on master help sign in
.ghc.environment.x86_64-linux-8.6.5deleted−17
since splitsnapshots
unifiedsplit
@@ -1,17 +0,0 @@
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.ymlnew file+43
@@ -0,0 +1,43 @@
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+54−2
@@ -1,3 +1,55 @@
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
1.stack-work/
25.stack-work/
2−laop.cabal
26+stack.yaml.lock
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]
3−*~
34+*~
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.ymlnew file+47
@@ -0,0 +1,47 @@
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.mdnew file+17
@@ -0,0 +1,17 @@
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.mddeleted−3
@@ -1,3 +0,0 @@
1−# Changelog for laop
2−
3−## Unreleased changes
LICENSE+17−26
@@ -1,30 +1,21 @@
1−Copyright Armando Santos (c) 2019
1+MIT License
2
2
3−All rights reserved.
3+Copyright (c) 2020 Armando Santos
4
4
5−Redistribution and use in source and binary forms, with or without
5+Permission is hereby granted, free of charge, to any person obtaining a copy
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
6−modification, are permitted provided that the following conditions are met:
10+furnished to do so, subject to the following conditions:
7
11
8− * Redistributions of source code must retain the above copyright
12+The above copyright notice and this permission notice shall be included in all
9− notice, this list of conditions and the following disclaimer.
13+copies or substantial portions of the Software.
10
14
11− * Redistributions in binary form must reproduce the above
15+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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
22−LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
16+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
23−A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
17+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
24−OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
18+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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
28−THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
19+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
29−(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
20+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
30−OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
21+SOFTWARE.
README.md+35−27
@@ -1,5 +1,11 @@
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+
3The LAoP discipline generalises relations and functions treating them as
9The LAoP discipline generalises relations and functions treating them as
4Boolean matrices and in turn consider these as arrows.
10Boolean matrices and in turn consider these as arrows.
5
11
@@ -10,36 +16,38 @@ motivation behind the library, the underlying theory, and implementation details
10This module offers many of the combinators mentioned in the work of
16This module offers many of the combinators mentioned in the work of
11[Macedo (2012)](https://repositorium.sdum.uminho.pt/handle/1822/22894) and [Oliveira (2012)](https://pdfs.semanticscholar.org/ccf5/27fa9179081223bffe8067edd81948644fc0.pdf).
17[Macedo (2012)](https://repositorium.sdum.uminho.pt/handle/1822/22894) and [Oliveira (2012)](https://pdfs.semanticscholar.org/ccf5/27fa9179081223bffe8067edd81948644fc0.pdf).
12
18
13−See the candidate package in hackage [here](https://hackage.haskell.org/package/laop-0.1.0.0)
19+See the package in hackage [here](https://hackage.haskell.org/package/laop-0.1.1.0)
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.
14
22
15## Features
23## Features
16
24
17−This library offers:
25+This library offers 3 main matrix programming modules:
18−
26+
19−- An internal module representation that uses normal datatypes (`Void`, `()`, `Either`) for matrix dimensions and two
27+- One in which matrices are typed with type level natural numbers;
20− type families `FromNat` and `Count` to make it easier to work with these type of matrices.
28+- One in which matrices are typed with arbitrary generic data types;
21−- An interfacing module that uses generalised types for the dimensions and is just a newtype wrapper
29+- One in which matrices are regarded as relations, i.e. boolean matrices;
22− around the internal matrix data type.
30+
23−- An interfacing module that uses type level naturals for the dimensions and is just a newtype wrapper
31+There's also an experimental module that uses matrices to represent probability
24− around the internal matrix data type.
32+distributions.
25−- An interfacing module that restricts the matrix contents to being only 0's or 1's (True
33+
26− and False). This module is called 'Relation' and offers many of the combinators seen in
34+The most interesting feature is that matrices are represented as an inductive data type.
27− AoP and Relational Calculus/Algebra.
35+Given this formulation, matrix algorithms can be expressed in a much more elegant and
28−- A very simple Probabilistic Programming module and several functions and data types to
36+calculational style than the traditional vector of vectors representation. This data type
29− make it easier to deal with sample space.
37+guarantees that a matrix will always have valid dimensions. It can also express block matrix
30−
38+computations naturally, which leads to total, efficient and statically typed manipulation
31−Given this, this new matrix formulation compared to other libraries one has much more advantages, such as:
39+and transformation functions.
32−
40+
33−- Has an inductive definition enabling writing matrix manipulation functions in a much more elegant and calculational way;
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.
34−- Statically typed dimensions;
42+
35−- Polymorphic data type dimensions;
43+Given this, this new matrix formulation compared to other libraries:
36−- Polymorphic matrix content;
44+
37−- Awesome dimension type inference;
45+- Is more compositional and polymorphic and does not have partial matrix manipulation functions (hence less chances for usage errors);
38−- Fast type natural conversion via `FromNat` type family;
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.
39−- Matrix `Junc` and `Split`-ing in O(1);
47+
40−- Matrix composition takes advantage of divide-and-conquer and fusion laws.
48+## Known issues
41−
49+
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.
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).
43
51
44## Notes
52## Notes
45
53
Setup.hsdeleted−2
@@ -1,2 +0,0 @@
1−import Distribution.Simple
2−main = defaultMain
app/Main.hsdeleted−7
@@ -1,7 +0,0 @@
1−module Main where
2−
3−import Examples
4−import Benchmarks
5−
6−main :: IO ()
7−main = benchmark
appveyor.ymlnew file+34
@@ -0,0 +1,34 @@
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
app/Benchmarks.hs → benchmark/Main.hsrenamed+16−18
@@ -8,38 +8,36 @@
8{-# LANGUAGE AllowAmbiguousTypes #-}
8{-# LANGUAGE AllowAmbiguousTypes #-}
9{-# LANGUAGE ScopedTypeVariables #-}
9{-# LANGUAGE ScopedTypeVariables #-}
10
10
11−module Benchmarks
12− ( benchmark
13− )
14− where
11+module Main (main) where
15
12
16import LAoP.Dist.Internal
13import LAoP.Dist.Internal
17import LAoP.Utils
14import LAoP.Utils
18−import LAoP.Matrix.Type hiding (CountableN, Countable, FromListsN)
15+import LAoP.Matrix.Type hiding (CountableN, Countable, FLN)
19−import qualified LAoP.Matrix.Type as T (FromListsN)
16+import qualified LAoP.Matrix.Type as T (FLN)
20import Criterion.Main
17import Criterion.Main
21import Control.DeepSeq
18import Control.DeepSeq
22import Test.QuickCheck
19import Test.QuickCheck
23import GHC.TypeLits
20import GHC.TypeLits
24import Data.Proxy
21import Data.Proxy
22+import Prelude hiding (id, (.))
25
23
26selectM2 ::
24selectM2 ::
27 ( Num e,
25 ( Num e,
28− T.FromListsN e b b,
26+ T.FLN b b,
29 CountableN b
27 CountableN b
30 ) => Matrix e cols (Either a b) -> Matrix e a b -> Matrix e cols b
28 ) => Matrix e cols (Either a b) -> Matrix e a b -> Matrix e cols b
31−selectM2 m y = junc y identity `comp` m
29+selectM2 m y = join y iden `comp` m
32
30
33selectD2 ::
31selectD2 ::
34− ( FromListsN b b,
32+ ( FLN b b,
35 CountableN b
33 CountableN b
36 ) => Dist (Either a b) -> Matrix Prob a b -> Dist b
34 ) => Dist (Either a b) -> Matrix Prob a b -> Dist b
37−selectD2 (D d) m = D (junc m identity `comp` d)
35+selectD2 (D d) m = D (join m iden `comp` d)
38
36
39−-- Composition with identity
37+-- Composition with iden
40−compId m = comp identity m
38+compId m = comp iden m
41
39
42−randomDist :: forall a . (Countable a, FromListsN () a) => Gen (Dist a)
40+randomDist :: forall a . (Countable a, FLN () a) => Gen (Dist a)
43randomDist = do
41randomDist = do
44 let size = fromInteger (natVal (Proxy :: Proxy (Count a)))
42 let size = fromInteger (natVal (Proxy :: Proxy (Count a)))
45 l <- vectorOf size (arbitrary :: Gen Prob)
43 l <- vectorOf size (arbitrary :: Gen Prob)
@@ -48,7 +46,7 @@ randomDist = do
48 m = fromLists lr
46 m = fromLists lr
49 return (D m)
47 return (D m)
50
48
51−randomMatrix :: forall a b . (CountableDimensions a b, FromListsN a b) => Gen (Matrix Prob a b)
49+randomMatrix :: forall a b . (CountableDims a b, FLN a b) => Gen (Matrix Prob a b)
52randomMatrix = do
50randomMatrix = do
53 let cols = fromInteger (natVal (Proxy :: Proxy (Count a)))
51 let cols = fromInteger (natVal (Proxy :: Proxy (Count a)))
54 rows = fromInteger (natVal (Proxy :: Proxy (Count b)))
52 rows = fromInteger (natVal (Proxy :: Proxy (Count b)))
@@ -107,7 +105,7 @@ normalize3 as l = let s = sum l
107 probs = map (/ s) l
105 probs = map (/ s) l
108 in zip as probs
106 in zip as probs
109
107
110−randomDistF :: forall a b . (CountableDimensions a b, CoArbitrary a, Arbitrary b) => Gen (Dist' (a -> b))
108+randomDistF :: forall a b . (CountableDims a b, CoArbitrary a, Arbitrary b) => Gen (Dist' (a -> b))
111randomDistF = do
109randomDistF = do
112 let a = fromInteger (natVal (Proxy :: Proxy (Count a)))
110 let a = fromInteger (natVal (Proxy :: Proxy (Count a)))
113 b = fromInteger (natVal (Proxy :: Proxy (Count b)))
111 b = fromInteger (natVal (Proxy :: Proxy (Count b)))
@@ -146,8 +144,8 @@ setupEnv2 = do
146 distList2 <- generate (resize 1 (randomDistF @(Natural 0 100) @(Natural 0 100)))
144 distList2 <- generate (resize 1 (randomDistF @(Natural 0 100) @(Natural 0 100)))
147 return (m21, m40, dist, dist2, distList1, distList2)
145 return (m21, m40, dist, dist2, distList1, distList2)
148
146
149−benchmark :: IO ()
147+main :: IO ()
150−benchmark = defaultMain [
148+main = defaultMain [
151 env setupEnv $ \ ~(m11, m12, m21, m22, m31, m32) -> bgroup "Matrix Composition" [
149 env setupEnv $ \ ~(m11, m12, m21, m22, m31, m32) -> bgroup "Matrix Composition" [
152 bgroup "10x10" [
150 bgroup "10x10" [
153 bench "WHNF - 10x10" $ whnf (comp m11) m12
151 bench "WHNF - 10x10" $ whnf (comp m11) m12
@@ -162,7 +160,7 @@ benchmark = defaultMain [
162 , bench "NF - 200x200" $ nf (comp m31) m32
160 , bench "NF - 200x200" $ nf (comp m31) m32
163 ],
161 ],
164 bgroup "200x200 - RULES" [
162 bgroup "200x200 - RULES" [
165− bench "No rules - 200x200" $ nf (comp m21) identity
163+ bench "No rules - 200x200" $ nf (comp m21) iden
166 , bench "Rules - 200x200" $ nf compId m21
164 , bench "Rules - 200x200" $ nf compId m21
167 ] ],
165 ] ],
168 env setupEnv2 $ \ ~(m21, m40, dist, dist2, dl1, dl2) -> bgroup "Matrix vs List - `select`" [
166 env setupEnv2 $ \ ~(m21, m40, dist, dist2, dl1, dl2) -> bgroup "Matrix vs List - `select`" [
hackage.shdeleted−10
@@ -1,10 +0,0 @@
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.gzdeleted

Binary file not shown.

laop.cabalnew file+89
@@ -0,0 +1,89 @@
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.yamldeleted−57
@@ -1,57 +0,0 @@
1−name: laop
2−version: 0.1.0.5
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− - -O2
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.htmldeleted−1169
@@ -1,1169 +0,0 @@
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2−<html>
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5− <title>criterion report</title>
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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 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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 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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 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t=options.interaction.redrawOverlayInterval;if(t==-1){drawOverlay();return}if(!redrawTimeout)redrawTimeout=setTimeout(drawOverlay,t)}function drawOverlay(){redrawTimeout=null;octx.save();overlay.clear();octx.translate(plotOffset.left,plotOffset.top);var i,hi;for(i=0;i<highlights.length;++i){hi=highlights[i];if(hi.series.bars.show)drawBarHighlight(hi.series,hi.point);else drawPointHighlight(hi.series,hi.point)}octx.restore();executeHooks(hooks.drawOverlay,[octx])}function highlight(s,point,auto){if(typeof s=="number")s=series[s];if(typeof point=="number"){var ps=s.datapoints.pointsize;point=s.datapoints.points.slice(ps*point,ps*(point+1))}var i=indexOfHighlight(s,point);if(i==-1){highlights.push({series:s,point:point,auto:auto});triggerRedrawOverlay()}else if(!auto)highlights[i].auto=false}function unhighlight(s,point){if(s==null&&point==null){highlights=[];triggerRedrawOverlay();return}if(typeof s=="number")s=series[s];if(typeof point=="number"){var 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co=$.color.parse(defaultColor);if(c.brightness!=null)co=co.scale("rgb",c.brightness);if(c.opacity!=null)co.a*=c.opacity;c=co.toString()}gradient.addColorStop(i/(l-1),c)}return gradient}}}$.plot=function(placeholder,data,options){var plot=new Plot($(placeholder),data,options,$.plot.plugins);return plot};$.plot.version="0.8.3";$.plot.plugins=[];$.fn.plot=function(data,options){return this.each(function(){$.plot(this,data,options)})};function floorInBase(n,base){return base*Math.floor(n/base)}})(jQuery);
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 invertY=false;if(ax[1].p2c(ax[1].min)<ax[1].p2c(ax[1].max)){invertY=true;var tmp=err[1].lowerCap;err[1].lowerCap=err[1].upperCap;err[1].upperCap=tmp}for(var i=0;i<s.datapoints.points.length;i+=ps){var errRanges=parseErrors(s,i);for(var e=0;e<err.length;e++){var minmax=[ax[e].min,ax[e].max];if(errRanges[e*err.length]){var x=points[i],y=points[i+1];var upper=[x,y][e]+errRanges[e*err.length+1],lower=[x,y][e]-errRanges[e*err.length];if(err[e].err=="x")if(y>ax[1].max||y<ax[1].min||upper<ax[0].min||lower>ax[0].max)continue;if(err[e].err=="y")if(x>ax[0].max||x<ax[0].min||upper<ax[1].min||lower>ax[1].max)continue;var drawUpper=true,drawLower=true;if(upper>minmax[1]){drawUpper=false;upper=minmax[1]}if(lower<minmax[0]){drawLower=false;lower=minmax[0]}if(err[e].err=="x"&&invertX||err[e].err=="y"&&invertY){var 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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drawPath(ctx,[[x-radius,lower],[x+radius,lower]])}else if($.isFunction(err.lowerCap)){if(err.err=="x")err.lowerCap(ctx,lower,y,radius);else err.lowerCap(ctx,x,lower,radius)}}}function drawPath(ctx,pts){ctx.beginPath();ctx.moveTo(pts[0][0],pts[0][1]);for(var p=1;p<pts.length;p++)ctx.lineTo(pts[p][0],pts[p][1]);ctx.stroke()}function draw(plot,ctx){var plotOffset=plot.getPlotOffset();ctx.save();ctx.translate(plotOffset.left,plotOffset.top);$.each(plot.getData(),function(i,s){if(s.points.errorbars&&(s.points.xerr.show||s.points.yerr.show))drawSeriesErrors(plot,ctx,s)});ctx.restore()}function init(plot){plot.hooks.processRawData.push(processRawData);plot.hooks.draw.push(draw)}$.plot.plugins.push({init:init,options:options,name:"errorbars",version:"1.0"})})(jQuery);
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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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−-->
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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−<!--
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512− style="width:300px;height:278px;"></div></td>
513−-->
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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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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−-->
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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−-->
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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−-->
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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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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.pdfdeleted

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src/LAoP/Dist.hs+2−2
@@ -39,8 +39,8 @@ module LAoP.Dist
39 -- * Constraint type synonyms
39 -- * Constraint type synonyms
40 Countable,
40 Countable,
41 CountableN,
41 CountableN,
42− CountableDimensionsN,
42+ CountableDimsN,
43− FromListsN,
43+ FLN,
44 Liftable,
44 Liftable,
45 TrivialP,
45 TrivialP,
46
46
src/LAoP/Dist/Internal.hs+46−45
@@ -16,8 +16,8 @@ module LAoP.Dist.Internal
16
16
17 Countable,
17 Countable,
18 CountableN,
18 CountableN,
19− CountableDimensionsN,
19+ CountableDimsN,
20− FromListsN,
20+ FLN,
21 Liftable,
21 Liftable,
22 TrivialP,
22 TrivialP,
23
23
@@ -43,7 +43,8 @@ module LAoP.Dist.Internal
43 )
43 )
44 where
44 where
45
45
46−import LAoP.Matrix.Type hiding (TrivialP, Countable, CountableDimensions, CountableN, CountableDimensionsN, Liftable, FromListsN)
46+import LAoP.Matrix.Type hiding (TrivialP, Countable, CountableDims, CountableN, CountableDimsN, Liftable, FLN)
47+import Prelude hiding (id, (.))
47import qualified LAoP.Matrix.Internal as I
48import qualified LAoP.Matrix.Internal as I
48import LAoP.Utils
49import LAoP.Utils
49import GHC.TypeLits
50import GHC.TypeLits
@@ -61,18 +62,18 @@ newtype Dist a = D (Matrix Prob () a)
61 deriving (Show, Num, Eq, Ord, NFData) via (Matrix Prob () a)
62 deriving (Show, Num, Eq, Ord, NFData) via (Matrix Prob () a)
62
63
63-- | Constraint type synonyms to keep the type signatures less convoluted
64-- | Constraint type synonyms to keep the type signatures less convoluted
64−type Countable a = KnownNat (I.Count a)
65+type Countable a = KnownNat (I.Count a)
65−type CountableN a = KnownNat (I.Count (I.Normalize a))
66+type CountableN a = KnownNat (I.Count (I.Normalize a))
66−type CountableDimensionsN a b = (CountableN a, CountableN b)
67+type CountableDimsN a b = (CountableN a, CountableN b)
67−type FromListsN a b = I.FromLists Prob (I.Normalize a) (I.Normalize b)
68+type FLN a b = I.FL (I.Normalize a) (I.Normalize b)
68−type Liftable a b = (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num Prob, Ord Prob)
69+type Liftable a b = (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num Prob, Ord Prob)
69−type TrivialP a b = Normalize (a, b) ~ Normalize (Normalize a, Normalize b)
70+type TrivialP a b = Normalize (a, b) ~ Normalize (Normalize a, Normalize b)
70
71
71-- | Functor instance
72-- | Functor instance
72fmapD ::
73fmapD ::
73 ( Liftable a b,
74 ( Liftable a b,
74− CountableDimensionsN a b,
75+ CountableDimsN a b,
75− FromListsN b a
76+ FLN b a
76 )
77 )
77 =>
78 =>
78 (a -> b) -> Dist a -> Dist b
79 (a -> b) -> Dist a -> Dist b
@@ -84,17 +85,17 @@ unitD = D (one 1)
84
85
85-- | Applicative/Monoidal instance 'mult' function
86-- | Applicative/Monoidal instance 'mult' function
86multD ::
87multD ::
87− ( CountableDimensionsN a b,
88+ ( CountableDimsN a b,
88 CountableN (a, b),
89 CountableN (a, b),
89− FromListsN (a, b) a,
90+ FLN (a, b) a,
90− FromListsN (a, b) b,
91+ FLN (a, b) b,
91 TrivialP a b
92 TrivialP a b
92 ) => Dist a -> Dist b -> Dist (a, b)
93 ) => Dist a -> Dist b -> Dist (a, b)
93−multD (D a) (D b) = D (khatri a b)
94+multD (D a) (D b) = D (kr a b)
94
95
95-- | Selective instance function
96-- | Selective instance function
96selectD ::
97selectD ::
97− ( FromListsN b b,
98+ ( FLN b b,
98 CountableN b
99 CountableN b
99 ) => Dist (Either a b) -> Matrix Prob a b -> Dist b
100 ) => Dist (Either a b) -> Matrix Prob a b -> Dist b
100selectD (D d) m = D (selectM d m)
101selectD (D d) m = D (selectM d m)
@@ -103,31 +104,31 @@ selectD (D d) m = D (selectM d m)
103-- functions to apply to a given argument;
104-- functions to apply to a given argument;
104branchD ::
105branchD ::
105 ( Num e,
106 ( Num e,
106− CountableDimensionsN a b,
107+ CountableDimsN a b,
107− CountableDimensionsN c (Either b c),
108+ CountableDimsN c (Either b c),
108− FromListsN c b,
109+ FLN c b,
109− FromListsN a b,
110+ FLN a b,
110− FromListsN a a,
111+ FLN a a,
111− FromListsN b b,
112+ FLN b b,
112− FromListsN c c,
113+ FLN c c,
113− FromListsN b a,
114+ FLN b a,
114− FromListsN b c,
115+ FLN b c,
115− FromListsN (Either b c) b,
116+ FLN (Either b c) b,
116− FromListsN (Either b c) c
117+ FLN (Either b c) c
117 )
118 )
118 => Dist (Either a b) -> Matrix Prob a c -> Matrix Prob b c -> Dist c
119 => Dist (Either a b) -> Matrix Prob a c -> Matrix Prob b c -> Dist c
119branchD x l r = f x `selectD` g l `selectD` r
120branchD x l r = f x `selectD` g l `selectD` r
120 where
121 where
121− f (D m) = D (split (tr i1) (i1 `comp` tr i2) `comp` m)
122+ f (D m) = D (fork (tr i1) (i1 `comp` tr i2) `comp` m)
122 g m = i2 `comp` m
123 g m = i2 `comp` m
123
124
124-- | Branch on a Boolean value, skipping unnecessary computations.
125-- | Branch on a Boolean value, skipping unnecessary computations.
125ifD ::
126ifD ::
126− ( CountableDimensionsN a (Either () a),
127+ ( CountableDimsN a (Either () a),
127− FromListsN a a,
128+ FLN a a,
128− FromListsN a (),
129+ FLN a (),
129− FromListsN () a,
130+ FLN () a,
130− FromListsN (Either () a) a
131+ FLN (Either () a) a
131 )
132 )
132 => Dist Bool -> Dist a -> Dist a -> Dist a
133 => Dist Bool -> Dist a -> Dist a -> Dist a
133ifD x (D t) (D e) = branchD x' t e
134ifD x (D t) (D e) = branchD x' t e
@@ -135,7 +136,7 @@ ifD x (D t) (D e) = branchD x' t e
135 x' = bool (Right ()) (Left ()) `fmapD` x
136 x' = bool (Right ()) (Left ()) `fmapD` x
136
137
137-- | Monad instance 'return' function
138-- | Monad instance 'return' function
138−returnD :: forall a . (Enum a, FromListsN () a, Countable a) => a -> Dist a
139+returnD :: forall a . (Enum a, FLN () a, Countable a) => a -> Dist a
139returnD a = D (col l)
140returnD a = D (col l)
140 where
141 where
141 i = fromInteger $ natVal (Proxy :: Proxy (Count a))
142 i = fromInteger $ natVal (Proxy :: Proxy (Count a))
@@ -150,7 +151,7 @@ bindD (D d) m = D (m `comp` d)
150(??) ::
151(??) ::
151 ( Enum a,
152 ( Enum a,
152 Countable a,
153 Countable a,
153− FromListsN () a
154+ FLN () a
154 ) => (a -> Bool) -> Dist a -> Prob
155 ) => (a -> Bool) -> Dist a -> Prob
155(??) p d =
156(??) p d =
156 let l = toValues d
157 let l = toValues d
@@ -160,11 +161,11 @@ bindD (D d) m = D (m `comp` d)
160-- Distribution Construction
161-- Distribution Construction
161
162
162-- | Constructs a Bernoulli distribution
163-- | Constructs a Bernoulli distribution
163−choose :: (FromListsN () a) => Prob -> Dist a
164+choose :: (FLN () a) => Prob -> Dist a
164choose prob = D (col [prob, 1 - prob])
165choose prob = D (col [prob, 1 - prob])
165
166
166-- | Creates a distribution given a shape function
167-- | Creates a distribution given a shape function
167−shape :: (FromListsN () a) => (Prob -> Prob) -> [a] -> Dist a
168+shape :: (FLN () a) => (Prob -> Prob) -> [a] -> Dist a
168shape _ [] = error "Probability.shape: empty list"
169shape _ [] = error "Probability.shape: empty list"
169shape f xs =
170shape f xs =
170 let incr = 1 / fromIntegral (length xs - 1)
171 let incr = 1 / fromIntegral (length xs - 1)
@@ -172,23 +173,23 @@ shape f xs =
172 in fromFreqs (zip xs ps)
173 in fromFreqs (zip xs ps)
173
174
174-- | Constructs a Linear distribution
175-- | Constructs a Linear distribution
175−linear :: (FromListsN () a) => [a] -> Dist a
176+linear :: (FLN () a) => [a] -> Dist a
176linear = shape id
177linear = shape id
177
178
178-- | Constructs an Uniform distribution
179-- | Constructs an Uniform distribution
179−uniform :: (FromListsN () a) => [a] -> Dist a
180+uniform :: (FLN () a) => [a] -> Dist a
180uniform = shape (const 1)
181uniform = shape (const 1)
181
182
182-- | Constructs an Negative Exponential distribution
183-- | Constructs an Negative Exponential distribution
183−negExp :: (FromListsN () a) => [a] -> Dist a
184+negExp :: (FLN () a) => [a] -> Dist a
184negExp = shape (\x -> exp (-x))
185negExp = shape (\x -> exp (-x))
185
186
186-- | Constructs an Normal distribution
187-- | Constructs an Normal distribution
187−normal :: (FromListsN () a) => [a] -> Dist a
188+normal :: (FLN () a) => [a] -> Dist a
188normal = shape (normalCurve 0.5 0.5)
189normal = shape (normalCurve 0.5 0.5)
189
190
190-- | Transforms a 'Dist' into a list of pairs.
191-- | Transforms a 'Dist' into a list of pairs.
