qijingzheng / pysbt Goto Github PK
View Code? Open in Web Editor NEWA python implementation of spherical Bessel transform (SBT) based on algorithm proposed by J. Talman.
License: GNU General Public License v3.0
A python implementation of spherical Bessel transform (SBT) based on algorithm proposed by J. Talman.
License: GNU General Public License v3.0
We spotted this line
https://github.com/QijingZheng/pySBT/blob/main/pysbt/pysbt.py#L132
is implemented via a direct multiplication of gamma and sin function, which has large error when the t value is large.
The original paper proposes a more stable procedure, would you consider implement it in your package?
We were trying to implement the regularized potential from this paper All-Electron Plane-Wave Electronic Structure Calculations for solid-state DFT calculation. We use all-electron plane-wave, so we need to transform the regularized potential into the frequency space like Coulombic potential. But unlike the Couloumbic potential which has an analytical formula of
First, we ensured that the implementation of the DFT code and the SBT routine were correct. The test case is the energy gap between two diamond geometries, and the reference value was computed with quantum espresso (QE). Firstly the base DFT code can match the QE result with a sufficiently large FFT mesh. Then we test the correctness of the SBT routine by replacing Coulombic potential with Yukawa potential
However, we encountered strange numerical issues when we tried to perform SBT on the regularized potential (equation 4 in the paper). The
Also, the N=10000, rmin=1e-5, rmax=100
, and 2 is with N=100000, rmin=1e-5, rmax=1000
.
This also confirms that the oscillation is an artifact since the oscillation pattern is determined by the radius grid parameters.
However, the SBT is somewhat "self-consistent" in the sense that, we can perform iSBT on the SBT-transformed value and get back the regularized potential in real space pretty well. As shown in the plot below, the iSBT value aligns with the original function in real space very well:
The absolute error of the iSBT is quite small:
Now we have several hypothesis, either SBT cannot be applied in this case or there is some numerical instability in the current implementation. We would appreciate your insight on this. Thanks!
A declarative, efficient, and flexible JavaScript library for building user interfaces.
๐ Vue.js is a progressive, incrementally-adoptable JavaScript framework for building UI on the web.
TypeScript is a superset of JavaScript that compiles to clean JavaScript output.
An Open Source Machine Learning Framework for Everyone
The Web framework for perfectionists with deadlines.
A PHP framework for web artisans
Bring data to life with SVG, Canvas and HTML. ๐๐๐
JavaScript (JS) is a lightweight interpreted programming language with first-class functions.
Some thing interesting about web. New door for the world.
A server is a program made to process requests and deliver data to clients.
Machine learning is a way of modeling and interpreting data that allows a piece of software to respond intelligently.
Some thing interesting about visualization, use data art
Some thing interesting about game, make everyone happy.
We are working to build community through open source technology. NB: members must have two-factor auth.
Open source projects and samples from Microsoft.
Google โค๏ธ Open Source for everyone.
Alibaba Open Source for everyone
Data-Driven Documents codes.
China tencent open source team.