hmatrix-static (empty) → 0.1

raw patch · 16 files changed

+2485/−0 lines, 16 filesdep +arraydep +basedep +haskell-src-metasetup-changed

Dependencies added: array, base, haskell-src-meta, hmatrix, parsec, template-haskell, tfp

Files

• Data/Packed/Static.hs +29/−0
• Data/Packed/Static/Convert.hs +82/−0
• Data/Packed/Static/Imports.hs +33/−0
• Data/Packed/Static/Internal.hs +21/−0
• Data/Packed/Static/Internal/Matrix.hs +23/−0
• Data/Packed/Static/Internal/Vector.hs +50/−0
• Data/Packed/Static/Matrix.hs +487/−0
• Data/Packed/Static/ST.hs +119/−0
• Data/Packed/Static/Shapes.hs +142/−0
• Data/Packed/Static/Syntax.hs +223/−0
• Data/Packed/Static/Vector.hs +209/−0
• LICENSE +674/−0
• Numeric/LinearAlgebra/Static.hs +21/−0
• Numeric/LinearAlgebra/Static/Algorithms.hs +315/−0
• Setup.hs +4/−0
• hmatrix-static.cabal +53/−0

@@ -0,0 +1,29 @@+-----------------------------------------------------------------------------+-- |+-- Module      :  Data.Packed.Static+-- Copyright   :  (c) Reiner Pope 2008+-- License     :  GPL-style+--+-- Maintainer  :  Reiner Pope <reiner.pope@gmail.com>+-- Stability   :  provisional+-- Portability :  portable+--+-- Statically-dimensioned vectors and matrices.+--+-----------------------------------------------------------------------------+++module Data.Packed.Static(+     module Data.Packed.Static.Shapes,+     module Data.Packed.Static.Vector,+     module Data.Packed.Static.Matrix,+     module Data.Packed.Static.Syntax,+     module Data.Packed.Static.Imports,+ ) where++import Data.Packed.Static.Shapes+import Data.Packed.Static.Vector+import Data.Packed.Static.Matrix+import Data.Packed.Static.Syntax+import Data.Packed.Static.Imports+

@@ -0,0 +1,82 @@+-----------------------------------------------------------------------------+-- |+-- Module      :  Data.Packed.Static.Convert+-- Copyright   :  (c) Reiner Pope 2008+-- License     :  GPL-style+--+-- Maintainer  :  Reiner Pope <reiner.pope@gmail.com>+-- Stability   :  experimental+-- Portability :  portable+--+-- Conversions to other forms.+--+-----------------------------------------------------------------------------++module Data.Packed.Static.Convert where++import qualified Data.Packed.Convert as HS+import qualified Numeric.LinearAlgebra as H++import Data.Packed.Static.Shapes+import Data.Packed.Static.Internal+import Data.Packed.Static.Imports+import Data.Packed.Static.Vector+import Data.Packed.Static.Matrix++import Data.Array.MArray+import Data.Array.IArray+import Data.Array.Unboxed+import Data.Array.Storable+import Control.Monad.ST++-- | Constructs a vector from an hmatrix (dynamically-lengthed) vector.+fromHVectorU :: H.Vector t -> Vector Unknown t+fromHVectorU = wrapU++-- | Gives the underlying hmatrix representation.+toHVector :: Vector n t -> H.Vector t+toHVector = unWrap+++arrayFromVector :: (Storable t) => Vector n t -> Array Int t+arrayFromVector = HS.arrayFromVector . unVector++vectorFromArray :: Storable t => Array Int t -> Vector Unknown t+vectorFromArray = Vector . HS.vectorFromArray++mArrayFromVector :: (MArray b t (ST s), Storable t) =>                    Vector n t -> ST s (b Int t)+mArrayFromVector = HS.mArrayFromVector . unVector++vectorFromMArray :: (Storable t) => Array Int t -> Vector n t+vectorFromMArray = Vector . HS.vectorFromArray++vectorToStorableArray :: (Storable t) => +       Vector n t -> IO (StorableArray Int t)+vectorToStorableArray = HS.vectorToStorableArray . unVector++storableArrayToVector :: Storable t =>+       StorableArray Int t -> IO (Vector Unknown t)+storableArrayToVector = fmap Vector . HS.storableArrayToVector++-- | Constructs a vector from an hmatrix (dynamically-lengthed) vector.+fromHMatrixU :: H.Matrix t -> Matrix (Unknown,Unknown) t+fromHMatrixU = wrapU++-- | Gives the underlying hmatrix representation.+toHMatrix :: Matrix (m,n) t -> H.Matrix t+toHMatrix = unWrap+++arrayFromMatrix :: Matrix mn Double -> UArray (Int, Int) Double+arrayFromMatrix = HS.arrayFromMatrix . unMatrix++matrixFromArray :: UArray (Int, Int) Double -> Matrix mn Double+matrixFromArray = Matrix . HS.matrixFromArray++mArrayFromMatrix :: (MArray b Double m) =>+                    Matrix mn Double -> m (b (Int, Int) Double)+mArrayFromMatrix = HS.mArrayFromMatrix . unMatrix++matrixFromMArray :: (MArray a Double (ST s)) =>+                    a (Int, Int) Double -> ST s (Matrix mn Double)+matrixFromMArray = fmap Matrix . HS.matrixFromMArray

@@ -0,0 +1,33 @@+-----------------------------------------------------------------------------+-- |+-- Module      :  Data.Packed.Static.Imports+-- Copyright   :  (c) Reiner Pope 2008+-- License     :  GPL-style+--+-- Maintainer  :  Reiner Pope <reiner.pope@gmail.com>+-- Stability   :  experimental+-- Portability :  portable+--+-- Useful imports from other packages. In particular:+-- imports from TFP, Foreign.Storable, and HMatrix.+--+-----------------------------------------------------------------------------++module Data.Packed.Static.Imports(+   H.Element,+   H.Field,+   H.Linear,+   F.Storable,+   module Types.Data.Num,+   True,+   (:<=:),+   Min,+  ) where++import qualified Numeric.LinearAlgebra as H+import qualified Foreign.Storable as F++import Types.Data.Num+import Types.Data.Bool(True)+import Types.Data.Ord((:<=:), Min)+

@@ -0,0 +1,21 @@+-----------------------------------------------------------------------------+-- |+-- Module      :  Data.Packed.Static.Internal+-- Copyright   :  (c) Reiner Pope 2008+-- License     :  GPL-style+--+-- Maintainer  :  Reiner Pope <reiner.pope@gmail.com>+-- Stability   :  experimental+-- Portability :  portable+--+-- Internals.+--+-----------------------------------------------------------------------------++module Data.Packed.Static.Internal(+   module Data.Packed.Static.Internal.Vector,+   module Data.Packed.Static.Internal.Matrix,+  ) where++import Data.Packed.Static.Internal.Vector+import Data.Packed.Static.Internal.Matrix

@@ -0,0 +1,23 @@+-----------------------------------------------------------------------------+-- |+-- Module      :  Data.Packed.Static.Internal.Matrix+-- Copyright   :  (c) Reiner Pope 2008+-- License     :  GPL-style+--+-- Maintainer  :  Reiner Pope <reiner.pope@gmail.com>+-- Stability   :  experimental+-- Portability :  portable+--+-- Matrix newtype definition.+--+-----------------------------------------------------------------------------+++module Data.Packed.Static.Internal.Matrix(+   Matrix(..),+ ) where++import qualified Numeric.LinearAlgebra as H++-- | A matrix with @m@ rows, @n@ columns.+newtype Matrix mn t = Matrix { unMatrix :: H.Matrix t } deriving()

@@ -0,0 +1,50 @@+-----------------------------------------------------------------------------+-- |+-- Module      :  Data.Packed.Static.Internal.Vector+-- Copyright   :  (c) Reiner Pope 2008+-- License     :  GPL-style+--+-- Maintainer  :  Reiner Pope <reiner.pope@gmail.com>+-- Stability   :  experimental+-- Portability :  portable+--+-- Vector newtype definition.+--+-----------------------------------------------------------------------------+++module Data.Packed.Static.Internal.Vector(+   Vector(..),+ ) where++import qualified Numeric.LinearAlgebra as H++-- | A vector with elements of type @t@ and length @n@.+-- The type @n@ encodes the vector's length, and will+-- usually either be 'Unknown' or will satisfy 'PositiveT'.+-- +-- Operations which return vectors of length 'Unknown'+-- will return vectors whose lengths are determined+-- at runtime. All operations which mention 'Unknown'+-- lengths will have names ending in an uppercase U,+-- for example 'fromListU', 'subVectorU'.+-- +-- The use of 'Unknown' facilitates manipulation+-- of dynamically-lengthed vectors without+-- using continuations for each operation, since+-- most operations work equally well for lengthed+-- as well as unlengthed vectors. When vectors+-- of 'Unknown' length are used, runtime length+-- mismatches may arise, and the system is as safe+-- as hmatrix.+-- +-- When the length of every vector is known, if+-- the code typechecks, then there will be+-- no runtime vector length mismatches. Equivalently,+-- there will be no runtime vector length mismatches+-- if:+-- +--   * no unsafe functions are used; and +-- +--   * no functions mentioning 'Unknown' are used, i.e. no functions with suffix U are used.+newtype Vector n t = Vector { unVector :: H.Vector t } 

