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Questions tagged [numerical-methods]

Algorithms which solve mathematical problems by means of numerical approximation (as opposed to symbolic computation).

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6 votes
1 answer
618 views

Numerical integration with Numba

I'm a bit new to working with Numba, but I got the gist of it. I wonder if there any more advanced tricks to make four nested for loops even faster that what I have ...
8 votes
3 answers
304 views

Integrator 2.0: A Simple Integrator in C++17

This is a follow up of A simple definite integrator class of a single variable in C++. I took most of the advice from Emma X and some from sudo rm -rf slash. Here is my fully revised code: Integrator....
5 votes
2 answers
2k views

A simple definite integrator class of a single variable in C++

I have written a simple Integrator class in C++17 that can perform either a definite single integration of a single variable or a definite double integration of a ...
4 votes
3 answers
2k views

Two dimensional bicubic interpolation implementation in C

This is a follow-up question for Two dimensional bicubic interpolation implementation in Matlab and Two dimensional gaussian image generator in C. Besides the Matlab version code, I am attempting to ...
1 vote
1 answer
249 views

Implementing Preconditioned conjugate gradient

I have implemented the Preconditioned Conjugate Gradient (PCG) method for solving a system of linear equations in Python and I would appreciate it if someone could verify its correctness since I am ...
0 votes
0 answers
40 views

cubic spline routine

I tried to implement the cubic spline algorithm in cython. I want to ask how I can make the code more efficient in terms of speed. Any suggestions or references ...
2 votes
1 answer
158 views

Minimalistic implementation of Leapfrog integration algorithm

Please review this C++ listing of an implementation of Leapfrog integration. Was the algorithm implemented correctly? ...
14 votes
4 answers
2k views

Numerical integration in C++: Newton-Cotes formulas

I have tried my hand with implementing simple quadrature formulas in C++. Definite integral: $$\int_a^b f(x) dx$$ Domain of integration \$[a, b]\$ divided into \$n\$ intervals of equal length \$h = (b ...
2 votes
1 answer
283 views

Finite difference estimation of partial derivatives for arbitrary grids in python

I am currently working on testing some codes on python to solve differential equations by finite differences, but some problems and equations i am dealing with are: Too big to keep manually writing ...
18 votes
3 answers
4k views

Simulating a two-body collision problem to find digits of Pi

I came across a nice video on 3Blue1Brown's channel that highlights a very indirect way to find the digits in Pi. I'd suggest watching the whole video, but briefly: The setup is as above. A "small" ...
4 votes
1 answer
571 views

Runge-Kutta 4 implementation in Rust

This is a toy problem. I want to try using Rust for numerical modeling, but I found zero tutorials for this kind of stuff. I also just started learning Rust yesterday, so please bear with me. Usually ...
10 votes
3 answers
205 views

Reinventing the Math Functions

Just for practice in the mathematical side of programming, I decided to rewrite the math functions, with the addition of the root() function, which the Math library ...
2 votes
1 answer
235 views

Integration loop over multiple doping and temperature levels

I want to perform some calculations on a large dataset. The code can be found below, where I want to calculate the values for 'results_nr' over a large loop (1000 x 910) values. Can you help me out ...
0 votes
1 answer
255 views

Parallelise numerical integration with OpenMP in C++

I would like to parallelise with OpenMP a one-dimensional integral using the integrate() function implemented in the Boost library. I found a rather obscure ...
2 votes
3 answers
166 views

Calculating square roots using binary search

I'm trying to find the square root of a number (num) using binary search in Rust. I'm new to Rust, but I've done quite a bit of programming in other languages, ...
7 votes
7 answers
1k views

A probability distribution function, to be called repeatedly during numerical integration

I am trying to speed up as much a possible this function in C++. As I explained in another post, Implementing multidimensional integral for a custom function in C++, this function will be used inside ...
2 votes
2 answers
398 views

