on 7bbce48 help sign in
.ghc.environment.x86_64-linux-8.6.5new file+17
since splitsnapshots
unifiedsplit
@@ -0,0 +1,17 @@
1+-- This is a GHC environment file written by cabal. This means you can
2+-- run ghc or ghci and get the environment of the project as a whole.
3+-- But you still need to use cabal repl $target to get the environment
4+-- of specific components (libs, exes, tests etc) because each one can
5+-- have its own source dirs, cpp flags etc.
6+--
7+clear-package-db
8+global-package-db
9+package-db /home/bolt/.cabal/store/ghc-8.6.5/package.db
10+package-db packagedb/ghc-8.6.5
11+package-id laop-0.1.0.0-inplace
12+package-id base-4.12.0.0
13+package-id ghc-prim-0.5.3
14+package-id rts
15+package-id integer-gmp-1.0.2.0
16+package-id deepseq-1.4.4.0
17+package-id array-0.5.3.0
.github/workflows/ci.ymldeleted−43
@@ -1,43 +0,0 @@
1−name: CI
2−
3−# Trigger the workflow on push or pull request, but only for the master branch
4−on:
5− pull_request:
6− push:
7− branches: [master]
8−
9−jobs:
10− build:
11− name: ghc ${{ matrix.ghc }}
12− runs-on: ubuntu-16.04
13− strategy:
14− matrix:
15− cabal: ["3.0"]
16− ghc:
17− - "8.6.5"
18− - "8.8.3"
19−
20− steps:
21− - uses: actions/checkout@v2
22− if: github.event.action == 'opened' || github.event.action == 'synchronize' || github.event.ref == 'refs/heads/master'
23−
24− - uses: actions/setup-haskell@v1
25− name: Setup Haskell
26− with:
27− ghc-version: ${{ matrix.ghc }}
28− cabal-version: ${{ matrix.cabal }}
29−
30− - uses: actions/cache@v1
31− name: Cache ~/.cabal/store
32− with:
33− path: ~/.cabal/store
34− key: ${{ runner.os }}-${{ matrix.ghc }}-cabal
35−
36− - name: Build
37− run: |
38− cabal v2-update
39− cabal v2-build --enable-tests --enable-benchmarks
40−
41− - name: Test
42− run: |
43− cabal v2-test --enable-tests
.gitignore+2−54
@@ -1,55 +1,3 @@
1−### Haskell
2−dist
3−dist-*
4−cabal-dev
5−*.o
6−*.hi
7−*.chi
8−*.chs.h
9−*.dyn_o
10−*.dyn_hi
11−*.prof
12−*.aux
13−*.hp
14−*.eventlog
15−.virtualenv
16−.hsenv
17−.hpc
18−.cabal-sandbox/
19−cabal.sandbox.config
20−cabal.config
21−cabal.project.local
22−.ghc.environment.*
23−.HTF/
24−# Stack
25.stack-work/
1.stack-work/
26−stack.yaml.lock
2+laop.cabal
27−
28−### IDE/support
29−# Vim
30−[._]*.s[a-v][a-z]
31−[._]*.sw[a-p]
32−[._]s[a-v][a-z]
33−[._]sw[a-p]
34−*~
3+*~
35−tags
36−
37−# IntellijIDEA
38−.idea/
39−.ideaHaskellLib/
40−*.iml
41−
42−# Atom
43−.haskell-ghc-mod.json
44−
45−# VS
46−.vscode/
47−
48−# Emacs
49−*#
50−.dir-locals.el
51−TAGS
52−
53−# other
54−.DS_Store
55−hackage.sh
.travis.ymldeleted−47
@@ -1,47 +0,0 @@
1−sudo: true
2−language: haskell
3−
4−git:
5− depth: 5
6−
7−cabal: "3.0"
8−
9−cache:
10− directories:
11− - "$HOME/.cabal/store"
12− - "$HOME/.stack"
13− - "$TRAVIS_BUILD_DIR/.stack-work"
14−
15−matrix:
16− include:
17− - ghc: 8.6.5
18− - ghc: 8.8.3
19−
20− - ghc: 8.8.3
21− env: STACK_YAML="$TRAVIS_BUILD_DIR/stack-8.8.3.yaml"
22−
23− - ghc: 8.6.5
24− env: STACK_YAML="$TRAVIS_BUILD_DIR/stack.yaml"
25−
26−
27−install:
28− - |
29− if [ -z "$STACK_YAML" ]; then
30− cabal v2-update
31− cabal v2-build --enable-tests --enable-benchmarks
32− else
33− curl -sSL https://get.haskellstack.org/ | sh
34− stack --version
35− stack build --system-ghc --test --bench --no-run-tests --no-run-benchmarks
36− fi
37−
38−script:
39− - |
40− if [ -z "$STACK_YAML" ]; then
41− cabal v2-test --enable-tests
42− else
43− stack test --system-ghc
44− fi
45−
46−notifications:
47− email: false
CHANGELOG.mddeleted−17
@@ -1,17 +0,0 @@
1−# Changelog
2−
3−`laop` uses [PVP Versioning][1].
4−The changelog is available [on GitHub][2].
5−
6−## 0.1.1.1
7−
8−* Bump base version to work with cabal
9−
10−## 0.1.1.0
11−
12−* Package is more organized and now has tests and benchmarks separated
13−* Repository is more organized and clean
14−* Added CI
15−
16−[1]: https://pvp.haskell.org
17−[2]: https://github.com/bolt12/laop2/releases
ChangeLog.mdnew file+3
@@ -0,0 +1,3 @@
1+# Changelog for laop
2+
3+## Unreleased changes
LICENSE+26−17
@@ -1,21 +1,30 @@
1−MIT License
1+Copyright Armando Santos (c) 2019
2
2
3−Copyright (c) 2020 Armando Santos
3+All rights reserved.
4
4
5−Permission is hereby granted, free of charge, to any person obtaining a copy
5+Redistribution and use in source and binary forms, with or without
6−of this software and associated documentation files (the "Software"), to deal
7−in the Software without restriction, including without limitation the rights
8−to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
9−copies of the Software, and to permit persons to whom the Software is
10−furnished to do so, subject to the following conditions:
6+modification, are permitted provided that the following conditions are met:
11
7
12−The above copyright notice and this permission notice shall be included in all
8+ * Redistributions of source code must retain the above copyright
13−copies or substantial portions of the Software.
9+ notice, this list of conditions and the following disclaimer.
14
10
15−THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
11+ * Redistributions in binary form must reproduce the above
12+ copyright notice, this list of conditions and the following
13+ disclaimer in the documentation and/or other materials provided
14+ with the distribution.
15+
16+ * Neither the name of Armando Santos nor the names of other
17+ contributors may be used to endorse or promote products derived
18+ from this software without specific prior written permission.
19+
20+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
21+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
16−IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
22+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
17−FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
23+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
18−AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
24+OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
25+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
26+LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
27+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
19−LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
28+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
20−OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
29+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
21−SOFTWARE.
30+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
README.md+27−35
@@ -1,11 +1,5 @@
1# laop - Linear Algebra of Programming library
1# laop - Linear Algebra of Programming library
2
2
3−[![GitHub CI](https://github.com/bolt12/laop/workflows/CI/badge.svg)](https://github.com/bolt12/laop/actions)
4−[![Build status](https://img.shields.io/travis/bolt12/laop.svg?logo=travis)](https://travis-ci.org/bolt12/laop)
5−[![Hackage](https://img.shields.io/hackage/v/laop.svg?logo=haskell)](https://hackage.haskell.org/package/laop)
6−[![Stackage Lts](http://stackage.org/package/laop/badge/lts)](http://stackage.org/lts/package/laop)
7−[![Stackage Nightly](http://stackage.org/package/laop/badge/nightly)](http://stackage.org/nightly/package/laop)
8−
9The LAoP discipline generalises relations and functions treating them as
3The LAoP discipline generalises relations and functions treating them as
10Boolean matrices and in turn consider these as arrows.
4Boolean matrices and in turn consider these as arrows.
11
5
@@ -16,38 +10,36 @@ motivation behind the library, the underlying theory, and implementation details
16This module offers many of the combinators mentioned in the work of
10This module offers many of the combinators mentioned in the work of
17[Macedo (2012)](https://repositorium.sdum.uminho.pt/handle/1822/22894) and [Oliveira (2012)](https://pdfs.semanticscholar.org/ccf5/27fa9179081223bffe8067edd81948644fc0.pdf).
11[Macedo (2012)](https://repositorium.sdum.uminho.pt/handle/1822/22894) and [Oliveira (2012)](https://pdfs.semanticscholar.org/ccf5/27fa9179081223bffe8067edd81948644fc0.pdf).
18
12
19−See the package in hackage [here](https://hackage.haskell.org/package/laop-0.1.1.0)
13+See the candidate package in hackage [here](https://hackage.haskell.org/package/laop-0.1.0.0)
20−
21−A Functional Pearl has been written and can be regarded as the [reference document](https://github.com/bolt12/tymfgg-pearl) for this library.
22
14
23## Features
15## Features
24
16
25−This library offers 3 main matrix programming modules:
17+This library offers:
26−
18+
27−- One in which matrices are typed with type level natural numbers;
19+- An internal module representation that uses normal datatypes (`Void`, `()`, `Either`) for matrix dimensions and two
28−- One in which matrices are typed with arbitrary generic data types;
20+ type families `FromNat` and `Count` to make it easier to work with these type of matrices.
29−- One in which matrices are regarded as relations, i.e. boolean matrices;
21+- An interfacing module that uses generalised types for the dimensions and is just a newtype wrapper
30−
22+ around the internal matrix data type.
31−There's also an experimental module that uses matrices to represent probability
23+- An interfacing module that uses type level naturals for the dimensions and is just a newtype wrapper
32−distributions.
24+ around the internal matrix data type.
33−
25+- An interfacing module that restricts the matrix contents to being only 0's or 1's (True
34−The most interesting feature is that matrices are represented as an inductive data type.
26+ and False). This module is called 'Relation' and offers many of the combinators seen in
35−Given this formulation, matrix algorithms can be expressed in a much more elegant and
27+ AoP and Relational Calculus/Algebra.
36−calculational style than the traditional vector of vectors representation. This data type
28+- A very simple Probabilistic Programming module and several functions and data types to
37−guarantees that a matrix will always have valid dimensions. It can also express block matrix
29+ make it easier to deal with sample space.
38−computations naturally, which leads to total, efficient and statically typed manipulation
30+
39−and transformation functions.
31+Given this, this new matrix formulation compared to other libraries one has much more advantages, such as:
40−
32+
41−Like matrix multiplication, other common operations, such as matrix transposition, benefit from a block-oriented structure that leads to a simple and natural divide-and-conquer algorithmic solution. Performance wise, this means that without much effort we can obtain optimal cache-oblivious algorithms.
33+- Has an inductive definition enabling writing matrix manipulation functions in a much more elegant and calculational way;
42−
34+- Statically typed dimensions;
43−Given this, this new matrix formulation compared to other libraries:
35+- Polymorphic data type dimensions;
44−
36+- Polymorphic matrix content;
45−- Is more compositional and polymorphic and does not have partial matrix manipulation functions (hence less chances for usage errors);
37+- Awesome dimension type inference;
46−- Our implementation of matrices enables simple manipulation of submatrices, making it particularly suitable for formal verification and equation reasoning, using the mathematical framework defined by the linear algebra of programming. Furthermore, the data type constructors ensure that the matrices of this kind are sound, i.e. malformed matrices with incorrect dimensions of the sort, can not be constructed.
38+- Fast type natural conversion via `FromNat` type family;
47−
39+- Matrix `Junc` and `Split`-ing in O(1);
48−## Known issues
40+- Matrix composition takes advantage of divide-and-conquer and fusion laws.
49−
41+
50−Unfortunately, due to the use of type-level programming features, this approach sometimes requires type dimensions to be constrainted, in some way, impossible to write idiomatic Arrow instances, for example. Type inference isn't perfect, when it comes to infer the types of matrices which dimensions are computed using type level naturals multiplication, the compiler needs type annotations in order to succeed. And not all kinds of programs can be modeled using matrices, namely programs that deal with arbitrary infinite data types such as lists or integers (although there are some workarounds).
42+Unfortunately, this approach does not solve the issue of type dimensions being in some way constrainted making it impossible to write Arrow instances, for example. Type inference isn't perfect, when it comes to infer the types of matrices which dimensions are computed using type level naturals multiplication, the compiler needs type annotations in order to succeed.
51
43
52## Notes
44## Notes
53
45
Setup.hsnew file+2
@@ -0,0 +1,2 @@
1+import Distribution.Simple
2+main = defaultMain
benchmark/Main.hs → app/Benchmarks.hsrenamed+24−31
@@ -8,36 +8,35 @@
8{-# LANGUAGE AllowAmbiguousTypes #-}
8{-# LANGUAGE AllowAmbiguousTypes #-}
9{-# LANGUAGE ScopedTypeVariables #-}
9{-# LANGUAGE ScopedTypeVariables #-}
10
10
11+module Benchmarks
12+ ( benchmark
13+ )
11−module Main (main) where
14+ where
12
15
13import LAoP.Dist.Internal
16import LAoP.Dist.Internal
14import LAoP.Utils
17import LAoP.Utils
15−import LAoP.Matrix.Type hiding (CountableN, Countable, FLN)
18+import LAoP.Matrix.Type hiding (CountableN, Countable, FromListsN)
16−import qualified LAoP.Matrix.Type as T (FLN)
19+import qualified LAoP.Matrix.Type as T (FromListsN)
17import Criterion.Main
20import Criterion.Main
18import Control.DeepSeq
21import Control.DeepSeq
19import Test.QuickCheck
22import Test.QuickCheck
20import GHC.TypeLits
23import GHC.TypeLits
21import Data.Proxy
24import Data.Proxy
22−import Prelude hiding (id, (.))
23
25
24selectM2 ::
26selectM2 ::
25 ( Num e,
27 ( Num e,
26− T.FLN b b,
28+ T.FromListsN e b b,
27 CountableN b
29 CountableN b
28 ) => Matrix e cols (Either a b) -> Matrix e a b -> Matrix e cols b
30 ) => Matrix e cols (Either a b) -> Matrix e a b -> Matrix e cols b
29−selectM2 m y = join y iden `comp` m
31+selectM2 m y = junc y identity `comp` m
30
32
31selectD2 ::
33selectD2 ::
32− ( FLN b b,
34+ ( FromListsN b b,
33 CountableN b
35 CountableN b
34 ) => Dist (Either a b) -> Matrix Prob a b -> Dist b
36 ) => Dist (Either a b) -> Matrix Prob a b -> Dist b
35−selectD2 (D d) m = D (join m iden `comp` d)
37+selectD2 (D d) m = D (junc m identity `comp` d)
36−
37−-- Composition with iden
38−compId m = comp iden m
39
38
40−randomDist :: forall a . (Countable a, FLN () a) => Gen (Dist a)
39+randomDist :: forall a . (Countable a, FromListsN () a) => Gen (Dist a)
41randomDist = do
40randomDist = do
42 let size = fromInteger (natVal (Proxy :: Proxy (Count a)))
41 let size = fromInteger (natVal (Proxy :: Proxy (Count a)))
43 l <- vectorOf size (arbitrary :: Gen Prob)
42 l <- vectorOf size (arbitrary :: Gen Prob)
@@ -46,7 +45,7 @@ randomDist = do
46 m = fromLists lr
45 m = fromLists lr
47 return (D m)
46 return (D m)
48
47
49−randomMatrix :: forall a b . (CountableDims a b, FLN a b) => Gen (Matrix Prob a b)
48+randomMatrix :: forall a b . (CountableDimensions a b, FromListsN a b) => Gen (Matrix Prob a b)
50randomMatrix = do
49randomMatrix = do
51 let cols = fromInteger (natVal (Proxy :: Proxy (Count a)))
50 let cols = fromInteger (natVal (Proxy :: Proxy (Count a)))
52 rows = fromInteger (natVal (Proxy :: Proxy (Count b)))
51 rows = fromInteger (natVal (Proxy :: Proxy (Count b)))
@@ -105,14 +104,12 @@ normalize3 as l = let s = sum l
105 probs = map (/ s) l
104 probs = map (/ s) l
106 in zip as probs
105 in zip as probs
107
106
108−randomDistF :: forall a b . (CountableDims a b, CoArbitrary a, Arbitrary b) => Gen (Dist' (a -> b))
107+randomDistF :: forall a b . (CoArbitrary a, Arbitrary b) => Gen (Dist' (a -> b))
109randomDistF = do
108randomDistF = do
110− let a = fromInteger (natVal (Proxy :: Proxy (Count a)))
111− b = fromInteger (natVal (Proxy :: Proxy (Count b)))
112− size = a * b
109+ let size = 200
113 l <- vectorOf size (arbitrary :: Gen Prob)
110 l <- vectorOf size (arbitrary :: Gen Prob)
114 l2 <- vectorOf size (arbitrary :: Gen (a -> b))
111 l2 <- vectorOf size (arbitrary :: Gen (a -> b))
115− let !ln = normalize3 l2 (map P l)
112+ let ln = normalize3 l2 (map P l)
116 return (D' ln)
113 return (D' ln)
117
114
118instance CoArbitrary (Natural a b)
115instance CoArbitrary (Natural a b)
@@ -137,15 +134,15 @@ setupEnv = do
137
134
138setupEnv2 = do
135setupEnv2 = do
139 m21 <- generate (resize 1 (randomMatrix @(Natural 0 100) @(Natural 0 100) ))
136 m21 <- generate (resize 1 (randomMatrix @(Natural 0 100) @(Natural 0 100) ))
140− m40 <- generate (resize 1 (randomMatrix @(Natural 0 100) @(Either (Natural 0 100) (Natural 0 100) )))
137+ m40 <- generate (resize 1 (randomMatrix @(Natural 0 300) @(Either (Natural 0 100) (Natural 0 100) )))
141− dist <- generate (resize 1 (randomDist @(Either (Natural 0 100) (Natural 0 100)) ))
138+ dist <- generate (resize 1 (randomDist @(Either (Natural 0 1000) (Natural 0 1000)) ))
142− dist2 <- generate (resize 1 (randomMatrix @(Natural 0 100) @(Natural 0 100) ))
139+ dist2 <- generate (resize 1 (randomMatrix @(Natural 0 1000) @(Natural 0 1000) ))
143− distList1 <- generate (resize 1 (randomDist2 @(Either (Natural 0 100) (Natural 0 100))))
140+ distList1 <- generate (resize 1 (randomDist2 @(Either (Natural 0 1000) (Natural 0 1000))))
144− distList2 <- generate (resize 1 (randomDistF @(Natural 0 100) @(Natural 0 100)))
141+ distList2 <- generate (resize 1 (randomDistF @(Natural 0 1000) @(Natural 0 1000)))
145 return (m21, m40, dist, dist2, distList1, distList2)
142 return (m21, m40, dist, dist2, distList1, distList2)
146
143
147−main :: IO ()
144+benchmark :: IO ()
148−main = defaultMain [
145+benchmark = defaultMain [
149 env setupEnv $ \ ~(m11, m12, m21, m22, m31, m32) -> bgroup "Matrix Composition" [
146 env setupEnv $ \ ~(m11, m12, m21, m22, m31, m32) -> bgroup "Matrix Composition" [
150 bgroup "10x10" [
147 bgroup "10x10" [
151 bench "WHNF - 10x10" $ whnf (comp m11) m12
148 bench "WHNF - 10x10" $ whnf (comp m11) m12
@@ -158,18 +155,14 @@ main = defaultMain [
158 bgroup "200x200" [
155 bgroup "200x200" [
159 bench "WHNF - 200x200" $ whnf (comp m31) m32
156 bench "WHNF - 200x200" $ whnf (comp m31) m32
160 , bench "NF - 200x200" $ nf (comp m31) m32
157 , bench "NF - 200x200" $ nf (comp m31) m32
161− ],
162− bgroup "200x200 - RULES" [
163− bench "No rules - 200x200" $ nf (comp m21) iden
164− , bench "Rules - 200x200" $ nf compId m21
165 ] ],
158 ] ],
166 env setupEnv2 $ \ ~(m21, m40, dist, dist2, dl1, dl2) -> bgroup "Matrix vs List - `select`" [
159 env setupEnv2 $ \ ~(m21, m40, dist, dist2, dl1, dl2) -> bgroup "Matrix vs List - `select`" [
167− bgroup "Distribution `select` - 100+100 / 100x100" [
160+ bgroup "Distribution" [
168 bench "List Distribution - Applicative version" $ nf (select dl1) dl2
161 bench "List Distribution - Applicative version" $ nf (select dl1) dl2
169 , bench "Matrix Distribution - Applicative version" $ nf (selectD2 dist) dist2
162 , bench "Matrix Distribution - Applicative version" $ nf (selectD2 dist) dist2
170 , bench "Matrix Distribution - Selective version" $ nf (selectD dist) dist2
163 , bench "Matrix Distribution - Selective version" $ nf (selectD dist) dist2
171 ],
164 ],
172− bgroup "Matrix `select` - 100x(100+100) / 100x100" [
165+ bgroup "Matrix `select`" [
173 bench "Applicative version" $ nf (selectM2 m40) m21
166 bench "Applicative version" $ nf (selectM2 m40) m21
174 , bench "Selective version" $ nf (selectM m40) m21
167 , bench "Selective version" $ nf (selectM m40) m21
175 ] ] ]
168 ] ] ]
test/Examples/Readme.hs → app/Examples.hsrenamed+31−56
@@ -1,10 +1,10 @@
1−{-# LANGUAGE GADTs #-}
2{-# LANGUAGE DeriveGeneric #-}
1{-# LANGUAGE DeriveGeneric #-}
3{-# LANGUAGE FlexibleContexts #-}
2{-# LANGUAGE FlexibleContexts #-}
3+{-# LANGUAGE TypeOperators #-}
4{-# LANGUAGE TypeApplications #-}
4{-# LANGUAGE TypeApplications #-}
5{-# LANGUAGE DataKinds #-}
5{-# LANGUAGE DataKinds #-}
6
6
7−module Examples.Readme
7+module Examples
8 ( exec
8 ( exec
9 )
9 )
10 where
10 where
@@ -15,12 +15,13 @@ import LAoP.Utils
15import LAoP.Dist
15import LAoP.Dist
16import GHC.TypeLits
16import GHC.TypeLits
17import Data.Coerce
17import Data.Coerce
18−import qualified GHC.Generics as G
18+import GHC.Generics
19+import Control.Category hiding (id)
19−import Prelude hiding (id, (.))
20+import Prelude hiding ((.))
20
21
21-- Monty Hall Problem
22-- Monty Hall Problem
22data Outcome = Win | Lose
23data Outcome = Win | Lose
23− deriving (Bounded, Enum, Eq, Show, G.Generic)
24+ deriving (Bounded, Enum, Eq, Show, Generic)
24
25
25switch :: Outcome -> Outcome
26switch :: Outcome -> Outcome
26switch Win = Lose
27switch Win = Lose
@@ -30,7 +31,7 @@ firstChoice :: Matrix Double () Outcome
30firstChoice = col [1/3, 2/3]
31firstChoice = col [1/3, 2/3]
31
32
32secondChoice :: Matrix Double Outcome Outcome
33secondChoice :: Matrix Double Outcome Outcome
33−secondChoice = fromF switch
34+secondChoice = fromF' switch
34
35
35-- Dice sum
36-- Dice sum
36
37
@@ -39,7 +40,7 @@ type SS = Natural 1 6 -- Sample Space
39sumSS :: SS -> SS -> Natural 2 12
40sumSS :: SS -> SS -> Natural 2 12
40sumSS = coerceNat (+)
41sumSS = coerceNat (+)
41
42
42−sumSSM = fromF (uncurry sumSS)
43+sumSSM = fromF' (uncurry sumSS)
43
44
44condition :: (Int, Int) -> Int -> Int
45condition :: (Int, Int) -> Int -> Int
45condition (fst, snd) thrd = if fst == snd
46condition (fst, snd) thrd = if fst == snd
@@ -49,64 +50,38 @@ condition (fst, snd) thrd = if fst == snd
49conditionSS :: (SS, SS) -> SS -> Natural 3 18
50conditionSS :: (SS, SS) -> SS -> Natural 3 18
50conditionSS = coerceNat2 condition
51conditionSS = coerceNat2 condition
51
52
52−conditionalThrows = fromF (uncurry conditionSS) . kr (kr die die) die
53+conditionalThrows = fromF' (uncurry conditionSS) . khatri (khatri die die) die
53
54
54die :: Matrix Double () SS
55die :: Matrix Double () SS
55die = col $ map (const (1/6)) [nat @1 @6 1 .. nat 6]
56die = col $ map (const (1/6)) [nat @1 @6 1 .. nat 6]
56
57
57-- Sprinkler
58-- Sprinkler
58−data G = Dry | Wet
59− deriving (Bounded, Enum, Eq, Show, G.Generic)
60
59
61−data S = Off | On
60+rain :: Matrix Double () Bool
62− deriving (Bounded, Enum, Eq, Show, G.Generic)
61+rain = col [0.8, 0.2]
63
62
64−data R = No | Yes
63+sprinkler :: Matrix Double Bool Bool
65− deriving (Bounded, Enum, Eq, Show, G.Generic)
64+sprinkler = fromLists [[0.6, 0.99], [0.4, 0.01]]
66
65
67−rain :: Matrix Double () R
68−rain = matrixBuilder gen
69− where
70− gen (_, No) = 0.8
71− gen (_, Yes) = 0.2
72−
73−sprinkler :: Matrix Double R S
74−sprinkler = matrixBuilder gen
75− where
76− gen (No, Off) = 0.6
77− gen (No, On) = 0.4
78− gen (Yes, Off) = 0.99
79− gen (Yes, On) = 0.01
80−
81−grass :: Matrix Double (S, R) G
66+grass :: Matrix Double (Bool, Bool) Bool
82−grass = matrixBuilder gen
67+grass = fromLists [[1, 0.2, 0.1, 0.01], [0, 0.8, 0.9, 0.99]]
83− where
84− gen ((Off, No), Dry) = 1
85− gen ((Off, Yes), Dry) = 0.2
86− gen ((On, No), Dry) = 0.1
87− gen ((On, Yes), Dry) = 0.01
88− gen ((Off, No), Wet) = 0
89− gen ((Off, Yes), Wet) = 0.8
90− gen ((On, No), Wet) = 0.9
91− gen ((On, Yes), Wet) = 0.99
92−
93−tag f = kr f id
94
68
95−state g s r = tag g . tag s . r
69+state :: Matrix Double () (Bool, (Bool, Bool))
70+state = khatri grass identity . khatri sprinkler identity . rain
96
71
97−grass_wet :: Matrix Double () (G, (S, R)) -> Matrix Double One One
72+grass_wet :: Matrix Double (Bool, (Bool, Bool)) One
98−grass_wet state = row [0,1] . fstM . state
73+grass_wet = row [0,1] . kp1
99
74
100−rainning :: Matrix Double (G, (S, R)) One
75+rainning :: Matrix Double (Bool, (Bool, Bool)) One
101−rainning = row [0,1] . sndM . sndM
76+rainning = row [0,1] . kp2 . kp2
102
77
103-- Alcuin Puzzle
78-- Alcuin Puzzle
104
79
105data Being = Farmer | Fox | Goose | Beans
80data Being = Farmer | Fox | Goose | Beans
106− deriving (Bounded, Enum, Eq, Show, G.Generic)
81+ deriving (Bounded, Enum, Eq, Show, Generic)
107
82
108data Bank = LeftB | RightB
83data Bank = LeftB | RightB
109− deriving (Bounded, Enum, Eq, Show, G.Generic)
84+ deriving (Bounded, Enum, Eq, Show, Generic)
110
85
111eats :: Being -> Being -> Bool
86eats :: Being -> Being -> Bool
112eats Fox Goose = True
87eats Fox Goose = True
@@ -121,21 +96,21 @@ cross LeftB = RightB
121cross RightB = LeftB
96cross RightB = LeftB
122
97
123crossR :: R.Relation Bank Bank
98crossR :: R.Relation Bank Bank
124−crossR = R.fromF cross
99+crossR = R.fromF' cross
125
100
126-- | Initial state, everyone in the left bank
101-- | Initial state, everyone in the left bank
127locationLeft :: Being -> Bank
102locationLeft :: Being -> Bank
128locationLeft _ = LeftB
103locationLeft _ = LeftB
129
104
130locationLeftR :: R.Relation Being Bank
105locationLeftR :: R.Relation Being Bank
131−locationLeftR = R.fromF locationLeft
106+locationLeftR = R.fromF' locationLeft
132
107
133-- | Initial state, everyone in the right bank
108-- | Initial state, everyone in the right bank
134locationRight :: Being -> Bank
109locationRight :: Being -> Bank
135locationRight _ = RightB
110locationRight _ = RightB
136
111
137locationRightR :: R.Relation Being Bank
112locationRightR :: R.Relation Being Bank
138−locationRightR = R.fromF locationRight
113+locationRightR = R.fromF' locationRight
139
114
140-- Properties
115-- Properties
141
116
@@ -152,7 +127,7 @@ inv :: R.Relation Being Bank -> Bool
152inv w = (w `R.comp` canEat w) `R.sse` (w `R.comp` farmer)
127inv w = (w `R.comp` canEat w) `R.sse` (w `R.comp` farmer)
153 where
128 where
154 farmer :: R.Relation Being Being
129 farmer :: R.Relation Being Being
155− farmer = R.fromF (const Farmer)
130+ farmer = R.fromF' (const Farmer)
156
131
157-- Arbitrary state
132-- Arbitrary state
158bankState :: Being -> Bank -> Bool
133bankState :: Being -> Bank -> Bool
@@ -171,14 +146,14 @@ exec = do
171 putStrLn "Monty Hall Problem solution:"
146 putStrLn "Monty Hall Problem solution:"
172 prettyPrint (secondChoice . firstChoice)
147 prettyPrint (secondChoice . firstChoice)
173 putStrLn "\n Sum of dices probability:"
148 putStrLn "\n Sum of dices probability:"
174− prettyPrint (sumSSM . kr die die)
149+ prettyPrint (sumSSM `comp` khatri die die)
175 putStrLn "\n Conditional dice throw:"
150 putStrLn "\n Conditional dice throw:"
176 prettyPrint conditionalThrows
151 prettyPrint conditionalThrows
177 putStrLn "\n Checking that the last result is indeed a distribution: "
152 putStrLn "\n Checking that the last result is indeed a distribution: "
178− prettyPrint (bang . sumSSM . kr die die)
153+ prettyPrint (bang . sumSSM . khatri die die)
179 putStrLn "\n Probability of grass being wet:"
154 putStrLn "\n Probability of grass being wet:"
180− prettyPrint (grass_wet (state grass sprinkler rain))
155+ prettyPrint (grass_wet . state)
181 putStrLn "\n Probability of rain:"
156 putStrLn "\n Probability of rain:"
182− prettyPrint (rainning . state grass sprinkler rain)
157+ prettyPrint (rainning . state)
183 putStrLn "\n Is the arbitrary state a valid state? (Alcuin Puzzle)"
158 putStrLn "\n Is the arbitrary state a valid state? (Alcuin Puzzle)"
184 print (inv bankStateR)
159 print (inv bankStateR)
app/Main.hsnew file+7
@@ -0,0 +1,7 @@
1+module Main where
2+
3+import Examples
4+import Benchmarks
5+
6+main :: IO ()
7+main = benchmark
app/Spreadsheets.hsnew file+61
@@ -0,0 +1,61 @@
1+{-# LANGUAGE DataKinds #-}
2+{-# LANGUAGE GADTs #-}
3+{-# LANGUAGE FlexibleContexts #-}
4+{-# LANGUAGE DeriveGeneric #-}
5+module Spreadsheets
6+ (
7+ )
8+ where
9+
10+import LAoP.Matrix.Type
11+import qualified LAoP.Matrix.Internal as I
12+import GHC.Generics
13+
14+data Student = Student1 | Student2 | Student3 | Student4
15+ deriving (Eq, Show, Enum, Bounded, Generic)
16+
17+data Question = Question1 | Question2 | Question3 | Question4
18+ deriving (Eq, Show, Enum, Bounded, Generic)
19+
20+data Results = Test | Exam | Final
21+ deriving (Eq, Show, Enum, Bounded, Generic)
22+
23+test :: Matrix Float One Results
24+test = point Test
25+
26+exam :: Matrix Float One Results
27+exam = point Exam
28+
29+final :: Matrix Float One Results
30+final = point Final
31+
32+m :: Matrix Float Question Student
33+m = fromLists [[95, 90, 100, 40], [20, 90, 90, 0], [30, 20, 95, 0], [50, 80, 100, 30]]
34+
35+w :: Matrix Float Question One
36+w = fromLists [[0.2, 0.3, 0.2, 0.3]]
37+
38+xls :: Matrix Float Question One
39+ -> Matrix Float Question Student
40+ -> Matrix Float Student One
41+ -> Matrix Float (Either Question Results) (Either One Student)
42+xls w m t = junc (split w m) (split zeros r)
43+ where
44+ rExam = m `comp` tr w
45+ rTest = tr t
46+ rFinal = rTest `maxPP` rExam
47+ rAux = junc rTest (junc rExam rFinal)
48+ r = tr (converter `comp` tr rAux)
49+ converter = junc test (junc exam final)
50+
51+-- | Overloaded, point-wise 'max' function
52+maxPP_ :: Ord e => I.Matrix e a b -> I.Matrix e a b -> I.Matrix e a b
53+maxPP_ I.Empty I.Empty = I.Empty
54+maxPP_ (I.One a) (I.One b) = I.One (a `max` b)
55+maxPP_ (I.Junc a b) (I.Junc c d) = I.Junc (maxPP_ a c) (maxPP_ b d)
56+maxPP_ (I.Split a b) (I.Split c d) = I.Split (maxPP_ a c) (maxPP_ b d)
57+maxPP_ x@(I.Split _ _) y@(I.Junc _ _) = maxPP_ x (I.abideJS y)
58+maxPP_ x@(I.Junc _ _) y@(I.Split _ _) = maxPP_ (I.abideJS x) y
59+
60+maxPP :: Ord e => Matrix e a b -> Matrix e a b -> Matrix e a b
61+maxPP (M a) (M b) = M (maxPP_ a b)
appveyor.ymldeleted−34
@@ -1,34 +0,0 @@
1−clone_folder: "c:\\WORK"
2−clone_depth: 5
3−
4−# Do not build feature branch with open Pull Requests
5−skip_branch_with_pr: true
6−
7−platform:
8− - x86_64
9−
10−cache:
11− - "C:\\SR"
12− - dist-newstyle
13−
14−environment:
15− global:
16− CABOPTS: --store-dir=C:\\SR
17−
18− matrix:
19− - GHCVER: 8.6.5
20−
21−install:
22− - choco source add -n mistuke -s https://www.myget.org/F/mistuke/api/v2
23− - choco install -y cabal --version 2.4.1.0
24− - choco install -y ghc --version 8.6.3
25− - refreshenv
26−
27−before_build:
28− - cabal --version
29− - ghc --version
30− - cabal %CABOPTS% v2-update
31−
32−build_script:
33− - cabal %CABOPTS% v2-build --enable-tests
34− - cabal %CABOPTS% v2-test --enable-tests
hackage.shnew file+10
@@ -0,0 +1,10 @@
1+#!/bin/sh
2+set -e
3+
4+dir=$(mktemp -d dist-docs.XXXXXX)
5+trap 'rm -r "$dir"' EXIT
6+
7+# assumes cabal 2.4 or later
8+cabal v2-haddock --builddir="$dir" --haddock-for-hackage --enable-doc
9+
10+cabal upload -d $dir/*-docs.tar.gz --publish
laop-0.1.0.0-docs.tar.gznew file

Binary file not shown.

laop.cabaldeleted−89
@@ -1,89 +0,0 @@
1−cabal-version: 2.4
2−name: laop
3−version: 0.1.1.1
4−synopsis: Matrix programming library
5−description: Matrix programming library that uses a type-safe inductive definition
6− inspired by the Linear Algebra of Programming
7−homepage: https://github.com/bolt12/laop
8−bug-reports: https://github.com/bolt12/laop/issues
9−license: MIT
10−license-file: LICENSE
11−author: Armando Santos
12−maintainer: Armando Santos <armandoifsantos@gmail.com>
13−copyright: 2020 Armando Santos
14−category: Data
15−build-type: Simple
16−extra-doc-files: README.md
17− CHANGELOG.md
18−tested-with: GHC == 8.6.5
19− GHC == 8.8.3
20−
21−source-repository head
22− type: git
23− location: https://github.com/bolt12/laop.git
24−
25−common common-options
26− build-depends: base >= 4.12.0.0 && < 5,
27− deepseq
28−
29− ghc-options: -Wall
30− -Wcompat
31− -Widentities
32− -Wincomplete-uni-patterns
33− -Wincomplete-record-updates
34− if impl(ghc >= 8.0)
35− ghc-options: -Wredundant-constraints
36− if impl(ghc >= 8.2)
37− ghc-options: -fhide-source-paths
38− if impl(ghc >= 8.4)
39− ghc-options: -Wmissing-export-lists
40− -Wpartial-fields
41− if impl(ghc >= 8.8)
42− ghc-options: -Wmissing-deriving-strategies
43−
44− default-language: Haskell2010
45−
46−library
47− import: common-options
48− hs-source-dirs: src
49− exposed-modules: LAoP.Dist
50− LAoP.Dist.Internal
51− LAoP.Matrix.Internal
52− LAoP.Matrix.Nat
53− LAoP.Matrix.Type
54− LAoP.Relation
55− LAoP.Relation.Internal
56− LAoP.Utils
57− LAoP.Utils.Internal
58−
59−test-suite laop-test
60− import: common-options
61− type: exitcode-stdio-1.0
62− hs-source-dirs: test
63− other-modules: Examples.Readme
64− main-is: Spec.hs
65− build-depends: laop
66− ghc-options: -threaded
67− -rtsopts
68− -with-rtsopts=-N
69− -funfolding-use-threshold=16
70− -fexcess-precision
71− -optc-O3
72− -optc-ffast-math
73−
74−benchmark laop-benchmark
75− import: common-options
76− type: exitcode-stdio-1.0
77− hs-source-dirs: benchmark
78− main-is: Main.hs
79− build-depends: criterion
80− , QuickCheck
81− , deepseq
82− , laop
83− ghc-options: -threaded
84− -rtsopts
85− -with-rtsopts=-N
86− -funfolding-use-threshold=16
87− -fexcess-precision
88− -optc-O3
89− -optc-ffast-math
package.yamlnew file+57
@@ -0,0 +1,57 @@
1+name: laop
2+version: 0.1.0.3
3+github: "bolt12/laop"
4+license: BSD3
5+author: "Armando Santos"
6+maintainer: "armandoifsantos@gmail.com"
7+copyright: "MIT"
8+
9+extra-source-files:
10+- README.md
11+- ChangeLog.md
12+
13+# Metadata used when publishing your package
14+# synopsis: Short description of your package
15+category: Data
16+
17+# To avoid duplicated efforts in documentation and dealing with the
18+# complications of embedding Haddock markup inside cabal files, it is
19+# common to point users to the README.md file.