191−toValues :: forall a . (Enum a, Countable a, FromListsN () a) => Dist a -> [(a, Prob)]
192+toValues :: forall a . (Enum a, Countable a, FLN () a) => Dist a -> [(a, Prob)]
192toValues (D d) =
193toValues (D d) =
193 let rows = fromInteger (natVal (Proxy :: Proxy (Count a)))
194 let rows = fromInteger (natVal (Proxy :: Proxy (Count a)))
194 probs = toList d
195 probs = toList d
@@ -196,7 +197,7 @@ toValues (D d) =
196 in res
197 in res
197
198
198-- | Pretty a distribution
199-- | Pretty a distribution
199−prettyDist :: forall a. (Show a, Enum a, Countable a, FromListsN () a) => Dist a -> String
200+prettyDist :: forall a. (Show a, Enum a, Countable a, FLN () a) => Dist a -> String
200prettyDist d =
201prettyDist d =
201 let values = sortBy (\(a, p1) (b, p2) -> compare p2 p1) (toValues @a d)
202 let values = sortBy (\(a, p1) (b, p2) -> compare p2 p1) (toValues @a d)
202 w = maximum (map (length . show . fst) values)
203 w = maximum (map (length . show . fst) values)
@@ -208,12 +209,12 @@ prettyDist d =
208 showR n x = show x ++ " "
209 showR n x = show x ++ " "
209
210
210-- | Pretty Print a distribution
211-- | Pretty Print a distribution
211−prettyPrintDist :: forall a . (Show a, Enum a, Countable a, FromListsN () a) => Dist a -> IO ()
212+prettyPrintDist :: forall a . (Show a, Enum a, Countable a, FLN () a) => Dist a -> IO ()
212prettyPrintDist = putStrLn . prettyDist @a
213prettyPrintDist = putStrLn . prettyDist @a
213
214
214-- Auxiliary functions
215-- Auxiliary functions
215
216
216−fromFreqs :: (FromListsN () a) => [(a,Prob)] -> Dist a
217+fromFreqs :: (FLN () a) => [(a,Prob)] -> Dist a
217fromFreqs xs = D (col (map (\(x,p) -> p/q) xs))
218fromFreqs xs = D (col (map (\(x,p) -> p/q) xs))
218 where q = sum $ map snd xs
219 where q = sum $ map snd xs
219
220
src/LAoP/Matrix/Internal.hs+371−390
@@ -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--
@@ -43,17 +43,26 @@ 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+
52 -- * Primitives
62 -- * Primitives
53− empty,
54 one,
63 one,
55− junc,
64+ join,
56− split,
65+ fork,
57
66
58 -- * Auxiliary type families
67 -- * Auxiliary type families
59 FromNat,
68 FromNat,
@@ -66,6 +75,7 @@ module LAoP.Matrix.Internal
66 toLists,
75 toLists,
67 toList,
76 toList,
68 matrixBuilder,
77 matrixBuilder,
78+ matrixBuilder',
69 row,
79 row,
70 col,
80 col,
71 zeros,
81 zeros,
@@ -76,11 +86,17 @@ module LAoP.Matrix.Internal
76 -- * Misc
86 -- * Misc
77 -- ** Get dimensions
87 -- ** Get dimensions
78 columns,
88 columns,
89+ columns',
79 rows,
90 rows,
91+ rows',
80
92
81 -- ** Matrix Transposition
93 -- ** Matrix Transposition
82 tr,
94 tr,
83
95
96+ -- ** Scalar multiplication/division of matrices
97+ (.|),
98+ (./),
99+
84 -- ** Selective operator
100 -- ** Selective operator
85 select,
101 select,
86 branch,
102 branch,
@@ -89,16 +105,19 @@ module LAoP.Matrix.Internal
89 cond,
105 cond,
90
106
91 -- ** Matrix "abiding"
107 -- ** Matrix "abiding"
92− abideJS,
108+ abideJF,
93− abideSJ,
109+ abideFJ,
110+
111+ -- ** Zip matrices
112+ zipWithM,
94
113
95 -- * Biproduct approach
114 -- * Biproduct approach
96− -- ** Split
115+ -- ** Fork
97 (===),
116 (===),
98 -- *** Projections
117 -- *** Projections
99 p1,
118 p1,
100 p2,
119 p2,
101− -- ** Junc
120+ -- ** Join
102 (|||),
121 (|||),
103 -- *** Injections
122 -- *** Injections
104 i1,
123 i1,
@@ -111,12 +130,13 @@ module LAoP.Matrix.Internal
111
130
112 -- | Note that given the restrictions imposed it is not possible to
131 -- | Note that given the restrictions imposed it is not possible to
113 -- implement the standard type classes present in standard Haskell.
132 -- implement the standard type classes present in standard Haskell.
133+
114 -- *** Matrix pairing projections
134 -- *** Matrix pairing projections
115− kp1,
135+ fstM,
116− kp2,
136+ sndM,
117
137
118 -- *** Matrix pairing
138 -- *** Matrix pairing
119− khatri,
139+ kr,
120
140
121 -- * Matrix composition and lifting
141 -- * Matrix composition and lifting
122
142
@@ -124,10 +144,10 @@ module LAoP.Matrix.Internal
124
144
125 -- | Note that given the restrictions imposed it is not possible to
145 -- | Note that given the restrictions imposed it is not possible to
126 -- implement the standard type classes present in standard Haskell.
146 -- implement the standard type classes present in standard Haskell.
127− identity,
147+ iden,
128 comp,
148 comp,
129− fromF,
130 fromF',
149 fromF',
150+ fromF,
131
151
132 -- * Matrix printing
152 -- * Matrix printing
133 pretty,
153 pretty,
@@ -156,20 +176,20 @@ import Data.Kind
156import Data.List
176import Data.List
157import Data.Maybe
177import Data.Maybe
158import Data.Proxy
178import Data.Proxy
179+import Data.Typeable
159import Data.Void
180import Data.Void
160import GHC.TypeLits
181import GHC.TypeLits
161import Data.Type.Equality
182import Data.Type.Equality
162import GHC.Generics
183import GHC.Generics
163import Control.DeepSeq
184import Control.DeepSeq
164−import Control.Category
185+import Prelude hiding (id, (.))
165−import Prelude hiding ((.))
186+import qualified Prelude (id, (.))
166
187
167-- | LAoP (Linear Algebra of Programming) Inductive Matrix definition.
188-- | LAoP (Linear Algebra of Programming) Inductive Matrix definition.
168data Matrix e cols rows where
189data Matrix e cols rows where
169− Empty :: Matrix e Void Void
170 One :: e -> Matrix e () ()
190 One :: e -> Matrix e () ()
171− Junc :: Matrix e a rows -> Matrix e b rows -> Matrix e (Either a b) rows
191+ Join :: Matrix e a rows -> Matrix e b rows -> Matrix e (Either a b) rows
172− Split :: Matrix e cols a -> Matrix e cols b -> Matrix e cols (Either a b)
192+ Fork :: Matrix e cols a -> Matrix e cols b -> Matrix e cols (Either a b)
173
193
174deriving instance (Show e) => Show (Matrix e cols rows)
194deriving instance (Show e) => Show (Matrix e cols rows)
175
195
@@ -196,7 +216,6 @@ type family Count (d :: Type) :: Nat where
196--
216--
197-- Thanks to Li-Yao Xia this type family is super fast.
217-- Thanks to Li-Yao Xia this type family is super fast.
198type family FromNat (n :: Nat) :: Type where
218type family FromNat (n :: Nat) :: Type where
199− FromNat 0 = Void
200 FromNat 1 = ()
219 FromNat 1 = ()
201 FromNat n = FromNat' (Mod n 2 == 0) (FromNat (Div n 2))
220 FromNat n = FromNat' (Mod n 2 == 0) (FromNat (Div n 2))
202
221
@@ -213,105 +232,79 @@ type family Normalize (d :: Type) :: Type where
213-- | Constraint type synonyms to keep the type signatures less convoluted
232-- | Constraint type synonyms to keep the type signatures less convoluted
214type Countable a = KnownNat (Count a)
233type Countable a = KnownNat (Count a)
215type CountableN a = KnownNat (Count (Normalize a))
234type CountableN a = KnownNat (Count (Normalize a))
216−type CountableDimensions a b = (Countable a, Countable b)
235+type CountableDims a b = (Countable a, Countable b)
217−type CountableDimensionsN a b = (CountableN a, CountableN b)
236+type CountableDimsN a b = (CountableN a, CountableN b)
237+type FL a b = FromLists a b
218−type FromListsN e a b = FromLists e (Normalize a) (Normalize b)
238+type FLN a b = FromLists (Normalize a) (Normalize b)
219type Liftable e a b = (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num e, Ord e)
239type Liftable e a b = (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num e, Ord e)
220type Trivial a = FromNat (Count a) ~ a
240type Trivial a = FromNat (Count a) ~ a
221
241
222−-- | It isn't possible to implement the 'id' function so it's
242+-- | It is possible to implement a constrained version of the category type
223−-- implementation is 'undefined'. However 'comp' can be and this partial
243+-- class.
224−-- class implementation exists just to make the code more readable.
225−--
226−-- Please use 'identity' instead.
227instance (Num e) => Category (Matrix e) where
244instance (Num e) => Category (Matrix e) where
228− id = undefined
245+ type Object (Matrix e) a = (FL a a, Countable a)
246+ id = iden
229− (.) = comp
247+ (.) = comp
230
248
231instance NFData e => NFData (Matrix e cols rows) where
249instance NFData e => NFData (Matrix e cols rows) where
232− rnf Empty = ()
233− rnf (One e) = rnf e
250+ rnf (One e) = rnf e
234− rnf (Junc a b) = rnf a `seq` rnf b
251+ rnf (Join a b) = rnf a `seq` rnf b
235− rnf (Split a b) = rnf a `seq` rnf b
252+ rnf (Fork a b) = rnf a `seq` rnf b
236
253
237instance Eq e => Eq (Matrix e cols rows) where
254instance Eq e => Eq (Matrix e cols rows) where
238− Empty == Empty = True
239− (One a) == (One b) = a == b
255+ (One a) == (One b) = a == b
240− (Junc a b) == (Junc c d) = a == c && b == d
256+ (Join a b) == (Join c d) = a == c && b == d
241− (Split a b) == (Split c d) = a == c && b == d
257+ (Fork a b) == (Fork c d) = a == c && b == d
242− x@(Split _ _) == y@(Junc _ _) = x == abideJS y
258+ x@(Fork _ _) == y@(Join _ _) = x == abideJF y
243− x@(Junc _ _) == y@(Split _ _) = abideJS x == y
259+ x@(Join _ _) == y@(Fork _ _) = abideJF x == y
244
260
245instance Num e => Num (Matrix e cols rows) where
261instance 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
246
267
247− Empty + Empty = Empty
248− (One a) + (One b) = One (a + b)
249− (Junc a b) + (Junc c d) = Junc (a + c) (b + d)
250− (Split a b) + (Split c d) = Split (a + c) (b + d)
251− x@(Split _ _) + y@(Junc _ _) = x + abideJS y
252− x@(Junc _ _) + y@(Split _ _) = abideJS x + y
253−
254− Empty - Empty = Empty
255− (One a) - (One b) = One (a - b)
256− (Junc a b) - (Junc c d) = Junc (a - c) (b - d)
257− (Split a b) - (Split c d) = Split (a - c) (b - d)
258− x@(Split _ _) - y@(Junc _ _) = x - abideJS y
259− x@(Junc _ _) - y@(Split _ _) = abideJS x - y
260−
261− Empty * Empty = Empty
262− (One a) * (One b) = One (a * b)
263− (Junc a b) * (Junc c d) = Junc (a * c) (b * d)
264− (Split a b) * (Split c d) = Split (a * c) (b * d)
265− x@(Split _ _) * y@(Junc _ _) = x * abideJS y
266− x@(Junc _ _) * y@(Split _ _) = abideJS x * y
267−
268− abs Empty = Empty
269− abs (One a) = One (abs a)
268+ abs (One a) = One (abs a)
270− abs (Junc a b) = Junc (abs a) (abs b)
269+ abs (Join a b) = Join (abs a) (abs b)
271− abs (Split a b) = Split (abs a) (abs b)
270+ abs (Fork a b) = Fork (abs a) (abs b)
272−
271+
273− signum Empty = Empty
274− signum (One a) = One (signum a)
272+ signum (One a) = One (signum a)
275− signum (Junc a b) = Junc (signum a) (signum b)
273+ signum (Join a b) = Join (signum a) (signum b)
276− signum (Split a b) = Split (signum a) (signum b)
274+ signum (Fork a b) = Fork (signum a) (signum b)
277
275
278instance Ord e => Ord (Matrix e cols rows) where
276instance Ord e => Ord (Matrix e cols rows) where
279− Empty <= Empty = True
280− (One a) <= (One b) = a <= b
277+ (One a) <= (One b) = a <= b
281− (Junc a b) <= (Junc c d) = (a <= c) && (b <= d)
278+ (Join a b) <= (Join c d) = (a <= c) && (b <= d)
282− (Split a b) <= (Split c d) = (a <= c) && (b <= d)
279+ (Fork a b) <= (Fork c d) = (a <= c) && (b <= d)
283− x@(Split _ _) <= y@(Junc _ _) = x <= abideJS y
280+ x@(Fork _ _) <= y@(Join _ _) = x <= abideJF y
284− x@(Junc _ _) <= y@(Split _ _) = abideJS x <= y
281+ x@(Join _ _) <= y@(Fork _ _) = abideJF x <= y
285
282
286-- Primitives
283-- Primitives
287
284
288−-- | Empty matrix constructor
289−empty :: Matrix e Void Void
290−empty = Empty
291−
292-- | Unit matrix constructor
285-- | Unit matrix constructor
293one :: e -> Matrix e () ()
286one :: e -> Matrix e () ()
294one = One
287one = One
295
288
296−-- | Matrix 'Junc' constructor
289+-- | Matrix 'Join' constructor
297−junc :: Matrix e a rows -> Matrix e b rows -> Matrix e (Either a b) rows
290+join :: Matrix e a rows -> Matrix e b rows -> Matrix e (Either a b) rows
298−junc = Junc
291+join = Join
299
292
300infixl 3 |||
293infixl 3 |||
301
294
302−-- | Matrix 'Junc' constructor
295+-- | Matrix 'Join' constructor
303(|||) :: Matrix e a rows -> Matrix e b rows -> Matrix e (Either a b) rows
296(|||) :: Matrix e a rows -> Matrix e b rows -> Matrix e (Either a b) rows
304−(|||) = Junc
297+(|||) = Join
305
298
306−-- | Matrix 'Split' constructor
299+-- | Matrix 'Fork' constructor
307−split :: Matrix e cols a -> Matrix e cols b -> Matrix e cols (Either a b)
300+fork :: Matrix e cols a -> Matrix e cols b -> Matrix e cols (Either a b)
308−split = Split
301+fork = Fork
309
302
310infixl 2 ===
303infixl 2 ===
311
304
312−-- | Matrix 'Split' constructor
305+-- | Matrix 'Fork' constructor
313(===) :: Matrix e cols a -> Matrix e cols b -> Matrix e cols (Either a b)
306(===) :: Matrix e cols a -> Matrix e cols b -> Matrix e cols (Either a b)
314−(===) = Split
307+(===) = Fork
315
308
316-- Construction
309-- Construction
317
310
@@ -319,84 +312,101 @@ infixl 2 ===
319--
312--
320-- Given that it is not possible to branch on types at the term level type
313-- Given that it is not possible to branch on types at the term level type
321-- classes are needed very much like an inductive definition but on types.
314-- classes are needed very much like an inductive definition but on types.
322−class FromLists e cols rows where
315+class FromLists cols rows where
323 -- | Build a matrix out of a list of list of elements. Throws a runtime
316 -- | Build a matrix out of a list of list of elements. Throws a runtime
324 -- error if the dimensions do not match.
317 -- error if the dimensions do not match.
325 fromLists :: [[e]] -> Matrix e cols rows
318 fromLists :: [[e]] -> Matrix e cols rows
326
319
327−instance FromLists e Void Void where
320+instance FromLists () () where
328− fromLists [] = Empty
329− fromLists _ = error "Wrong dimensions"
330−
331−instance {-# OVERLAPPING #-} FromLists e () () where
332 fromLists [[e]] = One e
321 fromLists [[e]] = One e
333 fromLists _ = error "Wrong dimensions"
322 fromLists _ = error "Wrong dimensions"
334
323
335−instance {-# OVERLAPPING #-} (FromLists e cols ()) => FromLists e (Either () cols) () where
324+instance (FromLists cols ()) => FromLists (Either () cols) () where
336− fromLists [h : t] = Junc (One h) (fromLists [t])
325+ fromLists [h : t] = Join (One h) (fromLists [t])
337 fromLists _ = error "Wrong dimensions"
326 fromLists _ = error "Wrong dimensions"
338
327
328+instance {-# OVERLAPPABLE #-}
339−instance {-# OVERLAPPABLE #-} (FromLists e a (), FromLists e b (), Countable a) => FromLists e (Either a b) () where
329+ (FromLists a (), FromLists b (), Countable a) => FromLists (Either a b) () where
340− fromLists [l] =
330+ fromLists [l] =
341 let rowsA = fromInteger (natVal (Proxy :: Proxy (Count a)))
331 let rowsA = fromInteger (natVal (Proxy :: Proxy (Count a)))
342− in Junc (fromLists [take rowsA l]) (fromLists [drop rowsA l])
332+ in Join (fromLists [take rowsA l]) (fromLists [drop rowsA l])
343 fromLists _ = error "Wrong dimensions"
333 fromLists _ = error "Wrong dimensions"
344
334
345−instance {-# OVERLAPPING #-} (FromLists e () rows) => FromLists e () (Either () rows) where
335+instance (FromLists () rows) => FromLists () (Either () rows) where
346− fromLists ([h] : t) = Split (One h) (fromLists t)
336+ fromLists ([h] : t) = Fork (One h) (fromLists t)
347 fromLists _ = error "Wrong dimensions"
337 fromLists _ = error "Wrong dimensions"
348
338
339+instance {-# OVERLAPPABLE #-}
349−instance {-# OVERLAPPABLE #-} (FromLists e () a, FromLists e () b, Countable a) => FromLists e () (Either a b) where
340+ (FromLists () a, FromLists () b, Countable a) => FromLists () (Either a b) where
350− fromLists l@([_] : _) =
341+ fromLists l@([_] : _) =
351 let rowsA = fromInteger (natVal (Proxy :: Proxy (Count a)))
342 let rowsA = fromInteger (natVal (Proxy :: Proxy (Count a)))
352− in Split (fromLists (take rowsA l)) (fromLists (drop rowsA l))
343+ in Fork (fromLists (take rowsA l)) (fromLists (drop rowsA l))
353 fromLists _ = error "Wrong dimensions"
344 fromLists _ = error "Wrong dimensions"
354
345
355−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
346+instance (FromLists (Either a b) c, FromLists (Either a b) d, Countable c)
347+ => FromLists (Either a b) (Either c d) where
356 fromLists l@(h : t) =
348 fromLists l@(h : t) =
357 let lh = length h
349 let lh = length h
358 rowsC = fromInteger (natVal (Proxy :: Proxy (Count c)))
350 rowsC = fromInteger (natVal (Proxy :: Proxy (Count c)))
359− condition = all (== lh) (map length t)
351+ condition = all ((== lh) . length) t
360 in if lh > 0 && condition
352 in if lh > 0 && condition
361− then Split (fromLists (take rowsC l)) (fromLists (drop rowsC l))
353+ then Fork (fromLists (take rowsC l)) (fromLists (drop rowsC l))
362 else error "Not all rows have the same length"
354 else error "Not all rows have the same length"
363
355
364-- | Matrix builder function. Constructs a matrix provided with
356-- | Matrix builder function. Constructs a matrix provided with
365−-- a construction function.
357+-- a construction function that operates with indices.
366−matrixBuilder ::
358+matrixBuilder' ::
367 forall e cols rows.
359 forall e cols rows.
368− ( FromLists e cols rows,
360+ ( FL cols rows,
369− CountableDimensions cols rows
361+ CountableDims cols rows
370− ) =>
371− ((Int, Int) -> e) ->
372− Matrix e cols rows
362+ ) => ((Int, Int) -> e) -> Matrix e cols rows
373−matrixBuilder f =
363+matrixBuilder' f =
374 let c = fromInteger $ natVal (Proxy :: Proxy (Count cols))
364 let c = fromInteger $ natVal (Proxy :: Proxy (Count cols))
375 r = fromInteger $ natVal (Proxy :: Proxy (Count rows))
365 r = fromInteger $ natVal (Proxy :: Proxy (Count rows))
376 positions = [(a, b) | a <- [0 .. (r - 1)], b <- [0 .. (c - 1)]]
366 positions = [(a, b) | a <- [0 .. (r - 1)], b <- [0 .. (c - 1)]]
377 in fromLists . map (map f) . groupBy (\(x, _) (w, _) -> x == w) $ positions
367 in fromLists . map (map f) . groupBy (\(x, _) (w, _) -> x == w) $ positions
378
368
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+
379-- | Constructs a column vector matrix
389-- | Constructs a column vector matrix
380−col :: (FromLists e () rows) => [e] -> Matrix e () rows
390+col :: (FL () rows) => [e] -> Matrix e () rows
381col = fromLists . map (: [])
391col = fromLists . map (: [])
382
392
383-- | Constructs a row vector matrix
393-- | Constructs a row vector matrix
384−row :: (FromLists e cols ()) => [e] -> Matrix e cols ()
394+row :: (FL cols ()) => [e] -> Matrix e cols ()
385row = fromLists . (: [])
395row = fromLists . (: [])
386
396
387-- | Lifts functions to matrices with arbitrary dimensions.
397-- | Lifts functions to matrices with arbitrary dimensions.
388--
398--
389-- NOTE: Be careful to not ask for a matrix bigger than the cardinality of
399-- NOTE: Be careful to not ask for a matrix bigger than the cardinality of
390-- types @a@ or @b@ allows.
400-- types @a@ or @b@ allows.
391−fromF ::
401+fromF' ::
392 forall a b cols rows e.
402 forall a b cols rows e.
393 ( Liftable e a b,
403 ( Liftable e a b,
394− CountableDimensions cols rows,
404+ CountableDims cols rows,
395− FromLists e rows cols
405+ FL rows cols
396 ) =>
406 ) =>
397 (a -> b) ->
407 (a -> b) ->
398 Matrix e cols rows
408 Matrix e cols rows
399−fromF f =
409+fromF' f =
400 let minA = minBound @a
410 let minA = minBound @a
401 maxA = maxBound @a
411 maxA = maxBound @a
402 minB = minBound @b
412 minB = minBound @b
@@ -406,8 +416,8 @@ fromF f =
406 elementsA = take ccols [minA .. maxA]
416 elementsA = take ccols [minA .. maxA]
407 elementsB = take rrows [minB .. maxB]
417 elementsB = take rrows [minB .. maxB]
408 combinations = (,) <$> elementsA <*> elementsB
418 combinations = (,) <$> elementsA <*> elementsB
409− combAp = map snd . sort . map (\(a, b) -> if f a == b
419+ combAp = map snd . sort . map (\(a, b) -> if f a == b
410− then ((fromEnum a, fromEnum b), 1)
420+ then ((fromEnum a, fromEnum b), 1)
411 else ((fromEnum a, fromEnum b), 0)) $ combinations
421 else ((fromEnum a, fromEnum b), 0)) $ combinations
412 mList = buildList combAp rrows
422 mList = buildList combAp rrows
413 in tr $ fromLists mList
423 in tr $ fromLists mList
@@ -417,41 +427,23 @@ fromF f =
417
427
418-- | Lifts functions to matrices with dimensions matching @a@ and @b@
428-- | Lifts functions to matrices with dimensions matching @a@ and @b@
419-- cardinality's.
429-- cardinality's.
420−fromF' ::
430+fromF ::
421 forall a b e.
431 forall a b e.
422 ( Liftable e a b,
432 ( Liftable e a b,
423− CountableDimensionsN a b,
433+ CountableDimsN a b,
424− FromListsN e b a
434+ FLN b a
425 ) =>
435 ) =>
426 (a -> b) ->
436 (a -> b) ->
427 Matrix e (Normalize a) (Normalize b)
437 Matrix e (Normalize a) (Normalize b)
428−fromF' f =
438+fromF = fromF'
429− let minA = minBound @a
430− maxA = maxBound @a
431− minB = minBound @b
432− maxB = maxBound @b
433− ccols = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize a)))
434− rrows = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize b)))
435− elementsA = take ccols [minA .. maxA]
436− elementsB = take rrows [minB .. maxB]
437− combinations = (,) <$> elementsA <*> elementsB
438− combAp = map snd . sort . map (\(a, b) -> if f a == b
439− then ((fromEnum a, fromEnum b), 1)
440− else ((fromEnum a, fromEnum b), 0)) $ combinations
441− mList = buildList combAp rrows
442− in tr $ fromLists mList
443− where
444− buildList [] _ = []
445− buildList l r = take r l : buildList (drop r l) r
446
439
447-- Conversion
440-- Conversion
448
441
449-- | Converts a matrix to a list of lists of elements.
442-- | Converts a matrix to a list of lists of elements.
450toLists :: Matrix e cols rows -> [[e]]
443toLists :: Matrix e cols rows -> [[e]]
451−toLists Empty = []
452toLists (One e) = [[e]]
444toLists (One e) = [[e]]
453−toLists (Split l r) = toLists l ++ toLists r
445+toLists (Fork l r) = toLists l ++ toLists r
454−toLists (Junc l r) = zipWith (++) (toLists l) (toLists r)
446+toLists (Join l r) = zipWith (++) (toLists l) (toLists r)
455
447
456-- | Converts a matrix to a list of elements.
448-- | Converts a matrix to a list of elements.
457toList :: Matrix e cols rows -> [e]
449toList :: Matrix e cols rows -> [e]
@@ -460,38 +452,38 @@ toList = concat . toLists
460-- Zeros Matrix
452-- Zeros Matrix
461
453
462-- | The zero matrix. A matrix wholly filled with zeros.
454-- | The zero matrix. A matrix wholly filled with zeros.
463−zeros :: (Num e, FromLists e cols rows, CountableDimensions cols rows) => Matrix e cols rows
455+zeros :: (Num e, FL cols rows, CountableDims cols rows) => Matrix e cols rows
464−zeros = matrixBuilder (const 0)
456+zeros = matrixBuilder' (const 0)
465
457
466-- Ones Matrix
458-- Ones Matrix
467
459
468-- | The ones matrix. A matrix wholly filled with ones.
460-- | The ones matrix. A matrix wholly filled with ones.
469--
461--
470-- Also known as T (Top) matrix.
462-- Also known as T (Top) matrix.
471−ones :: (Num e, FromLists e cols rows, CountableDimensions cols rows) => Matrix e cols rows
463+ones :: (Num e, FL cols rows, CountableDims cols rows) => Matrix e cols rows
472−ones = matrixBuilder (const 1)
464+ones = matrixBuilder' (const 1)
473
465
474-- Const Matrix
466-- Const Matrix
475
467
476-- | The constant matrix constructor. A matrix wholly filled with a given
468-- | The constant matrix constructor. A matrix wholly filled with a given
477-- value.
469-- value.
478−constant :: (Num e, FromLists e cols rows, CountableDimensions cols rows) => e -> Matrix e cols rows
470+constant :: (Num e, FL cols rows, CountableDims cols rows) => e -> Matrix e cols rows
479−constant e = matrixBuilder (const e)
471+constant e = matrixBuilder' (const e)
480
472
481-- Bang Matrix
473-- Bang Matrix
482
474
483-- | The T (Top) row vector matrix.
475-- | The T (Top) row vector matrix.
484−bang :: forall e cols. (Num e, Enum e, FromLists e cols (), Countable cols) => Matrix e cols ()
476+bang :: forall e cols. (Num e, Enum e, FL cols (), Countable cols) => Matrix e cols ()
485bang =
477bang =
486 let c = fromInteger $ natVal (Proxy :: Proxy (Count cols))
478 let c = fromInteger $ natVal (Proxy :: Proxy (Count cols))
487 in fromLists [take c [1, 1 ..]]
