src/Gargantext/Core/Methods/Matrix/Accelerate/Utils.hs

   1 {-|
   2 Module      : Gargantext.Core.Methods.Matrix.Accelerate.Utils
   3 Description :
   4 Copyright   : (c) CNRS, 2017-Present
   5 License     : AGPL + CECILL v3
   6 Maintainer  : team@gargantext.org
   7 Stability   : experimental
   8 Portability : POSIX
   9
  10 This module aims at implementig distances of terms context by context is
  11 the same referential of corpus.
  12
  13 Implementation use Accelerate library which enables GPU and CPU computation:
  14
  15   * Manuel M. T. Chakravarty, Gabriele Keller, Sean Lee, Trevor L. McDonell, and Vinod Grover.
  16     [Accelerating Haskell Array Codes with Multicore GPUs][CKLM+11].
  17     In _DAMP '11: Declarative Aspects of Multicore Programming_, ACM, 2011.
  18
  19   * Trevor L. McDonell, Manuel M. T. Chakravarty, Vinod Grover, and Ryan R. Newton.
  20     [Type-safe Runtime Code Generation: Accelerate to LLVM][MCGN15].
  21     In _Haskell '15: The 8th ACM SIGPLAN Symposium on Haskell_, ACM, 2015.
  22
  23 -}
  24
  25 {-# LANGUAGE TypeFamilies        #-}
  26 {-# LANGUAGE TypeOperators       #-}
  27 {-# LANGUAGE ScopedTypeVariables #-}
  28 {-# LANGUAGE ViewPatterns        #-}
  29
  30 module Gargantext.Core.Methods.Matrix.Accelerate.Utils
  31   where
  32
  33 import qualified Data.Foldable as P (foldl1)
  34 import Debug.Trace (trace)
  35 import Data.Array.Accelerate
  36 import Data.Array.Accelerate.Array.Sugar (Elt(..), Shape(..), Slice(..), (:.))
  37 import Data.Array.Accelerate.Smart (Exp(..))
  38 import Data.Array.Accelerate.Interpreter (run)
  39 import qualified Gargantext.Prelude as P
  40 import Data.Array.Accelerate.LinearAlgebra hiding (Matrix, transpose, Vector)
  41
  42 -----------------------------------------------------------------------
  43 -- | Main operators
  44 -- Matrix Multiplication
  45 (#*#) :: ( Shape ix
  46         , Slice ix
  47         , Elt a
  48         , P.Num (Exp a)
  49         )
  50      => Acc (Array ((ix :. Int) :. Int) a)
  51      -> Acc (Array ((ix :. Int) :. Int) a)
  52      -> Acc (Array ((ix :. Int) :. Int) a)
  53 (#*#) = multiplyMatrixMatrix
  54
  55
  56 -- | Matrix cell by cell multiplication
  57 (.*) :: ( Shape ix
  58         , Slice ix
  59         , Elt a
  60         , P.Num (Exp a)
  61         )
  62      => Acc (Array ((ix :. Int) :. Int) a)
  63      -> Acc (Array ((ix :. Int) :. Int) a)
  64      -> Acc (Array ((ix :. Int) :. Int) a)
  65 (.*) = zipWith (*)
  66
  67 (.**) :: ( Shape ix
  68         , Slice ix
  69         , Elt a
  70         , P.Num (Exp a)
  71         )
  72      => Acc (Array ((ix :. Int) :. Int) a)
  73      -> Acc (Array ((ix :. Int) :. Int) a)
  74 (.**) m = (.*) m m
  75
  76
  77 (./) :: ( Shape ix
  78         , Slice ix
  79         , Elt a
  80         , P.Num (Exp a)
  81         , P.Fractional (Exp a)
  82         )
  83      => Acc (Array ((ix :. Int) :. Int) a)
  84      -> Acc (Array ((ix :. Int) :. Int) a)
  85      -> Acc (Array ((ix :. Int) :. Int) a)
  86 (./) = zipWith (/)
  87