20+description: Please see the README on GitHub at <https://github.com/bolt12/laop#readme>
21+
22+dependencies:
23+- base >= 4.7 && < 5
24+- deepseq
25+
26+library:
27+ source-dirs: src
28+
29+executables:
30+ laop-exe:
31+ main: Main.hs
32+ source-dirs: app
33+ ghc-options:
34+ - -threaded
35+ - -rtsopts
36+ - -with-rtsopts=-N
37+ - -funfolding-use-threshold=16
38+ - -fexcess-precision # Good for doubles
39+ - -optc-O3 # Good for doubles
40+ - -optc-ffast-math # Good for doubles
41+ - -O # Optimize
42+ dependencies:
43+ - laop
44+ - criterion
45+ - deepseq
46+ - QuickCheck
47+
48+tests:
49+ laop-test:
50+ main: Spec.hs
51+ source-dirs: test
52+ ghc-options:
53+ - -threaded
54+ - -rtsopts
55+ - -with-rtsopts=-N
56+ dependencies:
57+ - laop
report-lazy.htmlnew file+1169
@@ -0,0 +1,1169 @@
1+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
2+<html>
3+ <head>
4+ <meta http-equiv="Content-Type" content="text/html; charset=utf-8">
5+ <title>criterion report</title>
6+ <script language="javascript" type="text/javascript">
7+ /*! jQuery v3.3.1 | (c) JS Foundation and other contributors | jquery.org/license */
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i,axisOptions,axisCount,fontSize=placeholder.css("font-size"),fontSizeDefault=fontSize?+fontSize.replace("px",""):13,fontDefaults={style:placeholder.css("font-style"),size:Math.round(.8*fontSizeDefault),variant:placeholder.css("font-variant"),weight:placeholder.css("font-weight"),family:placeholder.css("font-family")};axisCount=options.xaxes.length||1;for(i=0;i<axisCount;++i){axisOptions=options.xaxes[i];if(axisOptions&&!axisOptions.tickColor){axisOptions.tickColor=axisOptions.color}axisOptions=$.extend(true,{},options.xaxis,axisOptions);options.xaxes[i]=axisOptions;if(axisOptions.font){axisOptions.font=$.extend({},fontDefaults,axisOptions.font);if(!axisOptions.font.color){axisOptions.font.color=axisOptions.color}if(!axisOptions.font.lineHeight){axisOptions.font.lineHeight=Math.round(axisOptions.font.size*1.15)}}}axisCount=options.yaxes.length||1;for(i=0;i<axisCount;++i){axisOptions=options.yaxes[i];if(axisOptions&&!axisOptions.tickColor){axisOptions.tickColor=axisOptions.color}axisOptions=$.extend(true,{},options.yaxis,axisOptions);options.yaxes[i]=axisOptions;if(axisOptions.font){axisOptions.font=$.extend({},fontDefaults,axisOptions.font);if(!axisOptions.font.color){axisOptions.font.color=axisOptions.color}if(!axisOptions.font.lineHeight){axisOptions.font.lineHeight=Math.round(axisOptions.font.size*1.15)}}}if(options.xaxis.noTicks&&options.xaxis.ticks==null)options.xaxis.ticks=options.xaxis.noTicks;if(options.yaxis.noTicks&&options.yaxis.ticks==null)options.yaxis.ticks=options.yaxis.noTicks;if(options.x2axis){options.xaxes[1]=$.extend(true,{},options.xaxis,options.x2axis);options.xaxes[1].position="top";if(options.x2axis.min==null){options.xaxes[1].min=null}if(options.x2axis.max==null){options.xaxes[1].max=null}}if(options.y2axis){options.yaxes[1]=$.extend(true,{},options.yaxis,options.y2axis);options.yaxes[1].position="right";if(options.y2axis.min==null){options.yaxes[1].min=null}if(options.y2axis.max==null){options.yaxes[1].max=null}}if(options.grid.coloredAreas)options.grid.markings=options.grid.coloredAreas;if(options.grid.coloredAreasColor)options.grid.markingsColor=options.grid.coloredAreasColor;if(options.lines)$.extend(true,options.series.lines,options.lines);if(options.points)$.extend(true,options.series.points,options.points);if(options.bars)$.extend(true,options.series.bars,options.bars);if(options.shadowSize!=null)options.series.shadowSize=options.shadowSize;if(options.highlightColor!=null)options.series.highlightColor=options.highlightColor;for(i=0;i<options.xaxes.length;++i)getOrCreateAxis(xaxes,i+1).options=options.xaxes[i];for(i=0;i<options.yaxes.length;++i)getOrCreateAxis(yaxes,i+1).options=options.yaxes[i];for(var n in hooks)if(options.hooks[n]&&options.hooks[n].length)hooks[n]=hooks[n].concat(options.hooks[n]);executeHooks(hooks.processOptions,[options])}function setData(d){series=parseData(d);fillInSeriesOptions();processData()}function parseData(d){var res=[];for(var i=0;i<d.length;++i){var s=$.extend(true,{},options.series);if(d[i].data!=null){s.data=d[i].data;delete d[i].data;$.extend(true,s,d[i]);d[i].data=s.data}else s.data=d[i];res.push(s)}return res}function axisNumber(obj,coord){var a=obj[coord+"axis"];if(typeof a=="object")a=a.n;if(typeof a!="number")a=1;return a}function allAxes(){return $.grep(xaxes.concat(yaxes),function(a){return a})}function canvasToAxisCoords(pos){var res={},i,axis;for(i=0;i<xaxes.length;++i){axis=xaxes[i];if(axis&&axis.used)res["x"+axis.n]=axis.c2p(pos.left)}for(i=0;i<yaxes.length;++i){axis=yaxes[i];if(axis&&axis.used)res["y"+axis.n]=axis.c2p(pos.top)}if(res.x1!==undefined)res.x=res.x1;if(res.y1!==undefined)res.y=res.y1;return res}function axisToCanvasCoords(pos){var res={},i,axis,key;for(i=0;i<xaxes.length;++i){axis=xaxes[i];if(axis&&axis.used){key="x"+axis.n;if(pos[key]==null&&axis.n==1)key="x";if(pos[key]!=null){res.left=axis.p2c(pos[key]);break}}}for(i=0;i<yaxes.length;++i){axis=yaxes[i];if(axis&&axis.used){key="y"+axis.n;if(pos[key]==null&&axis.n==1)key="y";if(pos[key]!=null){res.top=axis.p2c(pos[key]);break}}}return res}function getOrCreateAxis(axes,number){if(!axes[number-1])axes[number-1]={n:number,direction:axes==xaxes?"x":"y",options:$.extend(true,{},axes==xaxes?options.xaxis:options.yaxis)};return axes[number-1]}function fillInSeriesOptions(){var neededColors=series.length,maxIndex=-1,i;for(i=0;i<series.length;++i){var sc=series[i].color;if(sc!=null){neededColors--;if(typeof sc=="number"&&sc>maxIndex){maxIndex=sc}}}if(neededColors<=maxIndex){neededColors=maxIndex+1}var c,colors=[],colorPool=options.colors,colorPoolSize=colorPool.length,variation=0;for(i=0;i<neededColors;i++){c=$.color.parse(colorPool[i%colorPoolSize]||"#666");if(i%colorPoolSize==0&&i){if(variation>=0){if(variation<.5){variation=-variation-.2}else variation=0}else variation=-variation}colors[i]=c.scale("rgb",1+variation)}var colori=0,s;for(i=0;i<series.length;++i){s=series[i];if(s.color==null){s.color=colors[colori].toString();++colori}else if(typeof s.color=="number")s.color=colors[s.color].toString();if(s.lines.show==null){var v,show=true;for(v in s)if(s[v]&&s[v].show){show=false;break}if(show)s.lines.show=true}if(s.lines.zero==null){s.lines.zero=!!s.lines.fill}s.xaxis=getOrCreateAxis(xaxes,axisNumber(s,"x"));s.yaxis=getOrCreateAxis(yaxes,axisNumber(s,"y"))}}function processData(){var topSentry=Number.POSITIVE_INFINITY,bottomSentry=Number.NEGATIVE_INFINITY,fakeInfinity=Number.MAX_VALUE,i,j,k,m,length,s,points,ps,x,y,axis,val,f,p,data,format;function updateAxis(axis,min,max){if(min<axis.datamin&&min!=-fakeInfinity)axis.datamin=min;if(max>axis.datamax&&max!=fakeInfinity)axis.datamax=max}$.each(allAxes(),function(_,axis){axis.datamin=topSentry;axis.datamax=bottomSentry;axis.used=false});for(i=0;i<series.length;++i){s=series[i];s.datapoints={points:[]};executeHooks(hooks.processRawData,[s,s.data,s.datapoints])}for(i=0;i<series.length;++i){s=series[i];data=s.data;format=s.datapoints.format;if(!format){format=[];format.push({x:true,number:true,required:true});format.push({y:true,number:true,required:true});if(s.bars.show||s.lines.show&&s.lines.fill){var autoscale=!!(s.bars.show&&s.bars.zero||s.lines.show&&s.lines.zero);format.push({y:true,number:true,required:false,defaultValue:0,autoscale:autoscale});if(s.bars.horizontal){delete format[format.length-1].y;format[format.length-1].x=true}}s.datapoints.format=format}if(s.datapoints.pointsize!=null)continue;s.datapoints.pointsize=format.length;ps=s.datapoints.pointsize;points=s.datapoints.points;var insertSteps=s.lines.show&&s.lines.steps;s.xaxis.used=s.yaxis.used=true;for(j=k=0;j<data.length;++j,k+=ps){p=data[j];var nullify=p==null;if(!nullify){for(m=0;m<ps;++m){val=p[m];f=format[m];if(f){if(f.number&&val!=null){val=+val;if(isNaN(val))val=null;else if(val==Infinity)val=fakeInfinity;else if(val==-Infinity)val=-fakeInfinity}if(val==null){if(f.required)nullify=true;if(f.defaultValue!=null)val=f.defaultValue}}points[k+m]=val}}if(nullify){for(m=0;m<ps;++m){val=points[k+m];if(val!=null){f=format[m];if(f.autoscale!==false){if(f.x){updateAxis(s.xaxis,val,val)}if(f.y){updateAxis(s.yaxis,val,val)}}}points[k+m]=null}}else{if(insertSteps&&k>0&&points[k-ps]!=null&&points[k-ps]!=points[k]&&points[k-ps+1]!=points[k+1]){for(m=0;m<ps;++m)points[k+ps+m]=points[k+m];points[k+1]=points[k-ps+1];k+=ps}}}}for(i=0;i<series.length;++i){s=series[i];executeHooks(hooks.processDatapoints,[s,s.datapoints])}for(i=0;i<series.length;++i){s=series[i];points=s.datapoints.points;ps=s.datapoints.pointsize;format=s.datapoints.format;var xmin=topSentry,ymin=topSentry,xmax=bottomSentry,ymax=bottomSentry;for(j=0;j<points.length;j+=ps){if(points[j]==null)continue;for(m=0;m<ps;++m){val=points[j+m];f=format[m];if(!f||f.autoscale===false||val==fakeInfinity||val==-fakeInfinity)continue;if(f.x){if(val<xmin)xmin=val;if(val>xmax)xmax=val}if(f.y){if(val<ymin)ymin=val;if(val>ymax)ymax=val}}}if(s.bars.show){var delta;switch(s.bars.align){case"left":delta=0;break;case"right":delta=-s.bars.barWidth;break;default:delta=-s.bars.barWidth/2}if(s.bars.horizontal){ymin+=delta;ymax+=delta+s.bars.barWidth}else{xmin+=delta;xmax+=delta+s.bars.barWidth}}updateAxis(s.xaxis,xmin,xmax);updateAxis(s.yaxis,ymin,ymax)}$.each(allAxes(),function(_,axis){if(axis.datamin==topSentry)axis.datamin=null;if(axis.datamax==bottomSentry)axis.datamax=null})}function setupCanvases(){placeholder.css("padding",0).children().filter(function(){return!$(this).hasClass("flot-overlay")&&!$(this).hasClass("flot-base")}).remove();if(placeholder.css("position")=="static")placeholder.css("position","relative");surface=new Canvas("flot-base",placeholder);overlay=new Canvas("flot-overlay",placeholder);ctx=surface.context;octx=overlay.context;eventHolder=$(overlay.element).unbind();var existing=placeholder.data("plot");if(existing){existing.shutdown();overlay.clear()}placeholder.data("plot",plot)}function bindEvents(){if(options.grid.hoverable){eventHolder.mousemove(onMouseMove);eventHolder.bind("mouseleave",onMouseLeave)}if(options.grid.clickable)eventHolder.click(onClick);executeHooks(hooks.bindEvents,[eventHolder])}function shutdown(){if(redrawTimeout)clearTimeout(redrawTimeout);eventHolder.unbind("mousemove",onMouseMove);eventHolder.unbind("mouseleave",onMouseLeave);eventHolder.unbind("click",onClick);executeHooks(hooks.shutdown,[eventHolder])}function setTransformationHelpers(axis){function identity(x){return x}var s,m,t=axis.options.transform||identity,it=axis.options.inverseTransform;if(axis.direction=="x"){s=axis.scale=plotWidth/Math.abs(t(axis.max)-t(axis.min));m=Math.min(t(axis.max),t(axis.min))}else{s=axis.scale=plotHeight/Math.abs(t(axis.max)-t(axis.min));s=-s;m=Math.max(t(axis.max),t(axis.min))}if(t==identity)axis.p2c=function(p){return(p-m)*s};else axis.p2c=function(p){return(t(p)-m)*s};if(!it)axis.c2p=function(c){return m+c/s};else axis.c2p=function(c){return it(m+c/s)}}function measureTickLabels(axis){var opts=axis.options,ticks=axis.ticks||[],labelWidth=opts.labelWidth||0,labelHeight=opts.labelHeight||0,maxWidth=labelWidth||(axis.direction=="x"?Math.floor(surface.width/(ticks.length||1)):null),legacyStyles=axis.direction+"Axis "+axis.direction+axis.n+"Axis",layer="flot-"+axis.direction+"-axis flot-"+axis.direction+axis.n+"-axis "+legacyStyles,font=opts.font||"flot-tick-label tickLabel";for(var i=0;i<ticks.length;++i){var t=ticks[i];if(!t.label)continue;var info=surface.getTextInfo(layer,t.label,font,null,maxWidth);labelWidth=Math.max(labelWidth,info.width);labelHeight=Math.max(labelHeight,info.height)}axis.labelWidth=opts.labelWidth||labelWidth;axis.labelHeight=opts.labelHeight||labelHeight}function allocateAxisBoxFirstPhase(axis){var lw=axis.labelWidth,lh=axis.labelHeight,pos=axis.options.position,isXAxis=axis.direction==="x",tickLength=axis.options.tickLength,axisMargin=options.grid.axisMargin,padding=options.grid.labelMargin,innermost=true,outermost=true,first=true,found=false;$.each(isXAxis?xaxes:yaxes,function(i,a){if(a&&(a.show||a.reserveSpace)){if(a===axis){found=true}else if(a.options.position===pos){if(found){outermost=false}else{innermost=false}}if(!found){first=false}}});if(outermost){axisMargin=0}if(tickLength==null){tickLength=first?"full":5}if(!isNaN(+tickLength))padding+=+tickLength;if(isXAxis){lh+=padding;if(pos=="bottom"){plotOffset.bottom+=lh+axisMargin;axis.box={top:surface.height-plotOffset.bottom,height:lh}}else{axis.box={top:plotOffset.top+axisMargin,height:lh};plotOffset.top+=lh+axisMargin}}else{lw+=padding;if(pos=="left"){axis.box={left:plotOffset.left+axisMargin,width:lw};plotOffset.left+=lw+axisMargin}else{plotOffset.right+=lw+axisMargin;axis.box={left:surface.width-plotOffset.right,width:lw}}}axis.position=pos;axis.tickLength=tickLength;axis.box.padding=padding;axis.innermost=innermost}function allocateAxisBoxSecondPhase(axis){if(axis.direction=="x"){axis.box.left=plotOffset.left-axis.labelWidth/2;axis.box.width=surface.width-plotOffset.left-plotOffset.right+axis.labelWidth}else{axis.box.top=plotOffset.top-axis.labelHeight/2;axis.box.height=surface.height-plotOffset.bottom-plotOffset.top+axis.labelHeight}}function adjustLayoutForThingsStickingOut(){var minMargin=options.grid.minBorderMargin,axis,i;if(minMargin==null){minMargin=0;for(i=0;i<series.length;++i)minMargin=Math.max(minMargin,2*(series[i].points.radius+series[i].points.lineWidth/2))}var margins={left:minMargin,right:minMargin,top:minMargin,bottom:minMargin};$.each(allAxes(),function(_,axis){if(axis.reserveSpace&&axis.ticks&&axis.ticks.length){if(axis.direction==="x"){margins.left=Math.max(margins.left,axis.labelWidth/2);margins.right=Math.max(margins.right,axis.labelWidth/2)}else{margins.bottom=Math.max(margins.bottom,axis.labelHeight/2);margins.top=Math.max(margins.top,axis.labelHeight/2)}}});plotOffset.left=Math.ceil(Math.max(margins.left,plotOffset.left));plotOffset.right=Math.ceil(Math.max(margins.right,plotOffset.right));plotOffset.top=Math.ceil(Math.max(margins.top,plotOffset.top));plotOffset.bottom=Math.ceil(Math.max(margins.bottom,plotOffset.bottom))}function setupGrid(){var i,axes=allAxes(),showGrid=options.grid.show;for(var a in plotOffset){var margin=options.grid.margin||0;plotOffset[a]=typeof margin=="number"?margin:margin[a]||0}executeHooks(hooks.processOffset,[plotOffset]);for(var a in plotOffset){if(typeof options.grid.borderWidth=="object"){plotOffset[a]+=showGrid?options.grid.borderWidth[a]:0}else{plotOffset[a]+=showGrid?options.grid.borderWidth:0}}$.each(axes,function(_,axis){var axisOpts=axis.options;axis.show=axisOpts.show==null?axis.used:axisOpts.show;axis.reserveSpace=axisOpts.reserveSpace==null?axis.show:axisOpts.reserveSpace;setRange(axis)});if(showGrid){var allocatedAxes=$.grep(axes,function(axis){return axis.show||axis.reserveSpace});$.each(allocatedAxes,function(_,axis){setupTickGeneration(axis);setTicks(axis);snapRangeToTicks(axis,axis.ticks);measureTickLabels(axis)});for(i=allocatedAxes.length-1;i>=0;--i)allocateAxisBoxFirstPhase(allocatedAxes[i]);adjustLayoutForThingsStickingOut();$.each(allocatedAxes,function(_,axis){allocateAxisBoxSecondPhase(axis)})}plotWidth=surface.width-plotOffset.left-plotOffset.right;plotHeight=surface.height-plotOffset.bottom-plotOffset.top;$.each(axes,function(_,axis){setTransformationHelpers(axis)});if(showGrid){drawAxisLabels()}insertLegend()}function setRange(axis){var opts=axis.options,min=+(opts.min!=null?opts.min:axis.datamin),max=+(opts.max!=null?opts.max:axis.datamax),delta=max-min;if(delta==0){var widen=max==0?1:.01;if(opts.min==null)min-=widen;if(opts.max==null||opts.min!=null)max+=widen}else{var margin=opts.autoscaleMargin;if(margin!=null){if(opts.min==null){min-=delta*margin;if(min<0&&axis.datamin!=null&&axis.datamin>=0)min=0}if(opts.max==null){max+=delta*margin;if(max>0&&axis.datamax!=null&&axis.datamax<=0)max=0}}}axis.min=min;axis.max=max}function setupTickGeneration(axis){var opts=axis.options;var noTicks;if(typeof opts.ticks=="number"&&opts.ticks>0)noTicks=opts.ticks;else noTicks=.3*Math.sqrt(axis.direction=="x"?surface.width:surface.height);var delta=(axis.max-axis.min)/noTicks,dec=-Math.floor(Math.log(delta)/Math.LN10),maxDec=opts.tickDecimals;if(maxDec!=null&&dec>maxDec){dec=maxDec}var magn=Math.pow(10,-dec),norm=delta/magn,size;if(norm<1.5){size=1}else if(norm<3){size=2;if(norm>2.25&&(maxDec==null||dec+1<=maxDec)){size=2.5;++dec}}else if(norm<7.5){size=5}else{size=10}size*=magn;if(opts.minTickSize!=null&&size<opts.minTickSize){size=opts.minTickSize}axis.delta=delta;axis.tickDecimals=Math.max(0,maxDec!=null?maxDec:dec);axis.tickSize=opts.tickSize||size;if(opts.mode=="time"&&!axis.tickGenerator){throw new Error("Time mode requires the flot.time plugin.")}if(!axis.tickGenerator){axis.tickGenerator=function(axis){var ticks=[],start=floorInBase(axis.min,axis.tickSize),i=0,v=Number.NaN,prev;do{prev=v;v=start+i*axis.tickSize;ticks.push(v);++i}while(v<axis.max&&v!=prev);return ticks};axis.tickFormatter=function(value,axis){var factor=axis.tickDecimals?Math.pow(10,axis.tickDecimals):1;var formatted=""+Math.round(value*factor)/factor;if(axis.tickDecimals!=null){var decimal=formatted.indexOf(".");var precision=decimal==-1?0:formatted.length-decimal-1;if(precision<axis.tickDecimals){return(precision?formatted:formatted+".")+(""+factor).substr(1,axis.tickDecimals-precision)}}return formatted}}if($.isFunction(opts.tickFormatter))axis.tickFormatter=function(v,axis){return""+opts.tickFormatter(v,axis)};if(opts.alignTicksWithAxis!=null){var otherAxis=(axis.direction=="x"?xaxes:yaxes)[opts.alignTicksWithAxis-1];if(otherAxis&&otherAxis.used&&otherAxis!=axis){var niceTicks=axis.tickGenerator(axis);if(niceTicks.length>0){if(opts.min==null)axis.min=Math.min(axis.min,niceTicks[0]);if(opts.max==null&&niceTicks.length>1)axis.max=Math.max(axis.max,niceTicks[niceTicks.length-1])}axis.tickGenerator=function(axis){var ticks=[],v,i;for(i=0;i<otherAxis.ticks.length;++i){v=(otherAxis.ticks[i].v-otherAxis.min)/(otherAxis.max-otherAxis.min);v=axis.min+v*(axis.max-axis.min);ticks.push(v)}return ticks};if(!axis.mode&&opts.tickDecimals==null){var extraDec=Math.max(0,-Math.floor(Math.log(axis.delta)/Math.LN10)+1),ts=axis.tickGenerator(axis);if(!(ts.length>1&&/\..*0$/.test((ts[1]-ts[0]).toFixed(extraDec))))axis.tickDecimals=extraDec}}}}function setTicks(axis){var oticks=axis.options.ticks,ticks=[];if(oticks==null||typeof oticks=="number"&&oticks>0)ticks=axis.tickGenerator(axis);else if(oticks){if($.isFunction(oticks))ticks=oticks(axis);else ticks=oticks}var i,v;axis.ticks=[];for(i=0;i<ticks.length;++i){var label=null;var t=ticks[i];if(typeof t=="object"){v=+t[0];if(t.length>1)label=t[1]}else v=+t;if(label==null)label=axis.tickFormatter(v,axis);if(!isNaN(v))axis.ticks.push({v:v,label:label})}}function snapRangeToTicks(axis,ticks){if(axis.options.autoscaleMargin&&ticks.length>0){if(axis.options.min==null)axis.min=Math.min(axis.min,ticks[0].v);if(axis.options.max==null&&ticks.length>1)axis.max=Math.max(axis.max,ticks[ticks.length-1].v)}}function draw(){surface.clear();executeHooks(hooks.drawBackground,[ctx]);var grid=options.grid;if(grid.show&&grid.backgroundColor)drawBackground();if(grid.show&&!grid.aboveData){drawGrid()}for(var i=0;i<series.length;++i){executeHooks(hooks.drawSeries,[ctx,series[i]]);drawSeries(series[i])}executeHooks(hooks.draw,[ctx]);if(grid.show&&grid.aboveData){drawGrid()}surface.render();triggerRedrawOverlay()}function extractRange(ranges,coord){var axis,from,to,key,axes=allAxes();for(var i=0;i<axes.length;++i){axis=axes[i];if(axis.direction==coord){key=coord+axis.n+"axis";if(!ranges[key]&&axis.n==1)key=coord+"axis";if(ranges[key]){from=ranges[key].from;to=ranges[key].to;break}}}if(!ranges[key]){axis=coord=="x"?xaxes[0]:yaxes[0];from=ranges[coord+"1"];to=ranges[coord+"2"]}if(from!=null&&to!=null&&from>to){var tmp=from;from=to;to=tmp}return{from:from,to:to,axis:axis}}function drawBackground(){ctx.save();ctx.translate(plotOffset.left,plotOffset.top);ctx.fillStyle=getColorOrGradient(options.grid.backgroundColor,plotHeight,0,"rgba(255, 255, 255, 0)");ctx.fillRect(0,0,plotWidth,plotHeight);ctx.restore()}function drawGrid(){var i,axes,bw,bc;ctx.save();ctx.translate(plotOffset.left,plotOffset.top);var markings=options.grid.markings;if(markings){if($.isFunction(markings)){axes=plot.getAxes();axes.xmin=axes.xaxis.min;axes.xmax=axes.xaxis.max;axes.ymin=axes.yaxis.min;axes.ymax=axes.yaxis.max;markings=markings(axes)}for(i=0;i<markings.length;++i){var m=markings[i],xrange=extractRange(m,"x"),yrange=extractRange(m,"y");if(xrange.from==null)xrange.from=xrange.axis.min;if(xrange.to==null)xrange.to=xrange.axis.max;
19+if(yrange.from==null)yrange.from=yrange.axis.min;if(yrange.to==null)yrange.to=yrange.axis.max;if(xrange.to<xrange.axis.min||xrange.from>xrange.axis.max||yrange.to<yrange.axis.min||yrange.from>yrange.axis.max)continue;xrange.from=Math.max(xrange.from,xrange.axis.min);xrange.to=Math.min(xrange.to,xrange.axis.max);yrange.from=Math.max(yrange.from,yrange.axis.min);yrange.to=Math.min(yrange.to,yrange.axis.max);var xequal=xrange.from===xrange.to,yequal=yrange.from===yrange.to;if(xequal&&yequal){continue}xrange.from=Math.floor(xrange.axis.p2c(xrange.from));xrange.to=Math.floor(xrange.axis.p2c(xrange.to));yrange.from=Math.floor(yrange.axis.p2c(yrange.from));yrange.to=Math.floor(yrange.axis.p2c(yrange.to));if(xequal||yequal){var lineWidth=m.lineWidth||options.grid.markingsLineWidth,subPixel=lineWidth%2?.5:0;ctx.beginPath();ctx.strokeStyle=m.color||options.grid.markingsColor;ctx.lineWidth=lineWidth;if(xequal){ctx.moveTo(xrange.to+subPixel,yrange.from);ctx.lineTo(xrange.to+subPixel,yrange.to)}else{ctx.moveTo(xrange.from,yrange.to+subPixel);ctx.lineTo(xrange.to,yrange.to+subPixel)}ctx.stroke()}else{ctx.fillStyle=m.color||options.grid.markingsColor;ctx.fillRect(xrange.from,yrange.to,xrange.to-xrange.from,yrange.from-yrange.to)}}}axes=allAxes();bw=options.grid.borderWidth;for(var j=0;j<axes.length;++j){var axis=axes[j],box=axis.box,t=axis.tickLength,x,y,xoff,yoff;if(!axis.show||axis.ticks.length==0)continue;ctx.lineWidth=1;if(axis.direction=="x"){x=0;if(t=="full")y=axis.position=="top"?0:plotHeight;else y=box.top-plotOffset.top+(axis.position=="top"?box.height:0)}else{y=0;if(t=="full")x=axis.position=="left"?0:plotWidth;else x=box.left-plotOffset.left+(axis.position=="left"?box.width:0)}if(!axis.innermost){ctx.strokeStyle=axis.options.color;ctx.beginPath();xoff=yoff=0;if(axis.direction=="x")xoff=plotWidth+1;else yoff=plotHeight+1;if(ctx.lineWidth==1){if(axis.direction=="x"){y=Math.floor(y)+.5}else{x=Math.floor(x)+.5}}ctx.moveTo(x,y);ctx.lineTo(x+xoff,y+yoff);ctx.stroke()}ctx.strokeStyle=axis.options.tickColor;ctx.beginPath();for(i=0;i<axis.ticks.length;++i){var v=axis.ticks[i].v;xoff=yoff=0;if(isNaN(v)||v<axis.min||v>axis.max||t=="full"&&(typeof bw=="object"&&bw[axis.position]>0||bw>0)&&(v==axis.min||v==axis.max))continue;if(axis.direction=="x"){x=axis.p2c(v);yoff=t=="full"?-plotHeight:t;if(axis.position=="top")yoff=-yoff}else{y=axis.p2c(v);xoff=t=="full"?-plotWidth:t;if(axis.position=="left")xoff=-xoff}if(ctx.lineWidth==1){if(axis.direction=="x")x=Math.floor(x)+.5;else y=Math.floor(y)+.5}ctx.moveTo(x,y);ctx.lineTo(x+xoff,y+yoff)}ctx.stroke()}if(bw){bc=options.grid.borderColor;if(typeof bw=="object"||typeof bc=="object"){if(typeof bw!=="object"){bw={top:bw,right:bw,bottom:bw,left:bw}}if(typeof bc!=="object"){bc={top:bc,right:bc,bottom:bc,left:bc}}if(bw.top>0){ctx.strokeStyle=bc.top;ctx.lineWidth=bw.top;ctx.beginPath();ctx.moveTo(0-bw.left,0-bw.top/2);ctx.lineTo(plotWidth,0-bw.top/2);ctx.stroke()}if(bw.right>0){ctx.strokeStyle=bc.right;ctx.lineWidth=bw.right;ctx.beginPath();ctx.moveTo(plotWidth+bw.right/2,0-bw.top);ctx.lineTo(plotWidth+bw.right/2,plotHeight);ctx.stroke()}if(bw.bottom>0){ctx.strokeStyle=bc.bottom;ctx.lineWidth=bw.bottom;ctx.beginPath();ctx.moveTo(plotWidth+bw.right,plotHeight+bw.bottom/2);ctx.lineTo(0,plotHeight+bw.bottom/2);ctx.stroke()}if(bw.left>0){ctx.strokeStyle=bc.left;ctx.lineWidth=bw.left;ctx.beginPath();ctx.moveTo(0-bw.left/2,plotHeight+bw.bottom);ctx.lineTo(0-bw.left/2,0);ctx.stroke()}}else{ctx.lineWidth=bw;ctx.strokeStyle=options.grid.borderColor;ctx.strokeRect(-bw/2,-bw/2,plotWidth+bw,plotHeight+bw)}}ctx.restore()}function drawAxisLabels(){$.each(allAxes(),function(_,axis){var box=axis.box,legacyStyles=axis.direction+"Axis "+axis.direction+axis.n+"Axis",layer="flot-"+axis.direction+"-axis flot-"+axis.direction+axis.n+"-axis "+legacyStyles,font=axis.options.font||"flot-tick-label tickLabel",tick,x,y,halign,valign;surface.removeText(layer);if(!axis.show||axis.ticks.length==0)return;for(var i=0;i<axis.ticks.length;++i){tick=axis.ticks[i];if(!tick.label||tick.v<axis.min||tick.v>axis.max)continue;if(axis.direction=="x"){halign="center";x=plotOffset.left+axis.p2c(tick.v);if(axis.position=="bottom"){y=box.top+box.padding}else{y=box.top+box.height-box.padding;valign="bottom"}}else{valign="middle";y=plotOffset.top+axis.p2c(tick.v);if(axis.position=="left"){x=box.left+box.width-box.padding;halign="right"}else{x=box.left+box.padding}}surface.addText(layer,x,y,tick.label,font,null,null,halign,valign)}})}function drawSeries(series){if(series.lines.show)drawSeriesLines(series);if(series.bars.show)drawSeriesBars(series);if(series.points.show)drawSeriesPoints(series)}function drawSeriesLines(series){function plotLine(datapoints,xoffset,yoffset,axisx,axisy){var points=datapoints.points,ps=datapoints.pointsize,prevx=null,prevy=null;ctx.beginPath();for(var i=ps;i<points.length;i+=ps){var x1=points[i-ps],y1=points[i-ps+1],x2=points[i],y2=points[i+1];if(x1==null||x2==null)continue;if(y1<=y2&&y1<axisy.min){if(y2<axisy.min)continue;x1=(axisy.min-y1)/(y2-y1)*(x2-x1)+x1;y1=axisy.min}else if(y2<=y1&&y2<axisy.min){if(y1<axisy.min)continue;x2=(axisy.min-y1)/(y2-y1)*(x2-x1)+x1;y2=axisy.min}if(y1>=y2&&y1>axisy.max){if(y2>axisy.max)continue;x1=(axisy.max-y1)/(y2-y1)*(x2-x1)+x1;y1=axisy.max}else if(y2>=y1&&y2>axisy.max){if(y1>axisy.max)continue;x2=(axisy.max-y1)/(y2-y1)*(x2-x1)+x1;y2=axisy.max}if(x1<=x2&&x1<axisx.min){if(x2<axisx.min)continue;y1=(axisx.min-x1)/(x2-x1)*(y2-y1)+y1;x1=axisx.min}else if(x2<=x1&&x2<axisx.min){if(x1<axisx.min)continue;y2=(axisx.min-x1)/(x2-x1)*(y2-y1)+y1;x2=axisx.min}if(x1>=x2&&x1>axisx.max){if(x2>axisx.max)continue;y1=(axisx.max-x1)/(x2-x1)*(y2-y1)+y1;x1=axisx.max}else if(x2>=x1&&x2>axisx.max){if(x1>axisx.max)continue;y2=(axisx.max-x1)/(x2-x1)*(y2-y1)+y1;x2=axisx.max}if(x1!=prevx||y1!=prevy)ctx.moveTo(axisx.p2c(x1)+xoffset,axisy.p2c(y1)+yoffset);prevx=x2;prevy=y2;ctx.lineTo(axisx.p2c(x2)+xoffset,axisy.p2c(y2)+yoffset)}ctx.stroke()}function plotLineArea(datapoints,axisx,axisy){var points=datapoints.points,ps=datapoints.pointsize,bottom=Math.min(Math.max(0,axisy.min),axisy.max),i=0,top,areaOpen=false,ypos=1,segmentStart=0,segmentEnd=0;while(true){if(ps>0&&i>points.length+ps)break;i+=ps;var x1=points[i-ps],y1=points[i-ps+ypos],x2=points[i],y2=points[i+ypos];if(areaOpen){if(ps>0&&x1!=null&&x2==null){segmentEnd=i;ps=-ps;ypos=2;continue}if(ps<0&&i==segmentStart+ps){ctx.fill();areaOpen=false;ps=-ps;ypos=1;i=segmentStart=segmentEnd+ps;continue}}if(x1==null||x2==null)continue;if(x1<=x2&&x1<axisx.min){if(x2<axisx.min)continue;y1=(axisx.min-x1)/(x2-x1)*(y2-y1)+y1;x1=axisx.min}else if(x2<=x1&&x2<axisx.min){if(x1<axisx.min)continue;y2=(axisx.min-x1)/(x2-x1)*(y2-y1)+y1;x2=axisx.min}if(x1>=x2&&x1>axisx.max){if(x2>axisx.max)continue;y1=(axisx.max-x1)/(x2-x1)*(y2-y1)+y1;x1=axisx.max}else if(x2>=x1&&x2>axisx.max){if(x1>axisx.max)continue;y2=(axisx.max-x1)/(x2-x1)*(y2-y1)+y1;x2=axisx.max}if(!areaOpen){ctx.beginPath();ctx.moveTo(axisx.p2c(x1),axisy.p2c(bottom));areaOpen=true}if(y1>=axisy.max&&y2>=axisy.max){ctx.lineTo(axisx.p2c(x1),axisy.p2c(axisy.max));ctx.lineTo(axisx.p2c(x2),axisy.p2c(axisy.max));continue}else if(y1<=axisy.min&&y2<=axisy.min){ctx.lineTo(axisx.p2c(x1),axisy.p2c(axisy.min));ctx.lineTo(axisx.p2c(x2),axisy.p2c(axisy.min));continue}var x1old=x1,x2old=x2;if(y1<=y2&&y1<axisy.min&&y2>=axisy.min){x1=(axisy.min-y1)/(y2-y1)*(x2-x1)+x1;y1=axisy.min}else if(y2<=y1&&y2<axisy.min&&y1>=axisy.min){x2=(axisy.min-y1)/(y2-y1)*(x2-x1)+x1;y2=axisy.min}if(y1>=y2&&y1>axisy.max&&y2<=axisy.max){x1=(axisy.max-y1)/(y2-y1)*(x2-x1)+x1;y1=axisy.max}else if(y2>=y1&&y2>axisy.max&&y1<=axisy.max){x2=(axisy.max-y1)/(y2-y1)*(x2-x1)+x1;y2=axisy.max}if(x1!=x1old){ctx.lineTo(axisx.p2c(x1old),axisy.p2c(y1))}ctx.lineTo(axisx.p2c(x1),axisy.p2c(y1));ctx.lineTo(axisx.p2c(x2),axisy.p2c(y2));if(x2!=x2old){ctx.lineTo(axisx.p2c(x2),axisy.p2c(y2));ctx.lineTo(axisx.p2c(x2old),axisy.p2c(y2))}}}ctx.save();ctx.translate(plotOffset.left,plotOffset.top);ctx.lineJoin="round";var lw=series.lines.lineWidth,sw=series.shadowSize;if(lw>0&&sw>0){ctx.lineWidth=sw;ctx.strokeStyle="rgba(0,0,0,0.1)";var angle=Math.PI/18;plotLine(series.datapoints,Math.sin(angle)*(lw/2+sw/2),Math.cos(angle)*(lw/2+sw/2),series.xaxis,series.yaxis);ctx.lineWidth=sw/2;plotLine(series.datapoints,Math.sin(angle)*(lw/2+sw/4),Math.cos(angle)*(lw/2+sw/4),series.xaxis,series.yaxis)}ctx.lineWidth=lw;ctx.strokeStyle=series.color;var fillStyle=getFillStyle(series.lines,series.color,0,plotHeight);if(fillStyle){ctx.fillStyle=fillStyle;plotLineArea(series.datapoints,series.xaxis,series.yaxis)}if(lw>0)plotLine(series.datapoints,0,0,series.xaxis,series.yaxis);ctx.restore()}function drawSeriesPoints(series){function plotPoints(datapoints,radius,fillStyle,offset,shadow,axisx,axisy,symbol){var points=datapoints.points,ps=datapoints.pointsize;for(var i=0;i<points.length;i+=ps){var x=points[i],y=points[i+1];if(x==null||x<axisx.min||x>axisx.max||y<axisy.min||y>axisy.max)continue;ctx.beginPath();x=axisx.p2c(x);y=axisy.p2c(y)+offset;if(symbol=="circle")ctx.arc(x,y,radius,0,shadow?Math.PI:Math.PI*2,false);else symbol(ctx,x,y,radius,shadow);ctx.closePath();if(fillStyle){ctx.fillStyle=fillStyle;ctx.fill()}ctx.stroke()}}ctx.save();ctx.translate(plotOffset.left,plotOffset.top);var lw=series.points.lineWidth,sw=series.shadowSize,radius=series.points.radius,symbol=series.points.symbol;if(lw==0)lw=1e-4;if(lw>0&&sw>0){var w=sw/2;ctx.lineWidth=w;ctx.strokeStyle="rgba(0,0,0,0.1)";plotPoints(series.datapoints,radius,null,w+w/2,true,series.xaxis,series.yaxis,symbol);ctx.strokeStyle="rgba(0,0,0,0.2)";plotPoints(series.datapoints,radius,null,w/2,true,series.xaxis,series.yaxis,symbol)}ctx.lineWidth=lw;ctx.strokeStyle=series.color;plotPoints(series.datapoints,radius,getFillStyle(series.points,series.color),0,false,series.xaxis,series.yaxis,symbol);ctx.restore()}function drawBar(x,y,b,barLeft,barRight,fillStyleCallback,axisx,axisy,c,horizontal,lineWidth){var left,right,bottom,top,drawLeft,drawRight,drawTop,drawBottom,tmp;if(horizontal){drawBottom=drawRight=drawTop=true;drawLeft=false;left=b;right=x;top=y+barLeft;bottom=y+barRight;if(right<left){tmp=right;right=left;left=tmp;drawLeft=true;drawRight=false}}else{drawLeft=drawRight=drawTop=true;drawBottom=false;left=x+barLeft;right=x+barRight;bottom=b;top=y;if(top<bottom){tmp=top;top=bottom;bottom=tmp;drawBottom=true;drawTop=false}}if(right<axisx.min||left>axisx.max||top<axisy.min||bottom>axisy.max)return;if(left<axisx.min){left=axisx.min;drawLeft=false}if(right>axisx.max){right=axisx.max;drawRight=false}if(bottom<axisy.min){bottom=axisy.min;drawBottom=false}if(top>axisy.max){top=axisy.max;drawTop=false}left=axisx.p2c(left);bottom=axisy.p2c(bottom);right=axisx.p2c(right);top=axisy.p2c(top);if(fillStyleCallback){c.fillStyle=fillStyleCallback(bottom,top);c.fillRect(left,top,right-left,bottom-top)}if(lineWidth>0&&(drawLeft||drawRight||drawTop||drawBottom)){c.beginPath();c.moveTo(left,bottom);if(drawLeft)c.lineTo(left,top);else c.moveTo(left,top);if(drawTop)c.lineTo(right,top);else c.moveTo(right,top);if(drawRight)c.lineTo(right,bottom);else c.moveTo(right,bottom);if(drawBottom)c.lineTo(left,bottom);else c.moveTo(left,bottom);c.stroke()}}function drawSeriesBars(series){function plotBars(datapoints,barLeft,barRight,fillStyleCallback,axisx,axisy){var points=datapoints.points,ps=datapoints.pointsize;for(var i=0;i<points.length;i+=ps){if(points[i]==null)continue;drawBar(points[i],points[i+1],points[i+2],barLeft,barRight,fillStyleCallback,axisx,axisy,ctx,series.bars.horizontal,series.bars.lineWidth)}}ctx.save();ctx.translate(plotOffset.left,plotOffset.top);ctx.lineWidth=series.bars.lineWidth;ctx.strokeStyle=series.color;var barLeft;switch(series.bars.align){case"left":barLeft=0;break;case"right":barLeft=-series.bars.barWidth;break;default:barLeft=-series.bars.barWidth/2}var fillStyleCallback=series.bars.fill?function(bottom,top){return getFillStyle(series.bars,series.color,bottom,top)}:null;plotBars(series.datapoints,barLeft,barLeft+series.bars.barWidth,fillStyleCallback,series.xaxis,series.yaxis);ctx.restore()}function getFillStyle(filloptions,seriesColor,bottom,top){var fill=filloptions.fill;if(!fill)return null;if(filloptions.fillColor)return getColorOrGradient(filloptions.fillColor,bottom,top,seriesColor);var c=$.color.parse(seriesColor);c.a=typeof fill=="number"?fill:.4;c.normalize();return c.toString()}function insertLegend(){if(options.legend.container!=null){$(options.legend.container).html("")}else{placeholder.find(".legend").remove()}if(!options.legend.show){return}var fragments=[],entries=[],rowStarted=false,lf=options.legend.labelFormatter,s,label;for(var i=0;i<series.length;++i){s=series[i];if(s.label){label=lf?lf(s.label,s):s.label;if(label){entries.push({label:label,color:s.color})}}}if(options.legend.sorted){if($.isFunction(options.legend.sorted)){entries.sort(options.legend.sorted)}else if(options.legend.sorted=="reverse"){entries.reverse()}else{var ascending=options.legend.sorted!="descending";entries.sort(function(a,b){return a.label==b.label?0:a.label<b.label!=ascending?1:-1})}}for(var i=0;i<entries.length;++i){var entry=entries[i];if(i%options.legend.noColumns==0){if(rowStarted)fragments.push("</tr>");fragments.push("<tr>");rowStarted=true}fragments.push('<td class="legendColorBox"><div style="border:1px solid '+options.legend.labelBoxBorderColor+';padding:1px"><div style="width:4px;height:0;border:5px solid '+entry.color+';overflow:hidden"></div></div></td>'+'<td class="legendLabel">'+entry.label+"</td>")}if(rowStarted)fragments.push("</tr>");if(fragments.length==0)return;var table='<table style="font-size:smaller;color:'+options.grid.color+'">'+fragments.join("")+"</table>";if(options.legend.container!=null)$(options.legend.container).html(table);else{var pos="",p=options.legend.position,m=options.legend.margin;if(m[0]==null)m=[m,m];if(p.charAt(0)=="n")pos+="top:"+(m[1]+plotOffset.top)+"px;";else if(p.charAt(0)=="s")pos+="bottom:"+(m[1]+plotOffset.bottom)+"px;";if(p.charAt(1)=="e")pos+="right:"+(m[0]+plotOffset.right)+"px;";else if(p.charAt(1)=="w")pos+="left:"+(m[0]+plotOffset.left)+"px;";var legend=$('<div class="legend">'+table.replace('style="','style="position:absolute;'+pos+";")+"</div>").appendTo(placeholder);if(options.legend.backgroundOpacity!=0){var c=options.legend.backgroundColor;if(c==null){c=options.grid.backgroundColor;if(c&&typeof c=="string")c=$.color.parse(c);else c=$.color.extract(legend,"background-color");c.a=1;c=c.toString()}var div=legend.children();$('<div style="position:absolute;width:'+div.width()+"px;height:"+div.height()+"px;"+pos+"background-color:"+c+';"> </div>').prependTo(legend).css("opacity",options.legend.backgroundOpacity)}}}var highlights=[],redrawTimeout=null;function findNearbyItem(mouseX,mouseY,seriesFilter){var maxDistance=options.grid.mouseActiveRadius,smallestDistance=maxDistance*maxDistance+1,item=null,foundPoint=false,i,j,ps;for(i=series.length-1;i>=0;--i){if(!seriesFilter(series[i]))continue;var s=series[i],axisx=s.xaxis,axisy=s.yaxis,points=s.datapoints.points,mx=axisx.c2p(mouseX),my=axisy.c2p(mouseY),maxx=maxDistance/axisx.scale,maxy=maxDistance/axisy.scale;ps=s.datapoints.pointsize;if(axisx.options.inverseTransform)maxx=Number.MAX_VALUE;if(axisy.options.inverseTransform)maxy=Number.MAX_VALUE;if(s.lines.show||s.points.show){for(j=0;j<points.length;j+=ps){var x=points[j],y=points[j+1];if(x==null)continue;if(x-mx>maxx||x-mx<-maxx||y-my>maxy||y-my<-maxy)continue;var dx=Math.abs(axisx.p2c(x)-mouseX),dy=Math.abs(axisy.p2c(y)-mouseY),dist=dx*dx+dy*dy;if(dist<smallestDistance){smallestDistance=dist;item=[i,j/ps]}}}if(s.bars.show&&!item){var barLeft,barRight;switch(s.bars.align){case"left":barLeft=0;break;case"right":barLeft=-s.bars.barWidth;break;default:barLeft=-s.bars.barWidth/2}barRight=barLeft+s.bars.barWidth;for(j=0;j<points.length;j+=ps){var x=points[j],y=points[j+1],b=points[j+2];if(x==null)continue;if(series[i].bars.horizontal?mx<=Math.max(b,x)&&mx>=Math.min(b,x)&&my>=y+barLeft&&my<=y+barRight:mx>=x+barLeft&&mx<=x+barRight&&my>=Math.min(b,y)&&my<=Math.max(b,y))item=[i,j/ps]}}}if(item){i=item[0];j=item[1];ps=series[i].datapoints.pointsize;return{datapoint:series[i].datapoints.points.slice(j*ps,(j+1)*ps),dataIndex:j,series:series[i],seriesIndex:i}}return null}function onMouseMove(e){if(options.grid.hoverable)triggerClickHoverEvent("plothover",e,function(s){return s["hoverable"]!=false})}function onMouseLeave(e){if(options.grid.hoverable)triggerClickHoverEvent("plothover",e,function(s){return false})}function onClick(e){triggerClickHoverEvent("plotclick",e,function(s){return s["clickable"]!=false})}function triggerClickHoverEvent(eventname,event,seriesFilter){var offset=eventHolder.offset(),canvasX=event.pageX-offset.left-plotOffset.left,canvasY=event.pageY-offset.top-plotOffset.top,pos=canvasToAxisCoords({left:canvasX,top:canvasY});pos.pageX=event.pageX;pos.pageY=event.pageY;var item=findNearbyItem(canvasX,canvasY,seriesFilter);if(item){item.pageX=parseInt(item.series.xaxis.p2c(item.datapoint[0])+offset.left+plotOffset.left,10);item.pageY=parseInt(item.series.yaxis.p2c(item.datapoint[1])+offset.top+plotOffset.top,10)}if(options.grid.autoHighlight){for(var i=0;i<highlights.length;++i){var h=highlights[i];if(h.auto==eventname&&!(item&&h.series==item.series&&h.point[0]==item.datapoint[0]&&h.point[1]==item.datapoint[1]))unhighlight(h.series,h.point)}if(item)highlight(item.series,item.datapoint,eventname)}placeholder.trigger(eventname,[pos,item])}function triggerRedrawOverlay(){var 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21+ <script language="javascript" type="text/javascript">
22+ /* Javascript plotting library for jQuery, version 0.8.3.
23+
24+Copyright (c) 2007-2014 IOLA and Ole Laursen.
25+Licensed under the MIT license.
26+
27+*/
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29+ </script>
30+ <script language="javascript" type="text/javascript">
31+ /* Javascript plotting library for jQuery, version 0.8.3.
32+
33+Copyright (c) 2007-2014 IOLA and Ole Laursen.
34+Licensed under the MIT license.
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256+ </style>
257+ <![endif]-->
258+ </head>
259+ <body>
260+ <div id="wrap">
261+ <div id="main" class="body">
262+ <h1>criterion performance measurements</h1>
263+
264+<h2>overview</h2>
265+
266+<p><a href="#grokularation">want to understand this report?</a></p>
267+
268+<div id="overview" class="ovchart" style="width:900px;height:100px;"></div>
269+
270+<h2><a name="b0">Matrix Composition/10x10/WHNF - 10x10</a></h2>
271+ <table width="100%">
272+ <tbody>
273+ <tr>
274+ <td><div id="kde0" class="kdechart"
275+ style="width:450px;height:278px;"></div></td>
276+ <td><div id="time0" class="timechart"
277+ style="width:450px;height:278px;"></div></td>
278+<!--
279+ <td><div id="cycle0" class="cyclechart"
280+ style="width:300px;height:278px;"></div></td>
281+-->
282+ </tr>
283+ </tbody>
284+ </table>
285+
286+ <table>
287+ <thead class="analysis">
288+ <th></th>
289+ <th class="cibound"
290+ title="0.95 confidence level">lower bound</th>
291+ <th>estimate</th>
292+ <th class="cibound"
293+ title="0.95 confidence level">upper bound</th>
294+ </thead>
295+ <tbody>
296+ <tr>
297+ <td>OLS regression</td>
298+ <td><span class="confinterval olstimelb0">xxx</span></td>
299+ <td><span class="olstimept0">xxx</span></td>
300+ <td><span class="confinterval olstimeub0">xxx</span></td>
301+ </tr>
302+ <tr>
303+ <td>R&#xb2; goodness-of-fit</td>
304+ <td><span class="confinterval olsr2lb0">xxx</span></td>
305+ <td><span class="olsr2pt0">xxx</span></td>
306+ <td><span class="confinterval olsr2ub0">xxx</span></td>
307+ </tr>
308+ <tr>
309+ <td>Mean execution time</td>
310+ <td><span class="confinterval citime">2.429905310206746e-8</span></td>
311+ <td><span class="time">2.4514866756029205e-8</span></td>
312+ <td><span class="confinterval citime">2.48855951010762e-8</span></td>
313+ </tr>
314+ <tr>
315+ <td>Standard deviation</td>
316+ <td><span class="confinterval citime">6.998202238158643e-10</span></td>
317+ <td><span class="time">9.647785488002723e-10</span></td>
318+ <td><span class="confinterval citime">1.4224955576371737e-9</span></td>
319+ </tr>
320+ </tbody>
321+ </table>
322+
323+ <span class="outliers">
324+ <p>Outlying measurements have severe
325+ (<span class="percent">0.6233390798012226</span>%)
326+ effect on estimated standard deviation.</p>
327+ </span>
328+<h2><a name="b1">Matrix Composition/10x10/NF - 10x10</a></h2>
329+ <table width="100%">
330+ <tbody>
331+ <tr>
332+ <td><div id="kde1" class="kdechart"
333+ style="width:450px;height:278px;"></div></td>
334+ <td><div id="time1" class="timechart"
335+ style="width:450px;height:278px;"></div></td>
336+<!--
337+ <td><div id="cycle1" class="cyclechart"
338+ style="width:300px;height:278px;"></div></td>
339+-->
340+ </tr>
341+ </tbody>
342+ </table>
343+
344+ <table>
345+ <thead class="analysis">
346+ <th></th>
347+ <th class="cibound"
348+ title="0.95 confidence level">lower bound</th>
349+ <th>estimate</th>
350+ <th class="cibound"
351+ title="0.95 confidence level">upper bound</th>
352+ </thead>
353+ <tbody>
354+ <tr>
355+ <td>OLS regression</td>
356+ <td><span class="confinterval olstimelb1">xxx</span></td>
357+ <td><span class="olstimept1">xxx</span></td>
358+ <td><span class="confinterval olstimeub1">xxx</span></td>
359+ </tr>
360+ <tr>
361+ <td>R&#xb2; goodness-of-fit</td>
362+ <td><span class="confinterval olsr2lb1">xxx</span></td>
363+ <td><span class="olsr2pt1">xxx</span></td>
364+ <td><span class="confinterval olsr2ub1">xxx</span></td>
365+ </tr>
366+ <tr>
367+ <td>Mean execution time</td>
368+ <td><span class="confinterval citime">2.0370099798754226e-4</span></td>
369+ <td><span class="time">2.0678688880349948e-4</span></td>
370+ <td><span class="confinterval citime">2.120795744857106e-4</span></td>
371+ </tr>
372+ <tr>
373+ <td>Standard deviation</td>
374+ <td><span class="confinterval citime">9.393316405757422e-6</span></td>
375+ <td><span class="time">1.2679488723877765e-5</span></td>
376+ <td><span class="confinterval citime">1.685081532022437e-5</span></td>
377+ </tr>
378+ </tbody>
379+ </table>
380+
381+ <span class="outliers">
382+ <p>Outlying measurements have severe
383+ (<span class="percent">0.5927893628180484</span>%)
384+ effect on estimated standard deviation.</p>
385+ </span>
386+<h2><a name="b2">Matrix Composition/100x100/WHNF - 100x100</a></h2>
387+ <table width="100%">
388+ <tbody>
389+ <tr>
390+ <td><div id="kde2" class="kdechart"
391+ style="width:450px;height:278px;"></div></td>
392+ <td><div id="time2" class="timechart"
393+ style="width:450px;height:278px;"></div></td>
394+<!--
395+ <td><div id="cycle2" class="cyclechart"
396+ style="width:300px;height:278px;"></div></td>
397+-->
398+ </tr>
399+ </tbody>
400+ </table>
401+
402+ <table>
403+ <thead class="analysis">
404+ <th></th>
405+ <th class="cibound"
406+ title="0.95 confidence level">lower bound</th>
407+ <th>estimate</th>
408+ <th class="cibound"
409+ title="0.95 confidence level">upper bound</th>
410+ </thead>
411+ <tbody>
412+ <tr>
413+ <td>OLS regression</td>
414+ <td><span class="confinterval olstimelb2">xxx</span></td>
415+ <td><span class="olstimept2">xxx</span></td>
416+ <td><span class="confinterval olstimeub2">xxx</span></td>
417+ </tr>
418+ <tr>
419+ <td>R&#xb2; goodness-of-fit</td>
420+ <td><span class="confinterval olsr2lb2">xxx</span></td>
421+ <td><span class="olsr2pt2">xxx</span></td>
422+ <td><span class="confinterval olsr2ub2">xxx</span></td>
423+ </tr>
424+ <tr>
425+ <td>Mean execution time</td>
426+ <td><span class="confinterval citime">2.0050477013786835e-8</span></td>
427+ <td><span class="time">2.032500748180748e-8</span></td>
428+ <td><span class="confinterval citime">2.076846088643864e-8</span></td>
429+ </tr>
430+ <tr>
431+ <td>Standard deviation</td>
432+ <td><span class="confinterval citime">8.13204445187969e-10</span></td>
433+ <td><span class="time">1.1748079988373767e-9</span></td>
434+ <td><span class="confinterval citime">1.9440744217217704e-9</span></td>
435+ </tr>
436+ </tbody>
437+ </table>
438+
439+ <span class="outliers">
440+ <p>Outlying measurements have severe
441+ (<span class="percent">0.783687156722499</span>%)
442+ effect on estimated standard deviation.</p>
443+ </span>
444+<h2><a name="b3">Matrix Composition/100x100/NF - 100x100</a></h2>
445+ <table width="100%">
446+ <tbody>
447+ <tr>
448+ <td><div id="kde3" class="kdechart"
449+ style="width:450px;height:278px;"></div></td>
450+ <td><div id="time3" class="timechart"
451+ style="width:450px;height:278px;"></div></td>
452+<!--
453+ <td><div id="cycle3" class="cyclechart"
454+ style="width:300px;height:278px;"></div></td>
455+-->
456+ </tr>
457+ </tbody>
458+ </table>
459+
460+ <table>
461+ <thead class="analysis">
462+ <th></th>
463+ <th class="cibound"
464+ title="0.95 confidence level">lower bound</th>
465+ <th>estimate</th>
466+ <th class="cibound"
467+ title="0.95 confidence level">upper bound</th>
468+ </thead>
469+ <tbody>
470+ <tr>
471+ <td>OLS regression</td>
472+ <td><span class="confinterval olstimelb3">xxx</span></td>
473+ <td><span class="olstimept3">xxx</span></td>
474+ <td><span class="confinterval olstimeub3">xxx</span></td>
475+ </tr>
476+ <tr>
477+ <td>R&#xb2; goodness-of-fit</td>
478+ <td><span class="confinterval olsr2lb3">xxx</span></td>
479+ <td><span class="olsr2pt3">xxx</span></td>
480+ <td><span class="confinterval olsr2ub3">xxx</span></td>
481+ </tr>
482+ <tr>
483+ <td>Mean execution time</td>
484+ <td><span class="confinterval citime">0.3498868480000965</span></td>
485+ <td><span class="time">0.3562973993334708</span></td>
486+ <td><span class="confinterval citime">0.36268595299998196</span></td>
487+ </tr>
488+ <tr>
489+ <td>Standard deviation</td>
490+ <td><span class="confinterval citime">3.523610261477639e-3</span></td>
491+ <td><span class="time">7.81042655007339e-3</span></td>
492+ <td><span class="confinterval citime">9.18947292446396e-3</span></td>
493+ </tr>
494+ </tbody>
495+ </table>
496+
497+ <span class="outliers">
498+ <p>Outlying measurements have moderate
499+ (<span class="percent">0.1875</span>%)
500+ effect on estimated standard deviation.</p>
501+ </span>
502+<h2><a name="b4">Matrix Composition/200x200/WHNF - 200x200</a></h2>
503+ <table width="100%">
504+ <tbody>
505+ <tr>
506+ <td><div id="kde4" class="kdechart"
507+ style="width:450px;height:278px;"></div></td>
508+ <td><div id="time4" class="timechart"
509+ style="width:450px;height:278px;"></div></td>
510+<!--
511+ <td><div id="cycle4" class="cyclechart"
512+ style="width:300px;height:278px;"></div></td>
513+-->
514+ </tr>
515+ </tbody>
516+ </table>
517+
518+ <table>
519+ <thead class="analysis">
520+ <th></th>
521+ <th class="cibound"
522+ title="0.95 confidence level">lower bound</th>
523+ <th>estimate</th>
524+ <th class="cibound"
525+ title="0.95 confidence level">upper bound</th>
526+ </thead>
527+ <tbody>
528+ <tr>
529+ <td>OLS regression</td>
530+ <td><span class="confinterval olstimelb4">xxx</span></td>
531+ <td><span class="olstimept4">xxx</span></td>
532+ <td><span class="confinterval olstimeub4">xxx</span></td>
533+ </tr>
534+ <tr>
535+ <td>R&#xb2; goodness-of-fit</td>
536+ <td><span class="confinterval olsr2lb4">xxx</span></td>
537+ <td><span class="olsr2pt4">xxx</span></td>
538+ <td><span class="confinterval olsr2ub4">xxx</span></td>
539+ </tr>
540+ <tr>
541+ <td>Mean execution time</td>
542+ <td><span class="confinterval citime">2.0235240565823596e-8</span></td>
543+ <td><span class="time">2.0667543937993357e-8</span></td>
544+ <td><span class="confinterval citime">2.143971075518602e-8</span></td>
545+ </tr>
546+ <tr>
547+ <td>Standard deviation</td>
548+ <td><span class="confinterval citime">1.1209286317154773e-9</span></td>
549+ <td><span class="time">1.8602778611455406e-9</span></td>
550+ <td><span class="confinterval citime">2.8888629297529752e-9</span></td>
551+ </tr>
552+ </tbody>
553+ </table>
554+
555+ <span class="outliers">
556+ <p>Outlying measurements have severe
557+ (<span class="percent">0.8983666121212811</span>%)
558+ effect on estimated standard deviation.</p>
559+ </span>
560+<h2><a name="b5">Matrix Composition/200x200/NF - 200x200</a></h2>
561+ <table width="100%">
562+ <tbody>
563+ <tr>
564+ <td><div id="kde5" class="kdechart"
565+ style="width:450px;height:278px;"></div></td>
566+ <td><div id="time5" class="timechart"
567+ style="width:450px;height:278px;"></div></td>
568+<!--
569+ <td><div id="cycle5" class="cyclechart"
570+ style="width:300px;height:278px;"></div></td>
571+-->
572+ </tr>
573+ </tbody>
574+ </table>
575+
576+ <table>
577+ <thead class="analysis">
578+ <th></th>
579+ <th class="cibound"
580+ title="0.95 confidence level">lower bound</th>
581+ <th>estimate</th>
582+ <th class="cibound"
583+ title="0.95 confidence level">upper bound</th>
584+ </thead>
585+ <tbody>
586+ <tr>
587+ <td>OLS regression</td>
588+ <td><span class="confinterval olstimelb5">xxx</span></td>
589+ <td><span class="olstimept5">xxx</span></td>
590+ <td><span class="confinterval olstimeub5">xxx</span></td>
591+ </tr>
592+ <tr>
593+ <td>R&#xb2; goodness-of-fit</td>
594+ <td><span class="confinterval olsr2lb5">xxx</span></td>
595+ <td><span class="olsr2pt5">xxx</span></td>
596+ <td><span class="confinterval olsr2ub5">xxx</span></td>
597+ </tr>
598+ <tr>
599+ <td>Mean execution time</td>
600+ <td><span class="confinterval citime">4.562200145314364</span></td>
601+ <td><span class="time">4.623436544688502</span></td>
602+ <td><span class="confinterval citime">4.66968996875039</span></td>
603+ </tr>
604+ <tr>
605+ <td>Standard deviation</td>
606+ <td><span class="confinterval citime">3.460169931915702e-2</span></td>
607+ <td><span class="time">6.412809734921064e-2</span></td>
608+ <td><span class="confinterval citime">8.889305315202672e-2</span></td>
609+ </tr>
610+ </tbody>
611+ </table>
612+
613+ <span class="outliers">
614+ <p>Outlying measurements have moderate
615+ (<span class="percent">0.18749999999999997</span>%)
616+ effect on estimated standard deviation.</p>
617+ </span>
618+<h2><a name="b6">Matrix vs List - `select`/Distribution `select` - 100+100 / 100x100/List Distribution - Applicative version</a></h2>
619+ <table width="100%">
620+ <tbody>
621+ <tr>
622+ <td><div id="kde6" class="kdechart"
623+ style="width:450px;height:278px;"></div></td>
624+ <td><div id="time6" class="timechart"
625+ style="width:450px;height:278px;"></div></td>
626+<!--
627+ <td><div id="cycle6" class="cyclechart"
628+ style="width:300px;height:278px;"></div></td>
629+-->
630+ </tr>
631+ </tbody>
632+ </table>
633+
634+ <table>
635+ <thead class="analysis">
636+ <th></th>
637+ <th class="cibound"
638+ title="0.95 confidence level">lower bound</th>
639+ <th>estimate</th>
640+ <th class="cibound"
641+ title="0.95 confidence level">upper bound</th>
642+ </thead>
643+ <tbody>
644+ <tr>
645+ <td>OLS regression</td>
646+ <td><span class="confinterval olstimelb6">xxx</span></td>
647+ <td><span class="olstimept6">xxx</span></td>
648+ <td><span class="confinterval olstimeub6">xxx</span></td>
649+ </tr>
650+ <tr>
651+ <td>R&#xb2; goodness-of-fit</td>
652+ <td><span class="confinterval olsr2lb6">xxx</span></td>
653+ <td><span class="olsr2pt6">xxx</span></td>
654+ <td><span class="confinterval olsr2ub6">xxx</span></td>
655+ </tr>
656+ <tr>
657+ <td>Mean execution time</td>
658+ <td><span class="confinterval citime">2.2228158466256596</span></td>
659+ <td><span class="time">2.3105826970010335</span></td>
660+ <td><span class="confinterval citime">2.477541572751458</span></td>
661+ </tr>
662+ <tr>
663+ <td>Standard deviation</td>
664+ <td><span class="confinterval citime">1.668510235695031e-3</span></td>
665+ <td><span class="time">0.16563995052316</span></td>
666+ <td><span class="confinterval citime">0.19608795539767002</span></td>
667+ </tr>
668+ </tbody>
669+ </table>
670+
671+ <span class="outliers">
672+ <p>Outlying measurements have moderate
673+ (<span class="percent">0.2024935146554294</span>%)
674+ effect on estimated standard deviation.</p>
675+ </span>
676+<h2><a name="b7">Matrix vs List - `select`/Distribution `select` - 100+100 / 100x100/Matrix Distribution - Applicative version</a></h2>
677+ <table width="100%">
678+ <tbody>
679+ <tr>
680+ <td><div id="kde7" class="kdechart"
681+ style="width:450px;height:278px;"></div></td>
682+ <td><div id="time7" class="timechart"
683+ style="width:450px;height:278px;"></div></td>
684+<!--
685+ <td><div id="cycle7" class="cyclechart"
686+ style="width:300px;height:278px;"></div></td>
687+-->
688+ </tr>
689+ </tbody>
690+ </table>
691+
692+ <table>
693+ <thead class="analysis">
694+ <th></th>
695+ <th class="cibound"
696+ title="0.95 confidence level">lower bound</th>
697+ <th>estimate</th>
698+ <th class="cibound"
699+ title="0.95 confidence level">upper bound</th>
700+ </thead>
701+ <tbody>
702+ <tr>
703+ <td>OLS regression</td>
704+ <td><span class="confinterval olstimelb7">xxx</span></td>
705+ <td><span class="olstimept7">xxx</span></td>
706+ <td><span class="confinterval olstimeub7">xxx</span></td>
707+ </tr>
708+ <tr>
709+ <td>R&#xb2; goodness-of-fit</td>
710+ <td><span class="confinterval olsr2lb7">xxx</span></td>
711+ <td><span class="olsr2pt7">xxx</span></td>
712+ <td><span class="confinterval olsr2ub7">xxx</span></td>
713+ </tr>
714+ <tr>
715+ <td>Mean execution time</td>
716+ <td><span class="confinterval citime">2.4757740044307665e-3</span></td>
717+ <td><span class="time">2.672449312433179e-3</span></td>
718+ <td><span class="confinterval citime">3.145392355479385e-3</span></td>
719+ </tr>
720+ <tr>
721+ <td>Standard deviation</td>
722+ <td><span class="confinterval citime">4.61354238444537e-4</span></td>
723+ <td><span class="time">9.064184723100453e-4</span></td>
724+ <td><span class="confinterval citime">1.692293726555292e-3</span></td>
725+ </tr>
726+ </tbody>
727+ </table>
728+
729+ <span class="outliers">
730+ <p>Outlying measurements have severe
731+ (<span class="percent">0.9598911701243743</span>%)
732+ effect on estimated standard deviation.</p>
733+ </span>
734+<h2><a name="b8">Matrix vs List - `select`/Distribution `select` - 100+100 / 100x100/Matrix Distribution - Selective version</a></h2>
735+ <table width="100%">
736+ <tbody>
737+ <tr>
738+ <td><div id="kde8" class="kdechart"
739+ style="width:450px;height:278px;"></div></td>
740+ <td><div id="time8" class="timechart"
741+ style="width:450px;height:278px;"></div></td>
742+<!--
743+ <td><div id="cycle8" class="cyclechart"
744+ style="width:300px;height:278px;"></div></td>
745+-->
746+ </tr>
747+ </tbody>
748+ </table>
749+
750+ <table>
751+ <thead class="analysis">
752+ <th></th>
753+ <th class="cibound"
754+ title="0.95 confidence level">lower bound</th>
755+ <th>estimate</th>
756+ <th class="cibound"
757+ title="0.95 confidence level">upper bound</th>
758+ </thead>
759+ <tbody>
760+ <tr>
761+ <td>OLS regression</td>
762+ <td><span class="confinterval olstimelb8">xxx</span></td>
763+ <td><span class="olstimept8">xxx</span></td>
764+ <td><span class="confinterval olstimeub8">xxx</span></td>
765+ </tr>
766+ <tr>
767+ <td>R&#xb2; goodness-of-fit</td>
768+ <td><span class="confinterval olsr2lb8">xxx</span></td>
769+ <td><span class="olsr2pt8">xxx</span></td>
770+ <td><span class="confinterval olsr2ub8">xxx</span></td>
771+ </tr>
772+ <tr>
773+ <td>Mean execution time</td>
774+ <td><span class="confinterval citime">1.0094556598949091e-3</span></td>
775+ <td><span class="time">1.0459672120901292e-3</span></td>
776+ <td><span class="confinterval citime">1.1900093977774448e-3</span></td>
777+ </tr>
778+ <tr>
779+ <td>Standard deviation</td>
780+ <td><span class="confinterval citime">4.936441129145525e-5</span></td>
781+ <td><span class="time">2.169293235834326e-4</span></td>
782+ <td><span class="confinterval citime">4.929920714921142e-4</span></td>
783+ </tr>
784+ </tbody>
785+ </table>
786+
787+ <span class="outliers">
788+ <p>Outlying measurements have severe
789+ (<span class="percent">0.9240968489851639</span>%)
790+ effect on estimated standard deviation.</p>
791+ </span>
792+<h2><a name="b9">Matrix vs List - `select`/Matrix `select` - 100x(100+100) / 100x100/Applicative version</a></h2>
793+ <table width="100%">
794+ <tbody>
795+ <tr>
796+ <td><div id="kde9" class="kdechart"
797+ style="width:450px;height:278px;"></div></td>
798+ <td><div id="time9" class="timechart"
799+ style="width:450px;height:278px;"></div></td>
800+<!--
801+ <td><div id="cycle9" class="cyclechart"
802+ style="width:300px;height:278px;"></div></td>
803+-->
804+ </tr>
805+ </tbody>
806+ </table>
807+
808+ <table>
809+ <thead class="analysis">
810+ <th></th>
811+ <th class="cibound"
812+ title="0.95 confidence level">lower bound</th>
813+ <th>estimate</th>
814+ <th class="cibound"
815+ title="0.95 confidence level">upper bound</th>
816+ </thead>
817+ <tbody>
818+ <tr>
819+ <td>OLS regression</td>
820+ <td><span class="confinterval olstimelb9">xxx</span></td>
821+ <td><span class="olstimept9">xxx</span></td>
822+ <td><span class="confinterval olstimeub9">xxx</span></td>
823+ </tr>
824+ <tr>
825+ <td>R&#xb2; goodness-of-fit</td>
826+ <td><span class="confinterval olsr2lb9">xxx</span></td>
827+ <td><span class="olsr2pt9">xxx</span></td>
828+ <td><span class="confinterval olsr2ub9">xxx</span></td>
829+ </tr>
830+ <tr>
831+ <td>Mean execution time</td>
832+ <td><span class="confinterval citime">1.1142126609993284</span></td>
833+ <td><span class="time">1.1506916786456713</span></td>
834+ <td><span class="confinterval citime">1.1642280000833125</span></td>
835+ </tr>
836+ <tr>
837+ <td>Standard deviation</td>
838+ <td><span class="confinterval citime">3.115381125098793e-3</span></td>
839+ <td><span class="time">2.468474748870533e-2</span></td>
840+ <td><span class="confinterval citime">3.126079530343771e-2</span></td>
841+ </tr>
842+ </tbody>
843+ </table>
844+
845+ <span class="outliers">
846+ <p>Outlying measurements have moderate
847+ (<span class="percent">0.1875</span>%)
848+ effect on estimated standard deviation.</p>
849+ </span>
850+<h2><a name="b10">Matrix vs List - `select`/Matrix `select` - 100x(100+100) / 100x100/Selective version</a></h2>
851+ <table width="100%">
852+ <tbody>
853+ <tr>
854+ <td><div id="kde10" class="kdechart"
855+ style="width:450px;height:278px;"></div></td>
856+ <td><div id="time10" class="timechart"
857+ style="width:450px;height:278px;"></div></td>
858+<!--
859+ <td><div id="cycle10" class="cyclechart"
860+ style="width:300px;height:278px;"></div></td>
861+-->
862+ </tr>
863+ </tbody>
864+ </table>
865+
866+ <table>
867+ <thead class="analysis">
868+ <th></th>
869+ <th class="cibound"
870+ title="0.95 confidence level">lower bound</th>
871+ <th>estimate</th>
872+ <th class="cibound"
873+ title="0.95 confidence level">upper bound</th>
874+ </thead>
875+ <tbody>
876+ <tr>
877+ <td>OLS regression</td>
878+ <td><span class="confinterval olstimelb10">xxx</span></td>
879+ <td><span class="olstimept10">xxx</span></td>
880+ <td><span class="confinterval olstimeub10">xxx</span></td>
881+ </tr>
882+ <tr>
883+ <td>R&#xb2; goodness-of-fit</td>
884+ <td><span class="confinterval olsr2lb10">xxx</span></td>
885+ <td><span class="olsr2pt10">xxx</span></td>
886+ <td><span class="confinterval olsr2ub10">xxx</span></td>
887+ </tr>
888+ <tr>
889+ <td>Mean execution time</td>
890+ <td><span class="confinterval citime">0.530786815458517</span></td>
891+ <td><span class="time">0.5400133454575856</span></td>
892+ <td><span class="confinterval citime">0.5473636064980383</span></td>
893+ </tr>
894+ <tr>
895+ <td>Standard deviation</td>
896+ <td><span class="confinterval citime">4.333057553316104e-3</span></td>
897+ <td><span class="time">9.71574644699696e-3</span></td>
898+ <td><span class="confinterval citime">1.3200731985635176e-2</span></td>
899+ </tr>
900+ </tbody>
901+ </table>
902+
903+ <span class="outliers">
904+ <p>Outlying measurements have moderate
905+ (<span class="percent">0.18749999999999997</span>%)
906+ effect on estimated standard deviation.</p>
907+ </span>
908+
909+ <h2><a name="grokularation">understanding this report</a></h2>
910+
911+ <p>In this report, each function benchmarked by criterion is assigned
912+ a section of its own. The charts in each section are active; if
913+ you hover your mouse over data points and annotations, you will see
914+ more details.</p>
915+
916+ <ul>
917+ <li>The chart on the left is a
918+ <a href="http://en.wikipedia.org/wiki/Kernel_density_estimation">kernel
919+ density estimate</a> (also known as a KDE) of time
920+ measurements. This graphs the probability of any given time
921+ measurement occurring. A spike indicates that a measurement of a
922+ particular time occurred; its height indicates how often that
923+ measurement was repeated.</li>
924+
925+ <li>The chart on the right is the raw data from which the kernel
926+ density estimate is built. The <i>x</i> axis indicates the
927+ number of loop iterations, while the <i>y</i> axis shows measured
928+ execution time for the given number of loop iterations. The
929+ line behind the values is the linear regression prediction of
930+ execution time for a given number of iterations. Ideally, all
931+ measurements will be on (or very near) this line.</li>
932+ </ul>
933+
934+ <p>Under the charts is a small table.