479 in fromLists [take c [1, 1 ..]]
488
480
489−-- Identity Matrix
481+-- iden Matrix
490
482
491−-- | Identity matrix.
483+-- | iden matrix.
492−identity :: (Num e, FromLists e cols cols, Countable cols) => Matrix e cols cols
484+iden :: forall e cols . (Num e, FL cols cols, Countable cols) => Matrix e cols cols
493−identity = matrixBuilder (bool 0 1 . uncurry (==))
485+iden = matrixBuilder' (bool 0 1 . uncurry (==))
494−{-# NOINLINE identity #-}
486+{-# NOINLINE iden #-}
495
487
496-- Matrix composition (MMM)
488-- Matrix composition (MMM)
497
489
@@ -500,65 +492,90 @@ identity = matrixBuilder (bool 0 1 . uncurry (==))
500-- This definition takes advantage of divide-and-conquer and fusion laws
492-- This definition takes advantage of divide-and-conquer and fusion laws
501-- from LAoP.
493-- from LAoP.
502comp :: (Num e) => Matrix e cr rows -> Matrix e cols cr -> Matrix e cols rows
494comp :: (Num e) => Matrix e cr rows -> Matrix e cols cr -> Matrix e cols rows
503−comp Empty Empty = Empty
504−comp (One a) (One b) = One (a * b)
495+comp (One a) (One b) = One (a * b)
505−comp (Junc a b) (Split c d) = comp a c + comp b d -- Divide-and-conquer law
496+comp (Join a b) (Fork c d) = comp a c + comp b d -- Divide-and-conquer law
506−comp (Split a b) c = Split (comp a c) (comp b c) -- Split fusion law
497+comp (Fork a b) c = Fork (comp a c) (comp b c) -- Fork fusion law
507−comp c (Junc a b) = Junc (comp c a) (comp c b) -- Junc fusion law
498+comp c (Join a b) = Join (comp c a) (comp c b) -- Join fusion law
508{-# NOINLINE comp #-}
499{-# NOINLINE comp #-}
509−{-# RULES
500+{-# RULES
510− "comp/identity1" forall m. comp m identity = m ;
501+ "comp/iden1" forall m. comp m iden = m ;
511− "comp/identity2" forall m. comp identity m = m
502+ "comp/iden2" forall m. comp iden m = m
512#-}
503#-}
513
504
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+
514-- Projections
523-- Projections
515
524
516-- | Biproduct first component projection
525-- | Biproduct first component projection
517−p1 :: forall e m n. (Num e, CountableDimensions n m, FromLists e n m, FromLists e m m) => Matrix e (Either m n) m
526+p1 :: (Num e, CountableDims n m, FL n m, FL m m) => Matrix e (Either m n) m
518−p1 =
527+p1 = join id zeros
519− let iden = identity :: Matrix e m m
520− zero = zeros :: Matrix e n m
521− in junc iden zero
522
528
523-- | Biproduct second component projection
529-- | Biproduct second component projection
524−p2 :: forall e m n. (Num e, CountableDimensions n m, FromLists e m n, FromLists e n n) => Matrix e (Either m n) n
530+p2 :: (Num e, CountableDims n m, FL m n, FL n n) => Matrix e (Either m n) n
525−p2 =
531+p2 = join zeros id
526− let iden = identity :: Matrix e n n
527− zero = zeros :: Matrix e m n
528− in junc zero iden
529
532
530-- Injections
533-- Injections
531
534
532-- | Biproduct first component injection
535-- | Biproduct first component injection
533−i1 :: (Num e, CountableDimensions n m, FromLists e n m, FromLists e m m) => Matrix e m (Either m n)
536+i1 :: (Num e, CountableDims n m, FL n m, FL m m) => Matrix e m (Either m n)
534i1 = tr p1
537i1 = tr p1
535
538
536-- | Biproduct second component injection
539-- | Biproduct second component injection
537−i2 :: (Num e, CountableDimensions n m, FromLists e m n, FromLists e n n) => Matrix e n (Either m n)
540+i2 :: (Num e, CountableDims n m, FL m n, FL n n) => Matrix e n (Either m n)
538i2 = tr p2
541i2 = tr p2
539
542
540-- Dimensions
543-- Dimensions
541
544
542-- | Obtain the number of rows.
545-- | Obtain the number of rows.
543--
546--
544−-- NOTE: The 'KnownNat' constaint is needed in order to obtain the
547+-- NOTE: The 'KnownNat' constraint is needed in order to obtain the
545−-- dimensions in constant time.
548+-- dimensions in constant time. For a version that doesn't require the
546−--
549+-- constraint see 'rows''.
547−-- TODO: A 'rows' function that does not need the 'KnownNat' constraint in
548−-- exchange for performance.
549rows :: forall e cols rows. (Countable rows) => Matrix e cols rows -> Int
550rows :: forall e cols rows. (Countable rows) => Matrix e cols rows -> Int
550rows _ = fromInteger $ natVal (Proxy :: Proxy (Count rows))
551rows _ = fromInteger $ natVal (Proxy :: Proxy (Count rows))
551
552
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+
552-- | Obtain the number of columns.
562-- | Obtain the number of columns.
553−--
554−-- NOTE: The 'KnownNat' constaint is needed in order to obtain the
555−-- dimensions in constant time.
556--
563--
557−-- TODO: A 'columns' function that does not need the 'KnownNat' constraint in
564+-- NOTE: The 'KnownNat' constraint is needed in order to obtain the
558−-- exchange for performance.
565+-- dimensions in constant time. For a version that doesn't require the
566+-- constraint see 'columns''.
559columns :: forall e cols rows. (Countable cols) => Matrix e cols rows -> Int
567columns :: forall e cols rows. (Countable cols) => Matrix e cols rows -> Int
560columns _ = fromInteger $ natVal (Proxy :: Proxy (Count cols))
568columns _ = fromInteger $ natVal (Proxy :: Proxy (Count cols))
561
569
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+
562-- Coproduct Bifunctor
579-- Coproduct Bifunctor
563
580
564infixl 5 -|-
581infixl 5 -|-
@@ -567,164 +584,161 @@ infixl 5 -|-
567(-|-) ::
584(-|-) ::
568 forall e n k m j.
585 forall e n k m j.
569 ( Num e,
586 ( Num e,
570− CountableDimensions j k,
587+ CountableDims j k,
571− FromLists e k k,
588+ FL k k,
572− FromLists e j k,
589+ FL j k,
573− FromLists e k j,
590+ FL k j,
574− FromLists e j j
591+ FL j j
575 ) =>
592 ) =>
576 Matrix e n k ->
593 Matrix e n k ->
577 Matrix e m j ->
594 Matrix e m j ->
578 Matrix e (Either n m) (Either k j)
595 Matrix e (Either n m) (Either k j)
579−(-|-) a b = Junc (i1 . a) (i2 . b)
596+(-|-) a b = Join (i1 . a) (i2 . b)
580
597
581-- Khatri Rao Product and projections
598-- Khatri Rao Product and projections
582
599
583-- | Khatri Rao product first component projection matrix.
600-- | Khatri Rao product first component projection matrix.
584−kp1 ::
601+fstM ::
585 forall e m k .
602 forall e m k .
586 ( Num e,
603 ( Num e,
587− CountableDimensions k m,
604+ CountableDims k m,
588− FromLists e (Normalize (m, k)) m,
605+ FL (Normalize (m, k)) m,
589 CountableN (m, k)
606 CountableN (m, k)
590 ) => Matrix e (Normalize (m, k)) m
607 ) => Matrix e (Normalize (m, k)) m
591−kp1 = matrixBuilder f
608+fstM = matrixBuilder' f
592 where
609 where
593 offset = fromInteger (natVal (Proxy :: Proxy (Count k)))
610 offset = fromInteger (natVal (Proxy :: Proxy (Count k)))
594 f (x, y)
611 f (x, y)
595 | y >= (x * offset) && y <= (x * offset + offset - 1) = 1
612 | y >= (x * offset) && y <= (x * offset + offset - 1) = 1
596− | otherwise = 0
613+ | otherwise = 0
597
614
598-- | Khatri Rao product second component projection matrix.
615-- | Khatri Rao product second component projection matrix.
599−kp2 ::
616+sndM ::
600 forall e m k .
617 forall e m k .
601 ( Num e,
618 ( Num e,
602− CountableDimensions k m,
619+ CountableDims k m,
603− FromLists e (Normalize (m, k)) k,
620+ FL (Normalize (m, k)) k,
604 CountableN (m, k)
621 CountableN (m, k)
605 ) => Matrix e (Normalize (m, k)) k
622 ) => Matrix e (Normalize (m, k)) k
606−kp2 = matrixBuilder f
623+sndM = matrixBuilder' f
607 where
624 where
608 offset = fromInteger (natVal (Proxy :: Proxy (Count k)))
625 offset = fromInteger (natVal (Proxy :: Proxy (Count k)))
609 f (x, y)
626 f (x, y)
610 | x == y || mod (y - x) offset == 0 = 1
627 | x == y || mod (y - x) offset == 0 = 1
611− | otherwise = 0
628+ | otherwise = 0
612
629
613-- | Khatri Rao Matrix product also known as matrix pairing.
630-- | Khatri Rao Matrix product also known as matrix pairing.
614--
631--
615-- NOTE: That this is not a true categorical product, see for instance:
632-- NOTE: That this is not a true categorical product, see for instance:
616−--
633+--
617-- @
634-- @
618−-- | kp1 . khatri a b == a
635+-- | fstM . kr a b == a
619−-- khatri a b ==> |
636+-- kr a b ==> |
620−-- | kp2 . khatri a b == b
637+-- | sndM . kr a b == b
621-- @
638-- @
622--
639--
623-- __Emphasis__ on the implication symbol.
640-- __Emphasis__ on the implication symbol.
624−khatri ::
641+kr ::
625− forall e cols a b.
642+ forall e cols a b.
626 ( Num e,
643 ( Num e,
627− CountableDimensions a b,
644+ CountableDims a b,
628 CountableN (a, b),
645 CountableN (a, b),
629− FromLists e (Normalize (a, b)) a,
646+ FL (Normalize (a, b)) a,
630− FromLists e (Normalize (a, b)) b
647+ FL (Normalize (a, b)) b
631 ) => Matrix e cols a -> Matrix e cols b -> Matrix e cols (Normalize (a, b))
648 ) => Matrix e cols a -> Matrix e cols b -> Matrix e cols (Normalize (a, b))
632−khatri a b =
649+kr a b =
633− let kp1' = kp1 @e @a @b
650+ let fstM' = fstM @e @a @b
634− kp2' = kp2 @e @a @b
651+ sndM' = sndM @e @a @b
635− in (tr kp1') . a * (tr kp2') . b
652+ in (tr fstM' . a) * (tr sndM' . b)
636
653
637-- Product Bifunctor (Kronecker)
654-- Product Bifunctor (Kronecker)
638
655
639infixl 4 ><
656infixl 4 ><
640
657
641-- | Matrix product functor also known as kronecker product
658-- | Matrix product functor also known as kronecker product
642−(><) ::
659+(><) ::
643− forall e m p n q.
660+ forall e m p n q.
644 ( Num e,
661 ( Num e,
645− CountableDimensions m n,
662+ CountableDims m n,
646− CountableDimensions p q,
663+ CountableDims p q,
647− CountableDimensionsN (m, n) (p, q),
664+ CountableDimsN (m, n) (p, q),
648− FromLists e (Normalize (m, n)) m,
665+ FL (Normalize (m, n)) m,
649− FromLists e (Normalize (m, n)) n,
666+ FL (Normalize (m, n)) n,
650− FromLists e (Normalize (p, q)) p,
667+ FL (Normalize (p, q)) p,
651− FromLists e (Normalize (p, q)) q
668+ FL (Normalize (p, q)) q
652− )
669+ )
653 => Matrix e m p -> Matrix e n q -> Matrix e (Normalize (m, n)) (Normalize (p, q))
670 => Matrix e m p -> Matrix e n q -> Matrix e (Normalize (m, n)) (Normalize (p, q))
654(><) a b =
671(><) a b =
655− let kp1' = kp1 @e @m @n
672+ let fstM' = fstM @e @m @n
656− kp2' = kp2 @e @m @n
673+ sndM' = sndM @e @m @n
657− in khatri (a . kp1') (b . kp2')
674+ in kr (a . fstM') (b . sndM')
658
675
659−-- Matrix abide Junc Split
676+-- Matrix abide Join Fork
660
677
661−-- | Matrix "abiding" followin the 'Junc'-'Split' abide law.
678+-- | Matrix "abiding" following the 'Join'-'Fork' exchange law.
662−--
679+--
663-- Law:
680-- Law:
664--
681--
665-- @
682-- @
666−-- 'Junc' ('Split' a c) ('Split' b d) == 'Split' ('Junc' a b) ('Junc' c d)
683+-- 'Join' ('Fork' a c) ('Fork' b d) == 'Fork' ('Join' a b) ('Join' c d)
667-- @
684-- @
668−abideJS :: Matrix e cols rows -> Matrix e cols rows
685+abideJF :: Matrix e cols rows -> Matrix e cols rows
669−abideJS (Junc (Split a c) (Split b d)) = Split (Junc (abideJS a) (abideJS b)) (Junc (abideJS c) (abideJS d)) -- Junc-Split abide law
686+abideJF (Join (Fork a c) (Fork b d)) = Fork (Join (abideJF a) (abideJF b)) (Join (abideJF c) (abideJF d)) -- Join-Fork abide law
670−abideJS Empty = Empty
671−abideJS (One e) = One e
687+abideJF (One e) = One e
672−abideJS (Junc a b) = Junc (abideJS a) (abideJS b)
688+abideJF (Join a b) = Join (abideJF a) (abideJF b)
673−abideJS (Split a b) = Split (abideJS a) (abideJS b)
689+abideJF (Fork a b) = Fork (abideJF a) (abideJF b)
674
690
675−-- Matrix abide Split Junc
691+-- Matrix abide Fork Join
676
692
677−-- | Matrix "abiding" followin the 'Split'-'Junc' abide law.
693+-- | Matrix "abiding" followin the 'Fork'-'Join' abide law.
678−--
694+--
679-- @
695-- @
680−-- 'Split' ('Junc' a b) ('Junc' c d) == 'Junc' ('Split' a c) ('Split' b d)
696+-- 'Fork' ('Join' a b) ('Join' c d) == 'Join' ('Fork' a c) ('Fork' b d)
681-- @
697-- @
682−abideSJ :: Matrix e cols rows -> Matrix e cols rows
698+abideFJ :: Matrix e cols rows -> Matrix e cols rows
683−abideSJ (Split (Junc a b) (Junc c d)) = Junc (Split (abideSJ a) (abideSJ c)) (Split (abideSJ b) (abideSJ d)) -- Split-Junc abide law
699+abideFJ (Fork (Join a b) (Join c d)) = Join (Fork (abideFJ a) (abideFJ c)) (Fork (abideFJ b) (abideFJ d)) -- Fork-Join abide law
684−abideSJ Empty = Empty
685−abideSJ (One e) = One e
700+abideFJ (One e) = One e
686−abideSJ (Junc a b) = Junc (abideSJ a) (abideSJ b)
701+abideFJ (Join a b) = Join (abideFJ a) (abideFJ b)
687−abideSJ (Split a b) = Split (abideSJ a) (abideSJ b)
702+abideFJ (Fork a b) = Fork (abideFJ a) (abideFJ b)
688
703
689-- Matrix transposition
704-- Matrix transposition
690
705
691-- | Matrix transposition.
706-- | Matrix transposition.
692tr :: Matrix e cols rows -> Matrix e rows cols
707tr :: Matrix e cols rows -> Matrix e rows cols
693−tr Empty = Empty
694−tr (One e) = One e
708+tr (One e) = One e
695−tr (Junc a b) = Split (tr a) (tr b)
709+tr (Join a b) = Fork (tr a) (tr b)
696−tr (Split a b) = Junc (tr a) (tr b)
710+tr (Fork a b) = Join (tr a) (tr b)
697
711
698-- Selective 'select' operator
712-- Selective 'select' operator
699
713
700-- | Selective functors 'select' operator equivalent inspired by the
714-- | Selective functors 'select' operator equivalent inspired by the
701-- ArrowMonad solution presented in the paper.
715-- ArrowMonad solution presented in the paper.
702−select :: (Num e, FromLists e b b, Countable b) => Matrix e cols (Either a b) -> Matrix e a b -> Matrix e cols b
716+select :: (Num e, FL b b, Countable b) => Matrix e cols (Either a b) -> Matrix e a b -> Matrix e cols b
703−select (Split a b) y = y . a + b -- Divide-and-conquer law
717+select (Fork a b) y = y . a + b -- Divide-and-conquer law
704−select (Junc (Split a c) (Split b d)) y = junc (y . a + c) (y . b + d) -- Pattern matching + DnC law
718+select (Join (Fork a c) (Fork b d)) y = join (y . a + c) (y . b + d) -- Pattern matching + DnC law
705−select m y = junc y identity . m
719+select m y = join y id . m
706
720
707branch ::
721branch ::
708 ( Num e,
722 ( Num e,
709− CountableDimensions a b,
723+ CountableDims a b,
710− CountableDimensions c (Either b c),
724+ CountableDims c (Either b c),
711− FromLists e c b,
725+ FL c b,
712− FromLists e a b,
726+ FL a b,
713− FromLists e a a,
727+ FL a a,
714− FromLists e b b,
728+ FL b b,
715− FromLists e c c,
729+ FL c c,
716− FromLists e b a,
730+ FL b a,
717− FromLists e b c,
731+ FL b c,
718− FromLists e (Either b c) b,
732+ FL (Either b c) b,
719− FromLists e (Either b c) c
733+ FL (Either b c) c
720 )
734 )
721 => Matrix e cols (Either a b) -> Matrix e a c -> Matrix e b c -> Matrix e cols c
735 => Matrix e cols (Either a b) -> Matrix e a c -> Matrix e b c -> Matrix e cols c
722branch x l r = f x `select` g l `select` r
736branch x l r = f x `select` g l `select` r
723 where
737 where
724− 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)
738+ f :: (Num e, Countable a, CountableDims b c, FL a b, FL c b, FL b b, FL b a, FL a a)
725 => Matrix e cols (Either a b) -> Matrix e cols (Either a (Either b c))
739 => Matrix e cols (Either a b) -> Matrix e cols (Either a (Either b c))
726− f m = split (tr i1) (i1 . tr i2) . m
740+ f m = fork (tr i1) (i1 . tr i2) . m
727− g :: (Num e, CountableDimensions b c, FromLists e b c, FromLists e c c) => Matrix e a c -> Matrix e a (Either b c)
741+ g :: (Num e, CountableDims b c, FL b c, FL c c) => Matrix e a c -> Matrix e a (Either b c)
728 g m = i2 . m
742 g m = i2 . m
729
743
730-- McCarthy's Conditional
744-- McCarthy's Conditional
@@ -733,9 +747,9 @@ branch x l r = f x `select` g l `select` r
733cond ::
747cond ::
734 ( Trivial cols,
748 ( Trivial cols,
735 Countable cols,
749 Countable cols,
736− FromLists e () cols,
750+ FL () cols,
737− FromLists e cols (),
751+ FL cols (),
738− FromLists e cols cols,
752+ FL cols cols,
739 Bounded a,
753 Bounded a,
740 Enum a,
754 Enum a,
741 Num e,
755 Num e,
@@ -743,14 +757,14 @@ cond ::
743 )
757 )
744 =>
758 =>
745 (a -> Bool) -> Matrix e cols rows -> Matrix e cols rows -> Matrix e cols rows
759 (a -> Bool) -> Matrix e cols rows -> Matrix e cols rows -> Matrix e cols rows
746−cond p f g = junc f g . grd p
760+cond p f g = join f g . grd p
747
761
748−grd ::
762+grd ::
749 ( Trivial q,
763 ( Trivial q,
750 Countable q,
764 Countable q,
751− FromLists e () q,
765+ FL () q,
752− FromLists e q (),
766+ FL q (),
753− FromLists e q q,
767+ FL q q,
754 Bounded a,
768 Bounded a,
755 Enum a,
769 Enum a,
756 Num e,
770 Num e,
@@ -758,44 +772,44 @@ grd ::
758 )
772 )
759 =>
773 =>
760 (a -> Bool) -> Matrix e q (Either q q)
774 (a -> Bool) -> Matrix e q (Either q q)
761−grd f = split (corr f) (corr (not . f))
775+grd f = fork (corr f) (corr (not . f))
762
776
763−corr ::
777+corr ::
764− forall e a q .
778+ forall e a q .
765 ( Trivial q,
779 ( Trivial q,
766 Countable q,
780 Countable q,
767− FromLists e () q,
781+ FL () q,
768− FromLists e q (),
782+ FL q (),
769− FromLists e q q,
783+ FL q q,
770 Liftable e a Bool
784 Liftable e a Bool
771− )
785+ )
772 => (a -> Bool) -> Matrix e q q
786 => (a -> Bool) -> Matrix e q q
773−corr p = let f = fromF p :: Matrix e q ()
787+corr p = let f = fromF' p :: Matrix e q ()
774− in khatri f (identity :: Matrix e q q)
788+ in kr f (id :: Matrix e q q)
775
789
776-- Pretty print
790-- Pretty print
777
791
778prettyAux :: Show e => [[e]] -> [[e]] -> String
792prettyAux :: Show e => [[e]] -> [[e]] -> String
779prettyAux [] _ = ""
793prettyAux [] _ = ""
780−prettyAux [[e]] m = "│ " ++ fill (show e) ++ " │\n"
794+prettyAux [[e]] m = "│ " ++ fill (show e) ++ " │\n"
781 where
795 where
782 v = fmap show m
796 v = fmap show m
783 widest = maximum $ fmap length v
797 widest = maximum $ fmap length v
784 fill str = replicate (widest - length str - 2) ' ' ++ str
798 fill str = replicate (widest - length str - 2) ' ' ++ str
785−prettyAux [h] m = "│ " ++ fill (unwords $ map show h) ++ " │\n"
799+prettyAux [h] m = "│ " ++ fill (unwords $ map show h) ++ " │\n"
786 where
800 where
787− v = fmap show m
801+ v = fmap show m
788− widest = maximum $ fmap length v
802+ widest = maximum $ fmap length v
789 fill str = replicate (widest - length str - 2) ' ' ++ str
803 fill str = replicate (widest - length str - 2) ' ' ++ str
790−prettyAux (h : t) l = "│ " ++ fill (unwords $ map show h) ++ " │\n" ++
804+prettyAux (h : t) l = "│ " ++ fill (unwords $ map show h) ++ " │\n" ++
791 prettyAux t l
805 prettyAux t l
792 where
806 where
793− v = fmap show l
807+ v = fmap show l
794− widest = maximum $ fmap length v
808+ widest = maximum $ fmap length v
795 fill str = replicate (widest - length str - 2) ' ' ++ str
809 fill str = replicate (widest - length str - 2) ' ' ++ str
796
810
797-- | Matrix pretty printer
811-- | Matrix pretty printer
798−pretty :: (CountableDimensions cols rows, Show e) => Matrix e cols rows -> String
812+pretty :: (CountableDims cols rows, Show e) => Matrix e cols rows -> String
799pretty m = concat
813pretty m = concat
800 [ "┌ ", unwords (replicate (columns m) blank), " ┐\n"
814 [ "┌ ", unwords (replicate (columns m) blank), " ┐\n"
801 , unlines
815 , unlines
@@ -803,16 +817,16 @@ pretty m = concat
803 , "└ ", unwords (replicate (columns m) blank), " ┘"
817 , "└ ", unwords (replicate (columns m) blank), " ┘"
804 ]
818 ]
805 where
819 where
806− strings = map show (toList m)
820+ strings = map show (toList m)
807− widest = maximum $ map length strings
821+ widest = maximum $ map length strings
808 fill str = replicate (widest - length str) ' ' ++ str
822 fill str = replicate (widest - length str) ' ' ++ str
809− blank = fill ""
823+ blank = fill ""
810 safeGet i j m
824 safeGet i j m
811 | i > rows m || j > columns m || i < 1 || j < 1 = Nothing
825 | i > rows m || j > columns m || i < 1 || j < 1 = Nothing
812 | otherwise = Just $ unsafeGet i j m (toList m)
826 | otherwise = Just $ unsafeGet i j m (toList m)
813 unsafeGet i j m l = l !! encode (columns m) (i,j)
827 unsafeGet i j m l = l !! encode (columns m) (i,j)
814− encode m (i,j) = (i-1)*m + j - 1
828+ encode m (i,j) = (i-1)*m + j - 1
815− getElem i j m =
829+ getElem i j m =
816 fromMaybe
830 fromMaybe
817 (error $
831 (error $
818 "getElem: Trying to get the "
832 "getElem: Trying to get the "
@@ -824,12 +838,20 @@ pretty m = concat
824 (safeGet i j m)
838 (safeGet i j m)
825
839
826-- | Matrix pretty printer
840-- | Matrix pretty printer
827−prettyPrint :: (CountableDimensions cols rows, Show e) => Matrix e cols rows -> IO ()
841+prettyPrint :: (CountableDims cols rows, Show e) => Matrix e cols rows -> IO ()
828prettyPrint = putStrLn . pretty
842prettyPrint = putStrLn . pretty
829
843
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+
830-- Relational operators functions
852-- Relational operators functions
831
853
832−type Boolean = Natural 0 1
854+type Boolean = Natural 0 1
833type Relation a b = Matrix Boolean a b
855type Relation a b = Matrix Boolean a b
834
856
835-- | Helper conversion function
857-- | Helper conversion function
@@ -845,54 +867,47 @@ fromBool False = nat 0
845
867
846-- | Relational negation
868-- | Relational negation
847negateM :: Relation cols rows -> Relation cols rows
869negateM :: Relation cols rows -> Relation cols rows
848−negateM Empty = Empty
849−negateM (One (Nat 0)) = One (Nat 1)
870+negateM (One (Nat p)) = One (Nat (negate p))
850−negateM (One (Nat 1)) = One (Nat 0)
851−negateM (Junc a b) = Junc (negateM a) (negateM b)
871+negateM (Join a b) = Join (negateM a) (negateM b)
852−negateM (Split a b) = Split (negateM a) (negateM b)
872+negateM (Fork a b) = Fork (negateM a) (negateM b)
853
873
854-- | Relational addition
874-- | Relational addition
855orM :: Relation cols rows -> Relation cols rows -> Relation cols rows
875orM :: Relation cols rows -> Relation cols rows -> Relation cols rows
856−orM Empty Empty = Empty
857−orM (One a) (One b) = One (fromBool (toBool a || toBool b))
876+orM (One a) (One b) = One (fromBool (toBool a || toBool b))
858−orM (Junc a b) (Junc c d) = Junc (orM a c) (orM b d)
877+orM (Join a b) (Join c d) = Join (orM a c) (orM b d)
859−orM (Split a b) (Split c d) = Split (orM a c) (orM b d)
878+orM (Fork a b) (Fork c d) = Fork (orM a c) (orM b d)
860−orM x@(Split _ _) y@(Junc _ _) = orM x (abideJS y)
879+orM x@(Fork _ _) y@(Join _ _) = orM x (abideJF y)
861−orM x@(Junc _ _) y@(Split _ _) = orM (abideJS x) y
880+orM x@(Join _ _) y@(Fork _ _) = orM (abideJF x) y
862
881
863-- | Relational multiplication
882-- | Relational multiplication
864andM :: Relation cols rows -> Relation cols rows -> Relation cols rows
883andM :: Relation cols rows -> Relation cols rows -> Relation cols rows
865−andM Empty Empty = Empty
866−andM (One a) (One b) = One (fromBool (toBool a && toBool b))
884+andM (One a) (One b) = One (fromBool (toBool a && toBool b))
867−andM (Junc a b) (Junc c d) = Junc (andM a c) (andM b d)
885+andM (Join a b) (Join c d) = Join (andM a c) (andM b d)
868−andM (Split a b) (Split c d) = Split (andM a c) (andM b d)
886+andM (Fork a b) (Fork c d) = Fork (andM a c) (andM b d)
869−andM x@(Split _ _) y@(Junc _ _) = andM x (abideJS y)
887+andM x@(Fork _ _) y@(Join _ _) = andM x (abideJF y)
870−andM x@(Junc _ _) y@(Split _ _) = andM (abideJS x) y
888+andM x@(Join _ _) y@(Fork _ _) = andM (abideJF x) y
871
889
872-- | Relational subtraction
890-- | Relational subtraction
873subM :: Relation cols rows -> Relation cols rows -> Relation cols rows
891subM :: Relation cols rows -> Relation cols rows -> Relation cols rows
874−subM Empty Empty = Empty
875−subM (One a) (One b) = if a - b < nat 0 then One (nat 0) else One (a - b)
892+subM (One a) (One b) = if a - b < nat 0 then One (nat 0) else One (a - b)
876−subM (Junc a b) (Junc c d) = Junc (subM a c) (subM b d)
893+subM (Join a b) (Join c d) = Join (subM a c) (subM b d)
877−subM (Split a b) (Split c d) = Split (subM a c) (subM b d)
894+subM (Fork a b) (Fork c d) = Fork (subM a c) (subM b d)
878−subM x@(Split _ _) y@(Junc _ _) = subM x (abideJS y)
895+subM x@(Fork _ _) y@(Join _ _) = subM x (abideJF y)
879−subM x@(Junc _ _) y@(Split _ _) = subM (abideJS x) y
896+subM x@(Join _ _) y@(Fork _ _) = subM (abideJF x) y
880
897
881-- | Matrix relational composition.
