Datasets:

mlfoundations-dev
/

stackexchange_scicomp

instruction stringlengths 43 28.1k	completion stringlengths 2 26.4k	conversations listlengths 2 2
Can you explain the difference between these two computational methods ?	Of course! However, you didn't specify which two computational methods you're referring to. Could you please provide the names or descriptions of the methods you would like me to compare?	[ { "from": "human", "value": "Can you explain the difference between these two computational methods ? \n" }, { "from": "gpt", "value": "Of course! However, you didn't specify which two computational methods you're referring to. Could you please provide the names or descriptions of the methods yo...
When VASP 5 was released, the performance was mostly slower than our make of VASP 4.6. I wrote it off as an optimization issue, and went on in my life. Then, in VASP 5.2, with the release notes, I realized that the it was all due to slower FFT, and is now fixed. Is there any way for me, as a user, to tell if the VASP m...	Yes, as a user, you can determine whether your VASP installation is built with the faster FFTW (Fastest Fourier Transform in the West) library by following these steps: 1. Check the Compilation Options: When you run VASP, it outputs information about the compilation options used. This information is typically disp...	[ { "from": "human", "value": "When VASP 5 was released, the performance was mostly slower than our make of VASP 4.6. I wrote it off as an optimization issue, and went on in my life. Then, in VASP 5.2, with the release notes, I realized that the it was all due to slower FFT, and is now fixed. Is there any way...
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 evaluate my trained classifier on the test data because the test data contains all the original attributes. Of course, if I ...	In Weka, when you perform feature selection on your training data, it is important to apply the same feature transformation to your test data to ensure that both datasets are aligned with the same set of features. Here’s how you can handle this situation effectively: 1. Use the Attribute Selection with a Filter: W...	[ { "from": "human", "value": "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 evaluate my trained classifier on the test data because the test data contains all ...
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, or does MKL have the upper hand for some tasks? If so, which ones?	ATLAS (Automatically Tuned Linear Algebra Software) and MKL (Math Kernel Library) are both highly optimized libraries for linear algebra operations, but they have different characteristics and performance profiles depending on the specific tasks and hardware. ### Performance Comparison 1. **Self-Tuning vs. Hand-Tunin...	[ { "from": "human", "value": "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, or does MKL have the upper hand for some tasks? If so, which ones? \n" }, ...
I often use inverse interval graphs to represent biologically relevant features along a genomic sequence. For example, given a (relatively) small genomic region, the graph would contain a node for each gene in the region, and there would be an edge between two nodes if the corresponding genes do not overlap (the comple...	Your project involving inverse interval graphs and the computation of maximal cliques is indeed interesting, and you've encountered a common challenge in graph theory. ### 1. Polynomial Runtime Guarantee Regarding the guarantee of polynomial runtime for algorithms like Chiba & Nishizeki’s, it is important to clarify ...	[ { "from": "human", "value": "I often use inverse interval graphs to represent biologically relevant features along a genomic sequence. For example, given a (relatively) small genomic region, the graph would contain a node for each gene in the region, and there would be an edge between two nodes if the corre...
Are there cases where Hartree-Fock is not a good approximation to compute equilibrium geometry when the molecule is in a non bond-breaking condition?	Yes, there are several cases where Hartree-Fock (HF) may not be a good approximation for computing equilibrium geometry, even in situations where the molecule is in a non bond-breaking condition. Here are some notable examples: 1. Electron Correlation: Hartree-Fock theory neglects electron correlation, which can b...	[ { "from": "human", "value": "Are there cases where Hartree-Fock is not a good approximation to compute equilibrium geometry when the molecule is in a non bond-breaking condition? \n" }, { "from": "gpt", "value": "Yes, there are several cases where Hartree-Fock (HF) may not be a good approximatio...
