documentation, more general cond, remove some unicode, minor changes

4 files changed, 73 insertions, 15 deletions

diff --git a/packages/base/src/Numeric/LinearAlgebra.hs b/packages/base/src/Numeric/LinearAlgebra.hs
index fe524cc..2e6b8ca 100644
--- a/packages/base/src/Numeric/LinearAlgebra.hs
+++ b/packages/base/src/Numeric/LinearAlgebra.hs
@@ -47,7 +47,7 @@ module Numeric.LinearAlgebra (
 
     -- * Products
     -- ** dot
-    dot, (<·>),
+    dot, (<.>),
     -- ** matrix-vector
     app, (#>), (<#), (!#>),
     -- ** matrix-matrix
@@ -240,7 +240,53 @@ nullspace m = nullspaceSVD (Left (1*eps)) m (rightSV m)
 -- | return an orthonormal basis of the range space of a matrix. See also 'orthSVD'.
 orth m = orthSVD (Left (1*eps)) m (leftSV m)
 
+{- | Experimental implementation of LU factorization
+     working on any Fractional element type, including 'Mod' n 'I' and 'Mod' n 'Z'.
+
+>>> let m = ident 5 + (5><5) [0..] :: Matrix (Z ./. 17)
+(5><5)
+ [  1,  1,  2,  3,  4
+ ,  5,  7,  7,  8,  9
+ , 10, 11, 13, 13, 14
+ , 15, 16,  0,  2,  2
+ ,  3,  4,  5,  6,  8 ]
+
+>>> let (l,u,p,s) = luFact $ luPacked' m
+>>> l
+(5><5)
+ [  1,  0, 0,  0, 0
+ ,  6,  1, 0,  0, 0
+ , 12,  7, 1,  0, 0
+ ,  7, 10, 7,  1, 0
+ ,  8,  2, 6, 11, 1 ]
+>>> u
+(5><5)
+ [ 15, 16,  0,  2,  2
+ ,  0, 13,  7, 13, 14
+ ,  0,  0, 15,  0, 11
+ ,  0,  0,  0, 15, 15
+ ,  0,  0,  0,  0,  1 ]
+
+-}
 luPacked' x = mutable (luST (magnit 0)) x
 
+{- | Experimental implementation of gaussian elimination
+     working on any Fractional element type, including 'Mod' n 'I' and 'Mod' n 'Z'.
+
+>>> let a = (2><2) [1,2,3,5] :: Matrix (Z ./. 13)
+(2><2)
+ [ 1, 2
+ , 3, 5 ]
+>>> b
+(2><3)
+ [ 5, 1, 3
+ , 8, 6, 3 ]
+
+>>> let x = linearSolve' a b
+(2><3)
+ [ 4,  7, 4
+ , 7, 10, 6 ]
+
+-}
 linearSolve' x y = gaussElim x y
 
diff --git a/packages/base/src/Numeric/LinearAlgebra/Data.hs b/packages/base/src/Numeric/LinearAlgebra/Data.hs
index fffc2bd..2a45771 100644
--- a/packages/base/src/Numeric/LinearAlgebra/Data.hs
+++ b/packages/base/src/Numeric/LinearAlgebra/Data.hs
@@ -1,3 +1,5 @@
+{-# LANGUAGE TypeOperators #-}
+
 --------------------------------------------------------------------------------
 {- |
 Module      :  Numeric.LinearAlgebra.Data
@@ -17,11 +19,11 @@ module Numeric.LinearAlgebra.Data(
     -- | 1D arrays are storable vectors from the vector package. There is no distinction
     --   between row and column vectors.
 
-    fromList, toList, vector, (|>),
+    fromList, toList, (|>), vector, range, idxs,
 
     -- * Matrix
 
-    matrix, (><), tr, tr',
+    (><), matrix, tr, tr',
 
     -- * Dimensions
 
@@ -43,7 +45,7 @@ module Numeric.LinearAlgebra.Data(
     Indexable(..),
 
     -- * Construction
-    scalar, Konst(..), Build(..), assoc, accum, linspace, range, idxs, -- ones, zeros,
+    scalar, Konst(..), Build(..), assoc, accum, linspace,  -- ones, zeros,
 
     -- * Diagonal
     ident, diag, diagl, diagRect, takeDiag,
@@ -53,16 +55,19 @@ module Numeric.LinearAlgebra.Data(
 
     -- * Matrix extraction
     Extractor(..), (??),
+
     takeRows, dropRows, takeColumns, dropColumns,
-    subMatrix, (?), (¿), fliprl, flipud, remap,
+    subMatrix, (?), (¿), fliprl, flipud,
+
+    remap,
 
     -- * Block matrix
     fromBlocks, (|||), (===), diagBlock, repmat, toBlocks, toBlocksEvery,
 
