47340db · laop · git.iko.soy

git.iko.soy/laop

Added inefficient row and column implementations

commit47340db5d2ce89631021e897be5c9d0f460b3e16 authoriko <ilyakooo0@gmail.com> dateSun 10 May 2020, 00:06 (6 years ago) parent87fd633

2 files changed+74−46

compare with master

unifiedsplit

src/LAoP/Matrix/Internal.hs+34−18 src/LAoP/Matrix/Type.hs+40−28

src/LAoP/Matrix/Internal.hs+34−18

@@ -30,7 +30,7 @@

3030-- motivation behind the library, the underlying theory, and implementation details.

3131--

3232-- This module offers many of the combinators mentioned in the work of

33−-- Macedo (2012) and Oliveira (2012).

33+-- Macedo (2012) and Oliveira (2012).

3434--

3535-- This is an Internal module and it is no supposed to be imported.

3636--

@@ -43,8 +43,8 @@ module LAoP.Matrix.Internal

4343 --

4444 -- There exists two type families that make it easier to write

4545 -- matrix dimensions: 'FromNat' and 'Count'. This approach

46− -- leads to a very straightforward implementation

47− -- of LAoP combinators.

46+ -- leads to a very straightforward implementation

47+ -- of LAoP combinators.

4848

4949 -- * Type safe matrix representation

5050 Matrix (..),

@@ -86,7 +86,9 @@ module LAoP.Matrix.Internal

8686 -- * Misc

8787 -- ** Get dimensions

8888 columns,

89+ columns',

8990 rows,

91+ rows',

9092

9193 -- ** Matrix Transposition

9294 tr,

@@ -334,7 +336,7 @@ instance {-# OVERLAPPING #-} (FromLists () rows) => FromLists () (Either () rows

334336 fromLists _ = error "Wrong dimensions"

335337

336338instance {-# OVERLAPPABLE #-} (FromLists () a, FromLists () b, Countable a) => FromLists () (Either a b) where

337− fromLists l@([_] : _) =

339+ fromLists l@([_] : _) =

338340 let rowsA = fromInteger (natVal (Proxy :: Proxy (Count a)))

339341 in Fork (fromLists (take rowsA l)) (fromLists (drop rowsA l))

340342 fromLists _ = error "Wrong dimensions"

@@ -510,7 +512,7 @@ comp (Join a b) (Fork c d) = comp a c + comp b d -- Divide-and-conquer l

510512comp (Fork a b) c = Fork (comp a c) (comp b c) -- Fork fusion law

511513comp c (Join a b) = Join (comp c a) (comp c b) -- Join fusion law

512514{-# NOINLINE comp #-}

513−{-# RULES

515+{-# RULES

514516 "comp/iden1" forall m. comp m iden = m ;

515517 "comp/iden2" forall m. comp iden m = m

516518#-}

@@ -557,24 +559,38 @@ i2 = tr p2

557559

558560-- | Obtain the number of rows.

559561--

560−-- NOTE: The 'KnownNat' constaint is needed in order to obtain the

561−-- dimensions in constant time.

562−--

563−-- TODO: A 'rows' function that does not need the 'KnownNat' constraint in

564−-- exchange for performance.

562+-- NOTE: The 'KnownNat' constraint is needed in order to obtain the

563+-- dimensions in constant time. For a version that doesn't require the

564+-- constraint see 'rows''.

565565rows :: forall e cols rows. (Countable rows) => Matrix e cols rows -> Int

566566rows _ = fromInteger $ natVal (Proxy :: Proxy (Count rows))

567567

568+-- | Obtain the number of rows in an inefficient manner, but without any

569+-- constraints.

570+--

571+-- For a more efficient version see 'rows'.

572+rows' :: Matrix e cols rows -> Int

573+rows' (One _) = 1

574+rows' (Join lhs _) = rows' lhs

575+rows' (Fork top bottom) = rows' top + rows' bottom

576+

568577-- | Obtain the number of columns.

569−--

570−-- NOTE: The 'KnownNat' constaint is needed in order to obtain the

571−-- dimensions in constant time.

572578--

573−-- TODO: A 'columns' function that does not need the 'KnownNat' constraint in

574−-- exchange for performance.

579+-- NOTE: The 'KnownNat' constraint is needed in order to obtain the

580+-- dimensions in constant time. For a version that doesn't require the

581+-- constraint see 'columns''.