  88 (.-) :: ( Shape ix
  89         , Slice ix
  90         , Elt a
  91         , P.Num (Exp a)
  92         , P.Fractional (Exp a)
  93         )
  94      => Acc (Array ((ix :. Int) :. Int) a)
  95      -> Acc (Array ((ix :. Int) :. Int) a)
  96      -> Acc (Array ((ix :. Int) :. Int) a)
  97 (.-) = zipWith (-)
  98
  99 (.+) :: ( Shape ix
 100         , Slice ix
 101         , Elt a
 102         , P.Num (Exp a)
 103         , P.Fractional (Exp a)
 104         )
 105      => Acc (Array ((ix :. Int) :. Int) a)
 106      -> Acc (Array ((ix :. Int) :. Int) a)
 107      -> Acc (Array ((ix :. Int) :. Int) a)
 108 (.+) = zipWith (+)
 109
 110 -----------------------------------------------------------------------
 111 matrixOne :: Num a => Dim -> Acc (Matrix a)
 112 matrixOne n' = ones
 113   where
 114     ones  = fill (index2 n n) 1
 115     n     = constant n'
 116
 117
 118 matrixIdentity :: Num a => Dim -> Acc (Matrix a)
 119 matrixIdentity n' =
 120         let zeros = fill (index2 n n) 0
 121             ones  = fill (index1 n)   1
 122             n = constant n'
 123         in
 124         permute const zeros (\(unindex1 -> i) -> index2 i i) ones
 125
 126
 127 matrixEye :: Num a => Dim -> Acc (Matrix a)
 128 matrixEye n' =
 129         let ones   = fill (index2 n n) 1
 130             zeros  = fill (index1 n)   0
 131             n = constant n'
 132         in
 133         permute const ones (\(unindex1 -> i) -> index2 i i) zeros
 134
 135
 136 diagNull :: Num a => Dim -> Acc (Matrix a) -> Acc (Matrix a)
 137 diagNull n m = zipWith (*) m (matrixEye n)
 138
 139 -----------------------------------------------------------------------
 140 _runExp :: Elt e => Exp e -> e
 141 _runExp e = indexArray (run (unit e)) Z
 142
 143 -----------------------------------------------------------------------
 144 -- | Define a vector
 145 --
 146 -- >>> vector 3
 147 -- Vector (Z :. 3) [0,1,2]
 148 vector :: Elt c => Int -> [c] -> (Array (Z :. Int) c)
 149 vector n l = fromList (Z :. n) l
 150
 151 -- | Define a matrix
 152 --
 153 -- >>> matrix 3 ([1..] :: [Double])
 154 -- Matrix (Z :. 3 :. 3)
 155 --   [ 1.0, 2.0, 3.0,
 156 --     4.0, 5.0, 6.0,
 157 --     7.0, 8.0, 9.0]
 158 matrix :: Elt c => Int -> [c] -> Matrix c
 159 matrix n l = fromList (Z :. n :. n) l
 160
 161 -- | Two ways to get the rank (as documentation)
 162 --
 163 -- >>> rank (matrix 3 ([1..] :: [Int]))
 164 -- 2
 165 rank :: (Matrix a) -> Int
 166 rank m = arrayRank $ arrayShape m
 167
 168 -----------------------------------------------------------------------
 169 -- | Dimension of a square Matrix
 170 -- How to force use with SquareMatrix ?
 171 type Dim = Int
 172
 173 -- | Get Dimension of a square Matrix
 174 --
 175 -- >>> dim (matrix 3 ([1..] :: [Int]))
 176 -- 3
 177 dim :: Matrix a -> Dim
 178 dim m = n
 179   where
 180     Z :. _ :. n = arrayShape m
 181     -- indexTail (arrayShape m)
 182
 183 -----------------------------------------------------------------------
 184
 185 -- | Sum of a Matrix by Column
 186 --
 187 -- >>> run $ matSumCol 3 (use $ matrix 3 [1..])