898-- | Matrix relational composition.
882compRel :: Relation cr rows -> Relation cols cr -> Relation cols rows
899compRel :: Relation cr rows -> Relation cols cr -> Relation cols rows
883−compRel Empty Empty = Empty
884−compRel (One a) (One b) = One (fromBool (toBool a && toBool b))
900+compRel (One a) (One b) = One (fromBool (toBool a && toBool b))
885−compRel (Junc a b) (Split c d) = orM (compRel a c) (compRel b d) -- Divide-and-conquer law
901+compRel (Join a b) (Fork c d) = orM (compRel a c) (compRel b d) -- Divide-and-conquer law
886−compRel (Split a b) c = Split (compRel a c) (compRel b c) -- Split fusion law
902+compRel (Fork a b) c = Fork (compRel a c) (compRel b c) -- Fork fusion law
887−compRel c (Junc a b) = Junc (compRel c a) (compRel c b) -- Junc fusion law
903+compRel c (Join a b) = Join (compRel c a) (compRel c b) -- Join fusion law
888
904
889-- | Matrix relational right division
905-- | Matrix relational right division
890divR :: Relation b c -> Relation b a -> Relation a c
906divR :: Relation b c -> Relation b a -> Relation a c
891−divR Empty Empty = Empty
892divR (One a) (One b) = One (fromBool (not (toBool b) || toBool a)) -- b implies a
907divR (One a) (One b) = One (fromBool (not (toBool b) || toBool a)) -- b implies a
893−divR (Junc a b) (Junc c d) = andM (divR a c) (divR b d)
908+divR (Join a b) (Join c d) = andM (divR a c) (divR b d)
894−divR (Split a b) c = Split (divR a c) (divR b c)
909+divR (Fork a b) c = Fork (divR a c) (divR b c)
895−divR c (Split a b) = Junc (divR c a) (divR c b)
910+divR c (Fork a b) = Join (divR c a) (divR c b)
896
911
897-- | Matrix relational left division
912-- | Matrix relational left division
898divL :: Relation c b -> Relation a b -> Relation a c
913divL :: Relation c b -> Relation a b -> Relation a c
@@ -908,86 +923,52 @@ divS s r = divL r s `intersection` divR (tr r) (tr s)
908--
923--
909-- NOTE: Be careful to not ask for a relation bigger than the cardinality of
924-- NOTE: Be careful to not ask for a relation bigger than the cardinality of
910-- types @a@ or @b@ allows.
925-- types @a@ or @b@ allows.
911−fromFRel ::
926+fromFRel' ::
912 forall a b cols rows.
927 forall a b cols rows.
913 ( Liftable Boolean a b,
928 ( Liftable Boolean a b,
914− CountableDimensions cols rows,
929+ CountableDims cols rows,
915− FromLists Boolean rows cols
930+ FL rows cols
916 ) =>
931 ) =>
917 (a -> b) ->
932 (a -> b) ->
918 Relation cols rows
933 Relation cols rows
919−fromFRel f =
934+fromFRel' = fromF'
920− let minA = minBound @a
921− maxA = maxBound @a
922− minB = minBound @b
923− maxB = maxBound @b
924− ccols = fromInteger $ natVal (Proxy :: Proxy (Count cols))
925− rrows = fromInteger $ natVal (Proxy :: Proxy (Count rows))
926− elementsA = take ccols [minA .. maxA]
927− elementsB = take rrows [minB .. maxB]
928− combinations = (,) <$> elementsA <*> elementsB
929− combAp = map snd . sort . map (\(a, b) -> if f a == b
930− then ((fromEnum a, fromEnum b), nat 1)
931− else ((fromEnum a, fromEnum b), nat 0)) $ combinations
932− mList = buildList combAp rrows
933− in tr $ fromLists mList
934− where
935− buildList [] _ = []
936− buildList l r = take r l : buildList (drop r l) r
937
935
938-- | Lifts functions to relations with dimensions matching @a@ and @b@
936-- | Lifts functions to relations with dimensions matching @a@ and @b@
939-- cardinality's.
937-- cardinality's.
940−fromFRel' ::
938+fromFRel ::
941 forall a b.
939 forall a b.
942 ( Liftable Boolean a b,
940 ( Liftable Boolean a b,
943− CountableDimensionsN a b,
941+ CountableDimsN a b,
944− FromLists Boolean (Normalize b) (Normalize a)
942+ FLN b a
945 ) =>
943 ) =>
946 (a -> b) ->
944 (a -> b) ->
947 Relation (Normalize a) (Normalize b)
945 Relation (Normalize a) (Normalize b)
948−fromFRel' f =
946+fromFRel = fromFRel'
949− let minA = minBound @a
950− maxA = maxBound @a
951− minB = minBound @b
952− maxB = maxBound @b
953− ccols = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize a)))
954− rrows = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize b)))
955− elementsA = take ccols [minA .. maxA]
956− elementsB = take rrows [minB .. maxB]
957− combinations = (,) <$> elementsA <*> elementsB
958− combAp = map snd . sort . map (\(a, b) -> if f a == b
959− then ((fromEnum a, fromEnum b), nat 1)
960− else ((fromEnum a, fromEnum b), nat 0)) $ combinations
961− mList = buildList combAp rrows
962− in tr $ fromLists mList
963− where
964− buildList [] _ = []
965− buildList l r = take r l : buildList (drop r l) r
966
947
967-- | Lifts a relation function to a Boolean Matrix
948-- | Lifts a relation function to a Boolean Matrix
968−toRel ::
949+toRel ::
969 forall a b.
950 forall a b.
970 ( Bounded a,
951 ( Bounded a,
971 Bounded b,
952 Bounded b,
972 Enum a,
953 Enum a,
973 Enum b,
954 Enum b,
974 Eq b,
955 Eq b,
975− CountableDimensionsN a b,
956+ CountableDims a b,
976− FromListsN Boolean b a
957+ FLN b a
977− )
958+ )
978 => (a -> b -> Bool) -> Relation (Normalize a) (Normalize b)
959 => (a -> b -> Bool) -> Relation (Normalize a) (Normalize b)
979toRel f =
960toRel f =
980 let minA = minBound @a
961 let minA = minBound @a
981 maxA = maxBound @a
962 maxA = maxBound @a
982 minB = minBound @b
963 minB = minBound @b
983 maxB = maxBound @b
964 maxB = maxBound @b
984− ccols = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize a)))
965+ ccols = fromInteger $ natVal (Proxy :: Proxy (Count a))
985− rrows = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize b)))
966+ rrows = fromInteger $ natVal (Proxy :: Proxy (Count b))
986 elementsA = take ccols [minA .. maxA]
967 elementsA = take ccols [minA .. maxA]
987 elementsB = take rrows [minB .. maxB]
968 elementsB = take rrows [minB .. maxB]
988 combinations = (,) <$> elementsA <*> elementsB
969 combinations = (,) <$> elementsA <*> elementsB
989− 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)
990− then ((fromEnum a, fromEnum b), nat 1)
971+ then ((fromEnum a, fromEnum b), nat 1)
991 else ((fromEnum a, fromEnum b), nat 0)) $ combinations
972 else ((fromEnum a, fromEnum b), nat 0)) $ combinations
992 mList = buildList combAp rrows
973 mList = buildList combAp rrows
993 in tr $ fromLists mList
974 in tr $ fromLists mList
src/LAoP/Matrix/Nat.hs+139−124
@@ -56,21 +56,20 @@ module LAoP.Matrix.Nat
56
56
57 -- * Constraint type synonyms
57 -- * Constraint type synonyms
58 Countable,
58 Countable,
59− CountableDimensions,
59+ CountableDims,
60 CountableN,
60 CountableN,
61 CountableNz,
61 CountableNz,
62− CountableDimensionsN,
62+ CountableDimsN,
63− FromListsN,
63+ FLN,
64− FromListsNz,
64+ FLNz,
65 Liftable,
65 Liftable,
66 TrivialE,
66 TrivialE,
67 TrivialP,
67 TrivialP,
68
68
69 -- * Primitives
69 -- * Primitives
70− empty,
71 one,
70 one,
72− junc,
71+ join,
73− split,
72+ fork,
74
73
75 -- * Auxiliary type families
74 -- * Auxiliary type families
76 I.FromNat,
75 I.FromNat,
@@ -78,11 +77,11 @@ module LAoP.Matrix.Nat
78 I.Normalize,
77 I.Normalize,
79
78
80 -- * Matrix construction and conversion
79 -- * Matrix construction and conversion
81− I.FromLists,
80+ I.FL,
82 fromLists,
81 fromLists,
83 toLists,
82 toLists,
84 toList,
83 toList,
85− matrixBuilder,
84+ matrixBuilder',
86 row,
85 row,
87 col,
86 col,
88 zeros,
87 zeros,
@@ -98,6 +97,10 @@ module LAoP.Matrix.Nat
98 -- ** Matrix Transposition
97 -- ** Matrix Transposition
99 tr,
98 tr,
100
99
100+ -- ** Scalar multiplication/division of matrices
101+ (.|),
102+ (./),
103+
101 -- ** Selective operator
104 -- ** Selective operator
102 select,
105 select,
103
106
@@ -105,16 +108,19 @@ module LAoP.Matrix.Nat
105 cond,
108 cond,
106
109
107 -- ** Matrix "abiding"
110 -- ** Matrix "abiding"
108− abideJS,
111+ abideJF,
109− abideSJ,
112+ abideFJ,
113+
114+ -- ** Zip Matrices
115+ zipWithM,
110
116
111 -- * Biproduct approach
117 -- * Biproduct approach
112− -- ** Split
118+ -- ** Fork
113 (===),
119 (===),
114 -- *** Projections
120 -- *** Projections
115 p1,
121 p1,
116 p2,
122 p2,
117− -- ** Junc
123+ -- ** Join
118 (|||),
124 (|||),
119 -- *** Injections
125 -- *** Injections
120 i1,
126 i1,
@@ -128,11 +134,11 @@ module LAoP.Matrix.Nat
128 -- | Note that given the restrictions imposed it is not possible to
134 -- | Note that given the restrictions imposed it is not possible to
129 -- implement the standard type classes present in standard Haskell.
135 -- implement the standard type classes present in standard Haskell.
130 -- *** Matrix pairing projections
136 -- *** Matrix pairing projections
131− kp1,
137+ fstM,
132− kp2,
138+ sndM,
133
139
134 -- *** Matrix pairing
140 -- *** Matrix pairing
135− khatri,
141+ kr,
136
142
137 -- * Matrix composition and lifting
143 -- * Matrix composition and lifting
138
144
@@ -140,10 +146,10 @@ module LAoP.Matrix.Nat
140
146
141 -- | Note that given the restrictions imposed it is not possible to
147 -- | Note that given the restrictions imposed it is not possible to
142 -- implement the standard type classes present in standard Haskell.
148 -- implement the standard type classes present in standard Haskell.
143− identity,
149+ iden,
144 comp,
150 comp,
145− fromF,
146 fromF',
151 fromF',
152+ fromF,
147
153
148 -- * Matrix printing
154 -- * Matrix printing
149 pretty,
155 pretty,
@@ -154,47 +160,34 @@ where
154import Data.Proxy
160import Data.Proxy
155import GHC.TypeLits
161import GHC.TypeLits
156import Control.DeepSeq
162import Control.DeepSeq
157−import qualified Control.Category as C
158import qualified LAoP.Matrix.Internal as I
163import qualified LAoP.Matrix.Internal as I
159
164
160newtype Matrix e (cols :: Nat) (rows :: Nat) = M (I.Matrix e (I.FromNat cols) (I.FromNat rows))
165newtype Matrix e (cols :: Nat) (rows :: Nat) = M (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))
166 deriving (Show, Num, Eq, Ord, NFData) via (I.Matrix e (I.FromNat cols) (I.FromNat rows))
162
167
163-- | Constraint type synonyms to keep the type signatures less convoluted
168-- | Constraint type synonyms to keep the type signatures less convoluted
164−type Countable a = KnownNat (I.Count a)
169+type Countable a = KnownNat (I.Count a)
165−type CountableDimensions a b = (Countable a, Countable b)
170+type CountableDims a b = (Countable a, Countable b)
166−type CountableN a = KnownNat (I.Count (I.FromNat a))
171+type CountableN a = KnownNat (I.Count (I.FromNat a))
167−type CountableNz a = KnownNat (I.Count (I.Normalize a))
172+type CountableNz a = KnownNat (I.Count (I.Normalize a))
168−type CountableDimensionsN a b = (CountableN a, CountableN b)
173+type CountableDimsN a b = (CountableN a, CountableN b)
169−type FromListsN e a b = I.FromLists e (I.FromNat a) (I.FromNat b)
174+type FLN e a b = I.FL (I.FromNat a) (I.FromNat b)
170−type FromListsNz e a b = I.FromLists e (I.Normalize a) (I.Normalize b)
175+type FLNz e a b = I.FL (I.Normalize a) (I.Normalize b)
171−type Liftable e a b = (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num e, Ord e)
176+type Liftable e a b = (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num e, Ord e)
172−type TrivialE a b = I.FromNat (a + b) ~ Either (I.FromNat a) (I.FromNat b)
177+type TrivialE a b = I.FromNat (a + b) ~ Either (I.FromNat a) (I.FromNat b)
173−type TrivialP a b = I.FromNat (a * b) ~ I.FromNat (I.Count (I.FromNat a) * I.Count (I.FromNat b))
178+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
183
179
184-- Primitives
180-- Primitives
185
181
186−empty :: Matrix e 0 0
187−empty = M I.Empty
188−
189one :: e -> Matrix e 1 1
182one :: e -> Matrix e 1 1
190one = M . I.One
183one = M . I.One
191
184
192−junc ::
185+join ::
193 (TrivialE a b) =>
186 (TrivialE a b) =>
194 Matrix e a rows ->
187 Matrix e a rows ->
195 Matrix e b rows ->
188 Matrix e b rows ->
196 Matrix e (a + b) rows
189 Matrix e (a + b) rows
197−junc (M a) (M b) = M (I.Junc a b)
190+join (M a) (M b) = M (I.Join a b)
198
191
199infixl 3 |||
192infixl 3 |||
200(|||) ::
193(|||) ::
@@ -202,14 +195,14 @@ infixl 3 |||
202 Matrix e a rows ->
195 Matrix e a rows ->
203 Matrix e b rows ->
196 Matrix e b rows ->
204 Matrix e (a + b) rows
197 Matrix e (a + b) rows
205−(|||) = junc
198+(|||) = join
206
199
207−split ::
200+fork ::
208 (TrivialE a b) =>
201 (TrivialE a b) =>
209 Matrix e cols a ->
202 Matrix e cols a ->
210 Matrix e cols b ->
203 Matrix e cols b ->
211 Matrix e cols (a + b)
204 Matrix e cols (a + b)
212−split (M a) (M b) = M (I.Split a b)
205+fork (M a) (M b) = M (I.Fork a b)
213
206
214infixl 2 ===
207infixl 2 ===
215(===) ::
208(===) ::
@@ -217,43 +210,45 @@ infixl 2 ===
217 Matrix e cols a ->
210 Matrix e cols a ->
218 Matrix e cols b ->
211 Matrix e cols b ->
219 Matrix e cols (a + b)
212 Matrix e cols (a + b)
220−(===) = split
213+(===) = fork
221
214
222-- Construction
215-- Construction
223
216
224−fromLists :: (FromListsN e cols rows) => [[e]] -> Matrix e cols rows
217+fromLists :: (FLN e cols rows) => [[e]] -> Matrix e cols rows
225fromLists = M . I.fromLists
218fromLists = M . I.fromLists
226
219
220+-- | Matrix builder function. Constructs a matrix provided with
221+-- a construction function that operates with indices.
227−matrixBuilder ::
222+matrixBuilder' ::
228− (FromListsN e cols rows, CountableN cols, CountableN rows)
223+ (FLN e cols rows, CountableN cols, CountableN rows)
229 => ((Int, Int) -> e) -> Matrix e cols rows
224 => ((Int, Int) -> e) -> Matrix e cols rows
230−matrixBuilder = M . I.matrixBuilder
225+matrixBuilder' = M . I.matrixBuilder'
231
226
232−col :: (I.FromLists e () (I.FromNat rows)) => [e] -> Matrix e 1 rows
227+col :: (I.FL () (I.FromNat rows)) => [e] -> Matrix e 1 rows
233col = M . I.col
228col = M . I.col
234
229
235−row :: (I.FromLists e (I.FromNat cols) ()) => [e] -> Matrix e cols 1
230+row :: (I.FL (I.FromNat cols) ()) => [e] -> Matrix e cols 1
236row = M . I.row
231row = M . I.row
237
232
238−fromF ::
233+fromF' ::
239 ( Liftable e a b,
234 ( Liftable e a b,
240 CountableN cols,
235 CountableN cols,
241 CountableN rows,
236 CountableN rows,
242− FromListsN e rows cols
237+ FLN e rows cols
243 ) =>
238 ) =>
244 (a -> b) ->
239 (a -> b) ->
245 Matrix e cols rows
240 Matrix e cols rows
246−fromF = M . I.fromF
241+fromF' = M . I.fromF'
247
242
248−fromF' ::
243+fromF ::
249 ( Liftable e a b,
244 ( Liftable e a b,
250 CountableNz a,
245 CountableNz a,
251 CountableNz b,
246 CountableNz b,
252− FromListsNz e b a
247+ FLNz e b a
253 ) =>
248 ) =>
254 (a -> b) ->
249 (a -> b) ->
255 Matrix e (I.Count a) (I.Count b)
250 Matrix e (I.Count a) (I.Count b)
256−fromF' = undefined -- M . I.fromF'
251+fromF = undefined -- M . I.fromF
257
252
258-- Conversion
253-- Conversion
259
254
@@ -266,21 +261,21 @@ toList (M m) = I.toList m
266-- Zeros Matrix
261-- Zeros Matrix
267
262
268zeros ::
263zeros ::
269− (Num e, FromListsN e cols rows, CountableN cols, CountableN rows) =>
264+ (Num e, FLN e cols rows, CountableN cols, CountableN rows) =>
270 Matrix e cols rows
265 Matrix e cols rows
271zeros = M I.zeros
266zeros = M I.zeros
272
267
273-- Ones Matrix
268-- Ones Matrix
274
269
275ones ::
270ones ::
276− (Num e, FromListsN e cols rows, CountableN cols, CountableN rows) =>
271+ (Num e, FLN e cols rows, CountableN cols, CountableN rows) =>
277 Matrix e cols rows
272 Matrix e cols rows
278ones = M I.ones
273ones = M I.ones
279
274
280-- Const Matrix
275-- Const Matrix
281
276
282constant ::
277constant ::
283− (Num e, FromListsN e cols rows, CountableN cols, CountableN rows) =>
278+ (Num e, FLN e cols rows, CountableN cols, CountableN rows) =>
284 e ->
279 e ->
285 Matrix e cols rows
280 Matrix e cols rows
286constant = M . I.constant
281constant = M . I.constant
@@ -289,27 +284,41 @@ constant = M . I.constant
289
284
290bang ::
285bang ::
291 forall e cols.
286 forall e cols.
292− (Num e, Enum e, I.FromLists e (I.FromNat cols) (), CountableN cols) =>
287+ (Num e, Enum e, I.FL (I.FromNat cols) (), CountableN cols) =>
293 Matrix e cols 1
288 Matrix e cols 1
294bang = M I.bang
289bang = M I.bang
295
290
296−-- Identity Matrix
291+-- iden Matrix
297
292
298−identity ::
293+iden ::
299− (Num e, FromListsN e cols cols, CountableN cols) =>
294+ (Num e, FLN e cols cols, CountableN cols) =>
300 Matrix e cols cols
295 Matrix e cols cols
301−identity = M I.identity
296+iden = M I.iden
302
297
303-- Matrix composition (MMM)
298-- Matrix composition (MMM)
304
299
305comp :: (Num e) => Matrix e cr rows -> Matrix e cols cr -> Matrix e cols rows
300comp :: (Num e) => Matrix e cr rows -> Matrix e cols cr -> Matrix e cols rows
306comp (M a) (M b) = M (I.comp a b)
301comp (M a) (M b) = M (I.comp a b)
307
302
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+
308p1 ::
317p1 ::
309 ( Num e,
318 ( Num e,
310− CountableDimensionsN n m,
319+ CountableDimsN n m,
311− FromListsN e n m,
320+ FLN e n m,
312− FromListsN e m m,
321+ FLN e m m,
313 TrivialE m n
322 TrivialE m n
314 ) =>
323 ) =>
315 Matrix e (m + n) m
324 Matrix e (m + n) m
@@ -317,9 +326,9 @@ p1 = M I.p1
317
326
318p2 ::
327p2 ::
319 ( Num e,
328 ( Num e,
320− CountableDimensionsN n m,
329+ CountableDimsN n m,
321− FromListsN e m n,
330+ FLN e m n,
322− FromListsN e n n,
331+ FLN e n n,
323 TrivialE m n
332 TrivialE m n
324 ) =>
333 ) =>
325 Matrix e (m + n) n
334 Matrix e (m + n) n
@@ -329,9 +338,9 @@ p2 = M I.p2
329
338
330i1 ::
339i1 ::
331 ( Num e,
340 ( Num e,
332− CountableDimensionsN n rows,
341+ CountableDimsN n rows,
333− FromListsN e n rows,
342+ FLN e n rows,
334− FromListsN e rows rows,
343+ FLN e rows rows,
335 TrivialE rows n
344 TrivialE rows n
336 ) =>
345 ) =>
337 Matrix e rows (rows + n)
346 Matrix e rows (rows + n)
@@ -339,9 +348,9 @@ i1 = tr p1
339
348
340i2 ::
349i2 ::
341 ( Num e,
350 ( Num e,
342− CountableDimensionsN rows m,
351+ CountableDimsN rows m,
343− FromListsN e m rows,
352+ FLN e m rows,
344− FromListsN e rows rows,
353+ FLN e rows rows,
345 TrivialE m rows
354 TrivialE m rows
346 ) =>
355 ) =>
347 Matrix e rows (m + rows)
356 Matrix e rows (m + rows)
@@ -355,16 +364,16 @@ rows (M m) = I.rows m
355columns :: (CountableN cols) => Matrix e cols rows -> Int
364columns :: (CountableN cols) => Matrix e cols rows -> Int
356columns (M m) = I.columns m
365columns (M m) = I.columns m
357
366
358−-- | Coproduct Bifunctor
359infixl 5 -|-
367infixl 5 -|-
360
368
369+-- | Coproduct Bifunctor (Direct sum)
361(-|-) ::
370(-|-) ::
362 ( Num e,
371 ( Num e,
363− CountableDimensionsN j k,
372+ CountableDimsN j k,
364− FromListsN e k k,
373+ FLN e k k,
365− FromListsN e j k,
374+ FLN e j k,
366− FromListsN e k j,
375+ FLN e k j,
367− FromListsN e j j,
376+ FLN e j j,
368 TrivialE n m,
377 TrivialE n m,
369 TrivialE k j
378 TrivialE k j
370 ) =>
379 ) =>
@@ -373,40 +382,42 @@ infixl 5 -|-
373 Matrix e (n + m) (k + j)
382 Matrix e (n + m) (k + j)
374(-|-) (M a) (M b) = M ((I.-|-) a b)
383(-|-) (M a) (M b) = M ((I.-|-) a b)
375
384
376−-- | Khatri Rao Product and projections
385+-- | Khatri Rao Product first projection
377−kp1 ::
386+fstM ::
378 forall e m k .
387 forall e m k .
379 ( Num e,
388 ( Num e,
380− CountableDimensionsN m k,
389+ CountableDimsN m k,
381 CountableN (m * k),
390 CountableN (m * k),
382− FromListsN e (m * k) m,
391+ FLN e (m * k) m,
383 TrivialP m k
392 TrivialP m k
384 ) => Matrix e (m * k) m
393 ) => Matrix e (m * k) m
385−kp1 = M (I.kp1 @e @(I.FromNat m) @(I.FromNat k))
394+fstM = M (I.fstM @e @(I.FromNat m) @(I.FromNat k))
386
395
387−kp2 ::
396+-- | Khatri Rao Product second projection
397+sndM ::
388 forall e m k.
398 forall e m k.
389 ( Num e,
399 ( Num e,
390− CountableDimensionsN k m,
400+ CountableDimsN k m,
391− FromListsN e (m * k) k,
401+ FLN e (m * k) k,
392 CountableN (m * k),
402 CountableN (m * k),
393 TrivialP m k
403 TrivialP m k
394 ) => Matrix e (m * k) k
404 ) => Matrix e (m * k) k
395−kp2 = M (I.kp2 @e @(I.FromNat m) @(I.FromNat k))
405+sndM = M (I.sndM @e @(I.FromNat m) @(I.FromNat k))
396
406
397−khatri ::
407+-- | Khatri Rao Product
408+kr ::
398 forall e cols a b.
