diff --git a/Data/Packed/Static.hs b/Data/Packed/Static.hs new file mode 100644 --- /dev/null +++ b/Data/Packed/Static.hs @@ -0,0 +1,29 @@ +----------------------------------------------------------------------------- +-- | +-- Module : Data.Packed.Static +-- Copyright : (c) Reiner Pope 2008 +-- License : GPL-style +-- +-- Maintainer : Reiner Pope +-- 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 + diff --git a/Data/Packed/Static/Convert.hs b/Data/Packed/Static/Convert.hs new file mode 100644 --- /dev/null +++ b/Data/Packed/Static/Convert.hs @@ -0,0 +1,82 @@ +----------------------------------------------------------------------------- +-- | +-- Module : Data.Packed.Static.Convert +-- Copyright : (c) Reiner Pope 2008 +-- License : GPL-style +-- +-- Maintainer : Reiner Pope +-- 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 diff --git a/Data/Packed/Static/Imports.hs b/Data/Packed/Static/Imports.hs new file mode 100644 --- /dev/null +++ b/Data/Packed/Static/Imports.hs @@ -0,0 +1,33 @@ +----------------------------------------------------------------------------- +-- | +-- Module : Data.Packed.Static.Imports +-- Copyright : (c) Reiner Pope 2008 +-- License : GPL-style +-- +-- Maintainer : Reiner Pope +-- 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) + diff --git a/Data/Packed/Static/Internal.hs b/Data/Packed/Static/Internal.hs new file mode 100644 --- /dev/null +++ b/Data/Packed/Static/Internal.hs @@ -0,0 +1,21 @@ +----------------------------------------------------------------------------- +-- | +-- Module : Data.Packed.Static.Internal +-- Copyright : (c) Reiner Pope 2008 +-- License : GPL-style +-- +-- Maintainer : Reiner Pope +-- 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 diff --git a/Data/Packed/Static/Internal/Matrix.hs b/Data/Packed/Static/Internal/Matrix.hs new file mode 100644 --- /dev/null +++ b/Data/Packed/Static/Internal/Matrix.hs @@ -0,0 +1,23 @@ +----------------------------------------------------------------------------- +-- | +-- Module : Data.Packed.Static.Internal.Matrix +-- Copyright : (c) Reiner Pope 2008 +-- License : GPL-style +-- +-- Maintainer : Reiner Pope +-- 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() diff --git a/Data/Packed/Static/Internal/Vector.hs b/Data/Packed/Static/Internal/Vector.hs new file mode 100644 --- /dev/null +++ b/Data/Packed/Static/Internal/Vector.hs @@ -0,0 +1,50 @@ +----------------------------------------------------------------------------- +-- | +-- Module : Data.Packed.Static.Internal.Vector +-- Copyright : (c) Reiner Pope 2008 +-- License : GPL-style +-- +-- Maintainer : Reiner Pope +-- 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 } diff --git a/Data/Packed/Static/Matrix.hs b/Data/Packed/Static/Matrix.hs new file mode 100644 --- /dev/null +++ b/Data/Packed/Static/Matrix.hs @@ -0,0 +1,487 @@ +----------------------------------------------------------------------------- +-- | +-- Module : Data.Packed.Static.Matrix +-- Copyright : (c) Reiner Pope 2008 +-- License : GPL-style +-- +-- Maintainer : Reiner Pope +-- 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 diff --git a/Data/Packed/Static/ST.hs b/Data/Packed/Static/ST.hs new file mode 100644 --- /dev/null +++ b/Data/Packed/Static/ST.hs @@ -0,0 +1,119 @@ +----------------------------------------------------------------------------- +-- | +-- Module : Data.Packed.Static.ST +-- Copyright : (c) Reiner Pope 2008 +-- License : GPL-style +-- +-- Maintainer : Reiner Pope +-- 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... +-} diff --git a/Data/Packed/Static/Shapes.hs b/Data/Packed/Static/Shapes.hs new file mode 100644 --- /dev/null +++ b/Data/Packed/Static/Shapes.hs @@ -0,0 +1,142 @@ +----------------------------------------------------------------------------- +-- | +-- Module : Data.Packed.Static.Shapes +-- Copyright : (c) Reiner Pope 2008 +-- License : GPL-style +-- +-- Maintainer : Reiner Pope +-- 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 diff --git a/Data/Packed/Static/Syntax.hs b/Data/Packed/Static/Syntax.hs new file mode 100644 --- /dev/null +++ b/Data/Packed/Static/Syntax.hs @@ -0,0 +1,223 @@ +----------------------------------------------------------------------------- +-- | +-- Module : Data.Packed.Static.Syntax +-- Copyright : (c) Reiner Pope 2008 +-- License : GPL-style +-- +-- Maintainer : Reiner Pope +-- 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 @[$matU|\|]@ as shorthand for @'forgetShapeU' [$mat|\|]@. + +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', +@[$vecU|\|]@ is just shorthand for @'forgetShapeU' [$vec|\|]@. -} +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 + diff --git a/Data/Packed/Static/Vector.hs b/Data/Packed/Static/Vector.hs new file mode 100644 --- /dev/null +++ b/Data/Packed/Static/Vector.hs @@ -0,0 +1,209 @@ +----------------------------------------------------------------------------- +-- | +-- Module : Data.Packed.Static.Vector +-- Copyright : (c) Reiner Pope 2008 +-- License : GPL-style +-- +-- Maintainer : Reiner Pope +-- 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) ++ " |]" + diff --git a/LICENSE b/LICENSE new file mode 100644 --- /dev/null +++ b/LICENSE @@ -0,0 +1,674 @@ + GNU GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. + 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. 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If not, see . + +Also add information on how to contact you by electronic and paper mail. + + If the program does terminal interaction, make it output a short +notice like this when it starts in an interactive mode: + + Copyright (C) + This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. + This is free software, and you are welcome to redistribute it + under certain conditions; type `show c' for details. + +The hypothetical commands `show w' and `show c' should show the appropriate +parts of the General Public License. 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 +. + + 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 +. diff --git a/Numeric/LinearAlgebra/Static.hs b/Numeric/LinearAlgebra/Static.hs new file mode 100644 --- /dev/null +++ b/Numeric/LinearAlgebra/Static.hs @@ -0,0 +1,21 @@ +----------------------------------------------------------------------------- +-- | +-- Module : Numeric.LinearAlgebra.Static +-- Copyright : (c) Reiner Pope 2008 +-- License : GPL-style +-- +-- Maintainer : Reiner Pope +-- 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 diff --git a/Numeric/LinearAlgebra/Static/Algorithms.hs b/Numeric/LinearAlgebra/Static/Algorithms.hs new file mode 100644 --- /dev/null +++ b/Numeric/LinearAlgebra/Static/Algorithms.hs @@ -0,0 +1,315 @@ +----------------------------------------------------------------------------- +-- | +-- Module : Numeric.LinearAlgebra.Static.Algorithms +-- Copyright : (c) Reiner Pope 2008 +-- License : GPL-style +-- +-- Maintainer : Reiner Pope +-- 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 + diff --git a/Setup.hs b/Setup.hs new file mode 100644 --- /dev/null +++ b/Setup.hs @@ -0,0 +1,4 @@ +#! /usr/bin/env runhaskell + +import Distribution.Simple +main = defaultMain diff --git a/hmatrix-static.cabal b/hmatrix-static.cabal new file mode 100644 --- /dev/null +++ b/hmatrix-static.cabal @@ -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 +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