I have a 50-base, artificially created RNA sequence and I would like to obtain its 3D structure. What software should I use for this purpose?	To obtain the 3D structure of an artificially created RNA sequence, you can use several software tools and web servers that are specifically designed for RNA modeling. Here are some popular options: 1. RNAfold: Part of the ViennaRNA package, RNAfold can predict the secondary structure of RNA sequences based on the...	[ { "from": "human", "value": "I have a 50-base, artificially created RNA sequence and I would like to obtain its 3D structure.\nWhat software should I use for this purpose?\n" }, { "from": "gpt", "value": "To obtain the 3D structure of an artificially created RNA sequence, you can use several sof...
My background is in genomics, but I have recently been working with problems related to protein structure. I wrote a few relevant programs in C, building my own PDB file parser from scratch in the process. I didn't worry about making a really robust parser, I just knew that building one myself would be the best way to ...	It's great to hear about your transition into working with protein structures! There are indeed several open-source libraries that you might find useful for handling protein structure data and performing related calculations in C or C++. Here are some notable options: 1. Biopolymer: This is a C++ library that prov...	[ { "from": "human", "value": "My background is in genomics, but I have recently been working with problems related to protein structure. I wrote a few relevant programs in C, building my own PDB file parser from scratch in the process. I didn't worry about making a really robust parser, I just knew that buil...
A recent answer mentioned the use of Fortuna or Mersenne Twister Random Number Generators (RNGs) to seed a Monte Carlo simulation. I hadn't heard of Fortuna before so I looked it up - looks like it is mainly intended for cryptographic use. I currently use a Mersenne Twister in production code to seed a K-Means algorith...	When it comes to choosing a random number generator (RNG) for algorithmic seeding applications like Monte Carlo simulations and K-Means clustering, both Mersenne Twister and Fortuna have their strengths and weaknesses. However, they serve different purposes and excel in different contexts. ### Mersenne Twister 1. **Q...	[ { "from": "human", "value": "A recent answer mentioned the use of Fortuna or Mersenne Twister Random Number Generators (RNGs) to seed a Monte Carlo simulation. I hadn't heard of Fortuna before so I looked it up - looks like it is mainly intended for cryptographic use.\nI currently use a Mersenne Twister in ...
The qsub command which submits PBS jobs has a -p option that allows you to set the priority. From the man page: Defines the priority of the job. The priority argument must be a integer between -1024 and +1023 inclusive. The default is no priority which is equivalent to a priority of zero. And that's all that is in ...	The priority setting in PBS (Portable Batch System) allows users to influence the order in which jobs are scheduled and executed on a computing cluster. Here's a more comprehensive explanation of how job priority works in PBS: 1. Priority Range: The priority can be set to an integer between -1024 and +1023. Higher...	[ { "from": "human", "value": "The qsub command which submits PBS jobs has a -p option that allows you to set the priority. From the man page:\n\nDefines the priority of the job. The priority argument must be a integer between -1024 and +1023 inclusive. The default is no priority which is equivalent to a pr...
I've been considering using a multigrid method to calculate the eigenvalues of a particular PDE. I know that multigrid is extremely good at finding the least eigenvalues and their associated eigenvectors, in part because these eigenvectors are very smooth. Is multigrid also a good method to calculate all the eigenval...	Multigrid methods are indeed very effective for solving certain types of eigenvalue problems, especially when it comes to finding the smallest eigenvalues and their corresponding eigenvectors. This effectiveness is primarily because the eigenvectors associated with the smallest eigenvalues typically exhibit smoothness,...	[ { "from": "human", "value": "I've been considering using a multigrid method to calculate the eigenvalues of a particular PDE. I know that multigrid is extremely good at finding the least eigenvalues and their associated eigenvectors, in part because these eigenvectors are very smooth. Is multigrid also a ...
