Questions tagged [numerical-methods]

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

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44
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8answers
8k views

Prettify math formula in code

I have a function to calculate the normal distribution in Python: ...
33
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8answers
9k views

PI Calculator, Interview Challenge

Greg Beech says here that he asks C# candidates to produce a formula that calculates PI Given that Pi can be estimated using the function \$4 * (1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \dots)\$. ...
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6answers
26k views

Monte Carlo pi calculation

In order to learn the basics of Monte Carlo I calculated pi with it. I also wrote an explanation of the reasoning behind the code. Down here you can see the circle with random points that I simulated ...
24
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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: ...
20
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9answers
4k views

Approximating constant π² to within error

This function takes as input float error and approximates constant π² to within error by computing this sum, term by term, until the difference between the new and the previous sum is less than error. ...
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" ...
14
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2answers
3k views

Pi by Monte-Carlo

I was inspired by this SO post to investigate a good Java8 way to calculate Pi based on simulation. I used a similar task to learn about parallel programming on both CUDA, and Intel Xeon Phi ...
13
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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 ...
13
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1answer
91 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 ...
12
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3answers
3k views

Definite Integral Approximation using the Trapezoidal Method

I wrote a program to calculate the value of Definite Integral of a function from a to b. It used the trapezoidal approximation ...
12
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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 ...
11
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6answers
4k views

Approximating the square root using an iterative method

I wrote this code, based on the Newton-Raphson method, to find the square root of a number. I'm wondering how I can optimise this code, as I am out of ideas. ...
11
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2answers
2k views

Calculate Pi using Monte Carlo

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11
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2answers
4k views

Sqrt (square root) function

As an exercise in learning Scala, I implemented a square root function like this: ...
11
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1answer
219 views

Calculate the closest point to many hyperbolic paraboloids

In this question I asked for a way to compute the closest projected point to a hyperbolic paraboloid using python. Using the iterative approximation answer, I'm able to use the code below to ...
10
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5answers
1k views

Probabilistic matchmaking simulation

The following is a problem I found on this wiki. What can I do to optimize my algorithm, and make this code more C++11? Write a program to discover the answer to this puzzle:"Let's say men and ...
10
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3answers
125 views

Reinventing the Math Functions

Just for practice in the mathematical side of programming, I decided to rewrite the math functions, with the addition of the root() function, which the Math library ...
10
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1answer
1k views

Generate iCalendar .ics files with events for astrological aspects

I'm relatively new to Python, coming from a deep C++ background. I'm mostly looking for feedback on how to make my code more idiomatic/pythonic, but I would welcome and appreciate any and all other ...
9
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1answer
594 views

Gamma function in Rust

The gamma function is one of a couple nice continuous extensions to the traditional factorial function. I used this Python program as a reference, which in turn, uses this Ada program. As the Ada ...
9
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3answers
612 views

Multithreaded Monte-Carlo Integration

I have a PR implementing multithreaded naive Monte-Carlo integration here. My requirements for the class are the following: It should support progress reporting, ETA, and graceful cancellation. It ...
9
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1answer
155 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....
9
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1answer
1k views

Approximating Pi, Monte Carlo integration

I wrote some code that uses Monte Carlo Integration to Approximate pi in Java and Akka. The tl;dr explanation is you can imagine throwing darts at a square with a circle inscribed inside of it. You ...
8
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3answers
6k views

Finding the root of a function by Bisection Method

The program has to look for a root in an interval [a,b]. The root should be declared with a certain accuracy eps. I.e it should ...
8
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4answers
1k views

Buffon's Needle experiment

I was working on a program that simulates the Buffon's Needle experiment. If anyone is not familiar with it, a Wiki link is provided - Buffons's Needle The point of Buffon's experiment is to find ...
8
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3answers
994 views

1D shock tube problem written in Fortran

I have written a simple Euler solver for the 1D shock tube problem. Eventually, I plan to extend this code to solve the full 3D compressible Navier-Stokes equations. Therefore, I want to start with ...
8
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2answers
765 views

Visualizing Newton-Raphson method for finding zeroes of a function

I have created a program to visualize the working of Newton-Raphson method to find the zeroes of a function: newton.m: ...
8
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1answer
177 views

Root finding and integration [closed]