     -- * Mapping functions
     conj, cmap, cmod,
-    
-    step, cond, ccompare, cselect,
+
+    step, cond,
 
     -- * Find elements
     find, maxIndex, minIndex, maxElement, minElement,
@@ -87,7 +92,7 @@ module Numeric.LinearAlgebra.Data(
     separable,
     fromArray2D,
     module Data.Complex,
-    R,C,I,Z,Mod,
+    R,C,I,Z,Mod, type(./.),
     Vector, Matrix, GMatrix, nRows, nCols
 
 ) where
diff --git a/packages/base/src/Numeric/LinearAlgebra/HMatrix.hs b/packages/base/src/Numeric/LinearAlgebra/HMatrix.hs
index 11c2487..8adaaaf 100644
--- a/packages/base/src/Numeric/LinearAlgebra/HMatrix.hs
+++ b/packages/base/src/Numeric/LinearAlgebra/HMatrix.hs
@@ -13,10 +13,13 @@ compatibility with previous version, to be removed
 
 module Numeric.LinearAlgebra.HMatrix (
     module Numeric.LinearAlgebra,
-    (¦),(——),ℝ,ℂ,
+    (¦),(——),ℝ,ℂ,(<·>)
 ) where
 
 import Numeric.LinearAlgebra
 import Internal.Util
 
+infixr 8 <·>
+(<·>) :: Numeric t => Vector t -> Vector t -> t
+(<·>) = dot
 
diff --git a/packages/base/src/Numeric/LinearAlgebra/Static.hs b/packages/base/src/Numeric/LinearAlgebra/Static.hs
index a657bd0..d0a790d 100644
--- a/packages/base/src/Numeric/LinearAlgebra/Static.hs
+++ b/packages/base/src/Numeric/LinearAlgebra/Static.hs
@@ -44,7 +44,7 @@ module Numeric.LinearAlgebra.Static(
     -- * Complex
     C, M, Her, her, 𝑖,
     -- * Products
-    (<>),(#>),(<·>),
+    (<>),(#>),(<.>),
     -- * Linear Systems
     linSolve, (<\>),
     -- * Factorizations
@@ -55,13 +55,13 @@ module Numeric.LinearAlgebra.Static(
     Disp(..), Domain(..),
     withVector, withMatrix,
     toRows, toColumns,
-    Sized(..), Diag(..), Sym, sym, mTm, unSym
+    Sized(..), Diag(..), Sym, sym, mTm, unSym, (<·>)
 ) where
 
 
 import GHC.TypeLits
 import Numeric.LinearAlgebra hiding (
-    (<>),(#>),(<·>),Konst(..),diag, disp,(===),(|||),
+    (<>),(#>),(<.>),Konst(..),diag, disp,(===),(|||),
     row,col,vector,matrix,linspace,toRows,toColumns,
     (<\>),fromList,takeDiag,svd,eig,eigSH,eigSH',
     eigenvalues,eigenvaluesSH,eigenvaluesSH',build,
@@ -207,6 +207,10 @@ infixr 8 <·>
 (<·>) :: R n -> R n -> ℝ
 (<·>) = dotR
 
+infixr 8 <.>
+(<.>) :: R n -> R n -> ℝ
+(<.>) = dotR
+
 --------------------------------------------------------------------------------
 
 class Diag m d | m -> d
@@ -496,7 +500,7 @@ appC m v = mkC (extract m LA.#> extract v)
 dotC :: KnownNat n => C n -> C n -> ℂ
 dotC (unwrap -> u) (unwrap -> v)
     | singleV u || singleV v = sumElements (conj u * v)
-    | otherwise = u LA.<·> v
+    | otherwise = u LA.<.> v
 
 
 crossC :: C 3 -> C 3 -> C 3
@@ -584,12 +588,12 @@ test = (ok,info)
       where
         q = tm :: L 10 3
 
-    thingD = vjoin [ud1 u, 1] LA.<·> tr m LA.#> m LA.#> ud1 v
+    thingD = vjoin [ud1 u, 1] LA.<.> tr m LA.#> m LA.#> ud1 v
       where
         m = LA.matrix 3 [1..30]
 
     precS = (1::Double) + (2::Double) * ((1 :: R 3) * (u & 6)) <·> konst 2 #> v
-    precD = 1 + 2 * vjoin[ud1 u, 6] LA.<·> LA.konst 2 (LA.size (ud1 u) +1, LA.size (ud1 v)) LA.#> ud1 v
+    precD = 1 + 2 * vjoin[ud1 u, 6] LA.<.> LA.konst 2 (LA.size (ud1 u) +1, LA.size (ud1 v)) LA.#> ud1 v
 
 
 splittest