@@ -0,0 +1,487 @@+-----------------------------------------------------------------------------+-- |+-- Module      :  Data.Packed.Static.Matrix+-- Copyright   :  (c) Reiner Pope 2008+-- License     :  GPL-style+--+-- Maintainer  :  Reiner Pope <reiner.pope@gmail.com>+-- Stability   :  experimental+-- Portability :  portable+--+-- Statically-dimensioned 2D matrices.+--+-----------------------------------------------------------------------------++module Data.Packed.Static.Matrix(+  Matrix,+  -- * Shaping+  refineMat,+  forgetRowsU,+  forgetColsU,+  atRows,+  atCols,+  withShape,+  withRows,+  withCols,+  withSquare,+  -- * To/from lists+  (><),+  matFromList,+  fromListsU,+  toLists,+  -- * To/from rows/column vectors+  fromRowsU,+  toRows,+  fromColumnsU,+  toColumns,+  fromBlocksU,+  asRow,+  asColumn,+  -- * Other operations+  rows,+  cols,+  trans,+  reshapeU,+  flatten,+  (@@>),+  repmatU,+  flipud,+  fliprl,+  subMatrixU,+  takeRows,+  dropRows,+  takeColumns,+  dropColumns,+  extractRowsU,+  ident,+  diag,+  diagRect,+  takeDiag, +  liftMatrix,+  -- * Conversions / file input+  format,+  readMatrix,+  fromFile,+  fromArray2D,+ ) where++import Data.Array++import Data.Maybe(fromJust)+import Data.List(intercalate,transpose)+import qualified Numeric.LinearAlgebra as H++import Data.Packed.Static.Shapes+import Data.Packed.Static.Imports+import Data.Packed.Static.Internal++instance ShapedContainer Matrix where+    type Unwrapped Matrix = H.Matrix+    unWrap = unMatrix+    wrapU = Matrix++    type UnknownShape Matrix = (Unknown, Unknown)+    unsafeReshape = Matrix . unMatrix++------ Shaping+refineMat :: forall m n t a. Matrix (m,n) t -> (forall m' n'. (PositiveT m', PositiveT n') => Matrix (m', n') t -> a) -> a+refineMat m k = fromJust.fromJust $ reifyPositiveD (toInteger $ rows m) (\r ->+                   reifyPositiveD (toInteger $ cols m) (\c -> +                         k (unsafeReshape m `atShape` (r,c))))++forgetRowsU :: Matrix (m,n) t -> Matrix (Unknown,n) t+forgetRowsU = unsafeReshape++forgetColsU :: Matrix (m,n) t -> Matrix (m,Unknown) t+forgetColsU = unsafeReshape++{- | Fixes a matrix's static row length.+Essentially a mechanism for partial type signatures:+you can specify the row length without specifying the +rest of matrix's type.++@\>ident \`atRows\` d5+[$mat| 1.0, 0.0, 0.0, 0.0, 0.0;+       0.0, 1.0, 0.0, 0.0, 0.0;+       0.0, 0.0, 1.0, 0.0, 0.0;+       0.0, 0.0, 0.0, 1.0, 0.0;+       0.0, 0.0, 0.0, 0.0, 1.0 |]@+-}+atRows :: Matrix (m,n) t -> m -> Matrix (m,n) t+atRows = const++{- | Fixes a matrix's static column length.++@\> ident \`atCols\` d4+[$mat| 1.0, 0.0, 0.0, 0.0;+       0.0, 1.0, 0.0, 0.0;+       0.0, 0.0, 1.0, 0.0;+       0.0, 0.0, 0.0, 1.0 |]@+-}+atCols :: Matrix (m,n) t -> n -> Matrix (m,n) t+atCols = const++withShape :: forall m n t. (PositiveT m, PositiveT n) => (Int -> Int -> Matrix (m,n) t) -> Matrix (m,n) t+withShape f = f m n where+    m = fromIntegerT (undefined :: m)+    n = fromIntegerT (undefined :: n)++withRows :: forall m n t. (PositiveT m) => (Int -> Matrix (m,n) t) -> Matrix (m,n) t+withRows = ($ m) where+    m = fromIntegerT (undefined :: m)++withCols :: forall m n t. (PositiveT n) => (Int -> Matrix (m,n) t) -> Matrix (m,n) t+withCols = ($ n) where+    n = fromIntegerT (undefined :: n)++withSquare :: forall n t. PositiveT n => (Int -> Matrix (n,n) t) -> Matrix (n,n) t+withSquare = ($ n) where+    n = fromIntegerT (undefined :: n)++--------- to/from lists+{- | Constructs a matrix from a list. The size+in the matrix's type and the list's length must agree or+else a runtime error will be raised.++@\> matFromList [1,2,3,4,5,6] \`atShape\` (d2,d3)+[$mat| 1.0, 2.0, 3.0;+       4.0, 5.0, 6.0 |]@+-}+matFromList :: (Element t, PositiveT m, PositiveT n) => [t] -> Matrix (m,n) t+matFromList xs = withShape (\m n -> Matrix $ (m H.>< n) xs)++{- | Constructs a matrix from a list. The size+in the matrix's type and the list's length must agree or+else a runtime error will be raised.++@\> (d2 >< d3)[1,2,3,4,5,6]+[$mat| 1.0, 2.0, 3.0;+       4.0, 5.0, 6.0 |]@+-}+(><) :: (PositiveT m, PositiveT n, Element t) => m -> n -> [t] -> Matrix (m,n) t+(><) m n xs = Matrix $ ((fromIntegerT m) H.>< (fromIntegerT n)) xs++{- | Constructs a matrix from a list of lists of elements.+Each sublist must be of equal size or a runtime error+will be raised.++@\> fromListsU [[1,2,3],[4,5,6]]+[$mat| 1.0, 2.0, 3.0;+       4.0, 5.0, 6.0 |]@+-}+fromListsU :: (Element t) => [[t]] -> Matrix (Unknown,Unknown) t+fromListsU = wrapU . H.fromLists++{- | Converts a matrix to a list of its rows, each as+a list.++@\> toLists [$mat|1,2,3;4,5,6|]+[[1.0,2.0,3.0],[4.0,5.0,6.0]]@+-}+toLists :: (Element t) => Matrix (m,n) t -> [[t]]+toLists = H.toLists . unMatrix++--------- to/from row/column vectors+{- | Interprets a vector as a 1-row matrix. ++@\> asRow [$vec|1,2,3|]+[$mat| 1.0, 2.0, 3.0 |]@+-}+asRow :: (Element a) => Vector n a -> Matrix (D1,n) a+asRow = Matrix . H.asRow . unVector++{- | Interprets a vector as a 1-column matrix.++@\> asColumn [$vec|1,2,3|]+[$mat| 1.0;+       2.0;+       3.0 |]@+-}+asColumn :: (Element a) => Vector n a -> Matrix (n,D1) a+asColumn = Matrix . H.asColumn . unVector++{- | Constructs a matrix from a list of rows.++@\> fromRowsU [[$vec|1,2,3|],[$vec|4,5,6|]]+[$mat| 1.0, 2.0, 3.0;+       4.0, 5.0, 6.0 |]@+-}+fromRowsU :: (Element t) => [Vector n t] -> Matrix (Unknown,n) t+fromRowsU = Matrix . H.fromRows . map unVector++{- | Converts a matrix to a list of its rows.++@\> toRows [$mat|1,2,3;4,5,6|]+[[$vec| 1.0, 2.0, 3.0 |],[$vec| 4.0, 5.0, 6.0 |]]@+-}+toRows :: (Element t) => Matrix (m,n) t -> [Vector n t]+toRows = map Vector . H.toRows . unMatrix++{- | Constructs a matrix from a list of columns.++@\> fromColumnsU [[$vec|1,2,3|],[$vec|4,5,6|]]+[$mat| 1.0, 4.0;+       2.0, 5.0;+       3.0, 6.0 |]@+-}+fromColumnsU :: (Element t) => [Vector n t] -> Matrix (n,Unknown) t+fromColumnsU = Matrix . H.fromColumns . map unVector++{- | Converts a matrix to a list of its columns.++@\> toColumns [$mat|1,2,3;4,5,6|]+[[$vec| 1.0, 4.0 |],[$vec| 2.0, 5.0 |],[$vec| 3.0, 6.0 |]]@+-}+toColumns :: (Element t) => Matrix (m,n) t -> [Vector m t]+toColumns = map Vector . H.toColumns . unMatrix++-------- other operations+{- | Returns the number of rows of the matrix.++@\> rows [$mat|1::Double,2,3;4,5,6|]+2@+-}+rows :: Matrix (m,n) t -> Int+rows = H.rows . unMatrix++{- | Returns the number of columns of the matrix.++@\> cols [$mat|1::Double,2,3;4,5,6|]+3@+-}+cols :: Matrix (m,n) t -> Int+cols = H.cols . unMatrix++{- | Matrix transpose.++@\> trans [$mat|1,2,3;4,5,6|]+[$mat| 1.0, 4.0;+       2.0, 5.0;+       3.0, 6.0 |]@+-}+trans :: Matrix (m,n) t -> Matrix (n,m) t+trans = Matrix . H.trans . unMatrix++--- we can't disappear the Int argument... (it would require type division)+{- | Reshapes a vector into a matrix, +with the specified number of columns. If the vector's length+is not a multiple of the required columns,+a runtime error is raised.++@\> reshapeU 3 [$vecU|1,2,3,4,5,6|]+[$mat| 1.0, 2.0, 3.0;+       4.0, 5.0, 6.0 |]@+-}+reshapeU :: (Element t) => Int -> Vector n t -> Matrix (Unknown,Unknown) t+reshapeU n = wrapU . H.reshape n . unVector++{- | Flattens a matrix into a vector.++@\> flatten [$mat|1,2,3;4,5,6|]+[$vec| 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 |]@+-}+flatten :: (Element t) => Matrix (m,n) t -> Vector (m :*: n) t+flatten = Vector . H.flatten . unMatrix++{- | Indexes a matrix.++@\> [$mat|1,2,3;4,5,6|] \@\@\> (1,2)+6.0@+-}+(@@>) :: (Storable t) => Matrix (m,n) t -> (Int, Int) -> t+(@@>) = (H.@@>) . unMatrix++--- I say the size is (Unknown,Unknown) so the users don't think they all+--- have to be of the same size.+{- | Constructs a matrix from blocks.++@\> fromBlocksU [[[$matU|1,2,3;4,5,6|],  [$matU|7,8,9;10,11,12|]],+               [[$matU|11,12,13;14,15,16|],[$matU|21,22,23;24,25,26|]]]+[$mat|  1.0,  2.0,  3.0,  7.0,  8.0,  9.0;+        4.0,  5.0,  6.0, 10.0, 11.0, 12.0;+       11.0, 12.0, 13.0, 21.0, 22.0, 23.0;+       14.0, 15.0, 16.0, 24.0, 25.0, 26.0 |]@+-}+fromBlocksU :: (Element t) => [[Matrix (Unknown,Unknown) t]] -> Matrix (Unknown,Unknown) t+fromBlocksU = Matrix . H.fromBlocks . map (map unMatrix)++{- | 'replicate' for matrices.++@\> repmatU [$mat|1;2|] 2 3+[$mat| 1.0, 1.0, 1.0;+       2.0, 2.0, 2.0;+       1.0, 1.0, 1.0;+       2.0, 2.0, 2.0 |]@+-}+repmatU :: (Element t) => Matrix (m,n) t -> Int -> Int -> Matrix (Unknown,Unknown) t+repmatU m i j = Matrix $ H.repmat (unMatrix m) i j++{- | Vertically flips a matrix.++@\> flipud [$mat|1,2,3;4,5,6|]+[$mat| 4.0, 5.0, 6.0;+       1.0, 2.0, 3.0 |]@+-}+flipud :: (Element t) => Matrix (m,n) t -> Matrix (m,n) t+flipud = Matrix . H.flipud . unMatrix++{- | Horizonatlly flips a matrix.++@\> fliprl [$mat|1,2,3;4,5,6|]+[$mat| 3.0, 2.0, 1.0;+       6.0, 5.0, 4.0 |]@+-}+fliprl :: (Element t) => Matrix (m,n) t -> Matrix (m,n) t+fliprl = Matrix . H.fliprl . unMatrix++{- | Extracts a submatrix.++@\> subMatrixU (0,1) (2,2) [$mat|1,2,3,4;5,6,7,8;9,10,11,12|]+[$mat| 2.0, 3.0;+       6.0, 7.0 |]@+-}+subMatrixU :: (Element a) => (Int, Int) -> (Int, Int) -> Matrix (m,n) a -> Matrix (Unknown,Unknown) a+subMatrixU a b = Matrix . H.subMatrix a b . unMatrix++{- | Takes rows from the top of the matrix +until the required size is reached.++@\> takeRows [$mat|1,2;3,4;5,6|] \`atRows\` d2+[$mat| 1.0, 2.0;+       3.0, 4.0 |]@+-}+takeRows :: (PositiveT m', Element t, (m' :<=: m) ~ True) => Matrix (m,n) t -> Matrix (m',n) t+takeRows a = withRows (\m -> Matrix $ H.takeRows m $ unMatrix a)++{- | Takes rows from the bottom of the matrix until+the required size is reached.++@\> dropRows [$mat|1,2;3,4;5,6|] \`atRows\` d2+[$mat| 3.0, 4.0;+       5.0, 6.0 |]@+-}+dropRows :: (PositiveT m', Element t, (m' :<=: m) ~ True) => Matrix (m,n) t -> Matrix (m',n) t+dropRows a = withRows (\m -> Matrix $ H.dropRows (rows a - m) $ unMatrix a)++{- | Takes columns from the left of the matrix until+the required size is reached.++@\> takeColumns [$mat|1,2,3;4,5,6|] \`atCols\` d2+[$mat| 1.0, 2.0;+       4.0, 5.0 |]@+-}+takeColumns :: (PositiveT n', Element t, (n' :<=: n) ~ True) => Matrix (m,n) t -> Matrix (m,n') t+takeColumns a = withCols (\n -> Matrix $ H.takeColumns n $ unMatrix a)++{- | Takes columns from the right of the matrix+until the required size is reached.++@\> dropColumns [$mat|1,2,3;4,5,6|] \`atCols\` d2+[$mat| 2.0, 3.0;+       5.0, 6.0 |]@+-}+dropColumns :: (PositiveT n', Element t, (n' :<=: n) ~ True) => Matrix (m,n) t -> Matrix (m,n') t+dropColumns a = withCols (\n -> Matrix $ H.dropColumns (cols a - n) $ unMatrix a)++{- | Extracts the given rows from a matrix.++@\> extractRowsU [1,0] [$mat|1,2;3,4;5,6|]+[$mat| 3.0, 4.0;+       1.0, 2.0 |]@+-}+extractRowsU :: (Element t) => [Int] -> Matrix (m,n) t -> Matrix (Unknown,n) t+extractRowsU is = Matrix . H.extractRows is . unMatrix++{- | Constructs the identity matrix of any given size.++@\> ident \`atRows\` d3+[$mat| 1.0, 0.0, 0.0;+       0.0, 1.0, 0.0;+       0.0, 0.0, 1.0 |]@+-}+ident :: (Element t, PositiveT n) => Matrix (n,n) t+ident = withSquare (Matrix . H.ident)++{- | Constructs a square matrix with the given vector as its diagonal.++@\> diag (linspace (1,3)) \`atRows\` d3+[$mat| 1.0, 0.0, 0.0;+       0.0, 2.0, 0.0;+       0.0, 0.0, 3.0 |]@+-}+diag :: (Element a) => Vector n a -> Matrix (n,n) a+diag = Matrix . H.diag . unVector++{- | Constructs a rectangular matrix with the given vector as its diagonal.++@\> diagRect (linspace (1,3)) \`atShape\` (d3,d4)+[$mat| 1.0, 0.0, 0.0, 0.0;+       0.0, 2.0, 0.0, 0.0;+       0.0, 0.0, 3.0, 0.0 |]++\> diagRect (linspace (1,3)) \`atShape\` (d4,d3)+[$mat| 1.0, 0.0, 0.0;+       0.0, 2.0, 0.0;+       0.0, 0.0, 3.0;+       0.0, 0.0, 0.0 |]@+-}+diagRect :: (Element a, PositiveT m, PositiveT n) => Vector (Min m n) a -> Matrix (m,n) a+diagRect v = withShape (\m n -> Matrix $ H.diagRect (unVector v) m n)++{- | Takes the diagonal from a matrix.++@\> takeDiag [$mat|1,2,3;4,5,6|]+[$vec| 1.0, 5.0 |]@+-}+takeDiag :: (Element t) => Matrix (m,n) t -> Vector (Min m n) t+takeDiag = Vector . H.takeDiag . unMatrix++{- | Operations on matrices viewed as operations on the vector of their elements ++@\> liftMatrix (+constant 2) [$mat|1,2,3;4,5,6|]+[$mat| 3.0, 4.0, 5.0;+       6.0, 7.0, 8.0 |]@+-}+liftMatrix :: (Element a, Element b) => (Vector (m :*: n) a -> Vector (m :*: n) b) -> Matrix (m,n) a -> Matrix (m,n) b+liftMatrix f = Matrix . H.liftMatrix (unVector . f . Vector) . unMatrix++liftMatrix2 :: (Element t, Element a, Element b) =>+               (Vector (m:*:n) a -> Vector (m:*:n) b -> Vector (m:*:n) t)+               -> Matrix (m,n) a+               -> Matrix (m,n) b+               -> Matrix (m,n) t+liftMatrix2 f a b = Matrix $ H.liftMatrix2 (\v w -> unVector $ f (Vector v) (Vector w)) (unMatrix a) (unMatrix b)++-- | See hmatrix's 'H.format'.+format :: (Element t) => String -> (t -> String) -> Matrix (m,n) t -> String+format s f = H.format s f . unMatrix++-- | See hmatrix's 'H.readMatrix'.+readMatrix :: String -> Matrix (Unknown,Unknown) Double+readMatrix = wrapU . H.readMatrix++-- | See hmatrix's 'H.fromFile'.+fromFile :: FilePath -> (Int, Int) -> IO (Matrix (Unknown,Unknown) Double)+fromFile f s = fmap wrapU $ H.fromFile f s++-- | See hmatrix's 'H.fromArray2D'.+fromArray2D :: (Element t) => Array (Int, Int) t -> Matrix (Unknown,Unknown) t+fromArray2D = wrapU . H.fromArray2D++++instance (Element e, Show e) => Show (Matrix (m,n) e) where+    show m = "[$mat| " ++ format2 ", " ";\n       " m ++ " |]"++-- internal helpers++pad n str = replicate (n - length str) ' ' ++ str++padLen :: [String] -> [String]+padLen as = map (pad len) as where+    len = maximum $ map length as++padLens :: [[String]] -> [[String]]+padLens = transpose . map padLen . transpose where++format2 comma semi mat = intercalate semi . map (intercalate comma) $ padLens . map (map show) $ toLists mat