575582columns :: forall e cols rows. (Countable cols) => Matrix e cols rows -> Int

576583columns _ = fromInteger $ natVal (Proxy :: Proxy (Count cols))

577584

585+-- | Obtain the number of columns in an inefficient manner, but without any

586+-- constraints.

587+--

588+-- For a more efficient version see 'columns'.

589+columns' :: Matrix e cols rows -> Int

590+columns' (One _) = 1

591+columns' (Join lhs rhs) = columns' lhs + columns' rhs

592+columns' (Fork top _) = columns' top

593+

578594-- Coproduct Bifunctor

579595

580596infixl 5 -|-

@@ -629,7 +645,7 @@ sndM = matrixBuilder' f

629645-- | Khatri Rao Matrix product also known as matrix pairing.

630646--

631647-- NOTE: That this is not a true categorical product, see for instance:

632−--

648+--

633649-- @

634650-- | fstM . kr a b == a

635651-- kr a b ==> |

@@ -665,7 +681,7 @@ infixl 4 ><

665681 FL (Normalize (m, n)) n,

666682 FL (Normalize (p, q)) p,

667683 FL (Normalize (p, q)) q

668− )

684+ )

669685 => Matrix e m p -> Matrix e n q -> Matrix e (Normalize (m, n)) (Normalize (p, q))

670686(><) a b =

671687 let fstM' = fstM @e @m @n

@@ -988,7 +1004,7 @@ toRel ::

9881004 Eq b,

9891005 CountableDimsN a b,

9901006 FLN b a

991− )

1007+ )

9921008 => (a -> b -> Bool) -> Relation (Normalize a) (Normalize b)

9931009toRel f =

9941010 let minA = minBound @a

src/LAoP/Matrix/Type.hs+40−28

@@ -104,8 +104,8 @@ module LAoP.Matrix.Type

104104 multM,

105105

106106 -- * Selective equivalent instance function

107− selectM,

108−

107+ selectM,

108+

109109 -- * Monad equivalent instance function

110110 returnM,

111111 bindM,

@@ -113,7 +113,9 @@ module LAoP.Matrix.Type

113113 -- * Misc

114114 -- ** Get dimensions

115115 columns,

116+ columns',

116117 rows,

118+ rows',

117119

118120 -- ** Matrix Transposition

119121 tr,

@@ -265,7 +267,7 @@ infixl 2 ===

265267-- Functor hierarchy

266268

267269-- | Functor instance equivalent function

268−fmapM ::

270+fmapM ::

269271 ( Liftable e a b,

270272 CountableDimsN a b,

271273 FLN b a

@@ -279,7 +281,7 @@ unitM :: (Num e) => Matrix e () ()

279281unitM = one 1

280282

281283-- | Applicative instance equivalent 'unit' function,

282−multM ::

284+multM ::

283285 ( CountableDimsN a b,

284286 CountableN (a, b),

285287 Num e,

@@ -290,8 +292,8 @@ multM ::

290292multM = kr

291293

292294-- | Monad instance equivalent 'return' function,

293−returnM ::

294− forall e a .

295+returnM ::

296+ forall e a .

295297 ( Num e,

296298 Enum e,

297299 Enum a,

@@ -387,7 +389,7 @@ toList (M m) = I.toList m

387389

388390-- | The zero matrix. A matrix wholly filled with zeros.

389391zeros ::

390− (Num e, FLN cols rows, CountableDimsN cols rows)

392+ (Num e, FLN cols rows, CountableDimsN cols rows)

391393 => Matrix e cols rows

392394zeros = M I.zeros

393395

@@ -397,7 +399,7 @@ zeros = M I.zeros

397399--

398400-- Also known as T (Top) matrix.

399401ones ::

400− (Num e, FLN cols rows, CountableDimsN cols rows)

402+ (Num e, FLN cols rows, CountableDimsN cols rows)

401403 => Matrix e cols rows

402404ones = M I.ones

403405

@@ -406,7 +408,7 @@ ones = M I.ones

406408-- | The constant matrix constructor. A matrix wholly filled with a given

407409-- value.

