10f021a · laop · git.iko.soy

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Merge branch 'master' of https://github.com/bolt12/laop

10f021aArmando Santos6 years ago

src/LAoP/Matrix/Internal.hs+34−18

compare with master

unifiedsplit

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

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

31--

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

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

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

34--

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

36--

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

43 --

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

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

46− -- leads to a very straightforward implementation

46+ -- leads to a very straightforward implementation

47− -- of LAoP combinators.

47+ -- of LAoP combinators.

49 -- * Type safe matrix representation

50 Matrix (..),

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

86 -- * Misc

87 -- ** Get dimensions

88 columns,

89+ columns',

89 rows,

90 rows,

91+ rows',

91 -- ** Matrix Transposition

93 -- ** Matrix Transposition

92 tr,

94 tr,

@@ -335,7 +337,7 @@ instance (FromLists () rows) => FromLists () (Either () rows) where

335 fromLists _ = error "Wrong dimensions"

337 fromLists _ = error "Wrong dimensions"

336

338

337instance {-# OVERLAPPABLE #-} (FromLists () a, FromLists () b, Countable a) => FromLists () (Either a b) where

339instance {-# OVERLAPPABLE #-} (FromLists () a, FromLists () b, Countable a) => FromLists () (Either a b) where

338− fromLists l@([_] : _) =

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

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

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

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

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

341 fromLists _ = error "Wrong dimensions"

343 fromLists _ = error "Wrong dimensions"

@@ -511,7 +513,7 @@ comp (Join a b) (Fork c d) = comp a c + comp b d -- Divide-and-conquer l

511comp (Fork a b) c = Fork (comp a c) (comp b c) -- Fork fusion law

513comp (Fork a b) c = Fork (comp a c) (comp b c) -- Fork fusion law

512comp c (Join a b) = Join (comp c a) (comp c b) -- Join fusion law

514comp c (Join a b) = Join (comp c a) (comp c b) -- Join fusion law

513{-# NOINLINE comp #-}

515{-# NOINLINE comp #-}

514−{-# RULES

516+{-# RULES

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

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

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

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

517#-}

519#-}

@@ -558,24 +560,38 @@ i2 = tr p2

558

560

559-- | Obtain the number of rows.

561-- | Obtain the number of rows.

560--

562--

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

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

562−-- dimensions in constant time.

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

563−--

565+-- constraint see 'rows''.

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

565−-- exchange for performance.

566rows :: forall e cols rows. (Countable rows) => Matrix e cols rows -> Int

567rows _ = fromInteger $ natVal (Proxy :: Proxy (Count rows))

568

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

570+-- constraints.

571+--

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

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

574+rows' (One _) = 1

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

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

577+

569-- | Obtain the number of columns.

578-- | Obtain the number of columns.

570−--

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

572−-- dimensions in constant time.

573--

579--

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

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

575−-- exchange for performance.

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

582+-- constraint see 'columns''.

576columns :: forall e cols rows. (Countable cols) => Matrix e cols rows -> Int

583columns :: forall e cols rows. (Countable cols) => Matrix e cols rows -> Int

577columns _ = fromInteger $ natVal (Proxy :: Proxy (Count cols))

584columns _ = fromInteger $ natVal (Proxy :: Proxy (Count cols))

578

585

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

587+-- constraints.

588+--

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

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

591+columns' (One _) = 1

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

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

594+

579-- Coproduct Bifunctor

595-- Coproduct Bifunctor

580

596

581infixl 5 -|-

597infixl 5 -|-

@@ -630,7 +646,7 @@ sndM = matrixBuilder' f

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

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

631--

647--

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

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

633−--

649+--

634-- @

650-- @

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

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

636-- kr a b ==> |

652-- kr a b ==> |

@@ -666,7 +682,7 @@ infixl 4 ><

666 FL (Normalize (m, n)) n,

682 FL (Normalize (m, n)) n,

667 FL (Normalize (p, q)) p,

683 FL (Normalize (p, q)) p,

668 FL (Normalize (p, q)) q

684 FL (Normalize (p, q)) q

669− )

685+ )

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

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

671(><) a b =

687(><) a b =

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

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

@@ -989,7 +1005,7 @@ toRel ::

989 Eq b,

1005 Eq b,

990 CountableDimsN a b,

1006 CountableDimsN a b,

991 FLN b a

1007 FLN b a

992− )

1008+ )

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

1009 => (a -> b -> Bool) -> Relation (Normalize a) (Normalize b)

994toRel f =

1010toRel f =

995 let minA = minBound @a

1011 let minA = minBound @a

src/LAoP/Matrix/Type.hs+40−28

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

104 multM,

105

106 -- * Selective equivalent instance function

107− selectM,

107+ selectM,

108−

108+

109 -- * Monad equivalent instance function

110 returnM,

111 bindM,

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

113 -- * Misc

114 -- ** Get dimensions

115 columns,

116+ columns',

116 rows,

117 rows,

118+ rows',

117

119

118 -- ** Matrix Transposition

120 -- ** Matrix Transposition

119 tr,

121 tr,

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

265-- Functor hierarchy

267-- Functor hierarchy

266

268

267-- | Functor instance equivalent function

269-- | Functor instance equivalent function

268−fmapM ::

