[Haskell-cafe] HMatrix Vector/Matrix interpolation ala Matlab interp/interp2 ??

[Claude Heiland-Allen]

Hi Phil,

On 22/01/11 14:07, gutti wrote:
>
> Dear Haskellers,
>
> I'm looking for Vector and especially Matric interpolation ala:
>
>      z = interp2 (xMatrix, yMatrix, zMatrix, x, y)
>
>     - x and y can be single values or also vectors or matrices
>     - indeally with the options nearest, linear, quadratic, qubic..
>
> Any hope that there is something similar especially using the HMatrix
> matrices (Matrix Double). - If I have to code it any suggestions ?
>
> Cheers Phil
>
>

I'm not sure if this is what you mean, as I'm not familiar with matlab, 
so apologies if this is totally a waste of time.. But I had a simple 
cubic interpolation implemented already, it wasn't too hard to lift it 
into matrices (there are many elevation permutations, I imagine), I used 
(fromLists ...stuff... toLists), but maybe there's a better way:


{-# LANGUAGE NoMonomorphismRestriction #-}
module Interpolate where

import Numeric.LinearAlgebra
import Data.List (zipWith5)

-- cubic interpolation
cubic t a b c d =
   let a1 = 0.5 * (c - a)
       a2 = a - 2.5 * b + 2.0 * c - 0.5 * d
       a3 = 0.5 * (d - a) + 1.5 * (b - c)
   in  ((a3 * t + a2) * t + a1) * t + b

-- boring manual lifting
liftMatrix5 f a b c d e =
   let la = toLists a
       lb = toLists b
       lc = toLists c
       ld = toLists d
       le = toLists e
   in  fromLists (zipWith5 (zipWith5 f) la lb lc ld le)

-- test
mt = (3><3) [0, 0.1 ..]
ma = (3><3) [0, 1 ..]
mb = (3><3) [0, 2 ..]
mc = (3><3) [0, 3 ..]
md = (3><3) [0, 4 ..]
test = liftMatrix5 cubic mt ma mb mc md

{- test output
(3><3)
  [                0.0,  2.1,  4.4
  ,                6.9,  9.6, 12.5
  , 15.600000000000001, 18.9, 22.4 ]
-}




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