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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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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 ...
blov's user avatar
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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 ...
John's user avatar
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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? ...
user366312's user avatar
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 ...
Klaus3's user avatar
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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 ...
Yuriy S's user avatar
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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 ...
thimoooh's user avatar
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 ...
CafféSospeso's user avatar
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 ...
CafféSospeso's user avatar
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, ...
cocomac's user avatar
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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 ...
CafféSospeso's user avatar
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? ...
John R.'s user avatar
  • 155
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 ...
Ξένη Γήινος's user avatar
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! ...
D G's user avatar
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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 +...
Steve's user avatar
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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 ...
Giogre's user avatar
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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 ...
Giogre's user avatar
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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. ...
frozenca's user avatar
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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). ...
frozenca's user avatar
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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 ...
AulwTheo's user avatar
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 <...
CafféSospeso's user avatar
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 ...
JimmyHu's user avatar
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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: ...
JimmyHu's user avatar
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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 ...
Roni Saiba's user avatar
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 ...
coderodde's user avatar
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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. ...
coderodde's user avatar
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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 ...
Edward's user avatar
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5 votes
3 answers
260 views

Optimizing an implementation of the RKF method

This is an algorithm regarding the RKF method: ...
Amirhossein Rezaei's user avatar
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 ...
Iwan Phillips's user avatar
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 ...
Luca Argenti's user avatar
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 ...
Iwan Phillips's user avatar
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 ...
FodderOverflow's user avatar
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: ...
Reinderien's user avatar
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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 ...
Vishal's user avatar
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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 ...
James Cagalawan's user avatar
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....
Francis Cugler's user avatar
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 ...
Francis Cugler's user avatar
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 ...
Blue's user avatar
  • 133
3 votes
1 answer
780 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 ...
Stavros Avramidis's user avatar
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). ...
mcocdawc's user avatar
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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. ...
Shankar_Dutt's user avatar
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: ...
das-g's user avatar
  • 179
3 votes
4 answers
1k views

Simpson's method for numerically computing the integration of a function

I have implemented the Simpson's rule for numerical integration. Check this video for the implemented function. ...
user366312's user avatar
1 vote
1 answer
1k views

What would be the computationally faster way to implement this 2D numerical integration?

I am interested in doing a 2D numerical integration. Right now I am using the scipy.integrate.dblquad but it is very slow. Please see the code below. My need is to ...
Shankar_Dutt's user avatar
1 vote
2 answers
596 views

Implementation of Newton's method of finding root of a function

The following is an implementation of Newton's method of finding root of a function. ...
user366312's user avatar
1 vote
2 answers
331 views

Simple definite integral calculator

I made this code to compute definite integrals in Processing. It works by getting the rectangle between the maximum value between the previous function value and the current function value, and then I ...
Simple coder's user avatar
4 votes
1 answer
192 views

Fortran 90 / openmp heat transfer simulation optimization

I'm a newbie playing around with Fortran 90 and openmp and wrote the code below (a simple 2D heat transfer simulation) for testing purposes. So far I don't see any speedup by using openmp / parallel ...
HotDogCannon's user avatar
1 vote
2 answers
459 views

Get the best rational approximations for any real number in builtin Python

Best rational approximations is a technical term and not subjective. The best rational approximations are the convergents of a value plus it's semi convergents that are closer to the original value ...
FodderOverflow's user avatar
4 votes
0 answers
96 views

Estimate area of cropped circle with Monte Carlo

I looking around and not finding anything, I developed a simple function for estimating the area of a possibly cropped circle inside a frame. It uses a very basic MC implementation. It is pretty fast ...
Gabriel's user avatar
  • 575
24 votes
4 answers
4k views

IEEE 754 square root with Newton-Raphson

I have an implementation of the sqrt function that uses a combination of IEEE 754, packed bitfields, and the Newton-Raphson algorithm: ...
S.S. Anne's user avatar
  • 1,725
13 votes
2 answers
1k views

Mean π: Archimedes vs. Gauss - π computation through generalized means

I've written this simplified code to compute Pi for educational/demonstration purposes. These methods are based upon the generalized means: see a presentation on Pi and the AGM. Archimedes' method ...
FodderOverflow's user avatar

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