935+ The first two rows are the results of a linear regression run
936+ on the measurements displayed in the right-hand chart.</p>
937+
938+ <ul>
939+ <li><i>OLS regression</i> indicates the
940+ time estimated for a single loop iteration using an ordinary
941+ least-squares regression model. This number is more accurate
942+ than the <i>mean</i> estimate below it, as it more effectively
943+ eliminates measurement overhead and other constant factors.</li>
944+ <li><i>R&#xb2; goodness-of-fit</i> is a measure of how
945+ accurately the linear regression model fits the observed
946+ measurements. If the measurements are not too noisy, R&#xb2;
947+ should lie between 0.99 and 1, indicating an excellent fit. If
948+ the number is below 0.99, something is confounding the accuracy
949+ of the linear model.</li>
950+ <li><i>Mean execution time</i> and <i>standard deviation</i> are
951+ statistics calculated from execution time
952+ divided by number of iterations.</li>
953+ </ul>
954+
955+ <p>We use a statistical technique called
956+ the <a href="http://en.wikipedia.org/wiki/Bootstrapping_(statistics)">bootstrap</a>
957+ to provide confidence intervals on our estimates. The
958+ bootstrap-derived upper and lower bounds on estimates let you see
959+ how accurate we believe those estimates to be. (Hover the mouse
960+ over the table headers to see the confidence levels.)</p>
961+
962+ <p>A noisy benchmarking environment can cause some or many
963+ measurements to fall far from the mean. These outlying
964+ measurements can have a significant inflationary effect on the
965+ estimate of the standard deviation. We calculate and display an
966+ estimate of the extent to which the standard deviation has been
967+ inflated by outliers.</p>
968+
969+<script type="text/javascript">
970+$(function () {
971+ function mangulate(rpt) {
972+ var measured = function(key) {
973+ var idx = rpt.reportKeys.indexOf(key);
974+ return rpt.reportMeasured.map(function(r) { return r[idx]; });
975+ };
976+ var lowerBound = function(est) {
977+ return est.estPoint - est.estError.confIntLDX;
978+ };
979+ var upperBound = function(est) {
980+ return est.estPoint + est.estError.confIntUDX;
981+ };
982+ var number = rpt.reportNumber;
983+ var name = rpt.reportName;
984+ var mean = rpt.reportAnalysis.anMean.estPoint;
985+ var iters = measured("iters");
986+ var times = measured("time");
987+ var kdetimes = rpt.reportKDEs[0].kdeValues;
988+ var kdepdf = rpt.reportKDEs[0].kdePDF;
989+
990+ var meanSecs = mean;
991+ var units = $.timeUnits(mean);
992+ var rgrs = rpt.reportAnalysis.anRegress[0];
993+ var scale = units[0];
994+ var olsTime = rgrs.regCoeffs.iters;
995+ $(".olstimept" + number).text(function() {
996+ return $.renderTime(olsTime.estPoint);
997+ });
998+ $(".olstimelb" + number).text(function() {
999+ return $.renderTime(lowerBound(olsTime));
1000+ });
1001+ $(".olstimeub" + number).text(function() {
1002+ return $.renderTime(upperBound(olsTime));
1003+ });
1004+ $(".olsr2pt" + number).text(function() {
1005+ return rgrs.regRSquare.estPoint.toFixed(3);
1006+ });
1007+ $(".olsr2lb" + number).text(function() {
1008+ return lowerBound(rgrs.regRSquare).toFixed(3);
1009+ });
1010+ $(".olsr2ub" + number).text(function() {
1011+ return upperBound(rgrs.regRSquare).toFixed(3);
1012+ });
1013+ mean *= scale;
1014+ kdetimes = $.scaleBy(scale, kdetimes);
1015+ var kq = $("#kde" + number);
1016+ var k = $.plot(kq,
1017+ [{ label: name + " time densities",
1018+ data: $.zip(kdetimes, kdepdf),
1019+ }],
1020+ { xaxis: { tickFormatter: $.unitFormatter(scale) },
1021+ yaxis: { ticks: false },
1022+ grid: { borderColor: "#777",
1023+ hoverable: true, markings: [ { color: '#6fd3fb',
1024+ lineWidth: 1.5, xaxis: { from: mean, to: mean } } ] },
1025+ });
1026+ var o = k.pointOffset({ x: mean, y: 0});
1027+ kq.append('<div class="meanlegend" title="' + $.renderTime(meanSecs) +
1028+ '" style="position:absolute;left:' + (o.left + 4) +
1029+ 'px;bottom:139px;">mean</div>');
1030+ $.addTooltip("#kde" + number,
1031+ function(secs) { return $.renderTime(secs / scale); });
1032+ var timepairs = new Array(times.length);
1033+ var lastiter = iters[iters.length-1];
1034+ var olspairs = [[0,0], [lastiter, lastiter * scale * olsTime.estPoint]];
1035+ for (var i = 0; i < times.length; i++)
1036+ timepairs[i] = [iters[i],times[i]*scale];
1037+ iterFormatter = function() {
1038+ var denom = 0;
1039+ return function(iters) {
1040+ if (iters == 0)
1041+ return '';
1042+ if (denom > 0)
1043+ return (iters / denom).toFixed();
1044+ var power;
1045+ if (iters >= 1e9) {
1046+ denom = '1e9'; power = '&#x2079;';
1047+ }
1048+ if (iters >= 1e6) {
1049+ denom = '1e6'; power = '&#x2076;';
1050+ }
1051+ else if (iters >= 1e3) {
1052+ denom = '1e3'; power = '&#xb3;';
1053+ }
1054+ else denom = 1;
1055+ if (denom > 1) {
1056+ iters = (iters / denom).toFixed();
1057+ iters += '&times;10' + power + ' iters';
1058+ } else {
1059+ iters += ' iters';
1060+ }
1061+ return iters;
1062+ };
1063+ };
1064+ $.plot($("#time" + number),
1065+ [{ label: "regression", data: olspairs,
1066+ lines: { show: true } },
1067+ { label: name + " times", data: timepairs,
1068+ points: { show: true } }],
1069+ { grid: { borderColor: "#777", hoverable: true },
1070+ xaxis: { tickFormatter: iterFormatter() },
1071+ yaxis: { tickFormatter: $.unitFormatter(scale) } });
1072+ $.addTooltip("#time" + number,
1073+ function(iters,secs) {
1074+ return ($.renderTime(secs / scale) + ' / ' +
1075+ iters.toLocaleString() + ' iters');
1076+ });
1077+ if (0) {
1078+ var cyclepairs = new Array(cycles.length);
1079+ for (var i = 0; i < cycles.length; i++)
1080+ cyclepairs[i] = [cycles[i],i];
1081+ $.plot($("#cycle" + number),
1082+ [{ label: name + " cycles",
1083+ data: cyclepairs }],
1084+ { points: { show: true },
1085+ grid: { borderColor: "#777", hoverable: true },
1086+ xaxis: { tickFormatter:
1087+ function(cycles,axis) { return cycles + ' cycles'; }},
1088+ yaxis: { ticks: false },
1089+ });
1090+ $.addTooltip("#cycles" + number, function(x,y) { return x + ' cycles'; });
1091+ }
1092+ };
1093+ var reports = 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vs List - `select`/Matrix `select` - 100x(100+100) / 100x100/Selective version","reportOutliers":{"highSevere":0,"highMild":0,"lowMild":0,"samplesSeen":4,"lowSevere":0},"reportMeasured":[[0.5517748849961208,0.8263997859999961,1320913854,1,null,null,null,null,null,null,null],[1.0859046559999115,1.626134200999985,2599589106,2,null,null,null,null,null,null,null],[1.609246867003094,2.446943054000002,3852436014,3,null,null,null,null,null,null,null],[2.1156421859996044,3.179338324999975,5064712443,4,null,null,null,null,null,null,null]]}];
1094+ reports.map(mangulate);
1095+
1096+ var benches = ["Matrix Composition/10x10/WHNF - 10x10","Matrix Composition/10x10/NF - 10x10","Matrix Composition/100x100/WHNF - 100x100","Matrix Composition/100x100/NF - 100x100","Matrix Composition/200x200/WHNF - 200x200","Matrix Composition/200x200/NF - 200x200","Matrix vs List - `select`/Distribution `select` - 100+100 / 100x100/List Distribution - Applicative version","Matrix vs List - `select`/Distribution `select` - 100+100 / 100x100/Matrix Distribution - Applicative version","Matrix vs List - `select`/Distribution `select` - 100+100 / 100x100/Matrix Distribution - Selective version","Matrix vs List - `select`/Matrix `select` - 100x(100+100) / 100x100/Applicative version","Matrix vs List - `select`/Matrix `select` - 100x(100+100) / 100x100/Selective version",];
1097+ var ylabels = [[-0,"<a href=\"#b0\">Matrix Composition/10x10/WHNF - 10x10</a>"],[-1,"<a href=\"#b1\">Matrix Composition/10x10/NF - 10x10</a>"],[-2,"<a href=\"#b2\">Matrix Composition/100x100/WHNF - 100x100</a>"],[-3,"<a href=\"#b3\">Matrix Composition/100x100/NF - 100x100</a>"],[-4,"<a href=\"#b4\">Matrix Composition/200x200/WHNF - 200x200</a>"],[-5,"<a href=\"#b5\">Matrix Composition/200x200/NF - 200x200</a>"],[-6,"<a href=\"#b6\">Matrix vs List - `select`/Distribution `select` - 100+100 / 100x100/List Distribution - Applicative version</a>"],[-7,"<a href=\"#b7\">Matrix vs List - `select`/Distribution `select` - 100+100 / 100x100/Matrix Distribution - Applicative version</a>"],[-8,"<a href=\"#b8\">Matrix vs List - `select`/Distribution `select` - 100+100 / 100x100/Matrix Distribution - Selective version</a>"],[-9,"<a href=\"#b9\">Matrix vs List - `select`/Matrix `select` - 100x(100+100) / 100x100/Applicative version</a>"],[-10,"<a href=\"#b10\">Matrix vs List - `select`/Matrix `select` - 100x(100+100) / 100x100/Selective version</a>"],];
1098+ var means = $.scaleTimes([2.4514866756029205e-8,2.0678688880349948e-4,2.032500748180748e-8,0.3562973993334708,2.0667543937993357e-8,4.623436544688502,2.3105826970010335,2.672449312433179e-3,1.0459672120901292e-3,1.1506916786456713,0.5400133454575856,]);
1099+ var stddevs = [9.647785488002723e-10,1.2679488723877765e-5,1.1748079988373767e-9,7.81042655007339e-3,1.8602778611455406e-9,6.412809734921064e-2,0.16563995052316,9.064184723100453e-4,2.169293235834326e-4,2.468474748870533e-2,9.71574644699696e-3,];
1100+ stddevs = $.scaleBy(means[1], stddevs);
1101+ var xs = [];
1102+ var prev = null;
1103+ var colors = ["#edc240","#afd8f8","#cb4b4b","#4da74d","#9440ed"];
1104+ var max_time = 0;
1105+ for (var i = 0; i < means[0].length; i++) {
1106+ var name = benches[i].split(/\//);
1107+ name.pop();
1108+ name = name.join('/');
1109+ if (name != prev) {
1110+ var color = colors[xs.length / 2 % colors.length];
1111+ xs.push({ data: [[means[0][i], -i]], label: name, color: color,
1112+ bars: { show: true, horizontal: true, barWidth: 0.75,
1113+ align: "center" } });
1114+ xs.push({ data: [[means[0][i], -i, stddevs[i]]], color: color,
1115+ lines: { show: false },
1116+ points: { radius: 0, errorbars: "x",
1117+ xerr: { show: true, radius: 5,
1118+ lowerCap: "-", upperCap: "-" } } });
1119+ prev = name;
1120+ } else {
1121+ xs[xs.length - 2].data.push([means[0][i], -i]);
1122+ xs[xs.length - 1].data.push([means[0][i], -i, stddevs[i]]);
1123+ }
1124+ max_time = Math.max(max_time, means[0][i] + stddevs[i]);
1125+ }
1126+ var oq = $("#overview");
1127+ var max_x = max_time * 1.02;
1128+ o = $.plot(oq, xs, { grid: { borderColor: "#777", hoverable: true },
1129+ legend: { show: xs.length > 1 },
1130+ xaxis: { max: max_x, zoomRange: [false, max_x], panRange: [0, max_x] },
1131+ yaxis: { ticks: ylabels, tickColor: '#ffffff', zoomRange: false, panRange: false },
1132+ zoom: { interactive: true, amount: 1.05 },
1133+ pan: { interactive: true } });
1134+ if (benches.length > 3)
1135+ o.getPlaceholder().height(28*benches.length);
1136+ o.resize();
1137+ o.setupGrid();
1138+ o.draw();
1139+ $.addTooltip("#overview", function(x,y) { return $.renderTime(x / means[1]); });
1140+});
1141+$(document).ready(function () {
1142+ $(".time").text(function(_, text) {
1143+ return $.renderTime(text);
1144+ });
1145+ $(".citime").text(function(_, text) {
1146+ return $.renderTime(text);
1147+ });
1148+ $(".percent").text(function(_, text) {
1149+ return (text*100).toFixed(1);
1150+ });
1151+ });
1152+</script>
1153+
1154+ </div>
1155+ </div>
1156+ <div id="footer">
1157+ <div class="body">
1158+ <div class="footfirst">
1159+ <h2>colophon</h2>
1160+ <p>This report was created using the
1161+ <a href="http://hackage.haskell.org/package/criterion">criterion</a>
1162+ benchmark execution and performance analysis tool.</p>
1163+ <p>Criterion is developed and maintained
1164+ by <a href="http://www.serpentine.com/blog/">Bryan O'Sullivan</a>.</p>
1165+ </div>
1166+ </div>
1167+ </div>
1168+ </body>
1169+</html>
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5+ <title>criterion report</title>
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series=[],options={colors:["#edc240","#afd8f8","#cb4b4b","#4da74d","#9440ed"],legend:{show:true,noColumns:1,labelFormatter:null,labelBoxBorderColor:"#ccc",container:null,position:"ne",margin:5,backgroundColor:null,backgroundOpacity:.85,sorted:null},xaxis:{show:null,position:"bottom",mode:null,font:null,color:null,tickColor:null,transform:null,inverseTransform:null,min:null,max:null,autoscaleMargin:null,ticks:null,tickFormatter:null,labelWidth:null,labelHeight:null,reserveSpace:null,tickLength:null,alignTicksWithAxis:null,tickDecimals:null,tickSize:null,minTickSize:null},yaxis:{autoscaleMargin:.02,position:"left"},xaxes:[],yaxes:[],series:{points:{show:false,radius:3,lineWidth:2,fill:true,fillColor:"#ffffff",symbol:"circle"},lines:{lineWidth:2,fill:false,fillColor:null,steps:false},bars:{show:false,lineWidth:2,barWidth:1,fill:true,fillColor:null,align:"left",horizontal:false,zero:true},shadowSize:3,highlightColor:null},grid:{show:true,aboveData:false,color:"#545454",backgroundColor:null,borderColor:null,tickColor:null,margin:0,labelMargin:5,axisMargin:8,borderWidth:2,minBorderMargin:null,markings:null,markingsColor:"#f4f4f4",markingsLineWidth:2,clickable:false,hoverable:false,autoHighlight:true,mouseActiveRadius:10},interaction:{redrawOverlayInterval:1e3/60},hooks:{}},surface=null,overlay=null,eventHolder=null,ctx=null,octx=null,xaxes=[],yaxes=[],plotOffset={left:0,right:0,top:0,bottom:0},plotWidth=0,plotHeight=0,hooks={processOptions:[],processRawData:[],processDatapoints:[],processOffset:[],drawBackground:[],drawSeries:[],draw:[],bindEvents:[],drawOverlay:[],shutdown:[]},plot=this;plot.setData=setData;plot.setupGrid=setupGrid;plot.draw=draw;plot.getPlaceholder=function(){return placeholder};plot.getCanvas=function(){return surface.element};plot.getPlotOffset=function(){return plotOffset};plot.width=function(){return plotWidth};plot.height=function(){return plotHeight};plot.offset=function(){var o=eventHolder.offset();o.left+=plotOffset.left;o.top+=plotOffset.top;return o};plot.getData=function(){return series};plot.getAxes=function(){var res={},i;$.each(xaxes.concat(yaxes),function(_,axis){if(axis)res[axis.direction+(axis.n!=1?axis.n:"")+"axis"]=axis});return res};plot.getXAxes=function(){return xaxes};plot.getYAxes=function(){return yaxes};plot.c2p=canvasToAxisCoords;plot.p2c=axisToCanvasCoords;plot.getOptions=function(){return options};plot.highlight=highlight;plot.unhighlight=unhighlight;plot.triggerRedrawOverlay=triggerRedrawOverlay;plot.pointOffset=function(point){return{left:parseInt(xaxes[axisNumber(point,"x")-1].p2c(+point.x)+plotOffset.left,10),top:parseInt(yaxes[axisNumber(point,"y")-1].p2c(+point.y)+plotOffset.top,10)}};plot.shutdown=shutdown;plot.destroy=function(){shutdown();placeholder.removeData("plot").empty();series=[];options=null;surface=null;overlay=null;eventHolder=null;ctx=null;octx=null;xaxes=[];yaxes=[];hooks=null;highlights=[];plot=null};plot.resize=function(){var width=placeholder.width(),height=placeholder.height();surface.resize(width,height);overlay.resize(width,height)};plot.hooks=hooks;initPlugins(plot);parseOptions(options_);setupCanvases();setData(data_);setupGrid();draw();bindEvents();function executeHooks(hook,args){args=[plot].concat(args);for(var i=0;i<hook.length;++i)hook[i].apply(this,args)}function initPlugins(){var classes={Canvas:Canvas};for(var i=0;i<plugins.length;++i){var p=plugins[i];p.init(plot,classes);if(p.options)$.extend(true,options,p.options)}}function parseOptions(opts){$.extend(true,options,opts);if(opts&&opts.colors){options.colors=opts.colors}if(options.xaxis.color==null)options.xaxis.color=$.color.parse(options.grid.color).scale("a",.22).toString();if(options.yaxis.color==null)options.yaxis.color=$.color.parse(options.grid.color).scale("a",.22).toString();if(options.xaxis.tickColor==null)options.xaxis.tickColor=options.grid.tickColor||options.xaxis.color;if(options.yaxis.tickColor==null)options.yaxis.tickColor=options.grid.tickColor||options.yaxis.color;if(options.grid.borderColor==null)options.grid.borderColor=options.grid.color;if(options.grid.tickColor==null)options.grid.tickColor=$.color.parse(options.grid.color).scale("a",.22).toString();var i,axisOptions,axisCount,fontSize=placeholder.css("font-size"),fontSizeDefault=fontSize?+fontSize.replace("px",""):13,fontDefaults={style:placeholder.css("font-style"),size:Math.round(.8*fontSizeDefault),variant:placeholder.css("font-variant"),weight:placeholder.css("font-weight"),family:placeholder.css("font-family")};axisCount=options.xaxes.length||1;for(i=0;i<axisCount;++i){axisOptions=options.xaxes[i];if(axisOptions&&!axisOptions.tickColor){axisOptions.tickColor=axisOptions.color}axisOptions=$.extend(true,{},options.xaxis,axisOptions);options.xaxes[i]=axisOptions;if(axisOptions.font){axisOptions.font=$.extend({},fontDefaults,axisOptions.font);if(!axisOptions.font.color){axisOptions.font.color=axisOptions.color}if(!axisOptions.font.lineHeight){axisOptions.font.lineHeight=Math.round(axisOptions.font.size*1.15)}}}axisCount=options.yaxes.length||1;for(i=0;i<axisCount;++i){axisOptions=options.yaxes[i];if(axisOptions&&!axisOptions.tickColor){axisOptions.tickColor=axisOptions.color}axisOptions=$.extend(true,{},options.yaxis,axisOptions);options.yaxes[i]=axisOptions;if(axisOptions.font){axisOptions.font=$.extend({},fontDefaults,axisOptions.font);if(!axisOptions.font.color){axisOptions.font.color=axisOptions.color}if(!axisOptions.font.lineHeight){axisOptions.font.lineHeight=Math.round(axisOptions.font.size*1.15)}}}if(options.xaxis.noTicks&&options.xaxis.ticks==null)options.xaxis.ticks=options.xaxis.noTicks;if(options.yaxis.noTicks&&options.yaxis.ticks==null)options.yaxis.ticks=options.yaxis.noTicks;if(options.x2axis){options.xaxes[1]=$.extend(true,{},options.xaxis,options.x2axis);options.xaxes[1].position="top";if(options.x2axis.min==null){options.xaxes[1].min=null}if(options.x2axis.max==null){options.xaxes[1].max=null}}if(options.y2axis){options.yaxes[1]=$.extend(true,{},options.yaxis,options.y2axis);options.yaxes[1].position="right";if(options.y2axis.min==null){options.yaxes[1].min=null}if(options.y2axis.max==null){options.yaxes[1].max=null}}if(options.grid.coloredAreas)options.grid.markings=options.grid.coloredAreas;if(options.grid.coloredAreasColor)options.grid.markingsColor=options.grid.coloredAreasColor;if(options.lines)$.extend(true,options.series.lines,options.lines);if(options.points)$.extend(true,options.series.points,options.points);if(options.bars)$.extend(true,options.series.bars,options.bars);if(options.shadowSize!=null)options.series.shadowSize=options.shadowSize;if(options.highlightColor!=null)options.series.highlightColor=options.highlightColor;for(i=0;i<options.xaxes.length;++i)getOrCreateAxis(xaxes,i+1).options=options.xaxes[i];for(i=0;i<options.yaxes.length;++i)getOrCreateAxis(yaxes,i+1).options=options.yaxes[i];for(var n in hooks)if(options.hooks[n]&&options.hooks[n].length)hooks[n]=hooks[n].concat(options.hooks[n]);executeHooks(hooks.processOptions,[options])}function setData(d){series=parseData(d);fillInSeriesOptions();processData()}function parseData(d){var res=[];for(var i=0;i<d.length;++i){var s=$.extend(true,{},options.series);if(d[i].data!=null){s.data=d[i].data;delete d[i].data;$.extend(true,s,d[i]);d[i].data=s.data}else s.data=d[i];res.push(s)}return res}function axisNumber(obj,coord){var a=obj[coord+"axis"];if(typeof a=="object")a=a.n;if(typeof a!="number")a=1;return a}function allAxes(){return $.grep(xaxes.concat(yaxes),function(a){return a})}function canvasToAxisCoords(pos){var res={},i,axis;for(i=0;i<xaxes.length;++i){axis=xaxes[i];if(axis&&axis.used)res["x"+axis.n]=axis.c2p(pos.left)}for(i=0;i<yaxes.length;++i){axis=yaxes[i];if(axis&&axis.used)res["y"+axis.n]=axis.c2p(pos.top)}if(res.x1!==undefined)res.x=res.x1;if(res.y1!==undefined)res.y=res.y1;return res}function axisToCanvasCoords(pos){var res={},i,axis,key;for(i=0;i<xaxes.length;++i){axis=xaxes[i];if(axis&&axis.used){key="x"+axis.n;if(pos[key]==null&&axis.n==1)key="x";if(pos[key]!=null){res.left=axis.p2c(pos[key]);break}}}for(i=0;i<yaxes.length;++i){axis=yaxes[i];if(axis&&axis.used){key="y"+axis.n;if(pos[key]==null&&axis.n==1)key="y";if(pos[key]!=null){res.top=axis.p2c(pos[key]);break}}}return res}function getOrCreateAxis(axes,number){if(!axes[number-1])axes[number-1]={n:number,direction:axes==xaxes?"x":"y",options:$.extend(true,{},axes==xaxes?options.xaxis:options.yaxis)};return axes[number-1]}function fillInSeriesOptions(){var neededColors=series.length,maxIndex=-1,i;for(i=0;i<series.length;++i){var sc=series[i].color;if(sc!=null){neededColors--;if(typeof sc=="number"&&sc>maxIndex){maxIndex=sc}}}if(neededColors<=maxIndex){neededColors=maxIndex+1}var c,colors=[],colorPool=options.colors,colorPoolSize=colorPool.length,variation=0;for(i=0;i<neededColors;i++){c=$.color.parse(colorPool[i%colorPoolSize]||"#666");if(i%colorPoolSize==0&&i){if(variation>=0){if(variation<.5){variation=-variation-.2}else variation=0}else variation=-variation}colors[i]=c.scale("rgb",1+variation)}var colori=0,s;for(i=0;i<series.length;++i){s=series[i];if(s.color==null){s.color=colors[colori].toString();++colori}else if(typeof s.color=="number")s.color=colors[s.color].toString();if(s.lines.show==null){var v,show=true;for(v in s)if(s[v]&&s[v].show){show=false;break}if(show)s.lines.show=true}if(s.lines.zero==null){s.lines.zero=!!s.lines.fill}s.xaxis=getOrCreateAxis(xaxes,axisNumber(s,"x"));s.yaxis=getOrCreateAxis(yaxes,axisNumber(s,"y"))}}function processData(){var topSentry=Number.POSITIVE_INFINITY,bottomSentry=Number.NEGATIVE_INFINITY,fakeInfinity=Number.MAX_VALUE,i,j,k,m,length,s,points,ps,x,y,axis,val,f,p,data,format;function updateAxis(axis,min,max){if(min<axis.datamin&&min!=-fakeInfinity)axis.datamin=min;if(max>axis.datamax&&max!=fakeInfinity)axis.datamax=max}$.each(allAxes(),function(_,axis){axis.datamin=topSentry;axis.datamax=bottomSentry;axis.used=false});for(i=0;i<series.length;++i){s=series[i];s.datapoints={points:[]};executeHooks(hooks.processRawData,[s,s.data,s.datapoints])}for(i=0;i<series.length;++i){s=series[i];data=s.data;format=s.datapoints.format;if(!format){format=[];format.push({x:true,number:true,required:true});format.push({y:true,number:true,required:true});if(s.bars.show||s.lines.show&&s.lines.fill){var autoscale=!!(s.bars.show&&s.bars.zero||s.lines.show&&s.lines.zero);format.push({y:true,number:true,required:false,defaultValue:0,autoscale:autoscale});if(s.bars.horizontal){delete format[format.length-1].y;format[format.length-1].x=true}}s.datapoints.format=format}if(s.datapoints.pointsize!=null)continue;s.datapoints.pointsize=format.length;ps=s.datapoints.pointsize;points=s.datapoints.points;var insertSteps=s.lines.show&&s.lines.steps;s.xaxis.used=s.yaxis.used=true;for(j=k=0;j<data.length;++j,k+=ps){p=data[j];var nullify=p==null;if(!nullify){for(m=0;m<ps;++m){val=p[m];f=format[m];if(f){if(f.number&&val!=null){val=+val;if(isNaN(val))val=null;else if(val==Infinity)val=fakeInfinity;else if(val==-Infinity)val=-fakeInfinity}if(val==null){if(f.required)nullify=true;if(f.defaultValue!=null)val=f.defaultValue}}points[k+m]=val}}if(nullify){for(m=0;m<ps;++m){val=points[k+m];if(val!=null){f=format[m];if(f.autoscale!==false){if(f.x){updateAxis(s.xaxis,val,val)}if(f.y){updateAxis(s.yaxis,val,val)}}}points[k+m]=null}}else{if(insertSteps&&k>0&&points[k-ps]!=null&&points[k-ps]!=points[k]&&points[k-ps+1]!=points[k+1]){for(m=0;m<ps;++m)points[k+ps+m]=points[k+m];points[k+1]=points[k-ps+1];k+=ps}}}}for(i=0;i<series.length;++i){s=series[i];executeHooks(hooks.processDatapoints,[s,s.datapoints])}for(i=0;i<series.length;++i){s=series[i];points=s.datapoints.points;ps=s.datapoints.pointsize;format=s.datapoints.format;var xmin=topSentry,ymin=topSentry,xmax=bottomSentry,ymax=bottomSentry;for(j=0;j<points.length;j+=ps){if(points[j]==null)continue;for(m=0;m<ps;++m){val=points[j+m];f=format[m];if(!f||f.autoscale===false||val==fakeInfinity||val==-fakeInfinity)continue;if(f.x){if(val<xmin)xmin=val;if(val>xmax)xmax=val}if(f.y){if(val<ymin)ymin=val;if(val>ymax)ymax=val}}}if(s.bars.show){var delta;switch(s.bars.align){case"left":delta=0;break;case"right":delta=-s.bars.barWidth;break;default:delta=-s.bars.barWidth/2}if(s.bars.horizontal){ymin+=delta;ymax+=delta+s.bars.barWidth}else{xmin+=delta;xmax+=delta+s.bars.barWidth}}updateAxis(s.xaxis,xmin,xmax);updateAxis(s.yaxis,ymin,ymax)}$.each(allAxes(),function(_,axis){if(axis.datamin==topSentry)axis.datamin=null;if(axis.datamax==bottomSentry)axis.datamax=null})}function setupCanvases(){placeholder.css("padding",0).children().filter(function(){return!$(this).hasClass("flot-overlay")&&!$(this).hasClass("flot-base")}).remove();if(placeholder.css("position")=="static")placeholder.css("position","relative");surface=new Canvas("flot-base",placeholder);overlay=new Canvas("flot-overlay",placeholder);ctx=surface.context;octx=overlay.context;eventHolder=$(overlay.element).unbind();var existing=placeholder.data("plot");if(existing){existing.shutdown();overlay.clear()}placeholder.data("plot",plot)}function bindEvents(){if(options.grid.hoverable){eventHolder.mousemove(onMouseMove);eventHolder.bind("mouseleave",onMouseLeave)}if(options.grid.clickable)eventHolder.click(onClick);executeHooks(hooks.bindEvents,[eventHolder])}function shutdown(){if(redrawTimeout)clearTimeout(redrawTimeout);eventHolder.unbind("mousemove",onMouseMove);eventHolder.unbind("mouseleave",onMouseLeave);eventHolder.unbind("click",onClick);executeHooks(hooks.shutdown,[eventHolder])}function setTransformationHelpers(axis){function identity(x){return x}var s,m,t=axis.options.transform||identity,it=axis.options.inverseTransform;if(axis.direction=="x"){s=axis.scale=plotWidth/Math.abs(t(axis.max)-t(axis.min));m=Math.min(t(axis.max),t(axis.min))}else{s=axis.scale=plotHeight/Math.abs(t(axis.max)-t(axis.min));s=-s;m=Math.max(t(axis.max),t(axis.min))}if(t==identity)axis.p2c=function(p){return(p-m)*s};else axis.p2c=function(p){return(t(p)-m)*s};if(!it)axis.c2p=function(c){return m+c/s};else axis.c2p=function(c){return it(m+c/s)}}function measureTickLabels(axis){var opts=axis.options,ticks=axis.ticks||[],labelWidth=opts.labelWidth||0,labelHeight=opts.labelHeight||0,maxWidth=labelWidth||(axis.direction=="x"?Math.floor(surface.width/(ticks.length||1)):null),legacyStyles=axis.direction+"Axis "+axis.direction+axis.n+"Axis",layer="flot-"+axis.direction+"-axis flot-"+axis.direction+axis.n+"-axis "+legacyStyles,font=opts.font||"flot-tick-label tickLabel";for(var i=0;i<ticks.length;++i){var t=ticks[i];if(!t.label)continue;var info=surface.getTextInfo(layer,t.label,font,null,maxWidth);labelWidth=Math.max(labelWidth,info.width);labelHeight=Math.max(labelHeight,info.height)}axis.labelWidth=opts.labelWidth||labelWidth;axis.labelHeight=opts.labelHeight||labelHeight}function allocateAxisBoxFirstPhase(axis){var lw=axis.labelWidth,lh=axis.labelHeight,pos=axis.options.position,isXAxis=axis.direction==="x",tickLength=axis.options.tickLength,axisMargin=options.grid.axisMargin,padding=options.grid.labelMargin,innermost=true,outermost=true,first=true,found=false;$.each(isXAxis?xaxes:yaxes,function(i,a){if(a&&(a.show||a.reserveSpace)){if(a===axis){found=true}else if(a.options.position===pos){if(found){outermost=false}else{innermost=false}}if(!found){first=false}}});if(outermost){axisMargin=0}if(tickLength==null){tickLength=first?"full":5}if(!isNaN(+tickLength))padding+=+tickLength;if(isXAxis){lh+=padding;if(pos=="bottom"){plotOffset.bottom+=lh+axisMargin;axis.box={top:surface.height-plotOffset.bottom,height:lh}}else{axis.box={top:plotOffset.top+axisMargin,height:lh};plotOffset.top+=lh+axisMargin}}else{lw+=padding;if(pos=="left"){axis.box={left:plotOffset.left+axisMargin,width:lw};plotOffset.left+=lw+axisMargin}else{plotOffset.right+=lw+axisMargin;axis.box={left:surface.width-plotOffset.right,width:lw}}}axis.position=pos;axis.tickLength=tickLength;axis.box.padding=padding;axis.innermost=innermost}function allocateAxisBoxSecondPhase(axis){if(axis.direction=="x"){axis.box.left=plotOffset.left-axis.labelWidth/2;axis.box.width=surface.width-plotOffset.left-plotOffset.right+axis.labelWidth}else{axis.box.top=plotOffset.top-axis.labelHeight/2;axis.box.height=surface.height-plotOffset.bottom-plotOffset.top+axis.labelHeight}}function adjustLayoutForThingsStickingOut(){var minMargin=options.grid.minBorderMargin,axis,i;if(minMargin==null){minMargin=0;for(i=0;i<series.length;++i)minMargin=Math.max(minMargin,2*(series[i].points.radius+series[i].points.lineWidth/2))}var margins={left:minMargin,right:minMargin,top:minMargin,bottom:minMargin};$.each(allAxes(),function(_,axis){if(axis.reserveSpace&&axis.ticks&&axis.ticks.length){if(axis.direction==="x"){margins.left=Math.max(margins.left,axis.labelWidth/2);margins.right=Math.max(margins.right,axis.labelWidth/2)}else{margins.bottom=Math.max(margins.bottom,axis.labelHeight/2);margins.top=Math.max(margins.top,axis.labelHeight/2)}}});plotOffset.left=Math.ceil(Math.max(margins.left,plotOffset.left));plotOffset.right=Math.ceil(Math.max(margins.right,plotOffset.right));plotOffset.top=Math.ceil(Math.max(margins.top,plotOffset.top));plotOffset.bottom=Math.ceil(Math.max(margins.bottom,plotOffset.bottom))}function setupGrid(){var i,axes=allAxes(),showGrid=options.grid.show;for(var a in plotOffset){var margin=options.grid.margin||0;plotOffset[a]=typeof margin=="number"?margin:margin[a]||0}executeHooks(hooks.processOffset,[plotOffset]);for(var a in plotOffset){if(typeof options.grid.borderWidth=="object"){plotOffset[a]+=showGrid?options.grid.borderWidth[a]:0}else{plotOffset[a]+=showGrid?options.grid.borderWidth:0}}$.each(axes,function(_,axis){var axisOpts=axis.options;axis.show=axisOpts.show==null?axis.used:axisOpts.show;axis.reserveSpace=axisOpts.reserveSpace==null?axis.show:axisOpts.reserveSpace;setRange(axis)});if(showGrid){var allocatedAxes=$.grep(axes,function(axis){return axis.show||axis.reserveSpace});$.each(allocatedAxes,function(_,axis){setupTickGeneration(axis);setTicks(axis);snapRangeToTicks(axis,axis.ticks);measureTickLabels(axis)});for(i=allocatedAxes.length-1;i>=0;--i)allocateAxisBoxFirstPhase(allocatedAxes[i]);adjustLayoutForThingsStickingOut();$.each(allocatedAxes,function(_,axis){allocateAxisBoxSecondPhase(axis)})}plotWidth=surface.width-plotOffset.left-plotOffset.right;plotHeight=surface.height-plotOffset.bottom-plotOffset.top;$.each(axes,function(_,axis){setTransformationHelpers(axis)});if(showGrid){drawAxisLabels()}insertLegend()}function setRange(axis){var opts=axis.options,min=+(opts.min!=null?opts.min:axis.datamin),max=+(opts.max!=null?opts.max:axis.datamax),delta=max-min;if(delta==0){var widen=max==0?1:.01;if(opts.min==null)min-=widen;if(opts.max==null||opts.min!=null)max+=widen}else{var margin=opts.autoscaleMargin;if(margin!=null){if(opts.min==null){min-=delta*margin;if(min<0&&axis.datamin!=null&&axis.datamin>=0)min=0}if(opts.max==null){max+=delta*margin;if(max>0&&axis.datamax!=null&&axis.datamax<=0)max=0}}}axis.min=min;axis.max=max}function setupTickGeneration(axis){var opts=axis.options;var noTicks;if(typeof opts.ticks=="number"&&opts.ticks>0)noTicks=opts.ticks;else noTicks=.3*Math.sqrt(axis.direction=="x"?surface.width:surface.height);var delta=(axis.max-axis.min)/noTicks,dec=-Math.floor(Math.log(delta)/Math.LN10),maxDec=opts.tickDecimals;if(maxDec!=null&&dec>maxDec){dec=maxDec}var magn=Math.pow(10,-dec),norm=delta/magn,size;if(norm<1.5){size=1}else if(norm<3){size=2;if(norm>2.25&&(maxDec==null||dec+1<=maxDec)){size=2.5;++dec}}else if(norm<7.5){size=5}else{size=10}size*=magn;if(opts.minTickSize!=null&&size<opts.minTickSize){size=opts.minTickSize}axis.delta=delta;axis.tickDecimals=Math.max(0,maxDec!=null?maxDec:dec);axis.tickSize=opts.tickSize||size;if(opts.mode=="time"&&!axis.tickGenerator){throw new Error("Time mode requires the flot.time plugin.")}if(!axis.tickGenerator){axis.tickGenerator=function(axis){var ticks=[],start=floorInBase(axis.min,axis.tickSize),i=0,v=Number.NaN,prev;do{prev=v;v=start+i*axis.tickSize;ticks.push(v);++i}while(v<axis.max&&v!=prev);return ticks};axis.tickFormatter=function(value,axis){var factor=axis.tickDecimals?Math.pow(10,axis.tickDecimals):1;var formatted=""+Math.round(value*factor)/factor;if(axis.tickDecimals!=null){var decimal=formatted.indexOf(".");var precision=decimal==-1?0:formatted.length-decimal-1;if(precision<axis.tickDecimals){return(precision?formatted:formatted+".")+(""+factor).substr(1,axis.tickDecimals-precision)}}return formatted}}if($.isFunction(opts.tickFormatter))axis.tickFormatter=function(v,axis){return""+opts.tickFormatter(v,axis)};if(opts.alignTicksWithAxis!=null){var otherAxis=(axis.direction=="x"?xaxes:yaxes)[opts.alignTicksWithAxis-1];if(otherAxis&&otherAxis.used&&otherAxis!=axis){var niceTicks=axis.tickGenerator(axis);if(niceTicks.length>0){if(opts.min==null)axis.min=Math.min(axis.min,niceTicks[0]);if(opts.max==null&&niceTicks.length>1)axis.max=Math.max(axis.max,niceTicks[niceTicks.length-1])}axis.tickGenerator=function(axis){var ticks=[],v,i;for(i=0;i<otherAxis.ticks.length;++i){v=(otherAxis.ticks[i].v-otherAxis.min)/(otherAxis.max-otherAxis.min);v=axis.min+v*(axis.max-axis.min);ticks.push(v)}return ticks};if(!axis.mode&&opts.tickDecimals==null){var extraDec=Math.max(0,-Math.floor(Math.log(axis.delta)/Math.LN10)+1),ts=axis.tickGenerator(axis);if(!(ts.length>1&&/\..*0$/.test((ts[1]-ts[0]).toFixed(extraDec))))axis.tickDecimals=extraDec}}}}function setTicks(axis){var oticks=axis.options.ticks,ticks=[];if(oticks==null||typeof oticks=="number"&&oticks>0)ticks=axis.tickGenerator(axis);else if(oticks){if($.isFunction(oticks))ticks=oticks(axis);else ticks=oticks}var i,v;axis.ticks=[];for(i=0;i<ticks.length;++i){var label=null;var t=ticks[i];if(typeof t=="object"){v=+t[0];if(t.length>1)label=t[1]}else v=+t;if(label==null)label=axis.tickFormatter(v,axis);if(!isNaN(v))axis.ticks.push({v:v,label:label})}}function snapRangeToTicks(axis,ticks){if(axis.options.autoscaleMargin&&ticks.length>0){if(axis.options.min==null)axis.min=Math.min(axis.min,ticks[0].v);if(axis.options.max==null&&ticks.length>1)axis.max=Math.max(axis.max,ticks[ticks.length-1].v)}}function draw(){surface.clear();executeHooks(hooks.drawBackground,[ctx]);var grid=options.grid;if(grid.show&&grid.backgroundColor)drawBackground();if(grid.show&&!grid.aboveData){drawGrid()}for(var i=0;i<series.length;++i){executeHooks(hooks.drawSeries,[ctx,series[i]]);drawSeries(series[i])}executeHooks(hooks.draw,[ctx]);if(grid.show&&grid.aboveData){drawGrid()}surface.render();triggerRedrawOverlay()}function extractRange(ranges,coord){var axis,from,to,key,axes=allAxes();for(var i=0;i<axes.length;++i){axis=axes[i];if(axis.direction==coord){key=coord+axis.n+"axis";if(!ranges[key]&&axis.n==1)key=coord+"axis";if(ranges[key]){from=ranges[key].from;to=ranges[key].to;break}}}if(!ranges[key]){axis=coord=="x"?xaxes[0]:yaxes[0];from=ranges[coord+"1"];to=ranges[coord+"2"]}if(from!=null&&to!=null&&from>to){var tmp=from;from=to;to=tmp}return{from:from,to:to,axis:axis}}function drawBackground(){ctx.save();ctx.translate(plotOffset.left,plotOffset.top);ctx.fillStyle=getColorOrGradient(options.grid.backgroundColor,plotHeight,0,"rgba(255, 255, 255, 0)");ctx.fillRect(0,0,plotWidth,plotHeight);ctx.restore()}function drawGrid(){var i,axes,bw,bc;ctx.save();ctx.translate(plotOffset.left,plotOffset.top);var markings=options.grid.markings;if(markings){if($.isFunction(markings)){axes=plot.getAxes();axes.xmin=axes.xaxis.min;axes.xmax=axes.xaxis.max;axes.ymin=axes.yaxis.min;axes.ymax=axes.yaxis.max;markings=markings(axes)}for(i=0;i<markings.length;++i){var m=markings[i],xrange=extractRange(m,"x"),yrange=extractRange(m,"y");if(xrange.from==null)xrange.from=xrange.axis.min;if(xrange.to==null)xrange.to=xrange.axis.max;
19+if(yrange.from==null)yrange.from=yrange.axis.min;if(yrange.to==null)yrange.to=yrange.axis.max;if(xrange.to<xrange.axis.min||xrange.from>xrange.axis.max||yrange.to<yrange.axis.min||yrange.from>yrange.axis.max)continue;xrange.from=Math.max(xrange.from,xrange.axis.min);xrange.to=Math.min(xrange.to,xrange.axis.max);yrange.from=Math.max(yrange.from,yrange.axis.min);yrange.to=Math.min(yrange.to,yrange.axis.max);var xequal=xrange.from===xrange.to,yequal=yrange.from===yrange.to;if(xequal&&yequal){continue}xrange.from=Math.floor(xrange.axis.p2c(xrange.from));xrange.to=Math.floor(xrange.axis.p2c(xrange.to));yrange.from=Math.floor(yrange.axis.p2c(yrange.from));yrange.to=Math.floor(yrange.axis.p2c(yrange.to));if(xequal||yequal){var lineWidth=m.lineWidth||options.grid.markingsLineWidth,subPixel=lineWidth%2?.5:0;ctx.beginPath();ctx.strokeStyle=m.color||options.grid.markingsColor;ctx.lineWidth=lineWidth;if(xequal){ctx.moveTo(xrange.to+subPixel,yrange.from);ctx.lineTo(xrange.to+subPixel,yrange.to)}else{ctx.moveTo(xrange.from,yrange.to+subPixel);ctx.lineTo(xrange.to,yrange.to+subPixel)}ctx.stroke()}else{ctx.fillStyle=m.color||options.grid.markingsColor;ctx.fillRect(xrange.from,yrange.to,xrange.to-xrange.from,yrange.from-yrange.to)}}}axes=allAxes();bw=options.grid.borderWidth;for(var j=0;j<axes.length;++j){var axis=axes[j],box=axis.box,t=axis.tickLength,x,y,xoff,yoff;if(!axis.show||axis.ticks.length==0)continue;ctx.lineWidth=1;if(axis.direction=="x"){x=0;if(t=="full")y=axis.position=="top"?0:plotHeight;else y=box.top-plotOffset.top+(axis.position=="top"?box.height:0)}else{y=0;if(t=="full")x=axis.position=="left"?0:plotWidth;else x=box.left-plotOffset.left+(axis.position=="left"?box.width:0)}if(!axis.innermost){ctx.strokeStyle=axis.options.color;ctx.beginPath();xoff=yoff=0;if(axis.direction=="x")xoff=plotWidth+1;else yoff=plotHeight+1;if(ctx.lineWidth==1){if(axis.direction=="x"){y=Math.floor(y)+.5}else{x=Math.floor(x)+.5}}ctx.moveTo(x,y);ctx.lineTo(x+xoff,y+yoff);ctx.stroke()}ctx.strokeStyle=axis.options.tickColor;ctx.beginPath();for(i=0;i<axis.ticks.length;++i){var v=axis.ticks[i].v;xoff=yoff=0;if(isNaN(v)||v<axis.min||v>axis.max||t=="full"&&(typeof bw=="object"&&bw[axis.position]>0||bw>0)&&(v==axis.min||v==axis.max))continue;if(axis.direction=="x"){x=axis.p2c(v);yoff=t=="full"?-plotHeight:t;if(axis.position=="top")yoff=-yoff}else{y=axis.p2c(v);xoff=t=="full"?-plotWidth:t;if(axis.position=="left")xoff=-xoff}if(ctx.lineWidth==1){if(axis.direction=="x")x=Math.floor(x)+.5;else y=Math.floor(y)+.5}ctx.moveTo(x,y);ctx.lineTo(x+xoff,y+yoff)}ctx.stroke()}if(bw){bc=options.grid.borderColor;if(typeof bw=="object"||typeof bc=="object"){if(typeof bw!=="object"){bw={top:bw,right:bw,bottom:bw,left:bw}}if(typeof bc!=="object"){bc={top:bc,right:bc,bottom:bc,left:bc}}if(bw.top>0){ctx.strokeStyle=bc.top;ctx.lineWidth=bw.top;ctx.beginPath();ctx.moveTo(0-bw.left,0-bw.top/2);ctx.lineTo(plotWidth,0-bw.top/2);ctx.stroke()}if(bw.right>0){ctx.strokeStyle=bc.right;ctx.lineWidth=bw.right;ctx.beginPath();ctx.moveTo(plotWidth+bw.right/2,0-bw.top);ctx.lineTo(plotWidth+bw.right/2,plotHeight);ctx.stroke()}if(bw.bottom>0){ctx.strokeStyle=bc.bottom;ctx.lineWidth=bw.bottom;ctx.beginPath();ctx.moveTo(plotWidth+bw.right,plotHeight+bw.bottom/2);ctx.lineTo(0,plotHeight+bw.bottom/2);ctx.stroke()}if(bw.left>0){ctx.strokeStyle=bc.left;ctx.lineWidth=bw.left;ctx.beginPath();ctx.moveTo(0-bw.left/2,plotHeight+bw.bottom);ctx.lineTo(0-bw.left/2,0);ctx.stroke()}}else{ctx.lineWidth=bw;ctx.strokeStyle=options.grid.borderColor;ctx.strokeRect(-bw/2,-bw/2,plotWidth+bw,plotHeight+bw)}}ctx.restore()}function drawAxisLabels(){$.each(allAxes(),function(_,axis){var box=axis.box,legacyStyles=axis.direction+"Axis "+axis.direction+axis.n+"Axis",layer="flot-"+axis.direction+"-axis flot-"+axis.direction+axis.n+"-axis "+legacyStyles,font=axis.options.font||"flot-tick-label tickLabel",tick,x,y,halign,valign;surface.removeText(layer);if(!axis.show||axis.ticks.length==0)return;for(var i=0;i<axis.ticks.length;++i){tick=axis.ticks[i];if(!tick.label||tick.v<axis.min||tick.v>axis.max)continue;if(axis.direction=="x"){halign="center";x=plotOffset.left+axis.p2c(tick.v);if(axis.position=="bottom"){y=box.top+box.padding}else{y=box.top+box.height-box.padding;valign="bottom"}}else{valign="middle";y=plotOffset.top+axis.p2c(tick.v);if(axis.position=="left"){x=box.left+box.width-box.padding;halign="right"}else{x=box.left+box.padding}}surface.addText(layer,x,y,tick.label,font,null,null,halign,valign)}})}function drawSeries(series){if(series.lines.show)drawSeriesLines(series);if(series.bars.show)drawSeriesBars(series);if(series.points.show)drawSeriesPoints(series)}function drawSeriesLines(series){function plotLine(datapoints,xoffset,yoffset,axisx,axisy){var points=datapoints.points,ps=datapoints.pointsize,prevx=null,prevy=null;ctx.beginPath();for(var i=ps;i<points.length;i+=ps){var x1=points[i-ps],y1=points[i-ps+1],x2=points[i],y2=points[i+1];if(x1==null||x2==null)continue;if(y1<=y2&&y1<axisy.min){if(y2<axisy.min)continue;x1=(axisy.min-y1)/(y2-y1)*(x2-x1)+x1;y1=axisy.min}else if(y2<=y1&&y2<axisy.min){if(y1<axisy.min)continue;x2=(axisy.min-y1)/(y2-y1)*(x2-x1)+x1;y2=axisy.min}if(y1>=y2&&y1>axisy.max){if(y2>axisy.max)continue;x1=(axisy.max-y1)/(y2-y1)*(x2-x1)+x1;y1=axisy.max}else if(y2>=y1&&y2>axisy.max){if(y1>axisy.max)continue;x2=(axisy.max-y1)/(y2-y1)*(x2-x1)+x1;y2=axisy.max}if(x1<=x2&&x1<axisx.min){if(x2<axisx.min)continue;y1=(axisx.min-x1)/(x2-x1)*(y2-y1)+y1;x1=axisx.min}else if(x2<=x1&&x2<axisx.min){if(x1<axisx.min)continue;y2=(axisx.min-x1)/(x2-x1)*(y2-y1)+y1;x2=axisx.min}if(x1>=x2&&x1>axisx.max){if(x2>axisx.max)continue;y1=(axisx.max-x1)/(x2-x1)*(y2-y1)+y1;x1=axisx.max}else if(x2>=x1&&x2>axisx.max){if(x1>axisx.max)continue;y2=(axisx.max-x1)/(x2-x1)*(y2-y1)+y1;x2=axisx.max}if(x1!=prevx||y1!=prevy)ctx.moveTo(axisx.p2c(x1)+xoffset,axisy.p2c(y1)+yoffset);prevx=x2;prevy=y2;ctx.lineTo(axisx.p2c(x2)+xoffset,axisy.p2c(y2)+yoffset)}ctx.stroke()}function plotLineArea(datapoints,axisx,axisy){var points=datapoints.points,ps=datapoints.pointsize,bottom=Math.min(Math.max(0,axisy.min),axisy.max),i=0,top,areaOpen=false,ypos=1,segmentStart=0,segmentEnd=0;while(true){if(ps>0&&i>points.length+ps)break;i+=ps;var x1=points[i-ps],y1=points[i-ps+ypos],x2=points[i],y2=points[i+ypos];if(areaOpen){if(ps>0&&x1!=null&&x2==null){segmentEnd=i;ps=-ps;ypos=2;continue}if(ps<0&&i==segmentStart+ps){ctx.fill();areaOpen=false;ps=-ps;ypos=1;i=segmentStart=segmentEnd+ps;continue}}if(x1==null||x2==null)continue;if(x1<=x2&&x1<axisx.min){if(x2<axisx.min)continue;y1=(axisx.min-x1)/(x2-x1)*(y2-y1)+y1;x1=axisx.min}else if(x2<=x1&&x2<axisx.min){if(x1<axisx.min)continue;y2=(axisx.min-x1)/(x2-x1)*(y2-y1)+y1;x2=axisx.min}if(x1>=x2&&x1>axisx.max){if(x2>axisx.max)continue;y1=(axisx.max-x1)/(x2-x1)*(y2-y1)+y1;x1=axisx.max}else if(x2>=x1&&x2>axisx.max){if(x1>axisx.max)continue;y2=(axisx.max-x1)/(x2-x1)*(y2-y1)+y1;x2=axisx.max}if(!areaOpen){ctx.beginPath();ctx.moveTo(axisx.p2c(x1),axisy.p2c(bottom));areaOpen=true}if(y1>=axisy.max&&y2>=axisy.max){ctx.lineTo(axisx.p2c(x1),axisy.p2c(axisy.max));ctx.lineTo(axisx.p2c(x2),axisy.p2c(axisy.max));continue}else if(y1<=axisy.min&&y2<=axisy.min){ctx.lineTo(axisx.p2c(x1),axisy.p2c(axisy.min));ctx.lineTo(axisx.p2c(x2),axisy.p2c(axisy.min));continue}var x1old=x1,x2old=x2;if(y1<=y2&&y1<axisy.min&&y2>=axisy.min){x1=(axisy.min-y1)/(y2-y1)*(x2-x1)+x1;y1=axisy.min}else if(y2<=y1&&y2<axisy.min&&y1>=axisy.min){x2=(axisy.min-y1)/(y2-y1)*(x2-x1)+x1;y2=axisy.min}if(y1>=y2&&y1>axisy.max&&y2<=axisy.max){x1=(axisy.max-y1)/(y2-y1)*(x2-x1)+x1;y1=axisy.max}else if(y2>=y1&&y2>axisy.max&&y1<=axisy.max){x2=(axisy.max-y1)/(y2-y1)*(x2-x1)+x1;y2=axisy.max}if(x1!=x1old){ctx.lineTo(axisx.p2c(x1old),axisy.p2c(y1))}ctx.lineTo(axisx.p2c(x1),axisy.p2c(y1));ctx.lineTo(axisx.p2c(x2),axisy.p2c(y2));if(x2!=x2old){ctx.lineTo(axisx.p2c(x2),axisy.p2c(y2));ctx.lineTo(axisx.p2c(x2old),axisy.p2c(y2))}}}ctx.save();ctx.translate(plotOffset.left,plotOffset.top);ctx.lineJoin="round";var lw=series.lines.lineWidth,sw=series.shadowSize;if(lw>0&&sw>0){ctx.lineWidth=sw;ctx.strokeStyle="rgba(0,0,0,0.1)";var angle=Math.PI/18;plotLine(series.datapoints,Math.sin(angle)*(lw/2+sw/2),Math.cos(angle)*(lw/2+sw/2),series.xaxis,series.yaxis);ctx.lineWidth=sw/2;plotLine(series.datapoints,Math.sin(angle)*(lw/2+sw/4),Math.cos(angle)*(lw/2+sw/4),series.xaxis,series.yaxis)}ctx.lineWidth=lw;ctx.strokeStyle=series.color;var fillStyle=getFillStyle(series.lines,series.color,0,plotHeight);if(fillStyle){ctx.fillStyle=fillStyle;plotLineArea(series.datapoints,series.xaxis,series.yaxis)}if(lw>0)plotLine(series.datapoints,0,0,series.xaxis,series.yaxis);ctx.restore()}function drawSeriesPoints(series){function plotPoints(datapoints,radius,fillStyle,offset,shadow,axisx,axisy,symbol){var points=datapoints.points,ps=datapoints.pointsize;for(var i=0;i<points.length;i+=ps){var x=points[i],y=points[i+1];if(x==null||x<axisx.min||x>axisx.max||y<axisy.min||y>axisy.max)continue;ctx.beginPath();x=axisx.p2c(x);y=axisy.p2c(y)+offset;if(symbol=="circle")ctx.arc(x,y,radius,0,shadow?Math.PI:Math.PI*2,false);else symbol(ctx,x,y,radius,shadow);ctx.closePath();if(fillStyle){ctx.fillStyle=fillStyle;ctx.fill()}ctx.stroke()}}ctx.save();ctx.translate(plotOffset.left,plotOffset.top);var lw=series.points.lineWidth,sw=series.shadowSize,radius=series.points.radius,symbol=series.points.symbol;if(lw==0)lw=1e-4;if(lw>0&&sw>0){var w=sw/2;ctx.lineWidth=w;ctx.strokeStyle="rgba(0,0,0,0.1)";plotPoints(series.datapoints,radius,null,w+w/2,true,series.xaxis,series.yaxis,symbol);ctx.strokeStyle="rgba(0,0,0,0.2)";plotPoints(series.datapoints,radius,null,w/2,true,series.xaxis,series.yaxis,symbol)}ctx.lineWidth=lw;ctx.strokeStyle=series.color;plotPoints(series.datapoints,radius,getFillStyle(series.points,series.color),0,false,series.xaxis,series.yaxis,symbol);ctx.restore()}function drawBar(x,y,b,barLeft,barRight,fillStyleCallback,axisx,axisy,c,horizontal,lineWidth){var left,right,bottom,top,drawLeft,drawRight,drawTop,drawBottom,tmp;if(horizontal){drawBottom=drawRight=drawTop=true;drawLeft=false;left=b;right=x;top=y+barLeft;bottom=y+barRight;if(right<left){tmp=right;right=left;left=tmp;drawLeft=true;drawRight=false}}else{drawLeft=drawRight=drawTop=true;drawBottom=false;left=x+barLeft;right=x+barRight;bottom=b;top=y;if(top<bottom){tmp=top;top=bottom;bottom=tmp;drawBottom=true;drawTop=false}}if(right<axisx.min||left>axisx.max||top<axisy.min||bottom>axisy.max)return;if(left<axisx.min){left=axisx.min;drawLeft=false}if(right>axisx.max){right=axisx.max;drawRight=false}if(bottom<axisy.min){bottom=axisy.min;drawBottom=false}if(top>axisy.max){top=axisy.max;drawTop=false}left=axisx.p2c(left);bottom=axisy.p2c(bottom);right=axisx.p2c(right);top=axisy.p2c(top);if(fillStyleCallback){c.fillStyle=fillStyleCallback(bottom,top);c.fillRect(left,top,right-left,bottom-top)}if(lineWidth>0&&(drawLeft||drawRight||drawTop||drawBottom)){c.beginPath();c.moveTo(left,bottom);if(drawLeft)c.lineTo(left,top);else c.moveTo(left,top);if(drawTop)c.lineTo(right,top);else c.moveTo(right,top);if(drawRight)c.lineTo(right,bottom);else c.moveTo(right,bottom);if(drawBottom)c.lineTo(left,bottom);else c.moveTo(left,bottom);c.stroke()}}function drawSeriesBars(series){function plotBars(datapoints,barLeft,barRight,fillStyleCallback,axisx,axisy){var points=datapoints.points,ps=datapoints.pointsize;for(var i=0;i<points.length;i+=ps){if(points[i]==null)continue;drawBar(points[i],points[i+1],points[i+2],barLeft,barRight,fillStyleCallback,axisx,axisy,ctx,series.bars.horizontal,series.bars.lineWidth)}}ctx.save();ctx.translate(plotOffset.left,plotOffset.top);ctx.lineWidth=series.bars.lineWidth;ctx.strokeStyle=series.color;var barLeft;switch(series.bars.align){case"left":barLeft=0;break;case"right":barLeft=-series.bars.barWidth;break;default:barLeft=-series.bars.barWidth/2}var fillStyleCallback=series.bars.fill?function(bottom,top){return getFillStyle(series.bars,series.color,bottom,top)}:null;plotBars(series.datapoints,barLeft,barLeft+series.bars.barWidth,fillStyleCallback,series.xaxis,series.yaxis);ctx.restore()}function getFillStyle(filloptions,seriesColor,bottom,top){var fill=filloptions.fill;if(!fill)return null;if(filloptions.fillColor)return getColorOrGradient(filloptions.fillColor,bottom,top,seriesColor);var c=$.color.parse(seriesColor);c.a=typeof fill=="number"?fill:.4;c.normalize();return c.toString()}function insertLegend(){if(options.legend.container!=null){$(options.legend.container).html("")}else{placeholder.find(".legend").remove()}if(!options.legend.show){return}var fragments=[],entries=[],rowStarted=false,lf=options.legend.labelFormatter,s,label;for(var i=0;i<series.length;++i){s=series[i];if(s.label){label=lf?lf(s.label,s):s.label;if(label){entries.push({label:label,color:s.color})}}}if(options.legend.sorted){if($.isFunction(options.legend.sorted)){entries.sort(options.legend.sorted)}else if(options.legend.sorted=="reverse"){entries.reverse()}else{var ascending=options.legend.sorted!="descending";entries.sort(function(a,b){return a.label==b.label?0:a.label<b.label!=ascending?1:-1})}}for(var i=0;i<entries.length;++i){var entry=entries[i];if(i%options.legend.noColumns==0){if(rowStarted)fragments.push("</tr>");fragments.push("<tr>");rowStarted=true}fragments.push('<td class="legendColorBox"><div style="border:1px solid '+options.legend.labelBoxBorderColor+';padding:1px"><div style="width:4px;height:0;border:5px solid '+entry.color+';overflow:hidden"></div></div></td>'+'<td class="legendLabel">'+entry.label+"</td>")}if(rowStarted)fragments.push("</tr>");if(fragments.length==0)return;var table='<table style="font-size:smaller;color:'+options.grid.color+'">'+fragments.join("")+"</table>";if(options.legend.container!=null)$(options.legend.container).html(table);else{var 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20+ </script>
21+ <script language="javascript" type="text/javascript">
22+ /* Javascript plotting library for jQuery, version 0.8.3.
