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1500 questions
7
votes
5 answers
Where can I find a database of simple chemical structures in XYZ format?
As from Title. Where can I find a database of simple chemical structures in XYZ format, possibly with a simple CAS -> XYZ or InChi -> XYZ REST service ?
Stefano Borini
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7
votes
2 answers
implementing higher order derivatives for finite element
I am implementing higher order derivatives for FEM. Example, to solve a Poisson problem, biharmonic or triharmonic PDE one needs first, second or third order derivatives respectively.
As usually done in FEM, there is a mapping from a reference…
uli.xu
- 173
- 1
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7
votes
1 answer
Why does LSODA fail to integrate the logistic function?
I'm comparing some of the different ODE integrators in scipy.integrate.ode on solving the logistic function:
$$x(t) = \frac{1}{1+e^{-rt}}$$
$$\dot{x} = rx(1-x)$$
I've heard that LSODA should be very good, so I was a bit surprised to find that it…
joh
- 173
- 3
7
votes
3 answers
Mixed Finite Element Method for the Stokes System—Some Implementation Details
I am currently working on my bachelor’s diploma. The research concerns mixed finite element method for the 2D Stokes system
$$
- \Delta \boldsymbol u + \nabla p = \boldsymbol f, \quad \boldsymbol x \in \Omega \subset \mathbb R^2, \\
\nabla \cdot…
56th
- 901
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- 10
7
votes
1 answer
What would be a good approach to solving this large data non-linear least squares optimisation
Introduction to Problem
I'm using a Truncated Signed Distance Function to perform 3D reconstruction from depth images.
Essentially I have a large voxel grid where each voxel contains the signed distance to an implicit surface. The surface can be…
Dave Durbin
- 73
- 4
7
votes
1 answer
What is the fastest way to compute the sum of the singular values of a matrix?
Is there a faster way to compute the nuclear norm (trace norm, sum of singular values) of a matrix A than computing SVD(A) directly (or diagonalizing A^*A)?
I am particularly interested in the case where A is square. Assuming that A is real would…
Brent
- 171
- 4
7
votes
3 answers
How to separate a solver from computational experiments in a correct way?
I do computational work as a PhD student and I try to find a correct way to separate code (solver) from the computational experiments based on this solver.
Basically, each project that I do revolves around one particular solver (MATLAB or Python…
Dmitry Kabanov
- 508
- 3
- 11
7
votes
3 answers
How do I reliably generate random numbers in Python distributed across multiple nodes?
Consider the following scenario: I want to perform a large Monte Carlo simulation across a compute cluster with several nodes. To avoid excessive transmission of data, I am going to generate random data for my simulation on the individual nodes.…
Thomas Arildsen
- 321
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- 6
7
votes
1 answer
Efficient algorithm for solving linear system with symmetric near-tridiagonal matrix?
I would like to solve the linear system $\mathbf{A}\mathbf{x}=\mathbf{b}$, with
$$\mathbf{A}=\mathbf{T}+\mathbf{C}$$
where $\mathbf{T}$ is a symmetric tridiagonal matrix and $\mathbf{C}$ is a corner-only matrix:
$$\mathbf{C}=\begin{pmatrix}
0& 0 &…
Arturo don Juan
- 489
- 2
- 8
7
votes
1 answer
Tikhonov (Ridge) Regression and Normalization
For a typical Ridge Regression method for solving an inverse problem
$$
\min_x ||A~x - b||^2 + \lambda^2||\Gamma~x||^2
$$
Which has an analytical solution of
$$
\hat{x}_{est}=(A^TA+\lambda^2 \Gamma^T\Gamma)^{-1} A^T b
$$
How should $A, \lambda, x,…
abnowack
- 255
- 1
- 4
7
votes
3 answers
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 array.
Is it correct to say that passing a variable…
DukeZhou
- 179
- 5
7
votes
3 answers
Wanting to learn about matrix solvers
Edit: I was advised to replace the question with a more specific one.
Coming from a very theoretical background, I'm pretty ignorant about what practical matrix solvers exist. (I have been, and will continue to scour the web for information, but I…
rschwieb
- 173
- 1
- 7
7
votes
1 answer
Methods to Estimate Optimal Distance Measure for Multidimensional Data Set
My problem at hand pertains to choosing a distance measure for use in locally weighted regression. In my particular problem, I have a data set that is upwards of 10 dimensions, where the variables have different units (think distances, speeds,…
spektr
- 4,238
- 1
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7
votes
0 answers
What is some of the best software design you've seen in a numerical code?
I don't think I've ever seen any scientific computational software that I would consider "good" in terms of software design. I don't mean in terms of functionality, but in terms of good high-level design, coding standards, readability, etc. Most…
Aurelius
- 2,365
- 1
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- 19
7
votes
1 answer
Eigenvalues of $ab^T$
In deriving a Newton scheme, I end up with a Jacobian matrix of the form $J=I+ab^T$ where $a,b$ are vectors. For practical reasons, I want to approximate it by a symmetric positive definite matrix. Symmetrizing is easy: replace it by $J \approx…
Wolfgang Bangerth
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