Questions tagged [performance]

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

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Calculating the number of Flops of SPH density calculation

I would like to calculate the number of floating point operations (Flops) my code is performing in my machine. To do so, I would like to be sure I am counting the operations in the inner-most loop ...
25
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8answers
5k views

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 ...
-2
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1answer
63 views

How to get 10 in computer science, using the number 4 exactly four times, and two signs exactly and two operation + exactly? [closed]

How to get 10 in computer science, using the number 4 exactly four times, and two signs exactly and two operation + exactly ?
0
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1answer
98 views

What are the advantages and disadvantages of using norm error control in the MATLAB ODE suit?

In MATLAB's ODE suit, there seem to be two basic methods of controlling the Local Truncation Error (LTE) of the ODE which the user can choose from, namely: The absolute error control (default), ...
2
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1answer
34 views

In Eigen, can a sparse matrix contain vectors/objects instead of simple scalar values?

I need to have a sparse matrix whose elements are not simple numbers, but objects, e.g. a couple of floating point values and a bunch of integer indices. I am wondering if Eigen has something similar, ...
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2answers
8k views

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: ...
1
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1answer
67 views

An efficient algorithm to find Nearest Neighbours

So imagine I have a $m$ vectors each of dimension $d$. Lets call them, $\vec x_{i}$, with $i = 1, 2, 3, 4, 5, \dots, m$. Now the idea is to find the neighbours of $\vec x_{i}$ (calling them $\vec x_{j}...
5
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1answer
121 views

Accurate and efficient computation of the logarithm of the ratio of two sines

For exploratory work related to special function implementations, I need to compute $\log \frac{\sin y}{\sin x} $, where $0 \le x \le y \le 2x < \frac{\pi}{2}$. Cases with $x \approx y$ in ...
1
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1answer
496 views

How to calculate the number of floating point operations a task/ process requires? (not FLOP/s, but FLOP)

There have been many papers quoting FLOP to quote the performance of a specific approach in machine learning. For example, We trained two models with different capacities: BlazePose Full (6.9 MFlop, ...
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0answers
35 views

Why are "instructions retired" more stable than "cycles" or "task-clock" when using "perf"?

I tested the perf tool in Ubuntu 18.04 on a simple benchmark in our compiler (parsing some file). I ran perf several times and ...
2
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0answers
80 views

Whi are chi-squared distributions in (C++) boost::random and C++ STL faster than in boost::math?

I am trying to generate random chi-squared numbers in C++, according to some degree of freedom (which can be a float). Several libraries can be used for that purpose, among which the C++11 Standard ...
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0answers
71 views

Fastest way to solve linear programming with 6 complex inequalities and 5 nonnegative variables

I have a program where I need to solve a linear programming problem in a fast loop. The language I'm using is Java and any kind of bindings to other languages are not acceptable. Libraries might be ...
2
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1answer
210 views

Sparse matrix-matrix multiplication using AVX2

I have two sparse general matrices stored in CSR format I need to multiply. Is there any chance to gain performance using AVX2? In general the matrices are big (hundreds of millions of non-zeros and ...
9
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1answer
2k views

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 ...
0
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0answers
262 views

Parallel plate capacitor as simple superposition of Coulomb-fields

I am trying to calculate and visualize the electric field inside and outside of a parallel plate capacitor by assuming a uniform distribution of point charges on each plate and by adding up the ...
4
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2answers
406 views

Fastest Way to Mutiply $10^4$ 2x2 Matrices

In a code that I work with (written in python, but also tagging as matlab because numpy is so close and I could use it if need be), we use a transfer matrix method to compute the properties of a ...
2
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0answers
55 views

Avoid matrix multiplication in algebraic multigrid method

Currently when I try to solve a linear algebra system of the form of $A x =b$ I use the algebraic multigrid method. The algebraic multigrid method uses a Galerkin product to form the coarse grid ...
4
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1answer
83 views

Is operation count a reliable predictor of performance when comparing two formulations?

