{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE CPP #-}

-----------------------------------------------------------------------------
-- |
-- Module      :  Data.Packed.Matrix
-- Copyright   :  (c) Alberto Ruiz 2007-10
--
-- Maintainer  :  Alberto Ruiz <aruiz@um.es>
-- Stability   :  provisional
--
-- A Matrix representation suitable for numerical computations using LAPACK and GSL.
--
-- This module provides basic functions for manipulation of structure.

-----------------------------------------------------------------------------

module Data.Packed.Matrix (
Matrix,
Element,
rows,cols,
(><),
trans,
reshape, flatten,
fromLists, toLists, buildMatrix,
(@@>),
asRow, asColumn,
fromRows, toRows, fromColumns, toColumns,
fromBlocks, toBlocks, toBlocksEvery,
repmat,
flipud, fliprl,
subMatrix, takeRows, dropRows, takeColumns, dropColumns,
extractRows,
diagRect, takeDiag,
liftMatrix, liftMatrix2, liftMatrix2Auto,fromArray2D
) where

import Data.Packed.Internal
import qualified Data.Packed.ST as ST
import Data.List(transpose,intersperse)
import Data.Array
import Foreign.Storable

-------------------------------------------------------------------

#ifdef BINARY

import Data.Binary

instance (Binary a, Element a, Storable a) => Binary (Matrix a) where
put m = do
let r = rows m
let c = cols m
put r
put c
mapM_ (\i -> mapM_ (\j -> put \$ m @@> (i,j)) [0..(c-1)]) [0..(r-1)]
get = do
r <- get
c <- get
xs <- replicateM r \$ replicateM c get
return \$ fromLists xs

#endif

-------------------------------------------------------------------

instance (Show a, Element a) => (Show (Matrix a)) where
show m = (sizes++) . dsp . map (map show) . toLists \$ m
where sizes = "("++show (rows m)++"><"++show (cols m)++")\n"

dsp as = (++" ]") . (" ["++) . init . drop 2 . unlines . map (" , "++) . map unwords' \$ transpose mtp
where
mt = transpose as
longs = map (maximum . map length) mt
mtp = zipWith (\a b -> map (pad a) b) longs mt
pad n str = replicate (n - length str) ' ' ++ str
unwords' = concat . intersperse ", "

------------------------------------------------------------------

where (thing,rest) = breakAt ']' s
(dims,listnums) = breakAt ')' thing
cs = read . init . fst. breakAt ')' . snd . breakAt '<' \$ dims
rs = read . snd . breakAt '(' .init . fst . breakAt '>' \$ dims

breakAt c l = (a++[c],tail b) where
(a,b) = break (==c) l

------------------------------------------------------------------

-- | creates a matrix from a vertical list of matrices
joinVert :: Element t => [Matrix t] -> Matrix t
joinVert ms = case common cols ms of
Nothing -> error "(impossible) joinVert on matrices with different number of columns"
Just c  -> reshape c \$ join (map flatten ms)

-- | creates a matrix from a horizontal list of matrices
joinHoriz :: Element t => [Matrix t] -> Matrix t
joinHoriz ms = trans. joinVert . map trans \$ ms

{- | Creates a matrix from blocks given as a list of lists of matrices.

Single row/column components are automatically expanded to match the
corresponding common row and column:

@\> let disp = putStr . dispf 2
\> let vector xs = fromList xs :: Vector Double
\> let diagl = diag . vector
\> let rowm = asRow . vector

\> disp \$ fromBlocks [[ident 5, 7, rowm[10,20]], [3, diagl[1,2,3], 0]]

8x10
1  0  0  0  0  7  7  7  10  20
0  1  0  0  0  7  7  7  10  20
0  0  1  0  0  7  7  7  10  20
0  0  0  1  0  7  7  7  10  20
0  0  0  0  1  7  7  7  10  20
3  3  3  3  3  1  0  0   0   0
3  3  3  3  3  0  2  0   0   0
3  3  3  3  3  0  0  3   0   0@
-}
fromBlocks :: Element t => [[Matrix t]] -> Matrix t

fromBlocksRaw mms = joinVert . map joinHoriz \$ mms

bc = case common length ms of
Just c -> c
Nothing -> error "fromBlocks requires rectangular [[Matrix]]"
rs = map (compatdim . map rows) ms
cs = map (compatdim . map cols) (transpose ms)
szs = sequence [rs,cs]
ms' = splitEvery bc \$ zipWith g szs (concat ms)

g [Just nr,Just nc] m
| nr == r && nc == c = m
| r == 1 && c == 1 = reshape nc (constantD x (nr*nc))
| r == 1 = fromRows (replicate nr (flatten m))
| otherwise = fromColumns (replicate nc (flatten m))
where
r = rows m
c = cols m
x = m@@>(0,0)
g _ _ = error "inconsistent dimensions in fromBlocks"

