8

In computational electromagnetism, there is a famous (or infamous because of the difficulties in some) set of test problems: Testing Electromagnetic Analysis Methods (T.E.A.M.). Some of them really need seriously state-of-art numerical techniques to get the correct simulation results aligned with the experimental data. For example, the conductor-coil ...


7

There are many good open-source implementations of root-finding methods out there already. One example is boost, whose implementation of Newton-Raphson and related methods you can find here. If you read its source code, you will be able to see what issues the authors wanted to address, and how they dealt with issues like convergence, user-specified tolerance ...


5

You can use Plot Digitizer and extract the data points in your image graph as a xml file and then you can parse it by using Python. It's pretty straightforward. You need to import the image of your graph into the software. Then calibrate the X and Y axes by specifying the $x_{min}$, $x_{max}$, $y_{min}$, and $y_{max}$ which are the min and max of X and Y ...


3

The most trivial pointsets are regular grid of points. They look innocent, but are the most difficult to handle in Voronoi/Laguerre codes because the Delaunay triangulation is non-unique, so they can be used to detect bugs in your code. They can be handled by adapted geometric predicates (see my publication [6] on geometric predicates and the references ...


3

One thing you can do for smoke testing is to take a known solution $x$ (you could generate it randomly or pick something convenient) and a known matrix $A$, and then set $b$ equal to $Ax$, and solve the equation $Ax = b$ to see if you recover your known solution. This method is known as the method of manufactured solutions. To avoid the influence of ...


3

There is a collection of reference PDE-constrained optimization problems maintained by Roland Herzog at TU-Chemnitz here.


2

So if I understand you right then what you're asking for is this: Given values $a_i,b_i$ as inputs and outputs $r_i=f(a_i,b_i)$, is there a way to identify $f(a,b)$? The answer is of course "yes", and it's not even particularly difficult to do. In fact, there are infinitely many solutions. Think, for example if you had only a single input parameters and ...


2

As I mentioned before, you can try with the Visible Human Project. You can also go with 3D Slicer sample data, e.g., the Knee Atlas or the Brain Atlas. Their terms are quite permissive: By downloading these data, you agree to acknowledge our contribution in any of your publications that result form the use of this atlas. There is also OpenfMRi, but you ...


2

If you're looking for large graphs or network data to test on. The Stanford Network Analysis Project (SNAP) has many large graph datasets typically in the form of an anonymized adjacency list. Some of their options include: Data Social networks: Facebook, Gplus, Twitter, bitcoin, etc. Citation networks: nodes represent papers, edges are citations. Web ...


1

You might want to give a try to DataHarvester. This tool claims to support ROOT, HBOOK, HDF, XML, SQLITE and input/output between them. See the following publication: W. Waltenberger, G. Richter, and H. V. Riedel, "DataHarvester—an abstraction layer for accessing scientific data from various sources," in Int. Conf. Computing High Energy Nuclear Phys., ...


1

The problem you proposes must be treated with care. The function $f$ must have zero mean in the domain $\Omega$,i.e. $$\int_\Omega{f\, dV}=0$$ Otherwise the problem is not well posed. Physically the terms of your equation mean: $\partial_tu$: the energy change of your system. $-\Delta u$:the diffusion of the temperature through the domain. $f$: Heat ...


1

The dataset is huge. So I would like to be more memory-efficient. The main point to consider is the following: […] most of the cells will be “unactivated”, i.e most of the elements of the matrix will store an empty list (no signal). This sounds as if an array of lists (or variably sized arrays) is just fine. In this case, the crucial factor for memory ...


1

Useful inclusion measures depend on whether you want to check pairwise similiarity or containment. For similiarity the Jaccard index is intuitive. For containment I would adapt it to what ratio of columns of my 'gold standard file' are in the file to check which is a common feature used in natural language problems. For the order of columns in a file, an ...


1

A practical complication of such travel time estimates is the time spent transferring from one line/train to another. If all you aim for is the minimum travel time, then there are simple relatively fast algorithms to find one or all of the "optimal" routes. See Dijkstra's shortest path algorithm for a single start and destination, or Floyd-Warshall ...


1

Have you looked at the Matrix Market? http://math.nist.gov/MatrixMarket/


1

Without knowing more about your data, it is not possible to do better than the exhaustive search. This would be memory efficient, but linear in time. If your data set does not contain local minima, you could simply follow the steepest descent. This still has a worst case linear time however. A possibly better solution would be the downhill-simplex ...


1

To convert from Rodrigues vector to a rotation matrix (and back) please check the MATLAB code here: http://www.cs.ucla.edu/~soatto/vision/courses/268/rodrigues.m So this gives you the rotation matrix. You use the translation parameters directly. Additionally, you might want to form the camera matrix. It would be a good idea to get a fully calibrated K (...


1

As pointed out in the previous answer, the concept you are looking for is sensitivity. You take the formula that computes the parameters of your regression line and compute the derivatives with respect to your point positions. These should be large for the three isolated points, indicating that moving them will have big influence.


1

As you mention you cannot devide by a metric, i guess you want a unit-less outcome. As the volume of a cylinder is always going to be cubic meters (decimeters or any scalefactor can be applied) you will need to devide it by something with the same dimension. Some options: The smallest cylinder that can hold the cloud The smallest cube/sphere that can hold ...


1

(I hope there is no objection to my tacking onto the end of this discussion. I'm new here, so please let me know if I have transgressed!) Test functions for evolutionary algorithms are now much more complicated than they were even 2 or 3 years ago, as can be seen by the suites used in competitions at conferences like the (very recent) 2015 Congress on ...


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