Questions tagged [efficiency]
The efficiency tag has no usage guidance.
68 questions
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Are there any efficient numerical methods to solve the recurrence relation of a function？
First, the recurrence relation is:
$$\pi_{k+1}(\omega)=(\omega-\alpha_k)\pi_{k}(\omega)-\beta_k\pi_{k-1}(\omega),$$
where
$$\alpha_k=\frac{\int_0^\Lambda\omega\pi_{k}^2(\omega)h^2(\omega)\text{d}\...
- 31
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36
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Fastest way to calculate the eigenvector with the largest eigenvalue for a 3*3 positive-definite matrix [duplicate]
As stated in the title: I have a 3 by 3 positive-definite matrix $M$. What I need is the eigenvector corresponding to the largest eigenvalue, since I am calculating the solution to maximize the value ...
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453
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How to leverage the GPU for parallel 3-body problem computations
I have a 3-body simulation which must run millions of times.
As far as I know, the GPU shines when it gets to preform simple operations on huge matrices/arrays. Currently I'm debugging and running my ...
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152
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Single precision vs double precision conjugate gradients
I tested my conjugate gradients implementation with float and double precision and contrary to my guess the double code was twice faster than the single precision code. The reason is that I need many ...
- 2,882
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114
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Efficient heat diffusion implementation with varying coefficients
I have the following heat diffusion equation:
\begin{alignat}{3}
\partial_t u(t, \vec{x}) &= g(\vec{x})\Delta u(t,\vec{x}), &\quad& \vec{x} \in\Omega, \, t\in(0,\infty],\\
\partial_n u(t,\...
- 2,882
2
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1
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93
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Best approach to simulating dynamics on networks
I have been recently getting into the field of various processes on networks. For example, stochastic processes like percolation, Ising models, various statistical-physics models; or deterministic ...
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3
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197
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Inefficient comparisons of custom data type C++
I've got some code that I need to squeeze every bit of both time and space out of. I'm looking for a better solution to the following problem.
For reasons outside of the scope of this question, I ...
- 113
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109
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Dense factorization specialized for RBF-FD method
In RBF-FD methods (see Fornberg & Flyer. A Primer on Radial Basis Functions with Application to the Geosciences. SIAM, 2015. Chapter 5.), the finite-difference stencil coefficients for a set of ...
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146
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Computing pairwise distances in a grid efficiently
I have a spline-based model where I have a set of control points in 3D space. I want to compute pairwise distances between every point on a regular 3D grid and these control points. Is there an ...
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168
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Efficiency of developing PDE solvers using sparse matrices versus loops
I am new to solving PDEs, but have been looking at different implementations of finite difference and finite volume schemes. One thing I have noticed in different implementations is that some ...
- 297
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724
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Incomplete Cholesky preconditioner for CG efficiency
I am currently solving the harmonic equation using a P1 FEM discretisation. The resulting matrix $A$ is SPD and fairly sparse so I use a preconditioned conjugate gradients (CG) solver to find a ...
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How asymmetric encryption is done very fast [closed]
In any asymmetric encryption specifications, there is a step where we need to calculate data ^ public_key mod e to get ...
2
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1
answer
410
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Solving stiff ODEs: Dealing with Jacobian terms which take too long to compute with finite differences
I have a system of PDEs describing atmospheric chemistry and transport. I use finite-differences to make my system of PDEs into a system of ~10,000 ODEs. I then integrate the ODEs forward in time with ...
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540
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How can I extract the banded or block diagonal part of a sparse matrix in MATLAB?
Given a large sparse (square) matrix in MATLAB, how can I extract the banded or the block-diagonal parts (of fixed size) of it efficiently?
These are useful operations when prototyping and testing ...
- 2,851
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303
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Methods to improve the efficiency and the memory requirement of LU factorization for complex symmetric system matrix
I want to solve a linear set of equations (Ax=b) using LU decomposition. My "A" matrix is a complex matrix which is ...
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705
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Effecient method for iterating over sparse dataset
Apologies if this isn't the appropriate forum for this question.
I have a set of elements that I need to iterate over as part of a modeling workflow. The elements exists over a set of dimensions (i, ...
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How can I optimize that loop?