@@ -0,0 +1,119 @@+-----------------------------------------------------------------------------+-- |+-- Module      :  Data.Packed.Static.ST+-- Copyright   :  (c) Reiner Pope 2008+-- License     :  GPL-style+--+-- Maintainer  :  Reiner Pope <reiner.pope@gmail.com>+-- Stability   :  experimental+-- Portability :  portable+--+-- Manipulation of Matrix and Vector in the ST monad.+--+-----------------------------------------------------------------------------++module Data.Packed.Static.ST where++import qualified Data.Packed.ST as HS+import qualified Numeric.LinearAlgebra as H++import Data.Packed.Static.Internal+import Data.Packed.Static.Imports++import Control.Monad.ST+++----- vectors+newtype STVector n s t = STVector { unSTVector :: HS.STVector s t }++newVector :: forall n s t. (Element t, PositiveT n) => t -> ST s (STVector n s t) +newVector a = fmap STVector (HS.newVector a n) where+    n = fromIntegerT (undefined :: n)++thawVector :: (Storable t) => Vector n t -> ST s (STVector n s t)+thawVector = fmap STVector . HS.thawVector . unVector++freezeVector :: (Storable t) => STVector n s1 t -> ST s2 (Vector n t)+freezeVector = fmap Vector . HS.freezeVector . unSTVector++runSTVector :: (Storable t) => (forall s. ST s (STVector n s t)) -> Vector n t+runSTVector = (Vector) . HS.runSTVector . (\v -> fmap unSTVector v) where++readVector :: (Storable t) => STVector n s t -> Int -> ST s t+readVector = HS.readVector . unSTVector++writeVector :: (Storable t) => STVector n s t -> Int -> t -> ST s ()+writeVector = HS.writeVector . unSTVector++modifyVector :: (Storable t) => STVector n s t -> Int -> (t -> t) -> ST s ()+modifyVector = HS.modifyVector . unSTVector++liftSTVector :: (Storable t) => (Vector n t -> c) -> STVector n s1 t -> ST s2 c+liftSTVector f v = HS.liftSTVector (f . Vector) (unSTVector v)++----- matrices+-- | A matrix with @m@ rows, @n@ columns.+newtype STMatrix mn s t = STMatrix { unSTMatrix :: HS.STMatrix s t }++newMatrix :: forall m n s t. (Element t, PositiveT m, PositiveT n) => t -> ST s (STMatrix (m, n) s t)+newMatrix t = fmap STMatrix $ HS.newMatrix t m n where+    m = fromIntegerT (undefined :: m)+    n = fromIntegerT (undefined :: n)++thawMatrix :: (Storable t) => Matrix (m, n) t -> ST s (STMatrix (m, n) s t)+thawMatrix = fmap STMatrix . HS.thawMatrix . unMatrix++freezeMatrix :: (Storable t) => STMatrix (m, n) s1 t -> ST s2 (Matrix (m, n) t)+freezeMatrix = fmap (Matrix) . HS.freezeMatrix . unSTMatrix++runSTMatrix :: (Storable t) => (forall s. ST s (STMatrix (m, n) s t)) -> Matrix (m, n) t+runSTMatrix = (Matrix) . HS.runSTMatrix . (\m -> fmap unSTMatrix m)++readMatrix :: (Storable t) => STMatrix (m, n) s t -> Int -> Int -> ST s t+readMatrix = HS.readMatrix . unSTMatrix++writeMatrix :: (Storable t) => STMatrix (m, n) s t -> Int -> Int -> t -> ST s ()+writeMatrix = HS.writeMatrix . unSTMatrix++modifyMatrix :: (Storable t) => STMatrix (m, n) s t -> Int -> Int -> (t -> t) -> ST s ()+modifyMatrix = HS.modifyMatrix . unSTMatrix++liftSTMatrix :: (Storable t) => (Matrix (m, n) t -> a) -> STMatrix (m, n) s1 t -> ST s2 a+liftSTMatrix f m = HS.liftSTMatrix (f . Matrix) (unSTMatrix m)++--------- unsafe+unsafeReadVector :: (Storable t) => STVector n s t -> Int -> ST s t+unsafeReadVector = HS.unsafeReadVector . unSTVector+unsafeWriteVector :: (Storable t) => STVector n s t -> Int -> t -> ST s ()+unsafeWriteVector = HS.unsafeWriteVector . unSTVector++unsafeThawVector :: (Storable t) => Vector n t -> ST s (STVector n s t)+unsafeThawVector = fmap STVector . HS.unsafeThawVector . unVector+unsafeFreezeVector :: (Storable t) => STVector n s1 t -> ST s2 (Vector n t)+unsafeFreezeVector =  fmap Vector . HS.unsafeFreezeVector . unSTVector++unsafeReadMatrix :: (Storable t) => STMatrix (m, n) s t -> Int -> Int -> ST s t+unsafeReadMatrix = HS.unsafeReadMatrix . unSTMatrix+unsafeWriteMatrix :: (Storable t) => STMatrix (m, n) s t -> Int -> Int -> t -> ST s ()+unsafeWriteMatrix = HS.unsafeWriteMatrix . unSTMatrix++unsafeThawMatrix :: (Storable t) => Matrix (m, n) t -> ST s (STMatrix (m, n) s t)+unsafeThawMatrix = fmap STMatrix . HS.unsafeThawMatrix . unMatrix+unsafeFreeMatrix :: (Storable t) => STMatrix (m, n) s1 t -> ST s2 (Matrix (m, n) t)+unsafeFreeMatrix = fmap (Matrix) . HS.unsafeFreezeMatrix . unSTMatrix+++{-+--- for a later refactoring:+class STMutable a where+    data STRep a :: * -> * -> * -> *+    unsafeThaw :: Storable t => a n t -> ST s (STRep a s n t)+    unsafeFreeze :: Storable t => STRep a s n t -> ST s (a n t)+    clone :: Storable t => STRep a s n t -> ST s (STRep a s n t)++instance STMutable Vector where+    newtype STRep Vector s n t = STVector { unSTVector :: HS.STVector s t }+    unsafeThaw = fmap STVector . HS.unsafeThawVector . unVector+    unsafeFreeze = fmap Vector . HS.unsafeFreezeVector . unSTVector+    clone = undefined -- no "clone" function is available in hmatrix right now...+-}