I am looking to solve a constrained optimization problem where I know the bounds on some of the variables (specifically a boxed constraint). $$ \arg \min_u f(u,x) $$ subject to $$ c(u,x) = 0 $$ $$ a \le d(u,x) \le b $$ where $u$ is a vector of design variables, $x$ is a vector of state variables, and $c(u,x)$ is an equ...	To solve your constrained optimization problem with the specified requirements, you can consider several optimization libraries and software packages that can handle optimization problems with equality constraints and box constraints. Here are some popular options: 1. Python Libraries: - SciPy: The `scipy.o...	[ { "from": "human", "value": "I am looking to solve a constrained optimization problem where I know the bounds on some of the variables (specifically a boxed constraint).\n$$ \\arg \\min_u f(u,x) $$\nsubject to\n$$ c(u,x) = 0 $$\n$$ a \\le d(u,x) \\le b $$\nwhere $u$ is a vector of design variables, $x$ is a...
Is it possible to get second order accuracy for hexahedral finite elements with fewer than 8 Gauss points without introducing unphysical modes? A single central Gauss point introduces an unphysical shearing mode, and the standard symmetric arrangement of 8 Gauss points is expensive compared to tetrahedral discretizati...	Achieving second-order accuracy in hexahedral finite element discretizations with fewer than 8 Gauss points can indeed be challenging, particularly when dealing with nonlinear elasticity problems like the ones described in your equations. To maintain stability and accuracy while avoiding the introduction of unphysical ...	[ { "from": "human", "value": "Is it possible to get second order accuracy for hexahedral finite elements with fewer than 8 Gauss points without introducing unphysical modes? A single central Gauss point introduces an unphysical shearing mode, and the standard symmetric arrangement of 8 Gauss points is expen...
I am looking for some clues for an optimization problem. My problem consists of arriving to a image by optimizing multiple layers with the pixel position probability. This is an overview of the problem: The first image on the left is a zoom of the greyscale image with only two grey values, followed by the probability ...	It sounds like you're working on a complex image optimization problem involving probabilistic representations of pixel values across multiple layers. Given the nature of your problem, you'll benefit from understanding several key concepts in optimization, image processing, and probabilistic modeling. Here are some step...	[ { "from": "human", "value": "I am looking for some clues for an optimization problem.\nMy problem consists of arriving to a image by optimizing multiple layers with the pixel position probability.\nThis is an overview of the problem:\n\nThe first image on the left is a zoom of the greyscale image with only ...
I recently encountered a case where I needed an integer division operation on a chip that lacked one (ARM Cortex-A8). While trying to research why that must be, I found out that in general division takes many more cycles than addition, subtraction or multiplication on pretty much any integer (or fixed-point) architectu...	Division, particularly integer division, is inherently a more complex operation than addition, subtraction, and multiplication due to the nature of how it is performed in digital logic. While it is true that addition, subtraction, and multiplication can often be implemented using relatively simple logic circuits (adder...	[ { "from": "human", "value": "I recently encountered a case where I needed an integer division operation on a chip that lacked one (ARM Cortex-A8). While trying to research why that must be, I found out that in general division takes many more cycles than addition, subtraction or multiplication on pretty muc...
I am using a basic singular value decomposition (via LAPACK) routine in FORTRAN to solve an overdetermined system in the form of $A\cdot X = B$ where $\mathrm{size}(A) = [m,n]$ with $m > n$. My sample data points come from a noisy sine function and I am trying to use linear regression with $x^i$ as my basis functions. ...	The phenomenon you are encountering is commonly known as overfitting in the context of polynomial regression. Let me explain what happens when you increase the degree of the polynomial too much. 1. Basis Functions and Degrees: When you fit a polynomial of degree \( N \) to your data, you are essentially using ...	[ { "from": "human", "value": "I am using a basic singular value decomposition (via LAPACK) routine in FORTRAN to solve an overdetermined system in the form of $A\\cdot X = B$ where $\\mathrm{size}(A) = [m,n]$ with $m > n$.\nMy sample data points come from a noisy sine function and I am trying to use linear r...