-----------------------------------------------------------

-- | Reverse rows
flipud :: Element t => Matrix t -> Matrix t
flipud m = fromRows . reverse . toRows \$ m

-- | Reverse columns
fliprl :: Element t => Matrix t -> Matrix t
fliprl m = fromColumns . reverse . toColumns \$ m

------------------------------------------------------------

{- | creates a rectangular diagonal matrix:

@> diagRect 7 (fromList [10,20,30]) 4 5 :: Matrix Double
(4><5)
[ 10.0,  7.0,  7.0, 7.0, 7.0
,  7.0, 20.0,  7.0, 7.0, 7.0
,  7.0,  7.0, 30.0, 7.0, 7.0
,  7.0,  7.0,  7.0, 7.0, 7.0 ]@
-}
diagRect :: (Storable t) => t -> Vector t -> Int -> Int -> Matrix t
diagRect z v r c = ST.runSTMatrix \$ do
m <- ST.newMatrix z r c
let d = min r c `min` (dim v)
mapM_ (\k -> ST.writeMatrix m k k (v@>k)) [0..d-1]
return m

-- | extracts the diagonal from a rectangular matrix
takeDiag :: (Element t) => Matrix t -> Vector t
takeDiag m = fromList [flatten m `at` (k*cols m+k) | k <- [0 .. min (rows m) (cols m) -1]]

------------------------------------------------------------

{- | An easy way to create a matrix:

@\> (2><3)[1..6]
(2><3)
[ 1.0, 2.0, 3.0
, 4.0, 5.0, 6.0 ]@

This is the format produced by the instances of Show (Matrix a), which
can also be used for input.

The input list is explicitly truncated, so that it can
safely be used with lists that are too long (like infinite lists).

Example:

@\> (2>|<3)[1..]
(2><3)
[ 1.0, 2.0, 3.0
, 4.0, 5.0, 6.0 ]@

-}
(><) :: (Storable a) => Int -> Int -> [a] -> Matrix a
r >< c = f where
f l | dim v == r*c = matrixFromVector RowMajor c v
| otherwise    = error \$ "inconsistent list size = "
++show (dim v) ++" in ("++show r++"><"++show c++")"
where v = fromList \$ take (r*c) l

----------------------------------------------------------------

-- | Creates a matrix with the first n rows of another matrix
takeRows :: Element t => Int -> Matrix t -> Matrix t
takeRows n mt = subMatrix (0,0) (n, cols mt) mt
-- | Creates a copy of a matrix without the first n rows
dropRows :: Element t => Int -> Matrix t -> Matrix t
dropRows n mt = subMatrix (n,0) (rows mt - n, cols mt) mt
-- |Creates a matrix with the first n columns of another matrix
takeColumns :: Element t => Int -> Matrix t -> Matrix t
takeColumns n mt = subMatrix (0,0) (rows mt, n) mt
-- | Creates a copy of a matrix without the first n columns
dropColumns :: Element t => Int -> Matrix t -> Matrix t
dropColumns n mt = subMatrix (0,n) (rows mt, cols mt - n) mt

----------------------------------------------------------------

{- | Creates a 'Matrix' from a list of lists (considered as rows).

@\> fromLists [[1,2],[3,4],[5,6]]
(3><2)
[ 1.0, 2.0
, 3.0, 4.0
, 5.0, 6.0 ]@
-}
fromLists :: Element t => [[t]] -> Matrix t
fromLists = fromRows . map fromList

-- | creates a 1-row matrix from a vector
asRow :: Storable a => Vector a -> Matrix a
asRow v = reshape (dim v) v

-- | creates a 1-column matrix from a vector
asColumn :: Storable a => Vector a -> Matrix a
asColumn v = reshape 1 v

{- | creates a Matrix of the specified size using the supplied function to
to map the row\/column position to the value at that row\/column position.