@@ -0,0 +1,142 @@+-----------------------------------------------------------------------------+-- |+-- Module      :  Data.Packed.Static.Shapes+-- Copyright   :  (c) Reiner Pope 2008+-- License     :  GPL-style+--+-- Maintainer  :  Reiner Pope <reiner.pope@gmail.com>+-- Stability   :  experimental+-- Portability :  portable+--+-- Shape-based functionality, common for matrices and vectors+--+-----------------------------------------------------------------------------++{-# LANGUAGE UndecidableInstances #-}++module Data.Packed.Static.Shapes (+     Unknown,+     ShapedContainer(..),+     atShape,+     shapeOf,+     forgetShapeU,+     unsafeWrap,+ ) where++import qualified Numeric.LinearAlgebra as H++-- | Uninhabited type. Represents unknown lengths.+-- Instances of 'ShapedContainer' use 'Unknown'+-- for the 'UnknownShape' type.+data Unknown++class ShapedContainer a where+    -- | Less-typed, hmatrix representation+    type Unwrapped a :: * -> *+    -- | Convert to hmatrix representation+    unWrap :: a s t -> Unwrapped a t+    -- | Convert from hmatrix representation+    wrapU :: Unwrapped a t -> a (UnknownShape a) t+    +    -- | standard \'unknown\' shape. For vectors, @Unknown@; for matrices, @(Unknown,Unknown)@.+    type UnknownShape a+    -- | Coerce the static shape. Unsafe; the user+    -- of this function has an obligation to prove that+    -- the object's dynamic shape is the same as that+    -- represented by s'.+    unsafeReshape :: a s t -> a s' t++-- | For type hints.+-- +-- @\> constant (5::Double) `atShape` d4+-- [$vec| 5.0, 5.0, 5.0, 5.0 |] :: Vector D4 Double@+--+-- Implementation:+-- +-- @atShape = const@.+atShape :: a s t -> s -> a s t+atShape = const++-- | For type hints.+--+-- @\> constant (5::Double) `atShape` shapeOf [$vec|1|]+-- [$vec| 5.0 |]@+--+-- Implementation:+--+-- @shapeOf _ = undefined@+shapeOf :: a s t -> s+shapeOf _ = undefined++-- | @unsafeWrap = unsafeReshape . wrapU@.+unsafeWrap :: ShapedContainer a => Unwrapped a t -> a s t+unsafeWrap = unsafeReshape . wrapU++-- | Changes the static shape to the UnknownShape.+-- Dynamic representation is unchanged.+forgetShapeU :: ShapedContainer a => a s t -> a (UnknownShape a) t+forgetShapeU = unsafeReshape++------- instances++liftH f = unsafeWrap . f . unWrap+liftH2 f a b = unsafeWrap $ f (unWrap a) (unWrap b)+liftH2' f a b = f (unWrap a) (unWrap b)++instance (ShapedContainer a, H.Container (Unwrapped a) e) => H.Container (a n) e where+    toComplex = uncurry $ liftH2 $ curry H.toComplex+    fromComplex m = let (a,b) = H.fromComplex $ unWrap m in (unsafeWrap a, unsafeWrap b)+    comp = liftH H.comp+    conj = liftH H.conj+    real = liftH H.real+    complex = liftH H.complex++instance (ShapedContainer a, H.Linear (Unwrapped a) e) => H.Linear (a n) e where+    scale e       = liftH (H.scale e)+    addConstant e = liftH (H.addConstant e)+    add           = liftH2 H.add+    sub           = liftH2 H.sub+    mul           = liftH2 H.mul+    divide        = liftH2 H.divide+    scaleRecip e  = liftH (H.scaleRecip e)+    equal         = liftH2' H.equal++instance (ShapedContainer a, Eq (Unwrapped a t)) => Eq (a s t) where+    (==) = liftH2' (==)++instance (ShapedContainer a, Show (a n e), Num (Unwrapped a e)) => Num (a n e) where+    (+) = liftH2 (+)+    (*) = liftH2 (*)+    (-) = liftH2 (-)+    negate = liftH negate+    abs = liftH abs+    signum = liftH signum+    fromInteger = error "fromInteger: Data.Packed.Static.Common"++instance (ShapedContainer a, Show (a n e), Fractional (Unwrapped a e)) => Fractional (a n e) where+    (/) = liftH2 (/)+    recip = liftH recip+    fromRational = error "fromRational: Data.Packed.Static.Common"++instance (ShapedContainer a, Show (a n e), Floating (Unwrapped a e)) => Floating (a n e) where+    pi      = error "pi: Data.Packed.Static.Common"+    exp     = liftH exp+    sqrt    = liftH sqrt+    log     = liftH log+    (**)    = liftH2 (**)+    logBase = liftH2 logBase+    sin     = liftH sin+    tan     = liftH tan+    cos     = liftH cos+    asin    = liftH asin+    atan    = liftH atan+    acos    = liftH acos+    sinh    = liftH sinh+    tanh    = liftH tanh+    cosh    = liftH cosh+    asinh   = liftH asinh+    atanh   = liftH atanh+    acosh   = liftH acosh++instance (ShapedContainer a, H.Normed (Unwrapped a e)) => H.Normed (a n e) where+    pnorm p = H.pnorm p . unWrap

