Questions tagged [performance]
Questions about the execution speed and memory usage of algorithms, data structures, languages and libraries.
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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 ...
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What makes Fortran fast?
Fortran has a special place in numerical programming. You can certainly make good and fast software in other languages, but Fortran keeps performing very well despite its age. Moreover, it's easier to ...
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7
answers
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Is algorithmic analysis by flop-counting obsolete?
In my numerical analysis courses, I learned to analyze the efficiency of algorithms by counting the number of floating-point operations (flops) they require, relative to the size of the problem. For ...
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How does the MATLAB backslash operator solve $Ax=b$ for square matrices?
I was comparing a few of my codes to "stock" MATLAB codes. I am surprised at the results.
I ran a sample code (Sparse Matrix)
...
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33
votes
5
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Performance differences between ATLAS and MKL?
ATLAS is a free BLAS/LAPACK replacement that tunes itself to the machine when compiled. MKL is the commercial library shipped by Intel. Are these two libraries comparable when it comes to performance, ...
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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 ...
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1
answer
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What is the preferred and efficient approach for interpolating multidimensional data?
What is the preferred and efficient approach for interpolating multidimensional data?
Things I'm worried about:
performance and memory for construction, single/batch evaluation
handling dimensions ...
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25
votes
8
answers
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Is it possible for user written algorithms to outperform libraries' built-in optimized functions?
I've always had this question in mind (even if it may sound vague), but in my numerical analysis courses we've always learned how to analyze and optimize code. However, since most linear algebra ...
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When should I use C++ expression templates in computational science, and when should I *not* use them?
Suppose that I'm working on a scientific code in C++. In a recent discussion with a colleague, it was argued that expression templates could be a really bad thing, potentially making software ...
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3
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Can diagonal plus fixed symmetric linear systems be solved in quadratic time after precomputation?
Is there an $O(n^3+n^2 k)$ method to solve $k$ linear systems of the form $(D_i + A) x_i = b_i$ where $A$ is a fixed SPD matrix and $D_i$ are positive diagonal matrices?
For example, if each $D_i$ is ...
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Intel Fortran Compiler: tips on optimization at compilation
I will start with my personal experience in our lab. Back in the ifort 9 and 10 days, we used to be quite aggressive with the optimizations, compiling with -O3 and processor specific flags (-xW -xSSE4....
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21
votes
1
answer
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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 ...
- 438
19
votes
6
answers
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To what extent is generic and meta-programming using C++ templates useful in computational science?
The C++ language provides generic programming and metaprogramming through templates. These techniques have found their way into many large-scale scientific computing packages (e.g., MPQC, LAMMPS, CGAL,...
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4
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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 ...
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16
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2
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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 ...
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15
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4
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How to deal with too much data?
Our plasma dynamics simulations often produce too much information. During the simulations we record various physical properties on a grid (x,y,z,t) that is as large as (8192x1024x1024x1500), for at ...
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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 ...
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14
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3
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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 ...
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13
votes
3
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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 ...
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13
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4
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FLOP counting for library functions
When evaluating the number of FLOPs in a simple function, one can often just go down the expression tallying basic arithmetic operators. However, in the case of mathematical statements involving even ...
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5
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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'...
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3
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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 ...
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3
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In what application cases are additive preconditioning schemes superior to multiplicative ones?
In both domain decomposition (DD) and multigrid (MG) methods, one may compose the application of the block updates or coarse corrections as either additive or multiplicative. For pointwise solvers, ...
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3
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How to properly calculate CPU and GPU FLOPS performance?
Problem
I'm trying to calculate CPU / GPU FLOPS performance but I'm not sure if I'm doing it correctly.
Let's say we have:
A Kaby Lake CPU (clock: 2.8 GHz, cores: 4, threads: 8)
A Pascal GPU (clock: ...
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12
votes
2
answers
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Octave: calculate distance between two matrices of vectors
Suppose I have two matrices Nx2, Mx2 representing N, M 2d vectors respectively.
Is there a simple and good way to calculate distances between each vector pair (n, m)?
The easy but inefficient way is ...
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11
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3
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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 ...
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11
votes
2
answers
869
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Faster Logistic Function
I've noticed that a fairly significant number of cycles in one of my programs are being consumed by the logistic function:
$$f(x)=\frac{1}{1+e^{-x}}$$
Is there a good approximation I can use to reduce ...
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11
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2
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359
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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 ...
11
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3
answers
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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 ...
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11
votes
1
answer
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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. ...
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10
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3
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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 ...
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3
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The real myth of GPU (specifically CUDA) really speed up FEM/CFD
Now I have been believing that FEM/CFD is supposed to be faster on a GPU unit - here I am using CUDA as solid example. However, I have not been able to find a convincing paper where the benchmark ...
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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, ...
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1
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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 ...
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4
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Are DAXPY, DCOPY, DSCAL overkills?
I have implemented CG in FORTRAN by linking it to Intel MKL.
When there are statements like:
(Refer Wikipedia)
p=r;
x=x+alpha*p
r=r-alpha*Ap;
or similar ...
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10
votes
1
answer
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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 ...
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3
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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 ...
9
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9
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2
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Is there an algorithm or graph theory that allows me to not need to store an intermediate matrix when calculating AT*Y1*A + BT*Y2*B?
I have a system of conductors for which there are two dense matrices of the (complex) mutual admittances, $Y_A$ and $Y_B$, which are symmetric. Then, an equivalent nodal admittance matrix $Y_N$ is ...
9
votes
1
answer
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Increasing computational performance by using 16 bit numbers
I recently found the following article where it was stated that using 16 bit numbers can be used to increase the computational performance of AI applications. According to the article numbers above 16 ...
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votes
2
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Integer operations vs floating point operations
I have been working with an algorithm, which uses
additions of floating point vectors,
(sparse matrix of floats)x(dense vector of floats) dot products
I recently found out that I can get the same ...
9
votes
3
answers
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What is the fastest opensource implementation of Bessel functions computation?
I'm looking for an open-source (to use and learn from) software which computes Bessel functions of integer order of real argument to double precision the fastest among all such implementations. ...
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2
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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 ...
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2
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Which Sparse Matrix Solver Libraries can I run on Android?
The title says most of it.
I'm looking for a lightweight and easy-to-use library that I can use for Android (NDK) projects.
For dense stuff I like using Eigen but I haven't found many comprehensive (...
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2
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397
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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 ...
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How do I compute the parallel overhead of a parallel code run on a single processor when no sequential code is available?
I'm profiling the performance of PETSc's linear solvers. As I understand it,
$$\text{speedup}=\frac{\text{Sequential Time}}{\text{Parallel Time}}.$$
I know that running the parallel code on one ...
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4
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(How) do you take into account memory fragmentation?
I use an example from finite element theory, but anybody who maintains a large datastructure and successively extends it will find something similar.
Suppose I have an unstructured mesh of points and ...
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1
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Hardware performance, floating point functions
First of all, hope I've found the right forum for this question, if I haven't please pass me on to a one which would fit better.
Out of curiosity from an argument with someone who may or may not be ...
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What is the best way to multiply a diagonal matrix (in fortran)
What is the best way to compute:
$$ 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 >> ...
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votes
2
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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 ...
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