270+fmapM ::

269 ( Liftable e a b,

271 ( Liftable e a b,

270 CountableDimsN a b,

272 CountableDimsN a b,

271 FLN b a

273 FLN b a

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

279unitM = one 1

281unitM = one 1

280

282

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

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

282−multM ::

284+multM ::

283 ( CountableDimsN a b,

285 ( CountableDimsN a b,

284 CountableN (a, b),

286 CountableN (a, b),

285 Num e,

287 Num e,

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

290multM = kr

292multM = kr

291

293

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

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

293−returnM ::

295+returnM ::

294− forall e a .

296+ forall e a .

295 ( Num e,

297 ( Num e,

296 Enum e,

298 Enum e,

297 Enum a,

299 Enum a,

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

387

389

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

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

389zeros ::

391zeros ::

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

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

391 => Matrix e cols rows

393 => Matrix e cols rows

392zeros = M I.zeros

394zeros = M I.zeros

393

395

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

397--

399--

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

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

399ones ::

401ones ::

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

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

401 => Matrix e cols rows

403 => Matrix e cols rows

402ones = M I.ones

404ones = M I.ones

403

405

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

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

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

407-- value.

409-- value.

408constant ::

410constant ::

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

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

410 => e -> Matrix e cols rows

412 => e -> Matrix e cols rows

411constant = M . I.constant

413constant = M . I.constant

412

414

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

420bang = M I.bang

422bang = M I.bang

421

423

422-- | Point constant relation

424-- | Point constant relation

423−point ::

425+point ::

424 ( Bounded a,

426 ( Bounded a,

425 Enum a,

427 Enum a,

426 Eq a,

428 Eq a,

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

449comp :: (Num e) => Matrix e cr rows -> Matrix e cols cr -> Matrix e cols rows

451comp :: (Num e) => Matrix e cr rows -> Matrix e cols cr -> Matrix e cols rows

450comp (M a) (M b) = M (I.comp a b)

452comp (M a) (M b) = M (I.comp a b)

451{-# NOINLINE comp #-}

453{-# NOINLINE comp #-}

452−{-# RULES

454+{-# RULES

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

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

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

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

455#-}

457#-}

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

514

516

515-- | Obtain the number of rows.

517-- | Obtain the number of rows.

516--

518--

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

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

518−-- dimensions in constant time.

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

519−--

521+-- constraint see 'rows''.

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

521−-- exchange for performance.

522rows :: (CountableN rows) => Matrix e cols rows -> Int

523rows (M m) = I.rows m

524

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+

525-- | Obtain the number of columns.

532-- | Obtain the number of columns.

526−--

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

528−-- dimensions in constant time.

529--

533--

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

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

531−-- exchange for performance.

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

536+-- constraint see 'columns''.

532columns :: (CountableN cols) => Matrix e cols rows -> Int

537columns :: (CountableN cols) => Matrix e cols rows -> Int

533columns (M m) = I.columns m

538columns (M m) = I.columns m

534

539

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+

535-- Coproduct Bifunctor

547-- Coproduct Bifunctor

536

548

537infixl 5 -|-

549infixl 5 -|-

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

553-- Khatri Rao Product and projections

565-- Khatri Rao Product and projections

554

566

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

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

556−fstM ::

568+fstM ::

557 forall e m k .

569 forall e m k .

558 ( Num e,

570 ( Num e,

559 CountableDimsN m k,

571 CountableDimsN m k,

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

564fstM = M (I.fstM @e @(I.Normalize m) @(I.Normalize k))

576fstM = M (I.fstM @e @(I.Normalize m) @(I.Normalize k))

565

577

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

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

567−sndM ::

579+sndM ::

568 forall e m k.

580 forall e m k.

569 ( Num e,

581 ( Num e,

570 CountableDimsN k m,

582 CountableDimsN k m,

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

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

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

578--

590--

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

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

580−--

592+--

581-- @

593-- @

582−-- | fstM . kr a b == a

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

583-- kr a b ==> |

595-- kr a b ==> |

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

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

585-- @

597-- @

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

625-- Matrix abide Join Fork

637-- Matrix abide Join Fork

626

638

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

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

628−--

640+--

629-- Law:

641-- Law:

630--

642--

631-- @

643-- @

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

637-- Matrix abide Fork Join

649-- Matrix abide Fork Join

638

650

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

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

640−--

652+--

641-- Law:

653-- Law:

642--

654--

643-- @

655-- @

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

656

668

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

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

658-- ArrowMonad solution presented in the paper.

670-- ArrowMonad solution presented in the paper.

659−selectM ::

671+selectM ::

660 ( Num e,

672 ( Num e,

661 FLN b b,

673 FLN b b,

662 CountableN b

674 CountableN b