409 forall e cols a b.
399 ( Num e,
410 ( Num e,
400− CountableDimensionsN a b,
411+ CountableDimsN a b,
401 CountableN (a * b),
412 CountableN (a * b),
402− FromListsN e (a * b) a,
413+ FLN e (a * b) a,
403− FromListsN e (a * b) b,
414+ FLN e (a * b) b,
404 TrivialP a b
415 TrivialP a b
405 ) => Matrix e cols a -> Matrix e cols b -> Matrix e cols (a * b)
416 ) => Matrix e cols a -> Matrix e cols b -> Matrix e cols (a * b)
406−khatri a b =
417+kr a b =
407− let kp1' = kp1 @e @a @b
418+ let fstM' = fstM @e @a @b
408− kp2' = kp2 @e @a @b
419+ sndM' = sndM @e @a @b
409− in comp (tr kp1') a * comp (tr kp2') b
420+ in comp (tr fstM') a * comp (tr sndM') b
410
421
411-- | Product Bifunctor (Kronecker)
422-- | Product Bifunctor (Kronecker)
412infixl 4 ><
423infixl 4 ><
@@ -414,28 +425,28 @@ infixl 4 ><
414(><) ::
425(><) ::
415 forall e m p n q.
426 forall e m p n q.
416 ( Num e,
427 ( Num e,
417− CountableDimensionsN m n,
428+ CountableDimsN m n,
418− CountableDimensionsN p q,
429+ CountableDimsN p q,
419− CountableDimensionsN (m * n) (p * q),
430+ CountableDimsN (m * n) (p * q),
420− FromListsN e (m * n) m,
431+ FLN e (m * n) m,
421− FromListsN e (m * n) n,
432+ FLN e (m * n) n,
422− FromListsN e (p * q) p,
433+ FLN e (p * q) p,
423− FromListsN e (p * q) q,
434+ FLN e (p * q) q,
424 TrivialP m n,
435 TrivialP m n,
425 TrivialP p q
436 TrivialP p q
426 ) => Matrix e m p -> Matrix e n q -> Matrix e (m * n) (p * q)
437 ) => Matrix e m p -> Matrix e n q -> Matrix e (m * n) (p * q)
427(><) a b =
438(><) a b =
428− let kp1' = kp1 @e @m @n
439+ let fstM' = fstM @e @m @n
429− kp2' = kp2 @e @m @n
440+ sndM' = sndM @e @m @n
430− in khatri (comp a kp1') (comp b kp2')
441+ in kr (comp a fstM') (comp b sndM')
431
442
432−-- | Matrix abide Junc Split
443+-- | Matrix abide Join Fork
433−abideJS :: Matrix e cols rows -> Matrix e cols rows
444+abideJF :: Matrix e cols rows -> Matrix e cols rows
434−abideJS (M m) = M (I.abideJS m)
445+abideJF (M m) = M (I.abideJF m)
435
446
436−-- | Matrix abide Split Junc
447+-- | Matrix abide Fork Join
437−abideSJ :: Matrix e cols rows -> Matrix e cols rows
448+abideFJ :: Matrix e cols rows -> Matrix e cols rows
438−abideSJ (M m) = M (I.abideSJ m)
449+abideFJ (M m) = M (I.abideFJ m)
439
450
440-- | Matrix transposition
451-- | Matrix transposition
441tr :: Matrix e cols rows -> Matrix e rows cols
452tr :: Matrix e cols rows -> Matrix e rows cols
@@ -444,7 +455,7 @@ tr (M m) = M (I.tr m)
444-- Selective 'select' operator
455-- Selective 'select' operator
445select ::
456select ::
446 ( Num e,
457 ( Num e,
447− FromListsN e rows1 rows1,
458+ FLN e rows1 rows1,
448 CountableN rows1,
459 CountableN rows1,
449 I.FromNat rows2 ~ I.FromNat rows1,
460 I.FromNat rows2 ~ I.FromNat rows1,
450 I.FromNat cols1 ~ I.FromNat cols2,
461 I.FromNat cols1 ~ I.FromNat cols2,
@@ -457,9 +468,9 @@ select (M m) (M y) = M (I.select m y)
457cond ::
468cond ::
458 ( I.FromNat (I.Count (I.FromNat cols)) ~ I.FromNat cols,
469 ( I.FromNat (I.Count (I.FromNat cols)) ~ I.FromNat cols,
459 CountableN cols,
470 CountableN cols,
460− I.FromLists e () (I.FromNat cols),
471+ I.FL () (I.FromNat cols),
461− I.FromLists e (I.FromNat cols) (),
472+ I.FL (I.FromNat cols) (),
462− FromListsN e cols cols,
473+ FLN e cols cols,
463 Liftable e a Bool
474 Liftable e a Bool
464 )
475 )
465 =>
476 =>
@@ -468,8 +479,12 @@ cond p (M a) (M b) = M (I.cond p a b)
468
479
469-- Pretty print
480-- Pretty print
470
481
471−pretty :: (CountableDimensionsN cols rows, Show e) => Matrix e cols rows -> String
482+pretty :: (CountableDimsN cols rows, Show e) => Matrix e cols rows -> String
472pretty (M m) = I.pretty m
483pretty (M m) = I.pretty m
473
484
474−prettyPrint :: (CountableDimensionsN cols rows, Show e) => Matrix e cols rows -> IO ()
485+prettyPrint :: (CountableDimsN cols rows, Show e) => Matrix e cols rows -> IO ()
475prettyPrint (M m) = I.prettyPrint m
486prettyPrint (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+224−180
@@ -1,11 +1,11 @@
1{-# LANGUAGE ConstraintKinds #-}
1{-# LANGUAGE ConstraintKinds #-}
2+{-# LANGUAGE TypeFamilies #-}
2{-# LANGUAGE AllowAmbiguousTypes #-}
3{-# LANGUAGE AllowAmbiguousTypes #-}
3{-# LANGUAGE DataKinds #-}
4{-# LANGUAGE DataKinds #-}
4{-# LANGUAGE DerivingVia #-}
5{-# LANGUAGE DerivingVia #-}
5{-# LANGUAGE FlexibleContexts #-}
6{-# LANGUAGE FlexibleContexts #-}
6{-# LANGUAGE FlexibleInstances #-}
7{-# LANGUAGE FlexibleInstances #-}
7{-# LANGUAGE GADTs #-}
8{-# 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− CountableDimensions,
61+ CountableDims,
62 CountableN,
62 CountableN,
63− CountableDimensionsN,
63+ CountableDimsN,
64− FromListsN,
64+ FLN,
65 Liftable,
65 Liftable,
66 Trivial,
66 Trivial,
67 TrivialP,
67 TrivialP,
@@ -71,10 +71,9 @@ module LAoP.Matrix.Type
71 One,
71 One,
72
72
73 -- * Primitives
73 -- * Primitives
74− empty,
75 one,
74 one,
76− junc,
75+ join,
77− split,
76+ fork,
78
77
79 -- * Auxiliary type families
78 -- * Auxiliary type families
80 I.FromNat,
79 I.FromNat,
@@ -86,6 +85,7 @@ module LAoP.Matrix.Type
86 fromLists,
85 fromLists,
87 toLists,
86 toLists,
88 toList,
87 toList,
88+ matrixBuilder',
89 matrixBuilder,
89 matrixBuilder,
90 row,
90 row,
91 col,
91 col,
@@ -104,8 +104,8 @@ module LAoP.Matrix.Type
104 multM,
104 multM,
105
105
106 -- * Selective equivalent instance function
106 -- * Selective equivalent instance function
107− selectM,
107+ selectM,
108−
108+
109 -- * Monad equivalent instance function
109 -- * Monad equivalent instance function
110 returnM,
110 returnM,
111 bindM,
111 bindM,
@@ -113,25 +113,34 @@ module LAoP.Matrix.Type
113 -- * Misc
113 -- * Misc
114 -- ** Get dimensions
114 -- ** Get dimensions
115 columns,
115 columns,
116+ columns',
116 rows,
117 rows,
118+ rows',
117
119
118 -- ** Matrix Transposition
120 -- ** Matrix Transposition
119 tr,
121 tr,
120
122
123+ -- ** Scalar multiplication/division of matrices
124+ (.|),
125+ (./),
126+
121 -- ** McCarthy's Conditional
127 -- ** McCarthy's Conditional
122 cond,
128 cond,
123
129
124 -- ** Matrix "abiding"
130 -- ** Matrix "abiding"
125− abideJS,
131+ abideJF,
126− abideSJ,
132+ abideFJ,
133+
134+ -- ** Zip Matrices
135+ zipWithM,
127
136
128 -- * Biproduct approach
137 -- * Biproduct approach
129− -- ** Split
138+ -- ** Fork
130 (===),
139 (===),
131 -- *** Projections
140 -- *** Projections
132 p1,
141 p1,
133 p2,
142 p2,
134− -- ** Junc
143+ -- ** Join
135 (|||),
144 (|||),
136 -- *** Injections
145 -- *** Injections
137 i1,
146 i1,
@@ -145,11 +154,11 @@ module LAoP.Matrix.Type
145 -- | Note that given the restrictions imposed it is not possible to
154 -- | Note that given the restrictions imposed it is not possible to
146 -- implement the standard type classes present in standard Haskell.
155 -- implement the standard type classes present in standard Haskell.
147 -- *** Matrix pairing projections
156 -- *** Matrix pairing projections
148− kp1,
157+ fstM,
149− kp2,
158+ sndM,
150
159
151 -- *** Matrix pairing
160 -- *** Matrix pairing
152− khatri,
161+ kr,
153
162
154 -- * Matrix composition and lifting
163 -- * Matrix composition and lifting
155
164
@@ -157,10 +166,10 @@ module LAoP.Matrix.Type
157
166
158 -- | Note that given the restrictions imposed it is not possible to
167 -- | Note that given the restrictions imposed it is not possible to
159 -- implement the standard type classes present in standard Haskell.
168 -- implement the standard type classes present in standard Haskell.
160− identity,
169+ iden,
161 comp,
170 comp,
162− fromF,
163 fromF',
171 fromF',
172+ fromF,
164
173
165 -- * Relation
174 -- * Relation
166 toRel,
175 toRel,
@@ -174,46 +183,44 @@ where
174import Data.Void
183import Data.Void
175import Data.Proxy
184import Data.Proxy
176import Data.Kind
185import Data.Kind
177−import GHC.TypeLits
186+import GHC.TypeLits
178import Control.DeepSeq
187import Control.DeepSeq
179import LAoP.Utils
188import LAoP.Utils
180−import qualified Control.Category as C
181import qualified LAoP.Matrix.Internal as I
189import qualified LAoP.Matrix.Internal as I
190+import Prelude hiding (id, (.))
182
191
183newtype Matrix e (cols :: Type) (rows :: Type) = M (I.Matrix e (I.Normalize cols) (I.Normalize rows))
192newtype Matrix e (cols :: Type) (rows :: Type) = M (I.Matrix e (I.Normalize cols) (I.Normalize rows))
184 deriving (Show, Num, Eq, Ord, NFData) via (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))
185
194
186-- | Constraint type synonyms to keep the type signatures less convoluted
195-- | Constraint type synonyms to keep the type signatures less convoluted
187−type Countable a = KnownNat (I.Count a)
196+type Countable a = KnownNat (I.Count a)
188−type CountableDimensions a b = (Countable a, Countable b)
197+type CountableDims a b = (Countable a, Countable b)
189−type CountableN a = KnownNat (I.Count (I.Normalize a))
198+type CountableN a = KnownNat (I.Count (I.Normalize a))
190−type CountableDimensionsN a b = (CountableN a, CountableN b)
199+type CountableDimsN a b = (CountableN a, CountableN b)
191−type FromListsN e a b = I.FromLists e (I.Normalize a) (I.Normalize b)
200+type FLN a b = I.FromLists (I.Normalize a) (I.Normalize b)
192−type Liftable e a b = (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num e, Ord e)
201+type Liftable e a b = (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num e, Ord e)
193−type Trivial a = I.Normalize (I.Normalize a) ~ I.Normalize (I.Normalize (I.Normalize a))
202+type Trivial a = I.Normalize (I.Normalize a) ~ I.Normalize (I.Normalize (I.Normalize a))
194−type Trivial2 a = I.Normalize a ~ I.Normalize (I.Normalize a)
203+type Trivial2 a = I.Normalize a ~ I.Normalize (I.Normalize a)
195−type Trivial3 a = I.FromNat (I.Count (I.Normalize (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)
196−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)
197−
206+
198−-- | It isn't possible to implement the 'id' function so it's
207+-- | It is possible to implement a constrained version of the category type
199−-- implementation is 'undefined'. However 'comp' can be and this partial
208+-- class.
200−-- class implementation exists just to make the code more readable.
201−--
202−-- Please use 'identity' instead.
203−instance (Num e) => C.Category (Matrix e) where
209+instance (Num e) => Category (Matrix e) where
204− id = undefined
210+ type Object (Matrix e) a = (FLN a a, CountableN a)
211+ id = iden
205− (.) = comp
212+ (.) = comp
206
213
207-- | Bifunctor equivalent function
214-- | Bifunctor equivalent function
208bimapM ::
215bimapM ::
209 ( Liftable e a b,
216 ( Liftable e a b,
210 Liftable e c d,
217 Liftable e c d,
211− CountableDimensionsN a c,
218+ CountableDimsN a c,
212− CountableDimensionsN b d,
219+ CountableDimsN b d,
213− FromListsN e d c,
220+ FLN d c,
214− FromListsN e b a
221+ FLN b a
215 ) => (a -> b) -> (c -> d) -> Matrix e a c -> Matrix e b d
222 ) => (a -> b) -> (c -> d) -> Matrix e a c -> Matrix e b d
216−bimapM f g m = fromF' g `comp` m `comp` tr (fromF' f)
223+bimapM f g m = fromF g . m . tr (fromF f)
217
224
218-- | Zero type alias
225-- | Zero type alias
219type Zero = Void
226type Zero = Void
@@ -223,78 +230,74 @@ type One = ()
223
230
224-- Primitives
231-- Primitives
225
232
226−-- | Empty matrix constructor
227−empty :: Matrix e Zero Zero
228−empty = M I.Empty
229−
230-- | Unit matrix constructor
233-- | Unit matrix constructor
231one :: e -> Matrix e One One
234one :: e -> Matrix e One One
232one = M . I.One
235one = M . I.One
233
236
234−-- | Matrix 'Junc' constructor
237+-- | Matrix 'Join' constructor
235−junc ::
238+join ::
236 Matrix e a rows ->
239 Matrix e a rows ->
237 Matrix e b rows ->
240 Matrix e b rows ->
238 Matrix e (Either a b) rows
241 Matrix e (Either a b) rows
239−junc (M a) (M b) = M (I.Junc a b)
242+join (M a) (M b) = M (I.Join a b)
240
243
241infixl 3 |||
244infixl 3 |||
242−-- | Matrix 'Junc' constructor
245+-- | Matrix 'Join' constructor
243(|||) ::
246(|||) ::
244 Matrix e a rows ->
247 Matrix e a rows ->
245 Matrix e b rows ->
248 Matrix e b rows ->
246 Matrix e (Either a b) rows
249 Matrix e (Either a b) rows
247−(|||) = junc
250+(|||) = join
248
251
249−-- | Matrix 'Split' constructor
252+-- | Matrix 'Fork' constructor
250−split ::
253+fork ::
251 Matrix e cols a ->
254 Matrix e cols a ->
252 Matrix e cols b ->
255 Matrix e cols b ->
253 Matrix e cols (Either a b)
256 Matrix e cols (Either a b)
254−split (M a) (M b) = M (I.Split a b)
257+fork (M a) (M b) = M (I.Fork a b)
255
258
256infixl 2 ===
259infixl 2 ===
257−-- | Matrix 'Split' constructor
260+-- | Matrix 'Fork' constructor
258(===) ::
261(===) ::
259 Matrix e cols a ->
262 Matrix e cols a ->
260 Matrix e cols b ->
263 Matrix e cols b ->
261 Matrix e cols (Either a b)
264 Matrix e cols (Either a b)
262−(===) = split
265+(===) = fork
263
266
264-- Functor hierarchy
267-- Functor hierarchy
265
268
266-- | Functor instance equivalent function
269-- | Functor instance equivalent function
267−fmapM ::
270+fmapM ::
268 ( Liftable e a b,
271 ( Liftable e a b,
269− CountableDimensionsN a b,
272+ CountableDimsN a b,
270− FromListsN e b a
273+ FLN b a
271 )
274 )
272 =>
275 =>
273 (a -> b) -> Matrix e c a -> Matrix e c b
276 (a -> b) -> Matrix e c a -> Matrix e c b
274−fmapM f m = fromF' f `comp` m
277+fmapM f m = fromF f . m
275
278
276-- | Applicative instance equivalent 'unit' function,
279-- | Applicative instance equivalent 'unit' function,
277unitM :: (Num e) => Matrix e () ()
280unitM :: (Num e) => Matrix e () ()
278unitM = one 1
281unitM = one 1
279
282
280-- | Applicative instance equivalent 'unit' function,
283-- | Applicative instance equivalent 'unit' function,
281−multM ::
284+multM ::
282− ( CountableDimensionsN a b,
285+ ( CountableDimsN a b,
283 CountableN (a, b),
286 CountableN (a, b),
284 Num e,
287 Num e,
285− FromListsN e (a, b) a,
288+ FLN (a, b) a,
286− FromListsN e (a, b) b,
289+ FLN (a, b) b,
287 TrivialP a b
290 TrivialP a b
288 ) => Matrix e c a -> Matrix e c b -> Matrix e c (a, b)
291 ) => Matrix e c a -> Matrix e c b -> Matrix e c (a, b)
289−multM = khatri
292+multM = kr
290
293
291-- | Monad instance equivalent 'return' function,
294-- | Monad instance equivalent 'return' function,
292−returnM ::
295+returnM ::
293− forall e a .
296+ forall e a .
294 ( Num e,
297 ( Num e,
295 Enum e,
298 Enum e,
296 Enum a,
299 Enum a,
297− FromListsN e () a,
300+ FLN () a,
298 Countable a
301 Countable a
299 ) => a -> Matrix e One a
302 ) => a -> Matrix e One a
300returnM a = col l
303returnM a = col l
@@ -311,51 +314,64 @@ bindM = flip comp
311
314
312-- | Build a matrix out of a list of list of elements. Throws a runtime
315-- | Build a matrix out of a list of list of elements. Throws a runtime
313-- error if the dimensions do not match.
316-- error if the dimensions do not match.
314−fromLists :: (FromListsN e cols rows) => [[e]] -> Matrix e cols rows
317+fromLists :: (FLN cols rows) => [[e]] -> Matrix e cols rows
315fromLists = M . I.fromLists
318fromLists = M . I.fromLists
316
319
317-- | Matrix builder function. Constructs a matrix provided with
320-- | Matrix builder function. Constructs a matrix provided with
318−-- a construction function.
321+-- a construction function that operates with indices.
319−matrixBuilder ::
322+matrixBuilder' ::
320− (FromListsN e cols rows, CountableDimensionsN cols rows )
323+ (FLN cols rows, CountableDimsN cols rows )
321 => ((Int, Int) -> e) -> Matrix e cols rows
324 => ((Int, Int) -> e) -> Matrix e cols rows
322−matrixBuilder = M . I.matrixBuilder
325+matrixBuilder' = M . I.matrixBuilder'
326+
327+-- | Matrix builder function. Constructs a matrix provided with
328+-- a construction function that operates with arbitrary types.
329+matrixBuilder ::
330+ ( FLN a b,
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
338+matrixBuilder f = M (I.matrixBuilder f)
323
339
324-- | Constructs a column vector matrix
340-- | Constructs a column vector matrix
325−col :: (FromListsN e () rows) => [e] -> Matrix e One rows
341+col :: (FLN () rows) => [e] -> Matrix e One rows
326col = M . I.col
342col = M . I.col
327
343
328-- | Constructs a row vector matrix
344-- | Constructs a row vector matrix
329−row :: (FromListsN e cols ()) => [e] -> Matrix e cols One
345+row :: (FLN cols ()) => [e] -> Matrix e cols One
330row = M . I.row
346row = M . I.row
331
347
332-- | Lifts functions to matrices with arbitrary dimensions.
348-- | Lifts functions to matrices with arbitrary dimensions.
333--
349--
334-- NOTE: Be careful to not ask for a matrix bigger than the cardinality of
350-- NOTE: Be careful to not ask for a matrix bigger than the cardinality of
335-- types @a@ or @b@ allows.
351-- types @a@ or @b@ allows.
336−fromF ::
352+fromF' ::
337 ( Liftable e a b,
353 ( Liftable e a b,
338− CountableDimensionsN cols rows,
354+ CountableDimsN cols rows,
339− FromListsN e rows cols
355+ FLN rows cols
340 ) =>
356 ) =>
341 (a -> b) -> Matrix e cols rows
357 (a -> b) -> Matrix e cols rows
342−fromF = M . I.fromF
358+fromF' = M . I.fromF'
343
359
344-- | Lifts functions to matrices with dimensions matching @a@ and @b@
360-- | Lifts functions to matrices with dimensions matching @a@ and @b@
345-- cardinality's.
361-- cardinality's.
346−fromF' ::
362+fromF ::
347 ( Liftable e a b,
363 ( Liftable e a b,
348− CountableDimensionsN a b,
364+ CountableDimsN a b,
349− FromListsN e b a
365+ FLN b a
350 ) =>
366 ) =>
351 (a -> b) -> Matrix e a b
367 (a -> b) -> Matrix e a b
352−fromF' = M . I.fromF'
368+fromF = M . I.fromF
353
369
354-- | Lifts relation functions to Boolean Matrix
370-- | Lifts relation functions to Boolean Matrix
355toRel ::
371toRel ::
356 ( Liftable (Natural 0 1) a b,
372 ( Liftable (Natural 0 1) a b,
357− CountableDimensionsN a b,
373+ CountableDims a b,
358− FromListsN (Natural 0 1) b a
374+ FLN b a
359 ) => (a -> b -> Bool) -> Matrix (Natural 0 1) a b
375 ) => (a -> b -> Bool) -> Matrix (Natural 0 1) a b
360toRel = M . I.toRel
376toRel = M . I.toRel
361
377
@@ -373,7 +389,7 @@ toList (M m) = I.toList m
373
389
374-- | The zero matrix. A matrix wholly filled with zeros.
390-- | The zero matrix. A matrix wholly filled with zeros.
375zeros ::
391zeros ::
376− (Num e, FromListsN e cols rows, CountableDimensionsN cols rows)
392+ (Num e, FLN cols rows, CountableDimsN cols rows)
377 => Matrix e cols rows
393 => Matrix e cols rows
378zeros = M I.zeros
394zeros = M I.zeros
379
395
@@ -383,7 +399,7 @@ zeros = M I.zeros
383--
399--
384-- Also known as T (Top) matrix.
400-- Also known as T (Top) matrix.
385ones ::
401ones ::
386− (Num e, FromListsN e cols rows, CountableDimensionsN cols rows)
402+ (Num e, FLN cols rows, CountableDimsN cols rows)
387 => Matrix e cols rows
403 => Matrix e cols rows
388ones = M I.ones
404ones = M I.ones
389
405
@@ -392,7 +408,7 @@ ones = M I.ones
392-- | The constant matrix constructor. A matrix wholly filled with a given
408-- | The constant matrix constructor. A matrix wholly filled with a given
393-- value.
409-- value.
394constant ::
410constant ::
395− (Num e, FromListsN e cols rows, CountableDimensionsN cols rows)
411+ (Num e, FLN cols rows, CountableDimsN cols rows)
396 => e -> Matrix e cols rows
412 => e -> Matrix e cols rows
397constant = M . I.constant
413constant = M . I.constant
398
414
@@ -401,30 +417,30 @@ constant = M . I.constant
401-- | The T (Top) row vector matrix.
417-- | The T (Top) row vector matrix.
402bang ::
418bang ::
403 forall e cols.
419 forall e cols.
404− (Num e, Enum e, FromListsN e cols (), CountableN cols) =>
420+ (Num e, Enum e, FLN cols (), CountableN cols) =>
405 Matrix e cols One
421 Matrix e cols One
406bang = M I.bang
422bang = M I.bang
407
423
408-- | Point constant relation
424-- | Point constant relation
409−point ::
425+point ::
410 ( Bounded a,
426 ( Bounded a,
411 Enum a,
427 Enum a,
412 Eq a,
428 Eq a,
413 Num e,
429 Num e,
414 Ord e,
430 Ord e,
415 CountableN a,
431 CountableN a,
416− FromListsN e a One
432+ FLN a One
417 ) => a -> Matrix e One a
433 ) => a -> Matrix e One a
418−point = fromF' . const
434+point = fromF . const
419
435
420−-- Identity Matrix
436+-- iden Matrix
421
437
422−-- | Identity matrix
438+-- | iden matrix
423−identity ::
439+iden ::
424− (Num e, FromListsN e a a, CountableN a) =>
440+ (Num e, FLN a a, CountableN a) =>
425 Matrix e a a
441 Matrix e a a
426−identity = M I.identity
442+iden = M I.iden
427−{-# NOINLINE identity #-}
443+{-# NOINLINE iden #-}
428
444
429-- Matrix composition (MMM)
445-- Matrix composition (MMM)
430
446
@@ -435,17 +451,31 @@ identity = M I.identity
435comp :: (Num e) => Matrix e cr rows -> Matrix e cols cr -> Matrix e cols rows
451comp :: (Num e) => Matrix e cr rows -> Matrix e cols cr -> Matrix e cols rows
436comp (M a) (M b) = M (I.comp a b)
452comp (M a) (M b) = M (I.comp a b)
437{-# NOINLINE comp #-}
453{-# NOINLINE comp #-}
438−{-# RULES
454+{-# RULES
439− "comp/identity1" forall m. comp m identity = m ;
455+ "comp/iden1" forall m. comp m iden = m ;
440− "comp/identity2" forall m. comp identity m = m
456+ "comp/iden2" forall m. comp iden m = m
441#-}
457#-}
442
458
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+
443-- | Biproduct first component projection
473-- | Biproduct first component projection
444p1 ::
474p1 ::
445 ( Num e,
475 ( Num e,
446− CountableDimensionsN n m,
476+ CountableDimsN n m,
447− FromListsN e n m,
477+ FLN n m,
448− FromListsN e m m
478+ FLN m m
449 ) =>
479 ) =>
450 Matrix e (Either m n) m
480 Matrix e (Either m n) m
451p1 = M I.p1
481p1 = M I.p1
@@ -453,9 +483,9 @@ p1 = M I.p1
453-- | Biproduct second component projection
483-- | Biproduct second component projection
454p2 ::
484p2 ::
455 ( Num e,
485 ( Num e,
456− CountableDimensionsN n m,
486+ CountableDimsN n m,
457− FromListsN e m n,
487+ FLN m n,
458− FromListsN e n n
488+ FLN n n
459 ) =>
489 ) =>
460 Matrix e (Either m n) n
490 Matrix e (Either m n) n
461p2 = M I.p2
491p2 = M I.p2
@@ -465,9 +495,9 @@ p2 = M I.p2
465-- | Biproduct first component injection
495-- | Biproduct first component injection
466i1 ::
496i1 ::
467 ( Num e,
497 ( Num e,
468− CountableDimensionsN n m,
498+ CountableDimsN n m,
469− FromListsN e n m,
499+ FLN n m,
470− FromListsN e m m
500+ FLN m m
471 ) =>
501 ) =>
472 Matrix e m (Either m n)
502 Matrix e m (Either m n)
473i1 = tr p1
503i1 = tr p1
@@ -475,9 +505,9 @@ i1 = tr p1
475-- | Biproduct second component injection
505-- | Biproduct second component injection
476i2 ::
506i2 ::
477 ( Num e,
507 ( Num e,
478− CountableDimensionsN n m,
508+ CountableDimsN n m,
479− FromListsN e m n,
509+ FLN m n,
480− FromListsN e n n
510+ FLN n n
481 ) =>
511 ) =>
482 Matrix e n (Either m n)
512 Matrix e n (Either m n)
483i2 = tr p2
513i2 = tr p2
@@ -486,24 +516,34 @@ i2 = tr p2
486
516
487-- | Obtain the number of rows.
