## Tag: Statistical Programming

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Passing arguments by reference: An efficient choice

When you pass a matrix as an parameter (argument) to a SAS/IML module, the SAS/IML language does not create a copy of the matrix. That approach, known as "calling by value," is inefficient. It is well-known that languages that implement call-by-value semantics suffer performance penalties. In the SAS/IML language, matrices

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Divide and count: A test for spatial randomness

Last week I generated two kinds of random point patterns: one from the uniform distribution on a two-dimensional rectangle, the other by jittering a regular grid by a small amount. My show choir director liked the second method (jittering) better because of the way it looks on stage: there are

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Count the number of points in 2D bins

One of my New Year's resolutions is to learn a new area of statistics. I'm off to a good start, because I recently investigated an issue which started me thinking about spatial statistics—a branch of statistics that I have never formally studied. During the investigation, I asked myself: Given an

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Random uniform versus uniformly spaced: Applying statistics to show choir

I sing in the SAS-sponsored VocalMotion show choir. It's like an adult version of Glee, except we have more pregnancies and fewer slushie attacks. For many musical numbers, the choreographer arranges the 20 performers on stage in an orderly manner, such as four rows of five singers. But every once

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Count the number of points in bins efficiently

A histogram displays the number of points that fall into a specified set of bins. This blog post shows how to efficiently compute a SAS/IML vector that contains those counts. I stress the word "efficiently" because, as is often the case, a SAS/IML programmer has a variety of ways to

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Computing 200 factorial: Using PROC IML as a really BIG calculator

Have you ever wanted to compute the exact value of a really big number such as 200! = 200*199*...*2*1? You can do it—if you're willing to put forth some programming effort. This blog post shows you how. Jiangtang Hu's recent blog discusses his quest to compute large factorials in many programming languages.

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How to create a grid of values?

In a previous post, I described ways to create SAS/IML vectors that contain uniformly spaced values. The methods did not involve writing any loops. This post describes how to perform a similar operation: creating evenly spaced values on a two-dimensional grid. The DATA step solution is simple, but an efficient

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Hey! Those two people have the same initials!

"What is the chance that two people in a room of 20 share initials?" This was the question posed to me by a colleague who had been taking notes at a meeting with 20 people. He recorded each person's initials next to their comments and, upon editing the notes, was

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Computing probabilities can be tricky. And if you are a statistician and you get them wrong, you feel pretty foolish. That's why I like to run a quick simulation just to make sure that the numbers that I think are correct are, in fact, correct. My last post of 2010

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Creating a matrix with all combinations of zeros and ones

Over at the SAS/IML Discussion Forum, someone posted an interesting question about how to create a special matrix that contains all combinations of zeros and ones for a given size. Specifically, the problem is as follows. Given an integer n ≥ 1, produce a matrix with 2n rows and n

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New Year's resolutions for my blog

It's a New Year and I'm ready to make some resolutions. Last year I launched this blog with my Hello, World post in which I said: In this blog I intend to discuss, describe, and disseminate ideas related to statistical programming with the SAS/IML language.... I will present tips and

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Automating the Great Christmas Gift Exchange

In many families, siblings draw names so that each family member and spouse gives and receives exactly one present. This year there was a little bit of controversy when a family member noticed that once again she was assigned to give presents to me. This post includes my response to

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When I wake up early to write my blog, I often wonder, "Is anyone going to read this?" Apparently so. I started writing The DO Loop in September, 2010. Since then, I've posted about 60 entries about statistical programming with SAS/IML software. Since this is a statistical blog, it is

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The module that vanished

Recently, I needed to detect whether a matrix consists entirely of missing values. I wrote the following module: proc iml; /** Module to detect whether all elements of a matrix are missing values. Works for both numeric and character matrices. Version 1 (not optimal) **/ start isMissing(x); if type(x)='C' then

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How to find and fix programming errors

NOTE: SAS stopped shipping the SAS/IML Studio interface in 2018. The references in this article to IMLPlus and SAS/IML Studio are no longer relevant. There are three kinds of programming errors: parse-time errors, run-time errors, and logical errors. It doesn't matter what language you are using (SAS/IML, MATLAB, R, C/C++,

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Converting between correlation and covariance matrices

Both covariance matrices and correlation matrices are used frequently in multivariate statistics. You can easily compute covariance and correlation matrices from data by using SAS software. However, sometimes you are given a covariance matrix, but your numerical technique requires a correlation matrix. Other times you are given a correlation matrix,

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Computing covariance and correlation matrices

Sample covariance matrices and correlation matrices are used frequently in multivariate statistics. This post shows how to compute these matrices in SAS and use them in a SAS/IML program. There are two ways to compute these matrices: Compute the covariance and correlation with PROC CORR and read the results into

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Placing the digits of a number into a vector

I enjoy reading about the Le Monde puzzles (and other topics!) at Christian Robert's blog. Recently he asked how to convert a number with s digits into a numerical vector where each element of the vector contains the corresponding digit (by place value). For example, if the number is 4321,

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Ten reasons I'm thankful to be a statistical programmer

I am thankful to be a statistical programmer. When I wake up in the morning, I am eager to start my day. I love statistics, programming, and working at SAS, and I write my blog to share that joy. This a Golden Age for statistical programmers because theoretical ideas and

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Regression coefficients for orthogonal polynomials

In a previous post, I discussed computing regression coefficients in different polynomial bases and showed how the coefficients change when you change the basis functions. In particular, I showed how to convert the coefficients computed in one basis to coefficients computed with respect to a different basis. It turns out

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Free chapter: Getting Started with SAS/IML

I am pleased to announce that the fine folks at SAS Press have made Chapter 2 of my book, Statistical Programming with SAS/IML Software available as a free PDF document. The chapter is titled "Getting Started with the SAS/IML Matrix Programming Language," and it features More than 60 fully functional

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Regression coefficients for different polynomial bases

Suppose that you compute the coefficients of a polynomial regression by using a certain set of polynomial effects and that I compute coefficients for a different set of polynomial effects. Can I use my coefficients to find your coefficients? The answer is yes, and this article explains how. Standard Polynomial

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Sampling with replacement

Sampling with replacement is a useful technique for simulations and for resampling from data. Over at the SAS/IML Discussion Forum, there was a recent question about how to use SAS/IML software to sample with replacement from a set of events. I have previously blogged about efficient sampling, but this topic

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Evaluate an iterated integral

The SAS/IML language provides the QUAD function for evaluating one-dimensional integrals. You can also use the QUAD function to compute a double integral as an iterated integral. A One-Dimensional Integration Suppose you want to evaluate the following integral: To evaluate this integral in the SAS/IML language: Define a function module

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Creating a tridiagonal matrix

I was recently asked how to create a tridiagonal matrix in SAS/IML software. For example, how can you easily specify the following symmetric tridiagonal matrix without typing all of the zeros? proc iml; m = {1 6 0 0 0, 6 2 7 0 0, 0 7 3 8 0,

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Looping versus LOC-ing revisited

In a previous post, I discussed how to use the LOC function to eliminate loops over observations. Dale McLerran chimed in to remind me that another way to improve efficiency is to use subscript reduction operators. I ended my previous post by issuing a challenge: can you write an efficient

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Solving scrambled-word puzzles

Have you ever been stuck while trying to solve a scrambled-word puzzle? You stare and stare at the letters, but no word reveals itself? You are stumped. Stymied. I hope you didn't get stumped on the word puzzle I posted as an anniversary present for my wife. She breezed through