polya | A heuristic procedure for proving inequalities | Machine Learning library
kandi X-RAY | polya Summary
kandi X-RAY | polya Summary
Authors: Jeremy Avigad, Robert Y. Lewis, Cody Roux. Polya is a system designed to support interactive theorem proving by verifying the kinds of inequalities that arise in ordinary mathematical arguments. The method is described in the paper "A heuristic prover for real inequalities," available [online] The version of the system described in the paper is tagged "v0.2". The system is released under the [Apache 2.0 license] It is still an experimental prototype, and feedback is very welcome. For instructions on setting up and using Polya, see the file INSTALL.md.
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Top functions reviewed by kandi - BETA
- Updates blackboard
- Return the direction of a point
- Return the boundaries of a list of vertices
- Given a list of vertices and lin_j
- Updates the blacklist
- Convert a summand
- Raises AssertionError if one equivalence of one_equison
- Convert a Zero - comparison term to a comparison
- Announce the average run times
- Calculates the totient of the totient
- Update the blacklist
- Find the two lines that have the same info
- Return the root of the root at t
- Updates the coefficients of the covariance matrix
- Return True if the direction of this direction is equal to another
- R Return a list of all primes below N
- Solve a problem
- Compute the Compute equation
- Add a half - plane comparison of two lists
- Return the perfect root of a p
- Validate a claim
- Return True if points falls on the same side
- Return the halfplane of a given comp
- Return a list of Var objects
- Example of an example
- Update the blackboard
polya Key Features
polya Examples and Code Snippets
Community Discussions
Trending Discussions on polya
QUESTION
Currently, I check if my polygon lies within another polygon using polya.contains(polyb)
However, it is not necessary my polygon polyb lies completely inside polya. Is there a built-in method to check if three-fourth of the polygon is inside polya?
...ANSWER
Answered 2021-Mar-17 at 10:12I figured it out, posting my answer here if anyone else might need it. I used the hint given by Mr. T, the solution was extremely simple. I check if the overlapping area is within a certain threshold. It is also similar to the concept of IOU in Computer Vision.
QUESTION
I wish, for each polygon of a SpatialPolygonsDataFrame polyA (in my case each country in the wrold from wrld_simpl or GADM), and for each category of a categorical raster rcat, sum the values of another raster with quantitative values rquant. The final output would be a dataframe with the following columns: country name, category name, summed value.
I am familiar with bits of code but these do not fully allow me to figure out the right script to write. Is someone able to help me? Apologies for not providing a reproducible example here. Note that I'm working with rasters with 0.0083 resolution (ncell = 933120000), so I don't think converting the rasters to dataframes is a good idea.
The following script sums values from rquant for each polygon
...ANSWER
Answered 2020-Sep-06 at 22:15The way I ended up dealing with the data extraction was to first create a quantitative raster for each category of the categorical raster rcat (with values=NA for pixels under other categories and rquant values for pixels under the relevant category). Then, for each of these new rasters, I extracted their information per polygon using the velox package devtools::install_github('hunzikp/velox') - great for extracting dat from large datasets.
QUESTION
I have a class I want to pickle using this function:
...ANSWER
Answered 2020-Mar-23 at 18:41Unfortunately it looks like that pypolyagamma library you use doesn't currently support pickling/unpickling those objects, so in a word: you can't pickle them without modifying the library.
Furthermore, since it wraps a C++ class, the pickler/unpickler isn't trivial; it'd need to know what state from that wrapped class is necessary for the object to be in the same state after unpickling.
QUESTION
I have the following string
a = "AAWJBDJSDJBJSQQAAASDNDKSDKJSDKSJDDJKJSKJAAAAASKJDSJDKJSDKJDAAAAAAAA"
The first thing I do is count the A's in the line:
a.count("A")
This works fine.
The next thing I want to do is find the value of the longest overlapping "A". In this case it would be AAAAAAAA (8 times).
So i want my output to be:
The Longest polyA is 8
Does anyone know how I can do this?
...ANSWER
Answered 2019-Dec-03 at 23:51Best way to do this is with regular expressions:
QUESTION
I'm writing a code where I need to calculate the overlapping area of two polygons very frequently (one always is a square, the other one is a simple but in general non-convex polygon). However, using CGAL for this, I occasionally encounter segmentation faults. The following code provides a minimal example. Note that as soon as one of the point coordinates is moved by 0.001, everything works fine.
...ANSWER
Answered 2018-Nov-20 at 11:38If the first polygon is always convex (as most squares are) and you only care for the area of overlap, you can roll your own solution easily.