 188 -- Matrix (Z :. 3 :. 3)
 189 --   [ 12.0, 15.0, 18.0,
 190 --     12.0, 15.0, 18.0,
 191 --     12.0, 15.0, 18.0]
 192 matSumCol :: (Elt a, P.Num (Exp a)) => Dim -> Acc (Matrix a) -> Acc (Matrix a)
 193 matSumCol r mat = replicate (constant (Z :. (r :: Int) :. All)) $ sum $ transpose mat
 194
 195 matSumCol' :: (Elt a, P.Num (Exp a)) => Matrix a -> Matrix a
 196 matSumCol' m = run $ matSumCol n m'
 197   where
 198     n  = dim m
 199     m' = use m
 200
 201
 202 -- | Proba computes de probability matrix: all cells divided by thee sum of its column
 203 -- if you need get the probability on the lines, just transpose it
 204 --
 205 -- >>> run $ matProba 3 (use $ matrix 3 [1..])
 206 -- Matrix (Z :. 3 :. 3)
 207 --   [ 8.333333333333333e-2, 0.13333333333333333, 0.16666666666666666,
 208 --       0.3333333333333333,  0.3333333333333333,  0.3333333333333333,
 209 --       0.5833333333333334,  0.5333333333333333,                 0.5]
 210 matProba :: Dim -> Acc (Matrix Double) -> Acc (Matrix Double)
 211 matProba d mat = zipWith (/) mat (matSumCol d mat)
 212
 213 -- | Diagonal of the matrix
 214 --
 215 -- >>> run $ diag (use $ matrix 3 ([1..] :: [Int]))
 216 -- Vector (Z :. 3) [1,5,9]
 217 diag :: Elt e
 218      => Acc (Matrix e)
 219      -> Acc (Vector e)
 220 diag m = backpermute (indexTail (shape m))
 221                      (lift1 (\(Z :. x) -> (Z :. x :. (x :: Exp Int))))
 222                      m
 223
 224 -- | Divide by the Diagonal of the matrix
 225 --
 226 -- >>> run $ divByDiag 3 (use $ matrix 3 ([1..] :: [Double]))
 227 -- Matrix (Z :. 3 :. 3)
 228 --   [ 1.0, 0.4, 0.3333333333333333,
 229 --     4.0, 1.0, 0.6666666666666666,
 230 --     7.0, 1.6,                1.0]
 231 divByDiag :: Dim -> Acc (Matrix Double) -> Acc (Matrix Double)
 232 divByDiag d mat = zipWith (/) mat (replicate (constant (Z :. (d :: Int) :. All)) $ diag mat)
 233
 234 -----------------------------------------------------------------------
 235 -- | Filters the matrix with the minimum of maximums
 236 --
 237 -- >>> run $ matMiniMax $ use $ matrix 3 [1..]
 238 -- Matrix (Z :. 3 :. 3)
 239 --   [ 0.0, 4.0, 7.0,
 240 --     0.0, 5.0, 8.0,
 241 --     0.0, 6.0, 9.0]
 242 matMiniMax :: (Elt a, Ord a, P.Num a)
 243            => Acc (Matrix a)
 244            -> Acc (Matrix a)
 245 matMiniMax m = filterWith' miniMax' (constant 0) m
 246   where
 247     miniMax' = the $ minimum $ maximum m
 248
 249
 250 -- | Filters the matrix with a constant
 251 --
 252 -- >>> run $ matFilter 5 $ use $ matrix 3 [1..]
