LearnSciComp.jl

LearnSciComp is under-construction Julia package, which will have generic tools required for scientific computing by an under-grad or masters student. The purpose of the package is for now purely limited to learning. The documentation of some example-based blogs based on LearnSciComp tools can be found here.

What and How do I contribute ?

The guidelines and scope of contributions(pull-requests) that are accepted is also discussed in (https://scicompresources.github.io/). Please feel free to check Discussions for knowing current plans, or feel free to create an issue

How do I work and test LearnSciComp.jl locally on my computer?

1. Clone the repository through terminal with git clone https://github.com/SciCompResources/LearnSciComp.git
2. Test cases have been added in test folder. You may take a look!
3. Start Julia in your favourite IDEs(VS Code, Juno to name a few) or inside Julia REPL
4. Change directory by setting path to LearnSciComp folder using cd("path").
5. Enter package mode by pressing ]. Enter test to test any newly added tests-cases or newly features added.(And hope they pass!)

How to start with LearnSciComp.jl features wih julia ?

1. Get Julia installed through suitable Julia binaries at https://julialang.org/downloads/.
2. Start Julia in your favourite IDEs(VS Code, Juno to name a few) or inside Julia REPL
3. Enter package mode by pressing ]
4. Enter add https://github.com/SciCompResources/LearnSciComp.git while you are in package mode
5. Enter back to julia mode. Precompile by entering using LearnSciComp. This shall enable the features meantioned below

Features available currently

1. Deirvative tools - function fornberg to calculate weights of finite-difference formulas for arbitrary grid spacing.

"""
Central difference FD for second derivative, with order of accuracy= 2
    u''(xᵢ) = ( u(xᵢ-₁) - 2.u(xᵢ) + u(xᵢ+₁) ) / (Δx)^2

Consider,            i = 0,  Δx = 1
         therefore,  weights should be {1 , -2, 1}
"""
using LearnSciComp
order = 2;  # order of derivative you wish to approximate     
z = 0;      # location of point at which you wish to approximate the derivative
x = [-1, 0, 1];  # grid points over which the stencil is extended
julia> fornberg(order, z, x)
3-element Vector{Float64}:
  1.0
 -2.0
  1.0

You may also find hermite-based finite difference weights for arbitrary grid spacing by providing an optional argument dfdx = true as follows

order = 2;  # order of derivative you wish to approximate     
z = 0;      # location of point at which you wish to approximate the derivative, using weights of `f(x)` and `f'(x)`
x = [-1, 0, 1];  # grid points over which the stencil is extended
julia> d, e = fornberg(order, z, x;dfdx = true)
([2.0, -4.0, 2.0], [0.5, 0.0, -0.5]) 

where, d consists of weights of f(x) and e contains weights of f'(x)

2. Spectral tools - Discrete fourier transform function DFT_1, DFT_2, DIT_FFT_radix2 and DIT_FFT_radix2_mem which are basically less-effective but accurate version of Fast Fourier transform fft function in FFTW package.

Note: You may enter help mode in julia by pressing ? and entering the name of features, say fornberg to see the description of the feature