{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE FlexibleInstances #-}
module Numeric.LAPACK.Matrix.Plain.Format where
import qualified Numeric.LAPACK.Matrix.Layout.Private as Layout
import qualified Numeric.LAPACK.Matrix.Extent.Private as Extent
import qualified Numeric.LAPACK.Vector as Vector
import qualified Numeric.LAPACK.Output as Output
import qualified Numeric.LAPACK.Shape as ExtShape
import Numeric.LAPACK.Output (Output, formatRow, (<+>))
import Numeric.LAPACK.Matrix.Layout.Private
(Order(RowMajor, ColumnMajor), UnaryProxy)
import Numeric.LAPACK.Matrix.Private (Full)
import Numeric.LAPACK.Matrix.Extent.Private (Extent)
import Numeric.LAPACK.Scalar (conjugate)
import Numeric.LAPACK.Private (caseRealComplexFunc)
import qualified Numeric.Netlib.Class as Class
import qualified Type.Data.Num.Unary.Literal as TypeNum
import qualified Type.Data.Num.Unary as Unary
import Type.Data.Num (integralFromProxy)
import qualified Data.Array.Comfort.Storable.Unchecked as Array
import qualified Data.Array.Comfort.Boxed as BoxedArray
import qualified Data.Array.Comfort.Shape as Shape
import Data.Array.Comfort.Storable (Array)
import Data.Array.Comfort.Shape ((::+))
import Text.Printf (PrintfArg, printf)
import qualified Data.List.Match as Match
import qualified Data.List.HT as ListHT
import Data.Foldable (Foldable, fold)
import Data.List (mapAccumL, transpose)
import Data.Complex (Complex((:+)))
import Data.Ix (Ix)
import Control.Applicative ((<$>))
deflt :: String
deflt = "%.4g"
data Config =
Config {
configFormat :: String,
configEmpty :: String
}
defltConfig :: Config
defltConfig =
Config {
configFormat = deflt,
configEmpty = ""
}
class (Shape.C sh) => FormatArray sh where
formatArray :: (Class.Floating a, Output out) => Config -> Array sh a -> out
instance (Integral i) => FormatArray (Shape.ZeroBased i) where
formatArray = formatVector
instance (Integral i) => FormatArray (Shape.OneBased i) where
formatArray = formatVector
instance (Ix i) => FormatArray (Shape.Range i) where
formatArray = formatVector
instance (Integral i) => FormatArray (Shape.Shifted i) where
formatArray = formatVector
instance (Enum enum, Bounded enum) => FormatArray (Shape.Enumeration enum) where
formatArray = formatVector
instance (FormatArray sh) => FormatArray (Shape.Deferred sh) where
formatArray cfg =
formatArray cfg . Array.mapShape (\(Shape.Deferred sh) -> sh)
instance (FormatArray sh0, FormatArray sh1) => FormatArray (sh0::+sh1) where
formatArray cfg v =
formatArray cfg (Vector.takeLeft v)
<+>
formatArray cfg (Vector.takeRight v)
instance (Shape.C sh) => FormatArray (ExtShape.IntIndexed sh) where
formatArray = formatVector
formatVector ::
(Shape.C sh, Class.Floating a, Output out) => Config -> Array sh a -> out
formatVector cfg =
formatRow . map (Output.text . fold . printfFloating cfg) . Array.toList
instance
(Extent.Measure meas, Extent.C vert, Extent.C horiz,
Shape.C height, Shape.C width) =>
FormatArray (Layout.Full meas vert horiz height width) where
formatArray cfg = formatAligned (printfFloating cfg) . layoutFull
layoutFull ::
(Extent.Measure meas, Extent.C vert, Extent.C horiz,
Shape.C height, Shape.C width, Class.Floating a) =>
Full meas vert horiz height width a -> [[a]]
layoutFull m =
let Layout.Full order extent = Array.shape m
in splitRows order (Extent.dimensions extent) $ Array.toList m
instance
(Eq lower, Extent.Measure meas, Extent.C vert, Extent.C horiz,
Shape.C height, Shape.C width) =>
FormatArray (Layout.Split lower meas vert horiz height width) where
formatArray cfg =