I have two formulations to solve a problem (both give dense, complex and symmetric system). They are solved multiple times in a loop. I am trying to predict which is better to use. The first one ...
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0answers
21 views

Speedup of CPU Pipelining by number of steps [closed]

When a CPU has $K$ steps the speed up of using pipelining compared to non-pipelining is $K$. But what I want to know is, say I am a CPU designer and want to decide whether I should build $K$ or $N$ ...
1
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1answer
124 views

Vectorization of Jacobi iteration

Assume I have a linear system of $A x = b$ which I want to solve with Jacobi iteration. Matrix $A$ is given in CSR format. The vectors are dense. The code for Jacobi iteration is quite clear and can ...
2
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1answer
113 views

Efficiently finding binary vectors satisfying multiple conditions

I am trying to solve the following problem: Given a binary matrix $\mathbf{A} \in \{0,1\}^{m \times n}$ and a vector $\mathbf{b} \in \mathbb N^n$, does there exist a binary vector $\mathbf{c} \in \{0,...
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1answer
68 views

How to avoid unnecessary checks when inverting this LU decomposition

Background for the question I am currently working on a Matlab code in which the systems of linear equations $Ax_1 = b_1$, $Ax_2 = b_2$, ... have to be solved. As the matrix $A$ is constant during ...
2
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1answer
424 views

Implementation of Jacobi iteration

I have implemented the Jacobi iteration in C++ using a dense vector and a sparse matrix in CSR format. The code is as follows: ...
4
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1answer
355 views

Improve Mandelung constant code

I'm learning and improving my Python skills. I did a program in Python about Mandelung constant. But, I'm having kind of a problem. The Mangelung constant is calculated using this sum: $$ V_{total} =...
5
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0answers
328 views

Is there any catch on using `zgemm3m` vs regular `zgemm`?

I've just (to my embarrassment) encountered a BLAS-like extension of a matrix-matrix product subroutine gemm in Intel MKL: gemm3m...
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1answer
109 views

How to implement this even-odd matrix decomposition efficiently?

Note: This question has also been asked on stackoverflow - see https://stackoverflow.com/questions/57197910/how-to-implement-this-even-odd-matrix-decomposition-efficiently?noredirect=1#...
2
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2answers
79 views

Time complexity analysis

I want to know the time complexity of following code Say I have a list unique_element[] There is an array which contain elements {4,5,2,4,7,8,1,5,9,8,1} Now as per my code I want to find out the ...
5
votes
1answer
189 views

Whittaker-Shannon interpolation: Accuracy dies with speedup; can it be fixed?

With a truncated Whitaker-Shannon series (cardinal series) $$ f(t) = \sum_{j = 0}^{n-1} y_{j} \frac{\sin\left(\pi( \frac{t-t_0}{h} -j)\right)}{\pi\left(\frac{t-t_0}{h}-j\right)} $$ we can naively ...
3
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1answer
195 views

Radiation heat transfer between surfaces

I'm trying to model the temperature distribution over a curved surface. Apart from the heat equation, I need to take into account the energy emission/absorption through electromagnetic radiation. The ...
6
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2answers
2k views

Fast and Numerically Stable Pairwise Distance Algorithms

I'm looking for resources on fast, numerically stable pairwise euclidean distance algorithms. In particular, suppose $A \in \mathbb{R}^{M \times D}$ and $B \in \mathbb{R}^{N \times D}$ are two sets of ...
9
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2answers
4k views

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 ...
3
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1answer
415 views

MKL/FFTW performance of batch 1-D FFTs

MKL and FFTW offer 1-D FFTs that can operate on many inputs simultaneously - in other words, they can batch-transform the columns of some input matrix. Is the performance of these multi-transforms ...
3
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1answer
335 views

What is the fastest way to solve Ax=b (subject to constraints and an absolute term)

I am trying to solve/optimize $Ax=b$ in the least squares sense subject to box constraints; a few (less than 5) equality/inequality constraints; and an absolute function penalty (or some other ...
0
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1answer
272 views

CPU and GPU influence on task parallel execution performance

This question is mainly about hardware, but also about software. In my current work I have approximately 68 millions of combinations that I am iterating through, in parallel. For each of those ...
1
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1answer
1k views

