The Problem This is a problem for which no polynomial time solution exists, although a pseudo-polynomial (polynomial in the degree of the maximum element) does exist. In this paper, the algorithm proposed for the sum-function with full information is simple enough. For the original problem with the difference funcition, the algorithm is simple as well: … Continue reading Turnpike Problem (F#)
Category: F#
Decomposition Problem with F#, Dynamic Programming
As my former boss and mentor used to say, in order to understand recursion one must first understand recursion. This is funny, ha-ha, but if we tweak it slightly we get a really useful statement: in order to understand dynamic programming, one must first understand recursion. Here is an example. Sources Github: http://github.com/fierval/BioInfo Decomposition Problem … Continue reading Decomposition Problem with F#, Dynamic Programming
Fun with Alea.CUDA, F# Interactive, Charts
Source code for this post can be found on my GitHub. It's great to see technologies evolving over the years. Alea.CUDA has done so in leaps and bounds since the first time I laid eyes on it a couple of years ago. At the time the name seemed unfortunate and hinted at the "aleatic" programming … Continue reading Fun with Alea.CUDA, F# Interactive, Charts
Motif Finding with Gibbs Sampling (F#)
The Problem "Motif finding is a problem of finding common substrings of specified length in a set of strings. In bioinformatics, this is useful for finding transcription binding sites" (recap here). The problem is succinctly stated on Rosalind. Given a set of strings DNA of size t, find "most common" substrings of length k. "Most common" means, that substrings … Continue reading Motif Finding with Gibbs Sampling (F#)
Modelling Stochastically Independent Processes with F# Computation Expressions: Part 1
The idea for doing this is not new. There is an excellent series of posts closely tracing an article on applications of functional programming to probability. A colleague of mine has recently called my attention to his own post of two years ago, where he describes a monad that models stochastically independent events in Clojure. … Continue reading Modelling Stochastically Independent Processes with F# Computation Expressions: Part 1
Generating Permutations: Clojure or F#: Part 2
Marching on from the last post. Lazy Sequences This is my favorite feature ever. If I want to generate just a few of 10! (nobody even knows how much that is) permutations, I could: provided, the function is defined (as described in the first post): Here I am not sure which language I like more. … Continue reading Generating Permutations: Clojure or F#: Part 2
Generating Permutations: Clojure or F#: Part 1
The Alogirthm Recently, I have entered a brave (new?) world of Clojure and was looking for a small project to take it for a ride. I stopped on a popular/interesting enough little problem, that subsumed a certain interview question which I was once unfortunate enough to stumble through with half my brain tied behind my … Continue reading Generating Permutations: Clojure or F#: Part 1
Computing Self-Organizing Maps in a Massively Parallel Way with CUDA. Part 2: Algorithms
In the previous post I spoke briefly about motivations for implementing self-organizing maps in F# using GPU with CUDA. I have finally been able to outperform a single threaded C++ implementation by a factor of about 1.5. This is quite modest, but on the other hand rather impressive since we started out by being 60 … Continue reading Computing Self-Organizing Maps in a Massively Parallel Way with CUDA. Part 2: Algorithms
Computing Self-Organizing Maps in a Massively Parallel Way with CUDA. Part 1: F#
By 2017, it is expected that GPUs will no longer be an external accelerator to a CPU; instead, CPUs and GPUs will be integrated on the same die with a unified memory architecture. Such a system eliminates some of accelerator architectures’ historical challenges, including requiring the programmer to manage multiple memory spaces, suffering from bandwidth … Continue reading Computing Self-Organizing Maps in a Massively Parallel Way with CUDA. Part 1: F#
F# vs C#. Fold and Aggregate
Suppose you need to write a script that finds n files, all called based on some pattern, say "c:\temp\my_file_x.txt", where "x" is replaced by a range of numbers [1..30] for instance, reads the content of these files and glues them together. Suppose also that the files are very small, so you can keep them in … Continue reading F# vs C#. Fold and Aggregate