formatSeparateTriangle (printfFloating cfg) . layoutSplit
layoutSplit ::
(Eq lower, Extent.Measure meas, Extent.C vert, Extent.C horiz,
Shape.C height, Shape.C width, Class.Floating a) =>
Array (Layout.Split lower meas vert horiz height width) a -> [[a]]
layoutSplit m =
let Layout.Split _ order extent = Array.shape m
in splitRows order (Extent.dimensions extent) $ Array.toList m
instance (Shape.C size) => FormatArray (Layout.Hermitian size) where
formatArray = formatMirrored conjugate
instance (Shape.C size) => FormatArray (Layout.Symmetric size) where
formatArray = formatMirrored id
formatMirrored ::
(Shape.C size, Class.Floating a, Output out) =>
(a -> a) ->
Config ->
Array (Layout.Mosaic Layout.Packed mirror Shape.Upper size) a ->
out
formatMirrored adapt cfg m =
formatSeparateTriangle (printfFloating cfg) $ layoutMirrored adapt m
layoutMirrored ::
(Shape.C size, Class.Floating a) =>
(a -> a) ->
Array (Layout.Mosaic Layout.Packed mirror Shape.Upper size) a ->
[[a]]
layoutMirrored adapt m =
let Layout.Mosaic Layout.Packed _mirror Layout.Upper order size
= Array.shape m
in complementTriangle adapt order (Shape.size size) $ Array.toList m
complementTriangle ::
(Class.Floating a) => (a -> a) -> Order -> Int -> [a] -> [[a]]
complementTriangle adapt order n xs =
let mergeTriangles lower upper =
zipWith (++) (map (map adapt . init) lower) upper
in case order of
RowMajor ->
let tri = slice (take n $ iterate pred n) xs
trans = reverse $ transpose $ map reverse tri
in mergeTriangles trans tri
ColumnMajor ->
let tri = slice (take n [1..]) xs
in mergeTriangles tri (transpose tri)
formatDiagonal ::
(Shape.C size, Class.Floating a, Output out) =>
Config -> Order -> size -> [a] -> out
formatDiagonal cfg order size xs =
let n0 = Unary.unary TypeNum.u0
in formatAligned (printfFloatingMaybe cfg) $
padBanded (n0,n0) order (size,size) xs
instance
(Layout.UpLo uplo, Shape.C size) =>
FormatArray (Layout.Triangular uplo size) where
formatArray cfg = formatAligned (printfFloatingMaybe cfg) . layoutTriangular
layoutTriangular ::
(Layout.UpLo uplo, Shape.C size, Class.Floating a) =>
Array (Layout.Triangular uplo size) a -> [[Maybe a]]
layoutTriangular m =
let Layout.Mosaic Layout.Packed Layout.NoMirror uplo order size
= Array.shape m
in padTriangle uplo order (Shape.size size) $ Array.toList m
padTriangle ::
Layout.UpLoSingleton uplo -> Order -> Int -> [a] -> [[Maybe a]]
padTriangle uplo =
case uplo of
Layout.Lower -> padLowerTriangle
Layout.Upper -> padUpperTriangle
padUpperTriangle :: Order -> Int -> [a] -> [[Maybe a]]
padUpperTriangle order n xs =
let mxs = map Just xs
nothings = iterate (Nothing:) []
in case order of
RowMajor ->
zipWith (++) nothings (slice (take n $ iterate pred n) mxs)
ColumnMajor ->
transpose $
zipWith (++)
(slice (take n [1..]) mxs)
(reverse $ take n nothings)
padLowerTriangle :: Order -> Int -> [a] -> [[Maybe a]]
padLowerTriangle order n xs =
map (map Just) $
case order of
RowMajor -> slice (take n [1..]) xs
ColumnMajor ->
foldr (\(y:ys) zs -> [y] : zipWith (:) ys zs) []
(slice (take n $ iterate pred n) xs)
slice :: [Int] -> [a] -> [[a]]
slice ns xs =
snd $ mapAccumL (\ys n -> let (vs,ws) = splitAt n ys in (ws,vs)) xs ns
instance
(Unary.Natural sub, Unary.Natural super,
Extent.Measure meas, Extent.C vert, Extent.C horiz,
Shape.C height, Shape.C width) =>
FormatArray (Layout.Banded sub super meas vert horiz height width) where
formatArray cfg = formatAligned (printfFloatingMaybe cfg) . layoutBanded
layoutBanded ::
(Unary.Natural sub, Unary.Natural super,
Extent.Measure meas, Extent.C vert, Extent.C horiz,
