Blog Archives

Self-similar structures from Kronecker products

December 17, 2014
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Self-similar structures from Kronecker products

I recently posted an article about self-similar structures that arise in Pascal's triangle. Did you know that the Kronecker product (or direct product) can be used to create matrices that have self-similar structure? The basic idea is to start with a 0/1 matrix and compute a sequence of direct products […]

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Elementwise minimum and maximum operators

December 15, 2014
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Elementwise minimum and maximum operators

Like most programming languages, the SAS/IML language has many functions. However, the SAS/IML language also has quite a few operators. Operators can act on a matrix or on rows or columns of a matrix. They are less intuitive, but can be quite powerful because they enable you perform computations without […]

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A Christmas tree from Pascal’s triangle

December 10, 2014
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A Christmas tree from Pascal’s triangle

O Christmas tree, O Christmas tree, One year a fractal made thee! O Christmas tree, O Christmas tree, A heat map can display thee! From Pascal's matrix we define! Reflect across, divide by nine. O Christmas tree, O Christmas tree, Self-similar and so divine! Eventually I will run out of […]

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The direct product (Kronecker product) in SAS

December 8, 2014
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The direct product (Kronecker product) in SAS

There are many ways to multiply scalars, vectors, and matrices, but the Kronecker product (also called the direct product) is multiplication on steroids. The Kronecker product looks scary, but it is actually simple. The Kronecker product is merely a way to pack multiples of a matrix B into a block […]

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A matrix computation on Pascal’s triangle

December 5, 2014
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A matrix computation on Pascal’s triangle

A colleague asked me a question regarding my recent post about the Pascal triangle matrix. While responding to his question, I discovered a program that I had written in 1999 that computed with a Pascal triangle matrix. Wow, I've been computing with Pascal's triangle for 15 years! I don't know […]

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Pascal’s triangle in SAS

December 3, 2014
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Pascal’s triangle in SAS

Pascal's triangle is the name given to the triangular array of binomial coefficients. The nth row is the set of coefficients in the expansion of the binomial expression (1 + x)n. Complicated stuff, right? Well, yes and no. Pascal's triangle is known to many school children who have never heard of polynomials […]

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Pascal’s triangle in SAS

December 3, 2014
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Pascal’s triangle in SAS

Pascal's triangle is the name given to the triangular array of binomial coefficients. The nth row is the set of coefficients in the expansion of the binomial expression (1 + x)n. Complicated stuff, right? Well, yes and no. Pascal's triangle is known to many school children who have never heard of polynomials […]

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Compute maximum and minimum values for rows and columns in SAS

December 1, 2014
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Compute maximum and minimum values for rows and columns in SAS

A common question on SAS discussion forums is how to compute the minimum and maximum values across several variables. It is easy to compute statistics across rows by using the DATA step. This article shows how to compute the minimum and maximum values for each observation (across variables) and, for […]

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The Wishart distribution: Covariance matrices for multivariate normal data

November 26, 2014
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The Wishart distribution: Covariance matrices for multivariate normal data

I've written about how to generate a sample from a multivariate normal (MVN) distribution in SAS by using the RANDNORMAL function in SAS/IML software. Last week a SAS/IML programmer showed me a program that simulated MVN data and computed the resulting covariance matrix for each simulated sample. The purpose of […]

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Overview of new features in SAS/IML 13.1

November 24, 2014
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Overview of new features in SAS/IML 13.1

SAS software contains a lot of features, and each release adds more.To make sure that you do not miss new features that appear in the SAS/IML language, the word cloud on the right sidebar of my blog contains numbers that relate to SAS or SAS/IML releases. For example, you can […]

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