@@ -0,0 +1,223 @@+-----------------------------------------------------------------------------+-- |+-- Module      :  Data.Packed.Static.Syntax+-- Copyright   :  (c) Reiner Pope 2008+-- License     :  GPL-style+--+-- Maintainer  :  Reiner Pope <reiner.pope@gmail.com>+-- Stability   :  experimental+-- Portability :  portable+--+-- QuasiQuoting for matrices and vectors.+--+-- BIG WARNING: the expression quasiquoters for matrices and vectors+-- are broken for infix expressions. All operators will be assumed to+-- be left infix with infix level 9. To avoid unexpected parses, fully+-- parenthesise all infix expressions.+-----------------------------------------------------------------------------++module Data.Packed.Static.Syntax(+    mat,+    matU,+    vec,+    vecU,+    -- * Matrix views+    MatView,+    viewMat,+    -- * Vector views+    VecView,+    viewVec,+ ) where++import Data.Complex++import Control.Monad++import Language.Haskell.TH+import Language.Haskell.TH.Quote++import Types.Data.Num.Decimal.Literals.TH+import Data.Packed.Static.Imports+import Data.Packed.Static.Shapes+import Data.Packed.Static.Vector+import Data.Packed.Static.Matrix++import Text.Parsec+import Text.Parsec.Language+import Text.Parsec.String(Parser)+import qualified Text.Parsec.Token as T+++import Foreign.Storable++import qualified Language.Haskell.Meta.Parse as MP+++----- mat parser+-- | Required for the 'mat' pattern quasiquoter. See 'mat'.+data MatView n t = n :>< [[t]]+-- | Required for the 'mat' pattern quasiquoter. See 'mat'.+viewMat :: Element t => Matrix (m, n) t -> MatView (m, n) t+viewMat m = shapeOf m :>< toLists m++-- | The matrix quasiquoter for expressions and patterns. +-- +-- * Elements on the same row are separated by commas; rows +--   themselves are separated by semicolons. All whitespace is optional+-- +-- * The expression quasiquoter allows arbitrary Haskell +--   expressions as its elements; the pattern quasiquoter+--   requires that each element is a variable.+-- +-- * Using the quasiquoter for patterns requires that you+--   use the 'viewMat' view pattern first (this is a+--    workaround since Template Haskell doesn't yet support+--    view patterns).+-- +-- For example,+-- +-- @ example1 :: (Element t) => Matrix (D2,D3) t -> Matrix (D2,D2) t+-- example1 (viewMat -> [$mat|a, b, c;+--                            d, e, f|]) = [$mat|a+b,   b+c;+--                                               sin c, f  |]@+mat :: QuasiQuoter+mat = QuasiQuoter parseMatExp parseMatPat++{- | Quasiquoter for matrices of Unknown size. We should+just use @[$matU|\<text\>|]@ as shorthand for @'forgetShapeU' [$mat|\<text\>|]@.++No pattern quasiquoter exists, and I currently have+no plans to introduce one. -}+matU :: QuasiQuoter+matU = QuasiQuoter parseMatUExp (error "No pattern quasiquoter for matU. Use mat instead")++parseMat p s = do+  xs <- parsecToQ (sepBy (sepBy p comma) semi) s+  let rows = length xs+      cols = length $ head xs+  when (not $ all ((==cols) . length) xs) $ fail "Inconsistent row lengths in [$mat|...|]"+  return (xs,rows,cols)++parseMatExp s = do+  (xs,rows,cols) <- parseMat expr s+  [| ( $(decLiteralV $ fromIntegral rows) >< $(decLiteralV $ fromIntegral cols) )+                $(return $ ListE (concat xs)) |]++parseMatUExp s = do+  (xs,rows,cols) <- parseMat expr s+  [| fromListsU $(return $ ListE (map ListE xs)) |]++parseMatPat s = do+  (xs,rows,cols) <- parseMat identifier s+  conP '(:><) [ sigP wildP (tupleT 2 `appT` (decLiteralT $ fromIntegral rows) `appT` (decLiteralT $ fromIntegral cols))+              , listP (map (listP . map (varP . mkName)) xs) ]++------- vec parser+-- | Required for the 'vec' quasiquoter. See 'vec'.+data VecView n t = n :|> [t]++-- | Required for the 'vec' quasiquoter. See 'vec'.+viewVec :: (Storable t) => Vector n t -> VecView n t+viewVec v = shapeOf v :|> toList v++-- | The vector quasiquoter for expressions and patterns. This is+-- very similar to the 'mat' quasiquoter.+-- +--  * Elements are separated by commas; whitespace is ignored.+-- +--  * The expression quasiquoter allows arbitrary Haskell expressions for+--    each element; the pattern quasiquoter requires that each element is+--    a variable pattern.+-- +--  * The pattern quasiquoter must be preceeded by a the 'viewVec' view pattern.+-- +-- For example,+-- +-- @ example2 :: (Storable t, Num t) => Vector D2 t -> Vector D3 t+-- example2 (viewVec -> [$vec|a, b|]) = [$vec|a*b, 5, 7|]@+vec :: QuasiQuoter+vec = QuasiQuoter parseVecExp parseVecPat++{- | Quasiquoter for vectors of unknown lengths. Like 'matU', +@[$vecU|\<text\>|]@ is just shorthand for @'forgetShapeU' [$vec|\<text\>|]@. -}+vecU :: QuasiQuoter+vecU = QuasiQuoter parseVecUExp (error "No pattern quasiquoter for vecU. Use the vec quasiquoter instead")++--- Vec pattern parser+parseVec p s = parsecToQ (sepBy p comma) s++parseVecPat s = do+  xs <- parseVec identifier s+  conP '(:|>) [ sigP wildP (decLiteralT $ fromIntegral $ length xs)+                         , return $ ListP (map (VarP . mkName) xs)  ]++parseVecUExp s = [| fromListU $(ListE `liftM` parseVec expr s) |]++parseVecExp s = do+  xs <- parseVec expr s+  [| unsafeReshape (fromListU $(return $ ListE xs)) `atShape` $(decLiteralV (fromIntegral $ length xs)) |]+++----- Haskell parsing+-- | Does a simplistic parse using Parsec, which just counts brackets and escapes comments and string literals.+-- This parse accumulates text, which is then parsed properly using haskell-src-exts.+expr = do+  s <- outerCode+  case MP.parseExp s of+    Left err -> fail err+    Right exp -> return exp++infixr >>++p1 >>+ p2 = do+  x1 <- p1+  x2 <- p2+  return (x1 ++ x2)++p >/> q = do+  p' <- p+  notFollowedBy q+  return p'++codeChar = noneOf "{}()[]-,;\"\'" <|> (try (char '-' >/> char '-'))+innerCodeChar = codeChar <|> char ','++outerCode = fmap concat $ many (fmap return codeChar <|> codeChoices)+innerCode = fmap concat $ many (fmap return innerCodeChar <|> codeChoices)++codeChoices = (nestedCommentCode <|> singleLineCommentCode <|>+                  stringLit <|> charLit <|> bracesCode <|> parensCode <|> bracketsCode)++bracesCode = string "{" >>+ innerCode >>+ string "}"+parensCode = string "(" >>+ innerCode >>+ string ")"+bracketsCode = string "[" >>+ innerCode >>+ string "]"+nestedCommentCode = try (string "{-") >>+ insideNestedCode >>+ string "-}"+insideNestedCode = fmap concat $ many (nestedCommentCode <|> fmap return (noneOf "-") <|> try (string "-" >/> char '}'))+singleLineCommentCode = (try $ string "--") >>+ manyTill anyChar newline+stringLit = fmap show $ stringLiteral +charLit = fmap show $ charLiteral++identifier = T.identifier haskell+comma = T.comma haskell <?> "comma"+stringLiteral = T.stringLiteral haskell+charLiteral = T.charLiteral haskell+semi = T.semi haskell <?> "semicolon"++---- to be later moved to another library+parsecToQ :: Parser a -> String -> Q a+parsecToQ p s = do+    loc <- location+    let file       = loc_filename loc+        (line,col) = loc_start loc+        p' = do  pos <- getPosition+                 setPosition $+                      (flip setSourceName) file $+                      (flip setSourceLine) line $+                      (flip setSourceColumn) col $  pos+                 v <- p+                 eof+                 return v+    e <- case runParser p' () "" s of+      Left err -> fail $ show err+      Right e  -> return e+    return e+

