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21
votes
5answers
13k views

How can I numerically differentiate an unevenly sampled function?

Standard finite difference formulas are usable to numerically compute a derivative under the expectation that you have function values $f(x_k)$ at evenly spaced points, so that $h \equiv x_{k+1} - x_k$...
4
votes
1answer
94 views

Applicability of combinatorial and support preconditioner

There are several correspondences between matrices and graphs, e.g., each matrix is the adjacancy matrix of a weighted graph. The terms support preconditioner or combinatorial preconditioner refer to ...
8
votes
2answers
342 views

What is a good way to understand the overall structure of a code base?

Sometimes it is useful in my work to modify someone else open-source code or find out how to develop specific things for your own application. However, not all software have good documentation. What ...
8
votes
3answers
2k views

Scientific Programming on Mac using Objective-C/Cocoa for MATLAB Users

I want to get started on scientific programming on the Mac using Objective-C. I am very familiar with MATLAB which makes it easy to store complex-valued waveform data in vectors and generating plots. ...
24
votes
5answers
6k views

What are the main differences between PETSc and Trilinos?

As far as I can tell, the two big generic US Department of Energy computational science software frameworks are PETSc and Trilinos. They seem similar at first glance, beyond differences in language (...
7
votes
2answers
6k views

What does the priority of a PBS job really mean?

The qsub command which submits PBS jobs has a -p option that allows you to set the priority. From the man page: Defines the ...
7
votes
2answers
222 views

How can I tell which options PETSc was compiled with?

I'm working on a machine with a version of PETSc compiled by someone else. Is there a straightforward way to find out which options were used at compile time from the installation itself? For example,...
14
votes
3answers
649 views

PDEs in Many Dimensions

I know that most methods of finding approximate solutions to PDEs scale poorly with the number of dimensions, and that Monte Carlo is used for situations that call for ~100 dimensions. What are good ...
9
votes
1answer
637 views

What numerical quadrature to choose to integrate a function with singularities?

For example, I would like to numerically compute the $L^2$-norm of $\displaystyle u = \frac{1}{(x^2+y^2+z^2)^{1/3}}$ in some domain that includes zero, I tried Gauss quadrature and it fails, it is ...
17
votes
2answers
1k views

Which libraries have good high-level support for multigrid?

I'm planning to use multigrid to calulate some eigenvalues and vectors, and I noticed PETSc has high-level support for multigrid. The PETSc documentation says that this part of PETSc should not be ...
7
votes
2answers
262 views

Representing charges in computer programming

I'm preparing for a thesis in computer science on calculations based on concepts from Neuroelectrodynamics. In short this theory states, that information transfer is not done by spike time coding, ...
4
votes
2answers
328 views

best way to optimize a function with linear/non-linear parameters

I am trying to fit some raw data using a function of the form $f(r) = \sum_{i=1}^{K} d_kS_k(n_k,\alpha_k,r)$ where $S_k(n_k,\alpha_k,r) = \frac{\alpha_k ^{n_k+3}}{(n_k+2)!}r^{n_k}\exp(-\alpha_kr)$ ...
4
votes
0answers
250 views

Convergence rate of Monte-Carlo variance estimate

What is the convergence rate for Monte-Carlo variance estimate for a random variable $X \in {L^q}(\Omega ,R),2 < q < 4$?
6
votes
2answers
98 views

Performance of Lustre filesystems

The cluster I work on has a filesystem labelled as "fast" with no further explanation. But the filesystem type is "lustre", which strongly hints at a Lustre filesystem. While general information about ...
17
votes
5answers
2k views

Is there a good, easy-to-use, high quality open source CFD solver out there?

My thesis is on developing numerical methods for model reduction in combustion. I run my methods purely on the chemistry part of combustion simulations, and I have plenty of case studies for 0-D ...
7
votes
1answer
5k views

How does each process in bag of visual words image classification work?

I hope this is on topic, I found this through the proposal here: https://area51.meta.stackexchange.com/questions/320/shall-we-unite-computational-science-proposals A good visual description of BOW: ...
2
votes
1answer
552 views

Vegas, Monte Carlo multi integration, QCD

To do some calculation on QCD on Lattice, I needed a Monte Carlo multi integration. I wrote a a C++ program according to what I understood from the paper “ Lepage (1978) “ A New Algorith For Adaptive ...
24
votes
8answers
4k views

What software is good to use for parallel debugging?

I'm not running any parallel code right now, but I anticipate running parallel code in the future using a hybrid of OpenMP and MPI. Debuggers have been invaluable tools for me when running serial ...
7
votes
1answer
312 views

Richardson extrapolation for strong rate of convergence of SDE

Is it possible to apply Richardson extrapolation with Euler-Maruyama scheme to improve strong rate of convergence of stochastic differential equations?
11
votes
6answers
2k views

What open source tools are available to visualize molecular vibrations?

I would like to visualize a molecular vibration that is not a normal mode. I'd like to present a static, vectorial representation of the motion, and I would like some flexibility in the vector style (...
26
votes
10answers
712 views

Recommendations and experiences on which license to choose for software?

Developers of software have the choice to choose an appropriate license in accordance with the goal(s) of the work. Can anyone give some recommendations/experiences on which license to pick for ...
13
votes
2answers
450 views

Which time-integration methods should we use for hyperbolic PDEs?

