Tagged Questions
Algorithms which solve mathematical problems by means of numerical approximation (as opposed to symbolic computation).
3
votes
2answers
61 views
Estimating Pi with random darts on dartboard - high complexity issues
I've been trying to write nice snippet of code to simulate pi estimation by randomly throwing darts on a dartboard. While running the following code on high but reasonable numbers my mac doesn't plot. ...
7
votes
1answer
73 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 ...
3
votes
1answer
43 views
Polynomial curve-fitting over a large 3D data set
I have a list of 4 images, called listfile.list, which looks like this:
image1
image2
image3
image4
Each image has 10 frames containing a 2000 x 2000 array of ...
4
votes
1answer
124 views
Runge-Kutta 4th order using Python numexpr.evaluate()
I am implementing an ODE solver, where the user provides rates and coefficients as a string. ODE solver has to work with vectors. The best implementation I got so far is the following:
...
0
votes
1answer
66 views
A quartic polynomial in four variables, for numerical integration
About half year ago, I derived a integral of a piecewise polynomial, which was a complex formula. Below is one of that formula:
Obviously, the above formula has relationship with four varibles \$u_i,\...
3
votes
1answer
79 views
Multivariable Gradient Descent in Numpy
Just recently started learning ML, first I've gone through the notes of Ng's Coursera stuff. While I have nothing against Octave, I'm trying to solve exercises in Python. It's my beginning with that ...
0
votes
0answers
20 views
Arbitrary precision π (Circular Constant) in Java - MathCore #2
This post is the second in the MathCore series.
The previous post is here: Arbitrary Precision nth Principal Root in Java - MathCore #1
The posts are made incrementally, that is, the classes in the ...
5
votes
1answer
66 views
+50
Arbitrary Precision nth Principal Root in Java - MathCore #1
This post is the first in the MathCore series.
The next post is here: Arbitrary precision π (Circular Constant) in Java - MathCore #2
Disclaimer
My project is too big to be reviewed in a single ...
3
votes
0answers
53 views
Calculating Pi to a tolerance
I'm taking my first steps in the Scala world, though I'm not wholly unfamiliar with functional style.
Apparently one way of calculating Pi is to sum the terms of the infinite series:
$$4 * (\frac{1}{...
2
votes
0answers
28 views
Multithreaded Monte Carlo pi approximation with own pseudorandom number generator - follow up
This is a follow up of the question I posted previously here.
I made some changes, based in the answer by MikeMB, making use of asynchronous calls (with std::async ...
3
votes
1answer
50 views
Multithreaded Monte Carlo pi approximation with own pseudorandom number generator
I made a Monte Carlo pi approximation program, that makes use of multithreading and a pseudorandom number generator I wrote (the one from big_wheel.hpp, which I ...
4
votes
1answer
136 views
Compute Gini Coefficient
Recently, I was given a math assignment to calculate Gini Indexes for a table of percent distributions of aggregate income.
The table takes the form of:
...
3
votes
0answers
42 views
Computing nth roots of a number - SICP exercise 1.45
From SICP
Exercise 1.45:
We saw in 1.3.3 that attempting to compute square roots
by naively finding a fixed point of x/y does not converge, and that
this can be fixed by average damping.
...
3
votes
2answers
134 views
Euler's Method in C#
I was just looking for some feedback for my c# program to run Euler's method. I was just wondering on any possible improvements, refactoring, inefficiencies... the usual stuff you probably deal with ...
1
vote
1answer
49 views
Approximating pi/4 using Wallis Product - SICP exercise 1.31
From SICP
The sum procedure is only the simplest of a vast number of similar
abstractions that can be captured as higher-order procedures. Write an
analagous procedure called product that ...
2
votes
2answers
87 views
Calculating Pi with Android
I'm kind of new to Java but I am writing an Android app. Right now I'm working on an async task to calculate Pi but when I run it the memory usage increases alarmingly (+5MB per second). This one ...
4
votes
1answer
72 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!} + \...
6
votes
1answer
158 views
C++ HyperLogLog Implementation
I'm a scientific C programmer moving my way over to using Modern C++. I found myself needing a HyperLogLog implementation, and I wanted to use this for practice.
I plan to move a number of these ...
7
votes
1answer
176 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 ...
4
votes
4answers
187 views
5
votes
2answers
113 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, ...
2
votes
1answer
70 views
Calculation of elasticity for non-linear curve
I've written this code to calculate the elasticity for econometric analysis. Basically, this algorithm estimate the function:
$$\epsilon(x) = \frac{x}{f(x)}\ f'(x)$$
...
5
votes
1answer
68 views
Generate dictionary of points on n-sphere
This is a long-shot, but my question is to simply optimize this particular function in some code I have written:
...
2
votes
1answer
41 views
Evaluation of e^x with series expansion
My code calculates \$e^x\$ with series expansion. Is there any way to make it shorter and cleaner?
...
5
votes
1answer
157 views
Evaluating a series of Legendre polynomials
The following function represents the electrostatic potential, in spherical coordinates, due to a ring of charge \$q=1\$ and radius \$R=1\$, placed in the plane \$x\$-\$y\$:
$$\phi(r,\theta) = \sum_{...
