topologic | basic geometric primitives and fractals | Math library
kandi X-RAY | topologic Summary
kandi X-RAY | topologic Summary
Topologic is a programme that visualises basic primitives and fractals in arbitrary dimensional spaces. Primitives include simplices, cubes and spheres, and fractals include basic affine IFSs as well as fractal flames. Supported output methods include simple SVGs and OpenGL 3.2 and up. The actual calculations as well as most of the render tasks are performed by libefgy, a header-only C++ template library for maths.
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topologic Key Features
topologic Examples and Code Snippets
Lines of Code : 4License : Permissive (MIT)
Copy$ make "CFLAGS=-g -D MAXDEPTH=8"
$ ./topologic --version
Topologic CLI; Version 5
Maximum render depth of this binary is 8 dimensions.
$ make
# make PREFIX=/usr install
$ git clone --recursive https://github.com/ef-gy/topologic.git
Community Discussions
Trending Discussions on topologic
QUESTION
ANSWER
Answered 2021-May-20 at 11:31In general this is #P-complete. This particular graph happens to be series–parallel, however, which makes it easy. Graphs in series cause the number of possibilities for each graph to be multiplied. For the particular graph you show, there are three diamonds in series, each of which has two valid extensions, so there are eight possibilities.
QUESTION
I am trying to implement Knuth's topological sorting algorithm in C. When I search for online resources, all I see are implementations of Kahn's Algorithm and this kind of confuses me. Are they both the same? Or are they different? Here is my implementation based on what I have researched.
...ANSWER
Answered 2021-Apr-20 at 14:06If you read Knuth's TAOCP (The Art of Computer Programming) Volume 1, Section 2.2.3 in the 3rd Edn, you'll find Knuth's "Algorithm T (Topological sort)" and also the comment:
A topological sorting technique similar to Algorithm T (but without the important feature of the queue links) was first published by A. B. Kahn, CACM 5 (1962), 558-562.
This indicates that Knuth's Algorithm T is different from Kahn's algorithm.
QUESTION
I have an input data and some transformation functions t1, t2, t3, t4, t5, t6. Each of them requires some columns as input and outputs some columns.
...ANSWER
Answered 2021-May-02 at 20:52Build the transpose DAG and do depth-first search from the required columns?
QUESTION
Is there an algorithm that, given an unweighted directed acyclic graph, sorts all nodes into a list of sets of nodes such that
- the topological order is preserved (i.e., for all edges
u->v,voccurs in a set further down the list thanu) and - the length of the list is minimal.
Is there a name for this problem?
ExampleA possible sort for the graph below would be
...ANSWER
Answered 2021-Apr-26 at 13:17Define the stage index of each node to be zero if it has no predecessors, or one plus the max stage index of its predecessors. Put each node in the indicated stage.
The stage indices can be evaluated efficiently in topological order, making this an easy extension to your favorite topological sorting algorithm.
QUESTION
My question is: is there any algorithm that can convert a SMILES structure into a topological fingerprint? For example if glycerol is the input the answer would be 3 x -OH , 2x -CH2 and 1x -CH.
I'm trying to build a python script that can predict the density of a mixture using an artificial neural network. As an input I want to have the structure/fingerprint of my molecules starting from the SMILES structure.
I'm already familiar with -rdkit and the morganfingerprint but that is not what i'm looking for. I'm also aware that I can use the 'matching substructure' search in rdkit, but then I would have to define all the different subgroups. Is there any more convenient/shorter way?
Would love to hear your thoughts.
Cheers
...ANSWER
Answered 2021-Mar-29 at 09:09For most of the structures, there's no existing option to find the fragments. However, there's a module in rdkit that can provide you the number of fragments especially when it's a function group. Check it out here. As an example, let's say you want to find the number of aliphatic -OH groups in your molecule. You can simply call the following function to do that
QUESTION
I got totally stuck with this (integer) linear programming formulation task:
Input: directed edge-weighted graph which contains cycles.