408410constant ::

409− (Num e, FLN cols rows, CountableDimsN cols rows)

411+ (Num e, FLN cols rows, CountableDimsN cols rows)

410412 => e -> Matrix e cols rows

411413constant = M . I.constant

412414

@@ -420,7 +422,7 @@ bang ::

420422bang = M I.bang

421423

422424-- | Point constant relation

423−point ::

425+point ::

424426 ( Bounded a,

425427 Enum a,

426428 Eq a,

@@ -449,7 +451,7 @@ iden = M I.iden

449451comp :: (Num e) => Matrix e cr rows -> Matrix e cols cr -> Matrix e cols rows

450452comp (M a) (M b) = M (I.comp a b)

451453{-# NOINLINE comp #-}

452−{-# RULES

454+{-# RULES

453455 "comp/iden1" forall m. comp m iden = m ;

454456 "comp/iden2" forall m. comp iden m = m

455457#-}

@@ -514,24 +516,34 @@ i2 = tr p2

514516

515517-- | Obtain the number of rows.

516518--

517−-- NOTE: The 'KnownNat' constaint is needed in order to obtain the

518−-- dimensions in constant time.

519−--

520−-- TODO: A 'rows' function that does not need the 'KnownNat' constraint in

521−-- exchange for performance.

519+-- NOTE: The 'KnownNat' constraint is needed in order to obtain the

520+-- dimensions in constant time. For a version that doesn't require the

521+-- constraint see 'rows''.

522522rows :: (CountableN rows) => Matrix e cols rows -> Int

523523rows (M m) = I.rows m

524524

525+-- | Obtain the number of rows in an inefficient manner, but without any

526+-- constraints.

527+--

528+-- For a more efficient version see 'rows'.

529+rows' :: Matrix e cols rows -> Int

530+rows' (M m) = I.rows' m

531+

525532-- | Obtain the number of columns.

526−--

527−-- NOTE: The 'KnownNat' constaint is needed in order to obtain the

528−-- dimensions in constant time.

529533--

530−-- TODO: A 'columns' function that does not need the 'KnownNat' constraint in

531−-- exchange for performance.

534+-- NOTE: The 'KnownNat' constraint is needed in order to obtain the

535+-- dimensions in constant time. For a version that doesn't require the

536+-- constraint see 'columns''.

532537columns :: (CountableN cols) => Matrix e cols rows -> Int

533538columns (M m) = I.columns m

534539

540+-- | Obtain the number of columns in an inefficient manner, but without any

541+-- constraints.

542+--

543+-- For a more efficient version see 'columns'.

544+columns' :: Matrix e cols rows -> Int

545+columns' (M m) = I.columns' m

546+

535547-- Coproduct Bifunctor

536548

537549infixl 5 -|-

@@ -553,7 +565,7 @@ infixl 5 -|-

553565-- Khatri Rao Product and projections

554566

555567-- | Khatri Rao product first component projection matrix.

556−fstM ::

568+fstM ::

557569 forall e m k .

558570 ( Num e,

559571 CountableDimsN m k,

@@ -564,7 +576,7 @@ fstM ::

564576fstM = M (I.fstM @e @(I.Normalize m) @(I.Normalize k))

565577

566578-- | Khatri Rao product second component projection matrix.

567−sndM ::

579+sndM ::

568580 forall e m k.

569581 ( Num e,

570582 CountableDimsN k m,

@@ -577,9 +589,9 @@ sndM = M (I.sndM @e @(I.Normalize m) @(I.Normalize k))

577589-- | Khatri Rao Matrix product also known as matrix pairing.

578590--

579591-- NOTE: That this is not a true categorical product, see for instance:

580−--

592+--

581593-- @

582−-- | fstM . kr a b == a

594+-- | fstM . kr a b == a

583595-- kr a b ==> |

584596-- | sndM . kr a b == b

585597-- @

@@ -625,7 +637,7 @@ infixl 4 ><

625637-- Matrix abide Join Fork

626638

627639-- | Matrix "abiding" followin the 'Join'-'Fork' abide law.

628−--

640+--

629641-- Law:

630642--

631643-- @

@@ -637,7 +649,7 @@ abideJF (M m) = M (I.abideJF m)

637649-- Matrix abide Fork Join

638650

639651-- | Matrix "abiding" followin the 'Fork'-'Join' abide law.

640−--

652+--

641653-- Law:

642654--

643655-- @

@@ -656,7 +668,7 @@ tr (M m) = M (I.tr m)

656668

657669-- | Selective functors 'select' operator equivalent inspired by the

658670-- ArrowMonad solution presented in the paper.

659−selectM ::

671+selectM ::

660672 ( Num e,

661673 FLN b b,

662674 CountableN b