Consider the support line of one of the sides of the first polygon. You will implement clipping against a half plane, let us assume bounded by x=0, WLOG.
Create an empty output polygon. Then try all edges of the second polygon in turn. Assign every vertex the boolean condition x>=0. If the condition is different for both endpoints, append the intersection of the side with the axis x=0 to the new polygon; then if the condition is true for the final endpoint of the side, append it as well.
In the end, you'll get a new polygon which is the clipped version of the original. In case the clipped polygon should be disconnected, the algorithm will produce a connected polygon with extra connecting sides along x=0. But as regards the computation of the area, this doesn't matter at all.
Repeat with the four clipping sides and compute the area using the shoelace formula.
QUESTION
I have an object of type PolyaUrn
called myUrn
. I instantiate it and use some methods to manipulate it. Then, I get the int[]
field of myUrn
named ballCounts
. I pass this int[]
to a constructor to create a new object of type SimpleUrn
, named su
. However, when I try to call methods on su
I get a NullPointerException
. I am using the new
keyword to create an object of type SimpleUrn
and point to variable su
. I don't understand why I can't reference su
using the dereferencing operator .
Code below:
...ANSWER
Answered 2018-Nov-06 at 20:51You are shadowing ballCounts
in the SimpleUrn
constructor. Change this
QUESTION
I have been reading a lot about the sutherland hodgman polygon clipping algorithm and understand the general idea. However, when I see the actual implementation of it (like the one below), I get confused about the coordinate comparisons such as those in the intersection
and inside
methods. Therefore, I was wondering if someone could elaborate on what and why? I see a ton of videos and articles explaining the general concepts but I really have trouble finding some explanation of the actual details regarding the implementation.
ANSWER
Answered 2018-Jul-14 at 02:59You say you understand the general idea, presumably from reading something like Sutherland Hodgman Algorithm. That explains at a high level exactly what inside
and intersection
do.
As to the details of how they achieve their objectives, that is all just straight up text book linear algebra.
inside
is testing the sign of (cp2 - cp2)
cross (p - cp1)
and returning true
iff the sign is strictly greater than zero. You could rewrite the return statement as:
QUESTION
I'm trying to implement some draws using a polya urn scheme using Rcpp. Basically, I have a matrix I'm drawing from, and a 2nd matrix with weights proportional to the probabilities. After each draw, I need to increase the weight of whichever cell I drew.
I was running into some indexing errors which lead me to examine the sampling more generally, and I found that my weight matrix was getting modified by RcppArmadillo::sample. Two questions (1) is this behavior that I should have expected or is this a bug which I should report somewhere? (2) Any ideas on current work-around? Here's a reproducible example:
...ANSWER
Answered 2018-Jul-02 at 20:20That is known and documented behaviour.
You could do
i) Use Rcpp::clone()
to create a distinct copy of your SEXP
(ie NumericMatrix
).
ii) Use an Armadillo matrix instead and pass as const arma::mat & m
.
There are architectural reasons having to do with the way R organizes its data structure which mean that we cannot give you fast access (no copies!) and also protect against writes.
QUESTION
I am trying to recreate the Pólya urn model (https://en.wikipedia.org/wiki/Pólya_urn_model) in R, with ggplot. The model basically starts with 1 white and 1 black ball in an 'urn' and randomly chooses one ball and put it back together with a ball of the same color. I do this in R for lets say 10 iterations (so 10 times take out one ball and put it back together with another ball from the same color). And I run this say 5 times. Thus, i get a data frame of 5 columns (=for each run) and 10 rows (=for the iterations).
What I want is to illustrate is this but then this picture has a lot more trials and iterations obviously.
What I have so far is a data frame where each column is the fraction of white balls in the urn per trial/run and I would like to illustrate how the proportions changed for each iteration. And I want to show this separately for each run, so each run I would like to have in a different color.
I have looked through countless similar questions but did not find an answer. I think it's because my data frame has now 5 columns but when i reshape it then I get only a single column of the proportions and next to each I get a code illustrating which column it belonged to - but in this case ggplot only draws one single line in 4 colors.
...ANSWER
Answered 2018-May-18 at 11:59Using your df
you can do something like that:
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Install polya
You can use polya like any standard Python library. You will need to make sure that you have a development environment consisting of a Python distribution including header files, a compiler, pip, and git installed. Make sure that your pip, setuptools, and wheel are up to date. When using pip it is generally recommended to install packages in a virtual environment to avoid changes to the system.
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