Shape.C height, Shape.C width, Class.Floating a) =>
Array (Layout.Banded sub super meas vert horiz height width) a -> [[Maybe a]]
layoutBanded m =
let Layout.Banded offDiag order extent = Array.shape m
in padBanded offDiag order (Extent.dimensions extent) $ Array.toList m
padBanded ::
(Shape.C height, Shape.C width, Unary.Natural sub, Unary.Natural super) =>
(UnaryProxy sub, UnaryProxy super) -> Order ->
(height, width) -> [a] -> [[Maybe a]]
padBanded (sub,super) order (height,width) xs =
let slices =
ListHT.sliceVertical (Layout.bandedBreadth (sub,super)) xs
m = Shape.size height
n = Shape.size width
in case order of
RowMajor ->
map (take n) $
zipWith (shiftRow Nothing)
(iterate (1+) (- integralFromProxy sub))
(map (map Just) slices)
ColumnMajor ->
let ku = integralFromProxy super
in take m $ drop ku $
foldr
(\col mat ->
zipWith (:) (map Just col ++ repeat Nothing) ([]:mat))
(replicate (ku + m - n) [])
slices
instance
(Unary.Natural offDiag, Shape.C size) =>
FormatArray (Layout.BandedHermitian offDiag size) where
formatArray cfg =
formatSeparateTriangle (printfFloatingMaybe cfg) . layoutBandedHermitian
layoutBandedHermitian ::
(Unary.Natural offDiag, Shape.C sh, Class.Floating a) =>
Array (Layout.BandedHermitian offDiag sh) a -> [[Maybe a]]
layoutBandedHermitian m =
let Layout.BandedHermitian offDiag order size = Array.shape m
in padBandedHermitian offDiag order size $ Array.toList m
padBandedHermitian ::
(Unary.Natural offDiag, Shape.C size, Class.Floating a) =>
UnaryProxy offDiag -> Order -> size -> [a] -> [[Maybe a]]
padBandedHermitian offDiag order _size xs =
let k = integralFromProxy offDiag
slices = ListHT.sliceVertical (k + 1) xs
in case order of
RowMajor ->
foldr
(\row square ->
Match.take ([]:square) (map Just row)
:
zipWith (:)
(tail $ map (Just . conjugate) row ++ repeat Nothing)
square)
[] slices
ColumnMajor ->
zipWith (shiftRow Nothing) (iterate (1+) (-k)) $ map (map Just) $
zipWith (++)
(map (map conjugate . init) slices)
(drop k $
foldr
(\column band ->
zipWith (++) (map (:[]) column ++ repeat []) ([]:band))
(replicate k [])
slices)
shiftRow :: a -> Int -> [a] -> [a]
shiftRow pad k = if k<=0 then drop (-k) else (replicate k pad ++)
splitRows ::
(Shape.C height, Shape.C width) =>
Order -> (height, width) -> [a] -> [[a]]
splitRows order (height,width) =
case order of
RowMajor -> ListHT.sliceVertical (Shape.size width)
ColumnMajor -> ListHT.sliceHorizontal (Shape.size height)
formatAligned ::
(Functor f, Foldable f, Output out) =>
(a -> f String) -> [[a]] -> out
formatAligned printFmt =
Output.formatAligned . map (map (fmap Output.text . printFmt))
formatSeparateTriangle ::
(Functor f, Foldable f, Output out) =>
(a -> f String) -> [[a]] -> out
formatSeparateTriangle printFmt =
Output.formatSeparateTriangle . map (map (fmap Output.text . printFmt))
arrayFromList2 ::
(Extent.Measure meas, Extent.C vert, Extent.C horiz) =>
(Shape.C height, Shape.C width) =>
Extent meas vert horiz height width -> [[a]] ->
BoxedArray.Array (height, width) (Output.Separator, Maybe (Output.Style, a))
arrayFromList2 extent =
incompleteArrayFromList2 extent . map (map Just)
incompleteArrayFromList2 ::
(Extent.Measure meas, Extent.C vert, Extent.C horiz) =>
(Shape.C height, Shape.C width) =>
Extent meas vert horiz height width -> [[Maybe a]] ->
BoxedArray.Array (height, width) (Output.Separator, Maybe (Output.Style, a))
incompleteArrayFromList2 extent =
let (height, width) = Extent.dimensions extent in
let n = Shape.size width in
BoxedArray.fromList (height, width) . concat .