23+
24+Copyright (c) 2007-2014 IOLA and Ole Laursen.
25+Licensed under the MIT license.
26+
27+*/
28+(function($){var options={series:{points:{errorbars:null,xerr:{err:"x",show:null,asymmetric:null,upperCap:null,lowerCap:null,color:null,radius:null},yerr:{err:"y",show:null,asymmetric:null,upperCap:null,lowerCap:null,color:null,radius:null}}}};function processRawData(plot,series,data,datapoints){if(!series.points.errorbars)return;var format=[{x:true,number:true,required:true},{y:true,number:true,required:true}];var errors=series.points.errorbars;if(errors=="x"||errors=="xy"){if(series.points.xerr.asymmetric){format.push({x:true,number:true,required:true});format.push({x:true,number:true,required:true})}else format.push({x:true,number:true,required:true})}if(errors=="y"||errors=="xy"){if(series.points.yerr.asymmetric){format.push({y:true,number:true,required:true});format.push({y:true,number:true,required:true})}else format.push({y:true,number:true,required:true})}datapoints.format=format}function parseErrors(series,i){var points=series.datapoints.points;var exl=null,exu=null,eyl=null,eyu=null;var xerr=series.points.xerr,yerr=series.points.yerr;var eb=series.points.errorbars;if(eb=="x"||eb=="xy"){if(xerr.asymmetric){exl=points[i+2];exu=points[i+3];if(eb=="xy")if(yerr.asymmetric){eyl=points[i+4];eyu=points[i+5]}else eyl=points[i+4]}else{exl=points[i+2];if(eb=="xy")if(yerr.asymmetric){eyl=points[i+3];eyu=points[i+4]}else eyl=points[i+3]}}else if(eb=="y")if(yerr.asymmetric){eyl=points[i+2];eyu=points[i+3]}else eyl=points[i+2];if(exu==null)exu=exl;if(eyu==null)eyu=eyl;var errRanges=[exl,exu,eyl,eyu];if(!xerr.show){errRanges[0]=null;errRanges[1]=null}if(!yerr.show){errRanges[2]=null;errRanges[3]=null}return errRanges}function drawSeriesErrors(plot,ctx,s){var points=s.datapoints.points,ps=s.datapoints.pointsize,ax=[s.xaxis,s.yaxis],radius=s.points.radius,err=[s.points.xerr,s.points.yerr];var invertX=false;if(ax[0].p2c(ax[0].max)<ax[0].p2c(ax[0].min)){invertX=true;var tmp=err[0].lowerCap;err[0].lowerCap=err[0].upperCap;err[0].upperCap=tmp}var 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tmp=lower;lower=upper;upper=tmp;tmp=drawLower;drawLower=drawUpper;drawUpper=tmp;tmp=minmax[0];minmax[0]=minmax[1];minmax[1]=tmp}x=ax[0].p2c(x),y=ax[1].p2c(y),upper=ax[e].p2c(upper);lower=ax[e].p2c(lower);minmax[0]=ax[e].p2c(minmax[0]);minmax[1]=ax[e].p2c(minmax[1]);var lw=err[e].lineWidth?err[e].lineWidth:s.points.lineWidth,sw=s.points.shadowSize!=null?s.points.shadowSize:s.shadowSize;if(lw>0&&sw>0){var w=sw/2;ctx.lineWidth=w;ctx.strokeStyle="rgba(0,0,0,0.1)";drawError(ctx,err[e],x,y,upper,lower,drawUpper,drawLower,radius,w+w/2,minmax);ctx.strokeStyle="rgba(0,0,0,0.2)";drawError(ctx,err[e],x,y,upper,lower,drawUpper,drawLower,radius,w/2,minmax)}ctx.strokeStyle=err[e].color?err[e].color:s.color;ctx.lineWidth=lw;drawError(ctx,err[e],x,y,upper,lower,drawUpper,drawLower,radius,0,minmax)}}}}function 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29+ </script>
30+ <script language="javascript" type="text/javascript">
31+ /* Javascript plotting library for jQuery, version 0.8.3.
32+
33+Copyright (c) 2007-2014 IOLA and Ole Laursen.
34+Licensed under the MIT license.
35+
36+*/
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257+ <![endif]-->
258+ </head>
259+ <body>
260+ <div id="wrap">
261+ <div id="main" class="body">
262+ <h1>criterion performance measurements</h1>
263+
264+<h2>overview</h2>
265+
266+<p><a href="#grokularation">want to understand this report?</a></p>
267+
268+<div id="overview" class="ovchart" style="width:900px;height:100px;"></div>
269+
270+<h2><a name="b0">Matrix Composition/10x10/WHNF - 10x10</a></h2>
271+ <table width="100%">
272+ <tbody>
273+ <tr>
274+ <td><div id="kde0" class="kdechart"
275+ style="width:450px;height:278px;"></div></td>
276+ <td><div id="time0" class="timechart"
277+ style="width:450px;height:278px;"></div></td>
278+<!--
279+ <td><div id="cycle0" class="cyclechart"
280+ style="width:300px;height:278px;"></div></td>
281+-->
282+ </tr>
283+ </tbody>
284+ </table>
285+
286+ <table>
287+ <thead class="analysis">
288+ <th></th>
289+ <th class="cibound"
290+ title="0.95 confidence level">lower bound</th>
291+ <th>estimate</th>
292+ <th class="cibound"
293+ title="0.95 confidence level">upper bound</th>
294+ </thead>
295+ <tbody>
296+ <tr>
297+ <td>OLS regression</td>
298+ <td><span class="confinterval olstimelb0">xxx</span></td>
299+ <td><span class="olstimept0">xxx</span></td>
300+ <td><span class="confinterval olstimeub0">xxx</span></td>
301+ </tr>
302+ <tr>
303+ <td>R&#xb2; goodness-of-fit</td>
304+ <td><span class="confinterval olsr2lb0">xxx</span></td>
305+ <td><span class="olsr2pt0">xxx</span></td>
306+ <td><span class="confinterval olsr2ub0">xxx</span></td>
307+ </tr>
308+ <tr>
309+ <td>Mean execution time</td>
310+ <td><span class="confinterval citime">1.2439476132780966e-4</span></td>
311+ <td><span class="time">1.2521282696584778e-4</span></td>
312+ <td><span class="confinterval citime">1.2627361635087712e-4</span></td>
313+ </tr>
314+ <tr>
315+ <td>Standard deviation</td>
316+ <td><span class="confinterval citime">2.3769830641700065e-6</span></td>
317+ <td><span class="time">3.0000227210624054e-6</span></td>
318+ <td><span class="confinterval citime">3.868635052370606e-6</span></td>
319+ </tr>
320+ </tbody>
321+ </table>
322+
323+ <span class="outliers">
324+ <p>Outlying measurements have moderate
325+ (<span class="percent">0.19510840974237945</span>%)
326+ effect on estimated standard deviation.</p>
327+ </span>
328+<h2><a name="b1">Matrix Composition/10x10/NF - 10x10</a></h2>
329+ <table width="100%">
330+ <tbody>
331+ <tr>
332+ <td><div id="kde1" class="kdechart"
333+ style="width:450px;height:278px;"></div></td>
334+ <td><div id="time1" class="timechart"
335+ style="width:450px;height:278px;"></div></td>
336+<!--
337+ <td><div id="cycle1" class="cyclechart"
338+ style="width:300px;height:278px;"></div></td>
339+-->
340+ </tr>
341+ </tbody>
342+ </table>
343+
344+ <table>
345+ <thead class="analysis">
346+ <th></th>
347+ <th class="cibound"
348+ title="0.95 confidence level">lower bound</th>
349+ <th>estimate</th>
350+ <th class="cibound"
351+ title="0.95 confidence level">upper bound</th>
352+ </thead>
353+ <tbody>
354+ <tr>
355+ <td>OLS regression</td>
356+ <td><span class="confinterval olstimelb1">xxx</span></td>
357+ <td><span class="olstimept1">xxx</span></td>
358+ <td><span class="confinterval olstimeub1">xxx</span></td>
359+ </tr>
360+ <tr>
361+ <td>R&#xb2; goodness-of-fit</td>
362+ <td><span class="confinterval olsr2lb1">xxx</span></td>
363+ <td><span class="olsr2pt1">xxx</span></td>
364+ <td><span class="confinterval olsr2ub1">xxx</span></td>
365+ </tr>
366+ <tr>
367+ <td>Mean execution time</td>
368+ <td><span class="confinterval citime">1.4537321208713184e-4</span></td>
369+ <td><span class="time">1.532024430909428e-4</span></td>
370+ <td><span class="confinterval citime">1.6749129455977834e-4</span></td>
371+ </tr>
372+ <tr>
373+ <td>Standard deviation</td>
374+ <td><span class="confinterval citime">2.365045193527146e-5</span></td>
375+ <td><span class="time">3.649213223188502e-5</span></td>
376+ <td><span class="confinterval citime">5.3596936354843454e-5</span></td>
377+ </tr>
378+ </tbody>
379+ </table>
380+
381+ <span class="outliers">
382+ <p>Outlying measurements have severe
383+ (<span class="percent">0.9609582426012205</span>%)
384+ effect on estimated standard deviation.</p>
385+ </span>
386+<h2><a name="b2">Matrix Composition/100x100/WHNF - 100x100</a></h2>
387+ <table width="100%">
388+ <tbody>
389+ <tr>
390+ <td><div id="kde2" class="kdechart"
391+ style="width:450px;height:278px;"></div></td>
392+ <td><div id="time2" class="timechart"
393+ style="width:450px;height:278px;"></div></td>
394+<!--
395+ <td><div id="cycle2" class="cyclechart"
396+ style="width:300px;height:278px;"></div></td>
397+-->
398+ </tr>
399+ </tbody>
400+ </table>
401+
402+ <table>
403+ <thead class="analysis">
404+ <th></th>
405+ <th class="cibound"
406+ title="0.95 confidence level">lower bound</th>
407+ <th>estimate</th>
408+ <th class="cibound"
409+ title="0.95 confidence level">upper bound</th>
410+ </thead>
411+ <tbody>
412+ <tr>
413+ <td>OLS regression</td>
414+ <td><span class="confinterval olstimelb2">xxx</span></td>
415+ <td><span class="olstimept2">xxx</span></td>
416+ <td><span class="confinterval olstimeub2">xxx</span></td>
417+ </tr>
418+ <tr>
419+ <td>R&#xb2; goodness-of-fit</td>
420+ <td><span class="confinterval olsr2lb2">xxx</span></td>
421+ <td><span class="olsr2pt2">xxx</span></td>
422+ <td><span class="confinterval olsr2ub2">xxx</span></td>
423+ </tr>
424+ <tr>
425+ <td>Mean execution time</td>
426+ <td><span class="confinterval citime">0.11287564945528825</span></td>
427+ <td><span class="time">0.11922032795600032</span></td>
428+ <td><span class="confinterval citime">0.12600585030653141</span></td>
429+ </tr>
430+ <tr>
431+ <td>Standard deviation</td>
432+ <td><span class="confinterval citime">6.3874541360917384e-3</span></td>
433+ <td><span class="time">9.77563027930971e-3</span></td>
434+ <td><span class="confinterval citime">1.620035460618151e-2</span></td>
435+ </tr>
436+ </tbody>
437+ </table>
438+
439+ <span class="outliers">
440+ <p>Outlying measurements have moderate
441+ (<span class="percent">0.23184395941421526</span>%)
442+ effect on estimated standard deviation.</p>
443+ </span>
444+<h2><a name="b3">Matrix Composition/100x100/NF - 100x100</a></h2>
445+ <table width="100%">
446+ <tbody>
447+ <tr>
448+ <td><div id="kde3" class="kdechart"
449+ style="width:450px;height:278px;"></div></td>
450+ <td><div id="time3" class="timechart"
451+ style="width:450px;height:278px;"></div></td>
452+<!--
453+ <td><div id="cycle3" class="cyclechart"
454+ style="width:300px;height:278px;"></div></td>
455+-->
456+ </tr>
457+ </tbody>
458+ </table>
459+
460+ <table>
461+ <thead class="analysis">
462+ <th></th>
463+ <th class="cibound"
464+ title="0.95 confidence level">lower bound</th>
465+ <th>estimate</th>
466+ <th class="cibound"
467+ title="0.95 confidence level">upper bound</th>
468+ </thead>
469+ <tbody>
470+ <tr>
471+ <td>OLS regression</td>
472+ <td><span class="confinterval olstimelb3">xxx</span></td>
473+ <td><span class="olstimept3">xxx</span></td>
474+ <td><span class="confinterval olstimeub3">xxx</span></td>
475+ </tr>
476+ <tr>
477+ <td>R&#xb2; goodness-of-fit</td>
478+ <td><span class="confinterval olsr2lb3">xxx</span></td>
479+ <td><span class="olsr2pt3">xxx</span></td>
480+ <td><span class="confinterval olsr2ub3">xxx</span></td>
481+ </tr>
482+ <tr>
483+ <td>Mean execution time</td>
484+ <td><span class="confinterval citime">0.1110982578725974</span></td>
485+ <td><span class="time">0.11758616896428131</span></td>
486+ <td><span class="confinterval citime">0.12249179825349378</span></td>
487+ </tr>
488+ <tr>
489+ <td>Standard deviation</td>
490+ <td><span class="confinterval citime">5.369746750528417e-3</span></td>
491+ <td><span class="time">8.150134548496543e-3</span></td>
492+ <td><span class="confinterval citime">1.1065658668699107e-2</span></td>
493+ </tr>
494+ </tbody>
495+ </table>
496+
497+ <span class="outliers">
498+ <p>Outlying measurements have moderate
499+ (<span class="percent">0.22459068358328985</span>%)
500+ effect on estimated standard deviation.</p>
501+ </span>
502+<h2><a name="b4">Matrix Composition/200x200/WHNF - 200x200</a></h2>
503+ <table width="100%">
504+ <tbody>
505+ <tr>
506+ <td><div id="kde4" class="kdechart"
507+ style="width:450px;height:278px;"></div></td>
508+ <td><div id="time4" class="timechart"
509+ style="width:450px;height:278px;"></div></td>
510+<!--
511+ <td><div id="cycle4" class="cyclechart"
512+ style="width:300px;height:278px;"></div></td>
513+-->
514+ </tr>
515+ </tbody>
516+ </table>
517+
518+ <table>
519+ <thead class="analysis">
520+ <th></th>
521+ <th class="cibound"
522+ title="0.95 confidence level">lower bound</th>
523+ <th>estimate</th>
524+ <th class="cibound"
525+ title="0.95 confidence level">upper bound</th>
526+ </thead>
527+ <tbody>
528+ <tr>
529+ <td>OLS regression</td>
530+ <td><span class="confinterval olstimelb4">xxx</span></td>
531+ <td><span class="olstimept4">xxx</span></td>
532+ <td><span class="confinterval olstimeub4">xxx</span></td>
533+ </tr>
534+ <tr>
535+ <td>R&#xb2; goodness-of-fit</td>
536+ <td><span class="confinterval olsr2lb4">xxx</span></td>
537+ <td><span class="olsr2pt4">xxx</span></td>
538+ <td><span class="confinterval olsr2ub4">xxx</span></td>
539+ </tr>
540+ <tr>
541+ <td>Mean execution time</td>
542+ <td><span class="confinterval citime">0.9781591890205164</span></td>
543+ <td><span class="time">1.0404128327718354</span></td>
544+ <td><span class="confinterval citime">1.0852378857525764</span></td>
545+ </tr>
546+ <tr>
547+ <td>Standard deviation</td>
548+ <td><span class="confinterval citime">2.2371087252395228e-2</span></td>
549+ <td><span class="time">6.182803786470918e-2</span></td>
550+ <td><span class="confinterval citime">8.480026920295321e-2</span></td>
551+ </tr>
552+ </tbody>
553+ </table>
554+
555+ <span class="outliers">
556+ <p>Outlying measurements have moderate
557+ (<span class="percent">0.18749999999999994</span>%)
558+ effect on estimated standard deviation.</p>
559+ </span>
560+<h2><a name="b5">Matrix Composition/200x200/NF - 200x200</a></h2>
561+ <table width="100%">
562+ <tbody>
563+ <tr>
564+ <td><div id="kde5" class="kdechart"
565+ style="width:450px;height:278px;"></div></td>
566+ <td><div id="time5" class="timechart"
567+ style="width:450px;height:278px;"></div></td>
568+<!--
569+ <td><div id="cycle5" class="cyclechart"
570+ style="width:300px;height:278px;"></div></td>
571+-->
572+ </tr>
573+ </tbody>
574+ </table>
575+
576+ <table>
577+ <thead class="analysis">
578+ <th></th>
579+ <th class="cibound"
580+ title="0.95 confidence level">lower bound</th>
581+ <th>estimate</th>
582+ <th class="cibound"
583+ title="0.95 confidence level">upper bound</th>
584+ </thead>
585+ <tbody>
586+ <tr>
587+ <td>OLS regression</td>
588+ <td><span class="confinterval olstimelb5">xxx</span></td>
589+ <td><span class="olstimept5">xxx</span></td>
590+ <td><span class="confinterval olstimeub5">xxx</span></td>
591+ </tr>
592+ <tr>
593+ <td>R&#xb2; goodness-of-fit</td>
594+ <td><span class="confinterval olsr2lb5">xxx</span></td>
595+ <td><span class="olsr2pt5">xxx</span></td>
596+ <td><span class="confinterval olsr2ub5">xxx</span></td>
597+ </tr>
598+ <tr>
599+ <td>Mean execution time</td>
600+ <td><span class="confinterval citime">1.1011682298167216</span></td>
601+ <td><span class="time">1.1075485033964771</span></td>
602+ <td><span class="confinterval citime">1.1151673705599023</span></td>
603+ </tr>
604+ <tr>
605+ <td>Standard deviation</td>
606+ <td><span class="confinterval citime">2.193747621276998e-3</span></td>
607+ <td><span class="time">7.979551817654461e-3</span></td>
608+ <td><span class="confinterval citime">1.077654356866516e-2</span></td>
609+ </tr>
610+ </tbody>
611+ </table>
612+
613+ <span class="outliers">
614+ <p>Outlying measurements have moderate
615+ (<span class="percent">0.1875</span>%)
616+ effect on estimated standard deviation.</p>
617+ </span>
618+<h2><a name="b6">Matrix vs List - `select`/Distribution `select` - 100+100 / 100x100/List Distribution - Applicative version</a></h2>
619+ <table width="100%">
620+ <tbody>
621+ <tr>
622+ <td><div id="kde6" class="kdechart"
623+ style="width:450px;height:278px;"></div></td>
624+ <td><div id="time6" class="timechart"
625+ style="width:450px;height:278px;"></div></td>
626+<!--
627+ <td><div id="cycle6" class="cyclechart"
628+ style="width:300px;height:278px;"></div></td>
629+-->
630+ </tr>
631+ </tbody>
632+ </table>
633+
634+ <table>
635+ <thead class="analysis">
636+ <th></th>
637+ <th class="cibound"
638+ title="0.95 confidence level">lower bound</th>
639+ <th>estimate</th>
640+ <th class="cibound"
641+ title="0.95 confidence level">upper bound</th>
642+ </thead>
643+ <tbody>
644+ <tr>
645+ <td>OLS regression</td>
646+ <td><span class="confinterval olstimelb6">xxx</span></td>
647+ <td><span class="olstimept6">xxx</span></td>
648+ <td><span class="confinterval olstimeub6">xxx</span></td>
649+ </tr>
650+ <tr>
651+ <td>R&#xb2; goodness-of-fit</td>
652+ <td><span class="confinterval olsr2lb6">xxx</span></td>
653+ <td><span class="olsr2pt6">xxx</span></td>
654+ <td><span class="confinterval olsr2ub6">xxx</span></td>
655+ </tr>
656+ <tr>
657+ <td>Mean execution time</td>
658+ <td><span class="confinterval citime">2.338956891665778</span></td>
659+ <td><span class="time">2.3478542657700623</span></td>
660+ <td><span class="confinterval citime">2.359088486582247</span></td>
661+ </tr>
662+ <tr>
663+ <td>Standard deviation</td>
664+ <td><span class="confinterval citime">3.62336445641734e-3</span></td>
665+ <td><span class="time">1.2441745894453989e-2</span></td>
666+ <td><span class="confinterval citime">1.67050971444586e-2</span></td>
667+ </tr>
668+ </tbody>
669+ </table>
670+
671+ <span class="outliers">
672+ <p>Outlying measurements have moderate
673+ (<span class="percent">0.18749999999999997</span>%)
674+ effect on estimated standard deviation.</p>
675+ </span>
676+<h2><a name="b7">Matrix vs List - `select`/Distribution `select` - 100+100 / 100x100/Matrix Distribution - Applicative version</a></h2>
677+ <table width="100%">
678+ <tbody>
679+ <tr>
680+ <td><div id="kde7" class="kdechart"
681+ style="width:450px;height:278px;"></div></td>
682+ <td><div id="time7" class="timechart"
683+ style="width:450px;height:278px;"></div></td>
684+<!--
685+ <td><div id="cycle7" class="cyclechart"
686+ style="width:300px;height:278px;"></div></td>
687+-->
688+ </tr>
689+ </tbody>
690+ </table>
691+
692+ <table>
693+ <thead class="analysis">
694+ <th></th>
695+ <th class="cibound"
696+ title="0.95 confidence level">lower bound</th>
697+ <th>estimate</th>
698+ <th class="cibound"
699+ title="0.95 confidence level">upper bound</th>
700+ </thead>
701+ <tbody>
702+ <tr>
703+ <td>OLS regression</td>
704+ <td><span class="confinterval olstimelb7">xxx</span></td>
705+ <td><span class="olstimept7">xxx</span></td>
706+ <td><span class="confinterval olstimeub7">xxx</span></td>
707+ </tr>
708+ <tr>
709+ <td>R&#xb2; goodness-of-fit</td>
710+ <td><span class="confinterval olsr2lb7">xxx</span></td>
711+ <td><span class="olsr2pt7">xxx</span></td>
712+ <td><span class="confinterval olsr2ub7">xxx</span></td>
713+ </tr>
714+ <tr>
715+ <td>Mean execution time</td>
716+ <td><span class="confinterval citime">1.6422040204675979e-3</span></td>
717+ <td><span class="time">1.7931655457283859e-3</span></td>
718+ <td><span class="confinterval citime">1.9714955275173672e-3</span></td>
719+ </tr>
720+ <tr>
721+ <td>Standard deviation</td>
722+ <td><span class="confinterval citime">3.9388340187426643e-4</span></td>
723+ <td><span class="time">5.021999918501304e-4</span></td>
724+ <td><span class="confinterval citime">6.587054587998915e-4</span></td>
725+ </tr>
726+ </tbody>
727+ </table>
728+
729+ <span class="outliers">
730+ <p>Outlying measurements have severe
731+ (<span class="percent">0.9470035753933379</span>%)
732+ effect on estimated standard deviation.</p>
733+ </span>
734+<h2><a name="b8">Matrix vs List - `select`/Distribution `select` - 100+100 / 100x100/Matrix Distribution - Selective version</a></h2>
735+ <table width="100%">
736+ <tbody>
737+ <tr>
738+ <td><div id="kde8" class="kdechart"
739+ style="width:450px;height:278px;"></div></td>
740+ <td><div id="time8" class="timechart"
741+ style="width:450px;height:278px;"></div></td>
742+<!--
743+ <td><div id="cycle8" class="cyclechart"
744+ style="width:300px;height:278px;"></div></td>
745+-->
746+ </tr>
747+ </tbody>
748+ </table>
749+
750+ <table>
751+ <thead class="analysis">
752+ <th></th>
753+ <th class="cibound"
754+ title="0.95 confidence level">lower bound</th>
755+ <th>estimate</th>
756+ <th class="cibound"
757+ title="0.95 confidence level">upper bound</th>
758+ </thead>
759+ <tbody>
760+ <tr>
761+ <td>OLS regression</td>
762+ <td><span class="confinterval olstimelb8">xxx</span></td>
763+ <td><span class="olstimept8">xxx</span></td>
764+ <td><span class="confinterval olstimeub8">xxx</span></td>
765+ </tr>
766+ <tr>
767+ <td>R&#xb2; goodness-of-fit</td>
768+ <td><span class="confinterval olsr2lb8">xxx</span></td>
769+ <td><span class="olsr2pt8">xxx</span></td>
770+ <td><span class="confinterval olsr2ub8">xxx</span></td>
771+ </tr>
772+ <tr>
773+ <td>Mean execution time</td>
774+ <td><span class="confinterval citime">8.252875148785076e-4</span></td>
775+ <td><span class="time">9.038536710022285e-4</span></td>
776+ <td><span class="confinterval citime">1.0137042058789136e-3</span></td>
777+ </tr>
778+ <tr>
779+ <td>Standard deviation</td>
780+ <td><span class="confinterval citime">2.3352589892872938e-4</span></td>
781+ <td><span class="time">3.1773226135504875e-4</span></td>
782+ <td><span class="confinterval citime">4.273324974311236e-4</span></td>
783+ </tr>
784+ </tbody>
785+ </table>
786+
787+ <span class="outliers">
788+ <p>Outlying measurements have severe
789+ (<span class="percent">0.984823670419889</span>%)
790+ effect on estimated standard deviation.</p>
791+ </span>
792+<h2><a name="b9">Matrix vs List - `select`/Matrix `select` - 100x(100+100) / 100x100/Applicative version</a></h2>
793+ <table width="100%">
794+ <tbody>
795+ <tr>
796+ <td><div id="kde9" class="kdechart"
797+ style="width:450px;height:278px;"></div></td>
798+ <td><div id="time9" class="timechart"
799+ style="width:450px;height:278px;"></div></td>
800+<!--
801+ <td><div id="cycle9" class="cyclechart"
802+ style="width:300px;height:278px;"></div></td>
803+-->
804+ </tr>
805+ </tbody>
806+ </table>
807+
808+ <table>
809+ <thead class="analysis">
810+ <th></th>
811+ <th class="cibound"
812+ title="0.95 confidence level">lower bound</th>
813+ <th>estimate</th>
814+ <th class="cibound"
815+ title="0.95 confidence level">upper bound</th>
816+ </thead>
817+ <tbody>
818+ <tr>
819+ <td>OLS regression</td>
820+ <td><span class="confinterval olstimelb9">xxx</span></td>
821+ <td><span class="olstimept9">xxx</span></td>
822+ <td><span class="confinterval olstimeub9">xxx</span></td>
823+ </tr>
824+ <tr>
825+ <td>R&#xb2; goodness-of-fit</td>
826+ <td><span class="confinterval olsr2lb9">xxx</span></td>
827+ <td><span class="olsr2pt9">xxx</span></td>
828+ <td><span class="confinterval olsr2ub9">xxx</span></td>
829+ </tr>
830+ <tr>
831+ <td>Mean execution time</td>
832+ <td><span class="confinterval citime">0.20685697058300623</span></td>
833+ <td><span class="time">0.20792234497182815</span></td>
834+ <td><span class="confinterval citime">0.20898771936065005</span></td>
835+ </tr>
836+ <tr>
837+ <td>Standard deviation</td>
838+ <td><span class="confinterval citime">1.11631780898578e-3</span></td>
839+ <td><span class="time">1.5104002558460128e-3</span></td>
840+ <td><span class="confinterval citime">1.827809373068682e-3</span></td>
841+ </tr>
842+ </tbody>
843+ </table>
844+
845+ <span class="outliers">
846+ <p>Outlying measurements have moderate
847+ (<span class="percent">0.1388888888888886</span>%)
848+ effect on estimated standard deviation.</p>
849+ </span>
850+<h2><a name="b10">Matrix vs List - `select`/Matrix `select` - 100x(100+100) / 100x100/Selective version</a></h2>
851+ <table width="100%">
852+ <tbody>
853+ <tr>
854+ <td><div id="kde10" class="kdechart"
855+ style="width:450px;height:278px;"></div></td>
856+ <td><div id="time10" class="timechart"
857+ style="width:450px;height:278px;"></div></td>
858+<!--
859+ <td><div id="cycle10" class="cyclechart"
860+ style="width:300px;height:278px;"></div></td>
861+-->
862+ </tr>
863+ </tbody>
864+ </table>
865+
866+ <table>
867+ <thead class="analysis">
868+ <th></th>
869+ <th class="cibound"
870+ title="0.95 confidence level">lower bound</th>
871+ <th>estimate</th>
872+ <th class="cibound"
873+ title="0.95 confidence level">upper bound</th>
874+ </thead>
875+ <tbody>
876+ <tr>
877+ <td>OLS regression</td>
878+ <td><span class="confinterval olstimelb10">xxx</span></td>
879+ <td><span class="olstimept10">xxx</span></td>
880+ <td><span class="confinterval olstimeub10">xxx</span></td>
881+ </tr>
882+ <tr>
883+ <td>R&#xb2; goodness-of-fit</td>
884+ <td><span class="confinterval olsr2lb10">xxx</span></td>
885+ <td><span class="olsr2pt10">xxx</span></td>
886+ <td><span class="confinterval olsr2ub10">xxx</span></td>
887+ </tr>
888+ <tr>
889+ <td>Mean execution time</td>
890+ <td><span class="confinterval citime">0.1040023584088178</span></td>
891+ <td><span class="time">0.10482248682469514</span></td>
892+ <td><span class="confinterval citime">0.10534815795558282</span></td>
893+ </tr>
894+ <tr>
895+ <td>Standard deviation</td>
896+ <td><span class="confinterval citime">5.86339084666882e-4</span></td>
897+ <td><span class="time">1.080285904740125e-3</span></td>
898+ <td><span class="confinterval citime">1.5634852865472032e-3</span></td>
899+ </tr>
900+ </tbody>
901+ </table>
902+
903+ <span class="outliers">
904+ <p>Outlying measurements have slight
905+ (<span class="percent">9.87654320987654e-2</span>%)
906+ effect on estimated standard deviation.</p>
907+ </span>
908+
909+ <h2><a name="grokularation">understanding this report</a></h2>
910+
911+ <p>In this report, each function benchmarked by criterion is assigned
912+ a section of its own. The charts in each section are active; if
913+ you hover your mouse over data points and annotations, you will see
914+ more details.</p>
915+
916+ <ul>
917+ <li>The chart on the left is a
918+ <a href="http://en.wikipedia.org/wiki/Kernel_density_estimation">kernel
919+ density estimate</a> (also known as a KDE) of time
920+ measurements. This graphs the probability of any given time
921+ measurement occurring. A spike indicates that a measurement of a
922+ particular time occurred; its height indicates how often that
923+ measurement was repeated.</li>
924+
925+ <li>The chart on the right is the raw data from which the kernel
926+ density estimate is built. The <i>x</i> axis indicates the
927+ number of loop iterations, while the <i>y</i> axis shows measured
928+ execution time for the given number of loop iterations. The
929+ line behind the values is the linear regression prediction of
930+ execution time for a given number of iterations. Ideally, all
931+ measurements will be on (or very near) this line.</li>
932+ </ul>
933+
934+ <p>Under the charts is a small table.