517-- | Obtain the number of rows.
488--
518--
489−-- NOTE: The 'KnownNat' constaint is needed in order to obtain the
519+-- NOTE: The 'KnownNat' constraint is needed in order to obtain the
490−-- dimensions in constant time.
520+-- dimensions in constant time. For a version that doesn't require the
491−--
521+-- constraint see 'rows''.
492−-- TODO: A 'rows' function that does not need the 'KnownNat' constraint in
493−-- exchange for performance.
494rows :: (CountableN rows) => Matrix e cols rows -> Int
522rows :: (CountableN rows) => Matrix e cols rows -> Int
495rows (M m) = I.rows m
523rows (M m) = I.rows m
496
524
525+-- | Obtain the number of rows in an inefficient manner, but without any
526+-- constraints.
527+--
528+-- For a more efficient version see 'rows'.
529+rows' :: Matrix e cols rows -> Int
530+rows' (M m) = I.rows' m
531+
497-- | Obtain the number of columns.
532-- | Obtain the number of columns.
498−--
499−-- NOTE: The 'KnownNat' constaint is needed in order to obtain the
500−-- dimensions in constant time.
501--
533--
502−-- TODO: A 'columns' function that does not need the 'KnownNat' constraint in
534+-- NOTE: The 'KnownNat' constraint is needed in order to obtain the
503−-- exchange for performance.
535+-- dimensions in constant time. For a version that doesn't require the
536+-- constraint see 'columns''.
504columns :: (CountableN cols) => Matrix e cols rows -> Int
537columns :: (CountableN cols) => Matrix e cols rows -> Int
505columns (M m) = I.columns m
538columns (M m) = I.columns m
506
539
540+-- | Obtain the number of columns in an inefficient manner, but without any
541+-- constraints.
542+--
543+-- For a more efficient version see 'columns'.
544+columns' :: Matrix e cols rows -> Int
545+columns' (M m) = I.columns' m
546+
507-- Coproduct Bifunctor
547-- Coproduct Bifunctor
508
548
509infixl 5 -|-
549infixl 5 -|-
@@ -511,11 +551,11 @@ infixl 5 -|-
511-- | Matrix coproduct functor also known as matrix direct sum.
551-- | Matrix coproduct functor also known as matrix direct sum.
512(-|-) ::
552(-|-) ::
513 ( Num e,
553 ( Num e,
514− CountableDimensionsN j k,
554+ CountableDimsN j k,
515− FromListsN e k k,
555+ FLN k k,
516− FromListsN e j k,
556+ FLN j k,
517− FromListsN e k j,
557+ FLN k j,
518− FromListsN e j j
558+ FLN j j
519 ) =>
559 ) =>
520 Matrix e n k ->
560 Matrix e n k ->
521 Matrix e m j ->
561 Matrix e m j ->
@@ -525,98 +565,98 @@ infixl 5 -|-
525-- Khatri Rao Product and projections
565-- Khatri Rao Product and projections
526
566
527-- | Khatri Rao product first component projection matrix.
567-- | Khatri Rao product first component projection matrix.
528−kp1 ::
568+fstM ::
529 forall e m k .
569 forall e m k .
530 ( Num e,
570 ( Num e,
531− CountableDimensionsN m k,
571+ CountableDimsN m k,
532 CountableN (m, k),
572 CountableN (m, k),
533− FromListsN e (m, k) m,
573+ FLN (m, k) m,
534 TrivialP m k
574 TrivialP m k
535 ) => Matrix e (m, k) m
575 ) => Matrix e (m, k) m
536−kp1 = M (I.kp1 @e @(I.Normalize m) @(I.Normalize k))
576+fstM = M (I.fstM @e @(I.Normalize m) @(I.Normalize k))
537
577
538-- | Khatri Rao product second component projection matrix.
578-- | Khatri Rao product second component projection matrix.
539−kp2 ::
579+sndM ::
540 forall e m k.
580 forall e m k.
541 ( Num e,
581 ( Num e,
542− CountableDimensionsN k m,
582+ CountableDimsN k m,
543 CountableN (m, k),
583 CountableN (m, k),
544− FromListsN e (m, k) k,
584+ FLN (m, k) k,
545 TrivialP m k
585 TrivialP m k
546 ) => Matrix e (m, k) k
586 ) => Matrix e (m, k) k
547−kp2 = M (I.kp2 @e @(I.Normalize m) @(I.Normalize k))
587+sndM = M (I.sndM @e @(I.Normalize m) @(I.Normalize k))
548
588
549-- | Khatri Rao Matrix product also known as matrix pairing.
589-- | Khatri Rao Matrix product also known as matrix pairing.
550--
590--
551-- NOTE: That this is not a true categorical product, see for instance:
591-- NOTE: That this is not a true categorical product, see for instance:
552−--
592+--
553-- @
593-- @
554−-- | kp1 `comp` khatri a b == a
594+-- | fstM . kr a b == a
555−-- khatri a b ==> |
595+-- kr a b ==> |
556−-- | kp2 `comp` khatri a b == b
596+-- | sndM . kr a b == b
557-- @
597-- @
558--
598--
559-- __Emphasis__ on the implication symbol.
599-- __Emphasis__ on the implication symbol.
560−khatri ::
600+kr ::
561 forall e cols a b.
601 forall e cols a b.
562 ( Num e,
602 ( Num e,
563− CountableDimensionsN a b,
603+ CountableDimsN a b,
564 CountableN (a, b),
604 CountableN (a, b),
565− FromListsN e (a, b) a,
605+ FLN (a, b) a,
566− FromListsN e (a, b) b,
606+ FLN (a, b) b,
567 TrivialP a b
607 TrivialP a b
568 ) => Matrix e cols a -> Matrix e cols b -> Matrix e cols (a, b)
608 ) => Matrix e cols a -> Matrix e cols b -> Matrix e cols (a, b)
569−khatri a b =
609+kr a b =
570− let kp1' = kp1 @e @a @b
610+ let fstM' = fstM @e @a @b
571− kp2' = kp2 @e @a @b
611+ sndM' = sndM @e @a @b
572− in comp (tr kp1') a * comp (tr kp2') b
612+ in comp (tr fstM') a * comp (tr sndM') b
573
613
574-- Product Bifunctor (Kronecker)
614-- Product Bifunctor (Kronecker)
575
615
576infixl 4 ><
616infixl 4 ><
577
617
578−-- | Matrix product functor also known as kronecker product
618+-- | Matrix product functor also known as Kronecker product
579(><) ::
619(><) ::
580 forall e m p n q.
620 forall e m p n q.
581 ( Num e,
621 ( Num e,
582− CountableDimensionsN m n,
622+ CountableDimsN m n,
583− CountableDimensionsN p q,
623+ CountableDimsN p q,
584− CountableDimensionsN (m, n) (p, q),
624+ CountableDimsN (m, n) (p, q),
585− FromListsN e (m, n) m,
625+ FLN (m, n) m,
586− FromListsN e (m, n) n,
626+ FLN (m, n) n,
587− FromListsN e (p, q) p,
627+ FLN (p, q) p,
588− FromListsN e (p, q) q,
628+ FLN (p, q) q,
589 TrivialP m n,
629 TrivialP m n,
590 TrivialP p q
630 TrivialP p q
591 ) => Matrix e m p -> Matrix e n q -> Matrix e (m, n) (p, q)
631 ) => Matrix e m p -> Matrix e n q -> Matrix e (m, n) (p, q)
592(><) a b =
632(><) a b =
593− let kp1' = kp1 @e @m @n
633+ let fstM' = fstM @e @m @n
594− kp2' = kp2 @e @m @n
634+ sndM' = sndM @e @m @n
595− in khatri (comp a kp1') (comp b kp2')
635+ in kr (comp a fstM') (comp b sndM')
596
636
597−-- Matrix abide Junc Split
637+-- Matrix abide Join Fork
598
638
599−-- | Matrix "abiding" followin the 'Junc'-'Split' abide law.
639+-- | Matrix "abiding" followin the 'Join'-'Fork' abide law.
600−--
640+--
601-- Law:
641-- Law:
602--
642--
603-- @
643-- @
604−-- 'Junc' ('Split' a c) ('Split' b d) == 'Split' ('Junc' a b) ('Junc' c d)
644+-- 'Join' ('Fork' a c) ('Fork' b d) == 'Fork' ('Join' a b) ('Join' c d)
605-- @
645-- @
606−abideJS :: Matrix e cols rows -> Matrix e cols rows
646+abideJF :: Matrix e cols rows -> Matrix e cols rows
607−abideJS (M m) = M (I.abideJS m)
647+abideJF (M m) = M (I.abideJF m)
608
648
609−-- Matrix abide Split Junc
649+-- Matrix abide Fork Join
610
650
611−-- | Matrix "abiding" followin the 'Split'-'Junc' abide law.
651+-- | Matrix "abiding" followin the 'Fork'-'Join' abide law.
612−--
652+--
613-- Law:
653-- Law:
614--
654--
615-- @
655-- @
616−-- 'Split' ('Junc' a b) ('Junc' c d) == 'Junc' ('Split' a c) ('Split' b d)
656+-- 'Fork' ('Join' a b) ('Join' c d) == 'Join' ('Fork' a c) ('Fork' b d)
617-- @
657-- @
618−abideSJ :: Matrix e cols rows -> Matrix e cols rows
658+abideFJ :: Matrix e cols rows -> Matrix e cols rows
619−abideSJ (M m) = M (I.abideSJ m)
659+abideFJ (M m) = M (I.abideFJ m)
620
660
621-- Matrix transposition
661-- Matrix transposition
622
662
@@ -628,9 +668,9 @@ tr (M m) = M (I.tr m)
628
668
629-- | Selective functors 'select' operator equivalent inspired by the
669-- | Selective functors 'select' operator equivalent inspired by the
630-- ArrowMonad solution presented in the paper.
670-- ArrowMonad solution presented in the paper.
631−selectM ::
671+selectM ::
632 ( Num e,
672 ( Num e,
633− FromListsN e b b,
673+ FLN b b,
634 CountableN b
674 CountableN b
635 ) => Matrix e cols (Either a b) -> Matrix e a b -> Matrix e cols b
675 ) => Matrix e cols (Either a b) -> Matrix e a b -> Matrix e cols b
636selectM (M m) (M y) = M (I.select m y)
676selectM (M m) (M y) = M (I.select m y)
@@ -643,9 +683,9 @@ cond ::
643 Trivial2 a,
683 Trivial2 a,
644 Trivial3 a,
684 Trivial3 a,
645 CountableN a,
685 CountableN a,
646− FromListsN e () a,
686+ FLN () a,
647− FromListsN e a (),
687+ FLN a (),
648− FromListsN e a a,
688+ FLN a a,
649 Liftable e a Bool
689 Liftable e a Bool
650 )
690 )
651 =>
691 =>
@@ -655,9 +695,13 @@ cond p (M a) (M b) = M (I.cond p a b)
655-- Pretty print
695-- Pretty print
656
696
657-- | Matrix pretty printer
697-- | Matrix pretty printer
658−pretty :: (CountableDimensionsN cols rows, Show e) => Matrix e cols rows -> String
698+pretty :: (CountableDimsN cols rows, Show e) => Matrix e cols rows -> String
659pretty (M m) = I.pretty m
699pretty (M m) = I.pretty m
660
700
661-- | Matrix pretty printer
701-- | Matrix pretty printer
662−prettyPrint :: (CountableDimensionsN cols rows, Show e) => Matrix e cols rows -> IO ()
702+prettyPrint :: (CountableDimsN cols rows, Show e) => Matrix e cols rows -> IO ()
663prettyPrint (M m) = I.prettyPrint m
703prettyPrint (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+8−9
@@ -32,20 +32,19 @@ module LAoP.Relation
32
32
33 -- * Constraint type synonyms
33 -- * Constraint type synonyms
34 Countable,
34 Countable,
35− CountableDimensions,
35+ CountableDims,
36 CountableN,
36 CountableN,
37− CountableDimensionsN,
37+ CountableDimsN,
38− FromListsN,
38+ FLN,
39 Liftable,
39 Liftable,
40 Trivial,
40 Trivial,
41 TrivialP,
41 TrivialP,
42
42
43 -- * Primitives
43 -- * Primitives
44− empty,
45 one,
44 one,
46− junc,
45+ join,
47 (|||),
46 (|||),
48− split,
47+ fork,
49 (===),
48 (===),
50
49
51 -- * Auxiliary type families
50 -- * Auxiliary type families
@@ -108,8 +107,8 @@ module LAoP.Relation
108 splitR,
107 splitR,
109
108
110 -- ** Projections
109 -- ** Projections
111− p1,
110+ fstR,
112− p2,
111+ sndR,
113 -- ** Bifunctor
112 -- ** Bifunctor
114 (><),
113 (><),
115 -- * Relational coproduct
114 -- * Relational coproduct
@@ -148,7 +147,7 @@ module LAoP.Relation
148 cond,
147 cond,
149
148
150 -- * Relational composition and lifting
149 -- * Relational composition and lifting
151− identity,
150+ iden,
152 comp,
151 comp,
153 fromF,
152 fromF,
154 fromF',
153 fromF',
src/LAoP/Relation/Internal.hs+245−234
@@ -1,3 +1,4 @@
1+{-# LANGUAGE TypeFamilies #-}
1{-# LANGUAGE ConstraintKinds #-}
2{-# LANGUAGE ConstraintKinds #-}
2{-# LANGUAGE GADTs #-}
3{-# LANGUAGE GADTs #-}
3{-# LANGUAGE UndecidableInstances #-}
4{-# LANGUAGE UndecidableInstances #-}
@@ -42,20 +43,19 @@ module LAoP.Relation.Internal
42
43
43 -- * Constraint type synonyms
44 -- * Constraint type synonyms
44 Countable,
45 Countable,
45− CountableDimensions,
46+ CountableDims,
46 CountableN,
47 CountableN,
47− CountableDimensionsN,
48+ CountableDimsN,
48− FromListsN,
49+ FLN,
49 Liftable,
50 Liftable,
50 Trivial,
51 Trivial,
51 TrivialP,
52 TrivialP,
52
53
53 -- * Primitives
54 -- * Primitives
54− empty,
55 one,
55 one,
56− junc,
56+ join,
57 (|||),
57 (|||),
58− split,
58+ fork,
59 (===),
59 (===),
60
60
61 -- * Auxiliary type families
61 -- * Auxiliary type families
@@ -66,14 +66,15 @@ module LAoP.Relation.Internal
66 -- * Matrix construction and conversion
66 -- * Matrix construction and conversion
67 I.FromLists,
67 I.FromLists,
68 fromLists,
68 fromLists,
69− fromF,
70 fromF',
69 fromF',
70+ fromF,
71 toRel,
71 toRel,
72 toLists,
72 toLists,
73 toList,
73 toList,
74 toBool,
74 toBool,
75 pt,
75 pt,
76 belongs,
76 belongs,
77+ relationBuilder',
77 relationBuilder,
78 relationBuilder,
78 zeros,
79 zeros,
79 ones,
80 ones,
@@ -118,8 +119,8 @@ module LAoP.Relation.Internal
118 splitR,
119 splitR,
119
120
120 -- ** Projections
121 -- ** Projections
121− p1,
122+ fstR,
122− p2,
123+ sndR,
123 -- ** Bifunctor
124 -- ** Bifunctor
124 (><),
125 (><),
125 -- * Relational coproduct
126 -- * Relational coproduct
@@ -158,10 +159,10 @@ module LAoP.Relation.Internal
158 cond,
159 cond,
159
160
160 -- * Relational composition and lifting
161 -- * Relational composition and lifting
161− identity,
162+ iden,
162 comp,
163 comp,
163− fromF,
164 fromF',
164 fromF',
165+ fromF,
165
166
166 -- ** Relational application
167 -- ** Relational application
167 pointAp,
168 pointAp,
@@ -177,9 +178,9 @@ import Data.Void
177import qualified LAoP.Matrix.Internal as I
178import qualified LAoP.Matrix.Internal as I
178import LAoP.Utils.Internal
179import LAoP.Utils.Internal
179import Control.DeepSeq
180import Control.DeepSeq
180−import qualified Control.Category as C
181import Data.Bool
181import Data.Bool
182import GHC.TypeLits
182import GHC.TypeLits
183+import Prelude hiding (id, (.))
183
184
184-- | Boolean type synonym for working with boolean matrices
185-- | Boolean type synonym for working with boolean matrices
185type Boolean = Natural 0 1
186type Boolean = Natural 0 1
@@ -192,32 +193,30 @@ newtype Relation a b = R (I.Matrix Boolean (I.Normalize a) (I.Normalize b))
192deriving instance (Read (I.Matrix Boolean (I.Normalize a) (I.Normalize b))) => Read (Relation a b)
193deriving instance (Read (I.Matrix Boolean (I.Normalize a) (I.Normalize b))) => Read (Relation a b)
193
194
194-- | Constraint type synonyms to keep the type signatures less convoluted
195-- | Constraint type synonyms to keep the type signatures less convoluted
195−type Countable a = KnownNat (I.Count a)
196+type Countable a = KnownNat (I.Count a)
196−type CountableDimensions a b = (Countable a, Countable b)
197+type CountableDims a b = (Countable a, Countable b)
197−type CountableN a = KnownNat (I.Count (I.Normalize a))
198+type CountableN a = KnownNat (I.Count (I.Normalize a))
198−type CountableDimensionsN a b = (CountableN a, CountableN b)
199+type CountableDimsN a b = (CountableN a, CountableN b)
199−type FromListsN a b = I.FromLists Boolean (I.Normalize a) (I.Normalize b)
200+type FLN a b = I.FromLists (I.Normalize a) (I.Normalize b)
200−type Liftable a b = (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num Boolean, Ord Boolean)
201+type Liftable a b = (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num Boolean, Ord Boolean)
201−type Trivial a = I.Normalize a ~ I.Normalize (I.Normalize a)
202+type Trivial a = I.Normalize a ~ I.Normalize (I.Normalize a)
202−type TrivialP a b = I.Normalize (a, b) ~ I.Normalize (I.Normalize a, I.Normalize b)
203+type TrivialP a b = I.Normalize (a, b) ~ I.Normalize (I.Normalize a, I.Normalize b)
203−
204+
204−-- | It isn't possible to implement the 'id' function so it's
205+-- | It is possible to implement a constrained version of the category type
205−-- implementation is 'undefined'. However 'comp' can be and this partial
206+-- class.
206−-- class implementation exists just to make the code more readable.
207−--
208−-- Please use 'identity' instead.
209−instance C.Category Relation where
207+instance Category Relation where
210− id = undefined
208+ type Object Relation a = (FLN a a, CountableN a)
209+ id = iden
211− (.) = comp
210+ (.) = comp
212
211
213instance Num (Relation a b) where
212instance Num (Relation a b) where
214− -- | Matrix addition becomes Boolean matrix disjunction
213+ -- | Matrix addition becomes Boolean matrix disjointion
215 (R a) + (R b) = R (I.orM a b)
214 (R a) + (R b) = R (I.orM a b)
216
215
217 -- | Matrix subtraction becomes Relational subtraction
216 -- | Matrix subtraction becomes Relational subtraction
218 (R a) - (R b) = R (I.subM a b)
217 (R a) - (R b) = R (I.subM a b)
219
218
220− -- | Matrix multiplication becomes Boolean matrix conjunction
219+ -- | Matrix multiplication becomes Boolean matrix conjointion
221 (R a) * (R b) = R (I.andM a b)
220 (R a) * (R b) = R (I.andM a b)
222
221
223 -- | Matrix negation becomes Boolean matrix negation
222 -- | Matrix negation becomes Boolean matrix negation
@@ -229,83 +228,92 @@ type One = ()
229
228
230-- Primitives
229-- Primitives
231
230
232−-- | Empty matrix constructor
233−empty :: Relation Zero Zero
234−empty = R I.Empty
235−
236-- | Unit matrix constructor
231-- | Unit matrix constructor
237one :: Boolean -> Relation One One
232one :: Boolean -> Relation One One
238one = R . I.One
233one = R . I.One
239
234
240−-- | Boolean Matrix 'Junc' constructor, also known as relational coproduct.
235+-- | Boolean Matrix 'Join' constructor, also known as relational coproduct.
241--
236--
242-- See 'eitherR'.
237-- See 'eitherR'.
243−junc :: Relation a c -> Relation b c -> Relation (Either a b) c
238+join :: Relation a c -> Relation b c -> Relation (Either a b) c
244−junc (R a) (R b) = R (I.Junc a b)
239+join (R a) (R b) = R (I.Join a b)
245
240
246infixl 3 |||
241infixl 3 |||
247−-- | Boolean Matrix 'Junc' constructor
242+-- | Boolean Matrix 'Join' constructor
248--
243--
249-- See 'eitherR'.
244-- See 'eitherR'.
250(|||) ::
245(|||) ::
251 Relation a c ->
246 Relation a c ->
252 Relation b c ->
247 Relation b c ->
253 Relation (Either a b) c
248 Relation (Either a b) c
254−(|||) = junc
249+(|||) = join
255
250
256−-- | Boolean Matrix 'Split' constructor, also known as relational product.
251+-- | Boolean Matrix 'Fork' constructor, also known as relational product.
257−split :: Relation c a -> Relation c b -> Relation c (Either a b)
252+fork :: Relation c a -> Relation c b -> Relation c (Either a b)
258−split (R a) (R b) = R (I.Split a b)
253+fork (R a) (R b) = R (I.Fork a b)
259
254
260infixl 2 ===
255infixl 2 ===
261−-- | Boolean Matrix 'Split' constructor
256+-- | Boolean Matrix 'Fork' constructor
262(===) ::
257(===) ::
263 Relation c a ->
258 Relation c a ->
264 Relation c b ->
259 Relation c b ->
265 Relation c (Either a b)
260 Relation c (Either a b)
266−(===) = split
261+(===) = fork
267
262
268-- Construction
263-- Construction
269
264
270-- | Build a matrix out of a list of list of elements. Throws a runtime
265-- | Build a matrix out of a list of list of elements. Throws a runtime
271-- error if the dimensions do not match.
266-- error if the dimensions do not match.
272−fromLists :: (FromListsN a b) => [[Boolean]] -> Relation a b
267+fromLists :: (FLN a b) => [[Boolean]] -> Relation a b
273fromLists = R . I.fromLists
268fromLists = R . I.fromLists
274
269
275−-- | Matrix builder function. Constructs a matrix provided with
270+-- | Relation builder function. Constructs a relation provided with
276−-- a construction function.
271+-- a construction function that operates with indices.
277−relationBuilder ::
272+relationBuilder' ::
278− (FromListsN a b, CountableDimensionsN a b) =>
273+ (FLN a b, CountableDimsN a b) =>
279 ((Int, Int) -> Boolean) -> Relation 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.
279+relationBuilder ::
280+ ( FLN 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
280relationBuilder = R . I.matrixBuilder
288relationBuilder = R . I.matrixBuilder
281
289
282-- | Lifts functions to matrices with arbitrary dimensions.
290-- | Lifts functions to matrices with arbitrary dimensions.
283--
291--
284-- 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
285-- types @a@ or @b@ allows.
293-- types @a@ or @b@ allows.
286−fromF ::
294+fromF' ::
287 ( Liftable a b,
295 ( Liftable a b,
288− CountableDimensionsN c d,
296+ CountableDimsN c d,
289− FromListsN d c
297+ FLN d c
290 )
298 )
291 => (a -> b) -> Relation c d
299 => (a -> b) -> Relation c d
292−fromF f = R (I.fromFRel f)
300+fromF' f = R (I.fromFRel' f)
293
301
294-- | Lifts functions to matrices with dimensions matching @a@ and @b@
302-- | Lifts functions to matrices with dimensions matching @a@ and @b@
295-- cardinality's.
303-- cardinality's.
296−fromF' ::
304+fromF ::
297 ( Liftable a b,
305 ( Liftable a b,
298− CountableDimensionsN a b,
306+ CountableDimsN a b,
299− FromListsN b a
307+ FLN b a
300 )
308 )
301 => (a -> b) -> Relation a b
309 => (a -> b) -> Relation a b
302−fromF' f = R (I.fromFRel' f)
310+fromF f = R (I.fromFRel f)
303
311
304-- | Lifts relation functions to 'Relation'
312-- | Lifts relation functions to 'Relation'
305toRel ::
313toRel ::
306 ( Liftable a b,
314 ( Liftable a b,
307− CountableDimensionsN a b,
315+ CountableDims a b,
308− FromListsN b a
316+ FLN b a
309 )
317 )
310 => (a -> b -> Bool) -> Relation a b
318 => (a -> b -> Bool) -> Relation a b
311toRel = R . I.toRel
319toRel = R . I.toRel
@@ -314,9 +322,9 @@ toRel = R . I.toRel
314fromRel ::
322fromRel ::
315 ( Liftable a b,
323 ( Liftable a b,
316 Eq a,
324 Eq a,
317− CountableDimensionsN a b,
325+ CountableDimsN a b,
318− FromListsN a One,
326+ FLN a One,
319− FromListsN b One
327+ FLN b One
320 )
328 )
321 => Relation a b -> (a -> b -> Bool)
329 => Relation a b -> (a -> b -> Bool)
322fromRel r a b = pointApBool a b r
330fromRel r a b = pointApBool a b r
@@ -340,12 +348,12 @@ toBool r = case toList r of
340-- | Power transpose.
348-- | Power transpose.
341--
349--
342-- Maps a relation to a set valued function.
350-- Maps a relation to a set valued function.