map (map ((,) Output.Space) .
ListHT.padRight Nothing n . map (fmap ((,) Output.Stored)))
splitArrayFromList2 ::
(Extent.Measure meas, Extent.C vert, Extent.C horiz) =>
(Shape.C height, Shape.C width) =>
Extent meas vert horiz height width -> [[a]] ->
BoxedArray.Array (height, width) (Output.Separator, Maybe (Output.Style, a))
splitArrayFromList2 extent =
incompleteSplitArrayFromList2 extent . map (map Just)
incompleteSplitArrayFromList2 ::
(Extent.Measure meas, Extent.C vert, Extent.C horiz) =>
(Shape.C height, Shape.C width) =>
Extent meas vert horiz height width -> [[Maybe a]] ->
BoxedArray.Array (height, width) (Output.Separator, Maybe (Output.Style, a))
incompleteSplitArrayFromList2 extent =
let (height, width) = Extent.dimensions extent in
let n = Shape.size width in
BoxedArray.fromList (height, width) . concat .
Output.decorateTriangle
(\seps styles row ->
zip seps $ ListHT.padRight Nothing n $
zipWith (\s r -> (,) s <$> r) styles row)
toRows ::
(Shape.C height, Shape.C width) =>
BoxedArray.Array (height,width) a -> [[a]]
toRows arr =
case BoxedArray.toList arr of
[] -> replicate (Shape.size $ fst $ BoxedArray.shape arr) []
xs -> ListHT.sliceVertical (Shape.size $ snd $ BoxedArray.shape arr) xs
toColumns ::
(Shape.C height, Shape.C width) =>
BoxedArray.Array (height,width) a -> [[a]]
toColumns arr =
ListHT.sliceHorizontal (Shape.size $ snd $ BoxedArray.shape arr) $
BoxedArray.toList arr
data TupleShape a = TupleShape
instance (Class.Floating a) => Shape.C (TupleShape a) where
size sh = caseRealComplexFunc sh 1 2
type Tuple a = BoxedArray.Array (TupleShape a)
fillTuple :: (Class.Floating a) => b -> Tuple a b
fillTuple = BoxedArray.replicate TupleShape
newtype ToTuple a = ToTuple {getToTuple :: a -> Tuple a String}
printfFloatingPlain :: (Class.Floating a) => String -> a -> Tuple a String
printfFloatingPlain fmt =
getToTuple $
Class.switchFloating
(ToTuple $ fillTuple . printf fmt)
(ToTuple $ fillTuple . printf fmt)
(ToTuple $ printfComplex fmt)
(ToTuple $ printfComplex fmt)
printfFloating :: (Class.Floating a) => Config -> a -> Tuple a String
printfFloating cfg = printfFloatingPlain (configFormat cfg)
printfFloatingMaybe ::
(Class.Floating a) => Config -> Maybe a -> Tuple a String
printfFloatingMaybe cfg =
maybe (fillTuple $ configEmpty cfg) (printfFloating cfg)
printfComplex ::
(PrintfArg a, Class.Real a) =>
String -> Complex a -> Tuple (Complex a) String
printfComplex fmt (r:+i) =
if i<0 || isNegativeZero i
then complexTuple (printf (fmt ++ "-") r) (printf (fmt ++ "i") (-i))
else complexTuple (printf (fmt ++ "+") r) (printf (fmt ++ "i") i)
complexTuple :: (Class.Real a) => b -> b -> Tuple (Complex a) b
complexTuple b0 b1 = BoxedArray.fromList TupleShape [b0,b1]