935+ The first two rows are the results of a linear regression run
936+ on the measurements displayed in the right-hand chart.</p>
937+
938+ <ul>
939+ <li><i>OLS regression</i> indicates the
940+ time estimated for a single loop iteration using an ordinary
941+ least-squares regression model. This number is more accurate
942+ than the <i>mean</i> estimate below it, as it more effectively
943+ eliminates measurement overhead and other constant factors.</li>
944+ <li><i>R&#xb2; goodness-of-fit</i> is a measure of how
945+ accurately the linear regression model fits the observed
946+ measurements. If the measurements are not too noisy, R&#xb2;
947+ should lie between 0.99 and 1, indicating an excellent fit. If
948+ the number is below 0.99, something is confounding the accuracy
949+ of the linear model.</li>
950+ <li><i>Mean execution time</i> and <i>standard deviation</i> are
951+ statistics calculated from execution time
952+ divided by number of iterations.</li>
953+ </ul>
954+
955+ <p>We use a statistical technique called
956+ the <a href="http://en.wikipedia.org/wiki/Bootstrapping_(statistics)">bootstrap</a>
957+ to provide confidence intervals on our estimates. The
958+ bootstrap-derived upper and lower bounds on estimates let you see
959+ how accurate we believe those estimates to be. (Hover the mouse
960+ over the table headers to see the confidence levels.)</p>
961+
962+ <p>A noisy benchmarking environment can cause some or many
963+ measurements to fall far from the mean. These outlying
964+ measurements can have a significant inflationary effect on the
965+ estimate of the standard deviation. We calculate and display an
966+ estimate of the extent to which the standard deviation has been
967+ inflated by outliers.</p>
968+
969+<script type="text/javascript">
970+$(function () {
971+ function mangulate(rpt) {
972+ var measured = function(key) {
973+ var idx = rpt.reportKeys.indexOf(key);
974+ return rpt.reportMeasured.map(function(r) { return r[idx]; });
975+ };
976+ var lowerBound = function(est) {
977+ return est.estPoint - est.estError.confIntLDX;
978+ };
979+ var upperBound = function(est) {
980+ return est.estPoint + est.estError.confIntUDX;
981+ };
982+ var number = rpt.reportNumber;
983+ var name = rpt.reportName;
984+ var mean = rpt.reportAnalysis.anMean.estPoint;
985+ var iters = measured("iters");
986+ var times = measured("time");
987+ var kdetimes = rpt.reportKDEs[0].kdeValues;
988+ var kdepdf = rpt.reportKDEs[0].kdePDF;
989+
990+ var meanSecs = mean;
991+ var units = $.timeUnits(mean);
992+ var rgrs = rpt.reportAnalysis.anRegress[0];
993+ var scale = units[0];
994+ var olsTime = rgrs.regCoeffs.iters;
995+ $(".olstimept" + number).text(function() {
996+ return $.renderTime(olsTime.estPoint);
997+ });
998+ $(".olstimelb" + number).text(function() {
999+ return $.renderTime(lowerBound(olsTime));
1000+ });
1001+ $(".olstimeub" + number).text(function() {
1002+ return $.renderTime(upperBound(olsTime));
1003+ });
1004+ $(".olsr2pt" + number).text(function() {
1005+ return rgrs.regRSquare.estPoint.toFixed(3);
1006+ });
1007+ $(".olsr2lb" + number).text(function() {
1008+ return lowerBound(rgrs.regRSquare).toFixed(3);
1009+ });
1010+ $(".olsr2ub" + number).text(function() {
1011+ return upperBound(rgrs.regRSquare).toFixed(3);
1012+ });
1013+ mean *= scale;
1014+ kdetimes = $.scaleBy(scale, kdetimes);
1015+ var kq = $("#kde" + number);
1016+ var k = $.plot(kq,
1017+ [{ label: name + " time densities",
1018+ data: $.zip(kdetimes, kdepdf),
1019+ }],
1020+ { xaxis: { tickFormatter: $.unitFormatter(scale) },
1021+ yaxis: { ticks: false },
1022+ grid: { borderColor: "#777",
1023+ hoverable: true, markings: [ { color: '#6fd3fb',
1024+ lineWidth: 1.5, xaxis: { from: mean, to: mean } } ] },
1025+ });
1026+ var o = k.pointOffset({ x: mean, y: 0});
1027+ kq.append('<div class="meanlegend" title="' + $.renderTime(meanSecs) +
1028+ '" style="position:absolute;left:' + (o.left + 4) +
1029+ 'px;bottom:139px;">mean</div>');
1030+ $.addTooltip("#kde" + number,
1031+ function(secs) { return $.renderTime(secs / scale); });
1032+ var timepairs = new Array(times.length);
1033+ var lastiter = iters[iters.length-1];
1034+ var olspairs = [[0,0], [lastiter, lastiter * scale * olsTime.estPoint]];
1035+ for (var i = 0; i < times.length; i++)
1036+ timepairs[i] = [iters[i],times[i]*scale];
1037+ iterFormatter = function() {
1038+ var denom = 0;
1039+ return function(iters) {
1040+ if (iters == 0)
1041+ return '';
1042+ if (denom > 0)
1043+ return (iters / denom).toFixed();
1044+ var power;
1045+ if (iters >= 1e9) {
1046+ denom = '1e9'; power = '&#x2079;';
1047+ }
1048+ if (iters >= 1e6) {
1049+ denom = '1e6'; power = '&#x2076;';
1050+ }
1051+ else if (iters >= 1e3) {
1052+ denom = '1e3'; power = '&#xb3;';
1053+ }
1054+ else denom = 1;
1055+ if (denom > 1) {
1056+ iters = (iters / denom).toFixed();
1057+ iters += '&times;10' + power + ' iters';
1058+ } else {
1059+ iters += ' iters';
1060+ }
1061+ return iters;
1062+ };
1063+ };
1064+ $.plot($("#time" + number),
1065+ [{ label: "regression", data: olspairs,
1066+ lines: { show: true } },
1067+ { label: name + " times", data: timepairs,
1068+ points: { show: true } }],
1069+ { grid: { borderColor: "#777", hoverable: true },
1070+ xaxis: { tickFormatter: iterFormatter() },
1071+ yaxis: { tickFormatter: $.unitFormatter(scale) } });
1072+ $.addTooltip("#time" + number,
1073+ function(iters,secs) {
1074+ return ($.renderTime(secs / scale) + ' / ' +
1075+ iters.toLocaleString() + ' iters');
1076+ });
1077+ if (0) {
1078+ var cyclepairs = new Array(cycles.length);
1079+ for (var i = 0; i < cycles.length; i++)
1080+ cyclepairs[i] = [cycles[i],i];
1081+ $.plot($("#cycle" + number),
1082+ [{ label: name + " cycles",
1083+ data: cyclepairs }],
1084+ { points: { show: true },
1085+ grid: { borderColor: "#777", hoverable: true },
1086+ xaxis: { tickFormatter:
1087+ function(cycles,axis) { return cycles + ' cycles'; }},
1088+ yaxis: { ticks: false },
1089+ });
1090+ $.addTooltip("#cycles" + number, function(x,y) { return x + ' cycles'; });
1091+ }
1092+ };
1093+ var reports = 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5.74022328738263,198.24867754298504,200.80476812394366,203.40745996135448,206.05564499683274,208.74814194616124,211.483696256168,214.26098025579506,217.07859350159382,219.93506331721932,222.8288455257753,225.75832537321077,228.72181864026476,231.71757293983077,234.743769195937,237.7985232999503,240.87988793897756,243.98585459089855,247.11435567988246,250.2632668857592,253.43040960009748,256.6135535214294,259.81041938161354,263.0186817949905,266.23597222162084,269.45988203563496,272.6879656894476,275.9177439644175,279.14670729834177,282.3723191800945,285.5920196016181,288.80322855748557,292.0033495822404,295.1897733158224,298.35988108746085,301.5110485086036,304.6406490656087,307.7460577031905,310.8246543898474,313.8738276568349,316.890978102553,319.87352185461174,322.8188939822101,325.72455185190194,328.5879784202445,331.40668545730455,334.1782166954518,336.9001508983749,339.5701048457337,342.18573622937765,344.7447464575498,347.2448833640071,349.68394381947684,352.0597762433634,354.3702830140909,356.6134227769339,358.78721264863213,360.8897303185112,362.9191160462313,364.8735745566676,366.7513768327729,368.5508618075936,370.27043795690435,371.90858479417835,373.46385426983807,374.9348720769198,376.3203388654396,377.61903136786486,378.82980343818366,379.95158700710596,380.9833929559502,381.9243119117425,382.7735149660073,383.53025431963823,384.1938638561284,384.763759645293,385.2394403794502,385.62048774383334,385.9065667227972,386.0974258431443,386.19289735565735]}],"reportKeys":["time","cpuTime","cycles","iters","allocated","numGcs","bytesCopied","mutatorWallSeconds","mutatorCpuSeconds","gcWallSeconds","gcCpuSeconds"],"reportNumber":10,"reportName":"Matrix vs List - `select`/Matrix `select` - 100x(100+100) / 100x100/Selective version","reportOutliers":{"highSevere":0,"highMild":0,"lowMild":1,"samplesSeen":9,"lowSevere":1},"reportMeasured":[[0.10571737300051609,0.11498943799999495,253082205,1,null,null,null,null,null,null,null],[0.20503710999764735,0.2236939250000063,490849758,2,null,null,null,null,null,null,null],[0.3154179129996919,0.3483325570000062,755093574,3,null,null,null,null,null,null,null],[0.4191888959976495,0.4561294789999977,1003516533,4,null,null,null,null,null,null,null],[0.5181254039998748,0.5682963769999958,1240363008,5,null,null,null,null,null,null,null],[0.6331990399994538,0.6939013260000024,1515841326,6,null,null,null,null,null,null,null],[0.7407626480053295,0.8104755810000057,1773341469,7,null,null,null,null,null,null,null],[0.8413410299981479,0.9205585280000008,2014122510,8,null,null,null,null,null,null,null],[0.9457272610015934,1.032770167999999,2264014116,9,null,null,null,null,null,null,null]]}];
1094+ reports.map(mangulate);
1095+
1096+ var benches = ["Matrix Composition/10x10/WHNF - 10x10","Matrix Composition/10x10/NF - 10x10","Matrix Composition/100x100/WHNF - 100x100","Matrix Composition/100x100/NF - 100x100","Matrix Composition/200x200/WHNF - 200x200","Matrix Composition/200x200/NF - 200x200","Matrix vs List - `select`/Distribution `select` - 100+100 / 100x100/List Distribution - Applicative version","Matrix vs List - `select`/Distribution `select` - 100+100 / 100x100/Matrix Distribution - Applicative version","Matrix vs List - `select`/Distribution `select` - 100+100 / 100x100/Matrix Distribution - Selective version","Matrix vs List - `select`/Matrix `select` - 100x(100+100) / 100x100/Applicative version","Matrix vs List - `select`/Matrix `select` - 100x(100+100) / 100x100/Selective version",];
1097+ var ylabels = [[-0,"<a href=\"#b0\">Matrix Composition/10x10/WHNF - 10x10</a>"],[-1,"<a href=\"#b1\">Matrix Composition/10x10/NF - 10x10</a>"],[-2,"<a href=\"#b2\">Matrix Composition/100x100/WHNF - 100x100</a>"],[-3,"<a href=\"#b3\">Matrix Composition/100x100/NF - 100x100</a>"],[-4,"<a href=\"#b4\">Matrix Composition/200x200/WHNF - 200x200</a>"],[-5,"<a href=\"#b5\">Matrix Composition/200x200/NF - 200x200</a>"],[-6,"<a href=\"#b6\">Matrix vs List - `select`/Distribution `select` - 100+100 / 100x100/List Distribution - Applicative version</a>"],[-7,"<a href=\"#b7\">Matrix vs List - `select`/Distribution `select` - 100+100 / 100x100/Matrix Distribution - Applicative version</a>"],[-8,"<a href=\"#b8\">Matrix vs List - `select`/Distribution `select` - 100+100 / 100x100/Matrix Distribution - Selective version</a>"],[-9,"<a href=\"#b9\">Matrix vs List - `select`/Matrix `select` - 100x(100+100) / 100x100/Applicative version</a>"],[-10,"<a href=\"#b10\">Matrix vs List - `select`/Matrix `select` - 100x(100+100) / 100x100/Selective version</a>"],];
1098+ var means = $.scaleTimes([1.2521282696584778e-4,1.532024430909428e-4,0.11922032795600032,0.11758616896428131,1.0404128327718354,1.1075485033964771,2.3478542657700623,1.7931655457283859e-3,9.038536710022285e-4,0.20792234497182815,0.10482248682469514,]);
1099+ var stddevs = [3.0000227210624054e-6,3.649213223188502e-5,9.77563027930971e-3,8.150134548496543e-3,6.182803786470918e-2,7.979551817654461e-3,1.2441745894453989e-2,5.021999918501304e-4,3.1773226135504875e-4,1.5104002558460128e-3,1.080285904740125e-3,];
1100+ stddevs = $.scaleBy(means[1], stddevs);
1101+ var xs = [];
1102+ var prev = null;
1103+ var colors = ["#edc240","#afd8f8","#cb4b4b","#4da74d","#9440ed"];
1104+ var max_time = 0;
1105+ for (var i = 0; i < means[0].length; i++) {
1106+ var name = benches[i].split(/\//);
1107+ name.pop();
1108+ name = name.join('/');
1109+ if (name != prev) {
1110+ var color = colors[xs.length / 2 % colors.length];
1111+ xs.push({ data: [[means[0][i], -i]], label: name, color: color,
1112+ bars: { show: true, horizontal: true, barWidth: 0.75,
1113+ align: "center" } });
1114+ xs.push({ data: [[means[0][i], -i, stddevs[i]]], color: color,
1115+ lines: { show: false },
1116+ points: { radius: 0, errorbars: "x",
1117+ xerr: { show: true, radius: 5,
1118+ lowerCap: "-", upperCap: "-" } } });
1119+ prev = name;
1120+ } else {
1121+ xs[xs.length - 2].data.push([means[0][i], -i]);
1122+ xs[xs.length - 1].data.push([means[0][i], -i, stddevs[i]]);
1123+ }
1124+ max_time = Math.max(max_time, means[0][i] + stddevs[i]);
1125+ }
1126+ var oq = $("#overview");
1127+ var max_x = max_time * 1.02;
1128+ o = $.plot(oq, xs, { grid: { borderColor: "#777", hoverable: true },
1129+ legend: { show: xs.length > 1 },
1130+ xaxis: { max: max_x, zoomRange: [false, max_x], panRange: [0, max_x] },
1131+ yaxis: { ticks: ylabels, tickColor: '#ffffff', zoomRange: false, panRange: false },
1132+ zoom: { interactive: true, amount: 1.05 },
1133+ pan: { interactive: true } });
1134+ if (benches.length > 3)
1135+ o.getPlaceholder().height(28*benches.length);
1136+ o.resize();
1137+ o.setupGrid();
1138+ o.draw();
1139+ $.addTooltip("#overview", function(x,y) { return $.renderTime(x / means[1]); });
1140+});
1141+$(document).ready(function () {
1142+ $(".time").text(function(_, text) {
1143+ return $.renderTime(text);
1144+ });
1145+ $(".citime").text(function(_, text) {
1146+ return $.renderTime(text);
1147+ });
1148+ $(".percent").text(function(_, text) {
1149+ return (text*100).toFixed(1);
1150+ });
1151+ });
1152+</script>
1153+
1154+ </div>
1155+ </div>
1156+ <div id="footer">
1157+ <div class="body">
1158+ <div class="footfirst">
1159+ <h2>colophon</h2>
1160+ <p>This report was created using the
1161+ <a href="http://hackage.haskell.org/package/criterion">criterion</a>
1162+ benchmark execution and performance analysis tool.</p>
1163+ <p>Criterion is developed and maintained
1164+ by <a href="http://www.serpentine.com/blog/">Bryan O'Sullivan</a>.</p>
1165+ </div>
1166+ </div>
1167+ </div>
1168+ </body>
1169+</html>
report-strict.pdfnew file

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src/LAoP/Dist.hs+2−4
@@ -39,8 +39,8 @@ module LAoP.Dist
39 -- * Constraint type synonyms
39 -- * Constraint type synonyms
40 Countable,
40 Countable,
41 CountableN,
41 CountableN,
42− CountableDimsN,
42+ CountableDimensionsN,
43− FLN,
43+ FromListsN,
44 Liftable,
44 Liftable,
45 TrivialP,
45 TrivialP,
46
46
@@ -53,8 +53,6 @@ module LAoP.Dist
53
53
54 -- * Selective equivalent functions
54 -- * Selective equivalent functions
55 selectD,
55 selectD,
56− branchD,
57− ifD,
58
56
59 -- * Monad equivalent functions
57 -- * Monad equivalent functions
60 returnD,
58 returnD,
src/LAoP/Dist/Internal.hs+28−67
@@ -16,8 +16,8 @@ module LAoP.Dist.Internal
16
16
17 Countable,
17 Countable,
18 CountableN,
18 CountableN,
19− CountableDimsN,
19+ CountableDimensionsN,
20− FLN,
20+ FromListsN,
21 Liftable,
21 Liftable,
22 TrivialP,
22 TrivialP,
23
23
@@ -25,8 +25,6 @@ module LAoP.Dist.Internal
25 unitD,
25 unitD,
26 multD,
26 multD,
27 selectD,
27 selectD,
28− branchD,
29− ifD,
30 returnD,
28 returnD,
31 bindD,
29 bindD,
32 (??),
30 (??),
@@ -43,15 +41,13 @@ module LAoP.Dist.Internal
43 )
41 )
44 where
42 where
45
43
46−import LAoP.Matrix.Type hiding (TrivialP, Countable, CountableDims, CountableN, CountableDimsN, Liftable, FLN)
44+import LAoP.Matrix.Type hiding (TrivialP, Countable, CountableDimensions, CountableN, CountableDimensionsN, Liftable, FromListsN)
47−import Prelude hiding (id, (.))
48import qualified LAoP.Matrix.Internal as I
45import qualified LAoP.Matrix.Internal as I
49import LAoP.Utils
46import LAoP.Utils
50import GHC.TypeLits
47import GHC.TypeLits
51import Data.Proxy
48import Data.Proxy
52import Data.List (sortBy)
49import Data.List (sortBy)
53import Control.DeepSeq
50import Control.DeepSeq
54−import Data.Bool
55
51
56-- | Type synonym for probability value
52-- | Type synonym for probability value
57type Prob = Double
53type Prob = Double
@@ -62,18 +58,18 @@ newtype Dist a = D (Matrix Prob () a)
62 deriving (Show, Num, Eq, Ord, NFData) via (Matrix Prob () a)
58 deriving (Show, Num, Eq, Ord, NFData) via (Matrix Prob () a)
63
59
64-- | Constraint type synonyms to keep the type signatures less convoluted
60-- | Constraint type synonyms to keep the type signatures less convoluted
65−type Countable a = KnownNat (I.Count a)
61+type Countable a = KnownNat (I.Count a)
66−type CountableN a = KnownNat (I.Count (I.Normalize a))
62+type CountableN a = KnownNat (I.Count (I.Normalize a))
67−type CountableDimsN a b = (CountableN a, CountableN b)
63+type CountableDimensionsN a b = (CountableN a, CountableN b)
68−type FLN a b = I.FL (I.Normalize a) (I.Normalize b)
64+type FromListsN a b = I.FromLists Prob (I.Normalize a) (I.Normalize b)
69−type Liftable a b = (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num Prob, Ord Prob)
65+type Liftable a b = (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num Prob, Ord Prob)
70−type TrivialP a b = Normalize (a, b) ~ Normalize (Normalize a, Normalize b)
66+type TrivialP a b = Normalize (a, b) ~ Normalize (Normalize a, Normalize b)
71
67
72-- | Functor instance
68-- | Functor instance
73fmapD ::
69fmapD ::
74 ( Liftable a b,
70 ( Liftable a b,
75− CountableDimsN a b,
71+ CountableDimensionsN a b,
76− FLN b a
72+ FromListsN b a
77 )
73 )
78 =>
74 =>
79 (a -> b) -> Dist a -> Dist b
75 (a -> b) -> Dist a -> Dist b
@@ -85,58 +81,23 @@ unitD = D (one 1)
85
81
86-- | Applicative/Monoidal instance 'mult' function
82-- | Applicative/Monoidal instance 'mult' function
87multD ::
83multD ::
88− ( CountableDimsN a b,
84+ ( CountableDimensionsN a b,
89 CountableN (a, b),
85 CountableN (a, b),
90− FLN (a, b) a,
86+ FromListsN (a, b) a,
91− FLN (a, b) b,
87+ FromListsN (a, b) b,
92 TrivialP a b
88 TrivialP a b
93 ) => Dist a -> Dist b -> Dist (a, b)
89 ) => Dist a -> Dist b -> Dist (a, b)
94−multD (D a) (D b) = D (kr a b)
90+multD (D a) (D b) = D (khatri a b)
95
91
96-- | Selective instance function
92-- | Selective instance function
97selectD ::
93selectD ::
98− ( FLN b b,
94+ ( FromListsN b b,
99 CountableN b
95 CountableN b
100 ) => Dist (Either a b) -> Matrix Prob a b -> Dist b
96 ) => Dist (Either a b) -> Matrix Prob a b -> Dist b
101selectD (D d) m = D (selectM d m)
97selectD (D d) m = D (selectM d m)
102
98
103−-- | Chooses which of the two given effectful
104−-- functions to apply to a given argument;
105−branchD ::
106− ( Num e,
107− CountableDimsN a b,
108− CountableDimsN c (Either b c),
109− FLN c b,
110− FLN a b,
111− FLN a a,
112− FLN b b,
113− FLN c c,
114− FLN b a,
115− FLN b c,
116− FLN (Either b c) b,
117− FLN (Either b c) c
118− )
119− => Dist (Either a b) -> Matrix Prob a c -> Matrix Prob b c -> Dist c
120−branchD x l r = f x `selectD` g l `selectD` r
121− where
122− f (D m) = D (fork (tr i1) (i1 `comp` tr i2) `comp` m)
123− g m = i2 `comp` m
124−
125−-- | Branch on a Boolean value, skipping unnecessary computations.
126−ifD ::
127− ( CountableDimsN a (Either () a),
128− FLN a a,
129− FLN a (),
130− FLN () a,
131− FLN (Either () a) a
132− )
133− => Dist Bool -> Dist a -> Dist a -> Dist a
134−ifD x (D t) (D e) = branchD x' t e
135− where
136− x' = bool (Right ()) (Left ()) `fmapD` x
137−
138-- | Monad instance 'return' function
99-- | Monad instance 'return' function
139−returnD :: forall a . (Enum a, FLN () a, Countable a) => a -> Dist a
100+returnD :: forall a . (Enum a, FromListsN () a, Countable a) => a -> Dist a
140returnD a = D (col l)
101returnD a = D (col l)
141 where
102 where
142 i = fromInteger $ natVal (Proxy :: Proxy (Count a))
103 i = fromInteger $ natVal (Proxy :: Proxy (Count a))
@@ -151,7 +112,7 @@ bindD (D d) m = D (m `comp` d)
151(??) ::
112(??) ::
152 ( Enum a,
113 ( Enum a,
153 Countable a,
114 Countable a,
154− FLN () a
115+ FromListsN () a
155 ) => (a -> Bool) -> Dist a -> Prob
116 ) => (a -> Bool) -> Dist a -> Prob
156(??) p d =
117(??) p d =
157 let l = toValues d
118 let l = toValues d
@@ -161,11 +122,11 @@ bindD (D d) m = D (m `comp` d)
161-- Distribution Construction
122-- Distribution Construction
162
123
163-- | Constructs a Bernoulli distribution
124-- | Constructs a Bernoulli distribution
164−choose :: (FLN () a) => Prob -> Dist a
125+choose :: (FromListsN () a) => Prob -> Dist a
165choose prob = D (col [prob, 1 - prob])
126choose prob = D (col [prob, 1 - prob])
166
127
167-- | Creates a distribution given a shape function
128-- | Creates a distribution given a shape function
168−shape :: (FLN () a) => (Prob -> Prob) -> [a] -> Dist a
129+shape :: (FromListsN () a) => (Prob -> Prob) -> [a] -> Dist a
169shape _ [] = error "Probability.shape: empty list"
130shape _ [] = error "Probability.shape: empty list"
170shape f xs =
131shape f xs =
171 let incr = 1 / fromIntegral (length xs - 1)
132 let incr = 1 / fromIntegral (length xs - 1)
@@ -173,23 +134,23 @@ shape f xs =
173 in fromFreqs (zip xs ps)
134 in fromFreqs (zip xs ps)
174
135
175-- | Constructs a Linear distribution
136-- | Constructs a Linear distribution
176−linear :: (FLN () a) => [a] -> Dist a
137+linear :: (FromListsN () a) => [a] -> Dist a
177linear = shape id
138linear = shape id
178
139
179-- | Constructs an Uniform distribution
140-- | Constructs an Uniform distribution
180−uniform :: (FLN () a) => [a] -> Dist a
141+uniform :: (FromListsN () a) => [a] -> Dist a
181uniform = shape (const 1)
142uniform = shape (const 1)
182
143
183-- | Constructs an Negative Exponential distribution
144-- | Constructs an Negative Exponential distribution
184−negExp :: (FLN () a) => [a] -> Dist a
145+negExp :: (FromListsN () a) => [a] -> Dist a
185negExp = shape (\x -> exp (-x))
146negExp = shape (\x -> exp (-x))
186
147
187-- | Constructs an Normal distribution
148-- | Constructs an Normal distribution
188−normal :: (FLN () a) => [a] -> Dist a
149+normal :: (FromListsN () a) => [a] -> Dist a
189normal = shape (normalCurve 0.5 0.5)
150normal = shape (normalCurve 0.5 0.5)
190
151
191-- | Transforms a 'Dist' into a list of pairs.
152-- | Transforms a 'Dist' into a list of pairs.
192−toValues :: forall a . (Enum a, Countable a, FLN () a) => Dist a -> [(a, Prob)]
153+toValues :: forall a . (Enum a, Countable a, FromListsN () a) => Dist a -> [(a, Prob)]
193toValues (D d) =
154toValues (D d) =
194 let rows = fromInteger (natVal (Proxy :: Proxy (Count a)))
155 let rows = fromInteger (natVal (Proxy :: Proxy (Count a)))
195 probs = toList d
156 probs = toList d
@@ -197,7 +158,7 @@ toValues (D d) =
197 in res
158 in res
198
159
199-- | Pretty a distribution
160-- | Pretty a distribution
200−prettyDist :: forall a. (Show a, Enum a, Countable a, FLN () a) => Dist a -> String
161+prettyDist :: forall a. (Show a, Enum a, Countable a, FromListsN () a) => Dist a -> String
201prettyDist d =
162prettyDist d =
202 let values = sortBy (\(a, p1) (b, p2) -> compare p2 p1) (toValues @a d)
163 let values = sortBy (\(a, p1) (b, p2) -> compare p2 p1) (toValues @a d)
203 w = maximum (map (length . show . fst) values)
164 w = maximum (map (length . show . fst) values)
@@ -209,12 +170,12 @@ prettyDist d =
209 showR n x = show x ++ " "
170 showR n x = show x ++ " "
210
171
211-- | Pretty Print a distribution
172-- | Pretty Print a distribution
212−prettyPrintDist :: forall a . (Show a, Enum a, Countable a, FLN () a) => Dist a -> IO ()
173+prettyPrintDist :: forall a . (Show a, Enum a, Countable a, FromListsN () a) => Dist a -> IO ()
213prettyPrintDist = putStrLn . prettyDist @a
174prettyPrintDist = putStrLn . prettyDist @a
214
175
215-- Auxiliary functions
176-- Auxiliary functions
216
177
217−fromFreqs :: (FLN () a) => [(a,Prob)] -> Dist a
178+fromFreqs :: (FromListsN () a) => [(a,Prob)] -> Dist a
218fromFreqs xs = D (col (map (\(x,p) -> p/q) xs))
179fromFreqs xs = D (col (map (\(x,p) -> p/q) xs))
219 where q = sum $ map snd xs
180 where q = sum $ map snd xs
220
181
src/LAoP/Matrix/Internal.hs+396−396
@@ -30,7 +30,7 @@
30-- motivation behind the library, the underlying theory, and implementation details.
30-- motivation behind the library, the underlying theory, and implementation details.
31--
31--
32-- This module offers many of the combinators mentioned in the work of
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--
34--
35-- This is an Internal module and it is no supposed to be imported.
35-- This is an Internal module and it is no supposed to be imported.
36--
36--
@@ -43,26 +43,17 @@ module LAoP.Matrix.Internal
43 --
43 --
44 -- There exists two type families that make it easier to write
44 -- There exists two type families that make it easier to write
45 -- matrix dimensions: 'FromNat' and 'Count'. This approach
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.
48
48
49 -- * Type safe matrix representation
49 -- * Type safe matrix representation
50 Matrix (..),
50 Matrix (..),
51
51
52− -- * Constraint type aliases
53− Countable,
54− CountableDims,
55− CountableN,
56− CountableDimsN,
57− FL,
58− FLN,
59− Liftable,
60− Trivial,
61−
62 -- * Primitives
52 -- * Primitives
53+ empty,
63 one,
54 one,
64− join,
55+ junc,
65− fork,
56+ split,
66
57
67 -- * Auxiliary type families
58 -- * Auxiliary type families
68 FromNat,
59 FromNat,
@@ -75,7 +66,6 @@ module LAoP.Matrix.Internal
75 toLists,
66 toLists,
76 toList,
67 toList,
77 matrixBuilder,
68 matrixBuilder,
78− matrixBuilder',
79 row,
69 row,
80 col,
70 col,
81 zeros,
71 zeros,
@@ -86,17 +76,11 @@ module LAoP.Matrix.Internal
86 -- * Misc
76 -- * Misc
87 -- ** Get dimensions
77 -- ** Get dimensions
88 columns,
78 columns,
89− columns',
90 rows,
79 rows,
91− rows',
92
80
93 -- ** Matrix Transposition
81 -- ** Matrix Transposition
94 tr,
82 tr,
95
83
96− -- ** Scalar multiplication/division of matrices
97− (.|),
98− (./),
99−
100 -- ** Selective operator
84 -- ** Selective operator
101 select,
85 select,
102 branch,
86 branch,
@@ -105,19 +89,16 @@ module LAoP.Matrix.Internal
105 cond,
89 cond,
106
90
107 -- ** Matrix "abiding"
91 -- ** Matrix "abiding"
108− abideJF,
92+ abideJS,
109− abideFJ,
93+ abideSJ,
110−
111− -- ** Zip matrices
112− zipWithM,
113
94
114 -- * Biproduct approach
95 -- * Biproduct approach
115− -- ** Fork
96+ -- ** Split
116 (===),
97 (===),
117 -- *** Projections
98 -- *** Projections
118 p1,
99 p1,
119 p2,
100 p2,
120− -- ** Join
101+ -- ** Junc
121 (|||),
102 (|||),
122 -- *** Injections
103 -- *** Injections
123 i1,
104 i1,
@@ -130,13 +111,12 @@ module LAoP.Matrix.Internal
130
111
131 -- | Note that given the restrictions imposed it is not possible to
112 -- | Note that given the restrictions imposed it is not possible to
132 -- implement the standard type classes present in standard Haskell.
113 -- implement the standard type classes present in standard Haskell.
133−
134 -- *** Matrix pairing projections
114 -- *** Matrix pairing projections
135− fstM,
115+ kp1,
136− sndM,
116+ kp2,
137
117
138 -- *** Matrix pairing
118 -- *** Matrix pairing
139− kr,
119+ khatri,
140
120
141 -- * Matrix composition and lifting
121 -- * Matrix composition and lifting
142
122
@@ -144,10 +124,10 @@ module LAoP.Matrix.Internal
144
124
145 -- | Note that given the restrictions imposed it is not possible to
125 -- | Note that given the restrictions imposed it is not possible to
146 -- implement the standard type classes present in standard Haskell.
126 -- implement the standard type classes present in standard Haskell.
147− iden,
127+ identity,
148 comp,
128 comp,
149− fromF',
150 fromF,
129 fromF,
130+ fromF',
151
131
152 -- * Matrix printing
132 -- * Matrix printing
153 pretty,
133 pretty,
@@ -174,22 +154,21 @@ import LAoP.Utils.Internal
174import Data.Bool
154import Data.Bool
175import Data.Kind
155import Data.Kind
176import Data.List
156import Data.List
177−import Data.Maybe
178import Data.Proxy
157import Data.Proxy
179−import Data.Typeable
180import Data.Void
158import Data.Void
181import GHC.TypeLits
159import GHC.TypeLits
182import Data.Type.Equality
160import Data.Type.Equality
183import GHC.Generics
161import GHC.Generics
184import Control.DeepSeq
162import Control.DeepSeq
163+import Control.Category
185−import Prelude hiding (id, (.))
164+import Prelude hiding ((.))
186−import qualified Prelude (id, (.))
187
165
188-- | LAoP (Linear Algebra of Programming) Inductive Matrix definition.
166-- | LAoP (Linear Algebra of Programming) Inductive Matrix definition.
189data Matrix e cols rows where
167data Matrix e cols rows where
168+ Empty :: Matrix e Void Void
190 One :: e -> Matrix e () ()
169 One :: e -> Matrix e () ()
191− Join :: Matrix e a rows -> Matrix e b rows -> Matrix e (Either a b) rows
170+ Junc :: Matrix e a rows -> Matrix e b rows -> Matrix e (Either a b) rows
192− Fork :: Matrix e cols a -> Matrix e cols b -> Matrix e cols (Either a b)
171+ Split :: Matrix e cols a -> Matrix e cols b -> Matrix e cols (Either a b)
193
172
194deriving instance (Show e) => Show (Matrix e cols rows)
173deriving instance (Show e) => Show (Matrix e cols rows)
195
174
@@ -216,95 +195,122 @@ type family Count (d :: Type) :: Nat where
216--
195--
217-- Thanks to Li-Yao Xia this type family is super fast.
196-- Thanks to Li-Yao Xia this type family is super fast.
218type family FromNat (n :: Nat) :: Type where
197type family FromNat (n :: Nat) :: Type where
198+ FromNat 0 = Void
219 FromNat 1 = ()
199 FromNat 1 = ()
220 FromNat n = FromNat' (Mod n 2 == 0) (FromNat (Div n 2))
200 FromNat n = FromNat' (Mod n 2 == 0) (FromNat (Div n 2))
221
201
222type family FromNat' (b :: Bool) (m :: Type) :: Type where
202type family FromNat' (b :: Bool) (m :: Type) :: Type where
223− FromNat' 'True m = Either m m
203+ FromNat' 'True m = Either m m
224 FromNat' 'False m = Either () (Either m m)
204 FromNat' 'False m = Either () (Either m m)
225
205
226-- | Type family that normalizes the representation of a given data
206-- | Type family that normalizes the representation of a given data
227-- structure
207-- structure
228type family Normalize (d :: Type) :: Type where
208type family Normalize (d :: Type) :: Type where
229− Normalize (Either a b) = Either (Normalize a) (Normalize b)
209+ Normalize (Either a b) = Either (Normalize a) (Normalize b)
230− Normalize d = FromNat (Count d)
210+ Normalize d = FromNat (Count d)
231
211
232-- | Constraint type synonyms to keep the type signatures less convoluted
212-- | Constraint type synonyms to keep the type signatures less convoluted
233type Countable a = KnownNat (Count a)
213type Countable a = KnownNat (Count a)
234type CountableN a = KnownNat (Count (Normalize a))
214type CountableN a = KnownNat (Count (Normalize a))
235−type CountableDims a b = (Countable a, Countable b)
215+type CountableDimensions a b = (Countable a, Countable b)
236−type CountableDimsN a b = (CountableN a, CountableN b)
216+type CountableDimensionsN a b = (CountableN a, CountableN b)
237−type FL a b = FromLists a b
238−type FLN a b = FromLists (Normalize a) (Normalize b)
217+type FromListsN e a b = FromLists e (Normalize a) (Normalize b)
239type Liftable e a b = (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num e, Ord e)
218type Liftable e a b = (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num e, Ord e)
240type Trivial a = FromNat (Count a) ~ a
219type Trivial a = FromNat (Count a) ~ a
241
220
242−-- | It is possible to implement a constrained version of the category type
221+-- | It isn't possible to implement the 'id' function so it's
243−-- class.
222+-- implementation is 'undefined'. However 'comp' can be and this partial
223+-- class implementation exists just to make the code more readable.
224+--
225+-- Please use 'identity' instead.
244instance (Num e) => Category (Matrix e) where
226instance (Num e) => Category (Matrix e) where
245− type Object (Matrix e) a = (FL a a, Countable a)
227+ id = undefined
246− id = iden
247− (.) = comp
228+ (.) = comp
248
229
249instance NFData e => NFData (Matrix e cols rows) where
230instance NFData e => NFData (Matrix e cols rows) where
231+ rnf Empty = ()
250− rnf (One e) = rnf e
232+ rnf (One e) = rnf e
251− rnf (Join a b) = rnf a `seq` rnf b
233+ rnf (Junc a b) = rnf a `seq` rnf b
252− rnf (Fork a b) = rnf a `seq` rnf b
234+ rnf (Split a b) = rnf a `seq` rnf b
253
235
254instance Eq e => Eq (Matrix e cols rows) where
236instance Eq e => Eq (Matrix e cols rows) where
237+ Empty == Empty = True
255− (One a) == (One b) = a == b
238+ (One a) == (One b) = a == b
256− (Join a b) == (Join c d) = a == c && b == d
239+ (Junc a b) == (Junc c d) = a == c && b == d
257− (Fork a b) == (Fork c d) = a == c && b == d
240+ (Split a b) == (Split c d) = a == c && b == d
258− x@(Fork _ _) == y@(Join _ _) = x == abideJF y
241+ x@(Split _ _) == y@(Junc _ _) = x == abideJS y
259− x@(Join _ _) == y@(Fork _ _) = abideJF x == y
242+ x@(Junc _ _) == y@(Split _ _) = abideJS x == y
260
243
261instance Num e => Num (Matrix e cols rows) where
244instance Num e => Num (Matrix e cols rows) where
262− a + b = zipWithM (+) a b
263−
264− a - b = zipWithM (-) a b
265−
266− a * b = zipWithM (*) a b
267
245
246+ Empty + Empty = Empty
247+ (One a) + (One b) = One (a + b)
248+ (Junc a b) + (Junc c d) = Junc (a + c) (b + d)
249+ (Split a b) + (Split c d) = Split (a + c) (b + d)
250+ x@(Split _ _) + y@(Junc _ _) = x + abideJS y
251+ x@(Junc _ _) + y@(Split _ _) = abideJS x + y
252+
253+ Empty - Empty = Empty
254+ (One a) - (One b) = One (a - b)
255+ (Junc a b) - (Junc c d) = Junc (a - c) (b - d)
256+ (Split a b) - (Split c d) = Split (a - c) (b - d)
257+ x@(Split _ _) - y@(Junc _ _) = x - abideJS y
258+ x@(Junc _ _) - y@(Split _ _) = abideJS x - y
259+
260+ Empty * Empty = Empty
261+ (One a) * (One b) = One (a * b)
262+ (Junc a b) * (Junc c d) = Junc (a * c) (b * d)
263+ (Split a b) * (Split c d) = Split (a * c) (b * d)
264+ x@(Split _ _) * y@(Junc _ _) = x * abideJS y
265+ x@(Junc _ _) * y@(Split _ _) = abideJS x * y
266+
267+ abs Empty = Empty
268− abs (One a) = One (abs a)
268+ abs (One a) = One (abs a)
269− abs (Join a b) = Join (abs a) (abs b)
269+ abs (Junc a b) = Junc (abs a) (abs b)
270− abs (Fork a b) = Fork (abs a) (abs b)
270+ abs (Split a b) = Split (abs a) (abs b)
271−
271+
272+ signum Empty = Empty
272− signum (One a) = One (signum a)
273+ signum (One a) = One (signum a)
273− signum (Join a b) = Join (signum a) (signum b)
274+ signum (Junc a b) = Junc (signum a) (signum b)
274− signum (Fork a b) = Fork (signum a) (signum b)
275+ signum (Split a b) = Split (signum a) (signum b)
275
276
276instance Ord e => Ord (Matrix e cols rows) where
277instance Ord e => Ord (Matrix e cols rows) where
278+ Empty <= Empty = True
277− (One a) <= (One b) = a <= b
279+ (One a) <= (One b) = a <= b
278− (Join a b) <= (Join c d) = (a <= c) && (b <= d)
280+ (Junc a b) <= (Junc c d) = (a <= c) && (b <= d)
279− (Fork a b) <= (Fork c d) = (a <= c) && (b <= d)
281+ (Split a b) <= (Split c d) = (a <= c) && (b <= d)
280− x@(Fork _ _) <= y@(Join _ _) = x <= abideJF y
282+ x@(Split _ _) <= y@(Junc _ _) = x <= abideJS y
281− x@(Join _ _) <= y@(Fork _ _) = abideJF x <= y
283+ x@(Junc _ _) <= y@(Split _ _) = abideJS x <= y
282
284
283-- Primitives
285-- Primitives
284
286
287+-- | Empty matrix constructor
288+empty :: Matrix e Void Void
289+empty = Empty
290+
285-- | Unit matrix constructor
291-- | Unit matrix constructor
286one :: e -> Matrix e () ()
292one :: e -> Matrix e () ()
287one = One
293one = One
288
294
289−-- | Matrix 'Join' constructor
295+-- | Matrix 'Junc' constructor
290−join :: Matrix e a rows -> Matrix e b rows -> Matrix e (Either a b) rows
296+junc :: Matrix e a rows -> Matrix e b rows -> Matrix e (Either a b) rows
291−join = Join
297+junc = Junc
292
298
293infixl 3 |||
299infixl 3 |||
294
300
295−-- | Matrix 'Join' constructor
301+-- | Matrix 'Junc' constructor
296(|||) :: Matrix e a rows -> Matrix e b rows -> Matrix e (Either a b) rows
302(|||) :: Matrix e a rows -> Matrix e b rows -> Matrix e (Either a b) rows
297−(|||) = Join
303+(|||) = Junc
298
304
299−-- | Matrix 'Fork' constructor
305+-- | Matrix 'Split' constructor
300−fork :: Matrix e cols a -> Matrix e cols b -> Matrix e cols (Either a b)
306+split :: Matrix e cols a -> Matrix e cols b -> Matrix e cols (Either a b)
301−fork = Fork
307+split = Split
302
308
303infixl 2 ===
309infixl 2 ===
304
310
305−-- | Matrix 'Fork' constructor
311+-- | Matrix 'Split' constructor
306(===) :: Matrix e cols a -> Matrix e cols b -> Matrix e cols (Either a b)
312(===) :: Matrix e cols a -> Matrix e cols b -> Matrix e cols (Either a b)
307−(===) = Fork
313+(===) = Split
308
314
309-- Construction
315-- Construction
310
316
@@ -312,101 +318,84 @@ infixl 2 ===
312--
318--
313-- Given that it is not possible to branch on types at the term level type
319-- Given that it is not possible to branch on types at the term level type
314-- classes are needed very much like an inductive definition but on types.
320-- classes are needed very much like an inductive definition but on types.
315−class FromLists cols rows where
321+class FromLists e cols rows where
316 -- | Build a matrix out of a list of list of elements. Throws a runtime
322 -- | Build a matrix out of a list of list of elements. Throws a runtime
317 -- error if the dimensions do not match.
323 -- error if the dimensions do not match.
318 fromLists :: [[e]] -> Matrix e cols rows
324 fromLists :: [[e]] -> Matrix e cols rows
319
325
320−instance FromLists () () where
326+instance FromLists e Void Void where
327+ fromLists [] = Empty
328+ fromLists _ = error "Wrong dimensions"
329+
330+instance {-# OVERLAPPING #-} FromLists e () () where
321 fromLists [[e]] = One e
331 fromLists [[e]] = One e
322 fromLists _ = error "Wrong dimensions"
332 fromLists _ = error "Wrong dimensions"
323
333
324−instance (FromLists cols ()) => FromLists (Either () cols) () where
334+instance {-# OVERLAPPING #-} (FromLists e cols ()) => FromLists e (Either () cols) () where
325− fromLists [h : t] = Join (One h) (fromLists [t])
335+ fromLists [h : t] = Junc (One h) (fromLists [t])
326 fromLists _ = error "Wrong dimensions"
336 fromLists _ = error "Wrong dimensions"
327
337
328−instance {-# OVERLAPPABLE #-}
329− (FromLists a (), FromLists b (), Countable a) => FromLists (Either a b) () where
338+instance {-# OVERLAPPABLE #-} (FromLists e a (), FromLists e b (), Countable a) => FromLists e (Either a b) () where
330− fromLists [l] =
339+ fromLists [l] =
331 let rowsA = fromInteger (natVal (Proxy :: Proxy (Count a)))
340 let rowsA = fromInteger (natVal (Proxy :: Proxy (Count a)))
332− in Join (fromLists [take rowsA l]) (fromLists [drop rowsA l])
341+ in Junc (fromLists [take rowsA l]) (fromLists [drop rowsA l])
333 fromLists _ = error "Wrong dimensions"
342 fromLists _ = error "Wrong dimensions"
334
343
335−instance (FromLists () rows) => FromLists () (Either () rows) where
344+instance {-# OVERLAPPING #-} (FromLists e () rows) => FromLists e () (Either () rows) where
336− fromLists ([h] : t) = Fork (One h) (fromLists t)
345+ fromLists ([h] : t) = Split (One h) (fromLists t)
337 fromLists _ = error "Wrong dimensions"
346 fromLists _ = error "Wrong dimensions"
338
347
339−instance {-# OVERLAPPABLE #-}
340− (FromLists () a, FromLists () b, Countable a) => FromLists () (Either a b) where
348+instance {-# OVERLAPPABLE #-} (FromLists e () a, FromLists e () b, Countable a) => FromLists e () (Either a b) where
341− fromLists l@([_] : _) =
349+ fromLists l@([_] : _) =
342 let rowsA = fromInteger (natVal (Proxy :: Proxy (Count a)))
350 let rowsA = fromInteger (natVal (Proxy :: Proxy (Count a)))
343− in Fork (fromLists (take rowsA l)) (fromLists (drop rowsA l))
351+ in Split (fromLists (take rowsA l)) (fromLists (drop rowsA l))
344 fromLists _ = error "Wrong dimensions"
352 fromLists _ = error "Wrong dimensions"
345
353
346−instance (FromLists (Either a b) c, FromLists (Either a b) d, Countable c)
354+instance {-# OVERLAPPABLE #-} (FromLists e (Either a b) c, FromLists e (Either a b) d, Countable c) => FromLists e (Either a b) (Either c d) where
347− => FromLists (Either a b) (Either c d) where
348 fromLists l@(h : t) =
355 fromLists l@(h : t) =
349 let lh = length h
356 let lh = length h
350 rowsC = fromInteger (natVal (Proxy :: Proxy (Count c)))
357 rowsC = fromInteger (natVal (Proxy :: Proxy (Count c)))
351− condition = all ((== lh) . length) t
358+ condition = all (== lh) (map length t)
352 in if lh > 0 && condition
359 in if lh > 0 && condition
353− then Fork (fromLists (take rowsC l)) (fromLists (drop rowsC l))
360+ then Split (fromLists (take rowsC l)) (fromLists (drop rowsC l))
354 else error "Not all rows have the same length"
361 else error "Not all rows have the same length"
355
362
356-- | Matrix builder function. Constructs a matrix provided with
363-- | Matrix builder function. Constructs a matrix provided with
357−-- a construction function that operates with indices.
364+-- a construction function.
358−matrixBuilder' ::
365+matrixBuilder ::
359 forall e cols rows.
366 forall e cols rows.
360− ( FL cols rows,
367+ ( FromLists e cols rows,
361− CountableDims cols rows
368+ CountableDimensions cols rows
369+ ) =>
370+ ((Int, Int) -> e) ->
362− ) => ((Int, Int) -> e) -> Matrix e cols rows
371+ Matrix e cols rows
363−matrixBuilder' f =
372+matrixBuilder f =
364 let c = fromInteger $ natVal (Proxy :: Proxy (Count cols))
373 let c = fromInteger $ natVal (Proxy :: Proxy (Count cols))
365 r = fromInteger $ natVal (Proxy :: Proxy (Count rows))
374 r = fromInteger $ natVal (Proxy :: Proxy (Count rows))
366 positions = [(a, b) | a <- [0 .. (r - 1)], b <- [0 .. (c - 1)]]
375 positions = [(a, b) | a <- [0 .. (r - 1)], b <- [0 .. (c - 1)]]
367 in fromLists . map (map f) . groupBy (\(x, _) (w, _) -> x == w) $ positions
376 in fromLists . map (map f) . groupBy (\(x, _) (w, _) -> x == w) $ positions
368
377
369−-- | Matrix builder function. Constructs a matrix provided with
370−-- a construction function that operates with arbitrary types.
371−matrixBuilder ::
372− forall e a b.
373− ( FLN a b,
374− Enum a,
375− Enum b,
376− Bounded a,
377− Bounded b,
378− Eq a,
379− Countable b
380− ) => ((a, b) -> e) -> Matrix e (Normalize a) (Normalize b)
381−matrixBuilder f =
382− let r = fromInteger $ natVal (Proxy :: Proxy (Count b))
383− positions = [(a, b) | a <- [minBound .. maxBound], b <- [minBound .. maxBound]]
384− in fromLists . map (map f) . transpose . buildList r $ positions
385− where
386− buildList _ [] = []
387− buildList r l = take r l : buildList r (drop r l)
388−
389-- | Constructs a column vector matrix
378-- | Constructs a column vector matrix
390−col :: (FL () rows) => [e] -> Matrix e () rows
379+col :: (FromLists e () rows) => [e] -> Matrix e () rows
391col = fromLists . map (: [])
380col = fromLists . map (: [])
392
381
393-- | Constructs a row vector matrix
382-- | Constructs a row vector matrix
394−row :: (FL cols ()) => [e] -> Matrix e cols ()
383+row :: (FromLists e cols ()) => [e] -> Matrix e cols ()
395row = fromLists . (: [])
384row = fromLists . (: [])
396
385
397-- | Lifts functions to matrices with arbitrary dimensions.
386-- | Lifts functions to matrices with arbitrary dimensions.
398--
387--
399-- NOTE: Be careful to not ask for a matrix bigger than the cardinality of
388-- NOTE: Be careful to not ask for a matrix bigger than the cardinality of
400-- types @a@ or @b@ allows.
389-- types @a@ or @b@ allows.
401−fromF' ::
390+fromF ::
402 forall a b cols rows e.
391 forall a b cols rows e.
403 ( Liftable e a b,
392 ( Liftable e a b,
404− CountableDims cols rows,
393+ CountableDimensions cols rows,
405− FL rows cols
394+ FromLists e rows cols
406 ) =>
395 ) =>
407 (a -> b) ->
396 (a -> b) ->
408 Matrix e cols rows
397 Matrix e cols rows
409−fromF' f =
398+fromF f =
410 let minA = minBound @a
399 let minA = minBound @a
411 maxA = maxBound @a
400 maxA = maxBound @a
412 minB = minBound @b
401 minB = minBound @b
@@ -416,8 +405,8 @@ fromF' f =
416 elementsA = take ccols [minA .. maxA]
405 elementsA = take ccols [minA .. maxA]
417 elementsB = take rrows [minB .. maxB]
406 elementsB = take rrows [minB .. maxB]
418 combinations = (,) <$> elementsA <*> elementsB
407 combinations = (,) <$> elementsA <*> elementsB
419− combAp = map snd . sort . map (\(a, b) -> if f a == b
408+ combAp = map snd . sort . map (\(a, b) -> if f a == b
420− then ((fromEnum a, fromEnum b), 1)
409+ then ((fromEnum a, fromEnum b), 1)
421 else ((fromEnum a, fromEnum b), 0)) $ combinations
410 else ((fromEnum a, fromEnum b), 0)) $ combinations
422 mList = buildList combAp rrows
411 mList = buildList combAp rrows
423 in tr $ fromLists mList
412 in tr $ fromLists mList
@@ -427,23 +416,41 @@ fromF' f =
427
416
428-- | Lifts functions to matrices with dimensions matching @a@ and @b@
417-- | Lifts functions to matrices with dimensions matching @a@ and @b@
429-- cardinality's.
418-- cardinality's.
430−fromF ::
419+fromF' ::
431 forall a b e.
420 forall a b e.
432 ( Liftable e a b,
421 ( Liftable e a b,
433− CountableDimsN a b,
422+ CountableDimensionsN a b,
434− FLN b a
423+ FromListsN e b a
435 ) =>
424 ) =>
436 (a -> b) ->
425 (a -> b) ->
437 Matrix e (Normalize a) (Normalize b)
426 Matrix e (Normalize a) (Normalize b)
438−fromF = fromF'
427+fromF' f =
428+ let minA = minBound @a
429+ maxA = maxBound @a
430+ minB = minBound @b
431+ maxB = maxBound @b
432+ ccols = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize a)))
433+ rrows = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize b)))
434+ elementsA = take ccols [minA .. maxA]
435+ elementsB = take rrows [minB .. maxB]
436+ combinations = (,) <$> elementsA <*> elementsB
437+ combAp = map snd . sort . map (\(a, b) -> if f a == b
438+ then ((fromEnum a, fromEnum b), 1)
439+ else ((fromEnum a, fromEnum b), 0)) $ combinations
440+ mList = buildList combAp rrows
441+ in tr $ fromLists mList
442+ where
443+ buildList [] _ = []
444+ buildList l r = take r l : buildList (drop r l) r
439
445
440-- Conversion
446-- Conversion
441
447
442-- | Converts a matrix to a list of lists of elements.
448-- | Converts a matrix to a list of lists of elements.
443toLists :: Matrix e cols rows -> [[e]]
449toLists :: Matrix e cols rows -> [[e]]
450+toLists Empty = []
444toLists (One e) = [[e]]
451toLists (One e) = [[e]]
445−toLists (Fork l r) = toLists l ++ toLists r
452+toLists (Split l r) = toLists l ++ toLists r
446−toLists (Join l r) = zipWith (++) (toLists l) (toLists r)
453+toLists (Junc l r) = zipWith (++) (toLists l) (toLists r)
447
454
448-- | Converts a matrix to a list of elements.
455-- | Converts a matrix to a list of elements.
449toList :: Matrix e cols rows -> [e]
456toList :: Matrix e cols rows -> [e]
@@ -452,38 +459,38 @@ toList = concat . toLists
452-- Zeros Matrix
459-- Zeros Matrix
453
460
454-- | The zero matrix. A matrix wholly filled with zeros.
461-- | The zero matrix. A matrix wholly filled with zeros.
455−zeros :: (Num e, FL cols rows, CountableDims cols rows) => Matrix e cols rows
462+zeros :: (Num e, FromLists e cols rows, CountableDimensions cols rows) => Matrix e cols rows
456−zeros = matrixBuilder' (const 0)
463+zeros = matrixBuilder (const 0)
457
464
458-- Ones Matrix
465-- Ones Matrix
459
466
460-- | The ones matrix. A matrix wholly filled with ones.
467-- | The ones matrix. A matrix wholly filled with ones.
461--
468--
462-- Also known as T (Top) matrix.
469-- Also known as T (Top) matrix.
463−ones :: (Num e, FL cols rows, CountableDims cols rows) => Matrix e cols rows
470+ones :: (Num e, FromLists e cols rows, CountableDimensions cols rows) => Matrix e cols rows
464−ones = matrixBuilder' (const 1)
471+ones = matrixBuilder (const 1)
465
472
466-- Const Matrix
473-- Const Matrix
467
474
468-- | The constant matrix constructor. A matrix wholly filled with a given
475-- | The constant matrix constructor. A matrix wholly filled with a given
469-- value.
476-- value.
470−constant :: (Num e, FL cols rows, CountableDims cols rows) => e -> Matrix e cols rows
477+constant :: (Num e, FromLists e cols rows, CountableDimensions cols rows) => e -> Matrix e cols rows
471−constant e = matrixBuilder' (const e)
478+constant e = matrixBuilder (const e)
472
479
473-- Bang Matrix
480-- Bang Matrix
474
481
475-- | The T (Top) row vector matrix.
482-- | The T (Top) row vector matrix.
476−bang :: forall e cols. (Num e, Enum e, FL cols (), Countable cols) => Matrix e cols ()
483+bang :: forall e cols. (Num e, Enum e, FromLists e cols (), Countable cols) => Matrix e cols ()
477bang =
484bang =
478 let c = fromInteger $ natVal (Proxy :: Proxy (Count cols))
485 let c = fromInteger $ natVal (Proxy :: Proxy (Count cols))
479 in fromLists [take c [1, 1 ..]]
486 in fromLists [take c [1, 1 ..]]
480
487
481−-- iden Matrix
488+-- Identity Matrix
482
489
483−-- | iden matrix.
490+-- | Identity matrix.
484−iden :: forall e cols . (Num e, FL cols cols, Countable cols) => Matrix e cols cols
491+identity :: (Num e, FromLists e cols cols, Countable cols) => Matrix e cols cols
485−iden = matrixBuilder' (bool 0 1 . uncurry (==))
492+identity = matrixBuilder (bool 0 1 . uncurry (==))
486−{-# NOINLINE iden #-}
493+{-# NOINLINE identity #-}
487
494
488-- Matrix composition (MMM)
495-- Matrix composition (MMM)
489
496
@@ -492,90 +499,65 @@ iden = matrixBuilder' (bool 0 1 . uncurry (==))
492-- This definition takes advantage of divide-and-conquer and fusion laws
499-- This definition takes advantage of divide-and-conquer and fusion laws
493-- from LAoP.
500-- from LAoP.
494comp :: (Num e) => Matrix e cr rows -> Matrix e cols cr -> Matrix e cols rows
501comp :: (Num e) => Matrix e cr rows -> Matrix e cols cr -> Matrix e cols rows
502+comp Empty Empty = Empty
495−comp (One a) (One b) = One (a * b)
503+comp (One a) (One b) = One (a * b)
496−comp (Join a b) (Fork c d) = comp a c + comp b d -- Divide-and-conquer law
504+comp (Junc a b) (Split c d) = comp a c + comp b d -- Divide-and-conquer law
497−comp (Fork a b) c = Fork (comp a c) (comp b c) -- Fork fusion law
505+comp (Split a b) c = Split (comp a c) (comp b c) -- Split fusion law
498−comp c (Join a b) = Join (comp c a) (comp c b) -- Join fusion law
506+comp c (Junc a b) = Junc (comp c a) (comp c b) -- Junc fusion law
499{-# NOINLINE comp #-}
507{-# NOINLINE comp #-}
500−{-# RULES
508+{-# RULES
501− "comp/iden1" forall m. comp m iden = m ;
509+ "comp/identity1" forall m. comp m identity = m ;
502− "comp/iden2" forall m. comp iden m = m
510+ "comp/identity2" forall m. comp identity m = m
503#-}
511#-}
504
512
505−-- Scalar multiplication of matrices
506−
507−infixl 7 .|
508−-- | Scalar multiplication of matrices.
509−(.|) :: Num e => e -> Matrix e cols rows -> Matrix e cols rows
510−(.|) e (One a) = One (e * a)
511−(.|) e (Join a b) = Join (e .| a) (e .| b)
512−(.|) e (Fork a b) = Fork (e .| a) (e .| b)
513−
514−-- Scalar division of matrices
515−
516−infixl 7 ./
517−-- | Scalar multiplication of matrices.
518−(./) :: Fractional e => Matrix e cols rows -> e -> Matrix e cols rows
519−(./) (One a) e = One (a / e)
520−(./) (Join a b) e = Join (a ./ e) (b ./ e)
521−(./) (Fork a b) e = Fork (a ./ e) (b ./ e)
522−
523-- Projections
513-- Projections
524
514
525-- | Biproduct first component projection
515-- | Biproduct first component projection
526−p1 :: (Num e, CountableDims n m, FL n m, FL m m) => Matrix e (Either m n) m
516+p1 :: forall e m n. (Num e, CountableDimensions n m, FromLists e n m, FromLists e m m) => Matrix e (Either m n) m
527−p1 = join id zeros
517+p1 =
518+ let iden = identity :: Matrix e m m
519+ zero = zeros :: Matrix e n m
520+ in junc iden zero
528
521
529-- | Biproduct second component projection
522-- | Biproduct second component projection
530−p2 :: (Num e, CountableDims n m, FL m n, FL n n) => Matrix e (Either m n) n
523+p2 :: forall e m n. (Num e, CountableDimensions n m, FromLists e m n, FromLists e n n) => Matrix e (Either m n) n
531−p2 = join zeros id
524+p2 =
525+ let iden = identity :: Matrix e n n
526+ zero = zeros :: Matrix e m n
527+ in junc zero iden
532
528
533-- Injections
529-- Injections
534
530
535-- | Biproduct first component injection
531-- | Biproduct first component injection
536−i1 :: (Num e, CountableDims n m, FL n m, FL m m) => Matrix e m (Either m n)
532+i1 :: (Num e, CountableDimensions n m, FromLists e n m, FromLists e m m) => Matrix e m (Either m n)
537i1 = tr p1
533i1 = tr p1
538
534
539-- | Biproduct second component injection
535-- | Biproduct second component injection
540−i2 :: (Num e, CountableDims n m, FL m n, FL n n) => Matrix e n (Either m n)
536+i2 :: (Num e, CountableDimensions n m, FromLists e m n, FromLists e n n) => Matrix e n (Either m n)
541i2 = tr p2
537i2 = tr p2
542
538
543-- Dimensions
539-- Dimensions
544
540
545-- | Obtain the number of rows.
541-- | Obtain the number of rows.
546--
542--
547−-- NOTE: The 'KnownNat' constraint is needed in order to obtain the
543+-- NOTE: The 'KnownNat' constaint is needed in order to obtain the
548−-- dimensions in constant time. For a version that doesn't require the
544+-- dimensions in constant time.