343−pt ::
351+pt ::
344 ( Liftable a b,
352 ( Liftable a b,
345 Eq a,
353 Eq a,
346− CountableDimensionsN a b,
354+ CountableDimsN a b,
347− FromListsN a One,
355+ FLN a One,
348− FromListsN b One
356+ FLN b One
349 )
357 )
350 => Relation a b -> (a -> List b)
358 => Relation a b -> (a -> List b)
351pt r a =
359pt r a =
@@ -357,8 +365,8 @@ belongs ::
357 ( Bounded a,
365 ( Bounded a,
358 Enum a,
366 Enum a,
359 Eq a,
367 Eq a,
360− CountableDimensionsN (List a) a,
368+ CountableDims (List a) a,
361− FromListsN a (List a)
369+ FLN a (List a)
362 )
370 )
363 => Relation (List a) a
371 => Relation (List a) a
364belongs = toRel elemR
372belongs = toRel elemR
@@ -370,16 +378,16 @@ belongs = toRel elemR
370-- | 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
371-- with elements of type @b@.
379-- with elements of type @b@.
372--
380--
373−-- Also known as ⊥ (Bottom) Relation or empty Relation.
381+-- Also known as ⊥ (Bottom) Relation.
374--
382--
375-- @
383-- @
376−-- r ``comp`` ⊥ == ⊥ ``comp`` r == ⊥
384+-- r `.` ⊥ == ⊥ `.` r == ⊥
377-- ⊥ ``sse`` R && R ``sse`` T == True
385-- ⊥ ``sse`` R && R ``sse`` T == True
378-- @
386-- @
379zeros ::
387zeros ::
380− (FromListsN a b, CountableDimensionsN a b) =>
388+ (FLN a b, CountableDimsN a b) =>
381 Relation a b
389 Relation a b
382−zeros = relationBuilder (const (nat 0))
390+zeros = relationBuilder' (const (nat 0))
383
391
384-- Ones Matrix
392-- Ones Matrix
385
393
@@ -392,43 +400,43 @@ zeros = relationBuilder (const (nat 0))
392-- ⊥ ``sse`` R && R ``sse`` T == True
400-- ⊥ ``sse`` R && R ``sse`` T == True
393-- @
401-- @
394ones ::
402ones ::
395− (FromListsN a b, CountableDimensionsN a b) =>
403+ (FLN a b, CountableDimsN a b) =>
396 Relation a b
404 Relation a b
397−ones = relationBuilder (const (nat 1))
405+ones = relationBuilder' (const (nat 1))
398
406
399-- Bang Matrix
407-- Bang Matrix
400
408
401-- | The T (Top) row vector relation.
409-- | The T (Top) row vector relation.
402bang ::
410bang ::
403− (FromListsN a One, CountableN a) =>
411+ (FLN a One, CountableN a) =>
404 Relation a One
412 Relation a One
405bang = ones
413bang = ones
406
414
407-- | Point constant relation
415-- | Point constant relation
408−point ::
416+point ::
409 ( Bounded a,
417 ( Bounded a,
410 Enum a,
418 Enum a,
411 Eq a,
419 Eq a,
412 CountableN a,
420 CountableN a,
413− FromListsN a One
421+ FLN a One
414 ) => a -> Relation One a
422 ) => a -> Relation One a
415−point = fromF' . const
423+point = fromF . const
416
424
417−-- Identity Matrix
425+-- iden Matrix
418
426
419−-- | Identity matrix
427+-- | iden matrix
420--
428--
421-- @
429-- @
422−-- 'identity' ``comp`` r == r == r ``comp`` 'identity'
430+-- 'iden' `.` r == r == r `.` 'iden'
423-- @
431-- @
424−identity ::
432+iden ::
425− (FromListsN a a, CountableN a) => Relation a a
433+ (FLN a a, CountableN a) => Relation a a
426−identity = relationBuilder (bool (nat 0) (nat 1) . uncurry (==))
434+iden = relationBuilder' (bool (nat 0) (nat 1) . uncurry (==))
427
435
428-- | Relational composition
436-- | Relational composition
429--
437--
430-- @
438-- @
431−-- r ``comp`` (s ``comp`` p) = (r ``comp`` s) ``comp`` p
439+-- r `.` (s `.` p) = (r `.` s) `.` p
432-- @
440-- @
433comp :: Relation b c -> Relation a b -> Relation a c
441comp :: Relation b c -> Relation a b -> Relation a c
434comp (R a) (R b) = R (I.compRel a b)
442comp (R a) (R b) = R (I.compRel a b)
@@ -476,7 +484,7 @@ shrunkBy r s = r `intersection` divR s (conv r)
476-- r ``overriddenBy`` r == r
484-- r ``overriddenBy`` r == r
477-- @
485-- @
478overriddenBy ::
486overriddenBy ::
479− ( FromListsN b b,
487+ ( FLN b b,
480 CountableN b
488 CountableN b
481 ) => Relation a b -> Relation a b -> Relation a b
489 ) => Relation a b -> Relation a b -> Relation a b
482overriddenBy r s = s `union` r `intersection` divR zeros (conv s)
490overriddenBy r s = s `union` r `intersection` divR zeros (conv s)
@@ -488,11 +496,11 @@ overriddenBy r s = s `union` r `intersection` divR zeros (conv s)
488pointAp ::
496pointAp ::
489 ( Liftable a b,
497 ( Liftable a b,
490 Eq a,
498 Eq a,
491− CountableDimensionsN a b,
499+ CountableDimsN a b,
492− FromListsN a One,
500+ FLN a One,
493− FromListsN b One
501+ FLN b One
494 ) => a -> b -> Relation a b -> Relation One One
502 ) => a -> b -> Relation a b -> Relation One One
495−pointAp a b r = conv (point b) `comp` r `comp` point a
503+pointAp a b r = conv (point b) . r . point a
496
504
497-- | Relational application
505-- | Relational application
498--
506--
@@ -500,11 +508,11 @@ pointAp a b r = conv (point b) `comp` r `comp` point a
500pointApBool ::
508pointApBool ::
501 ( Liftable a b,
509 ( Liftable a b,
502 Eq a,
510 Eq a,
503− CountableDimensionsN a b,
511+ CountableDimsN a b,
504− FromListsN a One,
512+ FLN a One,
505− FromListsN b One
513+ FLN b One
506 ) => a -> b -> Relation a b -> Bool
514 ) => a -> b -> Relation a b -> Bool
507−pointApBool a b r = toBool $ conv (point b) `comp` r `comp` point a
515+pointApBool a b r = toBool $ conv (point b) . r . point a
508
516
509-- | Relational converse
517-- | Relational converse
510--
518--
@@ -530,7 +538,7 @@ iff r s = r == s
530
538
531-- | Relational intersection
539-- | Relational intersection
532--
540--
533−-- Lifts pointwise conjunction.
541+-- Lifts pointwise conjointion.
534--
542--
535-- @
543-- @
536-- (r ``intersection`` s) ``intersection`` t == r ``intersection`` (s ``intersection`` t)
544-- (r ``intersection`` s) ``intersection`` t == r ``intersection`` (s ``intersection`` t)
@@ -541,13 +549,13 @@ intersection a b = a * b
541
549
542-- | Relational union
550-- | Relational union
543--
551--
544−-- Lifts pointwise disjunction.
552+-- Lifts pointwise disjointion.
545--
553--
546-- @
554-- @
547-- (r ``union`` s) ``union`` t == r `'union' (s ``union`` t)
555-- (r ``union`` s) ``union`` t == r `'union' (s ``union`` t)
548-- r ``union`` s ``sse`` x == r ``sse`` x && s ``sse`` x
556-- r ``union`` s ``sse`` x == r ``sse`` x && s ``sse`` x
549−-- r ``comp`` (s ``union`` t) == (r ``comp`` s) ``union`` (r ``comp`` t)
557+-- r `.` (s ``union`` t) == (r `.` s) ``union`` (r `.` t)
550−-- (s ``union`` t) ``comp`` r == (s ``comp`` r) ``union`` (t ``comp`` r)
558+-- (s ``union`` t) `.` r == (s `.` r) ``union`` (t `.` r)
551-- @
559-- @
552union :: Relation a b -> Relation a b -> Relation a b
560union :: Relation a b -> Relation a b -> Relation a b
553union a b = a + b
561union a b = a + b
@@ -555,46 +563,46 @@ union a b = a + b
555-- | Relation Kernel
563-- | Relation Kernel
556--
564--
557-- @
565-- @
558−-- 'ker' r == 'conv' r ``comp`` r
566+-- 'ker' r == 'conv' r `.` r
559-- 'ker' r == 'img' ('conv' r)
567-- 'ker' r == 'img' ('conv' r)
560-- @
568-- @
561ker :: Relation a b -> Relation a a
569ker :: Relation a b -> Relation a a
562−ker r = conv r `comp` r
570+ker r = conv r . r
563
571
564-- | Relation Image
572-- | Relation Image
565--
573--
566-- @
574-- @
567−-- 'img' r == r ``comp`` conv r
575+-- 'img' r == r `.` conv r
568-- 'img' r == 'ker' ('conv' r)
576-- 'img' r == 'ker' ('conv' r)
569-- @
577-- @
570img :: Relation a b -> Relation b b
578img :: Relation a b -> Relation b b
571−img r = r `comp` conv r
579+img r = r . conv r
572
580
573-- | Function division. Special case of 'divS'.
581-- | Function division. Special case of 'divS'.
574--
582--
575-- 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
576-- 'entire'.
584-- 'entire'.
577--
585--
578−-- @'divisionF' f g == 'conv' g ``comp`` f@
586+-- @'divisionF' f g == 'conv' g `.` f@
579divisionF :: Relation a c -> Relation b c -> Relation a b
587divisionF :: Relation a c -> Relation b c -> Relation a b
580−divisionF f g = conv g `comp` f
588+divisionF f g = conv g . f
581
589
582-- Taxonomy of binary relations
590-- Taxonomy of binary relations
583
591
584-- | A 'Relation' @r@ is 'simple' 'iff' @'coreflexive' ('img' r)@
592-- | A 'Relation' @r@ is 'simple' 'iff' @'coreflexive' ('img' r)@
585−simple :: (CountableN b, FromListsN b b) => Relation a b -> Bool
593+simple :: (CountableN b, FLN b b) => Relation a b -> Bool
586simple = coreflexive . img
594simple = coreflexive . img
587
595
588-- | A 'Relation' @r@ is 'injective' 'iff' @'coreflexive' ('ker' r)@
596-- | A 'Relation' @r@ is 'injective' 'iff' @'coreflexive' ('ker' r)@
589−injective :: (CountableN a, FromListsN a a) => Relation a b -> Bool
597+injective :: (CountableN a, FLN a a) => Relation a b -> Bool
590injective = coreflexive . ker
598injective = coreflexive . ker
591
599
592-- | A 'Relation' @r@ is 'entire' 'iff' @'reflexive' ('ker' r)@
600-- | A 'Relation' @r@ is 'entire' 'iff' @'reflexive' ('ker' r)@
593−entire :: (CountableN a, FromListsN a a) => Relation a b -> Bool
601+entire :: (CountableN a, FLN a a) => Relation a b -> Bool
594entire = reflexive . ker
602entire = reflexive . ker
595
603
596-- | A 'Relation' @r@ is 'surjective' 'iff' @'reflexive' ('img' r)@
604-- | A 'Relation' @r@ is 'surjective' 'iff' @'reflexive' ('img' r)@
597−surjective :: (CountableN b, FromListsN b b) => Relation a b -> Bool
605+surjective :: (CountableN b, FLN b b) => Relation a b -> Bool
598surjective = reflexive . img
606surjective = reflexive . img
599
607
600-- | A 'Relation' @r@ is a 'function' 'iff' @'simple' r && 'entire' r@
608-- | A 'Relation' @r@ is a 'function' 'iff' @'simple' r && 'entire' r@
@@ -603,13 +611,13 @@ surjective = reflexive . img
603-- relations:
611-- relations:
604--
612--
605-- @
613-- @
606−-- f ``comp`` r ``sse`` s == r ``sse`` f ``comp`` s
614+-- f `.` r ``sse`` s == r ``sse`` f `.` s
607−-- r ``comp`` f ``sse`` s == r ``sse`` s ``comp`` f
615+-- r `.` f ``sse`` s == r ``sse`` s `.` f
608-- @
616-- @
609function ::
617function ::
610− ( CountableDimensionsN a b,
618+ ( CountableDimsN a b,
611− FromListsN a a,
619+ FLN a a,
612− FromListsN b b
620+ FLN b b
613 )
621 )
614 => Relation a b -> Bool
622 => Relation a b -> Bool
615function r = simple r && entire r
623function r = simple r && entire r
@@ -617,7 +625,7 @@ function r = simple r && entire r
617-- | A 'Relation' @r@ is a 'representation' 'iff' @'injective' r && 'entire' r@
625-- | A 'Relation' @r@ is a 'representation' 'iff' @'injective' r && 'entire' r@
618representation ::
626representation ::
619 ( CountableN a,
627 ( CountableN a,
620− FromListsN a a
628+ FLN a a
621 )
629 )
622 => Relation a b -> Bool
630 => Relation a b -> Bool
623representation r = injective r && entire r
631representation r = injective r && entire r
@@ -625,91 +633,91 @@ representation r = injective r && entire r
625-- | A 'Relation' @r@ is an 'abstraction' 'iff' @'surjective' r && 'simple' r@
633-- | A 'Relation' @r@ is an 'abstraction' 'iff' @'surjective' r && 'simple' r@
626abstraction ::
634abstraction ::
627 ( CountableN b,
635 ( CountableN b,
628− FromListsN b b
636+ FLN b b
629 )
637 )
630 => Relation a b -> Bool
638 => Relation a b -> Bool
631abstraction r = surjective r && simple r
639abstraction r = surjective r && simple r
632
640
633-- | A 'Relation' @r@ is a 'surjection' 'iff' @'function' r && 'abstraction' r@
641-- | A 'Relation' @r@ is a 'surjection' 'iff' @'function' r && 'abstraction' r@
634surjection ::
642surjection ::
635− ( CountableDimensionsN a b,
643+ ( CountableDimsN a b,
636− FromListsN a a,
644+ FLN a a,
637− FromListsN b b
645+ FLN b b
638 )
646 )
639 => Relation a b -> Bool
647 => Relation a b -> Bool
640surjection r = function r && abstraction r
648surjection r = function r && abstraction r
641
649
642-- | A 'Relation' @r@ is a 'injection' 'iff' @'function' r && 'representation' r@
650-- | A 'Relation' @r@ is a 'injection' 'iff' @'function' r && 'representation' r@
643injection ::
651injection ::
644− ( CountableDimensionsN a b,
652+ ( CountableDimsN a b,
645− FromListsN a a,
653+ FLN a a,
646− FromListsN b b
654+ FLN b b
647 )
655 )
648 => Relation a b -> Bool
656 => Relation a b -> Bool
649injection r = function r && representation r
657injection r = function r && representation r
650
658
651-- | A 'Relation' @r@ is an 'bijection' 'iff' @'injection' r && 'surjection' r@
659-- | A 'Relation' @r@ is an 'bijection' 'iff' @'injection' r && 'surjection' r@
652bijection ::
660bijection ::
653− ( CountableDimensionsN a b,
661+ ( CountableDimsN a b,
654− FromListsN b b,
662+ FLN b b,
655− FromListsN a a
663+ FLN a a
656 ) => Relation a b -> Bool
664 ) => Relation a b -> Bool
657bijection r = injection r && surjection r
665bijection r = injection r && surjection r
658
666
659-- Properties of relations
667-- Properties of relations
660
668
661−-- | A 'Relation' @r@ is 'reflexive' 'iff' @'identity' ``sse`` r@
669+-- | A 'Relation' @r@ is 'reflexive' 'iff' @'id' ``sse`` r@
662−reflexive :: (CountableN a, FromListsN a a) => Relation a a -> Bool
670+reflexive :: (CountableN a, FLN a a) => Relation a a -> Bool
663−reflexive r = identity <= r
671+reflexive r = id <= r
664
672
665−-- | A 'Relation' @r@ is 'coreflexive' 'iff' @r ``sse`` 'identity'@
673+-- | A 'Relation' @r@ is 'coreflexive' 'iff' @r ``sse`` 'id'@
666−coreflexive :: (CountableN a, FromListsN a a) => Relation a a -> Bool
674+coreflexive :: (CountableN a, FLN a a) => Relation a a -> Bool
667−coreflexive r = r <= identity
675+coreflexive r = r <= id
668
676
669−-- | A 'Relation' @r@ is 'transitive' 'iff' @(r ``comp`` r) ``sse`` r@
677+-- | A 'Relation' @r@ is 'transitive' 'iff' @(r `.` r) ``sse`` r@
670transitive :: Relation a a -> Bool
678transitive :: Relation a a -> Bool
671−transitive r = (r `comp` r) `sse` r
679+transitive r = (r . r) `sse` r
672
680
673-- | A 'Relation' @r@ is 'symmetric' 'iff' @r == 'conv' r@
681-- | A 'Relation' @r@ is 'symmetric' 'iff' @r == 'conv' r@
674symmetric :: Relation a a -> Bool
682symmetric :: Relation a a -> Bool
675symmetric r = r == conv r
683symmetric r = r == conv r
676
684
677−-- | A 'Relation' @r@ is anti-symmetric 'iff' @(r ``intersection`` 'conv' r) ``sse`` 'identity'@
685+-- | A 'Relation' @r@ is anti-symmetric 'iff' @(r ``intersection`` 'conv' r) ``sse`` 'id'@
678−antiSymmetric :: (CountableN a, FromListsN a a) => Relation a a -> Bool
686+antiSymmetric :: (CountableN a, FLN a a) => Relation a a -> Bool
679−antiSymmetric r = (r `intersection` conv r) `sse` identity
687+antiSymmetric r = (r `intersection` conv r) `sse` id
680
688
681−-- | A 'Relation' @r@ is 'irreflexive' 'iff' @(r ``intersection`` 'identity') == 'zeros'@
689+-- | A 'Relation' @r@ is 'irreflexive' 'iff' @(r ``intersection`` 'id') == 'zeros'@
682−irreflexive :: (CountableN a, FromListsN a a) => Relation a a -> Bool
690+irreflexive :: (CountableN a, FLN a a) => Relation a a -> Bool
683−irreflexive r = (r `intersection` identity) == zeros
691+irreflexive r = (r `intersection` id) == zeros
684
692
685-- | A 'Relation' @r@ is 'connected' 'iff' @(r ``union`` 'conv' r) == 'ones'@
693-- | A 'Relation' @r@ is 'connected' 'iff' @(r ``union`` 'conv' r) == 'ones'@
686−connected :: (CountableN a, FromListsN a a) => Relation a a -> Bool
694+connected :: (CountableN a, FLN a a) => Relation a a -> Bool
687connected r = (r `union` conv r) == ones
695connected r = (r `union` conv r) == ones
688
696
689-- | A 'Relation' @r@ is a 'preorder' 'iff' @'reflexive' r && 'transitive' r@
697-- | A 'Relation' @r@ is a 'preorder' 'iff' @'reflexive' r && 'transitive' r@
690−preorder :: (CountableN a, FromListsN a a) => Relation a a -> Bool
698+preorder :: (CountableN a, FLN a a) => Relation a a -> Bool
691preorder r = reflexive r && transitive r
699preorder r = reflexive r && transitive r
692
700
693-- | 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@
694−partialOrder :: (CountableN a, FromListsN a a) => Relation a a -> Bool
702+partialOrder :: (CountableN a, FLN a a) => Relation a a -> Bool
695partialOrder r = antiSymmetric r && preorder r
703partialOrder r = antiSymmetric r && preorder r
696
704
697-- | 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@
698−linearOrder :: (CountableN a, FromListsN a a) => Relation a a -> Bool
706+linearOrder :: (CountableN a, FLN a a) => Relation a a -> Bool
699linearOrder r = connected r && partialOrder r
707linearOrder r = connected r && partialOrder r
700
708
701-- | A 'Relation' @r@ is an 'equivalence' 'iff' @'symmetric' r && 'preorder' r@
709-- | A 'Relation' @r@ is an 'equivalence' 'iff' @'symmetric' r && 'preorder' r@
702−equivalence :: (CountableN a, FromListsN a a) => Relation a a -> Bool
710+equivalence :: (CountableN a, FLN a a) => Relation a a -> Bool
703equivalence r = symmetric r && preorder r
711equivalence r = symmetric r && preorder r
704
712
705-- | 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@
706−partialEquivalence :: (CountableN a, FromListsN a a) => Relation a a -> Bool
714+partialEquivalence :: (CountableN a, FLN a a) => Relation a a -> Bool
707partialEquivalence r = partialOrder r && equivalence r
715partialEquivalence r = partialOrder r && equivalence r
708
716
709-- | A 'Relation' @r@ is 'difunctional' or regular wherever
717-- | A 'Relation' @r@ is 'difunctional' or regular wherever
710−-- @r ``comp`` 'conv' r ``comp`` r == r@
718+-- @r `.` 'conv' r `.` r == r@
711difunctional :: Relation a b -> Bool
719difunctional :: Relation a b -> Bool
712−difunctional r = r `comp` conv r `comp` r == r
720+difunctional r = r . conv r . r == r
713
721
714-- Relational pairing
722-- Relational pairing
715
723
@@ -718,61 +726,61 @@ difunctional r = r `comp` conv r `comp` r == r
718-- 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:
719--
727--
720-- @
728-- @
721−-- | 'p1' ``comp`` 'splitR' a b ``sse`` a
729+-- | 'fstR' `.` 'splitR' a b ``sse`` a
722-- 'splitR' a b <=> |
730-- 'splitR' a b <=> |
723−-- | 'p2' ``comp`` 'splitR' a b ``sse`` b
731+-- | 'sndR' `.` 'splitR' a b ``sse`` b
724-- @
732-- @
725--
733--
726-- __Emphasis__ on the 'sse'.
734-- __Emphasis__ on the 'sse'.
727--
735--
728-- @
736-- @
729−-- 'splitR' r s ``comp`` f == 'splitR' (r ``comp`` f) (s ``comp`` f)
737+-- 'splitR' r s `.` f == 'splitR' (r `.` f) (s `.` f)
730−-- (R '><' S) ``comp`` 'splitR' p q == 'splitR' (r ``comp`` p) (s ``comp`` q)
738+-- (R '><' S) `.` 'splitR' p q == 'splitR' (r `.` p) (s `.` q)
731−-- 'conv' ('splitR' r s) ``comp`` 'splitR' x y == ('conv' r ``comp`` x) ``intersection`` ('conv' s ``comp`` y)
739+-- 'conv' ('splitR' r s) `.` 'splitR' x y == ('conv' r `.` x) ``intersection`` ('conv' s `.` y)
732-- @
740-- @
733--
741--
734-- @
742-- @
735-- '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)
736-- @
744-- @
737splitR ::
745splitR ::
738− ( CountableDimensionsN a b,
746+ ( CountableDimsN a b,
739 CountableN (a, b),
747 CountableN (a, b),
740− FromListsN (a, b) a,
748+ FLN (a, b) a,
741− FromListsN (a, b) b,
749+ FLN (a, b) b,
742 TrivialP a b
750 TrivialP a b
743 )
751 )
744 => Relation c a -> Relation c b -> Relation c (a, b)
752 => Relation c a -> Relation c b -> Relation c (a, b)
745−splitR (R f) (R g) = R (I.khatri f g)
753+splitR (R f) (R g) = R (I.kr f g)
746
754
747-- | Relational pairing first component projection
755-- | Relational pairing first component projection
748--
756--
749-- @
757-- @
750−-- 'p1' ``comp`` 'splitR' r s ``sse`` r
758+-- 'fstR' `.` 'splitR' r s ``sse`` r
751-- @
759-- @
752−p1 ::
760+fstR ::
753 forall a b .
761 forall a b .
754− ( CountableDimensionsN a b,
762+ ( CountableDimsN a b,
755 CountableN (a, b),
763 CountableN (a, b),
756− FromListsN (a, b) a,
764+ FLN (a, b) a,
757 TrivialP a b
765 TrivialP a b
758 )
766 )
759 => Relation (a, b) a
767 => Relation (a, b) a
760−p1 = R (I.kp1 @Boolean @(I.Normalize a) @(I.Normalize b))
768+fstR = R (I.fstM @Boolean @(I.Normalize a) @(I.Normalize b))
761
769
762-- | Relational pairing second component projection
770-- | Relational pairing second component projection
763--
771--
764-- @
772-- @
765−-- 'p2' ``comp`` 'splitR' r s ``sse`` s
773+-- 'sndR' `.` 'splitR' r s ``sse`` s
766-- @
774-- @
767−p2 ::
775+sndR ::
768 forall a b .
776 forall a b .
769− ( CountableDimensionsN a b,
777+ ( CountableDimsN a b,
770 CountableN (a, b),
778 CountableN (a, b),
771− FromListsN (a, b) b,
779+ FLN (a, b) b,
772 TrivialP a b
780 TrivialP a b
773 )
781 )
774 => Relation (a, b) b
782 => Relation (a, b) b
775−p2 = R (I.kp2 @Boolean @(I.Normalize a) @(I.Normalize b))
783+sndR = R (I.sndM @Boolean @(I.Normalize a) @(I.Normalize b))
776
784
777-- Relational pairing functor
785-- Relational pairing functor
778
786
@@ -780,17 +788,17 @@ infixl 4 ><
780-- | Relational pairing functor
788-- | Relational pairing functor
781--
789--
782-- @
790-- @
783−-- r '><' s == 'splitR' (r ``comp`` p1) (s ``comp`` p2)
791+-- r '><' s == 'splitR' (r `.` fstR) (s `.` sndR)
784−-- (r '><' s) ``comp`` (p '><' q) == (r ``comp`` p) '><' (s ``comp`` q)
792+-- (r '><' s) `.` (p '><' q) == (r `.` p) '><' (s `.` q)
785-- @
793-- @
786(><) ::
794(><) ::
787− ( CountableDimensionsN a b,
795+ ( CountableDimsN a b,
788− CountableDimensionsN c d,
796+ CountableDimsN c d,
789− CountableDimensionsN (a, c) (b, d),
797+ CountableDimsN (a, c) (b, d),
790− FromListsN (a, c) a,
798+ FLN (a, c) a,
791− FromListsN (a, c) c,
799+ FLN (a, c) c,
792− FromListsN (b, d) b,
800+ FLN (b, d) b,
793− FromListsN (b, d) d,
801+ FLN (b, d) d,
794 TrivialP a c,
802 TrivialP a c,
795 TrivialP b d
803 TrivialP b d
796 )
804 )
@@ -802,31 +810,31 @@ infixl 4 ><
802-- | Relational coproduct.
810-- | Relational coproduct.
