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Tag Archives: MATLAB
Implicit Expansion: A Powerful New Feature of MATLAB R2016b
The latest release of MATLAB, R2016b, contains a feature called implicit expansion, which is an extension of the scalar expansion that has been part of MATLAB for many years. Scalar expansion is illustrated by >> A = spiral(2), B = … Continue reading
The OneLine Maze Program in MATLAB
A classic oneline program for the Commodore 64 microcomputer is 10 PRINT CHR$(205.5+RND(1)); GOTO 10 This is essentially what was printed in the section “Random Graphics” of the Commodore 64 User’s Guide (1982). The program prints a random maze that … Continue reading
Iterating MATLAB Commands
Some MATLAB commands can be “applied to themselves”. A good example is help help, which provides help on the help function. For what other functions fun is fun fun a legal statement that produces something interesting? Here are some examples … Continue reading
Improved MATLAB Function Sqrtm
The MATLAB function sqrtm, for computing a square root of a matrix, first appeared in the 1980s. It was improved in MATLAB 5.3 (1999) and again in MATLAB 2015b. In this post I will explain how the recent changes have … Continue reading
A Collection of Invalid Correlation Matrices
I’ve written before (here) about the increasingly common problem of matrices that are supposed to be correlation matrices (symmetric and positive semidefinite with ones on the diagonal) turning out to have some negative eigenvalues. This is usually bad news because … Continue reading
Empty Matrices in MATLAB
What matrix has zero norm, unit determinant, and is its own inverse? The conventional answer would be that there is no such matrix. But the empty matrix [ ] in MATLAB satisfies these conditions: >> A = []; norm(A), det(A), … Continue reading
Updated Catalogue of Software for Matrix Functions
Edvin Deadman and I have updated the catalogue of software for matrix functions that we produced in 2014 (and which was discussed in this post). The new version, which has undergone some minor reorganization, is available here. It covers what … Continue reading
The Improved MATLAB Functions Expm and Logm
The matrix exponential is a ubiquitous matrix function, important both for theory and for practical computation. The matrix logarithm, an inverse to the exponential, is also increasingly used (see my earlier post, 400 Years of Logarithms). MATLAB R2015b introduced new … Continue reading
Corless and Fillion’s A Graduate Introduction to Numerical Methods from the Viewpoint of Backward Error Analysis
I acquired this book when it first came out in 2013 and have been dipping into it from time to time ever since. At 868 pages long, the book contains a lot of material and I have only sampled a … Continue reading
Anderson Acceleration
Anderson acceleration, also known in quantum chemistry as Pulay mixing or direct inversion in the iterative subspace (DIIS), is a technique for accelerating the convergence of a fixedpoint iteration. It has been widely used in electronic structure computations, but does … Continue reading