Implementing multidimensional integral for a custom function in C++

I am not an expert with C++, but I am trying to implement a 4-dimensional integral using GSL numerical integration approach. The code below shows the whole algorithm. Although it seems correct what I ...
1 vote
1 answer
108 views

Three efficient JavaScript functions that converge to pi extremely fast

I am learning JavaScript and decided to translate my Python scripts into JavaScript. Approximations of π are extremely popular programming challenges and I am sure they must be a staple of the ...
1 vote
1 answer
104 views

Calculate the value of PI in JS

I have created an algorithm which calculates the value of PI in JavaScript. Can this algorithm to be improved? ...
1 vote
1 answer
206 views

Calculating sine and cosine

Are there any thing that I have to consider to improve the following code in either performance and others? Any comments and suggestions are welcome! ...
2 votes
1 answer
317 views

Implementation of versatile IIR digital filter in C++

I have realized that all the digital filters of the IIR type have the same structure. They are described by difference equation in following form: $$ y(k) = b_0\cdot x(k) + b_1\cdot x(k-1) + \ldots +...
4 votes
1 answer
469 views

C++ bond mathematics calculator

I have written a program in C++ that processes financial bond mathematics, making extensive use of the valarray class, so that mathematical functions and operations ...
5 votes
0 answers
1k views

Two dimensional bicubic interpolation implementation in Matlab

I am attempting to implement two dimensional bicubic interpolation algorithm in Matlab. The input is a two dimensional array and the output is the interpolated result. The test input matrix: ...
3 votes
1 answer
122 views

libsvm++ : Rewritten libsvm in newer C++

The most famous library for Support Vector Machine (SVM) algorithm is libsvm (https://github.com/cjlin1/libsvm/), but I felt that its code style is too old, I rewrote in newer C++ as a hobby project. ...
4 votes
2 answers
1k views

C++: Linear Regression and Polynomial Regression

I wrote a simple linear/polynomial regressor based on my previous matrix project (https://github.com/frozenca/Ndim-Matrix). ...
8 votes
1 answer
1k views

Genetic algorithm to guess coefficient of a polynomial

I have tried to code a genetic algorithm to guess the coefficients of a degree 4 polynomial. The information initially provided is values of y = f(x) for different x using the original polynomial. I ...
2 votes
1 answer
207 views

Generating a matrix with each row having normalized weights

I just asked this question over Stack Over Flow on how to improve my code and reposting it here as someone on Stack Overflow recommended this platform. I have written two python functions and they are ...
8 votes
1 answer
372 views

Metropolis Monte Carlo Sampler in Rust

the following is an implementation of the standard Metropolis Hastings Monte Carlo sampler. You can read more about it here. At the end I am going to give you a link to the Rust playground, so you ...
3 votes
1 answer
281 views

Implementation of Multidimensional numerical integration in C++ and R

I'm trying to perform a 4-dimensional numerical integration in R using a function I wrote in C++ code which is then sourced in <...
2 votes
1 answer
69 views

A simple clusterness measure of data in one dimension using Java - follow-up 2

(See the previous version here.) This time, I have encorporated all the suggestions made by Marc. Also, I changed the type of points from Double to ...
1 vote
1 answer
53 views

A simple clusterness measure of data in one dimension using Java - follow-up

(See the previous version here.) (See the next version here.) This time, I have incorporated all the suggestions made by Roman; my new version follows. ...
1 vote
1 answer
97 views

A simple clusterness measure of data in one dimension using Java

(See the next follow-up here.) Problem definition Given \$X = (x_1, \dots, x_n)\$ such that \$x_1 \leq x_2 \leq \dots \leq x_n \$. Let \$x_{\min} = \min X = x_1\$, \$x_{\max} = \max X = x_n\$ and \$r =...
14 votes
1 answer
1k views

C++ class to create and evaluate Chebyshev approximations of arbitrary functions

I recently needed to create a function to approximate a complex trigonometric function on an embedded system without a floating point unit and without a fast trigonometric library. So I pulled out my ...
4 votes
1 answer
156 views