 253 -- Matrix (Z :. 3 :. 3)
 254 --   [ 0.0, 0.0, 7.0,
 255 --     0.0, 0.0, 8.0,
 256 --     0.0, 6.0, 9.0]
 257 filter' :: Double -> Acc (Matrix Double) -> Acc (Matrix Double)
 258 filter' t m = filterWith t 0 m
 259
 260 filterWith :: Double -> Double -> Acc (Matrix Double) -> Acc (Matrix Double)
 261 filterWith t v m = map (\x -> ifThenElse (x > (constant t)) x (constant v)) (transpose m)
 262
 263 filterWith' :: (Elt a, Ord a) => Exp a -> Exp a -> Acc (Matrix a) -> Acc (Matrix a)
 264 filterWith' t v m = map (\x -> ifThenElse (x > t) x v) m
 265
 266
 267 ------------------------------------------------------------------------
 268 ------------------------------------------------------------------------
 269
 270
 271
 272 -- | TODO use Lenses
 273 data Direction = MatCol (Exp Int) | MatRow (Exp Int) | Diag
 274
 275 nullOf :: Num a => Dim -> Direction -> Acc (Matrix a)
 276 nullOf n' dir =
 277         let ones   = fill (index2 n n) 1
 278             zeros  = fill (index2 n n) 0
 279             n = constant n'
 280         in
 281         permute const ones ( lift1 ( \(Z :. (i :: Exp Int) :. (_j:: Exp Int))
 282                                                 -> case dir of
 283                                                      MatCol m -> (Z :. i :. m)
 284                                                      MatRow m -> (Z :. m :. i)
 285                                                      Diag     -> (Z :. i :. i)
 286                                    )
 287                            )
 288                            zeros
 289
 290 nullOfWithDiag :: Num a => Dim -> Direction -> Acc (Matrix a)
 291 nullOfWithDiag n dir = zipWith (*) (nullOf n dir) (nullOf n Diag)
 292
 293
 294 divide :: (Elt a, Ord a, P.Fractional (Exp a), P.Num a)
 295     => Acc (Matrix a) -> Acc (Matrix a) -> Acc (Matrix a)
 296 divide = zipWith divide'
 297   where
 298     divide' a b = ifThenElse (b > (constant 0))
 299                              (a / b)
 300                              (constant 0)
 301
 302 -- | Nominator
 303 sumRowMin :: (Num a, Ord a) => Dim -> Acc (Matrix a) -> Acc (Matrix a)
 304 sumRowMin n m = {-trace (P.show $ run m') $-} m'
 305   where
 306     m' = reshape (shape m) vs
 307     vs = P.foldl1 (++)
 308        $ P.map (\z -> sumRowMin1 n (constant z) m) [0..n-1]
 309
 310 sumRowMin1 :: (Num a, Ord a) => Dim -> Exp Int -> Acc (Matrix a) -> Acc (Vector a)
 311 sumRowMin1 n x m = trace (P.show (run m,run $ transpose m)) $ m''
 312   where
 313     m'' = sum $ zipWith min (transpose m) m
 314     _m'  = zipWith (*) (zipWith (*) (nullOf n (MatCol x)) $ nullOfWithDiag n (MatRow x)) m
 315
 316 -- | Denominator
 317 sumColMin :: (Num a, Ord a) => Dim -> Acc (Matrix a) -> Acc (Matrix a)
 318 sumColMin n m = reshape (shape m) vs
 319   where
 320     vs = P.foldl1 (++)
 321        $ P.map (\z -> sumColMin1 n (constant z) m) [0..n-1]
 322
 323
 324 sumColMin1 :: (Num a) => Dim -> Exp Int -> Acc (Matrix a) -> Acc (Matrix a)
 325 sumColMin1 n x m = zipWith (*) (nullOfWithDiag n (MatCol x)) m
 326
 327
 328
 329 {- | WIP fun with indexes
 330 selfMatrix :: Num a => Dim -> Acc (Matrix a)
 331 selfMatrix n' =
 332         let zeros = fill (index2 n n) 0
 333             ones  = fill (index2 n n) 1
 334             n = constant n'
 335         in
 336         permute const ones ( lift1 ( \(Z :. (i :: Exp Int) :. (_j:: Exp Int))
 337                                                 -> -- ifThenElse (i /= j)
