Questions tagged [numerical-methods]

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

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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 ...
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1 vote
1 answer
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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? ...
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1 answer
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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 ...
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1 answer
99 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! ...
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2 votes
1 answer
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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 +...
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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 ...
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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 ...
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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. ...
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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). ...
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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 ...
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2D Discrete Fourier Transform using Fortran

I am solving the 2D Wave Equation using Fourier Transform. The Discrete Fourier Transform (and the inverse also) is done inside the kx-loop and ...
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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 <...
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4 votes
2 answers
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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 ...
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Two dimensional bicubic interpolation implementation for dlarray in Matlab

This is a follow-up question for Two dimensional bicubic interpolation implementation in Matlab. While I am working on neural network designing, I want to compare the effects between using padding and ...
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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: ...
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7 votes
1 answer
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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 ...
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1 answer
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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 ...
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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. ...
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14 votes
1 answer
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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 ...
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3 answers
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Optimizing an implementation of the RKF method

This is an algorithm regarding the RKF method: ...
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1 answer
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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 ...
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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 ...
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5 votes
1 answer
319 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 ...
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4 votes
1 answer
289 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 ...
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2 votes
1 answer
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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: ...
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4 votes
1 answer
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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 ...
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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 ...
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4 votes
0 answers
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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 the user: emma-x and some from user: sudo-rm-rf-slash Here is my fully revised ...
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4 votes
2 answers
833 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 ...
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3 votes
2 answers
559 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 ...
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3 votes
1 answer
130 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 ...
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3 votes
2 answers
59 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). ...
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1 vote
0 answers
99 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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7 votes
3 answers
4k 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: ...
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3 votes
4 answers
575 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. ...
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1 answer
94 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 ...
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1 vote
2 answers
86 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. ...
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1 vote
2 answers
147 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 ...
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4 votes
1 answer
104 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 ...
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1 vote
2 answers
194 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 ...
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4 votes
0 answers
79 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 ...
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24 votes
4 answers
3k 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: ...
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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 ...
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2 votes
1 answer
94 views

Arbitrary precision Euler-Mascheroni constant via a Brent-McMillan algorithm with no math module

Utilizing the below relation, I am able to compute the Euler constant to great precision on a single thread quickly and simply. My process is to compute the natural log via the AGM(utilizing Pi an ...
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1 vote
1 answer
58 views

Euler-Mascheroni Single Thread Speed Improvements

The below code was written to generate γ, for educational purposes. My general methodology is as follows: Compute Gamma via the accepted answer's algorithm here. In order to do this I need to ...
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4 votes
1 answer
429 views

Calculate the Euler-Mascheroni constant without the math module

The below code was written to generate γ, for educational purposes. Single threaded, no functional zeroes required, no binary splitting(which can all be used to compute competitively like y-cruncher, ...
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12 votes
3 answers
5k views

Python π = 1 + (1/2) + (1/3) + (1/4) - (1/5) + (1/6) + (1/7) + (1/8) + (1/9) - (1/10) ...1748 Euler

I wrote this code to show that my reddit post is correct. After the first two terms, the signs are determined as follows: If the denominator is a prime of the form 4m − 1, the sign is positive; if ...
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4 votes
2 answers
1k views

Trapezoidal rule for set of data

Here is the question from the book of Mark Newman-Computational Physics Exc 5.1 a) Read in the data and, using the trapezoidal rule, calculate from them the approximate distance traveled by the ...
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4 votes
1 answer
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Evaluating π using Monte Carlo methods - Serial vs OMP

I wrote this simple code for evaluating the π using Monte Carlo method. This is the serial version: ...
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13 votes
1 answer
134 views

Continuous Fourier integrals by Ooura's method

I have a PR implementing Ooura and Mori's method for continuous Fourier integrals. I used it here to compute an oscillatory integral that Mathematica got completely wrong, and then I thought "well ...
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