I need to populate a matrix $A_{kl}$, where
$$ k = (m-1)J+n$$
$$ l = (p-1)J+q$$
And
$$m,p = 1, 2, ..., I$$
$$n,q = 1, 2, ..., J$$
Its components are (mnpq). For ...
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868
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Fastest way to calculate the $2$-norm (or an upper bound for the $2$-norm) of the inverse of a matrix $A\in \mathbb{C}^{N\times N}$
I have a matrix $A\in \mathbb{C}^{N\times N}$ and I need to calculate $||A^{-1}||_{2}$ efficiently. Can it be done without having to evaluate the inverse explicitly?
In general, I am looking for ...
- 153
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88
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Reducing run time of a numerical calculation using a mex file in Matlab
I wrote a Matlab code that involves doing a numeric calculation (relaxation), but it is quite slow. I learned of the possibility of using a mex file to run a C code and integrate it into Matlab, so I ...
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What is the most efficient way to write 'for' loops in Matlab?
I have read that if, for example, I have a double for loop that runs over the indexes of a matrix, then putting the column running index in the outer loop is more ...
- 163
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113
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How to efficiently invert $K \otimes M+I_T\otimes \Sigma$?
I'm looking for a way to efficiently invert $$K \otimes M+I_T\otimes \Sigma$$ where the inverses for $M,K$ exist. $I_T$ is the identity matrix of dimension $T$, and $\Sigma$ is a diagonal matrix, with ...
3
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141
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How to justify using available code (in different language) for comparing algorithms
I have proposed an algorithm for a scheduling problem in a submitting paper. In the revision, the reviewer asked us to compare with another algorithm from the literature. Our algorithm is in MATLAB, ...
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265
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Why is the method of im2col with GEMM is more efficient than the method of direction implementation with SIMD in CNN
The convolutional layers are most computationally intense parts of Convolutional neural networks (CNNs).Currently the common approach to impement convolutional layers is to expand the image into a ...
- 203
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751
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Accurate and efficient computation of the inverse Langevin function
The Langevin function $\mathcal{L}(x) = \mathrm{coth}(x) - \frac{1}{x}$ occurs in computations related to elastomers and paramagnetic materials. It is easily computed accurately and with high ...
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103
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B-splines least squares with equality constraints
Can someone recommend the best way to solve a least squares fitting problem with B-splines, with additional equality constraints? I want to solve:
$$
\min_x || b - A x ||^2, \textrm{subject to: } C x =...
- 1,078
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127
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Solve $A^{-1} b$ when one column is replaced
Given square matrix $A_0$, vector $b$, vector $A_0^{-1}b$ and matrices $A_1, A_2, \dots, A_k$, in which each $A_i$ is generated from $A_{i-1}$ by replacing one single column, I would like to find an ...
- 241
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2
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193
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MATLAB Matrix Multiply Efficiency
I am using MATLAB to prototype a few matrix multiply techniques and compare efficiency. Eventually, I will move the prototype codes to C. It is for a homework assignment where we need to write an ...
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139
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How to improve the efficiency when I need to exhaustively pairwise millions of list in Python?
I have a m*n matrix (m>1000000, n>50000). What I want to do now is to pairwise every two rows of the matrix and do some further computation (e.g computing common elements of two rows, or reveal ...
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Half precision in Fortran
To improve the time efficiency of my code, I'd like to test a lower precision for real number, using e.g. half precision (2 bytes).
However, I'm not sure if I can do that in Fortran.
After playing ...
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2
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321
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Benefits of matrix multiply over inversion
I have two variations of an iterative algorithm. All the steps of both algorithms are equivalent except one. In this step:
Algorithm 1 needs to compute the matrix $ABA^T$ for matrices $A \in \mathbb{...
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490
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Why does PETSc matrix memory allocation improve performance so much?
Context
In the Portable, Extensible Toolkit for Scientific Computing (PETSc), the user often creates matrices and vectors. These objects are then used as input for other routines like iterative ...
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1
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909
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Plotting the same function multiple times on the same set of axes but with different parameters [Python]
I am currently trying to plot a function which describes linear perturbation growth in cosmology for different world models. I would like to be able to have all the curves on the same set of axes, but ...
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118
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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 (...
