src/Linear/Matrix.hs: add support for zero-length columns/matrices.

[numerical-analysis.git] / src / Linear / Matrix.hs

diff --git a/src/Linear/Matrix.hs b/src/Linear/Matrix.hs
index a06151db14262838394f473f83841f4766c62266..e8d7180fbc7717ef93ce3eb30ff55332aeef31b5 100644 (file)
--- a/src/Linear/Matrix.hs
+++ b/src/Linear/Matrix.hs
@@ -20,6 +20,7 @@ import Data.List (intercalate)
 import Data.Vector.Fixed (
   (!),
   generate,
+  mk0,
   mk1,
   mk2,
   mk3,
@@ -27,13 +28,13 @@ import Data.Vector.Fixed (
   mk5 )
 import qualified Data.Vector.Fixed as V (
   and,
+  foldl,
   fromList,
   head,
   ifoldl,
   ifoldr,
   imap,
   map,
-  maximum,
   replicate,
   reverse,
   toList,
@@ -43,7 +44,9 @@ import Linear.Vector ( Vec, delete )
 import Naturals
 import Normed ( Normed(..) )
 
-import NumericPrelude hiding ( (*), abs )
+-- We want the "max" that works on Ord, not the one that only works on
+-- Bool/Integer from the Lattice class!
+import NumericPrelude hiding ( (*), abs, max)
 import qualified NumericPrelude as NP ( (*) )
 import qualified Algebra.Absolute as Absolute ( C )
 import Algebra.Absolute ( abs )
@@ -56,12 +59,13 @@ import qualified Algebra.Module as Module ( C )
 import qualified Algebra.RealRing as RealRing ( C )
 import qualified Algebra.ToRational as ToRational ( C )
 import qualified Algebra.Transcendental as Transcendental ( C )
-import qualified Prelude as P ( map )
+import qualified Prelude as P ( map, max)
 
 -- | Our main matrix type.
 data Mat m n a = (Arity m, Arity n) => Mat (Vec m (Vec n a))
 
 -- Type synonyms for n-by-n matrices.
+type Mat0 a = Mat Z Z a
 type Mat1 a = Mat N1 N1 a
 type Mat2 a = Mat N2 N2 a
 type Mat3 a = Mat N3 N3 a
@@ -86,6 +90,7 @@ type Row5 a = Row N5 a
 -- | Type synonym for column vectors expressed as n-by-1 matrices.
 type Col n a = Mat n N1 a
 
+type Col0 a = Col Z a
 type Col1 a = Col N1 a
 type Col2 a = Col N2 a
 type Col3 a = Col N3 a
@@ -348,15 +353,21 @@ identity_matrix =
 --   >>> frobenius_norm (r - (transpose expected)) < 1e-12
 --   True
 --
-cholesky :: forall m n a. (Algebraic.C a, Arity m, Arity n)
-         => (Mat m n a) -> (Mat m n a)
-cholesky m = construct r
+cholesky :: forall m a. (Algebraic.C a, Arity m)
+         => (Mat m m a) -> (Mat m m a)
+cholesky m = ifoldl2 f zero m
   where
-    r :: Int -> Int -> a
-    r i j | i == j = sqrt(m !!! (i,j) - sum [(r k i)^2 | k <- [0..i-1]])
-          | i < j =
-              (((m !!! (i,j)) - sum [(r k i) NP.* (r k j) | k <- [0..i-1]]))/(r i i)
-          | otherwise = 0
+    f :: Int -> Int -> (Mat m m a) -> a -> (Mat m m a)
+    f i j cur_R _ = set_idx cur_R (i,j) (r cur_R i j)
+
+    r :: (Mat m m a) -> Int -> Int -> a
+    r cur_R i j
+      | i == j = sqrt(m !!! (i,j) - sum [(cur_R !!! (k,i))^2 | k <- [0..i-1]])
+      | i < j = (((m !!! (i,j))
+                  - sum [(cur_R !!! (k,i)) NP.* (cur_R !!! (k,j))
+                             | k <- [0..i-1]]))/(cur_R !!! (i,i))
+      | otherwise = 0
+
 
 
 -- | Returns True if the given matrix is upper-triangular, and False
@@ -606,8 +617,8 @@ instance (Absolute.C a,
           Algebraic.C a,
           ToRational.C a,
           Arity m)
-         => Normed (Col (S m) a) where
-  -- | Generic p-norms for vectors in R^n that are represented as n-by-1
+         => Normed (Col m a) where
+  -- | Generic p-norms for vectors in R^m that are represented as m-by-1
   --   matrices.
   --
   --   Examples:
@@ -622,6 +633,10 @@ instance (Absolute.C a,
   --   >>> norm_p 1 v1 :: Double
   --   2.0
   --
+  --   >>> let v1 = vec0d :: Col0 Double
+  --   >>> norm v1
+  --   0.0
+  --
   norm_p p (Mat rows) =
     (root p') $ sum [fromRational' (toRational $ abs x)^p' | x <- xs]
     where
@@ -637,7 +652,8 @@ instance (Absolute.C a,
   --   5
   --
   norm_infty (Mat rows) =
-    fromRational' $ toRational $ V.maximum $ V.map V.maximum rows
+    fromRational' $ toRational
+                      $ (V.foldl P.max 0) $ V.map (V.foldl P.max 0) rows
 
 
 -- | Compute the Frobenius norm of a matrix. This essentially treats
@@ -682,6 +698,9 @@ frobenius_norm matrix =
 --   >>> fixed_point g eps u0
 --   ((1.0728549599342185),(1.0820591495686167))
 --
+vec0d :: Col0 a
+vec0d = Mat mk0
+
 vec1d :: (a) -> Col1 a
 vec1d (x) = Mat (mk1 (mk1 x))