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A few weeks ago I started a series of posts on various things you could do with a functional fold. In the first post I mentioned that the idea came from a paper by Brian Beckman on Kalman filters and folds: This post was inspired by a paper by Brian Beckman (in progress) that shows how a Kalman filter can be implemented as a fold. From a Bayesian perspective, the thing that makes the Kalman filter

Presentation order People best understand computer programs in a different order than compilers do. This is a key idea of literate programming, and one that distinguishes literate programs from heavily commented programs. Traditional source code, no matter how heavily commented, is presented in the order dictated by the compiler. The computer is the primary audience. Literate programming is more h

Here’s an insightful paragraph from James Hague’s blog post Organization skills beat algorithmic wizardry: When it comes to writing code, the number one most important skill is how to keep a tangle of features from collapsing under the weight of its own complexity. I’ve worked on large telecommunications systems, console games, blogging software, a bunch of personal tools, and very rarely is there

Here I list some the symbols that come up frequently in math and describe how to represent them in TeX, HTML, XML, and Unicode. HTML provides a mnemonic form for 252 of the most common symbols. (See a full list from the W3C.) These are called "character entities." You can simply put Unicode characters directly into an HTML page as long as you have an input method and the content-type of your HTML

Gilad Bracha’s presentation on Dart is interesting even if, like me, you do not intend to learn Dart. He has some good one-liners, especially digs at JavaScript, and some interesting ideas about programming language design. (JavaScript comes up frequently in presentation because of its popularity and because Dart compiles to JavaScript.) Application programmers, unless they’ve committed serious cr

R programming for those coming from other languages Introduction Assignment and underscore Variable name gotchas Vectors Sequences Types Boolean operators Lists Matrices Missing values and NaNs Comments Functions Scope Misc. Other resources Ukrainian translation Other languages: Introduction I have written software professionally in perhaps a dozen programming languages, and the hardest language f

David Jacobs has written a long blog post Ruby is beautiful (but I’m moving to Python). [Update: link no longer available.] Here’s my summary. Ruby is much better than Java, but the Ruby community is too focused on web development and the language has no scientific library. Python has a lot of the same advantages as Ruby, is used for more than web programming, and has SciPy. Update: There is now a

Here’s an answer I gave on Stack Overflow to someone asking when it’s OK to use global variables. Here’s a cheap way to get rid of all global variables: put all your code in one big fat class and change the global variables to member variables. Nothing has changed as far as the maintainability of your code, but technically it no longer has global variables. It’s better to talk about size of scope

IEEE floating-point exceptions in C++ This page will answer the following questions. My program just printed out 1.#IND or 1.#INF (on Windows) or nan or inf (on Linux). What happened? How can I tell if a number is really a number and not a NaN or an infinity? How can I find out more details at runtime about kinds of NaNs and infinities? Do you have any sample code to show how this works? Where can

People who write Python choose to write Python. I don’t hear people say “I use Python at work because I have to, but I’d rather be writing Java.” But often I do hear people say they’d like to use Python if their job would allow it. There must be someone out there writing Python who would rather not, but I think that’s more common with other languages. My point isn’t that everyone loves Python, but

The most obvious way to compute the soft maximum can easily fail due to overflow or underflow. The soft maximum of x and y is defined by g(x, y) = log( exp(x) + exp(y) ). The most obvious way to turn the definition above into C code would be double SoftMaximum(double x, double y) { return log( exp(x) + exp(y) ); } This works for some values of x and y, but fails if x or y is large. For example, if

The new C++ standard includes a couple Python-like features that I ran across recently. There are other Python-like features in the new standard, but here I’ll discuss range-based for-loops and raw strings. In Python you loop over lists rather than incrementing a loop counter variable. For example, for p in [2, 3, 5, 7, 11]: print p Range-based for loops now let you do something similar in C++11:

Functional programming emphasizes “pure” functions, functions that have no side effects. When you call a pure function, all you need to know is the return value of the function. You can be confident that calling a function doesn’t leave any state changes that will effect future function calls. But pure functions are only pure at a certain level of abstraction. Every function has some side effect:

We help companies solve hard problems in mathematics, statistics, and computing. Let’s explore how we might work together. Given a hash value, can you determine what algorithm produced it? Or what algorithm probably produced it? Obviously if a hash value is 128 bits long, then a 128-bit algorithm produced it. Such a hash value might have been produced by MD5, but not by SHA-1, because the former p

Getting started with C++ TR1 regular expressions Overview Header and namespace C++ regular expression flavor Matching Retrieving matches Replacing matches Escape sequences Case-sensitivity Troubleshooting Overview This article is written for the benefit of someone familiar with regular expressions but not with the use of regular expressions in C++ via the TR1 (C++ Standards Committee Technical Rep

There is hardly ever a good reason to invert a matrix. What do you do if you need to solve Ax = b where A is an n x n matrix? Isn’t the solution A−1 b? Yes, theoretically. But that doesn’t mean you need to actually find A−1. Solving the equation Ax = b is faster than finding A−1. Books might write the problem as x = A−1 b, but that doesn’t mean they expect you to calculate it that way. What if you

Probability distributions have a surprising number inter-connections. A dashed line in the chart below indicates an approximate (limit) relationship between two distribution families. A solid line indicates an exact relationship: special case, sum, or transformation. Click on a distribution for the parameterization of that distribution. Click on an arrow for details on the relationship represented

Diagram of distribution relationships Probability distributions have a surprising number inter-connections. A dashed line in the chart below indicates an approximate (limit) relationship between two distribution families. A solid line indicates an exact relationship: special case, sum, or transformation. Click on a distribution for the parameterization of that distribution. Click on an arrow for d

Here are some notes on how to work with probability distributions using the SciPy numerical library for Python. Functions related to probability distributions are located in scipy.stats. The general pattern is scipy.stats.<distribution family>.<function> There are 81 supported continuous distribution families and 12 discrete distribution families. Some distributions have obvious names: gamma, cauc

Outline Introduction Assignment and underscore Variable name gotchas Vectors Sequences Types Boolean operators Lists Matrices Missing values and NaNs Comments Functions Scope Misc. Other resources Introduction I have written software professionally in perhaps a dozen programming languages, and the hardest language for me to learn has been R. The language is actually fairly simple, but it is unconv