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1k
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Is there any computational efficiency to global variables?
I'm wondering specifically in regard to a recursive function such as massive a game tree. I can't specifically say how big yet, but definitely pushing the limits of a given processor or processor ...
- 179
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Stiff ODEs coupled with PDEs (computational efficiency)
I am simulating in COMSOL a system of 3 coupled PDEs (parabolic & elliptic) along with 10 stiff ODEs. In order to have the system working, I am downsizing the time step size too much to achieve ...
- 187
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Difference between Brent's and Alefeld-Potra-Shi for root finding
I need to find the (unique) root of a nonlinear function $f(x)$, $x \in \mathbb{R}$.
For the record, $f(x)$ is the CDF of a probability density minus a constant $0 < p < 1$ (I am inverting the ...
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What is "good" parallel scaling?
I often hear the phrase "good" or "bad" parallel scaling/efficiency.
What exactly do people mean when they say that?
For example, let $p = 1,\ldots 16$ be the number of processing elements, and A and ...
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Efficient way to generate a list of possible matrices (all integer components) with a determinant $V$
I have an interesting problem from my research that I have been struggling to solve. One part of the problem involves generating all possible matrices, where each set contains three integer vectors, ...
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184
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Parallel efficiency
I would like to calculate efficiency of parallel alghoritm, using the number of computations instead of time computations.
In materials from my studies I have a formula like below:
$$ \eta(n,p) = \...
- 43
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1
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84
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Calculate proportions of exponentially weighted factors avoiding underflow problem
I am trying to implement in Python this ratio:
$\frac{w_t(i)}{\sum w_t(j)}$ where $w_t(i) = w_{t-1}(i)\cdot\exp{(-x_{t}(i))}$, i.e. the weights are exponentially decreasing without running into ...
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695
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Power series regression linear fit in VBA excel
I wrote a program that calculates the best fit in VBA excel for the following model
$$
y_k=c_1x_k+c_0+c_{-1}(x_k)^{-1}
$$
solving for the best fit parameters $c_1$, $c_0$, and $c_{-1}$. However I ...
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Performance based on the Roofline model
To somewhat follow up on the question asked here, I have been told that the Roofline model is one way of assessing the performance of any scientific code. Basically I compute the Arithmetic Intensity (...
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369
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Comparing various implementations/software packages for large-scale finite element simulations
I currently use FEniCS and Deal.II to solve various FEM problems. I am also writing my own implementation of these problems by directly implementing the data structures, routines, and solvers within ...
- 791
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824
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Efficient Implementation of the Log Sum Exp Log trick for Preventing Underflow erros
So I'm constructing a Gibbs sampler for a moderately sized graphical model, and I started encountering underflow errors (the computed relative frequencies were all very small). To get around this, I'...
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208
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most efficient way to calculate eigen states of a 2D or 3D potential (Matlab)
I know of several ways to calculated the eigen states of 1D potentials (i.e. DVR, Crank–Nicolson, etc). However I wonder what is the most efficient way to do the same for a N-Dimensional potential? ...
- 101
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1k
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Determining efficiency in MFLOPS/s of a parallel program
I am running some scientific (parallel) code and would like to obtain some performance profiling measurements. I want to obtain the "efficiency" of the code in terms of flops/s over theoretical (peak) ...
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91
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Help on writing sofware: general guidelines, in particular separation of computation and visualization
Although I already did some work in the intersection of theory and simulation I'm still very new to this field and I need some guidance. If anybody can give some recommendations for introductory ...
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1
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166
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Comparison of the time efficiency of an optimization problem formulated as a Network Flow model and Mixed Integer Programming
In combinatorial optimization, there are many problems that can be formulated as either Network Flow model or Mixed Integer Programming (MIP), e.g. supply chains, transportation, and graph-base ...
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Is there a complexity between $O(n)$ and $O(n \log n)$ [closed]
Is there a complexity degree that is bigger than $O(n)$ and smaller than $O(n \log n)$?
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What's the most efficient way to calculate the Wiger quasiprobability distribution?
I want to calculate the Wigner quasiprobability distribution function of a particular wavefunction. The definition suggests a few straightforward ways of calculating it, but I was wondering if there's ...
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