@@ -0,0 +1,209 @@+-----------------------------------------------------------------------------+-- |+-- Module      :  Data.Packed.Static.Vector+-- Copyright   :  (c) Reiner Pope 2008+-- License     :  GPL-style+--+-- Maintainer  :  Reiner Pope <reiner.pope@gmail.com>+-- Stability   :  experimental+-- Portability :  portable+--+-- Statically-dimensioned 1D vectors.+--+-----------------------------------------------------------------------------++module Data.Packed.Static.Vector(+   Vector,+   -- * Shaping+   -- | Functions manipulating a vector's (static) shape.+   refineVec,+   atDim,+   atShape,+   -- * To/from lists+   fromListU,+   toList,+   -- * Manipulation+   dim,+   (@>),+   subVectorU,+   joinU,+   constant,+   linspace,+   vectorMin,+   vectorMax,+   vectorMinIndex,+   vectorMaxIndex,+   liftVector,+   liftVector2,+ ) where++import Data.Maybe(fromJust)+import Data.List(intercalate)++import qualified Numeric.LinearAlgebra as H++import Data.Packed.Static.Shapes+import Data.Packed.Static.Imports+import Data.Packed.Static.Internal++instance ShapedContainer Vector where+    type Unwrapped Vector = H.Vector+    unWrap = unVector+    wrapU = Vector+                   +    type UnknownShape Vector = Unknown+    unsafeReshape = Vector . unVector++------ Shaping+-- | \"Reifies\" a Vector's length in types. Useful when vectors of length "Unknown"+-- need to be used for a statically-sized operations. For instance, if @v :: Vector Unknown Double@, +-- then we can write+-- +--    @refineVec v (\v -> forgetSize $ v + constant 5)@+-- +-- to add a constant vector of 5s with the appropriate size.+refineVec :: forall m t a. Vector m t -> (forall n. PositiveT n => Vector n t -> a) -> a+refineVec v k = fromJust $ reifyPositiveD (toInteger $ dim v) (\n -> k (unsafeReshape v `atShape` n))++withDim :: forall n a. PositiveT n => (Int -> Vector n a) -> Vector n a+withDim f = f n where+    n = fromIntegerT (undefined :: n)++{- | Sets an arbitrary-length vector to a specific value.++@\> constant 1 `atDim` 5+[$vec| 1.0, 1.0, 1.0, 1.0, 1.0 |]@+-}+atDim :: (forall n. PositiveT n => Vector n t) -> Int -> Vector Unknown t+atDim v n | n > 0     = fromJust $ reifyPositiveD (toInteger n) (\n -> forgetShapeU $ v `atShape` n)+          | otherwise = error $ "atDim: negative vector length: " ++ show n++-------- To / from lists+{- | Constructs a vector from all the elements of a list.++@\> fromListU [1,2,3,4,5]+[$vec| 1.0, 2.0, 3.0, 4.0, 5.0 |]@+-}+fromListU :: (Storable a) => [a] -> Vector Unknown a+fromListU = Vector . H.fromList++{- | Converts to a list of elements.++@\> toList [$vec|1,2,3|]+[1.0,2.0,3.0]@+-}+toList :: (Storable a) => Vector n a -> [a]+toList = H.toList . unVector++------ Other operations+{- | Vector's length.++@\> dim [$vec|1::Double,2,3|]+3@+-}+dim :: Vector n t -> Int+dim = H.dim . unVector++{- | Indexes a vector.++@\> [$vec|1,2,3|] \@\> 1+2.0@+-}+(@>) :: (Storable t) => Vector n t -> Int -> t+(@>) = (H.@>) . unVector++{- | Extracts a subvector.++@\> subVectorU 2 3 [$vec|1,2,3,4,5|]+[$vec| 3.0, 4.0, 5.0 |]@+-}+subVectorU :: (Storable t) => +              Int -- ^ Initial index+           -> Int -- ^ Length of resultant vector+           -> Vector n t+           -> Vector Unknown t+subVectorU a b = Vector . H.subVector a b . unVector++--- I say the input Size is unknown, although it can be anything,+--- so users don't think all the vectors must be of the same size.++{- | Joins each vector in the list.++@\> joinU [[$vecU|1,2,3|], [$vecU|4,5|]]+[$vec| 1.0, 2.0, 3.0, 4.0, 5.0 |]@+-}+joinU :: (Storable t) => [Vector Unknown t] -> Vector Unknown t+joinU = Vector . H.join . map unVector++{- | Creates a constant vector of any length. The length is+determined by the type.++@\> [$vec|1,2,3|] + constant 2+[$vec| 3.0, 4.0, 5.0 |]@+-}+constant :: (Element t, PositiveT n) => t -> Vector n t+constant a = withDim (Vector . H.constant a)++{- | Creates a vector of arbitrary length whose+components range linearly from a to b. The vector's+length is determined by its type.++@\> linspace (1,5) `atShape` d4+[$vec| 1.0, 2.333333333333333, 3.6666666666666665, 5.0 |]@+-}+linspace :: (PositiveT n) => (Double,Double) -> Vector n Double+linspace r = withDim (\n -> Vector $ H.linspace n r) where++{- | Gives the vector's minimum entry.++@\> vectorMin [$vec|1,2,3|]+1.0@+-}+vectorMin :: Vector n Double -> Double+vectorMin = H.vectorMin . unVector++{- | Gives the vector's maximum entry.++@\> vectorMax [$vec|1,2,3|]+3.0@+-}+vectorMax :: Vector n Double -> Double+vectorMax = H.vectorMax . unVector++{- | Gives the index of a vector's minimum entry.+@\> vectorMinIndex [$vec|1,2,3|]+0@+-}+vectorMinIndex :: Vector n Double -> Int+vectorMinIndex = H.vectorMinIndex . unVector++{- | Gives the index of a vector's maximum entry. ++@\> vectorMaxIndex [$vec|1,2,3|]+2@+-}+vectorMaxIndex :: Vector n Double -> Int+vectorMaxIndex = H.vectorMaxIndex . unVector++{- | 'map' for vectors.++@\> (*2) `liftVector` [$vec|1,2,3|]+[$vec| 2.0, 4.0, 6.0 |]@+-}+liftVector :: (Storable a, Storable b) => (a -> b) -> Vector n a -> Vector n b+liftVector f = Vector . H.liftVector f . unVector++--- note: this requires they are of the same size, whereas hmatrix allows+--- different sizes; it uses the minimum size.+{- | 'zipWith' for vectors. ++@\> liftVector2 (+) [$vec|1,2,3|] (constant 3)+[$vec| 4.0, 5.0, 6.0 |]@+-}+liftVector2 :: (Storable a, Storable b, Storable c) =>+               (a -> b -> c) -> Vector n a -> Vector n b -> Vector n c+liftVector2 f v1 v2 = Vector $ H.liftVector2 f (unVector v1) (unVector v2)++instance (Storable e, Show e) => Show (Vector n e) where+    show v = "[$vec| " ++ intercalate ", " (map show $ toList v) ++ " |]"+