803--
811--
804-- @
812-- @
805−-- | 'eitherR' a b ``comp`` 'i1' == a
813+-- | 'eitherR' a b `.` 'i1' == a
806-- 'eitherR' a b <=> |
814-- 'eitherR' a b <=> |
807−-- | 'eitherR' a b ``comp`` 'i2' == b
815+-- | 'eitherR' a b `.` 'i2' == b
808-- @
816-- @
809--
817--
810-- @
818-- @
811−-- 'eitherR' r s ``comp`` 'conv' ('eitherR' t u) == (r ``comp`` 'conv' t) ``union`` (s ``comp`` 'conv' u)
819+-- 'eitherR' r s `.` 'conv' ('eitherR' t u) == (r `.` 'conv' t) ``union`` (s `.` 'conv' u)
812-- @
820-- @
813--
821--
814-- @
822-- @
815-- '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)
816-- @
824-- @
817eitherR :: Relation a c -> Relation b c -> Relation (Either a b) c
825eitherR :: Relation a c -> Relation b c -> Relation (Either a b) c
818−eitherR = junc
826+eitherR = join
819
827
820-- | Relational coproduct first component injection
828-- | Relational coproduct first component injection
821--
829--
822-- @
830-- @
823−-- 'img' 'i1' ``union`` 'img' 'i2' == 'identity'
831+-- 'img' 'i1' ``union`` 'img' 'i2' == 'id'
824−-- 'i1' ``comp`` 'i2' = 'zeros'
832+-- 'i1' `.` 'i2' = 'zeros'
825-- @
833-- @
826i1 ::
834i1 ::
827− ( CountableDimensionsN a b,
835+ ( CountableDimsN a b,
828− FromListsN b a,
836+ FLN b a,
829− FromListsN a a
837+ FLN a a
830 )
838 )
831 => Relation a (Either a b)
839 => Relation a (Either a b)
832i1 = R I.i1
840i1 = R I.i1
@@ -834,13 +842,13 @@ i1 = R I.i1
834-- | Relational coproduct second component injection
842-- | Relational coproduct second component injection
835--
843--
836-- @
844-- @
837−-- 'img' 'i1' ``union`` 'img' 'i2' == 'identity'
845+-- 'img' 'i1' ``union`` 'img' 'i2' == 'id'
838−-- 'i1' ``comp`` 'i2' = 'zeros'
846+-- 'i1' `.` 'i2' = 'zeros'
839-- @
847-- @
840i2 ::
848i2 ::
841− ( CountableDimensionsN a b,
849+ ( CountableDimsN a b,
842− FromListsN a b,
850+ FLN a b,
843− FromListsN b b
851+ FLN b b
844 )
852 )
845 => Relation b (Either a b)
853 => Relation b (Either a b)
846i2 = R I.i2
854i2 = R I.i2
@@ -850,14 +858,14 @@ infixl 5 -|-
850-- | Relational coproduct functor.
858-- | Relational coproduct functor.
851--
859--
852-- @
860-- @
853−-- r '-|-' s == 'eitherR' ('i1' ``comp`` r) ('i2' ``comp`` s)
861+-- r '-|-' s == 'eitherR' ('i1' `.` r) ('i2' `.` s)
854-- @
862-- @
855(-|-) ::
863(-|-) ::
856− ( CountableDimensionsN b d,
864+ ( CountableDimsN b d,
857− FromListsN b b,
865+ FLN b b,
858− FromListsN d b,
866+ FLN d b,
859− FromListsN b d,
867+ FLN b d,
860− FromListsN d d
868+ FLN d d
861 )
869 )
862 => Relation a b -> Relation c d -> Relation (Either a c) (Either b d)
870 => Relation a b -> Relation c d -> Relation (Either a c) (Either b d)
863(-|-) (R a) (R b) = R ((I.-|-) a b)
871(-|-) (R a) (R b) = R ((I.-|-) a b)
@@ -870,20 +878,20 @@ infixl 5 -|-
870-- 'trans'/'untrans';
878-- 'trans'/'untrans';
871-- more-over, where each particular attribute is placed (input/output) is irrelevant.
879-- more-over, where each particular attribute is placed (input/output) is irrelevant.
872trans ::
880trans ::
873− ( CountableDimensionsN a b,
881+ ( CountableDimsN a b,
874 CountableN c,
882 CountableN c,
875− CountableDimensionsN (a, b) (c, b),
883+ CountableDimsN (a, b) (c, b),
876− FromListsN (c, b) c,
884+ FLN (c, b) c,
877− FromListsN (c, b) b,
885+ FLN (c, b) b,
878− FromListsN (a, b) a,
886+ FLN (a, b) a,
879− FromListsN (a, b) b,
887+ FLN (a, b) b,
880 Trivial (a, b),
888 Trivial (a, b),
881 Trivial (c, b),
889 Trivial (c, b),
882 TrivialP a b,
890 TrivialP a b,
883 TrivialP c b
891 TrivialP c b
884 )
892 )
885 => Relation (a, b) c -> Relation a (c, b)
893 => Relation (a, b) c -> Relation a (c, b)
886−trans r = splitR r p2 `comp` conv p1
894+trans r = splitR r sndR . conv fstR
887
895
888-- | Relational 'untrans'
896-- | Relational 'untrans'
889--
897--
@@ -891,107 +899,110 @@ trans r = splitR r p2 `comp` conv p1
891-- 'trans'/'untrans';
899-- 'trans'/'untrans';
892-- more-over, where each particular attribute is placed (input/output) is irrelevant.
900-- more-over, where each particular attribute is placed (input/output) is irrelevant.
893untrans ::
901untrans ::
894− ( CountableDimensionsN a b,
902+ ( CountableDimsN a b,
895 CountableN c,
903 CountableN c,
896− CountableDimensionsN (a, b) (c, b),
904+ CountableDimsN (a, b) (c, b),
897− FromListsN (c, b) c,
905+ FLN (c, b) c,
898− FromListsN (c, b) b,
906+ FLN (c, b) b,
899− FromListsN (a, b) b,
907+ FLN (a, b) b,
900− FromListsN (a, b) a,
908+ FLN (a, b) a,
901 Trivial (a, b),
909 Trivial (a, b),
902 Trivial (c, b),
910 Trivial (c, b),
903 TrivialP a b,
911 TrivialP a b,
904 TrivialP c b
912 TrivialP c b
905 )
913 )
906 => Relation a (c, b) -> Relation (a, b) c
914 => Relation a (c, b) -> Relation (a, b) c
907−untrans s = p1 `comp` conv (splitR (conv s) p2)
915+untrans s = fstR . conv (splitR (conv s) sndR)
908
916
909-- | Transforms predicate @p@ into a correflexive relation.
917-- | Transforms predicate @p@ into a correflexive relation.
910--
918--
911-- @
919-- @
912−-- 'predR' ('const' True) == 'identity'
920+-- 'predR' ('const' True) == 'id'
913-- 'predR' ('const' False) == 'zeros'
921-- 'predR' ('const' False) == 'zeros'
914-- @
922-- @
915--
923--
916-- @
924-- @
917−-- 'predR' q ``comp`` 'predR' p == 'predR' q ``union`` 'predR' p
925+-- 'predR' q `.` 'predR' p == 'predR' q ``union`` 'predR' p
918-- @
926-- @
919predR ::
927predR ::
920 ( Bounded a,
928 ( Bounded a,
921 Enum a,
929 Enum a,
930+ Countable a,
922 CountableN a,
931 CountableN a,
923− FromListsN a a,
932+ FLN a a,
924− FromListsN Bool a
933+ FLN Bool a
925 )
934 )
926 => Relation a Bool -> Relation a a
935 => Relation a Bool -> Relation a a
927−predR p = identity `intersection` divisionF (fromF' (const True)) p
936+predR p = id `intersection` divisionF (fromF (const True)) p
928
937
929-- | Equalizes functions @f@ and @g@.
938-- | Equalizes functions @f@ and @g@.
930-- That is, @'equalizer' f g@ is the largest coreflexive
939-- That is, @'equalizer' f g@ is the largest coreflexive
931-- that restricts @g@ so that @f@ and @g@ yield the same outputs.
940-- that restricts @g@ so that @f@ and @g@ yield the same outputs.
932--
941--
933-- @
942-- @
934−-- 'equalizer' r r == 'identity'
943+-- 'equalizer' r r == 'id'
935-- 'equalizer' ('point' True) ('point' False) == 'zeros'
944-- 'equalizer' ('point' True) ('point' False) == 'zeros'
936-- @
945-- @
937equalizer ::
946equalizer ::
938 ( CountableN a,
947 ( CountableN a,
939− FromListsN a a
948+ FLN a a
940 )
949 )
941 => Relation a b -> Relation a b -> Relation a a
950 => Relation a b -> Relation a b -> Relation a a
942−equalizer f g = identity `intersection` divisionF f g
951+equalizer f g = id `intersection` divisionF f g
943
952
944-- | Relational conditional guard.
953-- | Relational conditional guard.
945--
954--
946-- @
955-- @
947−-- 'guard' p = 'i2' ``overriddenBy`` 'i1' ``comp`` 'predR' p
956+-- 'guard' p = 'i2' ``overriddenBy`` 'i1' `.` 'predR' p
948-- @
957-- @
949−guard ::
958+guard ::
950 ( Bounded b,
959 ( Bounded b,
951 Enum b,
960 Enum b,
952 CountableN b,
961 CountableN b,
953− FromListsN b b,
962+ Countable b,
963+ FLN b b,
954− FromListsN Bool b
964+ FLN Bool b
955 ) => Relation b Bool -> Relation b (Either b b)
965 ) => Relation b Bool -> Relation b (Either b b)
956guard p = conv (eitherR (predR p) (predR (negate p)))
966guard p = conv (eitherR (predR p) (predR (negate p)))
957
967
958-- | Relational McCarthy's conditional.
968-- | Relational McCarthy's conditional.
959−cond ::
969+cond ::
960 ( Bounded b,
970 ( Bounded b,
961 Enum b,
971 Enum b,
972+ Countable b,
962 CountableN b,
973 CountableN b,
963− FromListsN b b,
974+ FLN b b,
964− FromListsN Bool b
975+ FLN Bool b
965− )
976+ )
966 => Relation b Bool -> Relation b c -> Relation b c -> Relation b c
977 => Relation b Bool -> Relation b c -> Relation b c -> Relation b c
967−cond p r s = eitherR r s `comp` guard p
978+cond p r s = eitherR r s . guard p
968
979
969-- | Relational domain.
980-- | Relational domain.
970--
981--
971-- For injective relations, 'domain' and 'ker'nel coincide,
982-- For injective relations, 'domain' and 'ker'nel coincide,
972−-- since @'ker' r ``sse`` 'identity'@ in such situations.
983+-- since @'ker' r ``sse`` 'id'@ in such situations.
973domain ::
984domain ::
974 ( CountableN a,
985 ( CountableN a,
975− FromListsN a a
986+ FLN a a
976 ) => Relation a b -> Relation a a
987 ) => Relation a b -> Relation a a
977−domain r = ker r `intersection` identity
988+domain r = ker r `intersection` id
978
989
979-- | Relational range.
990-- | Relational range.
980--
991--
981-- For functions, 'range' and 'img' (image) coincide,
992-- For functions, 'range' and 'img' (image) coincide,
982−-- since @'img' f ``sse`` 'identity'@ for any @f@.
993+-- since @'img' f ``sse`` id@ for any @f@.
983range ::
994range ::
984 ( CountableN b,
995 ( CountableN b,
985− FromListsN b b
996+ FLN b b
986 ) => Relation a b -> Relation b b
997 ) => Relation a b -> Relation b b
987−range r = img r `intersection` identity
998+range r = img r `intersection` id
988
999
989-- Relation pretty print
1000-- Relation pretty print
990
1001
991-- | Relation pretty printing
1002-- | Relation pretty printing
992−pretty :: (CountableDimensionsN a b) => Relation a b -> String
1003+pretty :: (CountableDimsN a b) => Relation a b -> String
993pretty (R a) = I.pretty a
1004pretty (R a) = I.pretty a
994
1005
995-- | Relation pretty printing
1006-- | Relation pretty printing
996−prettyPrint :: (CountableDimensionsN a b) => Relation a b -> IO ()
1007+prettyPrint :: (CountableDimsN a b) => Relation a b -> IO ()
997prettyPrint (R a) = I.prettyPrint a
1008prettyPrint (R a) = I.prettyPrint a
src/LAoP/Utils.hs+4−1
@@ -96,7 +96,10 @@ module LAoP.Utils
96 coerceNat3,
96 coerceNat3,
97
97
98 -- * List data type
98 -- * List data type
99− List (..)
99+ List (..),
100+
101+ -- * Category type-class
102+ Category(..)
100 )
103 )
101where
104where
102
105
src/LAoP/Utils/Internal.hs+28−2
@@ -1,9 +1,9 @@
1+{-# LANGUAGE TypeFamilies #-}
1{-# LANGUAGE DeriveGeneric #-}
2{-# LANGUAGE DeriveGeneric #-}
2{-# LANGUAGE TypeApplications #-}
3{-# LANGUAGE TypeApplications #-}
3{-# LANGUAGE DataKinds #-}
4{-# LANGUAGE DataKinds #-}
4{-# LANGUAGE FlexibleInstances #-}
5{-# LANGUAGE FlexibleInstances #-}
5{-# LANGUAGE GeneralizedNewtypeDeriving #-}
6{-# LANGUAGE GeneralizedNewtypeDeriving #-}
6−{-# LANGUAGE KindSignatures #-}
7{-# LANGUAGE ScopedTypeVariables #-}
7{-# LANGUAGE ScopedTypeVariables #-}
8
8
9module LAoP.Utils.Internal
9module LAoP.Utils.Internal
@@ -19,7 +19,10 @@ module LAoP.Utils.Internal
19 coerceNat3,
19 coerceNat3,
20
20
21 -- * 'List' data type
21 -- * 'List' data type
22− List (..)
22+ List (..),
23+
24+ -- * Category type class
25+ Category(..)
23 )
26 )
24where
27where
25
28
@@ -30,6 +33,9 @@ import Data.Maybe
30import GHC.TypeLits
33import GHC.TypeLits
31import Control.DeepSeq
34import Control.DeepSeq
32import GHC.Generics
35import GHC.Generics
36+import Data.Kind
37+import Prelude hiding (id, (.))
38+import qualified Prelude
33
39
34-- | Wrapper around 'Int's that have a restrictive semantic associated.
40-- | Wrapper around 'Int's that have a restrictive semantic associated.
35-- A value of type @'Natural' n m@ can only be instanciated with some 'Int'
41-- A value of type @'Natural' n m@ can only be instanciated with some 'Int'
@@ -168,3 +174,23 @@ instance
168 fromEnum (L x) =
174 fromEnum (L x) =
169 let as = [minBound .. maxBound]
175 let as = [minBound .. maxBound]
170 in fromMaybe (error "Does not exist") $ elemIndex x (powerset as)
176 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.yamlnew file+1
@@ -0,0 +1 @@
1+resolver: lts-15.5
stack.yaml+1−66
@@ -1,66 +1 @@
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
20−resolver: lts-14.18
1+resolver: lts-14.3
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: 524789
9+ size: 523878
10− url: https://raw.githubusercontent.com/commercialhaskell/stackage-snapshots/master/lts/14/18.yaml
10+ url: https://raw.githubusercontent.com/commercialhaskell/stackage-snapshots/master/lts/14/3.yaml
11− sha256: 646be71223e08234131c6989912e6011e01b9767bc447b6d466a35e14360bdf2
11+ sha256: 470c46c27746a48c7c50f829efc0cf00112787a7804ee4ac7a27754658f6d92c
12− original: lts-14.18
12+ original: lts-14.3
test/Examples/Quantum.hsnew file+31
@@ -0,0 +1,31 @@
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)
app/Examples.hs → test/Examples/Readme.hsrenamed+56−31
@@ -1,10 +1,10 @@
1+{-# LANGUAGE GADTs #-}
1{-# LANGUAGE DeriveGeneric #-}
2{-# LANGUAGE DeriveGeneric #-}
2{-# LANGUAGE FlexibleContexts #-}
3{-# LANGUAGE FlexibleContexts #-}
3−{-# LANGUAGE TypeOperators #-}
4{-# LANGUAGE TypeApplications #-}
4{-# LANGUAGE TypeApplications #-}
5{-# LANGUAGE DataKinds #-}
5{-# LANGUAGE DataKinds #-}
6
6
7−module Examples
7+module Examples.Readme
8 ( exec
8 ( exec
9 )
9 )
10 where
10 where
@@ -15,13 +15,12 @@ import LAoP.Utils
15import LAoP.Dist
15import LAoP.Dist
16import GHC.TypeLits
16import GHC.TypeLits
17import Data.Coerce
17import Data.Coerce
18−import GHC.Generics
18+import qualified GHC.Generics as G
19−import Control.Category hiding (id)
19+import Prelude hiding (id, (.))
20−import Prelude hiding ((.))
21
20
22-- Monty Hall Problem
21-- Monty Hall Problem
23data Outcome = Win | Lose
22data Outcome = Win | Lose
24− deriving (Bounded, Enum, Eq, Show, Generic)
23+ deriving (Bounded, Enum, Eq, Show, G.Generic)
25
24
26switch :: Outcome -> Outcome
25switch :: Outcome -> Outcome
27switch Win = Lose
26switch Win = Lose
@@ -31,7 +30,7 @@ firstChoice :: Matrix Double () Outcome
31firstChoice = col [1/3, 2/3]
30firstChoice = col [1/3, 2/3]
32
31
33secondChoice :: Matrix Double Outcome Outcome
32secondChoice :: Matrix Double Outcome Outcome
34−secondChoice = fromF' switch
33+secondChoice = fromF switch
35
34
36-- Dice sum
35-- Dice sum
37
36
@@ -40,7 +39,7 @@ type SS = Natural 1 6 -- Sample Space
40sumSS :: SS -> SS -> Natural 2 12
39sumSS :: SS -> SS -> Natural 2 12
41sumSS = coerceNat (+)
40sumSS = coerceNat (+)
42
41
43−sumSSM = fromF' (uncurry sumSS)
42+sumSSM = fromF (uncurry sumSS)
44
43
45condition :: (Int, Int) -> Int -> Int
44condition :: (Int, Int) -> Int -> Int
46condition (fst, snd) thrd = if fst == snd
45condition (fst, snd) thrd = if fst == snd
@@ -50,38 +49,64 @@ condition (fst, snd) thrd = if fst == snd
50conditionSS :: (SS, SS) -> SS -> Natural 3 18
49conditionSS :: (SS, SS) -> SS -> Natural 3 18
51conditionSS = coerceNat2 condition
50conditionSS = coerceNat2 condition
52
51
53−conditionalThrows = fromF' (uncurry conditionSS) . khatri (khatri die die) die
52+conditionalThrows = fromF (uncurry conditionSS) . kr (kr die die) die
54
53
55die :: Matrix Double () SS
54die :: Matrix Double () SS
56die = col $ map (const (1/6)) [nat @1 @6 1 .. nat 6]
55die = col $ map (const (1/6)) [nat @1 @6 1 .. nat 6]
57
56
58-- Sprinkler
57-- Sprinkler
58+data G = Dry | Wet
59+ deriving (Bounded, Enum, Eq, Show, G.Generic)
59
60
60−rain :: Matrix Double () Bool
61+data S = Off | On
61−rain = col [0.8, 0.2]
62+ deriving (Bounded, Enum, Eq, Show, G.Generic)
62
63
63−sprinkler :: Matrix Double Bool Bool
64+data R = No | Yes
64−sprinkler = fromLists [[0.6, 0.99], [0.4, 0.01]]
65+ deriving (Bounded, Enum, Eq, Show, G.Generic)
65
66
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+
66−grass :: Matrix Double (Bool, Bool) Bool
81+grass :: Matrix Double (S, R) G
67−grass = fromLists [[1, 0.2, 0.1, 0.01], [0, 0.8, 0.9, 0.99]]
82+grass = matrixBuilder gen
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
68
94
69−state :: Matrix Double () (Bool, (Bool, Bool))
95+state g s r = tag g . tag s . r
70−state = khatri grass identity . khatri sprinkler identity . rain
71
96
72−grass_wet :: Matrix Double (Bool, (Bool, Bool)) One
97+grass_wet :: Matrix Double () (G, (S, R)) -> Matrix Double One One
73−grass_wet = row [0,1] . kp1
98+grass_wet state = row [0,1] . fstM . state
74
99
75−rainning :: Matrix Double (Bool, (Bool, Bool)) One
100+rainning :: Matrix Double (G, (S, R)) One
76−rainning = row [0,1] . kp2 . kp2
101+rainning = row [0,1] . sndM . sndM
77
102
78-- Alcuin Puzzle
103-- Alcuin Puzzle
79
104
80data Being = Farmer | Fox | Goose | Beans
105data Being = Farmer | Fox | Goose | Beans
81− deriving (Bounded, Enum, Eq, Show, Generic)
106+ deriving (Bounded, Enum, Eq, Show, G.Generic)
82
107
83data Bank = LeftB | RightB
108data Bank = LeftB | RightB
84− deriving (Bounded, Enum, Eq, Show, Generic)
109+ deriving (Bounded, Enum, Eq, Show, G.Generic)
85
110
86eats :: Being -> Being -> Bool
111eats :: Being -> Being -> Bool
87eats Fox Goose = True
112eats Fox Goose = True
@@ -96,21 +121,21 @@ cross LeftB = RightB
96cross RightB = LeftB
121cross RightB = LeftB
97
122
98crossR :: R.Relation Bank Bank
123crossR :: R.Relation Bank Bank
99−crossR = R.fromF' cross
124+crossR = R.fromF cross
100
125
101-- | Initial state, everyone in the left bank
126-- | Initial state, everyone in the left bank
102locationLeft :: Being -> Bank
127locationLeft :: Being -> Bank
103locationLeft _ = LeftB
128locationLeft _ = LeftB
104
129
105locationLeftR :: R.Relation Being Bank
130locationLeftR :: R.Relation Being Bank
106−locationLeftR = R.fromF' locationLeft
131+locationLeftR = R.fromF locationLeft
107
132
108-- | Initial state, everyone in the right bank
133-- | Initial state, everyone in the right bank
109locationRight :: Being -> Bank
134locationRight :: Being -> Bank
110locationRight _ = RightB
135locationRight _ = RightB
111
136
112locationRightR :: R.Relation Being Bank
137locationRightR :: R.Relation Being Bank
113−locationRightR = R.fromF' locationRight
138+locationRightR = R.fromF locationRight
114
139
115-- Properties
140-- Properties
116
141
@@ -127,7 +152,7 @@ inv :: R.Relation Being Bank -> Bool
127inv w = (w `R.comp` canEat w) `R.sse` (w `R.comp` farmer)
152inv w = (w `R.comp` canEat w) `R.sse` (w `R.comp` farmer)
128 where
153 where
129 farmer :: R.Relation Being Being
154 farmer :: R.Relation Being Being
130− farmer = R.fromF' (const Farmer)
155+ farmer = R.fromF (const Farmer)
131
156
132-- Arbitrary state
157-- Arbitrary state
133bankState :: Being -> Bank -> Bool
158bankState :: Being -> Bank -> Bool
@@ -146,14 +171,14 @@ exec = do
146 putStrLn "Monty Hall Problem solution:"
171 putStrLn "Monty Hall Problem solution:"
147 prettyPrint (secondChoice . firstChoice)
172 prettyPrint (secondChoice . firstChoice)
148 putStrLn "\n Sum of dices probability:"
173 putStrLn "\n Sum of dices probability:"
149− prettyPrint (sumSSM `comp` khatri die die)
174+ prettyPrint (sumSSM . kr die die)
150 putStrLn "\n Conditional dice throw:"
175 putStrLn "\n Conditional dice throw:"
151 prettyPrint conditionalThrows
176 prettyPrint conditionalThrows
152 putStrLn "\n Checking that the last result is indeed a distribution: "
177 putStrLn "\n Checking that the last result is indeed a distribution: "
153− prettyPrint (bang . sumSSM . khatri die die)
178+ prettyPrint (bang . sumSSM . kr die die)
154 putStrLn "\n Probability of grass being wet:"
179 putStrLn "\n Probability of grass being wet:"
155− prettyPrint (grass_wet . state)
180+ prettyPrint (grass_wet (state grass sprinkler rain))
156 putStrLn "\n Probability of rain:"
181 putStrLn "\n Probability of rain:"
157− prettyPrint (rainning . state)
182+ prettyPrint (rainning . state grass sprinkler rain)
158 putStrLn "\n Is the arbitrary state a valid state? (Alcuin Puzzle)"
183 putStrLn "\n Is the arbitrary state a valid state? (Alcuin Puzzle)"
159 print (inv bankStateR)
184 print (inv bankStateR)
app/Spreadsheets.hs → test/Examples/Spreadsheets.hsrenamed+9−20
@@ -1,14 +1,11 @@
1−{-# LANGUAGE DataKinds #-}
2−{-# LANGUAGE GADTs #-}
3−{-# LANGUAGE FlexibleContexts #-}
4{-# LANGUAGE DeriveGeneric #-}
1{-# LANGUAGE DeriveGeneric #-}
5
2
6−module Spreadsheets
3+module Examples.Spreadsheets
7− where
8
4
5+import LAoP.Utils
9import LAoP.Matrix.Type
6import LAoP.Matrix.Type
10−import qualified LAoP.Matrix.Internal as I
11import GHC.Generics
7import GHC.Generics
8+import Prelude hiding (id, (.))
12
9
13data Student = Student1 | Student2 | Student3 | Student4
10data Student = Student1 | Student2 | Student3 | Student4
14 deriving (Eq, Show, Enum, Bounded, Generic)
11 deriving (Eq, Show, Enum, Bounded, Generic)
@@ -38,21 +35,13 @@ xls :: Matrix Float Question One
38 -> Matrix Float Question Student
35 -> Matrix Float Question Student
39 -> Matrix Float Student One
36 -> Matrix Float Student One
40 -> Matrix Float (Either Question Results) (Either One Student)
37 -> Matrix Float (Either Question Results) (Either One Student)
41−xls w m t = junc (split w m) (split zeros r)
38+xls w m t = join (fork w m) (fork zeros r)
42 where
39 where
43− rExam = m `comp` tr w
40+ rExam = m . tr w
44 rTest = tr t
41 rTest = tr t
45− rFinal = rTest `maxPP` rExam
42+ rFinal = rTest `maxPW` rExam
46− r = (rExam `comp` tr exam) + (rTest `comp` tr test) + (rFinal `comp` tr final)
43+ r = (rExam . tr exam) + (rTest . tr test) + (rFinal . tr final)
47
44
48-- | Overloaded, point-wise 'max' function
45-- | Overloaded, point-wise 'max' function
49−maxPP_ :: Ord e => I.Matrix e a b -> I.Matrix e a b -> I.Matrix e a b
46+maxPW :: Ord e => Matrix e a b -> Matrix e a b -> Matrix e a b
50−maxPP_ I.Empty I.Empty = I.Empty
47+maxPW = zipWithM max
51−maxPP_ (I.One a) (I.One b) = I.One (a `max` b)
52−maxPP_ (I.Junc a b) (I.Junc c d) = I.Junc (maxPP_ a c) (maxPP_ b d)
53−maxPP_ (I.Split a b) (I.Split c d) = I.Split (maxPP_ a c) (maxPP_ b d)
54−maxPP_ x@(I.Split _ _) y@(I.Junc _ _) = maxPP_ x (I.abideJS y)
55−maxPP_ x@(I.Junc _ _) y@(I.Split _ _) = maxPP_ (I.abideJS x) y
56−
57−maxPP :: Ord e => Matrix e a b -> Matrix e a b -> Matrix e a b
58−maxPP (M a) (M b) = M (maxPP_ a b)
test/Spec.hs+7−1
@@ -1,2 +1,8 @@
1+module Main (main) where
2+
3+import qualified Examples.Readme as RD
4+
1main :: IO ()
5main :: IO ()
2−main = putStrLn "Test suite not yet implemented"
6+main = do
7+ putStrLn ("Testing if README works" :: String)
8+ RD.exec