Questions tagged [numerical-methods]
Algorithms which solve mathematical problems by means of numerical approximation (as opposed to symbolic computation).
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questions
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Implementing basic polynomial interpolation
I am self-learning some numerical algorithms from the book Numerical methods in Scientific computing by Dahlquist/Bjorck. Problem 4.1.2 asks to write a program that ...
1
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0answers
26 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 ...
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0answers
19 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 ...
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1answer
63 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
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1answer
77 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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1answer
33 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
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1answer
142 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
101 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 ...
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0answers
68 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 ...
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2answers
152 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
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2answers
141 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
68 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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2answers
39 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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0answers
32 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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3answers
2k 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
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4answers
235 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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1answer
35 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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2answers
61 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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2answers
52 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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1answer
71 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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2answers
128 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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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 ...
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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 ...
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1answer
82 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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1answer
46 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
257 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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3answers
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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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2answers
348 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
170 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
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1answer
97 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
259 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
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0answers
154 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
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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
104 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
59 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
92 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
411 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 ...
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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 ...
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2answers
2k views
0
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1answer
58 views
A simple clusterness measure of data in one dimension using Java
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 = x_{\max} - x_{\min}\$. Also, ...
4
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1answer
238 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:
...
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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" ...
9
votes
1answer
173 views
Discrete Lanczos Derivatives
I have a PR implementing denoising discrete Lanczos derivatives, following this paper. The following code works well, but the design is a train wreck, and I was hoping to get some advice to improve it....
3
votes
3answers
110 views
A collection of vector functionals
I would like some feedback for a collection of what I call "vector functionals", by which I mean maps \$\ell\colon \mathbb{K}^{n} \to \mathbb{K}\$, where the field \$\mathbb{K} = \mathbb{R}\$ or \$\...
4
votes
1answer
176 views
Complex Newton's Method
I'm trying to build a complex Newton's method. I've submitted a PR here, where you can see the documentation and tests, as well as get a compiling example. I'd appreciate y'alls help reducing the ...
4
votes
0answers
111 views
Bisection and Newton's method for finding a root of an equation
In an attempt to learn Rust, I've written up implementations of the bisection method and Newton's method for finding roots of an equation. Both methods come in two variants: the first one searches for ...
7
votes
0answers
144 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 ...
5
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1answer
422 views
Verilog implementation of trapezoidal integration method
Any and all comments are welcome in this review.
Problem
I've been doing a lot with numerical integration methods recently and have mostly been programming in Python. But...speedups! And FPGAs are ...
7
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1answer
110 views
Implementing numerical integration in Python
I have this Python code that implements a rectangular numerical integration. It evaluates the (K-1)-dimensional integral for arbitrary integer \$K \geq 1\$
$$\int_{u_K = 0}^{\gamma}\int_{u_{K-1} = 0}^...
