 votes
1 answer
722 views

What is the impact of C++11 move semantics in the context of scientific computing?

C++11 introduces move semantics which can, for example, improve code performance in situations where C++03 would need to perform a copy construction or copy assignment. This article reports that ...
okmatija's user avatar
  • 505
20 votes
1 answer
3k views

How does the performance of Python/Numpy array operations scale with increasing array dimensions?

How do Python/Numpy arrays scale with increasing array dimensions? This is based on some behaviour I noticed while benchmarking Python code for this question: How to express this complicated ...
Nat Wilson's user avatar
6 votes
5 answers
303 views

Evaluate the sum

I want to evaluate the sum $$\sum_{k=1}^\infty \left(\frac{i+1}{\sqrt{2}}\right)^k\cdot k^{-\alpha}$$ where $i=\sqrt{-1}$ and $\alpha\in[\frac{3}{4},1]$ with 8 digits accuracy. If I am willing to ...
Qomo's user avatar
  • 61
13 votes
5 answers
2k views

Calculation of the sparsity structure for finite element matrices

Question: What methods are available to accurately and efficiently calculate the sparsity structure of a finite element matrix? Info: I'm working on a Poisson Pressure Equation solver, using Galerkin'...
John Edwardson's user avatar
2 votes
0 answers
600 views

Cusp Library performance worse than PETSC (GMRES 200 iterations) Why?

I wanted to compare the speeds of the GMRES implementations in the CUSP and the PETSc libraries. The matrix (A) used for testing was a 3d Laplacian matrix obtained by using the 7 point stencil on a ...
smilingbuddha's user avatar
11 votes
1 answer
259 views

Statistical models for local memory/compute, network latency, and bandwidth jitter in HPC

Parallel computation is frequently modeled using a deterministic local rate of computation, latency overhead, and network bandwidth. In reality, these are spatially variable and non-deterministic. ...
Jed Brown's user avatar
  • 25.7k
10 votes
3 answers
276 views

Literature references for modeling current and future energy costs of floating-point operations and data transfers

I am searching for the most important literature and slide references for modeling current and future energy costs of floating-point operations and data transfers across the CPU, memory, network, and ...
12 votes
3 answers
6k views

Memory usage in fortran when using an array of derived type with pointer

In this sample program I'm doing the same thing (at least I think so) in two different ways. I'm running this on my Linux pc and monitoring the memory usage with top. Using gfortran I find that in the ...
chris's user avatar
  • 1,045
8 votes
1 answer
3k views

How to get sparse complex matrices from my code to PETSc efficiently

What is the most efficient way to get a complex sparse matrix from my Fortran code to PETSc? I understand that this is problem dependent, so I tried to give as many relevant details as possible below. ...
Ondřej Čertík's user avatar
16 votes
2 answers
2k views

Open source implementation of rational approximation to a function

I am looking for some open source implementation (any of Python, C, C++, Fortran is fine) of rational approximation to a function. Something along the article [1]. I give it a function and it gives me ...
Ondřej Čertík's user avatar
4 votes
1 answer
129 views

Efficient way to find max height repetitive sub-trees in an object tree

I am trying to solve a problem of finding a max repetitive sub-tree in an object tree. By the object tree I mean a tree where each leaf and node has a name. Each leaf has a type and a value of that ...
Trident D'Gao's user avatar
9 votes
2 answers
398 views

Fastest way to find eigenpairs of a small nonsymmetric matrix on a GPU in shared memory

I have a problem where I need to find all positive (as in the eigenvalue is positive) eigenpairs of a small (usually smaller than 60x60) nonsymmetric matrix. I can stop calculating when the eigenvalue ...
Kantoku's user avatar
  • 91
3 votes
2 answers
216 views

Efficiently changing basis on many diagonal matrices

I have to perform a [complex] basis transformation on a large number of [real] diagonal matrices: $$ \langle b_i | A | b_j \rangle = \sum_k \langle b_i | \bar{b}_k\rangle \langle\bar{b}_k | A | \bar{b}...
Max Hutchinson's user avatar
8 votes
2 answers
310 views

How should I report profiling/timing information about my code?

I've seen a lot of publications in Computational Physics journals use different metrics for the performance of their code. Especially for GPGPU code, there seems to be a great variety of timing ...
limes's user avatar
  • 405
31 votes
4 answers
2k views

What tools or approaches are available to speed up code written in Python?

Background: I think I might want to port some code that calculates matrix exponential-vector products using a Krylov subspace method from MATLAB to Python. (Specifically, Jitse Niesen's expmvp ...
Geoff Oxberry's user avatar
4 votes
1 answer
569 views

Intersection of hyperplanes

A very basic question but i couldn't find another post about it: Given $p$ non parallel hyper-plane in $\mathbb{R}^p$: $\left(\begin{array}{cccc} c_{11} & a_{11} & .... & a_{1p} \\ ... &...
user189035's user avatar
11 votes
3 answers
3k views

What is the overhead in sparse matrix multiplication

Does matrix multiplication (both Mat*Mat, and Mat*Vec) scale with number of non-zeros, or with the size of the matrix? Or some combination of the two. What about with shape. For example, I have a ...
Andrew Spott's user avatar
  • 1,155
4 votes
2 answers
2k views

How should I build a 2D 5-point stencil Laplacian matrix in parallel?

I'm making a simple eigenvalue solver with SLEPc, using a 5-point stencil and the finite difference method. I want to be able to assemble the matrix in parallel. My first thought was just to use <...
Dan's user avatar
  • 3,355
11 votes
3 answers
314 views

How to implement efficient indexing function for two particle integrals <ij|kl>?

This is a simple symmetry enumeration problem. I give the full background here, but no knowledge of quantum chemistry is needed. The two particle integral $\langle ij|kl\rangle$ is: $$ \langle ...
Ondřej Čertík's user avatar
10 votes
3 answers
6k views

MATLAB matrix multiplication (the best computational approach)

I have to make a coordinates transformation between two reference systems (axes). For that, three matrices ($3\times3$) have to be multiplied due to some intermediate axes being used. I have thought ...
julianfperez's user avatar
68 votes
10 answers
16k views

What are some good strategies for improving the serial performance of my code?

I work in computational science, and as a result, I spend a non-trivial amount of my time trying to increase the scientific throughput of many codes, as well as understanding the efficiency of these ...
Aron Ahmadia's user avatar
  • 6,901
18 votes
4 answers
5k views

Portable multicore/NUMA memory allocation/initialization best practices

When memory bandwidth limited computations are performed in shared memory environments (e.g. threaded via OpenMP, Pthreads, or TBB), there is a dilemma of how to ensure that the memory is correctly ...
Jed Brown's user avatar
  • 25.7k