Implemented some form of LM optimization, but it's proper fucked somehow.

app/Main.hs

@@ -12,6 +12,7 @@ import Petzval.Optimization
 import Petzval.Types
 import Linear
 import Numeric.AD.Mode (Scalar, Mode)
+import qualified Numeric.LinearAlgebra as L
 
 bk7 = SellemeierMat [ (1.03961212,  6.00069867e-3 )
                     , (0.231792344, 2.00179144e-2 )
@@ -56,7 +57,7 @@ merit system = result
                   . rights
                   . map fst
                   . map (raytrace baked . createRay Nothing ep angle)
-                  $ spiralPattern 10)
+                  $ hexapolarPattern 6)
           $ [0, 7.07, 15]
 
 type Id a = a -> a
@@ -69,13 +70,17 @@ main =
       ep = (entrancePupil baked){position=20.4747094540}
       fa = 20
   in do
+    print $ L.norm_2  (L.fromList [3.0 , 4.0] :: L.Vector Double)
     putStrLn $ show ep
     putStrLn $ show $ rearFocalLength $ lensRTM baked
     putStrLn $ show $ mconcat (seidel ep fa baked :: [Seidel Double])
-    defaultMain [
+ {-   defaultMain [
       bgroup "merit" [ bench "system1" $ nf merit (system1 :: [Element SellemeierMat Double])
                      , bench "system2" $ nf merit (system2 :: [Element ConstMat Double])
                      ]
-      , bgroup "ad" [ bench "system1" $ nf (gradientAt (ix 1.thickness) merit) system1
+      , bgroup "ad" [ bench "system1" $ nf (gradientAt (ix 1.thickness) merit) system1,
+                      bench "system2" $ nf (gradientAt (ix 1.thickness) merit) system2
+
                     ]
       ]
+-}