 338                                                      --         (Z :. i :. j)
 339                                                               (Z :. i :. i)
 340                                     )) zeros
 341
 342 selfMatrix' :: (Elt a, P.Num (Exp a)) => Array DIM2 a -> Matrix a
 343 selfMatrix' m' = run $ selfMatrix n
 344   where
 345     n = dim m'
 346     m = use m'
 347 -}
 348 -------------------------------------------------
 349 -------------------------------------------------
 350 crossProduct :: Dim -> Acc (Matrix Double) -> Acc (Matrix Double)
 351 crossProduct n m = {-trace (P.show (run m',run m'')) $-} zipWith (*) m' m''
 352   where
 353     m'  = cross n m
 354     m'' = transpose $ cross n m
 355
 356
 357 crossT :: Matrix Double -> Matrix Double
 358 crossT  = run . transpose . use
 359
 360 crossProduct' :: Matrix Double -> Matrix Double
 361 crossProduct' m = run $ crossProduct n m'
 362   where
 363     n  = dim m
 364     m' = use m
 365
 366 runWith :: (Arrays c, Elt a1)
 367         => (Dim -> Acc (Matrix a1) -> a2 -> Acc c)
 368         -> Matrix a1
 369         -> a2
 370         -> c
 371 runWith f m = run . f (dim m) (use m)
 372
 373 -- | cross
 374 cross :: Dim -> Acc (Matrix Double) -> Acc (Matrix Double)
 375 cross n mat = diagNull n (matSumCol n $ diagNull n mat)
 376
 377 cross' :: Matrix Double -> Matrix Double
 378 cross' mat = run $ cross n mat'
 379   where
 380     mat' = use mat
 381     n    = dim mat
 382
 383
 384 {-
 385 -- | Hypothesis to test maybe later (or not)
 386 -- TODO ask accelerate for instances to ease such writtings:
 387 p_ :: (Elt e, P.Fractional (Exp e)) => Acc (Array DIM2 e) -> Acc (Array DIM2 e)
 388 p_ m = zipWith (/) m (n_ m)
 389   where
 390     n_ :: Elt e => Acc (SymetricMatrix e) -> Acc (Matrix e)
 391     n_ m = backpermute (shape m)
 392                          (lift1 ( \(Z :. (i :: Exp Int) :. (j:: Exp Int))
 393                                    -> (ifThenElse (i < j) (lift (Z :. j :. j)) (lift (Z :. i :. i)) :: Exp DIM2)
 394                                 )
 395                          ) m
 396 -}
 397
 398 theMatrixDouble :: Int -> Matrix Double
 399 theMatrixDouble n = run $ map fromIntegral (use $ theMatrixInt n)
 400
 401 theMatrixInt :: Int -> Matrix Int
 402 theMatrixInt n = matrix n (dataMatrix n)
 403   where
 404     dataMatrix :: Int -> [Int]
 405     dataMatrix x | (P.==) x 2 = [ 1, 1
 406                                 , 1, 2
 407                                 ]
 408
 409                  | (P.==) x 3 =  [ 1, 1, 2
 410                                  , 1, 2, 3
 411                                  , 2, 3, 4
 412                                  ]
 413                  | (P.==) x 4 =  [ 1, 1, 2, 3
 414                                  , 1, 2, 3, 4
 415                                  , 2, 3, 4, 5
 416                                  , 3, 4, 5, 6
 417                                  ]
 418                  | P.otherwise = P.undefined
 419
 420 {-
 421 theResult :: Int -> Matrix Double
 422 theResult n | (P.==) n 2 = let r = 1.6094379124341003 in [ 0, r, r, 0]
 423           | P.otherwise = [ 1, 1 ]
 424 -}
 425
 426
 427 colMatrix :: Elt e
 428           => Int -> [e] -> Acc (Array ((Z :. Int) :. Int) e)
 429 colMatrix n ns = replicate (constant (Z :. (n :: Int) :. All)) v
 430   where
 431     v = use $ vector (P.length ns) ns
 432
 433 -----------------------------------------------------------------------
 434