Goal: find set of edges, with minimal sum of their weights, such that if these edges are removed from the graph, the graph becomes acyclic.
EDIT: for anyone interested,I found out (with a little help from my friends), that you can use topological ordering to solve this problem. You just need to introduce a constraint for each edge such that:
topologicalOrder[ edge.parent ] << topologicalOrder[ edge.child ] + ( M * edgeInactive[edge])
where topologicalOrder[node] is an integer array of topological positions of nodes and edgeInactive is array of bools denoting whether the edge is active in the resulting (acyclic) graph.
M is the Big M method used for "turning off" the constraint when edgeActive[edge] == true.
Then you just need to minimize the sum of weights of inactive edges.
OLD (slower) solution:
My idea was to create a topological sorting of nodes (for an acyclic graph all edges would be oriented form left to right when topologically sorted), hovewer as I'm given graph with cycles I'll be looking for such topological ordering that the sum of edges directed from right to left is minimal.
This approach works but it's really slow...
(I'm trying to solve this problem with Gurobi but I think it's pretty much general Linear programming formulation problem.) My code:
...ANSWER
Answered 2021-Mar-25 at 12:20This looks like a (in general) NP-hard problem: minimum feedback arc set. At least this answer indicates this.
You probably will find more resources with this keyword.
I remember reading about ILP-formulation in regards to above problem when i did some ILP-work on Kemeny–Young method
Quickly looking for it on Google Scholar brings us to:
Ali, Alnur, and Marina Meilă. "Experiments with Kemeny ranking: What works when?." Mathematical Social Sciences 64.1 (2012): 28-40.
Which says:
"The above ILP formulation has been given before [10, 28]. This formulation can also be interpreted as solving the minimum weighted feedback arc set problem from computer science [10, 19]"
I guess you might start with this paper (Link to pdf as referenced by Google Scholar)
QUESTION
I am trying to convert a DAG to a binary tree. Consider the following graph
I want to have the following output for above tree.
Since A,B,C,E forms a diamond, to convert it into a tree, I need to move B and C into a line.
I have tried following:
- Topological Sort : Output is A -> D -> B -> C -> E -> F .
- Topological Sort with order : A -> [B,C,D] -> E -> F
Topological Path gives us a straight path. But, I want to preserve the sequence if possible i.e. A -> D. However, if there is a diamond, I want a node to only have one parent and sequence these parents as well.
Is there a way to generate a tree from a DAG for above cases?
...ANSWER
Answered 2021-Mar-09 at 17:01QUESTION
I want to make a scheduler of subjects with topological sort, but here I am using list comprehension analogue to DAG concepts.
The code:
...ANSWER
Answered 2021-Feb-26 at 06:49Check my code :
From your readIntoList function I just taken output and supply to updated topologicalSort
function.
QUESTION
I've created a custom BGL graph model, like in this answer: What is needed to use BGL algorithms on existing data structures ( edges and vertices as vector)?.
It adapts a custom data structure for use with some Boost.Graph algorithms. The linked answer was enough to get depth-first search working (Coliru) but I run into a problem when using boost::topological_sort:
ANSWER
Answered 2021-Feb-24 at 15:34As you correctly surmised, the error novel is telling you that there is no index map. That is required for the default color map:
UTIL/OUT:
color_map(ColorMap color)This is used by the algorithm to keep track of its progress through the graph. The typeColorMapmust be a model of Read/Write Property Map and its key type must be the graph's vertex descriptor type and the value type of the color map must modelColorValue.Default: an
iterator_property_mapcreated from astd::vectorofdefault_color_typeof sizenum_vertices(g)and using thei_mapfor the index map.
Indeed, the index map isn't even required if you fulfill the color map requirement yourself: Live On Coliru
QUESTION
I'm reformatting a bunch of data processing code. The original code first declare several functions, they have certain topological dependency(which means some function rely on other function's result), then calling them sequentially(using a correct topo sort):
...ANSWER
Answered 2021-Feb-24 at 14:47This is probably bad practice but you could use the global keyword on variables you wish to refer to outside the function.
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