@@ -0,0 +1,674 @@+                    GNU GENERAL PUBLIC LICENSE+                       Version 3, 29 June 2007++ Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>+ Everyone is permitted to copy and distribute verbatim copies+ of this license document, but changing it is not allowed.++                            Preamble++  The GNU General Public License is a free, copyleft license for+software and other kinds of works.++  The licenses for most software and other practical works are designed+to take away your freedom to share and change the works.  By contrast,+the GNU General Public License is intended to guarantee your freedom to+share and change all versions of a program--to make sure it remains free+software for all its users.  We, the Free Software Foundation, use the+GNU General Public License for most of our software; it applies also to+any other work released this way by its authors.  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Of course, your program's commands+might be different; for a GUI interface, you would use an "about box".++  You should also get your employer (if you work as a programmer) or school,+if any, to sign a "copyright disclaimer" for the program, if necessary.+For more information on this, and how to apply and follow the GNU GPL, see+<http://www.gnu.org/licenses/>.++  The GNU General Public License does not permit incorporating your program+into proprietary programs.  If your program is a subroutine library, you+may consider it more useful to permit linking proprietary applications with+the library.  If this is what you want to do, use the GNU Lesser General+Public License instead of this License.  But first, please read+<http://www.gnu.org/philosophy/why-not-lgpl.html>.

@@ -0,0 +1,21 @@+-----------------------------------------------------------------------------+-- |+-- Module      :  Numeric.LinearAlgebra.Static+-- Copyright   :  (c) Reiner Pope 2008+-- License     :  GPL-style+--+-- Maintainer  :  Reiner Pope <reiner.pope@gmail.com>+-- Stability   :  experimental+-- Portability :  portable+--+-- Main imported interface for this package.+--+-----------------------------------------------------------------------------++module Numeric.LinearAlgebra.Static(+  module Numeric.LinearAlgebra.Static.Algorithms,+  module Data.Packed.Static,+ ) where++import Numeric.LinearAlgebra.Static.Algorithms+import Data.Packed.Static