If we employ the Method of Lines for discretization (separate time and space discretization) of hyperbolic PDEs we obtain after spatial discretization by our favorite numerical method (fx. Finite ...
9
votes
2answers
993 views

numerical integration with possible division by 'zero'

I am trying to integrate $$\int^1_0 t^{2n+2}\exp\left({\frac{\alpha r_0}{t}}\right)dt$$ which is a simple transformation of $$\int^{\infty}_1 x^{2n}\exp(-\alpha r_0 x)dx$$ using $t = \frac1{x}$ ...
9
votes
1answer
226 views

Nested dissection on regular grid

When solving sparse linear systems using direct factorization methods, the ordering strategy used significantly impacts the fill-in factor of non-zero elements in the factors. One such ordering ...
7
votes
2answers
6k views

Looking for C/C++ implementations of sampling from multinomial and Dirichlet distributions

I'm looking for C/C++ implementations of functions that return random variates multinomial and Dirichlet distributions. This is in the context of a calculation for posterior predictive p-values, part ...
35
votes
2answers
7k views

Mathematical Libraries for OpenCL?

I am looking for information from anyone that has tried to use OpenCL in their scientific code. Has anyone tried (recently) ViennaCL? If so, how does it compare to cusp? What about OCLTools? Does it ...
6
votes
2answers
624 views

Is it possible to dynamically resize a sparse matrix in the Petsc library?

This may be a Petsc newbie question, but... I'm using Petsc to solve a large sparse linear system. The initial creation of the matrix is fairly slow, which I'm given to understand is largely due to ...
22
votes
6answers
3k views

Future of OpenCL?

The OpenCL programming paradigm promises to be a royalty free opens standard for heterogenous computing. Should we invest our time in developing software based on OpenCL? Pros/cons?
15
votes
2answers
1k views

Estimation of condition numbers for very large matrices

Which approaches are used in practice for estimating the condition number of large sparse matrices?
158
votes
10answers
121k views

Recommendations for a usable, fast C++ matrix library?

Does anyone have recommendations on a usable, fast C++ matrix library? What I mean by usable is the following: Matrix objects have an intuitive interface (ex.: I can use rows and columns while ...
8
votes
3answers
436 views

What should be the criteria for accepting/rejecting singular values?

I am solving a system using singular value decomposition. The singular values (before scaling) are: ...
35
votes
6answers
3k views

What attributes make a figure “professional-quality”?

I've heard people say that plots produced by ORIGIN tend to look polished and "professional," whereas plots produced by Mathematica do not. However, most plot-creation programs are quite configurable ...
7
votes
6answers
6k views

Python implementations of Gillespie's direct method

I'm looking for a decent implementation of Gillespie's Direct Method in Python, as if I code the algorithm myself I'm nigh positive I'll do it inefficiently. Anyone have a favorite?
8
votes
2answers
193 views

Is there one general approach to build a projection methods for different problems?

My question is probably going to be too general to answer it with a couple words. Could you please suggest a good reading in that case. Projection methods are used to reduce size of the solution space ...
44
votes
8answers
2k views

What are good ways to document scientific software?

Many times, when I've inherited or encountered scientific code written by other people (or occasionally, even my own work), I've noticed that documentation is either sparse or nonexistent. If I'm ...
3
votes
3answers
244 views

Evaluating $\binom{100}{i}a^i(1-a)^{(100-i)}$ in GMP-GNU

I want to calculate $\binom{100}{i}a^i(1-a)^{(100-i)}$ for different $i$ with $a=0.001$ using GMP-GNU. How can this be done?
8
votes
4answers
355 views

(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 ...
6
votes
1answer
452 views

An efficient 'drizzle' algorithm?

What efficient implementations of a 'drizzle' algorithm are available? The problem is, given a timestream of data in which each element is associated with a pixel in a map, how do you create that map?...
3
votes
2answers
1k views

Applying same feature selection to multiple data sets with Weka

I am using the Weka workbench to train a protein fold classifier. I imported my training data into Weka and performed PCA-based feature selection. This seems to have worked fine, but now I cannot ...
56
votes
12answers
32k views

C++ vs Fortran for HPC

In my computational science PhD program, we are working almost exclusively in C++ and Fortran. It seems like some professors prefer one over the other. I am wondering which one is 'better' or if one ...
12
votes
3answers
305 views

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, ...
46
votes
5answers
8k views

What are criteria to choose between finite-differences and finite-elements

I am used to thinking of finite-differences as a special case of finite-elements, on a very constrained grid. So what are the conditions on how to choose between Finite Difference Method (FDM) and ...
5
votes
5answers
819 views

Introductions to hp-FEM

do you know good introductions into or surveys $hp$-adaptive finite elements? In particular I do not know how the heuristics for choosing spatial refinement or increased polynomial degree are ...
11
votes
2answers
5k views

How to work with function pointers in Fortran in scientific programs

Here is a typical usage of function pointers in C. I would like to do something similar in Fortran. I have some ideas, but I would like to know if there is some canonical way to do so. The function ...
13
votes
1answer
1k views

What are possible methods to solve compressible Euler equations

I would like to write my own solver for compressible Euler equations, and most importantly I want it to work robustly in all situations. I would like it to be FE based (DG is ok). What are the ...
14
votes
4answers
348 views

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 ...
1
vote
0answers
57 views

Assembled human ESTs for annotation

I am annotating protein-coding genes in a region of the human genome and am looking for a set of assembled ESTs I can use as evidence for constructing gene models. A quick search of NCBI's SRA shows 4,...
16
votes
3answers
561 views

How should I study creating and programming HPC systems?

I'm in a field that doesn't necessarily do a great deal of HPC work, and when it does encounter it, it's often the result of researchers from other fields exploring new applications to their methods ...
4
votes
1answer
889 views

Sampling from posterior predictive distribution

First post. I'm working on this problem using Bayesian methods. In desperation I'm considering using p-values (shock horror), specifically posterior predictive p-values. So I need to simulate from the ...
4
votes
4answers
349 views

Approximate a distribution function from a finite sample

Say I have a simulation that produces a single floating point number as a result, and a different number is produced each time the simulation runs. These numbers are randomly distributed according to ...

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