I am running into a problem with COMSOL 4.2.0.187 on Ubuntu (both 10.04 LTS and 11.04). When using the option -np x with x > 1, COMSOL crashes systematically after a short, yet random amount of time with the following error: > [thread 140538491361024 also had an error] terminate called without an active exception > Ab...	The error you're encountering with COMSOL when using multiple processing cores (`-np x` where `x > 1`) can indeed be linked to threading or compatibility issues with the libraries on your system. Here are some steps you might consider to troubleshoot and potentially resolve the issue: 1. Update COMSOL: If possible...	[ { "from": "human", "value": "I am running into a problem with COMSOL 4.2.0.187 on Ubuntu (both 10.04 LTS and 11.04). When using the option -np x with x > 1, COMSOL crashes systematically after a short, yet random amount of time with the following error:\n> [thread 140538491361024 also had an error] terminat...
I was playing around with PETSc and noticed that when I run my program with more than one process via MPI it seems to run even slower! How can I check to see what is going on?	When you experience performance issues while running your PETSc application with multiple processes using MPI, there are several steps you can take to diagnose and resolve the problem. Here’s a systematic approach to understand what might be causing the slowdown: 1. Analyze the Problem Size: Ensure that your probl...	[ { "from": "human", "value": "I was playing around with PETSc and noticed that when I run my program with more than one process via MPI it seems to run even slower! How can I check to see what is going on?\n" }, { "from": "gpt", "value": "When you experience performance issues while running your ...
Given a real function of real variables, is there software available that can automatically generate numerically-accurate code to calculate the function over all inputs on a machine equipped with IEEE 754 arithmetic? For example, if the real function to be evaluated were: The software would consider catastrophic cance...	Yes, there are software tools and libraries that can help generate numerically-accurate code for evaluating real functions, particularly in the context of IEEE 754 arithmetic. Here are some options you might consider: ### 1. AutoDifferentiation Libraries Libraries like Stan, TensorFlow, and PyTorch off...	[ { "from": "human", "value": "Given a real function of real variables, is there software available that can automatically generate numerically-accurate code to calculate the function over all inputs on a machine equipped with IEEE 754 arithmetic?\nFor example, if the real function to be evaluated were:\n\nTh...
What efforts have been made to quantify the costs of the common numeric workhorse operations such as those found in LAPACK, BLAS, sparse matrix operations, etc.... We have several libraries which implement identical interfaces found in BLAS and LAPACK. I suspect these all have different strengths and weaknesses on vari...	The effort to quantify the performance of numerical libraries like BLAS (Basic Linear Algebra Subprograms), LAPACK (Linear Algebra PACKage), and their GPU or multi-core counterparts has been an ongoing area of research. There are several aspects to consider when evaluating the performance of these libraries across diff...	[ { "from": "human", "value": "What efforts have been made to quantify the costs of the common numeric workhorse operations such as those found in LAPACK, BLAS, sparse matrix operations, etc....\nWe have several libraries which implement identical interfaces found in BLAS and LAPACK. I suspect these all have ...
Engineers often insist on using locally conservative methods such as finite volume, conservative finite difference, or discontinuous Galerkin methods for solving PDEs. What can go wrong when using a method that is not locally conservative? Okay, so local conservation is important for hyperbolic PDEs, what about ellipti...	Using non-locally conservative methods for solving partial differential equations (PDEs) can lead to several issues, particularly in the context of hyperbolic PDEs, but also in some cases for elliptic PDEs. Here are some potential problems that can arise when using non-conservative methods: ### Hyperbolic PDEs 1. **No...	[ { "from": "human", "value": "Engineers often insist on using locally conservative methods such as finite volume, conservative finite difference, or discontinuous Galerkin methods for solving PDEs.\nWhat can go wrong when using a method that is not locally conservative?\nOkay, so local conservation is import...