General understanding of Intel MKL, threads and MPI

Preface I seem to lack a fundamental understanding of best practise recommendations given by Intels MKL user guides for using MKL in threaded applications. So let's clarify it together. Wording and ...
2
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1answer
388 views

Potential gain - Matlab vs C/C++ - assembly and eigenvalues

I have a Matlab code computing the solution to an eigenvalue PDE. It consists of two parts: assembly of the stiffness/rigidity matrices and solving a generalized eigenvalue problem. I mention that the ...
1
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1answer
1k views

Kronecker product among multiple arrays

I was wondering whether there is a smart and efficient way in Matlab to compute the kronecker product of several 1D arrays. What I mean is something like this ...
1
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2answers
184 views

Sign of integer determinant 4 by 4

I'm in the context of this publication: http://www.gilbertbernstein.com/resources/booleans2009.pdf I applied quantization to my point coordinates: All coordinates are integer lying in [0, 2 power 20]....
6
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1answer
2k views

Loop optimization with f2py, Cython and Numba

I tried to used f2py, Cython and Numba to make a simple loop structure be faster in python. Python implementation: ...
1
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1answer
396 views

Efficiency of Array Slicing

I have large arrays of data organized so that it can be processed efficiently using array processing libraries. However, there are times when I only need to process slices of the arrays where a slice ...
1
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0answers
604 views

Vectorizing Matrix Multiplication

I would like to do the following operation: I have a "4D" matrix A and a "3D" matrix B. Both A and B are actually 2D matrices, where for A, each element is a 2D matrix, and for B, each element is a 1D ...
0
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1answer
156 views

Find hidden sequence $a_n = a_{n-1} + T $ , with period $T$, given some "random" numbers

I have this data plotted on a graph in which all points have the same value on the y-axis, e.g a constant integer "c", while the x-axis is the time in seconds. So, for a c = 25 on the y-axis, there ...
3
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1answer
1k views

Why is the speed of the parts of the LU-decomposition so different?

I know that an easy way to solve the matrix problem $$A\cdot x=b$$ is the LU decomposition $$\begin{split} L,\,U&=\text{lu}(A)\\ y&=\text{solve}(L,\,b)\\ x&=\text{solve}(U,\,y) \end{split}$...
0
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1answer
69 views

Speeding up group apply in python

In my code it often happens that I need to calculate values for a group. For example, suppose there is the following data: ...
3
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0answers
403 views

MATLAB: solving multiple ODE systems in parallel

I have a system of parameterized ODEs that I would like to solve using MATLAB and its ode45 solver, and was wondering if it is possible to perform such a task in ...
1
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1answer
163 views

Efficiently determine whether a curve intersects a given rectangle?

Suppose we have a straight line in Cartesian space such that $$ x_k = x_0 + k \delta x, \quad \quad y_k = y_0 + k \delta y, \quad \quad z_k = z_0 + k \delta z $$ where $k$ can take any real value. If ...
1
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1answer
94 views

Declare variable to substitute one calculate only once

Frame of the question I am currently editing an add-on module to an ocean/circulation model, which is written in Fortran. The code of the main model is quite optimized with respect to short run time (...
3
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0answers
121 views

Finite difference method for coupled PDEs: optimizing performance (time step, iterations per step)

I'm solving coupled PDEs using finite difference method: Incompressible Navier-Stokes and the divergence-free induction equation (Maxwell's equations) with non-uniform electrical conductivity. The ...
5
votes
4answers
6k views

Beating typical BLAS libraries matrix multiplication performance

A dull matrix multiplication algorithm where we use the formula $$C_{ij}=\sum_{k}A_{ik}B_{kj}$$ By literally following this in 3 loops we'll get a very slow program, because we don't utilize ...
2
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2answers
2k views

CPU for ab-initio DFT calculations

I need to build a new desktop PC, where ab-initio DFT calculation going to be performed. I am searching for a CPU in value range 600 - 1000€. I was thinking about six-core Intel Core i7-6850K or 8-...