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statespacedev committed Sep 8, 2024
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header_pages:
- docs/about.md
- docs/photos.md
- docs/links.md
show_drafts: false
permalink: none
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title: "linpack"
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nsf funding at argonne national lab led to the fortran linear equation package linpack by the early seventies. it's closely tied to supercomputing and is the standard for [supercomputer benchmarking](https://en.wikipedia.org/wiki/LINPACK#World's_most_powerful_computer_by_year), from cdc and cray in the sixties and seventies through today.

[cleve moler](https://en.wikipedia.org/wiki/Cleve_Moler) and his advisor [george forsythe](https://en.wikipedia.org/wiki/George_Forsythe) at stanford in the sixties are of special interest in the linpack context. here's some comments from moler on 'computer solutions of linear algebraic systems', 1967, forsythe and moler

_this is a little book, it’s only less than 150 pages ... solving systems of simultaneous linear equations is arguably the most important computation in scientific computing, it underlies everything else ... if you were let’s say studying control theory or finite element computations in engineering at this time, you would have used this subroutine from this book in your own program_

here's a [good review](docs/inverse/1966%20forsythe.pdf) by forsythe of the state of the art in the fifties and sixties, particularly around matrix inversion.
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4 changes: 2 additions & 2 deletions _posts/2024-08-25-floating-point.md
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around 1950, fixed point binary representations were used for numbers. there was no floating point, and there was a strong current of thought that this was as it should be. if numbers were kept properly scaled, fixed point was all that was needed and floating point was an unnecessary compromise. von neumann was a champion of this view. what ended up actually happening is a curious bit of history involving the mit instrumentation laboratory, navigation, astronomy, and engineering.

a standard aerospace textbook by battin begins with a detailed description of how he and hal laning developed early missile guidance systems at the instrumentation laboratory in the fifties, particularly [q guidance](https://en.wikipedia.org/wiki/Q-guidance).
it turns out that at the same time hal laning was the lead programmer who brought floating point to the whirlwind computer in 1952. as part of that, he developed what may have been the first real compiler and high level language, called 'george' from 'let george do it'. here's a comment from john backus.
a standard aerospace textbook by [richard battin](https://en.wikipedia.org/wiki/Richard_Battin) begins with a detailed description of how he and [hal laning](https://en.wikipedia.org/wiki/J._Halcombe_Laning) developed early missile guidance systems at the instrumentation laboratory in the fifties, particularly [q guidance](https://en.wikipedia.org/wiki/Q-guidance).
it turns out that at the same time hal laning was the lead programmer who brought floating point to the whirlwind computer in 1952. as part of that, he developed what may have been the first real compiler and high level language, called 'george' from 'let george do it'. here's a comment from [john backus](https://en.wikipedia.org/wiki/John_Backus).

_laning was the first person to conceive of and implement what we would now call a true compiler_

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title: "simplex52"
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george dantzig joined rand santa monica in 1952 specifically to code simplex on practical hardware. at rand, william orchard-hays was assigned as dantzig's coder. this was at the same time that hal laning and richard battin began to code whirlwind and guidance systems for the mit instrumentation lab.
[george dantzig](https://en.wikipedia.org/wiki/George_Dantzig) joined rand santa monica in 1952 specifically to code simplex on practical hardware. at rand, william orchard-hays was assigned as dantzig's coder. this was at the same time that [hal laning](https://en.wikipedia.org/wiki/J._Halcombe_Laning) and [richard battin](https://en.wikipedia.org/wiki/Richard_Battin) began to code whirlwind and guidance systems for the mit instrumentation lab.

dantzig and orchard-hays went to work in 1953 with an [ibm cpc card programmed calculator 'poor man's eniac'](https://en.wikipedia.org/wiki/IBM_CPC). surprisingly, they were able to calculate a matrix inverse for each simplex iteration. less surprisingly, dantzig was 'appalled when he saw the result' using these inverses. fortunately he recalled the 'product-form inverse' algorithm, and this led to a second simplex implementation on the cpc, successful enough to remain in use for over twenty years.

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since the ibm cpc was the first hardware to run simplex, and among the earliest to perform matrix inversion, here are some more notes. it was a makeshift marriage of the 603 electronic multiplier 'multiplying punch' and a 405 accounting machine, put together by northrop aircraft with ibm help. ibm saw its popularity and commercialized it as the cpc in 1948. it was not a true stored program computer. there was no memory. it worked like an old-fashioned player piano, purely reacting to punched cards as they were fed through.

here's a copy of the original paper by dantzig and orchard-hays on the [product form inverse](docs/simplex/1953%20dantzig.pdf), and a [modern review](docs/simplex/2012%20pfi%20revisited.pdf). note this comment in the the original on the state of the art in 1952.
here's a copy of the original paper by dantzig and orchard-hays on the [product form inverse](docs/inverse/1953%20dantzig.pdf), and a [modern review](docs/inverse/2012%20pfi%20revisited.pdf). note this comment in the the original on the state of the art in 1952.

_using the ibm cpc, a novel feature results. when the inverse matrix is needed at one stage and its transpose at another, this is achieved simply by turning over the deck of cards representing the inverse._
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