I solve multi-species, compressible Navier-Stokes equations on a 3D structured grid. I have obtained a solution on a given grid (let's say a relatively coarse one). I want now to refine my grid and interpolate my previous solution on my new grid before restarting my simulation. Currently, we have an interpolation tool ...	When dealing with multi-species, compressible Navier-Stokes equations, maintaining accuracy during grid refinement and interpolation is indeed critical, especially when large gradients are present in the solution. It's great that you’ve explored several interpolation methods. Let's discuss your findings and potential a...	[ { "from": "human", "value": "I solve multi-species, compressible Navier-Stokes equations on a 3D structured grid. I have obtained a solution on a given grid (let's say a relatively coarse one). I want now to refine my grid and interpolate my previous solution on my new grid before restarting my simulation. ...
Automatic differentiation allows us to numerically evaluate the derivative of a program on a particular input. There is a theorem that this computation can done at a cost less than five times the cost to run the original program. This factor of five is an upper bound. In what situations can this cost be further reduce...	Automatic differentiation (AD) can significantly speed up the computation of derivatives, often making it feasible to compute gradients at a cost that is a small multiple of the original program's evaluation cost. The upper bound of five times is indeed a general guideline, but in practice, there are several ways to ac...	[ { "from": "human", "value": "Automatic differentiation allows us to numerically evaluate the derivative of a program on a particular input. There is a theorem that this computation can done at a cost less than five times the cost to run the original program. This factor of five is an upper bound. \nIn what ...
I am modelling a heat distribution in optical element irradiated by laser. System is radially symmetric, and element is thin, i.e. heat value depends only on distance from center. Heat is received via laser radiation and is removed from upper and lower sides of the element. A significant characteristic of the problem i...	Your problem is indeed interesting and involves complex dynamics due to the nonlinear dependencies of the absorption coefficient on temperature. Here are a few considerations regarding your question about the possibility of time-dependent distributions versus stationary states: ### Time-Dependent vs Stationary States ...	[ { "from": "human", "value": "I am modelling a heat distribution in optical element irradiated by laser. System is radially symmetric, and element is thin, i.e. heat value depends only on distance from center. Heat is received via laser radiation and is removed from upper and lower sides of the element. A si...
Multigrid methods usually solve Dirichlet problems on levels (e.g. point Jacobi or Gauss-Seidel). When using continuous finite element methods, it is much less expensive to assemble small Neumann problems than to assemble small Dirichlet problems. Non-overlapping domain decomposition methods such as BDDC (like FETI-DP)...	Yes, there is a way to solve "pinned" Neumann problems without losing level-independence in the context of multigrid methods. One approach is to use a technique called "Neumann smoothing" combined with appropriate coarse-grid corrections to mitigate the effects of the level dependence of the condition number. Here are...	[ { "from": "human", "value": "Multigrid methods usually solve Dirichlet problems on levels (e.g. point Jacobi or Gauss-Seidel). When using continuous finite element methods, it is much less expensive to assemble small Neumann problems than to assemble small Dirichlet problems. Non-overlapping domain decompos...
EEGLab doesn't work well due to the data being from a Neuromag MEG. Any thoughts for alternatives?	If you're encountering issues with EEGLab for analyzing data from a Neuromag MEG system, there are several alternative tools and approaches you can consider: 1. MNE-Python: This is a powerful open-source Python library specifically designed for processing and analyzing MEG and EEG data. It provides comprehensive t...	[ { "from": "human", "value": "EEGLab doesn't work well due to the data being from a Neuromag MEG. Any thoughts for alternatives?\n" }, { "from": "gpt", "value": "If you're encountering issues with EEGLab for analyzing data from a Neuromag MEG system, there are several alternative tools and approa...
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 triangles, where the points are given by coordinates (say $x$ and $y$) and the triangles each consist of three point ind...	Memory fragmentation is indeed a critical concern in practical scientific computing and high-performance computing (HPC), especially when dealing with dynamic data structures such as unstructured meshes in finite element methods (FEM). Fragmentation can lead to inefficient memory use, performance degradation, and even ...	[ { "from": "human", "value": "I use an example from finite element theory, but anybody who maintains a large datastructure and successively extends it will find something similar.\nSuppose I have an unstructured mesh of points and triangles, where the points are given by coordinates (say $x$ and $y$) and the...