@> buildMatrix 3 4 (\ (r,c) -> fromIntegral r * fromIntegral c)
(3><4)
[ 0.0, 0.0, 0.0, 0.0, 0.0
, 0.0, 1.0, 2.0, 3.0, 4.0
, 0.0, 2.0, 4.0, 6.0, 8.0]@

Hilbert matrix of order N:

@hilb n = buildMatrix n n (\(i,j)->1/(fromIntegral i + fromIntegral j +1))@

-}
buildMatrix :: Element a => Int -> Int -> ((Int, Int) -> a) -> Matrix a
buildMatrix rc cc f =
fromLists \$ map (map f)
\$ map (\ ri -> map (\ ci -> (ri, ci)) [0 .. (cc - 1)]) [0 .. (rc - 1)]

-----------------------------------------------------

fromArray2D :: (Storable e) => Array (Int, Int) e -> Matrix e
fromArray2D m = (r><c) (elems m)
where ((r0,c0),(r1,c1)) = bounds m
r = r1-r0+1
c = c1-c0+1

-- | rearranges the rows of a matrix according to the order given in a list of integers.
extractRows :: Element t => [Int] -> Matrix t -> Matrix t
extractRows l m = fromRows \$ extract (toRows m) l
where extract l' is = [l'!!i |i<-is]

{- | creates matrix by repetition of a matrix a given number of rows and columns

@> repmat (ident 2) 2 3 :: Matrix Double
(4><6)
[ 1.0, 0.0, 1.0, 0.0, 1.0, 0.0
, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0
, 1.0, 0.0, 1.0, 0.0, 1.0, 0.0
, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0 ]@

-}
repmat :: (Element t) => Matrix t -> Int -> Int -> Matrix t
repmat m r c = fromBlocks \$ splitEvery c \$ replicate (r*c) m

-- | A version of 'liftMatrix2' which automatically adapt matrices with a single row or column to match the dimensions of the other matrix.
liftMatrix2Auto :: (Element t, Element a, Element b) => (Vector a -> Vector b -> Vector t) -> Matrix a -> Matrix b -> Matrix t
liftMatrix2Auto f m1 m2
| compat' m1 m2 = lM f m1 m2

| r1 == 1  && c2 == 1 = lM f (repRows r2 m1) (repCols c1 m2)
| c1 == 1  && r2 == 1 = lM f (repCols c2 m1) (repRows r1 m2)

| r1 == r2 && c2 == 1 = lM f m1              (repCols c1 m2)
| r1 == r2 && c1 == 1 = lM f (repCols c2 m1) m2

| c1 == c2 && r2 == 1 = lM f m1              (repRows r1 m2)
| c1 == c2 && r1 == 1 = lM f (repRows r2 m1) m2

| otherwise    = error \$ "nonconformable matrices in liftMatrix2Auto: "
++ show (size m1) ++ ", " ++ show (size m2)
where
(r1,c1) = size m1
(r2,c2) = size m2

size m = (rows m, cols m)

lM f m1 m2 = reshape (max (cols m1) (cols m2)) (f (flatten m1) (flatten m2))

repRows n x = fromRows (replicate n (flatten x))
repCols n x = fromColumns (replicate n (flatten x))

compat' :: Matrix a -> Matrix b -> Bool
compat' m1 m2 = s1 == (1,1) || s2 == (1,1) || s1 == s2
where
s1 = size m1
s2 = size m2

------------------------------------------------------------

toBlockRows [r] m | r == rows m = [m]
toBlockRows rs m = map (reshape (cols m)) (takesV szs (flatten m))
where szs = map (* cols m) rs

toBlockCols [c] m | c == cols m = [m]
toBlockCols cs m = map trans . toBlockRows cs . trans \$ m

-- | Partition a matrix into blocks with the given numbers of rows and columns.
-- The remaining rows and columns are discarded.
toBlocks :: (Element t) => [Int] -> [Int] -> Matrix t -> [[Matrix t]]
toBlocks rs cs m = map (toBlockCols cs) . toBlockRows rs \$ m

-- | Fully partition a matrix into blocks of the same size. If the dimensions are not
-- a multiple of the given size the last blocks will be smaller.
toBlocksEvery :: (Element t) => Int -> Int -> Matrix t -> [[Matrix t]]
toBlocksEvery r c m = toBlocks rs cs m where
(qr,rr) = rows m `divMod` r
(qc,rc) = cols m `divMod` c
rs = replicate qr r ++ if rr > 0 then [rr] else []
cs = replicate qc c ++ if rc > 0 then [rc] else []

-------------------------------------------------------------------