549−-- constraint see 'rows''.
545+--
546+-- TODO: A 'rows' function that does not need the 'KnownNat' constraint in
547+-- exchange for performance.
550rows :: forall e cols rows. (Countable rows) => Matrix e cols rows -> Int
548rows :: forall e cols rows. (Countable rows) => Matrix e cols rows -> Int
551rows _ = fromInteger $ natVal (Proxy :: Proxy (Count rows))
549rows _ = fromInteger $ natVal (Proxy :: Proxy (Count rows))
552
550
553−-- | Obtain the number of rows in an inefficient manner, but without any
554−-- constraints.
555−--
556−-- For a more efficient version see 'rows'.
557−rows' :: Matrix e cols rows -> Int
558−rows' (One _) = 1
559−rows' (Join lhs _) = rows' lhs
560−rows' (Fork top bottom) = rows' top + rows' bottom
561−
562-- | Obtain the number of columns.
551-- | Obtain the number of columns.
552+--
553+-- NOTE: The 'KnownNat' constaint is needed in order to obtain the
554+-- dimensions in constant time.
563--
555--
564−-- NOTE: The 'KnownNat' constraint is needed in order to obtain the
556+-- TODO: A 'columns' function that does not need the 'KnownNat' constraint in
565−-- dimensions in constant time. For a version that doesn't require the
557+-- exchange for performance.
566−-- constraint see 'columns''.
567columns :: forall e cols rows. (Countable cols) => Matrix e cols rows -> Int
558columns :: forall e cols rows. (Countable cols) => Matrix e cols rows -> Int
568columns _ = fromInteger $ natVal (Proxy :: Proxy (Count cols))
559columns _ = fromInteger $ natVal (Proxy :: Proxy (Count cols))
569
560
570−-- | Obtain the number of columns in an inefficient manner, but without any
571−-- constraints.
572−--
573−-- For a more efficient version see 'columns'.
574−columns' :: Matrix e cols rows -> Int
575−columns' (One _) = 1
576−columns' (Join lhs rhs) = columns' lhs + columns' rhs
577−columns' (Fork top _) = columns' top
578−
579-- Coproduct Bifunctor
561-- Coproduct Bifunctor
580
562
581infixl 5 -|-
563infixl 5 -|-
@@ -584,161 +566,164 @@ infixl 5 -|-
584(-|-) ::
566(-|-) ::
585 forall e n k m j.
567 forall e n k m j.
586 ( Num e,
568 ( Num e,
587− CountableDims j k,
569+ CountableDimensions j k,
588− FL k k,
570+ FromLists e k k,
589− FL j k,
571+ FromLists e j k,
590− FL k j,
572+ FromLists e k j,
591− FL j j
573+ FromLists e j j
592 ) =>
574 ) =>
593 Matrix e n k ->
575 Matrix e n k ->
594 Matrix e m j ->
576 Matrix e m j ->
595 Matrix e (Either n m) (Either k j)
577 Matrix e (Either n m) (Either k j)
596−(-|-) a b = Join (i1 . a) (i2 . b)
578+(-|-) a b = Junc (i1 . a) (i2 . b)
597
579
598-- Khatri Rao Product and projections
580-- Khatri Rao Product and projections
599
581
600-- | Khatri Rao product first component projection matrix.
582-- | Khatri Rao product first component projection matrix.
601−fstM ::
583+kp1 ::
602 forall e m k .
584 forall e m k .
603 ( Num e,
585 ( Num e,
604− CountableDims k m,
586+ CountableDimensions k m,
605− FL (Normalize (m, k)) m,
587+ FromLists e (Normalize (m, k)) m,
606 CountableN (m, k)
588 CountableN (m, k)
607 ) => Matrix e (Normalize (m, k)) m
589 ) => Matrix e (Normalize (m, k)) m
608−fstM = matrixBuilder' f
590+kp1 = matrixBuilder f
609 where
591 where
610 offset = fromInteger (natVal (Proxy :: Proxy (Count k)))
592 offset = fromInteger (natVal (Proxy :: Proxy (Count k)))
611 f (x, y)
593 f (x, y)
612 | y >= (x * offset) && y <= (x * offset + offset - 1) = 1
594 | y >= (x * offset) && y <= (x * offset + offset - 1) = 1
613− | otherwise = 0
595+ | otherwise = 0
614
596
615-- | Khatri Rao product second component projection matrix.
597-- | Khatri Rao product second component projection matrix.
616−sndM ::
598+kp2 ::
617 forall e m k .
599 forall e m k .
618 ( Num e,
600 ( Num e,
619− CountableDims k m,
601+ CountableDimensions k m,
620− FL (Normalize (m, k)) k,
602+ FromLists e (Normalize (m, k)) k,
621 CountableN (m, k)
603 CountableN (m, k)
622 ) => Matrix e (Normalize (m, k)) k
604 ) => Matrix e (Normalize (m, k)) k
623−sndM = matrixBuilder' f
605+kp2 = matrixBuilder f
624 where
606 where
625 offset = fromInteger (natVal (Proxy :: Proxy (Count k)))
607 offset = fromInteger (natVal (Proxy :: Proxy (Count k)))
626 f (x, y)
608 f (x, y)
627 | x == y || mod (y - x) offset == 0 = 1
609 | x == y || mod (y - x) offset == 0 = 1
628− | otherwise = 0
610+ | otherwise = 0
629
611
630-- | Khatri Rao Matrix product also known as matrix pairing.
612-- | Khatri Rao Matrix product also known as matrix pairing.
631--
613--
632-- NOTE: That this is not a true categorical product, see for instance:
614-- NOTE: That this is not a true categorical product, see for instance:
633−--
615+--
634-- @
616-- @
635−-- | fstM . kr a b == a
617+-- | kp1 . khatri a b == a
636−-- kr a b ==> |
618+-- khatri a b ==> |
637−-- | sndM . kr a b == b
619+-- | kp2 . khatri a b == b
638-- @
620-- @
639--
621--
640-- __Emphasis__ on the implication symbol.
622-- __Emphasis__ on the implication symbol.
641−kr ::
623+khatri ::
642− forall e cols a b.
624+ forall e cols a b.
643 ( Num e,
625 ( Num e,
644− CountableDims a b,
626+ CountableDimensions a b,
645 CountableN (a, b),
627 CountableN (a, b),
646− FL (Normalize (a, b)) a,
628+ FromLists e (Normalize (a, b)) a,
647− FL (Normalize (a, b)) b
629+ FromLists e (Normalize (a, b)) b
648 ) => Matrix e cols a -> Matrix e cols b -> Matrix e cols (Normalize (a, b))
630 ) => Matrix e cols a -> Matrix e cols b -> Matrix e cols (Normalize (a, b))
649−kr a b =
631+khatri a b =
650− let fstM' = fstM @e @a @b
632+ let kp1' = kp1 @e @a @b
651− sndM' = sndM @e @a @b
633+ kp2' = kp2 @e @a @b
652− in (tr fstM' . a) * (tr sndM' . b)
634+ in (tr kp1') . a * (tr kp2') . b
653
635
654-- Product Bifunctor (Kronecker)
636-- Product Bifunctor (Kronecker)
655
637
656infixl 4 ><
638infixl 4 ><
657
639
658-- | Matrix product functor also known as kronecker product
640-- | Matrix product functor also known as kronecker product
659−(><) ::
641+(><) ::
660− forall e m p n q.
642+ forall e m p n q.
661 ( Num e,
643 ( Num e,
662− CountableDims m n,
644+ CountableDimensions m n,
663− CountableDims p q,
645+ CountableDimensions p q,
664− CountableDimsN (m, n) (p, q),
646+ CountableDimensionsN (m, n) (p, q),
665− FL (Normalize (m, n)) m,
647+ FromLists e (Normalize (m, n)) m,
666− FL (Normalize (m, n)) n,
648+ FromLists e (Normalize (m, n)) n,
667− FL (Normalize (p, q)) p,
649+ FromLists e (Normalize (p, q)) p,
668− FL (Normalize (p, q)) q
650+ FromLists e (Normalize (p, q)) q
669− )
651+ )
670 => Matrix e m p -> Matrix e n q -> Matrix e (Normalize (m, n)) (Normalize (p, q))
652 => Matrix e m p -> Matrix e n q -> Matrix e (Normalize (m, n)) (Normalize (p, q))
671(><) a b =
653(><) a b =
672− let fstM' = fstM @e @m @n
654+ let kp1' = kp1 @e @m @n
673− sndM' = sndM @e @m @n
655+ kp2' = kp2 @e @m @n
674− in kr (a . fstM') (b . sndM')
656+ in khatri (a . kp1') (b . kp2')
675
657
676−-- Matrix abide Join Fork
658+-- Matrix abide Junc Split
677
659
678−-- | Matrix "abiding" following the 'Join'-'Fork' exchange law.
660+-- | Matrix "abiding" followin the 'Junc'-'Split' abide law.
679−--
661+--
680-- Law:
662-- Law:
681--
663--
682-- @
664-- @
683−-- 'Join' ('Fork' a c) ('Fork' b d) == 'Fork' ('Join' a b) ('Join' c d)
665+-- 'Junc' ('Split' a c) ('Split' b d) == 'Split' ('Junc' a b) ('Junc' c d)
684-- @
666-- @
685−abideJF :: Matrix e cols rows -> Matrix e cols rows
667+abideJS :: Matrix e cols rows -> Matrix e cols rows
686−abideJF (Join (Fork a c) (Fork b d)) = Fork (Join (abideJF a) (abideJF b)) (Join (abideJF c) (abideJF d)) -- Join-Fork abide law
668+abideJS (Junc (Split a c) (Split b d)) = Split (Junc (abideJS a) (abideJS b)) (Junc (abideJS c) (abideJS d)) -- Junc-Split abide law
669+abideJS Empty = Empty
687−abideJF (One e) = One e
670+abideJS (One e) = One e
688−abideJF (Join a b) = Join (abideJF a) (abideJF b)
671+abideJS (Junc a b) = Junc (abideJS a) (abideJS b)
689−abideJF (Fork a b) = Fork (abideJF a) (abideJF b)
672+abideJS (Split a b) = Split (abideJS a) (abideJS b)
690
673
691−-- Matrix abide Fork Join
674+-- Matrix abide Split Junc
692
675
693−-- | Matrix "abiding" followin the 'Fork'-'Join' abide law.
676+-- | Matrix "abiding" followin the 'Split'-'Junc' abide law.
694−--
677+--
695-- @
678-- @
696−-- 'Fork' ('Join' a b) ('Join' c d) == 'Join' ('Fork' a c) ('Fork' b d)
679+-- 'Split' ('Junc' a b) ('Junc' c d) == 'Junc' ('Split' a c) ('Split' b d)
697-- @
680-- @
698−abideFJ :: Matrix e cols rows -> Matrix e cols rows
681+abideSJ :: Matrix e cols rows -> Matrix e cols rows
699−abideFJ (Fork (Join a b) (Join c d)) = Join (Fork (abideFJ a) (abideFJ c)) (Fork (abideFJ b) (abideFJ d)) -- Fork-Join abide law
682+abideSJ (Split (Junc a b) (Junc c d)) = Junc (Split (abideSJ a) (abideSJ c)) (Split (abideSJ b) (abideSJ d)) -- Split-Junc abide law
683+abideSJ Empty = Empty
700−abideFJ (One e) = One e
684+abideSJ (One e) = One e
701−abideFJ (Join a b) = Join (abideFJ a) (abideFJ b)
685+abideSJ (Junc a b) = Junc (abideSJ a) (abideSJ b)
702−abideFJ (Fork a b) = Fork (abideFJ a) (abideFJ b)
686+abideSJ (Split a b) = Split (abideSJ a) (abideSJ b)
703
687
704-- Matrix transposition
688-- Matrix transposition
705
689
706-- | Matrix transposition.
690-- | Matrix transposition.
707tr :: Matrix e cols rows -> Matrix e rows cols
691tr :: Matrix e cols rows -> Matrix e rows cols
692+tr Empty = Empty
708−tr (One e) = One e
693+tr (One e) = One e
709−tr (Join a b) = Fork (tr a) (tr b)
694+tr (Junc a b) = Split (tr a) (tr b)
710−tr (Fork a b) = Join (tr a) (tr b)
695+tr (Split a b) = Junc (tr a) (tr b)
711
696
712-- Selective 'select' operator
697-- Selective 'select' operator
713
698
714-- | Selective functors 'select' operator equivalent inspired by the
699-- | Selective functors 'select' operator equivalent inspired by the
715-- ArrowMonad solution presented in the paper.
700-- ArrowMonad solution presented in the paper.
716−select :: (Num e, FL b b, Countable b) => Matrix e cols (Either a b) -> Matrix e a b -> Matrix e cols b
701+select :: (Num e, FromLists e b b, Countable b) => Matrix e cols (Either a b) -> Matrix e a b -> Matrix e cols b
717−select (Fork a b) y = y . a + b -- Divide-and-conquer law
702+select (Split a b) y = y . a + b -- Divide-and-conquer law
718−select (Join (Fork a c) (Fork b d)) y = join (y . a + c) (y . b + d) -- Pattern matching + DnC law
703+select (Junc (Split a c) (Split b d)) y = junc (y . a + c) (y . b + d) -- Pattern matching + DnC law
719−select m y = join y id . m
704+select m y = junc y identity . m
720
705
721−branch ::
706+branch ::
722 ( Num e,
707 ( Num e,
723− CountableDims a b,
708+ CountableDimensions a b,
724− CountableDims c (Either b c),
709+ CountableDimensions c (Either b c),
725− FL c b,
710+ FromLists e c b,
726− FL a b,
711+ FromLists e a b,
727− FL a a,
712+ FromLists e a a,
728− FL b b,
713+ FromLists e b b,
729− FL c c,
714+ FromLists e c c,
730− FL b a,
715+ FromLists e b a,
731− FL b c,
716+ FromLists e b c,
732− FL (Either b c) b,
717+ FromLists e (Either b c) b,
733− FL (Either b c) c
718+ FromLists e (Either b c) c
734 )
719 )
735 => Matrix e cols (Either a b) -> Matrix e a c -> Matrix e b c -> Matrix e cols c
720 => Matrix e cols (Either a b) -> Matrix e a c -> Matrix e b c -> Matrix e cols c
736branch x l r = f x `select` g l `select` r
721branch x l r = f x `select` g l `select` r
737 where
722 where
738− f :: (Num e, Countable a, CountableDims b c, FL a b, FL c b, FL b b, FL b a, FL a a)
723+ f :: (Num e, Countable a, CountableDimensions b c, FromLists e a b, FromLists e c b, FromLists e b b, FromLists e b a, FromLists e a a)
739 => Matrix e cols (Either a b) -> Matrix e cols (Either a (Either b c))
724 => Matrix e cols (Either a b) -> Matrix e cols (Either a (Either b c))
740− f m = fork (tr i1) (i1 . tr i2) . m
725+ f m = split (tr i1) (i1 . tr i2) . m
741− g :: (Num e, CountableDims b c, FL b c, FL c c) => Matrix e a c -> Matrix e a (Either b c)
726+ g :: (Num e, CountableDimensions b c, FromLists e b c, FromLists e c c) => Matrix e a c -> Matrix e a (Either b c)
742 g m = i2 . m
727 g m = i2 . m
743
728
744-- McCarthy's Conditional
729-- McCarthy's Conditional
@@ -747,9 +732,9 @@ branch x l r = f x `select` g l `select` r
747cond ::
732cond ::
748 ( Trivial cols,
733 ( Trivial cols,
749 Countable cols,
734 Countable cols,
750− FL () cols,
735+ FromLists e () cols,
751− FL cols (),
736+ FromLists e cols (),
752− FL cols cols,
737+ FromLists e cols cols,
753 Bounded a,
738 Bounded a,
754 Enum a,
739 Enum a,
755 Num e,
740 Num e,
@@ -757,14 +742,14 @@ cond ::
757 )
742 )
758 =>
743 =>
759 (a -> Bool) -> Matrix e cols rows -> Matrix e cols rows -> Matrix e cols rows
744 (a -> Bool) -> Matrix e cols rows -> Matrix e cols rows -> Matrix e cols rows
760−cond p f g = join f g . grd p
745+cond p f g = junc f g . grd p
761
746
762−grd ::
747+grd ::
763 ( Trivial q,
748 ( Trivial q,
764 Countable q,
749 Countable q,
765− FL () q,
750+ FromLists e () q,
766− FL q (),
751+ FromLists e q (),
767− FL q q,
752+ FromLists e q q,
768 Bounded a,
753 Bounded a,
769 Enum a,
754 Enum a,
770 Num e,
755 Num e,
@@ -772,86 +757,60 @@ grd ::
772 )
757 )
773 =>
758 =>
774 (a -> Bool) -> Matrix e q (Either q q)
759 (a -> Bool) -> Matrix e q (Either q q)
775−grd f = fork (corr f) (corr (not . f))
760+grd f = split (corr f) (corr (not . f))
776
761
777−corr ::
762+corr ::
778− forall e a q .
763+ forall e a q .
779 ( Trivial q,
764 ( Trivial q,
780 Countable q,
765 Countable q,
781− FL () q,
766+ FromLists e () q,
782− FL q (),
767+ FromLists e q (),
783− FL q q,
768+ FromLists e q q,
784 Liftable e a Bool
769 Liftable e a Bool
785− )
770+ )
786 => (a -> Bool) -> Matrix e q q
771 => (a -> Bool) -> Matrix e q q
787−corr p = let f = fromF' p :: Matrix e q ()
772+corr p = let f = fromF p :: Matrix e q ()
788− in kr f (id :: Matrix e q q)
773+ in khatri f (identity :: Matrix e q q)
789
774
790-- Pretty print
775-- Pretty print
791
776
792prettyAux :: Show e => [[e]] -> [[e]] -> String
777prettyAux :: Show e => [[e]] -> [[e]] -> String
793prettyAux [] _ = ""
778prettyAux [] _ = ""
794−prettyAux [[e]] m = "│ " ++ fill (show e) ++ " │\n"
779+prettyAux [[e]] m = "│ " ++ fill (show e) ++ " │\n"
795 where
780 where
796 v = fmap show m
781 v = fmap show m
797 widest = maximum $ fmap length v
782 widest = maximum $ fmap length v
798 fill str = replicate (widest - length str - 2) ' ' ++ str
783 fill str = replicate (widest - length str - 2) ' ' ++ str
799−prettyAux [h] m = "│ " ++ fill (unwords $ map show h) ++ " │\n"
784+prettyAux [h] m = "│ " ++ fill (unwords $ map show h) ++ " │\n"
800 where
785 where
801− v = fmap show m
786+ v = fmap show m
802− widest = maximum $ fmap length v
787+ widest = maximum $ fmap length v
803 fill str = replicate (widest - length str - 2) ' ' ++ str
788 fill str = replicate (widest - length str - 2) ' ' ++ str
804−prettyAux (h : t) l = "│ " ++ fill (unwords $ map show h) ++ " │\n" ++
789+prettyAux (h : t) l = "│ " ++ fill (unwords $ map show h) ++ " │\n" ++
805 prettyAux t l
790 prettyAux t l
806 where
791 where
807− v = fmap show l
792+ v = fmap show l
808− widest = maximum $ fmap length v
793+ widest = maximum $ fmap length v
809 fill str = replicate (widest - length str - 2) ' ' ++ str
794 fill str = replicate (widest - length str - 2) ' ' ++ str
810
795
811-- | Matrix pretty printer
796-- | Matrix pretty printer
812−pretty :: (CountableDims cols rows, Show e) => Matrix e cols rows -> String
797+pretty :: (Countable cols, Show e) => Matrix e cols rows -> String
813−pretty m = concat
814− [ "┌ ", unwords (replicate (columns m) blank), " ┐\n"
798+pretty m = "┌ " ++ unwords (replicate (columns m) blank) ++ " ┐\n" ++
815− , unlines
799+ prettyAux (toLists m) (toLists m) ++
816− [ "│ " ++ unwords (fmap (\j -> fill $ show $ getElem i j m) [1..columns m]) ++ " │" | i <- [1..rows m] ]
817− , "└ ", unwords (replicate (columns m) blank), " ┘"
800+ "└ " ++ unwords (replicate (columns m) blank) ++ " ┘"
818− ]
819− where
801+ where
820− strings = map show (toList m)
802+ v = fmap show (toList m)
821− widest = maximum $ map length strings
803+ widest = maximum $ fmap length v
822 fill str = replicate (widest - length str) ' ' ++ str
804 fill str = replicate (widest - length str) ' ' ++ str
823− blank = fill ""
805+ blank = fill ""
824− safeGet i j m
825− | i > rows m || j > columns m || i < 1 || j < 1 = Nothing
826− | otherwise = Just $ unsafeGet i j m (toList m)
827− unsafeGet i j m l = l !! encode (columns m) (i,j)
828− encode m (i,j) = (i-1)*m + j - 1
829− getElem i j m =
830− fromMaybe
831− (error $
832− "getElem: Trying to get the "
833− ++ show (i, j)
834− ++ " element from a "
835− ++ show (rows m) ++ "x" ++ show (columns m)
836− ++ " matrix."
837− )
838− (safeGet i j m)
839
806
840-- | Matrix pretty printer
807-- | Matrix pretty printer
841−prettyPrint :: (CountableDims cols rows, Show e) => Matrix e cols rows -> IO ()
808+prettyPrint :: (Countable cols, Show e) => Matrix e cols rows -> IO ()
842prettyPrint = putStrLn . pretty
809prettyPrint = putStrLn . pretty
843
810
844−-- | Zip two matrices with a given binary function
845−zipWithM :: (e -> f -> g) -> Matrix e cols rows -> Matrix f cols rows -> Matrix g cols rows
846−zipWithM f (One a) (One b) = One (f a b)
847−zipWithM f (Join a b) (Join c d) = Join (zipWithM f a c) (zipWithM f b d)
848−zipWithM f (Fork a b) (Fork c d) = Fork (zipWithM f a c) (zipWithM f b d)
849−zipWithM f x@(Fork _ _) y@(Join _ _) = zipWithM f x (abideJF y)
850−zipWithM f x@(Join _ _) y@(Fork _ _) = zipWithM f (abideJF x) y
851−
852-- Relational operators functions
811-- Relational operators functions
853
812
854−type Boolean = Natural 0 1
813+type Boolean = Natural 0 1
855type Relation a b = Matrix Boolean a b
814type Relation a b = Matrix Boolean a b
856
815
857-- | Helper conversion function
816-- | Helper conversion function
@@ -867,47 +826,54 @@ fromBool False = nat 0
867
826
868-- | Relational negation
827-- | Relational negation
869negateM :: Relation cols rows -> Relation cols rows
828negateM :: Relation cols rows -> Relation cols rows
829+negateM Empty = Empty
870−negateM (One (Nat p)) = One (Nat (negate p))
830+negateM (One (Nat 0)) = One (Nat 1)
831+negateM (One (Nat 1)) = One (Nat 0)
871−negateM (Join a b) = Join (negateM a) (negateM b)
832+negateM (Junc a b) = Junc (negateM a) (negateM b)
872−negateM (Fork a b) = Fork (negateM a) (negateM b)
833+negateM (Split a b) = Split (negateM a) (negateM b)
873
834
874-- | Relational addition
835-- | Relational addition
875orM :: Relation cols rows -> Relation cols rows -> Relation cols rows
836orM :: Relation cols rows -> Relation cols rows -> Relation cols rows
837+orM Empty Empty = Empty
876−orM (One a) (One b) = One (fromBool (toBool a || toBool b))
838+orM (One a) (One b) = One (fromBool (toBool a || toBool b))
877−orM (Join a b) (Join c d) = Join (orM a c) (orM b d)
839+orM (Junc a b) (Junc c d) = Junc (orM a c) (orM b d)
878−orM (Fork a b) (Fork c d) = Fork (orM a c) (orM b d)
840+orM (Split a b) (Split c d) = Split (orM a c) (orM b d)
879−orM x@(Fork _ _) y@(Join _ _) = orM x (abideJF y)
841+orM x@(Split _ _) y@(Junc _ _) = orM x (abideJS y)
880−orM x@(Join _ _) y@(Fork _ _) = orM (abideJF x) y
842+orM x@(Junc _ _) y@(Split _ _) = orM (abideJS x) y
881
843
882-- | Relational multiplication
844-- | Relational multiplication
883andM :: Relation cols rows -> Relation cols rows -> Relation cols rows
845andM :: Relation cols rows -> Relation cols rows -> Relation cols rows
846+andM Empty Empty = Empty
884−andM (One a) (One b) = One (fromBool (toBool a && toBool b))
847+andM (One a) (One b) = One (fromBool (toBool a && toBool b))
885−andM (Join a b) (Join c d) = Join (andM a c) (andM b d)
848+andM (Junc a b) (Junc c d) = Junc (andM a c) (andM b d)
886−andM (Fork a b) (Fork c d) = Fork (andM a c) (andM b d)
849+andM (Split a b) (Split c d) = Split (andM a c) (andM b d)
887−andM x@(Fork _ _) y@(Join _ _) = andM x (abideJF y)
850+andM x@(Split _ _) y@(Junc _ _) = andM x (abideJS y)
888−andM x@(Join _ _) y@(Fork _ _) = andM (abideJF x) y
851+andM x@(Junc _ _) y@(Split _ _) = andM (abideJS x) y
889
852
890-- | Relational subtraction
853-- | Relational subtraction
891subM :: Relation cols rows -> Relation cols rows -> Relation cols rows
854subM :: Relation cols rows -> Relation cols rows -> Relation cols rows
855+subM Empty Empty = Empty
892−subM (One a) (One b) = if a - b < nat 0 then One (nat 0) else One (a - b)
856+subM (One a) (One b) = if a - b < nat 0 then One (nat 0) else One (a - b)
893−subM (Join a b) (Join c d) = Join (subM a c) (subM b d)
857+subM (Junc a b) (Junc c d) = Junc (subM a c) (subM b d)
894−subM (Fork a b) (Fork c d) = Fork (subM a c) (subM b d)
858+subM (Split a b) (Split c d) = Split (subM a c) (subM b d)
895−subM x@(Fork _ _) y@(Join _ _) = subM x (abideJF y)
859+subM x@(Split _ _) y@(Junc _ _) = subM x (abideJS y)
896−subM x@(Join _ _) y@(Fork _ _) = subM (abideJF x) y
860+subM x@(Junc _ _) y@(Split _ _) = subM (abideJS x) y
897
861
898-- | Matrix relational composition.
862-- | Matrix relational composition.
899compRel :: Relation cr rows -> Relation cols cr -> Relation cols rows
863compRel :: Relation cr rows -> Relation cols cr -> Relation cols rows
864+compRel Empty Empty = Empty
900−compRel (One a) (One b) = One (fromBool (toBool a && toBool b))
865+compRel (One a) (One b) = One (fromBool (toBool a && toBool b))
901−compRel (Join a b) (Fork c d) = orM (compRel a c) (compRel b d) -- Divide-and-conquer law
866+compRel (Junc a b) (Split c d) = orM (compRel a c) (compRel b d) -- Divide-and-conquer law
902−compRel (Fork a b) c = Fork (compRel a c) (compRel b c) -- Fork fusion law
867+compRel (Split a b) c = Split (compRel a c) (compRel b c) -- Split fusion law
903−compRel c (Join a b) = Join (compRel c a) (compRel c b) -- Join fusion law
868+compRel c (Junc a b) = Junc (compRel c a) (compRel c b) -- Junc fusion law
904
869
905-- | Matrix relational right division
870-- | Matrix relational right division
906divR :: Relation b c -> Relation b a -> Relation a c
871divR :: Relation b c -> Relation b a -> Relation a c
872+divR Empty Empty = Empty
907divR (One a) (One b) = One (fromBool (not (toBool b) || toBool a)) -- b implies a
873divR (One a) (One b) = One (fromBool (not (toBool b) || toBool a)) -- b implies a
908−divR (Join a b) (Join c d) = andM (divR a c) (divR b d)
874+divR (Junc a b) (Junc c d) = andM (divR a c) (divR b d)
909−divR (Fork a b) c = Fork (divR a c) (divR b c)
875+divR (Split a b) c = Split (divR a c) (divR b c)
910−divR c (Fork a b) = Join (divR c a) (divR c b)
876+divR c (Split a b) = Junc (divR c a) (divR c b)
911
877
912-- | Matrix relational left division
878-- | Matrix relational left division
913divL :: Relation c b -> Relation a b -> Relation a c
879divL :: Relation c b -> Relation a b -> Relation a c
@@ -923,52 +889,86 @@ divS s r = divL r s `intersection` divR (tr r) (tr s)
923--
889--
924-- NOTE: Be careful to not ask for a relation bigger than the cardinality of
890-- NOTE: Be careful to not ask for a relation bigger than the cardinality of
925-- types @a@ or @b@ allows.
891-- types @a@ or @b@ allows.
926−fromFRel' ::
892+fromFRel ::
927 forall a b cols rows.
893 forall a b cols rows.
928 ( Liftable Boolean a b,
894 ( Liftable Boolean a b,
929− CountableDims cols rows,
895+ CountableDimensions cols rows,
930− FL rows cols
896+ FromLists Boolean rows cols
931 ) =>
897 ) =>
932 (a -> b) ->
898 (a -> b) ->
933 Relation cols rows
899 Relation cols rows
934−fromFRel' = fromF'
900+fromFRel f =
901+ let minA = minBound @a
902+ maxA = maxBound @a
903+ minB = minBound @b
904+ maxB = maxBound @b
905+ ccols = fromInteger $ natVal (Proxy :: Proxy (Count cols))
906+ rrows = fromInteger $ natVal (Proxy :: Proxy (Count rows))
907+ elementsA = take ccols [minA .. maxA]
908+ elementsB = take rrows [minB .. maxB]
909+ combinations = (,) <$> elementsA <*> elementsB
910+ combAp = map snd . sort . map (\(a, b) -> if f a == b
911+ then ((fromEnum a, fromEnum b), nat 1)
912+ else ((fromEnum a, fromEnum b), nat 0)) $ combinations
913+ mList = buildList combAp rrows
914+ in tr $ fromLists mList
915+ where
916+ buildList [] _ = []
917+ buildList l r = take r l : buildList (drop r l) r
935
918
936-- | Lifts functions to relations with dimensions matching @a@ and @b@
919-- | Lifts functions to relations with dimensions matching @a@ and @b@
937-- cardinality's.
920-- cardinality's.
938−fromFRel ::
921+fromFRel' ::
939 forall a b.
922 forall a b.
940 ( Liftable Boolean a b,
923 ( Liftable Boolean a b,
941− CountableDimsN a b,
924+ CountableDimensionsN a b,
942− FLN b a
925+ FromLists Boolean (Normalize b) (Normalize a)
943 ) =>
926 ) =>
944 (a -> b) ->
927 (a -> b) ->
945 Relation (Normalize a) (Normalize b)
928 Relation (Normalize a) (Normalize b)
946−fromFRel = fromFRel'
929+fromFRel' f =
930+ let minA = minBound @a
931+ maxA = maxBound @a
932+ minB = minBound @b
933+ maxB = maxBound @b
934+ ccols = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize a)))
935+ rrows = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize b)))
936+ elementsA = take ccols [minA .. maxA]
937+ elementsB = take rrows [minB .. maxB]
938+ combinations = (,) <$> elementsA <*> elementsB
939+ combAp = map snd . sort . map (\(a, b) -> if f a == b
940+ then ((fromEnum a, fromEnum b), nat 1)
941+ else ((fromEnum a, fromEnum b), nat 0)) $ combinations
942+ mList = buildList combAp rrows
943+ in tr $ fromLists mList
944+ where
945+ buildList [] _ = []
946+ buildList l r = take r l : buildList (drop r l) r
947
947
948-- | Lifts a relation function to a Boolean Matrix
948-- | Lifts a relation function to a Boolean Matrix
949−toRel ::
949+toRel ::
950 forall a b.
950 forall a b.
951 ( Bounded a,
951 ( Bounded a,
952 Bounded b,
952 Bounded b,
953 Enum a,
953 Enum a,
954 Enum b,
954 Enum b,
955 Eq b,
955 Eq b,
956− CountableDims a b,
956+ CountableDimensionsN a b,
957− FLN b a
957+ FromListsN Boolean b a
958− )
958+ )
959 => (a -> b -> Bool) -> Relation (Normalize a) (Normalize b)
959 => (a -> b -> Bool) -> Relation (Normalize a) (Normalize b)
960toRel f =
960toRel f =
961 let minA = minBound @a
961 let minA = minBound @a
962 maxA = maxBound @a
962 maxA = maxBound @a
963 minB = minBound @b
963 minB = minBound @b
964 maxB = maxBound @b
964 maxB = maxBound @b
965− ccols = fromInteger $ natVal (Proxy :: Proxy (Count a))
965+ ccols = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize a)))
966− rrows = fromInteger $ natVal (Proxy :: Proxy (Count b))
966+ rrows = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize b)))
967 elementsA = take ccols [minA .. maxA]
967 elementsA = take ccols [minA .. maxA]
968 elementsB = take rrows [minB .. maxB]
968 elementsB = take rrows [minB .. maxB]
969 combinations = (,) <$> elementsA <*> elementsB
969 combinations = (,) <$> elementsA <*> elementsB
970− combAp = map snd . sort . map (\(a, b) -> if uncurry f (a, b)
970+ combAp = map snd . sort . map (\(a, b) -> if uncurry f (a, b)
971− then ((fromEnum a, fromEnum b), nat 1)
971+ then ((fromEnum a, fromEnum b), nat 1)
972 else ((fromEnum a, fromEnum b), nat 0)) $ combinations
972 else ((fromEnum a, fromEnum b), nat 0)) $ combinations
973 mList = buildList combAp rrows
973 mList = buildList combAp rrows
974 in tr $ fromLists mList
974 in tr $ fromLists mList
src/LAoP/Matrix/Nat.hs+124−139
@@ -56,20 +56,21 @@ module LAoP.Matrix.Nat
56
56
57 -- * Constraint type synonyms
57 -- * Constraint type synonyms
58 Countable,
58 Countable,
59− CountableDims,
59+ CountableDimensions,
60 CountableN,
60 CountableN,
61 CountableNz,
61 CountableNz,
62− CountableDimsN,
62+ CountableDimensionsN,
63− FLN,
63+ FromListsN,
64− FLNz,
64+ FromListsNz,
65 Liftable,
65 Liftable,
66 TrivialE,
66 TrivialE,
67 TrivialP,
67 TrivialP,
68
68
69 -- * Primitives
69 -- * Primitives
70+ empty,
70 one,
71 one,
71− join,
72+ junc,
72− fork,
73+ split,
73
74
74 -- * Auxiliary type families
75 -- * Auxiliary type families
75 I.FromNat,
76 I.FromNat,
@@ -77,11 +78,11 @@ module LAoP.Matrix.Nat
77 I.Normalize,
78 I.Normalize,
78
79
79 -- * Matrix construction and conversion
80 -- * Matrix construction and conversion
80− I.FL,
81+ I.FromLists,
81 fromLists,
82 fromLists,
82 toLists,
83 toLists,
83 toList,
84 toList,
84− matrixBuilder',
85+ matrixBuilder,
85 row,
86 row,
86 col,
87 col,
87 zeros,
88 zeros,
@@ -97,10 +98,6 @@ module LAoP.Matrix.Nat
97 -- ** Matrix Transposition
98 -- ** Matrix Transposition
98 tr,
99 tr,
99
100
100− -- ** Scalar multiplication/division of matrices
101− (.|),
102− (./),
103−
104 -- ** Selective operator
101 -- ** Selective operator
105 select,
102 select,
106
103
@@ -108,19 +105,16 @@ module LAoP.Matrix.Nat
108 cond,
105 cond,
109
106
110 -- ** Matrix "abiding"
107 -- ** Matrix "abiding"
111− abideJF,
108+ abideJS,
112− abideFJ,
109+ abideSJ,
113−
114− -- ** Zip Matrices
115− zipWithM,
116
110
117 -- * Biproduct approach
111 -- * Biproduct approach
118− -- ** Fork
112+ -- ** Split
119 (===),
113 (===),
120 -- *** Projections
114 -- *** Projections
121 p1,
115 p1,
122 p2,
116 p2,
123− -- ** Join
117+ -- ** Junc
124 (|||),
118 (|||),
125 -- *** Injections
119 -- *** Injections
126 i1,
120 i1,
@@ -134,11 +128,11 @@ module LAoP.Matrix.Nat
134 -- | Note that given the restrictions imposed it is not possible to
128 -- | Note that given the restrictions imposed it is not possible to
135 -- implement the standard type classes present in standard Haskell.
129 -- implement the standard type classes present in standard Haskell.
136 -- *** Matrix pairing projections
130 -- *** Matrix pairing projections
137− fstM,
131+ kp1,
138− sndM,
132+ kp2,
139
133
140 -- *** Matrix pairing
134 -- *** Matrix pairing
141− kr,
135+ khatri,
142
136
143 -- * Matrix composition and lifting
137 -- * Matrix composition and lifting
144
138
@@ -146,10 +140,10 @@ module LAoP.Matrix.Nat
146
140
147 -- | Note that given the restrictions imposed it is not possible to
141 -- | Note that given the restrictions imposed it is not possible to
148 -- implement the standard type classes present in standard Haskell.
142 -- implement the standard type classes present in standard Haskell.
149− iden,
143+ identity,
150 comp,
144 comp,
151− fromF',
152 fromF,
145 fromF,
146+ fromF',
153
147
154 -- * Matrix printing
148 -- * Matrix printing
155 pretty,
149 pretty,
@@ -160,34 +154,47 @@ where
160import Data.Proxy
154import Data.Proxy
161import GHC.TypeLits
155import GHC.TypeLits
162import Control.DeepSeq
156import Control.DeepSeq
157+import qualified Control.Category as C
163import qualified LAoP.Matrix.Internal as I
158import qualified LAoP.Matrix.Internal as I
164
159
165newtype Matrix e (cols :: Nat) (rows :: Nat) = M (I.Matrix e (I.FromNat cols) (I.FromNat rows))
160newtype Matrix e (cols :: Nat) (rows :: Nat) = M (I.Matrix e (I.FromNat cols) (I.FromNat rows))
166 deriving (Show, Num, Eq, Ord, NFData) via (I.Matrix e (I.FromNat cols) (I.FromNat rows))
161 deriving (Show, Num, Eq, Ord, NFData) via (I.Matrix e (I.FromNat cols) (I.FromNat rows))
167
162
168-- | Constraint type synonyms to keep the type signatures less convoluted
163-- | Constraint type synonyms to keep the type signatures less convoluted
169−type Countable a = KnownNat (I.Count a)
164+type Countable a = KnownNat (I.Count a)
170−type CountableDims a b = (Countable a, Countable b)
165+type CountableDimensions a b = (Countable a, Countable b)
171−type CountableN a = KnownNat (I.Count (I.FromNat a))
166+type CountableN a = KnownNat (I.Count (I.FromNat a))
172−type CountableNz a = KnownNat (I.Count (I.Normalize a))
167+type CountableNz a = KnownNat (I.Count (I.Normalize a))
173−type CountableDimsN a b = (CountableN a, CountableN b)
168+type CountableDimensionsN a b = (CountableN a, CountableN b)
174−type FLN e a b = I.FL (I.FromNat a) (I.FromNat b)
169+type FromListsN e a b = I.FromLists e (I.FromNat a) (I.FromNat b)
175−type FLNz e a b = I.FL (I.Normalize a) (I.Normalize b)
170+type FromListsNz e a b = I.FromLists e (I.Normalize a) (I.Normalize b)
176−type Liftable e a b = (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num e, Ord e)
171+type Liftable e a b = (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num e, Ord e)
177−type TrivialE a b = I.FromNat (a + b) ~ Either (I.FromNat a) (I.FromNat b)
172+type TrivialE a b = I.FromNat (a + b) ~ Either (I.FromNat a) (I.FromNat b)
178−type TrivialP a b = I.FromNat (a * b) ~ I.FromNat (I.Count (I.FromNat a) * I.Count (I.FromNat b))
173+type TrivialP a b = I.FromNat (a * b) ~ I.FromNat (I.Count (I.FromNat a) * I.Count (I.FromNat b))
174+
175+-- | It isn't possible to implement the 'id' function so it's
176+-- implementation is 'undefined'. However 'comp' can be and this partial
177+-- class implementation exists just to make the code more readable.
178+--
179+-- Please use 'identity' instead.
180+instance (Num e) => C.Category (Matrix e) where
181+ id = undefined
182+ (.) = comp
179
183
180-- Primitives
184-- Primitives
181
185
186+empty :: Matrix e 0 0
187+empty = M I.Empty
188+
182one :: e -> Matrix e 1 1
189one :: e -> Matrix e 1 1
183one = M . I.One
190one = M . I.One
184
191
185−join ::
192+junc ::
186 (TrivialE a b) =>
193 (TrivialE a b) =>
187 Matrix e a rows ->
194 Matrix e a rows ->
188 Matrix e b rows ->
195 Matrix e b rows ->
189 Matrix e (a + b) rows
196 Matrix e (a + b) rows
190−join (M a) (M b) = M (I.Join a b)
197+junc (M a) (M b) = M (I.Junc a b)
191
198
192infixl 3 |||
199infixl 3 |||
193(|||) ::
200(|||) ::
@@ -195,14 +202,14 @@ infixl 3 |||
195 Matrix e a rows ->
202 Matrix e a rows ->
196 Matrix e b rows ->
203 Matrix e b rows ->
197 Matrix e (a + b) rows
204 Matrix e (a + b) rows
198−(|||) = join
205+(|||) = junc
199
206
200−fork ::
207+split ::
201 (TrivialE a b) =>
208 (TrivialE a b) =>
202 Matrix e cols a ->
209 Matrix e cols a ->
203 Matrix e cols b ->
210 Matrix e cols b ->
204 Matrix e cols (a + b)
211 Matrix e cols (a + b)
205−fork (M a) (M b) = M (I.Fork a b)
212+split (M a) (M b) = M (I.Split a b)
206
213
207infixl 2 ===
214infixl 2 ===
208(===) ::
215(===) ::
@@ -210,45 +217,43 @@ infixl 2 ===
210 Matrix e cols a ->
217 Matrix e cols a ->
211 Matrix e cols b ->
218 Matrix e cols b ->
212 Matrix e cols (a + b)
219 Matrix e cols (a + b)
213−(===) = fork
220+(===) = split
214
221
215-- Construction
222-- Construction
216
223
217−fromLists :: (FLN e cols rows) => [[e]] -> Matrix e cols rows
224+fromLists :: (FromListsN e cols rows) => [[e]] -> Matrix e cols rows
218fromLists = M . I.fromLists
225fromLists = M . I.fromLists
219
226
220−-- | Matrix builder function. Constructs a matrix provided with
221−-- a construction function that operates with indices.
222−matrixBuilder' ::
227+matrixBuilder ::
223− (FLN e cols rows, CountableN cols, CountableN rows)
228+ (FromListsN e cols rows, CountableN cols, CountableN rows)
224 => ((Int, Int) -> e) -> Matrix e cols rows
229 => ((Int, Int) -> e) -> Matrix e cols rows
225−matrixBuilder' = M . I.matrixBuilder'
230+matrixBuilder = M . I.matrixBuilder
226
231
227−col :: (I.FL () (I.FromNat rows)) => [e] -> Matrix e 1 rows
232+col :: (I.FromLists e () (I.FromNat rows)) => [e] -> Matrix e 1 rows
228col = M . I.col
233col = M . I.col
229
234
230−row :: (I.FL (I.FromNat cols) ()) => [e] -> Matrix e cols 1
235+row :: (I.FromLists e (I.FromNat cols) ()) => [e] -> Matrix e cols 1
231row = M . I.row
236row = M . I.row
232
237
233−fromF' ::
238+fromF ::
234 ( Liftable e a b,
239 ( Liftable e a b,
235 CountableN cols,
240 CountableN cols,
236 CountableN rows,
241 CountableN rows,
237− FLN e rows cols
242+ FromListsN e rows cols
238 ) =>
243 ) =>
239 (a -> b) ->
244 (a -> b) ->
240 Matrix e cols rows
245 Matrix e cols rows
241−fromF' = M . I.fromF'
246+fromF = M . I.fromF
242
247
243−fromF ::
248+fromF' ::
244 ( Liftable e a b,
249 ( Liftable e a b,
245 CountableNz a,
250 CountableNz a,
246 CountableNz b,
251 CountableNz b,
247− FLNz e b a
252+ FromListsNz e b a
248 ) =>
253 ) =>
249 (a -> b) ->
254 (a -> b) ->
250 Matrix e (I.Count a) (I.Count b)
255 Matrix e (I.Count a) (I.Count b)
251−fromF = undefined -- M . I.fromF
256+fromF' = undefined -- M . I.fromF'
252
257
253-- Conversion
258-- Conversion
254
259
@@ -261,21 +266,21 @@ toList (M m) = I.toList m
261-- Zeros Matrix
266-- Zeros Matrix
262
267
263zeros ::
268zeros ::
264− (Num e, FLN e cols rows, CountableN cols, CountableN rows) =>
269+ (Num e, FromListsN e cols rows, CountableN cols, CountableN rows) =>
265 Matrix e cols rows
270 Matrix e cols rows
266zeros = M I.zeros
271zeros = M I.zeros
267
272
268-- Ones Matrix
273-- Ones Matrix
269
274
270ones ::
275ones ::
271− (Num e, FLN e cols rows, CountableN cols, CountableN rows) =>
276+ (Num e, FromListsN e cols rows, CountableN cols, CountableN rows) =>
272 Matrix e cols rows
277 Matrix e cols rows
273ones = M I.ones
278ones = M I.ones
274
279
275-- Const Matrix
280-- Const Matrix
276
281
277constant ::
282constant ::
278− (Num e, FLN e cols rows, CountableN cols, CountableN rows) =>
283+ (Num e, FromListsN e cols rows, CountableN cols, CountableN rows) =>
279 e ->
284 e ->
280 Matrix e cols rows
285 Matrix e cols rows
281constant = M . I.constant
286constant = M . I.constant
@@ -284,41 +289,27 @@ constant = M . I.constant
284
289
285bang ::
290bang ::
286 forall e cols.
291 forall e cols.
287− (Num e, Enum e, I.FL (I.FromNat cols) (), CountableN cols) =>
292+ (Num e, Enum e, I.FromLists e (I.FromNat cols) (), CountableN cols) =>
288 Matrix e cols 1
293 Matrix e cols 1
289bang = M I.bang
294bang = M I.bang
290
295
291−-- iden Matrix
296+-- Identity Matrix
292
297
293−iden ::
298+identity ::
294− (Num e, FLN e cols cols, CountableN cols) =>
299+ (Num e, FromListsN e cols cols, CountableN cols) =>
295 Matrix e cols cols
300 Matrix e cols cols
296−iden = M I.iden
301+identity = M I.identity
297
302
298-- Matrix composition (MMM)
303-- Matrix composition (MMM)
299
304
300comp :: (Num e) => Matrix e cr rows -> Matrix e cols cr -> Matrix e cols rows
305comp :: (Num e) => Matrix e cr rows -> Matrix e cols cr -> Matrix e cols rows
301comp (M a) (M b) = M (I.comp a b)
306comp (M a) (M b) = M (I.comp a b)
302
307
303−-- Scalar multiplication of matrices
304−
305−infixl 7 .|
306−-- | Scalar multiplication of matrices.
307−(.|) :: Num e => e -> Matrix e cols rows -> Matrix e cols rows
308−(.|) e (M m) = M (e I..| m)
309−
310−-- Scalar division of matrices
311−
312−infixl 7 ./
313−-- | Scalar multiplication of matrices.
314−(./) :: Fractional e => Matrix e cols rows -> e -> Matrix e cols rows
315−(./) (M m) e = M (m I../ e)
316−
317p1 ::
308p1 ::
318 ( Num e,
309 ( Num e,
319− CountableDimsN n m,
310+ CountableDimensionsN n m,
320− FLN e n m,
311+ FromListsN e n m,
321− FLN e m m,
312+ FromListsN e m m,
322 TrivialE m n
313 TrivialE m n
323 ) =>
314 ) =>
324 Matrix e (m + n) m
315 Matrix e (m + n) m
@@ -326,9 +317,9 @@ p1 = M I.p1
326
317
327p2 ::
318p2 ::
328 ( Num e,
319 ( Num e,
329− CountableDimsN n m,
320+ CountableDimensionsN n m,
330− FLN e m n,
321+ FromListsN e m n,
331− FLN e n n,
322+ FromListsN e n n,
332 TrivialE m n
323 TrivialE m n
333 ) =>
324 ) =>
334 Matrix e (m + n) n
325 Matrix e (m + n) n
@@ -338,9 +329,9 @@ p2 = M I.p2
338
329
339i1 ::
330i1 ::
340 ( Num e,
331 ( Num e,
341− CountableDimsN n rows,
332+ CountableDimensionsN n rows,
342− FLN e n rows,
333+ FromListsN e n rows,
343− FLN e rows rows,
334+ FromListsN e rows rows,
344 TrivialE rows n
335 TrivialE rows n
345 ) =>
336 ) =>
346 Matrix e rows (rows + n)
337 Matrix e rows (rows + n)
@@ -348,9 +339,9 @@ i1 = tr p1
348
339
349i2 ::
340i2 ::
350 ( Num e,
341 ( Num e,
351− CountableDimsN rows m,
342+ CountableDimensionsN rows m,
352− FLN e m rows,
343+ FromListsN e m rows,
353− FLN e rows rows,
344+ FromListsN e rows rows,
354 TrivialE m rows
345 TrivialE m rows
355 ) =>
346 ) =>
356 Matrix e rows (m + rows)
347 Matrix e rows (m + rows)
@@ -364,16 +355,16 @@ rows (M m) = I.rows m
364columns :: (CountableN cols) => Matrix e cols rows -> Int
355columns :: (CountableN cols) => Matrix e cols rows -> Int
365columns (M m) = I.columns m
356columns (M m) = I.columns m
366
357
358+-- | Coproduct Bifunctor
367infixl 5 -|-
359infixl 5 -|-
368
360
369−-- | Coproduct Bifunctor (Direct sum)
370(-|-) ::
361(-|-) ::
371 ( Num e,
362 ( Num e,
372− CountableDimsN j k,
363+ CountableDimensionsN j k,
373− FLN e k k,
364+ FromListsN e k k,
374− FLN e j k,
365+ FromListsN e j k,
375− FLN e k j,
366+ FromListsN e k j,
376− FLN e j j,
367+ FromListsN e j j,
377 TrivialE n m,
368 TrivialE n m,
378 TrivialE k j
369 TrivialE k j
379 ) =>
370 ) =>
@@ -382,42 +373,40 @@ infixl 5 -|-
382 Matrix e (n + m) (k + j)
373 Matrix e (n + m) (k + j)
383(-|-) (M a) (M b) = M ((I.-|-) a b)
374(-|-) (M a) (M b) = M ((I.-|-) a b)
384
375
385−-- | Khatri Rao Product first projection
376+-- | Khatri Rao Product and projections
386−fstM ::
377+kp1 ::
387 forall e m k .
378 forall e m k .
388 ( Num e,
379 ( Num e,
389− CountableDimsN m k,
380+ CountableDimensionsN m k,
390 CountableN (m * k),
381 CountableN (m * k),
391− FLN e (m * k) m,
382+ FromListsN e (m * k) m,
392 TrivialP m k
383 TrivialP m k
393 ) => Matrix e (m * k) m
384 ) => Matrix e (m * k) m
394−fstM = M (I.fstM @e @(I.FromNat m) @(I.FromNat k))
385+kp1 = M (I.kp1 @e @(I.FromNat m) @(I.FromNat k))
395
386
396−-- | Khatri Rao Product second projection
387+kp2 ::
397−sndM ::
398 forall e m k.
388 forall e m k.
399 ( Num e,
389 ( Num e,
400− CountableDimsN k m,
390+ CountableDimensionsN k m,
401− FLN e (m * k) k,
391+ FromListsN e (m * k) k,
402 CountableN (m * k),
392 CountableN (m * k),
403 TrivialP m k
393 TrivialP m k
404 ) => Matrix e (m * k) k
394 ) => Matrix e (m * k) k
405−sndM = M (I.sndM @e @(I.FromNat m) @(I.FromNat k))
395+kp2 = M (I.kp2 @e @(I.FromNat m) @(I.FromNat k))
406
396
407−-- | Khatri Rao Product
397+khatri ::
408−kr ::
409 forall e cols a b.
398 forall e cols a b.
410 ( Num e,
399 ( Num e,
411− CountableDimsN a b,
400+ CountableDimensionsN a b,
412 CountableN (a * b),
401 CountableN (a * b),
413− FLN e (a * b) a,
402+ FromListsN e (a * b) a,
414− FLN e (a * b) b,
403+ FromListsN e (a * b) b,
415 TrivialP a b
404 TrivialP a b
416 ) => Matrix e cols a -> Matrix e cols b -> Matrix e cols (a * b)
405 ) => Matrix e cols a -> Matrix e cols b -> Matrix e cols (a * b)
417−kr a b =
406+khatri a b =
418− let fstM' = fstM @e @a @b
407+ let kp1' = kp1 @e @a @b
419− sndM' = sndM @e @a @b
408+ kp2' = kp2 @e @a @b
420− in comp (tr fstM') a * comp (tr sndM') b
409+ in comp (tr kp1') a * comp (tr kp2') b
421
410
422-- | Product Bifunctor (Kronecker)
411-- | Product Bifunctor (Kronecker)
423infixl 4 ><
412infixl 4 ><
@@ -425,28 +414,28 @@ infixl 4 ><
425(><) ::
414(><) ::
426 forall e m p n q.
415 forall e m p n q.
