# 1976 Matrix Singular Value Decomposition Film

This blog is about a film that I made in 1976. Here is the link to a digital copy on YouTube: http://youtu.be/R9UoFyqJca8.

### Contents

#### Singular Value Decomposition

Today the SVD is widely used in scientific and engineering computation, but in 1976 it was relatively unknown. The first algorithm for its practical computation was published in 1965 by Gene Golub and Velvel Kahan. An important improvement was published in 1970 by Golub and Christian Reinsch. These Algol programs were the basis for Fortran subroutines in EISPACK in 1977 and LINPACK in 1979.

#### Los Alamos

In the 1970's I was a professor at the University of New Mexico and a visiting staff member at Los Alamos National Laboratory (which was then called Los Alamos Scientific Laboratory). This was before I started any work on MATLAB. At Los Alamos I consulted on the development of their computational math library. We wanted to make sure that the routines that we were developing for EISPACK and, eventually, LINPACK worked effectively on vector supercomputers.

There was a group at the Lab developing a library for computer graphics, which was also relatively new. Output was on microfilm and 16mm movie film. The film was developed overnight and made available in the computer center the next morning. The graphics techniques simulated pen and ink on paper and a rotating drum. 3-D projections involved hidden line calculations. Raster graphics and z-buffer algorithms had not yet been invented or were not yet available.

#### The Film

In 1976, Charlie Barnett in the Los Alamos film production group and I produced a 6-minute film titled "Matrices and Their Singular Values". I produced the computer animated graphics on the CDC 7600 with the EISPACK SVD code under development and the new graphics library written by Mel Pruitt. I also wrote the script for the movie. The guy at the beginning of the film is someone from Barnett's car pool. The hexagonal grid was his idea of a matrix.

In the 1970s, few people had seen the clip of the galloping Tacoma Narrows bridge, but now, with the internet, everybody has seen it many times. In the spirit of full disclosure, I have to admit that the SVD has nothing to do with the vibration of bridges.

#### Limited Release

This film has been in very limited release. I debuted the film during a talk at a SIAM meeting in Chicago shortly after we made it. Since then I have shown it at several other lectures in the late 1970's and early '80s. A few friends have shown it in some of their lectures. I suspect it has been seen only a few dozen times over the years. After all, to show it, someone had to haul a 16mm film projector into the seminar or class room.

#### Star Trek

The first Star Trek movie came out in 1979. The producers had asked Los Alamos for computer graphics to run on the displays on the bridge of the Enterprise. They chose our SVD movie to run on the science officer's display. So, if you look over Spock's shoulder as the Enterprise enters the nebula in search of Viger, you can glimpse a matrix being diagonalized by Givens transformations and the QR iteration.

#### LANL Retrieves Film

Some time ago I lost my copy of the film. But I recently found it listed on line in a record of old Los Alamos productions. I contacted the Lab and asked if they could retrieve it. They found it in a storage rack and said they could use this as an incentive to digitize some old films. They soon sent me a DVD and I uploaded it to YouTube. Here it is: http://youtu.be/R9UoFyqJca8.

Published with MATLAB® R2012b

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