I am trying to implement the modified Next Reaction Method with time varying propensities as mentioned in sections IV and V of this paper. At one step in the process this expression must be evaluated: ...
8
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1answer
975 views

Fitting multiple piecewise functions to data and return functions and derivatives as Fortran code

Background For a future workshop I'll have to fit arbitrary functions (independent variable is height z) to data from multiple sources (output of different ...
7
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3answers
1k views

Implementing numerical integration

I have this C++ code that implements a rectangular numerical integration. It evaluates the \$K\$-dimensional integral $$\int_{u_K = 0}^{\gamma}\int_{u_{K-1} = 0}^{\gamma-u_K}\cdots\int_{u_2}^{\...
7
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3answers
867 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: ...
7
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3answers
6k views

Implementation of Brent's Algorithm to find roots of a polynomial

I made a program that contains a root-finding algorithm for polynomials as a function and contains 3 test polynomials. The algorithm is Brent's method and is based entirely off the pseudocode from ...
7
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2answers
142 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 ...
7
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2answers
337 views

Monte Carlo estimation of the Hypergeometric Function

I am trying to implement the algorithm described in the paper Statistical Test for the Comparison of Samples from Mutational Spectra (Adams & Skopek, 1986) DOI: 10.1016/0022-2836(87)90669-3: $$p =...
7
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1answer
202 views

Monte Carlo Pi (MASM)

I'm currently trying to brush up on my assembly skills and, being at the FPU section of the tutorial, I implemented a very basic version of a Monte-Carlo-Algorithm to compute pi. I deliberately use ...
7
votes
1answer
375 views

2d linear Partial Differential Equation Solver using finite differences

This is code that solves partial differential equations on a rectangular domain using partial differences. fd_solve takes an equation, a partially filled in output, ...
7
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1answer
1k views

Computing exponential function by Taylor Series without overflow

The original question is to write a Fortran program to compute the sum of the first 20 terms in the exponential equation (for x=1,2,3,4,5): $$\sum_{n=0}^\infty \frac{x^n}{n!} = 1 + \frac{x^1}{1!} + \...
7
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1answer
106 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}^...
7
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1answer
2k views

Linear Interpolation C++

I have to write a collection of methods for performing linear, bilinear and trilinear interpolation. I have also to write some tests to show that interpolation is exact for polynomials (which should ...
7
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1answer
4k views

Python class that implements the Newton method

Here is a python function I wrote to implement the Newton method for optimization for the case where you are trying to optimize a function that takes a vector input and gives a scalar output. I use ...
7
votes
1answer
217 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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1answer
2k views

Numerical differentiation by finite differences

Numerical differentiation is known to be ill-conditioned unless using a Chebyshev series, but this requires global information about the function and a priori knowledge of a compact domain on which ...
7
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1answer
147 views

Computing max t such that tanh(pi*sinh(t)/2) <1

I'm looking for a way to quickly determine that maximum value of t such that tanh(pi/2 sinh(t)) is strictly less than 1, for a ...
7
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0answers
118 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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0answers
136 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 ...
6
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2answers
7k views

Compute a numerical derivative

Since I could not get numpy.gradient() to compute a derivative successfully, I wrote a script to compute it manually. Running the script below will output a plot of ...
6
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1answer
2k views

Iterative equation solver in Python

In order to solve a equation where the left hand side appears under an integral on the right hand side: $$ B(p^2) = C\int_0^{p^2}f_1\left(B(q^2),q^2\right)\mathrm{d}q^2 + C\int_{p^2}^{\Lambda^2} f_2\...
6
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2answers
768 views

Monte-Carlo method to estimate Pi runs slower in multiple threads, than in single thread

I'm learning Scala, and I wrote a program to estimate the value of Pi. When I'm using multiple threads, it takes 5-6 times longer to calculate the same iterations. I wrote a similar program in Java, ...
6
votes
1answer
299 views

Approximating π via Monte Carlo simulation

Inspired by a tweet linked to me by a friend and a Haskell implementation by her for the same problem, I decided to try my hand at approximating the value of π using everything in the Haskell standard ...
6
votes
1answer
83 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 ...
6
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1answer
3k views

Monte Carlo simulation to approximate the value of PI

This is a C++ implementation of a simple Monte Carlo simulation to approximate the value of pi. The program uses the standard library Mersenne twister engine to generate two random numbers between -1....