427 ( Num e,
416 ( Num e,
428− CountableDimsN m n,
417+ CountableDimensionsN m n,
429− CountableDimsN p q,
418+ CountableDimensionsN p q,
430− CountableDimsN (m * n) (p * q),
419+ CountableDimensionsN (m * n) (p * q),
431− FLN e (m * n) m,
420+ FromListsN e (m * n) m,
432− FLN e (m * n) n,
421+ FromListsN e (m * n) n,
433− FLN e (p * q) p,
422+ FromListsN e (p * q) p,
434− FLN e (p * q) q,
423+ FromListsN e (p * q) q,
435 TrivialP m n,
424 TrivialP m n,
436 TrivialP p q
425 TrivialP p q
437 ) => Matrix e m p -> Matrix e n q -> Matrix e (m * n) (p * q)
426 ) => Matrix e m p -> Matrix e n q -> Matrix e (m * n) (p * q)
438(><) a b =
427(><) a b =
439− let fstM' = fstM @e @m @n
428+ let kp1' = kp1 @e @m @n
440− sndM' = sndM @e @m @n
429+ kp2' = kp2 @e @m @n
441− in kr (comp a fstM') (comp b sndM')
430+ in khatri (comp a kp1') (comp b kp2')
442
431
443−-- | Matrix abide Join Fork
432+-- | Matrix abide Junc Split
444−abideJF :: Matrix e cols rows -> Matrix e cols rows
433+abideJS :: Matrix e cols rows -> Matrix e cols rows
445−abideJF (M m) = M (I.abideJF m)
434+abideJS (M m) = M (I.abideJS m)
446
435
447−-- | Matrix abide Fork Join
436+-- | Matrix abide Split Junc
448−abideFJ :: Matrix e cols rows -> Matrix e cols rows
437+abideSJ :: Matrix e cols rows -> Matrix e cols rows
449−abideFJ (M m) = M (I.abideFJ m)
438+abideSJ (M m) = M (I.abideSJ m)
450
439
451-- | Matrix transposition
440-- | Matrix transposition
452tr :: Matrix e cols rows -> Matrix e rows cols
441tr :: Matrix e cols rows -> Matrix e rows cols
@@ -455,7 +444,7 @@ tr (M m) = M (I.tr m)
455-- Selective 'select' operator
444-- Selective 'select' operator
456select ::
445select ::
457 ( Num e,
446 ( Num e,
458− FLN e rows1 rows1,
447+ FromListsN e rows1 rows1,
459 CountableN rows1,
448 CountableN rows1,
460 I.FromNat rows2 ~ I.FromNat rows1,
449 I.FromNat rows2 ~ I.FromNat rows1,
461 I.FromNat cols1 ~ I.FromNat cols2,
450 I.FromNat cols1 ~ I.FromNat cols2,
@@ -468,9 +457,9 @@ select (M m) (M y) = M (I.select m y)
468cond ::
457cond ::
469 ( I.FromNat (I.Count (I.FromNat cols)) ~ I.FromNat cols,
458 ( I.FromNat (I.Count (I.FromNat cols)) ~ I.FromNat cols,
470 CountableN cols,
459 CountableN cols,
471− I.FL () (I.FromNat cols),
460+ I.FromLists e () (I.FromNat cols),
472− I.FL (I.FromNat cols) (),
461+ I.FromLists e (I.FromNat cols) (),
473− FLN e cols cols,
462+ FromListsN e cols cols,
474 Liftable e a Bool
463 Liftable e a Bool
475 )
464 )
476 =>
465 =>
@@ -479,12 +468,8 @@ cond p (M a) (M b) = M (I.cond p a b)
479
468
480-- Pretty print
469-- Pretty print
481
470
482−pretty :: (CountableDimsN cols rows, Show e) => Matrix e cols rows -> String
471+pretty :: (CountableN cols, Show e) => Matrix e cols rows -> String
483pretty (M m) = I.pretty m
472pretty (M m) = I.pretty m
484
473
485−prettyPrint :: (CountableDimsN cols rows, Show e) => Matrix e cols rows -> IO ()
474+prettyPrint :: (CountableN cols, Show e) => Matrix e cols rows -> IO ()
486prettyPrint (M m) = I.prettyPrint m
475prettyPrint (M m) = I.prettyPrint m
487−
488−-- | Zip two matrices with a given binary function
489−zipWithM :: (e -> f -> g) -> Matrix e cols rows -> Matrix f cols rows -> Matrix g cols rows
490−zipWithM f (M a) (M b) = M (I.zipWithM f a b)
src/LAoP/Matrix/Type.hs+175−231
@@ -1,11 +1,11 @@
1{-# LANGUAGE ConstraintKinds #-}
1{-# LANGUAGE ConstraintKinds #-}
2−{-# LANGUAGE TypeFamilies #-}
3{-# LANGUAGE AllowAmbiguousTypes #-}
2{-# LANGUAGE AllowAmbiguousTypes #-}
4{-# LANGUAGE DataKinds #-}
3{-# LANGUAGE DataKinds #-}
5{-# LANGUAGE DerivingVia #-}
4{-# LANGUAGE DerivingVia #-}
6{-# LANGUAGE FlexibleContexts #-}
5{-# LANGUAGE FlexibleContexts #-}
7{-# LANGUAGE FlexibleInstances #-}
6{-# LANGUAGE FlexibleInstances #-}
8{-# LANGUAGE GADTs #-}
7{-# LANGUAGE GADTs #-}
8+{-# LANGUAGE KindSignatures #-}
9{-# LANGUAGE MultiParamTypeClasses #-}
9{-# LANGUAGE MultiParamTypeClasses #-}
10{-# LANGUAGE NoStarIsType #-}
10{-# LANGUAGE NoStarIsType #-}
11{-# LANGUAGE RankNTypes #-}
11{-# LANGUAGE RankNTypes #-}
@@ -58,10 +58,10 @@ module LAoP.Matrix.Type
58
58
59 -- * Constraint type aliases
59 -- * Constraint type aliases
60 Countable,
60 Countable,
61− CountableDims,
61+ CountableDimensions,
62 CountableN,
62 CountableN,
63− CountableDimsN,
63+ CountableDimensionsN,
64− FLN,
64+ FromListsN,
65 Liftable,
65 Liftable,
66 Trivial,
66 Trivial,
67 TrivialP,
67 TrivialP,
@@ -71,9 +71,10 @@ module LAoP.Matrix.Type
71 One,
71 One,
72
72
73 -- * Primitives
73 -- * Primitives
74+ empty,
74 one,
75 one,
75− join,
76+ junc,
76− fork,
77+ split,
77
78
78 -- * Auxiliary type families
79 -- * Auxiliary type families
79 I.FromNat,
80 I.FromNat,
@@ -85,7 +86,6 @@ module LAoP.Matrix.Type
85 fromLists,
86 fromLists,
86 toLists,
87 toLists,
87 toList,
88 toList,
88− matrixBuilder',
89 matrixBuilder,
89 matrixBuilder,
90 row,
90 row,
91 col,
91 col,
@@ -97,15 +97,14 @@ module LAoP.Matrix.Type
97
97
98 -- * Functor instance equivalent function
98 -- * Functor instance equivalent function
99 fmapM,
99 fmapM,
100− bimapM,
101
100
102 -- * Applicative/Monoidal instance equivalent functions
101 -- * Applicative/Monoidal instance equivalent functions
103 unitM,
102 unitM,
104 multM,
103 multM,
105
104
106 -- * Selective equivalent instance function
105 -- * Selective equivalent instance function
107− selectM,
106+ selectM,
108−
107+
109 -- * Monad equivalent instance function
108 -- * Monad equivalent instance function
110 returnM,
109 returnM,
111 bindM,
110 bindM,
@@ -113,34 +112,25 @@ module LAoP.Matrix.Type
113 -- * Misc
112 -- * Misc
114 -- ** Get dimensions
113 -- ** Get dimensions
115 columns,
114 columns,
116− columns',
117 rows,
115 rows,
118− rows',
119
116
120 -- ** Matrix Transposition
117 -- ** Matrix Transposition
121 tr,
118 tr,
122
119
123− -- ** Scalar multiplication/division of matrices
124− (.|),
125− (./),
126−
127 -- ** McCarthy's Conditional
120 -- ** McCarthy's Conditional
128 cond,
121 cond,
129
122
130 -- ** Matrix "abiding"
123 -- ** Matrix "abiding"
131− abideJF,
124+ abideJS,
132− abideFJ,
125+ abideSJ,
133−
134− -- ** Zip Matrices
135− zipWithM,
136
126
137 -- * Biproduct approach
127 -- * Biproduct approach
138− -- ** Fork
128+ -- ** Split
139 (===),
129 (===),
140 -- *** Projections
130 -- *** Projections
141 p1,
131 p1,
142 p2,
132 p2,
143− -- ** Join
133+ -- ** Junc
144 (|||),
134 (|||),
145 -- *** Injections
135 -- *** Injections
146 i1,
136 i1,
@@ -154,11 +144,11 @@ module LAoP.Matrix.Type
154 -- | Note that given the restrictions imposed it is not possible to
144 -- | Note that given the restrictions imposed it is not possible to
155 -- implement the standard type classes present in standard Haskell.
145 -- implement the standard type classes present in standard Haskell.
156 -- *** Matrix pairing projections
146 -- *** Matrix pairing projections
157− fstM,
147+ kp1,
158− sndM,
148+ kp2,
159
149
160 -- *** Matrix pairing
150 -- *** Matrix pairing
161− kr,
151+ khatri,
162
152
163 -- * Matrix composition and lifting
153 -- * Matrix composition and lifting
164
154
@@ -166,10 +156,10 @@ module LAoP.Matrix.Type
166
156
167 -- | Note that given the restrictions imposed it is not possible to
157 -- | Note that given the restrictions imposed it is not possible to
168 -- implement the standard type classes present in standard Haskell.
158 -- implement the standard type classes present in standard Haskell.
169− iden,
159+ identity,
170 comp,
160 comp,
171− fromF',
172 fromF,
161 fromF,
162+ fromF',
173
163
174 -- * Relation
164 -- * Relation
175 toRel,
165 toRel,
@@ -183,44 +173,35 @@ where
183import Data.Void
173import Data.Void
184import Data.Proxy
174import Data.Proxy
185import Data.Kind
175import Data.Kind
186−import GHC.TypeLits
176+import GHC.TypeLits
187import Control.DeepSeq
177import Control.DeepSeq
188import LAoP.Utils
178import LAoP.Utils
179+import qualified Control.Category as C
189import qualified LAoP.Matrix.Internal as I
180import qualified LAoP.Matrix.Internal as I
190−import Prelude hiding (id, (.))
191
181
192newtype Matrix e (cols :: Type) (rows :: Type) = M (I.Matrix e (I.Normalize cols) (I.Normalize rows))
182newtype Matrix e (cols :: Type) (rows :: Type) = M (I.Matrix e (I.Normalize cols) (I.Normalize rows))
193 deriving (Show, Num, Eq, Ord, NFData) via (I.Matrix e (I.Normalize cols) (I.Normalize rows))
183 deriving (Show, Num, Eq, Ord, NFData) via (I.Matrix e (I.Normalize cols) (I.Normalize rows))
194
184
195-- | Constraint type synonyms to keep the type signatures less convoluted
185-- | Constraint type synonyms to keep the type signatures less convoluted
196−type Countable a = KnownNat (I.Count a)
186+type Countable a = KnownNat (I.Count a)
197−type CountableDims a b = (Countable a, Countable b)
187+type CountableDimensions a b = (Countable a, Countable b)
198−type CountableN a = KnownNat (I.Count (I.Normalize a))
188+type CountableN a = KnownNat (I.Count (I.Normalize a))
199−type CountableDimsN a b = (CountableN a, CountableN b)
189+type CountableDimensionsN a b = (CountableN a, CountableN b)
200−type FLN a b = I.FromLists (I.Normalize a) (I.Normalize b)
190+type FromListsN e a b = I.FromLists e (I.Normalize a) (I.Normalize b)
201−type Liftable e a b = (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num e, Ord e)
191+type Liftable e a b = (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num e, Ord e)
202−type Trivial a = I.Normalize (I.Normalize a) ~ I.Normalize (I.Normalize (I.Normalize a))
192+type Trivial a = I.Normalize (I.Normalize a) ~ I.Normalize (I.Normalize (I.Normalize a))
203−type Trivial2 a = I.Normalize a ~ I.Normalize (I.Normalize a)
193+type Trivial2 a = I.Normalize a ~ I.Normalize (I.Normalize a)
204−type Trivial3 a = I.FromNat (I.Count (I.Normalize (I.Normalize a))) ~ I.Normalize (I.Normalize a)
194+type Trivial3 a = I.FromNat (I.Count (I.Normalize (I.Normalize a))) ~ I.Normalize (I.Normalize a)
205−type TrivialP a b = I.Normalize (a, b) ~ I.Normalize (I.Normalize a, I.Normalize b)
195+type TrivialP a b = I.Normalize (a, b) ~ I.Normalize (I.Normalize a, I.Normalize b)
206−
196+
207−-- | It is possible to implement a constrained version of the category type
197+-- | It isn't possible to implement the 'id' function so it's
208−-- class.
198+-- implementation is 'undefined'. However 'comp' can be and this partial
199+-- class implementation exists just to make the code more readable.
200+--
201+-- Please use 'identity' instead.
209−instance (Num e) => Category (Matrix e) where
202+instance (Num e) => C.Category (Matrix e) where
210− type Object (Matrix e) a = (FLN a a, CountableN a)
203+ id = undefined
211− id = iden
212− (.) = comp
204+ (.) = comp
213−
214−-- | Bifunctor equivalent function
215−bimapM ::
216− ( Liftable e a b,
217− Liftable e c d,
218− CountableDimsN a c,
219− CountableDimsN b d,
220− FLN d c,
221− FLN b a
222− ) => (a -> b) -> (c -> d) -> Matrix e a c -> Matrix e b d
223−bimapM f g m = fromF g . m . tr (fromF f)
224
205
225-- | Zero type alias
206-- | Zero type alias
226type Zero = Void
207type Zero = Void
@@ -230,74 +211,78 @@ type One = ()
230
211
231-- Primitives
212-- Primitives
232
213
214+-- | Empty matrix constructor
215+empty :: Matrix e Zero Zero
216+empty = M I.Empty
217+
233-- | Unit matrix constructor
218-- | Unit matrix constructor
234one :: e -> Matrix e One One
219one :: e -> Matrix e One One
235one = M . I.One
220one = M . I.One
236
221
237−-- | Matrix 'Join' constructor
222+-- | Matrix 'Junc' constructor
238−join ::
223+junc ::
239 Matrix e a rows ->
224 Matrix e a rows ->
240 Matrix e b rows ->
225 Matrix e b rows ->
241 Matrix e (Either a b) rows
226 Matrix e (Either a b) rows
242−join (M a) (M b) = M (I.Join a b)
227+junc (M a) (M b) = M (I.Junc a b)
243
228
244infixl 3 |||
229infixl 3 |||
245−-- | Matrix 'Join' constructor
230+-- | Matrix 'Junc' constructor
246(|||) ::
231(|||) ::
247 Matrix e a rows ->
232 Matrix e a rows ->
248 Matrix e b rows ->
233 Matrix e b rows ->
249 Matrix e (Either a b) rows
234 Matrix e (Either a b) rows
250−(|||) = join
235+(|||) = junc
251
236
252−-- | Matrix 'Fork' constructor
237+-- | Matrix 'Split' constructor
253−fork ::
238+split ::
254 Matrix e cols a ->
239 Matrix e cols a ->
255 Matrix e cols b ->
240 Matrix e cols b ->
256 Matrix e cols (Either a b)
241 Matrix e cols (Either a b)
257−fork (M a) (M b) = M (I.Fork a b)
242+split (M a) (M b) = M (I.Split a b)
258
243
259infixl 2 ===
244infixl 2 ===
260−-- | Matrix 'Fork' constructor
245+-- | Matrix 'Split' constructor
261(===) ::
246(===) ::
262 Matrix e cols a ->
247 Matrix e cols a ->
263 Matrix e cols b ->
248 Matrix e cols b ->
264 Matrix e cols (Either a b)
249 Matrix e cols (Either a b)
265−(===) = fork
250+(===) = split
266
251
267-- Functor hierarchy
252-- Functor hierarchy
268
253
269-- | Functor instance equivalent function
254-- | Functor instance equivalent function
270−fmapM ::
255+fmapM ::
271 ( Liftable e a b,
256 ( Liftable e a b,
272− CountableDimsN a b,
257+ CountableDimensionsN a b,
273− FLN b a
258+ FromListsN e b a
274 )
259 )
275 =>
260 =>
276 (a -> b) -> Matrix e c a -> Matrix e c b
261 (a -> b) -> Matrix e c a -> Matrix e c b
277−fmapM f m = fromF f . m
262+fmapM f m = fromF' f `comp` m
278
263
279-- | Applicative instance equivalent 'unit' function,
264-- | Applicative instance equivalent 'unit' function,
280unitM :: (Num e) => Matrix e () ()
265unitM :: (Num e) => Matrix e () ()
281unitM = one 1
266unitM = one 1
282
267
283-- | Applicative instance equivalent 'unit' function,
268-- | Applicative instance equivalent 'unit' function,
284−multM ::
269+multM ::
285− ( CountableDimsN a b,
270+ ( CountableDimensionsN a b,
286 CountableN (a, b),
271 CountableN (a, b),
287 Num e,
272 Num e,
288− FLN (a, b) a,
273+ FromListsN e (a, b) a,
289− FLN (a, b) b,
274+ FromListsN e (a, b) b,
290 TrivialP a b
275 TrivialP a b
291 ) => Matrix e c a -> Matrix e c b -> Matrix e c (a, b)
276 ) => Matrix e c a -> Matrix e c b -> Matrix e c (a, b)
292−multM = kr
277+multM = khatri
293
278
294-- | Monad instance equivalent 'return' function,
279-- | Monad instance equivalent 'return' function,
295−returnM ::
280+returnM ::
296− forall e a .
281+ forall e a .
297 ( Num e,
282 ( Num e,
298 Enum e,
283 Enum e,
299 Enum a,
284 Enum a,
300− FLN () a,
285+ FromListsN e () a,
301 Countable a
286 Countable a
302 ) => a -> Matrix e One a
287 ) => a -> Matrix e One a
303returnM a = col l
288returnM a = col l
@@ -314,64 +299,51 @@ bindM = flip comp
314
299
315-- | Build a matrix out of a list of list of elements. Throws a runtime
300-- | Build a matrix out of a list of list of elements. Throws a runtime
316-- error if the dimensions do not match.
301-- error if the dimensions do not match.
317−fromLists :: (FLN cols rows) => [[e]] -> Matrix e cols rows
302+fromLists :: (FromListsN e cols rows) => [[e]] -> Matrix e cols rows
318fromLists = M . I.fromLists
303fromLists = M . I.fromLists
319
304
320-- | Matrix builder function. Constructs a matrix provided with
305-- | Matrix builder function. Constructs a matrix provided with
321−-- a construction function that operates with indices.
306+-- a construction function.
322−matrixBuilder' ::
323− (FLN cols rows, CountableDimsN cols rows )
324− => ((Int, Int) -> e) -> Matrix e cols rows
325−matrixBuilder' = M . I.matrixBuilder'
326−
327−-- | Matrix builder function. Constructs a matrix provided with
328−-- a construction function that operates with arbitrary types.
329matrixBuilder ::
307matrixBuilder ::
330− ( FLN a b,
308+ (FromListsN e cols rows, CountableDimensionsN cols rows )
331− Enum a,
332− Enum b,
333− Bounded a,
334− Bounded b,
335− Eq a,
336− Countable b
337− ) => ((a, b) -> e) -> Matrix e a b
309+ => ((Int, Int) -> e) -> Matrix e cols rows
338−matrixBuilder f = M (I.matrixBuilder f)
310+matrixBuilder = M . I.matrixBuilder
339
311
340-- | Constructs a column vector matrix
312-- | Constructs a column vector matrix
341−col :: (FLN () rows) => [e] -> Matrix e One rows
313+col :: (FromListsN e () rows) => [e] -> Matrix e One rows
342col = M . I.col
314col = M . I.col
343
315
344-- | Constructs a row vector matrix
316-- | Constructs a row vector matrix
345−row :: (FLN cols ()) => [e] -> Matrix e cols One
317+row :: (FromListsN e cols ()) => [e] -> Matrix e cols One
346row = M . I.row
318row = M . I.row
347
319
348-- | Lifts functions to matrices with arbitrary dimensions.
320-- | Lifts functions to matrices with arbitrary dimensions.
349--
321--
350-- NOTE: Be careful to not ask for a matrix bigger than the cardinality of
322-- NOTE: Be careful to not ask for a matrix bigger than the cardinality of
351-- types @a@ or @b@ allows.
323-- types @a@ or @b@ allows.
352−fromF' ::
324+fromF ::
353 ( Liftable e a b,
325 ( Liftable e a b,
354− CountableDimsN cols rows,
326+ CountableDimensionsN cols rows,
355− FLN rows cols
327+ FromListsN e rows cols
356 ) =>
328 ) =>
357 (a -> b) -> Matrix e cols rows
329 (a -> b) -> Matrix e cols rows
358−fromF' = M . I.fromF'
330+fromF = M . I.fromF
359
331
360-- | Lifts functions to matrices with dimensions matching @a@ and @b@
332-- | Lifts functions to matrices with dimensions matching @a@ and @b@
361-- cardinality's.
333-- cardinality's.
362−fromF ::
334+fromF' ::
363 ( Liftable e a b,
335 ( Liftable e a b,
364− CountableDimsN a b,
336+ CountableDimensionsN a b,
365− FLN b a
337+ FromListsN e b a
366 ) =>
338 ) =>
367 (a -> b) -> Matrix e a b
339 (a -> b) -> Matrix e a b
368−fromF = M . I.fromF
340+fromF' = M . I.fromF'
369
341
370-- | Lifts relation functions to Boolean Matrix
342-- | Lifts relation functions to Boolean Matrix
371toRel ::
343toRel ::
372 ( Liftable (Natural 0 1) a b,
344 ( Liftable (Natural 0 1) a b,
373− CountableDims a b,
345+ CountableDimensionsN a b,
374− FLN b a
346+ FromListsN (Natural 0 1) b a
375 ) => (a -> b -> Bool) -> Matrix (Natural 0 1) a b
347 ) => (a -> b -> Bool) -> Matrix (Natural 0 1) a b
376toRel = M . I.toRel
348toRel = M . I.toRel
377
349
@@ -389,7 +361,7 @@ toList (M m) = I.toList m
389
361
390-- | The zero matrix. A matrix wholly filled with zeros.
362-- | The zero matrix. A matrix wholly filled with zeros.
391zeros ::
363zeros ::
392− (Num e, FLN cols rows, CountableDimsN cols rows)
364+ (Num e, FromListsN e cols rows, CountableDimensionsN cols rows)
393 => Matrix e cols rows
365 => Matrix e cols rows
394zeros = M I.zeros
366zeros = M I.zeros
395
367
@@ -399,7 +371,7 @@ zeros = M I.zeros
399--
371--
400-- Also known as T (Top) matrix.
372-- Also known as T (Top) matrix.
401ones ::
373ones ::
402− (Num e, FLN cols rows, CountableDimsN cols rows)
374+ (Num e, FromListsN e cols rows, CountableDimensionsN cols rows)
403 => Matrix e cols rows
375 => Matrix e cols rows
404ones = M I.ones
376ones = M I.ones
405
377
@@ -408,7 +380,7 @@ ones = M I.ones
408-- | The constant matrix constructor. A matrix wholly filled with a given
380-- | The constant matrix constructor. A matrix wholly filled with a given
409-- value.
381-- value.
410constant ::
382constant ::
411− (Num e, FLN cols rows, CountableDimsN cols rows)
383+ (Num e, FromListsN e cols rows, CountableDimensionsN cols rows)
412 => e -> Matrix e cols rows
384 => e -> Matrix e cols rows
413constant = M . I.constant
385constant = M . I.constant
414
386
@@ -417,30 +389,30 @@ constant = M . I.constant
417-- | The T (Top) row vector matrix.
389-- | The T (Top) row vector matrix.
418bang ::
390bang ::
419 forall e cols.
391 forall e cols.
420− (Num e, Enum e, FLN cols (), CountableN cols) =>
392+ (Num e, Enum e, FromListsN e cols (), CountableN cols) =>
421 Matrix e cols One
393 Matrix e cols One
422bang = M I.bang
394bang = M I.bang
423
395
424-- | Point constant relation
396-- | Point constant relation
425−point ::
397+point ::
426 ( Bounded a,
398 ( Bounded a,
427 Enum a,
399 Enum a,
428 Eq a,
400 Eq a,
429 Num e,
401 Num e,
430 Ord e,
402 Ord e,
431 CountableN a,
403 CountableN a,
432− FLN a One
404+ FromListsN e a One
433 ) => a -> Matrix e One a
405 ) => a -> Matrix e One a
434−point = fromF . const
406+point = fromF' . const
435
407
436−-- iden Matrix
408+-- Identity Matrix
437
409
438−-- | iden matrix
410+-- | Identity matrix
439−iden ::
411+identity ::
440− (Num e, FLN a a, CountableN a) =>
412+ (Num e, FromListsN e a a, CountableN a) =>
441 Matrix e a a
413 Matrix e a a
442−iden = M I.iden
414+identity = M I.identity
443−{-# NOINLINE iden #-}
415+{-# NOINLINE identity #-}
444
416
445-- Matrix composition (MMM)
417-- Matrix composition (MMM)
446
418
@@ -451,31 +423,17 @@ iden = M I.iden
451comp :: (Num e) => Matrix e cr rows -> Matrix e cols cr -> Matrix e cols rows
423comp :: (Num e) => Matrix e cr rows -> Matrix e cols cr -> Matrix e cols rows
452comp (M a) (M b) = M (I.comp a b)
424comp (M a) (M b) = M (I.comp a b)
453{-# NOINLINE comp #-}
425{-# NOINLINE comp #-}
454−{-# RULES
426+{-# RULES
455− "comp/iden1" forall m. comp m iden = m ;
427+ "comp/identity1" forall m. comp m identity = m ;
456− "comp/iden2" forall m. comp iden m = m
428+ "comp/identity2" forall m. comp identity m = m
457#-}
429#-}
458
430
459−-- Scalar multiplication of matrices
460−
461−infixl 7 .|
462−-- | Scalar multiplication of matrices.
463−(.|) :: Num e => e -> Matrix e cols rows -> Matrix e cols rows
464−(.|) e (M m) = M (e I..| m)
465−
466−-- Scalar division of matrices
467−
468−infixl 7 ./
469−-- | Scalar multiplication of matrices.
470−(./) :: Fractional e => Matrix e cols rows -> e -> Matrix e cols rows
471−(./) (M m) e = M (m I../ e)
472−
473-- | Biproduct first component projection
431-- | Biproduct first component projection
474p1 ::
432p1 ::
475 ( Num e,
433 ( Num e,
476− CountableDimsN n m,
434+ CountableDimensionsN n m,
477− FLN n m,
435+ FromListsN e n m,
478− FLN m m
436+ FromListsN e m m
479 ) =>
437 ) =>
480 Matrix e (Either m n) m
438 Matrix e (Either m n) m
481p1 = M I.p1
439p1 = M I.p1
@@ -483,9 +441,9 @@ p1 = M I.p1
483-- | Biproduct second component projection
441-- | Biproduct second component projection
484p2 ::
442p2 ::
485 ( Num e,
443 ( Num e,
486− CountableDimsN n m,
444+ CountableDimensionsN n m,
487− FLN m n,
445+ FromListsN e m n,
488− FLN n n
446+ FromListsN e n n
489 ) =>
447 ) =>
490 Matrix e (Either m n) n
448 Matrix e (Either m n) n
491p2 = M I.p2
449p2 = M I.p2
@@ -495,9 +453,9 @@ p2 = M I.p2
495-- | Biproduct first component injection
453-- | Biproduct first component injection
496i1 ::
454i1 ::
497 ( Num e,
455 ( Num e,
498− CountableDimsN n m,
456+ CountableDimensionsN n m,
499− FLN n m,
457+ FromListsN e n m,
500− FLN m m
458+ FromListsN e m m
501 ) =>
459 ) =>
502 Matrix e m (Either m n)
460 Matrix e m (Either m n)
503i1 = tr p1
461i1 = tr p1
@@ -505,9 +463,9 @@ i1 = tr p1
505-- | Biproduct second component injection
463-- | Biproduct second component injection
506i2 ::
464i2 ::
507 ( Num e,
465 ( Num e,
508− CountableDimsN n m,
466+ CountableDimensionsN n m,
509− FLN m n,
467+ FromListsN e m n,
510− FLN n n
468+ FromListsN e n n
511 ) =>
469 ) =>
512 Matrix e n (Either m n)
470 Matrix e n (Either m n)
513i2 = tr p2
471i2 = tr p2
@@ -516,34 +474,24 @@ i2 = tr p2
516
474
517-- | Obtain the number of rows.
475-- | Obtain the number of rows.
518--
476--
519−-- NOTE: The 'KnownNat' constraint is needed in order to obtain the
477+-- NOTE: The 'KnownNat' constaint is needed in order to obtain the
520−-- dimensions in constant time. For a version that doesn't require the
478+-- dimensions in constant time.
521−-- constraint see 'rows''.
479+--
480+-- TODO: A 'rows' function that does not need the 'KnownNat' constraint in
481+-- exchange for performance.
522rows :: (CountableN rows) => Matrix e cols rows -> Int
482rows :: (CountableN rows) => Matrix e cols rows -> Int
523rows (M m) = I.rows m
483rows (M m) = I.rows m
524
484
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−
532-- | Obtain the number of columns.
485-- | Obtain the number of columns.
486+--
487+-- NOTE: The 'KnownNat' constaint is needed in order to obtain the
488+-- dimensions in constant time.
533--
489--
534−-- NOTE: The 'KnownNat' constraint is needed in order to obtain the
490+-- TODO: A 'columns' function that does not need the 'KnownNat' constraint in
535−-- dimensions in constant time. For a version that doesn't require the
491+-- exchange for performance.
536−-- constraint see 'columns''.
537columns :: (CountableN cols) => Matrix e cols rows -> Int
492columns :: (CountableN cols) => Matrix e cols rows -> Int
538columns (M m) = I.columns m
493columns (M m) = I.columns m
539
494
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−
547-- Coproduct Bifunctor
495-- Coproduct Bifunctor
548
496
549infixl 5 -|-
497infixl 5 -|-
@@ -551,11 +499,11 @@ infixl 5 -|-
551-- | Matrix coproduct functor also known as matrix direct sum.
499-- | Matrix coproduct functor also known as matrix direct sum.
552(-|-) ::
500(-|-) ::
553 ( Num e,
501 ( Num e,
554− CountableDimsN j k,
502+ CountableDimensionsN j k,
555− FLN k k,
503+ FromListsN e k k,
556− FLN j k,
504+ FromListsN e j k,
557− FLN k j,
505+ FromListsN e k j,
558− FLN j j
506+ FromListsN e j j
559 ) =>
507 ) =>
560 Matrix e n k ->
508 Matrix e n k ->
561 Matrix e m j ->
509 Matrix e m j ->
@@ -565,98 +513,98 @@ infixl 5 -|-
565-- Khatri Rao Product and projections
513-- Khatri Rao Product and projections
566
514
567-- | Khatri Rao product first component projection matrix.
515-- | Khatri Rao product first component projection matrix.
568−fstM ::
516+kp1 ::
569 forall e m k .
517 forall e m k .
570 ( Num e,
518 ( Num e,
571− CountableDimsN m k,
519+ CountableDimensionsN m k,
572 CountableN (m, k),
520 CountableN (m, k),
573− FLN (m, k) m,
521+ FromListsN e (m, k) m,
574 TrivialP m k
522 TrivialP m k
575 ) => Matrix e (m, k) m
523 ) => Matrix e (m, k) m
576−fstM = M (I.fstM @e @(I.Normalize m) @(I.Normalize k))
524+kp1 = M (I.kp1 @e @(I.Normalize m) @(I.Normalize k))
577
525
578-- | Khatri Rao product second component projection matrix.
526-- | Khatri Rao product second component projection matrix.
579−sndM ::
527+kp2 ::
580 forall e m k.
528 forall e m k.
581 ( Num e,
529 ( Num e,
582− CountableDimsN k m,
530+ CountableDimensionsN k m,
583 CountableN (m, k),
531 CountableN (m, k),
584− FLN (m, k) k,
532+ FromListsN e (m, k) k,
585 TrivialP m k
533 TrivialP m k
586 ) => Matrix e (m, k) k
534 ) => Matrix e (m, k) k
587−sndM = M (I.sndM @e @(I.Normalize m) @(I.Normalize k))
535+kp2 = M (I.kp2 @e @(I.Normalize m) @(I.Normalize k))
588
536
589-- | Khatri Rao Matrix product also known as matrix pairing.
537-- | Khatri Rao Matrix product also known as matrix pairing.
590--
538--
591-- NOTE: That this is not a true categorical product, see for instance:
539-- NOTE: That this is not a true categorical product, see for instance:
592−--
540+--
593-- @
541-- @
594−-- | fstM . kr a b == a
542+-- | kp1 `comp` khatri a b == a
595−-- kr a b ==> |
543+-- khatri a b ==> |
596−-- | sndM . kr a b == b
544+-- | kp2 `comp` khatri a b == b
597-- @
545-- @
598--
546--
599-- __Emphasis__ on the implication symbol.
547-- __Emphasis__ on the implication symbol.
600−kr ::
548+khatri ::
601 forall e cols a b.
549 forall e cols a b.
602 ( Num e,
550 ( Num e,
603− CountableDimsN a b,
551+ CountableDimensionsN a b,
604 CountableN (a, b),
552 CountableN (a, b),
605− FLN (a, b) a,
553+ FromListsN e (a, b) a,
606− FLN (a, b) b,
554+ FromListsN e (a, b) b,
607 TrivialP a b
555 TrivialP a b
608 ) => Matrix e cols a -> Matrix e cols b -> Matrix e cols (a, b)
556 ) => Matrix e cols a -> Matrix e cols b -> Matrix e cols (a, b)
609−kr a b =
557+khatri a b =
610− let fstM' = fstM @e @a @b
558+ let kp1' = kp1 @e @a @b
611− sndM' = sndM @e @a @b
559+ kp2' = kp2 @e @a @b
612− in comp (tr fstM') a * comp (tr sndM') b
560+ in comp (tr kp1') a * comp (tr kp2') b
613
561
614-- Product Bifunctor (Kronecker)
562-- Product Bifunctor (Kronecker)
615
563
616infixl 4 ><
564infixl 4 ><
617
565
618−-- | Matrix product functor also known as Kronecker product
566+-- | Matrix product functor also known as kronecker product
619(><) ::
567(><) ::
620 forall e m p n q.
568 forall e m p n q.
621 ( Num e,
569 ( Num e,
622− CountableDimsN m n,
570+ CountableDimensionsN m n,
623− CountableDimsN p q,
571+ CountableDimensionsN p q,
624− CountableDimsN (m, n) (p, q),
572+ CountableDimensionsN (m, n) (p, q),
625− FLN (m, n) m,
573+ FromListsN e (m, n) m,
626− FLN (m, n) n,
574+ FromListsN e (m, n) n,
627− FLN (p, q) p,
575+ FromListsN e (p, q) p,
628− FLN (p, q) q,
576+ FromListsN e (p, q) q,
629 TrivialP m n,
577 TrivialP m n,
630 TrivialP p q
578 TrivialP p q
631 ) => Matrix e m p -> Matrix e n q -> Matrix e (m, n) (p, q)
579 ) => Matrix e m p -> Matrix e n q -> Matrix e (m, n) (p, q)
632(><) a b =
580(><) a b =
633− let fstM' = fstM @e @m @n
581+ let kp1' = kp1 @e @m @n
634− sndM' = sndM @e @m @n
582+ kp2' = kp2 @e @m @n
635− in kr (comp a fstM') (comp b sndM')
583+ in khatri (comp a kp1') (comp b kp2')
636
584
637−-- Matrix abide Join Fork
585+-- Matrix abide Junc Split
638
586
639−-- | Matrix "abiding" followin the 'Join'-'Fork' abide law.
587+-- | Matrix "abiding" followin the 'Junc'-'Split' abide law.
640−--
588+--
641-- Law:
589-- Law:
642--
590--
643-- @
591-- @
644−-- 'Join' ('Fork' a c) ('Fork' b d) == 'Fork' ('Join' a b) ('Join' c d)
592+-- 'Junc' ('Split' a c) ('Split' b d) == 'Split' ('Junc' a b) ('Junc' c d)
645-- @
593-- @
646−abideJF :: Matrix e cols rows -> Matrix e cols rows
594+abideJS :: Matrix e cols rows -> Matrix e cols rows
647−abideJF (M m) = M (I.abideJF m)
595+abideJS (M m) = M (I.abideJS m)
648
596
649−-- Matrix abide Fork Join
597+-- Matrix abide Split Junc
650
598
651−-- | Matrix "abiding" followin the 'Fork'-'Join' abide law.
599+-- | Matrix "abiding" followin the 'Split'-'Junc' abide law.
652−--
600+--
653-- Law:
601-- Law:
654--
602--
655-- @
603-- @
656−-- 'Fork' ('Join' a b) ('Join' c d) == 'Join' ('Fork' a c) ('Fork' b d)
604+-- 'Split' ('Junc' a b) ('Junc' c d) == 'Junc' ('Split' a c) ('Split' b d)
657-- @
605-- @
658−abideFJ :: Matrix e cols rows -> Matrix e cols rows
606+abideSJ :: Matrix e cols rows -> Matrix e cols rows
659−abideFJ (M m) = M (I.abideFJ m)
607+abideSJ (M m) = M (I.abideSJ m)
660
608
661-- Matrix transposition
609-- Matrix transposition
662
610
@@ -668,9 +616,9 @@ tr (M m) = M (I.tr m)
668
616
669-- | Selective functors 'select' operator equivalent inspired by the
617-- | Selective functors 'select' operator equivalent inspired by the
670-- ArrowMonad solution presented in the paper.
618-- ArrowMonad solution presented in the paper.
671−selectM ::
619+selectM ::
672 ( Num e,
620 ( Num e,
673− FLN b b,
621+ FromListsN e b b,
674 CountableN b
622 CountableN b
675 ) => Matrix e cols (Either a b) -> Matrix e a b -> Matrix e cols b
623 ) => Matrix e cols (Either a b) -> Matrix e a b -> Matrix e cols b
676selectM (M m) (M y) = M (I.select m y)
624selectM (M m) (M y) = M (I.select m y)
@@ -683,9 +631,9 @@ cond ::
683 Trivial2 a,
631 Trivial2 a,
684 Trivial3 a,
632 Trivial3 a,
685 CountableN a,
633 CountableN a,
686− FLN () a,
634+ FromListsN e () a,
687− FLN a (),
635+ FromListsN e a (),
688− FLN a a,
636+ FromListsN e a a,
689 Liftable e a Bool
637 Liftable e a Bool
690 )
638 )
691 =>
639 =>
@@ -695,13 +643,9 @@ cond p (M a) (M b) = M (I.cond p a b)
695-- Pretty print
643-- Pretty print
696
644
697-- | Matrix pretty printer
645-- | Matrix pretty printer
698−pretty :: (CountableDimsN cols rows, Show e) => Matrix e cols rows -> String
646+pretty :: (CountableN cols, Show e) => Matrix e cols rows -> String
699pretty (M m) = I.pretty m
647pretty (M m) = I.pretty m
700
648
701-- | Matrix pretty printer
649-- | Matrix pretty printer
702−prettyPrint :: (CountableDimsN cols rows, Show e) => Matrix e cols rows -> IO ()
650+prettyPrint :: (CountableN cols, Show e) => Matrix e cols rows -> IO ()
703prettyPrint (M m) = I.prettyPrint m
651prettyPrint (M m) = I.prettyPrint m
704−
705−-- | Zip two matrices with a given binary function
706−zipWithM :: (e -> f -> g) -> Matrix e a b -> Matrix f a b -> Matrix g a b
707−zipWithM f (M a) (M b) = M (I.zipWithM f a b)
src/LAoP/Relation.hs+11−8
@@ -32,19 +32,22 @@ module LAoP.Relation
32
32
33 -- * Constraint type synonyms
33 -- * Constraint type synonyms
34 Countable,
34 Countable,
35− CountableDims,
35+ CountableDimensions,
36 CountableN,
36 CountableN,
37− CountableDimsN,
37+ CountableDimensionsN,
38− FLN,
38+ FromListsN,
39 Liftable,
39 Liftable,
40 Trivial,
40 Trivial,
41+ TrivialE,
41 TrivialP,
42 TrivialP,
43+ TrivialP2,
42
44
43 -- * Primitives
45 -- * Primitives
46+ empty,
44 one,
47 one,
45− join,
48+ junc,
46 (|||),
49 (|||),
47− fork,
50+ split,
48 (===),
51 (===),
49
52
50 -- * Auxiliary type families
53 -- * Auxiliary type families
@@ -107,8 +110,8 @@ module LAoP.Relation
107 splitR,
110 splitR,
108
111
109 -- ** Projections
112 -- ** Projections
110− fstR,
113+ p1,
111− sndR,
114+ p2,
112 -- ** Bifunctor
115 -- ** Bifunctor
113 (><),
116 (><),
114 -- * Relational coproduct
117 -- * Relational coproduct
@@ -147,7 +150,7 @@ module LAoP.Relation
147 cond,
150 cond,
148
151
149 -- * Relational composition and lifting
152 -- * Relational composition and lifting
150− iden,
153+ identity,
151 comp,
154 comp,
152 fromF,
155 fromF,
153 fromF',
156 fromF',
src/LAoP/Relation/Internal.hs+254−250
@@ -1,4 +1,3 @@
1−{-# LANGUAGE TypeFamilies #-}
2{-# LANGUAGE ConstraintKinds #-}
1{-# LANGUAGE ConstraintKinds #-}
3{-# LANGUAGE GADTs #-}
2{-# LANGUAGE GADTs #-}
4{-# LANGUAGE UndecidableInstances #-}
3{-# LANGUAGE UndecidableInstances #-}
@@ -43,19 +42,22 @@ module LAoP.Relation.Internal
43
42
44 -- * Constraint type synonyms
43 -- * Constraint type synonyms
45 Countable,
44 Countable,
46− CountableDims,
45+ CountableDimensions,
47 CountableN,
46 CountableN,
48− CountableDimsN,
47+ CountableDimensionsN,
49− FLN,
48+ FromListsN,
50 Liftable,
49 Liftable,
51 Trivial,
50 Trivial,
51+ TrivialE,
52 TrivialP,
52 TrivialP,
53+ TrivialP2,
53
54
54 -- * Primitives
55 -- * Primitives
56+ empty,
55 one,
57 one,
56− join,
58+ junc,
57 (|||),
59 (|||),
58− fork,
60+ split,
59 (===),
61 (===),
60
62
61 -- * Auxiliary type families
63 -- * Auxiliary type families
@@ -66,15 +68,14 @@ module LAoP.Relation.Internal
66 -- * Matrix construction and conversion
68 -- * Matrix construction and conversion
67 I.FromLists,
69 I.FromLists,
68 fromLists,
70 fromLists,
69− fromF',
70 fromF,
71 fromF,
72+ fromF',
71 toRel,
73 toRel,
72 toLists,
74 toLists,
73 toList,
75 toList,
74 toBool,
76 toBool,
75 pt,
77 pt,
76 belongs,
78 belongs,
77− relationBuilder',
78 relationBuilder,
79 relationBuilder,
79 zeros,
80 zeros,
80 ones,
81 ones,
@@ -119,8 +120,8 @@ module LAoP.Relation.Internal
119 splitR,
120 splitR,
120
121
121 -- ** Projections
122 -- ** Projections
122− fstR,
123+ p1,
123− sndR,
124+ p2,
124 -- ** Bifunctor
125 -- ** Bifunctor
125 (><),
126 (><),
126 -- * Relational coproduct
127 -- * Relational coproduct
@@ -159,10 +160,10 @@ module LAoP.Relation.Internal
159 cond,
160 cond,
160
161
161 -- * Relational composition and lifting
162 -- * Relational composition and lifting
162− iden,
163+ identity,
163 comp,
164 comp,
164− fromF',
165 fromF,
165 fromF,
166+ fromF',
166
167
167 -- ** Relational application
168 -- ** Relational application
168 pointAp,
169 pointAp,
@@ -178,9 +179,9 @@ import Data.Void
178import qualified LAoP.Matrix.Internal as I
179import qualified LAoP.Matrix.Internal as I
179import LAoP.Utils.Internal
180import LAoP.Utils.Internal
180import Control.DeepSeq
181import Control.DeepSeq
182+import qualified Control.Category as C
181import Data.Bool
183import Data.Bool
182import GHC.TypeLits
184import GHC.TypeLits
183−import Prelude hiding (id, (.))
184
185
185-- | Boolean type synonym for working with boolean matrices
186-- | Boolean type synonym for working with boolean matrices
186type Boolean = Natural 0 1
187type Boolean = Natural 0 1
@@ -193,30 +194,34 @@ newtype Relation a b = R (I.Matrix Boolean (I.Normalize a) (I.Normalize b))
193deriving instance (Read (I.Matrix Boolean (I.Normalize a) (I.Normalize b))) => Read (Relation a b)
194deriving instance (Read (I.Matrix Boolean (I.Normalize a) (I.Normalize b))) => Read (Relation a b)
194
195
195-- | Constraint type synonyms to keep the type signatures less convoluted
196-- | Constraint type synonyms to keep the type signatures less convoluted
196−type Countable a = KnownNat (I.Count a)
197+type Countable a = KnownNat (I.Count a)
197−type CountableDims a b = (Countable a, Countable b)
198+type CountableDimensions a b = (Countable a, Countable b)
198−type CountableN a = KnownNat (I.Count (I.Normalize a))
199+type CountableN a = KnownNat (I.Count (I.Normalize a))
199−type CountableDimsN a b = (CountableN a, CountableN b)
200+type CountableDimensionsN a b = (CountableN a, CountableN b)
200−type FLN a b = I.FromLists (I.Normalize a) (I.Normalize b)
201+type FromListsN a b = I.FromLists Boolean (I.Normalize a) (I.Normalize b)
201−type Liftable a b = (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num Boolean, Ord Boolean)
202+type Liftable a b = (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num Boolean, Ord Boolean)
202−type Trivial a = I.Normalize a ~ I.Normalize (I.Normalize a)
203+type Trivial a = I.Normalize a ~ I.Normalize (I.Normalize a)
204+type TrivialE a b = I.Normalize (Either a b) ~ Either (I.Normalize a) (I.Normalize b)
203−type TrivialP a b = I.Normalize (a, b) ~ I.Normalize (I.Normalize a, I.Normalize b)
205+type TrivialP a b = I.Normalize (a, b) ~ I.Normalize (I.Normalize a, I.Normalize b)
204−
206+type TrivialP2 a b = I.Normalize (I.Normalize a, I.Normalize b) ~ I.Normalize (I.Normalize (a, b))
207+
205−-- | It is possible to implement a constrained version of the category type
208+-- | It isn't possible to implement the 'id' function so it's
206−-- class.
209+-- implementation is 'undefined'. However 'comp' can be and this partial
210+-- class implementation exists just to make the code more readable.
211+--
212+-- Please use 'identity' instead.
207−instance Category Relation where
213+instance C.Category Relation where
208− type Object Relation a = (FLN a a, CountableN a)
214+ id = undefined
209− id = iden
210− (.) = comp
215+ (.) = comp
211
216
212instance Num (Relation a b) where
217instance Num (Relation a b) where
213− -- | Matrix addition becomes Boolean matrix disjointion
218+ -- | Matrix addition becomes Boolean matrix disjunction
214 (R a) + (R b) = R (I.orM a b)
219 (R a) + (R b) = R (I.orM a b)
215
220
216 -- | Matrix subtraction becomes Relational subtraction
221 -- | Matrix subtraction becomes Relational subtraction
217 (R a) - (R b) = R (I.subM a b)
222 (R a) - (R b) = R (I.subM a b)
218
223
219− -- | Matrix multiplication becomes Boolean matrix conjointion
224+ -- | Matrix multiplication becomes Boolean matrix conjunction
220 (R a) * (R b) = R (I.andM a b)
225 (R a) * (R b) = R (I.andM a b)
221
226
222 -- | Matrix negation becomes Boolean matrix negation
227 -- | Matrix negation becomes Boolean matrix negation
@@ -228,92 +233,87 @@ type One = ()
228
233
229-- Primitives
234-- Primitives
230
235
236+-- | Empty matrix constructor
237+empty :: Relation Zero Zero
238+empty = R I.Empty
239+
231-- | Unit matrix constructor
240-- | Unit matrix constructor
232one :: Boolean -> Relation One One
241one :: Boolean -> Relation One One
233one = R . I.One
242one = R . I.One
234
243
235−-- | Boolean Matrix 'Join' constructor, also known as relational coproduct.
244+-- | Boolean Matrix 'Junc' constructor, also known as relational coproduct.
236--
245--
237-- See 'eitherR'.
246-- See 'eitherR'.
247+junc :: (TrivialE a b)
238−join :: Relation a c -> Relation b c -> Relation (Either a b) c
248+ => Relation a c -> Relation b c -> Relation (Either a b) c
239−join (R a) (R b) = R (I.Join a b)
249+junc (R a) (R b) = R (I.Junc a b)
240
250
241infixl 3 |||
251infixl 3 |||
242−-- | Boolean Matrix 'Join' constructor
252+-- | Boolean Matrix 'Junc' constructor
243--
253--
244-- See 'eitherR'.
254-- See 'eitherR'.
245(|||) ::
255(|||) ::
256+ (TrivialE a b) =>
246 Relation a c ->
257 Relation a c ->
247 Relation b c ->
258 Relation b c ->
248 Relation (Either a b) c
259 Relation (Either a b) c
249−(|||) = join
260+(|||) = junc
250
261
251−-- | Boolean Matrix 'Fork' constructor, also known as relational product.
262+-- | Boolean Matrix 'Split' constructor, also known as relational product.
263+split :: (TrivialE a b)
252−fork :: Relation c a -> Relation c b -> Relation c (Either a b)
264+ => Relation c a -> Relation c b -> Relation c (Either a b)
253−fork (R a) (R b) = R (I.Fork a b)
265+split (R a) (R b) = R (I.Split a b)
254
266
255infixl 2 ===
267infixl 2 ===
256−-- | Boolean Matrix 'Fork' constructor
268+-- | Boolean Matrix 'Split' constructor
257(===) ::
269(===) ::
270+ (TrivialE a b) =>
258 Relation c a ->
271 Relation c a ->
259 Relation c b ->
272 Relation c b ->
260 Relation c (Either a b)
273 Relation c (Either a b)
261−(===) = fork
274+(===) = split
262
275
263-- Construction
276-- Construction
264
277
265-- | Build a matrix out of a list of list of elements. Throws a runtime
278-- | Build a matrix out of a list of list of elements. Throws a runtime
266-- error if the dimensions do not match.
279-- error if the dimensions do not match.
267−fromLists :: (FLN a b) => [[Boolean]] -> Relation a b
280+fromLists :: (FromListsN a b) => [[Boolean]] -> Relation a b
268fromLists = R . I.fromLists
281fromLists = R . I.fromLists
269
282
270−-- | Relation builder function. Constructs a relation provided with
283+-- | Matrix builder function. Constructs a matrix provided with
271−-- a construction function that operates with indices.
272−relationBuilder' ::
273− (FLN a b, CountableDimsN a b) =>
274− ((Int, Int) -> Boolean) -> Relation a b
275−relationBuilder' = R . I.matrixBuilder'
276−
277−-- | Relation builder function. Constructs a relation provided with
278−-- a construction function that operates with arbitrary types.
284+-- a construction function.
279relationBuilder ::
285relationBuilder ::
280− ( FLN a b,
286+ (FromListsN a b, CountableDimensionsN a b) =>
281− Enum a,
282− Enum b,
283− Bounded a,
284− Bounded b,
285− Eq a,
286− CountableDims a b
287− ) => ((a, b) -> Boolean) -> Relation a b
287+ ((Int, Int) -> Boolean) -> Relation a b
288relationBuilder = R . I.matrixBuilder
288relationBuilder = R . I.matrixBuilder
289
289
290-- | Lifts functions to matrices with arbitrary dimensions.
290-- | Lifts functions to matrices with arbitrary dimensions.
291--
291--
292-- NOTE: Be careful to not ask for a matrix bigger than the cardinality of
292-- NOTE: Be careful to not ask for a matrix bigger than the cardinality of
293-- types @a@ or @b@ allows.
293-- types @a@ or @b@ allows.
294−fromF' ::
294+fromF ::
295 ( Liftable a b,
295 ( Liftable a b,
296− CountableDimsN c d,
296+ CountableDimensionsN c d,
297− FLN d c
297+ FromListsN d c
298 )
298 )
299 => (a -> b) -> Relation c d
299 => (a -> b) -> Relation c d
300−fromF' f = R (I.fromFRel' f)
300+fromF f = R (I.fromFRel f)
301
301
302-- | Lifts functions to matrices with dimensions matching @a@ and @b@
302-- | Lifts functions to matrices with dimensions matching @a@ and @b@
303-- cardinality's.
303-- cardinality's.
304−fromF ::
304+fromF' ::
305 ( Liftable a b,
305 ( Liftable a b,
306− CountableDimsN a b,
306+ CountableDimensionsN a b,
307− FLN b a
307+ FromListsN b a
308 )
308 )
309 => (a -> b) -> Relation a b
309 => (a -> b) -> Relation a b
310−fromF f = R (I.fromFRel f)
310+fromF' f = R (I.fromFRel' f)
311
311
312-- | Lifts relation functions to 'Relation'
312-- | Lifts relation functions to 'Relation'
313toRel ::
313toRel ::
314 ( Liftable a b,
314 ( Liftable a b,
315− CountableDims a b,
315+ CountableDimensionsN a b,
316− FLN b a
316+ FromListsN b a
317 )
317 )
318 => (a -> b -> Bool) -> Relation a b
318 => (a -> b -> Bool) -> Relation a b
319toRel = R . I.toRel
319toRel = R . I.toRel
@@ -322,9 +322,9 @@ toRel = R . I.toRel
322fromRel ::
322fromRel ::
323 ( Liftable a b,
323 ( Liftable a b,
324 Eq a,
324 Eq a,
325− CountableDimsN a b,
325+ CountableDimensionsN a b,
326− FLN a One,
326+ FromListsN a One,
327− FLN b One
327+ FromListsN b One
328 )
328 )
329 => Relation a b -> (a -> b -> Bool)
329 => Relation a b -> (a -> b -> Bool)
330fromRel r a b = pointApBool a b r
330fromRel r a b = pointApBool a b r
@@ -348,12 +348,12 @@ toBool r = case toList r of
348-- | Power transpose.
