Special Linear Systems and Cholesky Factorization for Programmers

#1

Post by disaster01 » Tue, Sep 19, 2017, 3:19 PM UTC

Special Linear Systems and Cholesky Factorization for Programmers
dragan.rocks

Re: Special Linear Systems and Cholesky Factorization for Programmers

#2

Post by dragandj » Tue, Sep 19, 2017, 3:32 PM UTC

Part 1: http://dragan.rocks/articles/17/Clojure-Numerics-1-Use-Matri...

Part 2: http://dragan.rocks/articles/17/Clojure-Numerics-2-General-L...

Linear Algebra Refresher:

http://dragan.rocks/articles/17/Clojure-Linear-Algebra-Refre...

Re: Special Linear Systems and Cholesky Factorization for Programmers

#3

Post by tw1010 » Tue, Sep 19, 2017, 3:37 PM UTC

This is awesome. I can't wait until the future when we'll get more informal blog posts from programmers about even more abstract subjects which thus far are dominated in exposition by academics (who very rarely innovate in how they present the material). The day I see a good engineer-style post on HN about sheaf theory or algebraic geometry will be amazing.

Re: Special Linear Systems and Cholesky Factorization for Programmers

#4

Post by dragandj » Tue, Sep 19, 2017, 3:39 PM UTC

dragandj wrote: post #2

Part 1: http://dragan.rocks/articles/17/Clojure-Numerics-1-Use-Matri... Part 2: http://dragan.rocks/articles/17/Clojure-Numerics-2-General-L... Linear Algebra Refresher: http://dragan.rocks/articles/17/Clojure-Linear-Algebra-Refre... http://dragan.rocks/articles/17/Clojure-Linear-Algebra-Refre... http://dragan.rocks/articles/17/Clojure-Linear-Algebra-Refre... http://dragan.rocks/articles/17/Clojure-Linear-Algebra-Ref…

And the source of the library used: https://github.com/uncomplicate/neanderthal

Re: Special Linear Systems and Cholesky Factorization for Programmers

#5

Post by dragandj » Tue, Sep 19, 2017, 3:41 PM UTC

tw1010 wrote: post #3

This is awesome. I can't wait until the future when we'll get more informal blog posts from programmers about even more abstract subjects which thus far are dominated in exposition by academics (who very rarely innovate in how they present the material). The day I see a good engineer-style post on HN about sheaf theory or algebraic geometry will be amazing.

Author here. I hope I won't spoil the future, since I work at a university, but I am also a programmer, and these libraries and tutorials have been made to be 100% practical with the working programmers as the target audience.

Re: Special Linear Systems and Cholesky Factorization for Programmers

#6

Post by amelius » Tue, Sep 19, 2017, 3:59 PM UTC

Since LAPACK is an excellent library for these matrix functions, why not use it, and translate it to Clojure instead of reinventing the wheel? (There's also a translator from Fortran to C).

Re: Special Linear Systems and Cholesky Factorization for Programmers

#7

Post by dragandj » Tue, Sep 19, 2017, 4:05 PM UTC

amelius wrote: post #6

Since LAPACK is an excellent library for these matrix functions, why not use it, and translate it to Clojure instead of reinventing the wheel? (There's also a translator from Fortran to C).

Because JVM does not have access to the hardware features needed to execute this efficiently. Also, the power of lapack comes from existing highly tuned implementations, not the interface itself. Reference BLAS and LAPACK are actually quite slow.

Re: Special Linear Systems and Cholesky Factorization for Programmers

#8

Post by santaclaus » Tue, Sep 19, 2017, 4:09 PM UTC

Now the real tough question is how do you pronounce Cholesky? I had a Polish math prof who was mad at the American pronunciation, but Cholesky was actually French, so should we actually pronounce it in the francophone style?

Re: Special Linear Systems and Cholesky Factorization for Programmers

#9

Post by makmanalp » Tue, Sep 19, 2017, 4:22 PM UTC

dragandj wrote: post #2

Part 1: http://dragan.rocks/articles/17/Clojure-Numerics-1-Use-Matri... Part 2: http://dragan.rocks/articles/17/Clojure-Numerics-2-General-L... Linear Algebra Refresher: http://dragan.rocks/articles/17/Clojure-Linear-Algebra-Refre... http://dragan.rocks/articles/17/Clojure-Linear-Algebra-Refre... http://dragan.rocks/articles/17/Clojure-Linear-Algebra-Refre... http://dragan.rocks/articles/17/Clojure-Linear-Algebra-Ref…

For linear algebra basics, I also especially recommend 3Blue1Brown's youtube channel and his "Essence of" series:

https://www.youtube.com/watch?v=kjBOesZCoqc&list=PLZHQObOWTQ...

I've never seen the material presented more clearly - it's completely visual and focused on building intuition first.

Re: Special Linear Systems and Cholesky Factorization for Programmers

#10

Post by [deleted] » Tue, Sep 19, 2017, 4:53 PM UTC

amelius wrote: post #6

Since LAPACK is an excellent library for these matrix functions, why not use it, and translate it to Clojure instead of reinventing the wheel? (There's also a translator from Fortran to C).

[deleted]