Volatility updating with Heston-Nandi model

I'm trying to program a volatility updating rule using iteration. I start with the well-known Heston-Nandi model where the returns dynamics are: $$ \left\{ \begin{array}{rcl} R_{t+1} &=&...
5 votes
3 answers
260 views

Optimizing an implementation of the RKF method

This is an algorithm regarding the RKF method: ...
1 vote
0 answers
125 views

A Bspline module for AMO

Here is a (reduced version of) a module for Bsplines, which I have used multiple times for my work on Atomic, Molecular, and Optical physics (AMO, in the trade lingo, a.k.a. "I love", in ...
1 vote
1 answer
73 views

generating stochastic coloured noise for many oscillators

I have a system of n oscillators which oscillate with time. To each of these oscillators I am adding a fluctuating coloured noise term with a different seed for each oscillator. Here is my code for ...
5 votes
2 answers
981 views

Gees - GPL Euler equation solver

As a little helper I recently had to write a code that solves the 1-D Euler equations. As it serves my purpose well I though others could make use of it as well. The homepage of the code can be found ...
4 votes
1 answer
485 views

Bounded spigot algorithms for e and pi in Python

I've written bounded spigot algorithms(Spigot Algorithm) for e and pi. I would like to understand if there is anything I can do to make this more efficient. I've done things already like move the ...
5 votes
1 answer
539 views

Using Euler-Maruyama method to solve Ornstein-Uhlenbeck equation (SDE)

I am trying to implement the Euler–Maruyama method and use it to solve the Ornstein–Uhlenbeck process. I am basing my code on the wikipedia page where a python implementation is shown. More generally ...
2 votes
1 answer
47 views

Vectorized type conversion for autocorrelation

I have a simple task as part of a larger autocorrelation DSP system - to convert from signed 16-bit integer audio samples to floating-point. This part is quite self-contained: ...
4 votes
1 answer
216 views

Modelling of partcle flow under electric field

This is my first modeling exercise on the particle flow. Recently, I read a paper https://acp.copernicus.org/articles/20/3181/2020/. After reading the paper, thought of modeling it in Python. It seems ...
7 votes
1 answer
3k views

Numerical differentiation by finite differences

Numerical differentiation is known to be ill-conditioned unless using a Chebyshev series, but this requires global information about the function and a priori knowledge of a compact domain on which ...
5 votes
1 answer
332 views

C++ - Logistic Regression Backpropagation with Gradient Descent

I implemented binary logistic regression for a single datapoint trained with the backpropagation algorithm to calculate derivatives for a gradient descent optimizer. I am primarily looking for ...
3 votes
2 answers
3k views

Implementing a Steepest Descent Algorithm

I am teaching myself some coding, and as my first "big" project I tried implementing a Steepest Descent algorithm to minimize the Rosenbrock function: $$f(x, y) = 100 (y - x^2)^2 + (1 - x)^2$$ The ...
3 votes
1 answer
781 views

Linear Interpolation for sorted arrays

I have made a linear interpolation functions as a side project of mine. It assumes everything is sorted before hand - x and f(x) are the same length. I would like to ask for: general recommendations ...
4 votes
1 answer
658 views

Polynomial implementation in Golang

I am writing a numerical analysis library in golang for which I need to implement a polynomial struct. Here is the source code: ...
3 votes
2 answers
102 views

Newton Raphson and polynomials in C

I have the following code, that defines: A polynomial struct with some useful functions. The newton Raphson algorithm for polynomials. and calculates sqrt(2). ...
7 votes
3 answers
6k views

pure Python Bézier curve implementation

I came up with this recursive pure-Python implementation of De Casteljau's algorithm for computing points on a Bézier curve: ...
1 vote
0 answers
249 views

Numerical Double Integration using numba and scipy

Please see the following code. I am using it to calculate the double integration. Please help me to improve the code. ...

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