348-- | Power transpose.
349--
349--
350-- Maps a relation to a set valued function.
350-- Maps a relation to a set valued function.
351−pt ::
351+pt ::
352 ( Liftable a b,
352 ( Liftable a b,
353 Eq a,
353 Eq a,
354− CountableDimsN a b,
354+ CountableDimensionsN a b,
355− FLN a One,
355+ FromListsN a One,
356− FLN b One
356+ FromListsN b One
357 )
357 )
358 => Relation a b -> (a -> List b)
358 => Relation a b -> (a -> List b)
359pt r a =
359pt r a =
@@ -365,8 +365,8 @@ belongs ::
365 ( Bounded a,
365 ( Bounded a,
366 Enum a,
366 Enum a,
367 Eq a,
367 Eq a,
368− CountableDims (List a) a,
368+ CountableDimensionsN (List a) a,
369− FLN a (List a)
369+ FromListsN a (List a)
370 )
370 )
371 => Relation (List a) a
371 => Relation (List a) a
372belongs = toRel elemR
372belongs = toRel elemR
@@ -378,16 +378,16 @@ belongs = toRel elemR
378-- | The zero relation. A relation where no element of type @a@ relates
378-- | The zero relation. A relation where no element of type @a@ relates
379-- with elements of type @b@.
379-- with elements of type @b@.
380--
380--
381−-- Also known as ⊥ (Bottom) Relation.
381+-- Also known as ⊥ (Bottom) Relation or empty Relation.
382--
382--
383-- @
383-- @
384−-- r `.` ⊥ == ⊥ `.` r == ⊥
384+-- r ``comp`` ⊥ == ⊥ ``comp`` r == ⊥
385-- ⊥ ``sse`` R && R ``sse`` T == True
385-- ⊥ ``sse`` R && R ``sse`` T == True
386-- @
386-- @
387zeros ::
387zeros ::
388− (FLN a b, CountableDimsN a b) =>
388+ (FromListsN a b, CountableDimensionsN a b) =>
389 Relation a b
389 Relation a b
390−zeros = relationBuilder' (const (nat 0))
390+zeros = relationBuilder (const (nat 0))
391
391
392-- Ones Matrix
392-- Ones Matrix
393
393
@@ -400,43 +400,43 @@ zeros = relationBuilder' (const (nat 0))
400-- ⊥ ``sse`` R && R ``sse`` T == True
400-- ⊥ ``sse`` R && R ``sse`` T == True
401-- @
401-- @
402ones ::
402ones ::
403− (FLN a b, CountableDimsN a b) =>
403+ (FromListsN a b, CountableDimensionsN a b) =>
404 Relation a b
404 Relation a b
405−ones = relationBuilder' (const (nat 1))
405+ones = relationBuilder (const (nat 1))
406
406
407-- Bang Matrix
407-- Bang Matrix
408
408
409-- | The T (Top) row vector relation.
409-- | The T (Top) row vector relation.
410bang ::
410bang ::
411− (FLN a One, CountableN a) =>
411+ (FromListsN a One, CountableN a) =>
412 Relation a One
412 Relation a One
413bang = ones
413bang = ones
414
414
415-- | Point constant relation
415-- | Point constant relation
416−point ::
416+point ::
417 ( Bounded a,
417 ( Bounded a,
418 Enum a,
418 Enum a,
419 Eq a,
419 Eq a,
420 CountableN a,
420 CountableN a,
421− FLN a One
421+ FromListsN a One
422 ) => a -> Relation One a
422 ) => a -> Relation One a
423−point = fromF . const
423+point = fromF' . const
424
424
425−-- iden Matrix
425+-- Identity Matrix
426
426
427−-- | iden matrix
427+-- | Identity matrix
428--
428--
429-- @
429-- @
430−-- 'iden' `.` r == r == r `.` 'iden'
430+-- 'identity' ``comp`` r == r == r ``comp`` 'identity'
431-- @
431-- @
432−iden ::
432+identity ::
433− (FLN a a, CountableN a) => Relation a a
433+ (FromListsN a a, CountableN a) => Relation a a
434−iden = relationBuilder' (bool (nat 0) (nat 1) . uncurry (==))
434+identity = relationBuilder (bool (nat 0) (nat 1) . uncurry (==))
435
435
436-- | Relational composition
436-- | Relational composition
437--
437--
438-- @
438-- @
439−-- r `.` (s `.` p) = (r `.` s) `.` p
439+-- r ``comp`` (s ``comp`` p) = (r ``comp`` s) ``comp`` p
440-- @
440-- @
441comp :: Relation b c -> Relation a b -> Relation a c
441comp :: Relation b c -> Relation a b -> Relation a c
442comp (R a) (R b) = R (I.compRel a b)
442comp (R a) (R b) = R (I.compRel a b)
@@ -484,7 +484,7 @@ shrunkBy r s = r `intersection` divR s (conv r)
484-- r ``overriddenBy`` r == r
484-- r ``overriddenBy`` r == r
485-- @
485-- @
486overriddenBy ::
486overriddenBy ::
487− ( FLN b b,
487+ ( FromListsN b b,
488 CountableN b
488 CountableN b
489 ) => Relation a b -> Relation a b -> Relation a b
489 ) => Relation a b -> Relation a b -> Relation a b
490overriddenBy r s = s `union` r `intersection` divR zeros (conv s)
490overriddenBy r s = s `union` r `intersection` divR zeros (conv s)
@@ -496,11 +496,11 @@ overriddenBy r s = s `union` r `intersection` divR zeros (conv s)
496pointAp ::
496pointAp ::
497 ( Liftable a b,
497 ( Liftable a b,
498 Eq a,
498 Eq a,
499− CountableDimsN a b,
499+ CountableDimensionsN a b,
500− FLN a One,
500+ FromListsN a One,
501− FLN b One
501+ FromListsN b One
502 ) => a -> b -> Relation a b -> Relation One One
502 ) => a -> b -> Relation a b -> Relation One One
503−pointAp a b r = conv (point b) . r . point a
503+pointAp a b r = conv (point b) `comp` r `comp` point a
504
504
505-- | Relational application
505-- | Relational application
506--
506--
@@ -508,11 +508,11 @@ pointAp a b r = conv (point b) . r . point a
508pointApBool ::
508pointApBool ::
509 ( Liftable a b,
509 ( Liftable a b,
510 Eq a,
510 Eq a,
511− CountableDimsN a b,
511+ CountableDimensionsN a b,
512− FLN a One,
512+ FromListsN a One,
513− FLN b One
513+ FromListsN b One
514 ) => a -> b -> Relation a b -> Bool
514 ) => a -> b -> Relation a b -> Bool
515−pointApBool a b r = toBool $ conv (point b) . r . point a
515+pointApBool a b r = toBool $ conv (point b) `comp` r `comp` point a
516
516
517-- | Relational converse
517-- | Relational converse
518--
518--
@@ -538,7 +538,7 @@ iff r s = r == s
538
538
539-- | Relational intersection
539-- | Relational intersection
540--
540--
541−-- Lifts pointwise conjointion.
541+-- Lifts pointwise conjunction.
542--
542--
543-- @
543-- @
544-- (r ``intersection`` s) ``intersection`` t == r ``intersection`` (s ``intersection`` t)
544-- (r ``intersection`` s) ``intersection`` t == r ``intersection`` (s ``intersection`` t)
@@ -549,13 +549,13 @@ intersection a b = a * b
549
549
550-- | Relational union
550-- | Relational union
551--
551--
552−-- Lifts pointwise disjointion.
552+-- Lifts pointwise disjunction.
553--
553--
554-- @
554-- @
555-- (r ``union`` s) ``union`` t == r `'union' (s ``union`` t)
555-- (r ``union`` s) ``union`` t == r `'union' (s ``union`` t)
556-- r ``union`` s ``sse`` x == r ``sse`` x && s ``sse`` x
556-- r ``union`` s ``sse`` x == r ``sse`` x && s ``sse`` x
557−-- r `.` (s ``union`` t) == (r `.` s) ``union`` (r `.` t)
557+-- r ``comp`` (s ``union`` t) == (r ``comp`` s) ``union`` (r ``comp`` t)
558−-- (s ``union`` t) `.` r == (s `.` r) ``union`` (t `.` r)
558+-- (s ``union`` t) ``comp`` r == (s ``comp`` r) ``union`` (t ``comp`` r)
559-- @
559-- @
560union :: Relation a b -> Relation a b -> Relation a b
560union :: Relation a b -> Relation a b -> Relation a b
561union a b = a + b
561union a b = a + b
@@ -563,46 +563,46 @@ union a b = a + b
563-- | Relation Kernel
563-- | Relation Kernel
564--
564--
565-- @
565-- @
566−-- 'ker' r == 'conv' r `.` r
566+-- 'ker' r == 'conv' r ``comp`` r
567-- 'ker' r == 'img' ('conv' r)
567-- 'ker' r == 'img' ('conv' r)
568-- @
568-- @
569ker :: Relation a b -> Relation a a
569ker :: Relation a b -> Relation a a
570−ker r = conv r . r
570+ker r = conv r `comp` r
571
571
572-- | Relation Image
572-- | Relation Image
573--
573--
574-- @
574-- @
575−-- 'img' r == r `.` conv r
575+-- 'img' r == r ``comp`` conv r
576-- 'img' r == 'ker' ('conv' r)
576-- 'img' r == 'ker' ('conv' r)
577-- @
577-- @
578img :: Relation a b -> Relation b b
578img :: Relation a b -> Relation b b
579−img r = r . conv r
579+img r = r `comp` conv r
580
580
581-- | Function division. Special case of 'divS'.
581-- | Function division. Special case of 'divS'.
582--
582--
583-- NOTE: _This is only valid_ if @f@ and @g@ are 'function's, i.e. 'simple' and
583-- NOTE: _This is only valid_ if @f@ and @g@ are 'function's, i.e. 'simple' and
584-- 'entire'.
584-- 'entire'.
585--
585--
586−-- @'divisionF' f g == 'conv' g `.` f@
586+-- @'divisionF' f g == 'conv' g ``comp`` f@
587divisionF :: Relation a c -> Relation b c -> Relation a b
587divisionF :: Relation a c -> Relation b c -> Relation a b
588−divisionF f g = conv g . f
588+divisionF f g = conv g `comp` f
589
589
590-- Taxonomy of binary relations
590-- Taxonomy of binary relations
591
591
592-- | A 'Relation' @r@ is 'simple' 'iff' @'coreflexive' ('img' r)@
592-- | A 'Relation' @r@ is 'simple' 'iff' @'coreflexive' ('img' r)@
593−simple :: (CountableN b, FLN b b) => Relation a b -> Bool
593+simple :: (CountableN b, FromListsN b b) => Relation a b -> Bool
594simple = coreflexive . img
594simple = coreflexive . img
595
595
596-- | A 'Relation' @r@ is 'injective' 'iff' @'coreflexive' ('ker' r)@
596-- | A 'Relation' @r@ is 'injective' 'iff' @'coreflexive' ('ker' r)@
597−injective :: (CountableN a, FLN a a) => Relation a b -> Bool
597+injective :: (CountableN a, FromListsN a a) => Relation a b -> Bool
598injective = coreflexive . ker
598injective = coreflexive . ker
599
599
600-- | A 'Relation' @r@ is 'entire' 'iff' @'reflexive' ('ker' r)@
600-- | A 'Relation' @r@ is 'entire' 'iff' @'reflexive' ('ker' r)@
601−entire :: (CountableN a, FLN a a) => Relation a b -> Bool
601+entire :: (CountableN a, FromListsN a a) => Relation a b -> Bool
602entire = reflexive . ker
602entire = reflexive . ker
603
603
604-- | A 'Relation' @r@ is 'surjective' 'iff' @'reflexive' ('img' r)@
604-- | A 'Relation' @r@ is 'surjective' 'iff' @'reflexive' ('img' r)@
605−surjective :: (CountableN b, FLN b b) => Relation a b -> Bool
605+surjective :: (CountableN b, FromListsN b b) => Relation a b -> Bool
606surjective = reflexive . img
606surjective = reflexive . img
607
607
608-- | A 'Relation' @r@ is a 'function' 'iff' @'simple' r && 'entire' r@
608-- | A 'Relation' @r@ is a 'function' 'iff' @'simple' r && 'entire' r@
@@ -611,13 +611,13 @@ surjective = reflexive . img
611-- relations:
611-- relations:
612--
612--
613-- @
613-- @
614−-- f `.` r ``sse`` s == r ``sse`` f `.` s
614+-- f ``comp`` r ``sse`` s == r ``sse`` f ``comp`` s
615−-- r `.` f ``sse`` s == r ``sse`` s `.` f
615+-- r ``comp`` f ``sse`` s == r ``sse`` s ``comp`` f
616-- @
616-- @
617function ::
617function ::
618− ( CountableDimsN a b,
618+ ( CountableDimensionsN a b,
619− FLN a a,
619+ FromListsN a a,
620− FLN b b
620+ FromListsN b b
621 )
621 )
622 => Relation a b -> Bool
622 => Relation a b -> Bool
623function r = simple r && entire r
623function r = simple r && entire r
@@ -625,7 +625,7 @@ function r = simple r && entire r
625-- | A 'Relation' @r@ is a 'representation' 'iff' @'injective' r && 'entire' r@
625-- | A 'Relation' @r@ is a 'representation' 'iff' @'injective' r && 'entire' r@
626representation ::
626representation ::
627 ( CountableN a,
627 ( CountableN a,
628− FLN a a
628+ FromListsN a a
629 )
629 )
630 => Relation a b -> Bool
630 => Relation a b -> Bool
631representation r = injective r && entire r
631representation r = injective r && entire r
@@ -633,91 +633,91 @@ representation r = injective r && entire r
633-- | A 'Relation' @r@ is an 'abstraction' 'iff' @'surjective' r && 'simple' r@
633-- | A 'Relation' @r@ is an 'abstraction' 'iff' @'surjective' r && 'simple' r@
634abstraction ::
634abstraction ::
635 ( CountableN b,
635 ( CountableN b,
636− FLN b b
636+ FromListsN b b
637 )
637 )
638 => Relation a b -> Bool
638 => Relation a b -> Bool
639abstraction r = surjective r && simple r
639abstraction r = surjective r && simple r
640
640
641-- | A 'Relation' @r@ is a 'surjection' 'iff' @'function' r && 'abstraction' r@
641-- | A 'Relation' @r@ is a 'surjection' 'iff' @'function' r && 'abstraction' r@
642surjection ::
642surjection ::
643− ( CountableDimsN a b,
643+ ( CountableDimensionsN a b,
644− FLN a a,
644+ FromListsN a a,
645− FLN b b
645+ FromListsN b b
646 )
646 )
647 => Relation a b -> Bool
647 => Relation a b -> Bool
648surjection r = function r && abstraction r
648surjection r = function r && abstraction r
649
649
650-- | A 'Relation' @r@ is a 'injection' 'iff' @'function' r && 'representation' r@
650-- | A 'Relation' @r@ is a 'injection' 'iff' @'function' r && 'representation' r@
651injection ::
651injection ::
652− ( CountableDimsN a b,
652+ ( CountableDimensionsN a b,
653− FLN a a,
653+ FromListsN a a,
654− FLN b b
654+ FromListsN b b
655 )
655 )
656 => Relation a b -> Bool
656 => Relation a b -> Bool
657injection r = function r && representation r
657injection r = function r && representation r
658
658
659-- | A 'Relation' @r@ is an 'bijection' 'iff' @'injection' r && 'surjection' r@
659-- | A 'Relation' @r@ is an 'bijection' 'iff' @'injection' r && 'surjection' r@
660bijection ::
660bijection ::
661− ( CountableDimsN a b,
661+ ( CountableDimensionsN a b,
662− FLN b b,
662+ FromListsN b b,
663− FLN a a
663+ FromListsN a a
664 ) => Relation a b -> Bool
664 ) => Relation a b -> Bool
665bijection r = injection r && surjection r
665bijection r = injection r && surjection r
666
666
667-- Properties of relations
667-- Properties of relations
668
668
669−-- | A 'Relation' @r@ is 'reflexive' 'iff' @'id' ``sse`` r@
669+-- | A 'Relation' @r@ is 'reflexive' 'iff' @'identity' ``sse`` r@
670−reflexive :: (CountableN a, FLN a a) => Relation a a -> Bool
670+reflexive :: (CountableN a, FromListsN a a) => Relation a a -> Bool
671−reflexive r = id <= r
671+reflexive r = identity <= r
672
672
673−-- | A 'Relation' @r@ is 'coreflexive' 'iff' @r ``sse`` 'id'@
673+-- | A 'Relation' @r@ is 'coreflexive' 'iff' @r ``sse`` 'identity'@
674−coreflexive :: (CountableN a, FLN a a) => Relation a a -> Bool
674+coreflexive :: (CountableN a, FromListsN a a) => Relation a a -> Bool
675−coreflexive r = r <= id
675+coreflexive r = r <= identity
676
676
677−-- | A 'Relation' @r@ is 'transitive' 'iff' @(r `.` r) ``sse`` r@
677+-- | A 'Relation' @r@ is 'transitive' 'iff' @(r ``comp`` r) ``sse`` r@
678transitive :: Relation a a -> Bool
678transitive :: Relation a a -> Bool
679−transitive r = (r . r) `sse` r
679+transitive r = (r `comp` r) `sse` r
680
680
681-- | A 'Relation' @r@ is 'symmetric' 'iff' @r == 'conv' r@
681-- | A 'Relation' @r@ is 'symmetric' 'iff' @r == 'conv' r@
682symmetric :: Relation a a -> Bool
682symmetric :: Relation a a -> Bool
683symmetric r = r == conv r
683symmetric r = r == conv r
684
684
685−-- | A 'Relation' @r@ is anti-symmetric 'iff' @(r ``intersection`` 'conv' r) ``sse`` 'id'@
685+-- | A 'Relation' @r@ is anti-symmetric 'iff' @(r ``intersection`` 'conv' r) ``sse`` 'identity'@
686−antiSymmetric :: (CountableN a, FLN a a) => Relation a a -> Bool
686+antiSymmetric :: (CountableN a, FromListsN a a) => Relation a a -> Bool
687−antiSymmetric r = (r `intersection` conv r) `sse` id
687+antiSymmetric r = (r `intersection` conv r) `sse` identity
688
688
689−-- | A 'Relation' @r@ is 'irreflexive' 'iff' @(r ``intersection`` 'id') == 'zeros'@
689+-- | A 'Relation' @r@ is 'irreflexive' 'iff' @(r ``intersection`` 'identity') == 'zeros'@
690−irreflexive :: (CountableN a, FLN a a) => Relation a a -> Bool
690+irreflexive :: (CountableN a, FromListsN a a) => Relation a a -> Bool
691−irreflexive r = (r `intersection` id) == zeros
691+irreflexive r = (r `intersection` identity) == zeros
692
692
693-- | A 'Relation' @r@ is 'connected' 'iff' @(r ``union`` 'conv' r) == 'ones'@
693-- | A 'Relation' @r@ is 'connected' 'iff' @(r ``union`` 'conv' r) == 'ones'@
694−connected :: (CountableN a, FLN a a) => Relation a a -> Bool
694+connected :: (CountableN a, FromListsN a a) => Relation a a -> Bool
695connected r = (r `union` conv r) == ones
695connected r = (r `union` conv r) == ones
696
696
697-- | A 'Relation' @r@ is a 'preorder' 'iff' @'reflexive' r && 'transitive' r@
697-- | A 'Relation' @r@ is a 'preorder' 'iff' @'reflexive' r && 'transitive' r@
698−preorder :: (CountableN a, FLN a a) => Relation a a -> Bool
698+preorder :: (CountableN a, FromListsN a a) => Relation a a -> Bool
699preorder r = reflexive r && transitive r
699preorder r = reflexive r && transitive r
700
700
701-- | A 'Relation' @r@ is a partial-order 'iff' @'antiSymmetric' r && 'preorder' r@
701-- | A 'Relation' @r@ is a partial-order 'iff' @'antiSymmetric' r && 'preorder' r@
702−partialOrder :: (CountableN a, FLN a a) => Relation a a -> Bool
702+partialOrder :: (CountableN a, FromListsN a a) => Relation a a -> Bool
703partialOrder r = antiSymmetric r && preorder r
703partialOrder r = antiSymmetric r && preorder r
704
704
705-- | A 'Relation' @r@ is a linear-order 'iff' @'connected' r && 'partialOrder' r@
705-- | A 'Relation' @r@ is a linear-order 'iff' @'connected' r && 'partialOrder' r@
706−linearOrder :: (CountableN a, FLN a a) => Relation a a -> Bool
706+linearOrder :: (CountableN a, FromListsN a a) => Relation a a -> Bool
707linearOrder r = connected r && partialOrder r
707linearOrder r = connected r && partialOrder r
708
708
709-- | A 'Relation' @r@ is an 'equivalence' 'iff' @'symmetric' r && 'preorder' r@
709-- | A 'Relation' @r@ is an 'equivalence' 'iff' @'symmetric' r && 'preorder' r@
710−equivalence :: (CountableN a, FLN a a) => Relation a a -> Bool
710+equivalence :: (CountableN a, FromListsN a a) => Relation a a -> Bool
711equivalence r = symmetric r && preorder r
711equivalence r = symmetric r && preorder r
712
712
713-- | A 'Relation' @r@ is a partial-equivalence 'iff' @'partialOrder' r && 'equivalence' r@
713-- | A 'Relation' @r@ is a partial-equivalence 'iff' @'partialOrder' r && 'equivalence' r@
714−partialEquivalence :: (CountableN a, FLN a a) => Relation a a -> Bool
714+partialEquivalence :: (CountableN a, FromListsN a a) => Relation a a -> Bool
715partialEquivalence r = partialOrder r && equivalence r
715partialEquivalence r = partialOrder r && equivalence r
716
716
717-- | A 'Relation' @r@ is 'difunctional' or regular wherever
717-- | A 'Relation' @r@ is 'difunctional' or regular wherever
718−-- @r `.` 'conv' r `.` r == r@
718+-- @r ``comp`` 'conv' r ``comp`` r == r@
719difunctional :: Relation a b -> Bool
719difunctional :: Relation a b -> Bool
720−difunctional r = r . conv r . r == r
720+difunctional r = r `comp` conv r `comp` r == r
721
721
722-- Relational pairing
722-- Relational pairing
723
723
@@ -726,61 +726,61 @@ difunctional r = r . conv r . r == r
726-- NOTE: That this is not a true categorical product, see for instance:
726-- NOTE: That this is not a true categorical product, see for instance:
727--
727--
728-- @
728-- @
729−-- | 'fstR' `.` 'splitR' a b ``sse`` a
729+-- | 'p1' ``comp`` 'splitR' a b ``sse`` a
730-- 'splitR' a b <=> |
730-- 'splitR' a b <=> |
731−-- | 'sndR' `.` 'splitR' a b ``sse`` b
731+-- | 'p2' ``comp`` 'splitR' a b ``sse`` b
732-- @
732-- @
733--
733--
734-- __Emphasis__ on the 'sse'.
734-- __Emphasis__ on the 'sse'.
735--
735--
736-- @
736-- @
737−-- 'splitR' r s `.` f == 'splitR' (r `.` f) (s `.` f)
737+-- 'splitR' r s ``comp`` f == 'splitR' (r ``comp`` f) (s ``comp`` f)
738−-- (R '><' S) `.` 'splitR' p q == 'splitR' (r `.` p) (s `.` q)
738+-- (R '><' S) ``comp`` 'splitR' p q == 'splitR' (r ``comp`` p) (s ``comp`` q)
739−-- 'conv' ('splitR' r s) `.` 'splitR' x y == ('conv' r `.` x) ``intersection`` ('conv' s `.` y)
739+-- 'conv' ('splitR' r s) ``comp`` 'splitR' x y == ('conv' r ``comp`` x) ``intersection`` ('conv' s ``comp`` y)
740-- @
740-- @
741--
741--
742-- @
742-- @
743-- 'eitherR' ('splitR' r s) ('splitR' t v) == 'splitR' ('eitherR' r t) ('eitherR' s v)
743-- 'eitherR' ('splitR' r s) ('splitR' t v) == 'splitR' ('eitherR' r t) ('eitherR' s v)
744-- @
744-- @
745splitR ::
745splitR ::
746− ( CountableDimsN a b,
746+ ( CountableDimensionsN a b,
747 CountableN (a, b),
747 CountableN (a, b),
748− FLN (a, b) a,
748+ FromListsN (a, b) a,
749− FLN (a, b) b,
749+ FromListsN (a, b) b,
750 TrivialP a b
750 TrivialP a b
751 )
751 )
752 => Relation c a -> Relation c b -> Relation c (a, b)
752 => Relation c a -> Relation c b -> Relation c (a, b)
753−splitR (R f) (R g) = R (I.kr f g)
753+splitR (R f) (R g) = R (I.khatri f g)
754
754
755-- | Relational pairing first component projection
755-- | Relational pairing first component projection
756--
756--
757-- @
757-- @
758−-- 'fstR' `.` 'splitR' r s ``sse`` r
758+-- 'p1' ``comp`` 'splitR' r s ``sse`` r
759-- @
759-- @
760−fstR ::
760+p1 ::
761 forall a b .
761 forall a b .
762− ( CountableDimsN a b,
762+ ( CountableDimensionsN a b,
763 CountableN (a, b),
763 CountableN (a, b),
764− FLN (a, b) a,
764+ FromListsN (a, b) a,
765 TrivialP a b
765 TrivialP a b
766 )
766 )
767 => Relation (a, b) a
767 => Relation (a, b) a
768−fstR = R (I.fstM @Boolean @(I.Normalize a) @(I.Normalize b))
768+p1 = R (I.kp1 @Boolean @(I.Normalize a) @(I.Normalize b))
769
769
770-- | Relational pairing second component projection
770-- | Relational pairing second component projection
771--
771--
772-- @
772-- @
773−-- 'sndR' `.` 'splitR' r s ``sse`` s
773+-- 'p2' ``comp`` 'splitR' r s ``sse`` s
774-- @
774-- @
775−sndR ::
775+p2 ::
776 forall a b .
776 forall a b .
777− ( CountableDimsN a b,
777+ ( CountableDimensionsN a b,
778 CountableN (a, b),
778 CountableN (a, b),
779− FLN (a, b) b,
779+ FromListsN (a, b) b,
780 TrivialP a b
780 TrivialP a b
781 )
781 )
782 => Relation (a, b) b
782 => Relation (a, b) b
783−sndR = R (I.sndM @Boolean @(I.Normalize a) @(I.Normalize b))
783+p2 = R (I.kp2 @Boolean @(I.Normalize a) @(I.Normalize b))
784
784
785-- Relational pairing functor
785-- Relational pairing functor
786
786
@@ -788,17 +788,17 @@ infixl 4 ><
788-- | Relational pairing functor
788-- | Relational pairing functor
789--
789--
790-- @
790-- @
791−-- r '><' s == 'splitR' (r `.` fstR) (s `.` sndR)
791+-- r '><' s == 'splitR' (r ``comp`` p1) (s ``comp`` p2)
792−-- (r '><' s) `.` (p '><' q) == (r `.` p) '><' (s `.` q)
792+-- (r '><' s) ``comp`` (p '><' q) == (r ``comp`` p) '><' (s ``comp`` q)
793-- @
793-- @
794(><) ::
794(><) ::
795− ( CountableDimsN a b,
795+ ( CountableDimensionsN a b,
796− CountableDimsN c d,
796+ CountableDimensionsN c d,
797− CountableDimsN (a, c) (b, d),
797+ CountableDimensionsN (a, c) (b, d),
798− FLN (a, c) a,
798+ FromListsN (a, c) a,
799− FLN (a, c) c,
799+ FromListsN (a, c) c,
800− FLN (b, d) b,
800+ FromListsN (b, d) b,
801− FLN (b, d) d,
801+ FromListsN (b, d) d,
802 TrivialP a c,
802 TrivialP a c,
803 TrivialP b d
803 TrivialP b d
804 )
804 )
@@ -810,31 +810,33 @@ infixl 4 ><
810-- | Relational coproduct.
810-- | Relational coproduct.
811--
811--
812-- @
812-- @
813−-- | 'eitherR' a b `.` 'i1' == a
813+-- | 'eitherR' a b ``comp`` 'i1' == a
814-- 'eitherR' a b <=> |
814-- 'eitherR' a b <=> |
815−-- | 'eitherR' a b `.` 'i2' == b
815+-- | 'eitherR' a b ``comp`` 'i2' == b
816-- @
816-- @
817--
817--
818-- @
818-- @
819−-- 'eitherR' r s `.` 'conv' ('eitherR' t u) == (r `.` 'conv' t) ``union`` (s `.` 'conv' u)
819+-- 'eitherR' r s ``comp`` 'conv' ('eitherR' t u) == (r ``comp`` 'conv' t) ``union`` (s ``comp`` 'conv' u)
820-- @
820-- @
821--
821--
822-- @
822-- @
823-- 'eitherR' ('splitR' r s) ('splitR' t v) == 'splitR' ('eitherR' r t) ('eitherR' s v)
823-- 'eitherR' ('splitR' r s) ('splitR' t v) == 'splitR' ('eitherR' r t) ('eitherR' s v)
824-- @
824-- @
825+eitherR :: (TrivialE a b)
825−eitherR :: Relation a c -> Relation b c -> Relation (Either a b) c
826+ => Relation a c -> Relation b c -> Relation (Either a b) c
826−eitherR = join
827+eitherR = junc
827
828
828-- | Relational coproduct first component injection
829-- | Relational coproduct first component injection
829--
830--
830-- @
831-- @
831−-- 'img' 'i1' ``union`` 'img' 'i2' == 'id'
832+-- 'img' 'i1' ``union`` 'img' 'i2' == 'identity'
832−-- 'i1' `.` 'i2' = 'zeros'
833+-- 'i1' ``comp`` 'i2' = 'zeros'
833-- @
834-- @
834i1 ::
835i1 ::
835− ( CountableDimsN a b,
836+ ( CountableDimensionsN a b,
836− FLN b a,
837+ FromListsN b a,
837− FLN a a
838+ FromListsN a a,
839+ TrivialE a b
838 )
840 )
839 => Relation a (Either a b)
841 => Relation a (Either a b)
840i1 = R I.i1
842i1 = R I.i1
@@ -842,13 +844,14 @@ i1 = R I.i1
842-- | Relational coproduct second component injection
844-- | Relational coproduct second component injection
843--
845--
844-- @
846-- @
845−-- 'img' 'i1' ``union`` 'img' 'i2' == 'id'
847+-- 'img' 'i1' ``union`` 'img' 'i2' == 'identity'
846−-- 'i1' `.` 'i2' = 'zeros'
848+-- 'i1' ``comp`` 'i2' = 'zeros'
847-- @
849-- @
848i2 ::
850i2 ::
849− ( CountableDimsN a b,
851+ ( CountableDimensionsN a b,
850− FLN a b,
852+ FromListsN a b,
851− FLN b b
853+ FromListsN b b,
854+ TrivialE a b
852 )
855 )
853 => Relation b (Either a b)
856 => Relation b (Either a b)
854i2 = R I.i2
857i2 = R I.i2
@@ -858,14 +861,16 @@ infixl 5 -|-
858-- | Relational coproduct functor.
861-- | Relational coproduct functor.
859--
862--
860-- @
863-- @
861−-- r '-|-' s == 'eitherR' ('i1' `.` r) ('i2' `.` s)
864+-- r '-|-' s == 'eitherR' ('i1' ``comp`` r) ('i2' ``comp`` s)
862-- @
865-- @
863(-|-) ::
866(-|-) ::
864− ( CountableDimsN b d,
867+ ( CountableDimensionsN b d,
865− FLN b b,
868+ FromListsN b b,
866− FLN d b,
869+ FromListsN d b,
867− FLN b d,
870+ FromListsN b d,
868− FLN d d
871+ FromListsN d d,
872+ TrivialE a c,
873+ TrivialE b d
869 )
874 )
870 => Relation a b -> Relation c d -> Relation (Either a c) (Either b d)
875 => Relation a b -> Relation c d -> Relation (Either a c) (Either b d)
871(-|-) (R a) (R b) = R ((I.-|-) a b)
876(-|-) (R a) (R b) = R ((I.-|-) a b)
@@ -878,20 +883,20 @@ infixl 5 -|-
878-- 'trans'/'untrans';
883-- 'trans'/'untrans';
879-- more-over, where each particular attribute is placed (input/output) is irrelevant.
884-- more-over, where each particular attribute is placed (input/output) is irrelevant.
880trans ::
885trans ::
881− ( CountableDimsN a b,
886+ ( CountableDimensionsN a b,
882 CountableN c,
887 CountableN c,
883− CountableDimsN (a, b) (c, b),
888+ CountableDimensionsN (a, b) (c, b),
884− FLN (c, b) c,
889+ FromListsN (c, b) c,
885− FLN (c, b) b,
890+ FromListsN (c, b) b,
886− FLN (a, b) a,
891+ FromListsN (a, b) a,
887− FLN (a, b) b,
892+ FromListsN (a, b) b,
888 Trivial (a, b),
893 Trivial (a, b),
889 Trivial (c, b),
894 Trivial (c, b),
890− TrivialP a b,
895+ TrivialP2 a b,
891− TrivialP c b
896+ TrivialP2 c b
892 )
897 )
893 => Relation (a, b) c -> Relation a (c, b)
898 => Relation (a, b) c -> Relation a (c, b)
894−trans r = splitR r sndR . conv fstR
899+trans r = splitR r p2 `comp` conv p1
895
900
896-- | Relational 'untrans'
901-- | Relational 'untrans'
897--
902--
@@ -899,110 +904,109 @@ trans r = splitR r sndR . conv fstR
899-- 'trans'/'untrans';
904-- 'trans'/'untrans';
900-- more-over, where each particular attribute is placed (input/output) is irrelevant.
905-- more-over, where each particular attribute is placed (input/output) is irrelevant.
901untrans ::
906untrans ::
902− ( CountableDimsN a b,
907+ ( CountableDimensionsN a b,
903 CountableN c,
908 CountableN c,
904− CountableDimsN (a, b) (c, b),
909+ CountableDimensionsN (a, b) (c, b),
905− FLN (c, b) c,
910+ FromListsN (c, b) c,
906− FLN (c, b) b,
911+ FromListsN (c, b) b,
907− FLN (a, b) b,
912+ FromListsN (a, b) b,
908− FLN (a, b) a,
913+ FromListsN (a, b) a,
909 Trivial (a, b),
914 Trivial (a, b),
910 Trivial (c, b),
915 Trivial (c, b),
911− TrivialP a b,
916+ TrivialP2 a b,
912− TrivialP c b
917+ TrivialP2 c b
913 )
918 )
914 => Relation a (c, b) -> Relation (a, b) c
919 => Relation a (c, b) -> Relation (a, b) c
915−untrans s = fstR . conv (splitR (conv s) sndR)
920+untrans s = p1 `comp` conv (splitR (conv s) p2)
916
921
917-- | Transforms predicate @p@ into a correflexive relation.
922-- | Transforms predicate @p@ into a correflexive relation.
918--
923--
919-- @
924-- @
920−-- 'predR' ('const' True) == 'id'
925+-- 'predR' ('const' True) == 'identity'
921-- 'predR' ('const' False) == 'zeros'
926-- 'predR' ('const' False) == 'zeros'
922-- @
927-- @
923--
928--
924-- @
929-- @
925−-- 'predR' q `.` 'predR' p == 'predR' q ``union`` 'predR' p
930+-- 'predR' q ``comp`` 'predR' p == 'predR' q ``union`` 'predR' p
926-- @
931-- @
927predR ::
932predR ::
928 ( Bounded a,
933 ( Bounded a,
929 Enum a,
934 Enum a,
930− Countable a,
931 CountableN a,
935 CountableN a,
932− FLN a a,
936+ FromListsN a a,
933− FLN Bool a
937+ FromListsN Bool a
934 )
938 )
935 => Relation a Bool -> Relation a a
939 => Relation a Bool -> Relation a a
936−predR p = id `intersection` divisionF (fromF (const True)) p
940+predR p = identity `intersection` divisionF (fromF' (const True)) p
937
941
938-- | Equalizes functions @f@ and @g@.
942-- | Equalizes functions @f@ and @g@.
939-- That is, @'equalizer' f g@ is the largest coreflexive
943-- That is, @'equalizer' f g@ is the largest coreflexive
940-- that restricts @g@ so that @f@ and @g@ yield the same outputs.
944-- that restricts @g@ so that @f@ and @g@ yield the same outputs.
941--
945--
942-- @
946-- @
943−-- 'equalizer' r r == 'id'
947+-- 'equalizer' r r == 'identity'
944-- 'equalizer' ('point' True) ('point' False) == 'zeros'
948-- 'equalizer' ('point' True) ('point' False) == 'zeros'
945-- @
949-- @
946equalizer ::
950equalizer ::
947 ( CountableN a,
951 ( CountableN a,
948− FLN a a
952+ FromListsN a a
949 )
953 )
950 => Relation a b -> Relation a b -> Relation a a
954 => Relation a b -> Relation a b -> Relation a a
951−equalizer f g = id `intersection` divisionF f g
955+equalizer f g = identity `intersection` divisionF f g
952
956
953-- | Relational conditional guard.
957-- | Relational conditional guard.
954--
958--
955-- @
959-- @
956−-- 'guard' p = 'i2' ``overriddenBy`` 'i1' `.` 'predR' p
960+-- 'guard' p = 'i2' ``overriddenBy`` 'i1' ``comp`` 'predR' p
957-- @
961-- @
958−guard ::
962+guard ::
959 ( Bounded b,
963 ( Bounded b,
960 Enum b,
964 Enum b,
961 CountableN b,
965 CountableN b,
962− Countable b,
966+ FromListsN b b,
963− FLN b b,
964− FLN Bool b
967+ FromListsN Bool b,
968+ TrivialE b b
965 ) => Relation b Bool -> Relation b (Either b b)
969 ) => Relation b Bool -> Relation b (Either b b)
966guard p = conv (eitherR (predR p) (predR (negate p)))
970guard p = conv (eitherR (predR p) (predR (negate p)))
967
971
968-- | Relational McCarthy's conditional.
972-- | Relational McCarthy's conditional.
969−cond ::
973+cond ::
970 ( Bounded b,
974 ( Bounded b,
971 Enum b,
975 Enum b,
972− Countable b,
973 CountableN b,
976 CountableN b,
974− FLN b b,
977+ FromListsN b b,
975− FLN Bool b
978+ FromListsN Bool b,
979+ TrivialE b b
976− )
980+ )
977 => Relation b Bool -> Relation b c -> Relation b c -> Relation b c
981 => Relation b Bool -> Relation b c -> Relation b c -> Relation b c
978−cond p r s = eitherR r s . guard p
982+cond p r s = eitherR r s `comp` guard p
979
983
980-- | Relational domain.
984-- | Relational domain.
981--
985--
982-- For injective relations, 'domain' and 'ker'nel coincide,
986-- For injective relations, 'domain' and 'ker'nel coincide,
983−-- since @'ker' r ``sse`` 'id'@ in such situations.
987+-- since @'ker' r ``sse`` 'identity'@ in such situations.
984domain ::
988domain ::
985 ( CountableN a,
989 ( CountableN a,
986− FLN a a
990+ FromListsN a a
987 ) => Relation a b -> Relation a a
991 ) => Relation a b -> Relation a a
988−domain r = ker r `intersection` id
992+domain r = ker r `intersection` identity
989
993
990-- | Relational range.
994-- | Relational range.
991--
995--
992-- For functions, 'range' and 'img' (image) coincide,
996-- For functions, 'range' and 'img' (image) coincide,
993−-- since @'img' f ``sse`` id@ for any @f@.
997+-- since @'img' f ``sse`` 'identity'@ for any @f@.
994range ::
998range ::
995 ( CountableN b,
999 ( CountableN b,
996− FLN b b
1000+ FromListsN b b
997 ) => Relation a b -> Relation b b
1001 ) => Relation a b -> Relation b b
998−range r = img r `intersection` id
1002+range r = img r `intersection` identity
999
1003
1000-- Relation pretty print
1004-- Relation pretty print
1001
1005
1002-- | Relation pretty printing
1006-- | Relation pretty printing
1003−pretty :: (CountableDimsN a b) => Relation a b -> String
1007+pretty :: (CountableN a) => Relation a b -> String
1004pretty (R a) = I.pretty a
1008pretty (R a) = I.pretty a
1005
1009
1006-- | Relation pretty printing
1010-- | Relation pretty printing
1007−prettyPrint :: (CountableDimsN a b) => Relation a b -> IO ()
1011+prettyPrint :: (CountableN a) => Relation a b -> IO ()
1008prettyPrint (R a) = I.prettyPrint a
1012prettyPrint (R a) = I.prettyPrint a
src/LAoP/Utils.hs+2−5
@@ -95,11 +95,8 @@ module LAoP.Utils
95 coerceNat2,
95 coerceNat2,
96 coerceNat3,
96 coerceNat3,
97
97
98− -- * List data type
98+ -- * Powerset data type
99− List (..),
99+ List (..)
100−
101− -- * Category type-class
102− Category(..)
103 )
100 )
104where
101where
105
102
src/LAoP/Utils/Internal.hs+74−30
@@ -1,13 +1,83 @@
1−{-# LANGUAGE TypeFamilies #-}
2{-# LANGUAGE DeriveGeneric #-}
1{-# LANGUAGE DeriveGeneric #-}
3{-# LANGUAGE TypeApplications #-}
2{-# LANGUAGE TypeApplications #-}
4{-# LANGUAGE DataKinds #-}
3{-# LANGUAGE DataKinds #-}
5{-# LANGUAGE FlexibleInstances #-}
4{-# LANGUAGE FlexibleInstances #-}
6{-# LANGUAGE GeneralizedNewtypeDeriving #-}
5{-# LANGUAGE GeneralizedNewtypeDeriving #-}
6+{-# LANGUAGE KindSignatures #-}
7{-# LANGUAGE ScopedTypeVariables #-}
7{-# LANGUAGE ScopedTypeVariables #-}
8
8
9module LAoP.Utils.Internal
9module LAoP.Utils.Internal
10− (
10+ ( -- | This is an internal module and it is not meant to be imported.
11+ --
12+ -- Utility module that provides the 'Natural' data type.
13+ -- The semantic associated with this data type is that
14+ -- it's meant to be a restricted 'Int' value. For example
15+ -- the type @Natural 6@ can only be instanciated with @Nat n@
16+ -- where @0 <= n <= 6@. Why, You might ask, because with normal
17+ -- 'Int's it is not possible to have a decent @Enum (Int, Int)@
18+ -- instance. See the following probabilistic programming model as and
19+ -- example:
20+ --
21+ -- We want to calculate the probability of the sum of two dice throws.
22+ -- To do this we start by defining the sample space:
23+ --
24+ -- @
25+ -- type SampleSpace = Int -- We think 'Int' are enough
26+ --
27+ -- die :: Dist Int 6
28+ -- die = unifrom [1..6]
29+ --
30+ -- -- Promote 'Int' addition to a matrix
31+ -- addM = fromF (uncurry (+)) -- Impossible
32+ -- @
33+ --
34+ -- The last line is impossible because @(Int, Int)@ does not have
35+ -- a good 'Enum' instance: @[(0, 1), (0, 2), .. (0, maxBound), (1, 0),
36+ -- ..]@. And we'd like the addition matrix to be of 36 columns by 12
37+ -- rows but limited to integers up to @6@!
38+ --
39+ -- One way to solve this issue is by defining and auxilary data type to
40+ -- represent the sample space:
41+ --
42+ -- @
43+ -- data SampleSpace = S1 | S2 | S3 | S4 | S5 | S6
44+ -- deriving (Show, Eq, Enum, Bounded) -- Enum and Bounded are
45+ -- important
46+ -- @
47+ --
48+ -- And write the sample space addition function:
49+ --
50+ -- @
51+ -- ssAdd :: SampleSpace -> SampleSpace -> Int
52+ -- ssAdd a b = (fromEnum a + 1) + (fromEnum b + 1)
53+ -- @
54+ --
55+ -- And then promote that function to matrix and everything is alright:
56+ --
57+ -- @
58+ -- ssAddM = fromF' (uncurry ssAdd)
59+ --
60+ -- dieSumProb = ssAddM `comp` (khatri die die)
61+ -- @
62+ --
63+ -- This is a nice solution for small sample spaces. But for larger ones
64+ -- it is not feasible to write a data type with hundreds of constructors
65+ -- and then write manipulation functions that need to deal with them.
66+ -- To mitigate this limitation the 'Natural' type comes a long way and
67+ -- allows one to model the sample in an easier way. See for instance:
68+ --
69+ -- @
70+ -- ssAdd :: Natural 6 -> Natural 6 -> Natural 12
71+ -- ssAdd = coerceNat (+)
72+ --
73+ -- ssAddM = fromF' (uncurry sumSS)
74+ --
75+ -- die :: Dist (Natural 6) 6
76+ -- die = uniform [nat @6 1 .. nat 6]
77+ --
78+ -- dieSumProb = ssAddM `comp` (khatri die die)
79+ -- @
80+ --
11 -- * 'Natural' data type
81 -- * 'Natural' data type
12 Natural(..),
82 Natural(..),
13 nat,
83 nat,
@@ -18,11 +88,8 @@ module LAoP.Utils.Internal
18 coerceNat2,
88 coerceNat2,
19 coerceNat3,
89 coerceNat3,
20
90
21− -- * 'List' data type
91+ -- * Powerset data type
22− List (..),
92+ List (..)
23−
24− -- * Category type class
25− Category(..)
26 )
93 )
27where
94where
28
95
@@ -33,9 +100,6 @@ import Data.Maybe
33import GHC.TypeLits
100import GHC.TypeLits
34import Control.DeepSeq
101import Control.DeepSeq
35import GHC.Generics
102import GHC.Generics
36−import Data.Kind
37−import Prelude hiding (id, (.))
38−import qualified Prelude
39
103
40-- | Wrapper around 'Int's that have a restrictive semantic associated.
104-- | Wrapper around 'Int's that have a restrictive semantic associated.
41-- A value of type @'Natural' n m@ can only be instanciated with some 'Int'
105-- A value of type @'Natural' n m@ can only be instanciated with some 'Int'
@@ -174,23 +238,3 @@ instance
174 fromEnum (L x) =
238 fromEnum (L x) =
175 let as = [minBound .. maxBound]
239 let as = [minBound .. maxBound]
176 in fromMaybe (error "Does not exist") $ elemIndex x (powerset as)
240 in fromMaybe (error "Does not exist") $ elemIndex x (powerset as)
177−
178−-- | Constrained category instance
179−class Category k where
180− type Object k o :: Constraint
181− type Object k o = ()
182− id :: Object k a => k a a
183− (.) :: k b c -> k a b -> k a c
184−
185−{-# RULES
186−"identity/left" forall p .
187− id . p = p
188−"identity/right" forall p .
189− p . id = p
190−"association" forall p q r .
191− (p . q) . r = p . (q . r)
192− #-}
193−
194−instance Category (->) where
195− id = Prelude.id
196− (.) = (Prelude..)
stack-8.8.3.yamldeleted−1
@@ -1 +0,0 @@
1−resolver: lts-15.5
stack.yaml+66−1
@@ -1 +1,66 @@
1+# This file was automatically generated by 'stack init'
2+#
3+# Some commonly used options have been documented as comments in this file.
4+# For advanced use and comprehensive documentation of the format, please see:
5+# https://docs.haskellstack.org/en/stable/yaml_configuration/
6+
7+# Resolver to choose a 'specific' stackage snapshot or a compiler version.
8+# A snapshot resolver dictates the compiler version and the set of packages
9+# to be used for project dependencies. For example:
10+#
11+# resolver: lts-3.5
12+# resolver: nightly-2015-09-21
13+# resolver: ghc-7.10.2
14+#
15+# The location of a snapshot can be provided as a file or url. Stack assumes
16+# a snapshot provided as a file might change, whereas a url resource does not.
17+#
18+# resolver: ./custom-snapshot.yaml
19+# resolver: https://example.com/snapshots/2018-01-01.yaml
1−resolver: lts-14.3
20+resolver: lts-14.18
21+
22+# User packages to be built.
23+# Various formats can be used as shown in the example below.
24+#
25+# packages:
26+# - some-directory
27+# - https://example.com/foo/bar/baz-0.0.2.tar.gz
28+# subdirs:
29+# - auto-update
30+# - wai
31+packages:
32+- .
33+# Dependency packages to be pulled from upstream that are not in the resolver.
34+# These entries can reference officially published versions as well as
35+# forks / in-progress versions pinned to a git hash. For example:
36+#
37+# extra-deps:
38+# - acme-missiles-0.3
39+# - git: https://github.com/commercialhaskell/stack.git
40+# commit: e7b331f14bcffb8367cd58fbfc8b40ec7642100a
41+#
42+# extra-deps: []
43+
44+# Override default flag values for local packages and extra-deps
45+# flags: {}
46+
47+# Extra package databases containing global packages
48+# extra-package-dbs: []
49+
50+# Control whether we use the GHC we find on the path
51+# system-ghc: true
52+#
53+# Require a specific version of stack, using version ranges
54+# require-stack-version: -any # Default
55+# require-stack-version: ">=2.1"
56+#
57+# Override the architecture used by stack, especially useful on Windows
58+# arch: i386
59+# arch: x86_64
60+#
61+# Extra directories used by stack for building
62+# extra-include-dirs: [/path/to/dir]
63+# extra-lib-dirs: [/path/to/dir]
64+#
65+# Allow a newer minor version of GHC than the snapshot specifies
66+# compiler-check: newer-minor
stack.yaml.lock+4−4
@@ -6,7 +6,7 @@
6packages: []
6packages: []
7snapshots:
7snapshots:
8- completed:
8- completed:
9− size: 523878
9+ size: 524789
10− url: https://raw.githubusercontent.com/commercialhaskell/stackage-snapshots/master/lts/14/3.yaml
10+ url: https://raw.githubusercontent.com/commercialhaskell/stackage-snapshots/master/lts/14/18.yaml
11− sha256: 470c46c27746a48c7c50f829efc0cf00112787a7804ee4ac7a27754658f6d92c
11+ sha256: 646be71223e08234131c6989912e6011e01b9767bc447b6d466a35e14360bdf2
12− original: lts-14.3
12+ original: lts-14.18
test/Examples/Quantum.hsdeleted−31
@@ -1,31 +0,0 @@
1−{-# LANGUAGE StandaloneDeriving #-}
2−module Examples.Quantum where
3−
4−import LAoP.Utils
5−import LAoP.Matrix.Type
6−import Data.Complex
7−import Prelude hiding (id, (.))
8−
9−deriving instance Ord a => Ord (Complex a)
10−
11−xor :: (Bool, Bool) -> Bool
12−xor (False, b) = b
13−xor (True, b) = not b
14−
15−ker :: Num e => Matrix e a b -> Matrix e a a
16−ker m = tr m . m
17−
18−cnot :: Matrix (Complex Double) (Bool, Bool) (Bool, Bool)
19−cnot = kr fstM (fromF xor)
20−
21−ccnot :: (Num e, Ord e) => Matrix e ((Bool, Bool), Bool) ((Bool, Bool), Bool)
22−ccnot = kr fstM (fromF f)
23− where
24− f = xor . tp (uncurry (&&)) id
25− tp f g (a,b) = (f a, g b)
26−
27−had :: Matrix (Complex Double) Bool Bool
28−had = (1/sqrt 2) .| fromLists [[1, 1], [1, -1]]
29−
30−bell :: Matrix (Complex Double) (Bool, Bool) (Bool, Bool)
31−bell = cnot . (had >< iden)
test/Examples/Spreadsheets.hsdeleted−47
@@ -1,47 +0,0 @@
1−{-# LANGUAGE DeriveGeneric #-}
2−
3−module Examples.Spreadsheets
4−
5−import LAoP.Utils
6−import LAoP.Matrix.Type
7−import GHC.Generics
8−import Prelude hiding (id, (.))
9−
10−data Student = Student1 | Student2 | Student3 | Student4
11− deriving (Eq, Show, Enum, Bounded, Generic)
12−
13−data Question = Question1 | Question2 | Question3 | Question4
14− deriving (Eq, Show, Enum, Bounded, Generic)
15−
16−data Results = Exam | Test | Final
17− deriving (Eq, Show, Enum, Bounded, Generic)
18−
19−test :: Matrix Float One Results
20−test = point Test
21−
22−exam :: Matrix Float One Results
23−exam = point Exam
24−
25−final :: Matrix Float One Results
26−final = point Final
27−
28−m :: Matrix Float Question Student
29−m = fromLists [[95, 90, 100, 40], [20, 90, 90, 0], [30, 20, 95, 0], [50, 80, 100, 30]]
30−
31−w :: Matrix Float Question One
32−w = fromLists [[0.2, 0.3, 0.2, 0.3]]
33−
34−xls :: Matrix Float Question One
35− -> Matrix Float Question Student
36− -> Matrix Float Student One
37− -> Matrix Float (Either Question Results) (Either One Student)
38−xls w m t = join (fork w m) (fork zeros r)
39− where
40− rExam = m . tr w
41− rTest = tr t
42− rFinal = rTest `maxPW` rExam
43− r = (rExam . tr exam) + (rTest . tr test) + (rFinal . tr final)
44−
45−-- | Overloaded, point-wise 'max' function
46−maxPW :: Ord e => Matrix e a b -> Matrix e a b -> Matrix e a b
47−maxPW = zipWithM max
test/Spec.hs+1−7
@@ -1,8 +1,2 @@
1−module Main (main) where
2−
3−import qualified Examples.Readme as RD
4−
5main :: IO ()
1main :: IO ()
6−main = do
2+main = putStrLn "Test suite not yet implemented"
7− putStrLn ("Testing if README works" :: String)
8− RD.exec