Questions tagged [numerical-methods]
Algorithms which solve mathematical problems by means of numerical approximation (as opposed to symbolic computation).
215
questions
0
votes
1
answer
24
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 ...
- 19
0
votes
0
answers
23
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 ...
- 1
2
votes
1
answer
115
views
Minimalistic implementation of Leapfrog integration algorithm
Please review this C++ listing of an implementation of Leapfrog integration.
Was the algorithm implemented correctly?
...
- 585
2
votes
1
answer
227
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 ...
- 123
4
votes
1
answer
429
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 ...
- 205
2
votes
1
answer
208
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 ...
- 21
0
votes
1
answer
231
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 ...
- 289
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 ...
- 289
2
votes
3
answers
152
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, ...
- 123
2
votes
2
answers
326
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 ...
- 289
1
vote
1
answer
82
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?
...
- 155
1
vote
1
answer
106
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 ...
- 3,014
1
vote
1
answer
170
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
242
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:
$$
y(k) = b_0\cdot x(k) + b_1\cdot x(k-1) + \ldots +...
- 355
4
votes
1
answer
400
views
C++ bond mathematics calculator
I have written a program in C++ that processes financial bond mathematics, making extensive use of the valarray class, so that mathematical functions and operations ...
- 331
14
votes
4
answers
2k
views
Numerical integration in C++: Newton-Cotes formulas
I have tried my hand with implementing simple quadrature formulas in C++.
Definite integral: $$\int_a^b f(x) dx$$
Domain of integration \$[a, b]\$ divided into \$n\$ intervals of equal length \$h = (b ...
- 331
3
votes
1
answer
110
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.
...
- 1,693
4
votes
2
answers
942
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).
...
- 1,693
2
votes
1
answer
173
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 ...
- 21
0
votes
0
answers
456
views
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 ...
- 1,132
3
votes
1
answer
256
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 <...
- 289
4
votes
2
answers
1k
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 ...
- 3,996
5
votes
0
answers
973
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:
...
- 3,996
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 ...
- 211
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 ...
- 27k
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.
...
- 27k
14
votes
1
answer
897
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 ...
- 65.3k
5
votes
3
answers
244
views
Optimizing an implementation of the RKF method
This is an algorithm regarding the RKF method:
...
1
vote
1
answer
70
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 ...
1
vote
0
answers
121
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 ...
- 302
5
votes
1
answer
477
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 ...
4
votes
1
answer
450
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 ...
- 633
2
votes
1
answer
45
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:
...
- 59.1k
4
votes
1
answer
206
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 ...
- 43
5
votes
1
answer
298
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 ...
- 139
4
votes
0
answers
166
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 the user: emma-x and some from user: sudo-rm-rf-slash
Here is my fully revised ...
- 975
4
votes
2
answers
1k
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 ...
- 975
3
votes
2
answers
2k
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 ...
- 133
3
votes
1
answer
603
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
...
3
votes
2
answers
89
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).
...
- 944
1
vote
0
answers
225
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.
...
- 31
7
votes
3
answers
5k
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:
...
- 179
3
votes
4
answers
987
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.
...
- 585
1
vote
1
answer
765
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 ...
- 31
1
vote
2
answers
487
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.
...
- 585
1
vote
2
answers
284
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 ...
- 119
4
votes
1
answer
176
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 ...
- 141
1
vote
2
answers
401
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 ...
- 633
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 ...
- 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:
...
- 1,716