@@ -0,0 +1,315 @@+-----------------------------------------------------------------------------+-- |+-- Module      :  Numeric.LinearAlgebra.Static.Algorithms+-- Copyright   :  (c) Reiner Pope 2008+-- License     :  GPL-style+--+-- Maintainer  :  Reiner Pope <reiner.pope@gmail.com>+-- Stability   :  experimental+-- Portability :  portable+--+-- Common operations.+--+-----------------------------------------------------------------------------++module Numeric.LinearAlgebra.Static.Algorithms(+    -- * Type hints+    matT,+    vecT,+    doubleT,+    complexT,+    -- * Multiplication                                           +    Mul(..),+    (<.>),+    -- * Concatenating+    (<->),+    (<|>),+    -- * Solving \/ inverting+    (<\>),+    linearSolve,+    inv,+    pinv,+    -- * Determinant \/ rank \/ condition number+    det,+    rank,+    rcond,+    -- * Eigensystems+    eig,+    eigSH,++    -- * Factorisations+    -- ** SVD+    svd,+    fullSVD,+    economySVDU,+    -- ** QR+    qr,+    -- ** Cholesky+    chol,+    -- ** Hessenberg+    hess,+    -- ** Schur+    schur,+    -- ** LU+    lu,+    luPacked,+    luSolve,++    -- * Matrix functions+    expm,+    sqrtm,+    matFunc,+    +    -- * Nullspace+    nullspacePrec,+    nullVector,++    -- * Norms+    pnorm,+    H.NormType(..),++    -- * Misc+    ctrans,+    eps,+    i,+    outer,+    kronecker,+ ) where++import Data.Complex++import Types.Data.Num+import Types.Data.Ord+import Types.Data.Bool++import Data.Packed.Static+import Data.Packed.Static.Internal++import qualified Numeric.LinearAlgebra as H+import           Numeric.LinearAlgebra(pnorm)++matT :: Matrix s t -> a+matT = const undefined++vecT :: Vector s t -> a+vecT = const undefined++doubleT :: a s Double -> x+doubleT = const undefined++complexT :: a s (Complex Double) -> x+complexT = const undefined++class Mul a b where+    -- | Overloaded matrix-matrix, matrix-vector, or vector-matrix product.+    --   The instances have type equalities to improve the quality of+    --   type inference.+    (<>) :: Field t => a t -> b t -> MulResult a b t+    type MulResult a b :: * -> *++instance (n ~ n') => Mul (Matrix (m,n)) (Matrix (n',p)) where+    a <> b = Matrix $ H.multiply (unMatrix a) (unMatrix b)+    type MulResult (Matrix (m,n)) (Matrix (n',p)) = Matrix (m,p)++instance (n ~ n') => Mul (Matrix (m,n)) (Vector n') where+    m <> v = Vector (unMatrix m H.<> unVector v)+    type MulResult (Matrix (m,n)) (Vector n') = Vector m++instance (m ~ m') => Mul (Vector m) (Matrix (m',n)) where+    v <> m = Vector (unVector v H.<> unMatrix m)+    type MulResult (Vector m) (Matrix (m',n)) = Vector n++-- | Dot product+(<.>) :: (Field t) => Vector n t -> Vector n t -> t+a <.> b = H.dot (unVector a) (unVector b)++class JoinableV a b where+    type JoinShapeV a b :: *+    -- | Overloaded matrix-matrix, matrix-vector, vector-matrix, or vector-vector+    --   vertical concatenation. The instances have type equalities+    --   to improve the quality of type inference.+    (<->) :: Element t => a t -> b t -> Matrix (JoinShapeV a b) t++instance JoinableV (Matrix (m,n)) (Matrix (p,n)) where+    type JoinShapeV (Matrix (m,n)) (Matrix (p,n)) = (m :+: p, n)+    m <-> n = Matrix (unMatrix m H.<-> unMatrix n)++instance JoinableV (Matrix (m,n)) (Vector n) where+    type JoinShapeV (Matrix (m,n)) (Vector n) = (m :+: D1, n)+    m <-> v = m <-> asRow v++instance JoinableV (Vector n) (Matrix (m,n)) where+    type JoinShapeV (Vector n) (Matrix (m,n)) = (D1 :+: m, n)+    v <-> m = asRow v <-> m++instance JoinableV (Vector n) (Vector n) where+    type JoinShapeV (Vector n) (Vector n) = (D2, n)+    v <-> w = asRow v <-> w++class JoinableH a b where+    type JoinShapeH a b :: *+    -- | Overloaded matrix-matrix, matrix-vector, vector-matrix,+    --   or vector-vector horizontal concatenation. The+    --   instances have type equalities to+    --   improve the quality of type inference.+    (<|>) :: Element t => a t -> b t -> Matrix (JoinShapeH a b) t++instance JoinableH (Matrix (m,n)) (Matrix (m,p)) where+    type JoinShapeH (Matrix (m,n)) (Matrix (m,p)) = (m,n:+:p)+    m <|> n = Matrix (unMatrix m H.<|> unMatrix n)++instance JoinableH (Matrix (m,n)) (Vector m) where+    type JoinShapeH (Matrix (m,n)) (Vector m) = (m,n:+:D1)+    m <|> v = m <|> asColumn v++instance JoinableH (Vector m) (Matrix (m,n)) where+    type JoinShapeH (Vector m) (Matrix (m,n)) = (m,D1 :+: n)+    v <|> m = asColumn v <|> m++instance JoinableH (Vector m) (Vector m) where+    type JoinShapeH (Vector m) (Vector m) = (m,D2)+    v <|> w = asColumn v <|> w++-- | Least squares solution of a linear equation.+(<\>) :: Field t => Matrix (m,n) t -> Vector m t -> Vector n t+(<\>) m = Vector . (H.<\>) (unMatrix m) . unVector++linearSolve :: (H.Field t) => Matrix (m,m) t -> Matrix (m,n) t -> Matrix (m,n) t+linearSolve a b = Matrix $ H.multiply (unMatrix a) (unMatrix b)++inv :: (H.Field t) => Matrix (m,m) t -> Matrix (m,m) t+inv = Matrix . H.inv . unMatrix++pinv :: (H.Field t) => Matrix (m,n) t -> Matrix (n,m) t+pinv = Matrix . H.pinv . unMatrix++det :: (H.Field t) => Matrix (m,m) t -> t+det = H.det . unMatrix++rank :: (H.Field t) => Matrix (m,n) t -> Int+rank = H.rank . unMatrix++rcond :: (H.Field t) => Matrix (m,n) t -> Double+rcond = H.rcond . unMatrix++--------- SVD+svd :: (H.Field t) => Matrix (m,n) t ->+   (Matrix (m,m) t, Vector (Min m n) Double, Matrix (n,n) t)+svd = svdBody++-- private+svdBody m = case H.svd $ unMatrix m of+          (a,b,c) -> (Matrix a, Vector b, Matrix c)+++fullSVD :: (H.Field t) => Matrix mn t+   -> (Matrix (m,m) t, Matrix (m,n) Double, Matrix (n,n) t)+fullSVD m = case H.full H.svd $ unMatrix m of+              (a,b,c) -> (Matrix a, Matrix b, Matrix c)++economySVDU :: (H.Field t) => Matrix (m,n) t -> +   (Matrix (m,Unknown) t, +    Vector Unknown Double, +    Matrix (n,Unknown) t)+economySVDU m = case H.economy H.svd $ unMatrix m of+                 (a,b,c) -> (Matrix a, Vector b, Matrix c)++---- eig+eig :: H.Field t =>+       Matrix (m,m) t+    -> (Vector m (H.Complex Double), +        Matrix (m,m) (H.Complex Double))+eig = liftEig H.eig++eigSH :: (H.Field t) => +         Matrix (m,m) t +      -> (Vector m Double, Matrix (m,m) t)+eigSH = liftEig H.eigSH++liftEig f m = case f $ unMatrix m of+                (a,b) -> (Vector a, Matrix b)++---- qr+qr :: (H.Field t) =>+      Matrix (m,n) t -> (Matrix (m,m) t, Matrix (m,n) t)+qr m = case H.qr $ unMatrix m of+         (a,b) -> (Matrix a, Matrix b)++--- cholesky+chol :: (H.Field t) => Matrix (m,m) t -> Matrix (m,m) t+chol = Matrix . H.chol . unMatrix++-- hessenberg+hess :: (H.Field t) =>+        Matrix (m,m) t -> (Matrix (m,m) t, Matrix (m,m) t)+hess m = case H.hess $ unMatrix m of+           (a,b) -> (Matrix a, Matrix b)++-- schur+schur :: (H.Field t) =>+         Matrix (m,m) t -> (Matrix (m,m) t, Matrix (m,m) t)+schur m = case H.schur $ unMatrix m of+            (a,b) -> (Matrix a, Matrix b)++-- lu+--- I hope these sizes is right !!+lu :: (H.Field t) =>+      Matrix (m,n) t +   -> (Matrix (m, Min m n) t, Matrix (Min m n, n) t, Matrix (m,m) t, t)+lu m = case H.lu $ unMatrix m of+         (a,b,c,d) -> (Matrix a, Matrix b, Matrix c, d)++luPacked :: (H.Field t) =>+            Matrix (m,n) t -> (Matrix (m,n) t, [Int])+luPacked m = case H.luPacked $ unMatrix m of+               (a,b) -> (Matrix a, b)++--- is this right?+luSolve :: (H.Field t) =>+           (Matrix (m,n) t, [Int]) +        -> Matrix (m,p) t -> Matrix (n,p) t+luSolve (Matrix lu,is) = Matrix . H.luSolve (lu,is) . unMatrix++----++expm :: (H.Field t) => Matrix (m,m) t -> Matrix (m,m) t+expm = Matrix . H.expm . unMatrix++sqrtm :: (H.Field t) => Matrix (m,m) t -> Matrix (m,m) t+sqrtm = Matrix . H.sqrtm . unMatrix++matFunc :: (H.Field t) => (Complex Double -> Complex Double)+        -> Matrix (m,m) t+        -> Matrix (m,m) (Complex Double)+matFunc f = Matrix . H.matFunc f . unMatrix++nullspacePrec :: (H.Field t) =>+                 Double -> Matrix (m,n) t -> [Vector n t]+nullspacePrec tol = map Vector . H.nullspacePrec tol . unMatrix++nullVector :: (H.Field t) =>+              Matrix (m, n) t -> Vector n t+nullVector = last . nullspacePrec 1++--- misc+ctrans :: (H.Field t) =>+          Matrix (m,n) t -> Matrix (n,m) t+ctrans = Matrix . H.ctrans . unMatrix++eps :: Double+eps = H.eps++i :: Complex Double+i = H.i++outer :: (H.Field t) =>+         Vector m t -> Vector n t -> Matrix (m,n) t+outer v w = Matrix $ H.outer (unVector v) (unVector w)++kronecker :: (H.Field t) =>+             Matrix (m,n) t -> Matrix (p,q) t -> Matrix (m :*: p, n :*: q) t+kronecker m n = Matrix $ H.kronecker (unMatrix m) (unMatrix n)++----+-- omitted: haussholder, unpackQR, unpackHess+

@@ -0,0 +1,4 @@+#! /usr/bin/env runhaskell++import Distribution.Simple+main = defaultMain

@@ -0,0 +1,53 @@+Name:          hmatrix-static+Version:       0.1+Synopsis:      hmatrix with vector and matrix sizes encoded in types+License:       GPL+License-file:  LICENSE+Author:	       Reiner Pope+Maintainer:    Reiner Pope <reiner.pope@gmail.com>+Stability:     experimental+Homepage:      http://code.haskell.org/hmatrix-static/+Description:   A thin, lightweight wrapper over hmatrix to support+               static checking of matrix and vector sizes (for instance,+	       addition of different-sized vectors will be disallowed+	       at compile-time). +	       .+	       Objects whose sizes are not statically known are given+	       the special size 'Unknown', which allows a syntactically+	       cheap way to step down to the statically unchecked system +	       of hmatrix. This is cheap in comparison to representing+	       unknown sizes with exisential types, which forces pervasive+	       continuation passing style.+	       .	    +	       WARNING: when using the QuasiQuoting in this package, +	       be aware of infix expressions. See the note in +	       "Data.Packed.Static.Syntax" for details.+Category:      Math+Tested-with:   GHC == 6.10.1+Cabal-Version: >= 1.6+build-type:    Simple++Library+  Exposed-Modules:+       Data.Packed.Static,+       Data.Packed.Static.Vector,+       Data.Packed.Static.Matrix,+       Data.Packed.Static.ST,+       Data.Packed.Static.Syntax,+       Data.Packed.Static.Convert,+       Data.Packed.Static.Imports,+       Data.Packed.Static.Shapes,+       Numeric.LinearAlgebra.Static,+       Numeric.LinearAlgebra.Static.Algorithms+  Other-Modules:+       Data.Packed.Static.Internal,+       Data.Packed.Static.Internal.Vector,+       Data.Packed.Static.Internal.Matrix+  Extensions:+       ScopedTypeVariables, FlexibleContexts,+       FlexibleInstances, MultiParamTypeClasses,+       Rank2Types, TypeFamilies, TypeOperators,+       EmptyDataDecls, TemplateHaskell++  Build-Depends: base==4.*, hmatrix==0.5.*, tfp==0.2.*, array==0.2.*, +                 haskell-src-meta>=0.0.3.1&&<0.0.4, parsec==3.*, template-haskell