Questions tagged [numerical-methods]
Algorithms which solve mathematical problems by means of numerical approximation (as opposed to symbolic computation).
196
questions
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2answers
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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 ...
0
votes
0answers
35 views
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 ...
2
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0answers
38 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:
...
7
votes
1answer
311 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
1answer
59 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
1answer
45 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.
...
14
votes
1answer
312 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 ...
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3answers
133 views
1
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1answer
51 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
0answers
82 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 ...
5
votes
1answer
150 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 ...
5
votes
1answer
175 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 ...
2
votes
1answer
36 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:
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4
votes
1answer
147 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 ...
5
votes
1answer
156 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 ...
4
votes
0answers
76 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 ...
4
votes
2answers
373 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 ...
3
votes
2answers
196 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
1answer
87 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
2answers
43 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).
...
1
vote
0answers
61 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
3answers
3k 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
4answers
318 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.
...
1
vote
1answer
46 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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vote
2answers
67 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
2answers
75 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 ...
4
votes
1answer
85 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 ...
1
vote
2answers
157 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 ...
4
votes
0answers
75 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 ...
24
votes
4answers
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:
...
13
votes
2answers
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 ...
2
votes
1answer
88 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 ...
1
vote
1answer
51 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 ...
4
votes
1answer
355 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, ...
12
votes
3answers
4k 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 ...
4
votes
2answers
652 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 ...
4
votes
1answer
278 views
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:
...
13
votes
1answer
114 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 ...
7
votes
1answer
279 views
Parallel Ramanujan's formula for 1/π calculation
I finished my university project for calculating \$1/\pi\$ and I would love to get some feedback.
Before you guys jump into this code please keep in mind newcomer to C++ just decided to use it for ...
7
votes
0answers
201 views
Numerical integration in cython
I have a set of nested functions that I need to call multiple times. I know scipy.quad is pretty fast, but I will need to call the integrator recursively and want ...
7
votes
2answers
144 views
Simple function that simulates survey results based on sample size and probability
What is this:
This is a simple function, part of a basic Monte Carlo simulation. It takes sample size and probability as parameters. It returns the simulation result (positive answers) plus the input ...
3
votes
1answer
107 views
Calculating pi via collisions
This code calculates pi via collisions; it asks for a user input of N which determines the mass of the second block. It is fully working, it just takes forever to run when N >= 2. I want to be able ...
3
votes
1answer
65 views
Monte Carlo pi animation
I have created a program that calculates pi using a Monte Carlo method. It also animates the process and displays the value as it is updated to show how it gets closer and closer to the actual value ...
6
votes
1answer
111 views
Monte Carlo errors estimation routine
I would value your opinion on the following piece of code. I am rather new to both Python and Monte Carlo analysis, so I was wondering whether the routine makes sense to more experienced and ...
2
votes
1answer
502 views
Java Pi Calculation using an Averaged-Leibniz formula
While trying to discover a way to calculate the digits of Pi faster with the Leibniz formula for Pi, I noticed that, if I took two consecuent numbers in the series, and calculate their average, I ...
7
votes
1answer
2k views
C++ Pi Calculator - Leibniz Formula
Yesterday I saw a CodeTrain video in where Daniel Shiffman tried to approximate Pi using the Leibniz series. It was interesting so I decided to try it too.
I wrote this console application with a ...
11
votes
2answers
2k views
1
vote
1answer
88 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 =...
4
votes
1answer
345 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:
...
16
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2answers
2k 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" ...