2
votes
1answer
314 views
Calculate the arclength
I am trying to estimate a good approximation for the arclength of the curve \$ y = \sqrt{1-x^2}\$ for \$x \in [0, 1]\$. I did this using a Bezièr curve, and made it so that the area under the two ...
5
votes
2answers
122 views
Monte Carlo simulation of amoeba population
I wrote a simple Python simulation to answer the "Amoeba" population question posed here:
A population of amoebas starts with 1. After 1 period that amoeba can divide into 1, 2, 3, or 0 (it can die)...
2
votes
0answers
52 views
Numerical differentiation using the y-intercept
I have a routine for determining the derivative of a function using the y-intercept (B) to infer the finite difference step (h). ...
4
votes
2answers
168 views
Calculating pi by adding areas of thin rectangles
I wrote a small program for fun to try to prove Pi by taking a certain precision and radius and using it to calculate the area of the circle. My method should be giving me an area that is just ...
5
votes
1answer
137 views
Visualizing Newton-Raphson method for finding zeroes of a function
I have created a program to visualize the working of Newton-Raphson method to find the zeroes of a function:
newton.m:
...
3
votes
2answers
397 views
Implementation of exp function in C using Taylor Series expansion
I am trying to write code to calcultate ex using:
$$e^x = \sum_{n=0}^\infty \frac{x^n}{n!} = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!} + \cdots $$
This is the code I have, which works ...
6
votes
3answers
205 views
1D shock tube problem written in Fortran
I have written a simple Euler solver for the 1D shock tube problem. Eventually, I plan to extend this code to solve the full 3D compressible Navier-Stokes equations. Therefore, I want to start with ...
4
votes
0answers
393 views
Linear Interpolation C++
I have to write a collection of methods for performing linear, bilinear and trilinear interpolation. I have also to write some tests to show that interpolation is exact for polynomials (which should ...
3
votes
1answer
60 views
Square root calculation in Scheme (SICP Exercise 1.7)
I have done exercise 1.7 in SICP (calculate square root precision when change in guesses is under a certain value), but I am calling the change-in-precision function twice in each iteration, which ...
4
votes
2answers
60 views
`atof` revisited
In an answer to this question I mentioned best effort. Here I try to explain what I meant. Please keep in mind that the implementation is intentionally incomplete (missing features such as ...
2
votes
1answer
67 views
Integer square root
This essentially performs the same function as exact-integer-sqrt in math.numeric-tower.
...
3
votes
1answer
63 views
Computing the double Integral using MonteCarlo techniques using Julia
I decided to try and learn Julia for doing scientific computing, and I decided to tackle the problem of finding
$$ \int_{D_{\frac{1}{4}}} x^4 + y^2 dA $$
where \$ D_{\frac{1}{4}} \$ is the part of ...
3
votes
1answer
85 views
Linear shooting method to solve a B.V.P
I have wrote a code to approximate the solution of a boundary value problem:
x'' = p(t)x'(t)+q(t)x(t)+r(t)
x(b) = beta in [a,b]
by using Runge-Kutta method ...
2
votes
1answer
260 views
Double integral solver in TI-84
Here's a program I made for estimating a double integral over a general region. It's pretty accurate, but it's VERY, VERY slow. (Getting an accurate enough result takes about 30 seconds)
Here's the ...
6
votes
1answer
101 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 ...
3
votes
4answers
312 views
Computing integer square roots in Java - follow-up
(See the previous iteration.)
My two previous methods for computing the integer square root of a number \$N\$ ran in the \$\mathcal{O}(\sqrt{N})\$ worst case time. Now I have added a method (...
7
votes
1answer
235 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 ...
10
votes
3answers
99 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 ...
5
votes
1answer
202 views
Newton's Method Polynomial solver in Ruby
I am learning Ruby programming from "Learn Ruby the Hard way" and I am doing the "Ruby koans".
I have heard a little bit about "Idiomatic" Ruby but I don't know much about it. How can I make it more ...
3
votes
1answer
141 views
Simple neural-network simulation in C++ (Round 4)
You may want to take a look at Rounds 1, 2, and 3, though that isn't necessary for understanding what's below.
The major change since Round 3 is that my code is much cleaner and I'm including ...
3
votes
1answer
124 views
Simple neural-network simulation in C++ (Round 3)
As I mentioned at the end of my Round 2 answer, I've needed to expand my code in order to produce faithfully the data needed for Figure 1 of this paper.
Unfortunately, the updates have made my script ...
3
votes
1answer
157 views
Simple neural-network simulation in C++ (Round 2)
Intro
Yesterday I posted this question. Since then, I've updated my code to incorporate these suggestions. I've also removed the dependence on C++11. Finally, I've made the following changes that ...
4
votes
1answer
486 views
Simple neural-network simulation in C++
The C++ code below simulates the timecourse of the membrane potential (V) of a population of 128 leaky integrate-and-fire ...
2
votes
1answer
76 views
Golden Section Search in Lisp
I implemented the golden section search algorithm recursively in Lisp. My code is:
...
3
votes
0answers
62 views
Decorator for setting up bracketing rootfinding functions
I'm looking for comments on the use of decorators for the following problem (validating initial guesses for bracketing rootfinding methods), as well as any other comments you might have on the design ...
