Re: [Haskell-cafe] A Performance Puzzle
Something Haskell has lacked for a long time is a good medium-duty linear system solver based on the LU decomposition. There are bindings to the usual C/Fortran libraries, but not one in pure Haskell. (An example "LU factorization" routine that does not do partial pivoting has been around for years, but lacking pivoting it can fail unexpectedly on well-conditioned inputs. Another Haskell LU decomposition using partial pivoting is around, but it uses an inefficient representation of the pivot matrix, so it's not suited to solving systems of more than 100 x 100, say.)
By medium duty I mean a linear system solver that can handle systems of (1000s) x (1000s) and uses Crout's efficient in-place algorithm. In short, a program does everything short of exploiting SIMD vector instructions for solving small subproblems.
Instead of complaining about this, I have written a little library that implements this. It contains an LU factorization function and an LU system solver. The LU factorization also returns the parity of the pivots ( = (-1)^(number of row swaps) ) so it can be used to calculate determinants. I used Gustavson's recursive (imperative) version of Crout's method. The implementation is quite simple and deserves to be better known by people using functional languages to do numeric work. The library can be downloaded from GitHub: https://github.com/gwright83/luSolve https://github.com/gwright83/luSolve Great news :)
Dominic Steinitz dominic@steinitz.org http://idontgetoutmuch.wordpress.com Twitter: @idontgetoutmuch
I just tried using Mersenne to generate the random matrices rather than `System.Random`. It is about 15% faster so I don’t think the actual RNG process is the culprit. Dominic Steinitz dominic@steinitz.org http://idontgetoutmuch.wordpress.com Twitter: @idontgetoutmuch
On 4 Aug 2018, at 10:02, dominic@steinitz.org wrote:
Something Haskell has lacked for a long time is a good medium-duty linear system solver based on the LU decomposition. There are bindings to the usual C/Fortran libraries, but not one in pure Haskell. (An example "LU factorization" routine that does not do partial pivoting has been around for years, but lacking pivoting it can fail unexpectedly on well-conditioned inputs. Another Haskell LU decomposition using partial pivoting is around, but it uses an inefficient representation of the pivot matrix, so it's not suited to solving systems of more than 100 x 100, say.)
By medium duty I mean a linear system solver that can handle systems of (1000s) x (1000s) and uses Crout's efficient in-place algorithm. In short, a program does everything short of exploiting SIMD vector instructions for solving small subproblems.
Instead of complaining about this, I have written a little library that implements this. It contains an LU factorization function and an LU system solver. The LU factorization also returns the parity of the pivots ( = (-1)^(number of row swaps) ) so it can be used to calculate determinants. I used Gustavson's recursive (imperative) version of Crout's method. The implementation is quite simple and deserves to be better known by people using functional languages to do numeric work. The library can be downloaded from GitHub: https://github.com/gwright83/luSolve https://github.com/gwright83/luSolve Great news :)
Dominic Steinitz dominic@steinitz.org mailto:dominic@steinitz.org http://idontgetoutmuch.wordpress.com http://idontgetoutmuch.wordpress.com/ Twitter: @idontgetoutmuch
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