Questions tagged [efficiency]

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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 ...
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  • 255
3 votes
1 answer
164 views

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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-1 votes
1 answer
78 views

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 ...
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2 votes
1 answer
221 views

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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3 votes
1 answer
180 views

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 ...
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2 votes
1 answer
198 views

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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  • 33
1 vote
1 answer
45 views

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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  • 119
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0 answers
65 views

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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5 votes
1 answer
486 views

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 ...
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  • 153
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0 answers
82 views

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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  • 163
12 votes
2 answers
3k views

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 ...
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  • 163
4 votes
2 answers
91 views

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 ...
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3 votes
1 answer
131 views

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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  • 133
1 vote
0 answers
215 views

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 ...
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8 votes
1 answer
414 views

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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1 vote
0 answers
66 views

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 =...
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  • 876
3 votes
1 answer
114 views

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 ...
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4 votes
2 answers
186 views

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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0 votes
1 answer
80 views

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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  • 3
5 votes
1 answer
767 views

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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0 votes
2 answers
159 views

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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  • 101
1 vote
1 answer
411 views

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 vote
1 answer
249 views

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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  • 33
1 vote
1 answer
100 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 (...
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7 votes
3 answers
1k views

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 ...
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  • 179
1 vote
0 answers
60 views

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 ...
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  • 157
2 votes
1 answer
199 views

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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  • 183
5 votes
4 answers
2k views

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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4 votes
1 answer
143 views

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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2 votes
1 answer
146 views

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) = \...
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1 vote
1 answer
68 views

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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  • 113
0 votes
1 answer
610 views

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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2 votes
1 answer
185 views

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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  • 771
7 votes
2 answers
331 views

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 ...
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  • 771
0 votes
0 answers
722 views

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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  • 9
0 votes
2 answers
195 views

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? ...
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  • 101
0 votes
3 answers
1k views

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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  • 771
1 vote
2 answers
82 views

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 vote
1 answer
129 views

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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10 votes
3 answers
853 views

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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1 vote
0 answers
72 views

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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  • 3,335
3 votes
2 answers
964 views

How to re-use the coefficient matrix decomposition result when solving linear systems by Eigen C++

My problem needs to solve dense symmetric linear systems something like: A x = b, A y = x, ...
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2 votes
1 answer
78 views

What is the fomula of polynomial time of solving positive definite symmetric linear system

For a positive definite symmetric linear system, Cholesky decomposition based method should be the best solver which has a rough n^3/3 flops requirement. What is ...
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2 votes
2 answers
177 views

Why the same program runs faster on an older computer?

I have the same single thread problem, which is something like a simple ...
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2 votes
1 answer
755 views

Efficient formulation of an SDP involving L1 norm

I am trying to reformulate the following problem to be solved efficiently (by MOSEK) $$ \min_{X} \text{Tr}(CX)+\lambda\sum_{i,j}|x_{i,j}| \\ \text{s.t.} \quad ||X||_F\le1 \quad \text{and} \quad X\ge 0 ...
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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, ...
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  • 153
4 votes
1 answer
2k views

calculation time in Fluent

I'm making a model of a square box where water comes in and the water level rises. I want it to be a transient, turbulent, VOF-model. The velocity of water entering changes in time ($-0.2$ to $0.2$ m/...
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  • 175
2 votes
1 answer
521 views

Trying to implement a simple/efficient combinations function in MATLAB

So, recently, I have found myself in the position of having to implement a combinations function in MATLAB. What I mean by this is the following: I simply need to list all possible combinations for an ...
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  • 123
4 votes
2 answers
194 views

Efficiency of Repeated Sparse Matrix-Vector Products

I recently read Wolfgang's answer to the question found here and found myself wondering about a related followup question. Assume you have two sparse matrices $A$ and $B$. You need to do the ...
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  • 4,567
10 votes
4 answers
3k views

Fast and accurate double precision implementation of incomplete gamma function

What is the state of the art way of implementing double precision special functions? I need the following integral: $$ F_m(t) = \int_0^1 u^{2m} e^{-tu^2} d u = {\gamma(m+{1\over 2}, t)\...
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