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1500 questions
13
votes
2 answers
What is the corresponding LAPACK function behind Matlab [Q,R,E]=qr(A)?
I currently trying to cheaply compute a good rank estimate for a matrix $A$. Therefore I compute a columnt pivoting QR decompostion using
[Q,R,E]=qr(A)
in Matlab. I estimate the rank of $A$ using
tol = size(A,n)*eps*norm(A,'fro');
r =…
M.K. aka Grisu
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13
votes
2 answers
Why does Matlab's integral outperform integrate.quad in Scipy?
I am experiencing some frustration over the way matlab handles numerical integration vs. Scipy. I observe the following differences in my test code below:
Matlab's version runs on average 24 times faster than my python equivalent!
Matlab's version…
Dipole
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13
votes
6 answers
Seeking a free symbolic regression software
Now that Formulize / Eureqa started charging $2500 a year for using it and having crippled the trial version, does anyone know of any replacements that can do similar things like find an equation given data points?
It was free, but is now out of the…
Rick T
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13
votes
2 answers
How can one mathematically describe the "cartoon" type of representation of proteins?
Proteins are typically represented in a cartoon form, with β sheets as arrows and α helices as coils:
I'm wondering, is there somewhere a reference that describes the construction of this representation? That is, what mathematical objects are used…
F'x
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13
votes
2 answers
Understanding the cost of adjoint method for pde-constrained optimization
I'm trying to understand how the adjoint-based optimization method works for a PDE constrained optimization. Particularly, I'm trying to understand why the adjoint method is more efficient for problems where the number of design variables is large,…
Paul
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13
votes
5 answers
How much should scientific software be optimized?
For applications requiring significant computational resources, high performance can be a critical factor when it comes to delivering scientific results or achieving "break-throughs" in reasonable time.
How much should time and effort should…
Allan P. Engsig-Karup
- 3,226
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13
votes
5 answers
On Finding Open Source Projects To Contribute To
This question has been asked a billion times on Stackoverflow however, the focus has always been on Non-Numerical Coding. I am looking for a project to contribute to within the confines of Numerical Computing and High Performance Computing. I would…
Inquest
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13
votes
3 answers
Is the Thomas algorithm the fastest way to solve a symmetric diagonally dominant sparse tridiagonal linear system
I am wondering if the Thomas algorithm is the fastest way (provably?) to solve a symmetric diagonally dominate sparse tridiagonal system in terms of algorithmic complexity (not looking for implementation packages like LAPACK etc). I know that both…
James
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- 31
13
votes
2 answers
What's the difference between conjugate gradient method and biconjugate gradient method
What's the difference between these two methods? Can a problem be solved by one method will be able to solved by the other? Can both/or one of them be parallelized with OpenMP and/or MPI?
user2196452
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- 6
13
votes
4 answers
Estimating hardware error probability
Say I run a supercomputer computation on 100k cores for 4 hours on http://www.nersc.gov/users/computational-systems/edison/configuration, exchanging about 4 PB of data over the network and performing about 4 TB of I/O. The calculation is all…
Geoffrey Irving
- 3,969
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- 41
13
votes
0 answers
Fast Eigenvalue and SVD Solver for Structured Matrices
I am looking for a fast Eigenvalue and SVD solver for small dense structured matrices (Hankel and Toeplitz). I have searched for efficient implementations in libraries like MKL but I am not able to find anything specific to structured matrices. I…
Sai Venkat
- 241
- 1
- 4
13
votes
1 answer
Purely rotational least squares match
Could anyone recommend a method for the following least-squares problem:
find $R \in \mathbb{R}^{3 \times 3}$ that minimizes: $\sum\limits_{i=0}^N (Rx_i - b_i)^2 \rightarrow \min$, where $R$ is a unitary (rotation) matrix.
I could get an…
Sergiy Migdalskiy
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13
votes
5 answers
Global maximization of expensive objective function
I am interested in globally maximizing a function of many ($\approx 30$) real parameters (a result of a complex simulation). However, the function in question is relatively expensive to evaluate, requiring about 2 days for each parameter set. I am…
AJK
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12
votes
1 answer
Enumeration of graphs deriving from Delaunay tessellations in 3D
Is there an algorithm that enumerates the graphs that correspond to some Delaunay tessellation of points in 3D?
If so, is there an efficient parameterization of geometries that correspond to any "Delaunay graph"?
I am looking to enumerate…
Deathbreath
- 1,042
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12
votes
3 answers
Given an SPD tridiagonal linear system, can we precompute so that any three indices can be linked in O(1) time?
Consider a symmetric positive definite tridiagonal linear system
$$A x = b$$
where $A \in \mathbb{R}^{n \times n}$ and $b \in \mathbb{R}^n$. Given three indices $0 \le i < j < k < n$, if we assume only equation rows strictly between $i$ and $k$…
Geoffrey Irving
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