From 898622d362b9dad42296af6298e20bc9f8410b63 Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Sun, 9 Sep 2012 18:20:56 -0400 Subject: [PATCH 1/1] Add the numerical-analysis Haskell library. --- Setup.hs | 2 + doc/LICENSE | 619 +++++++++++++++++++++++++++++++++++++++ makefile | 49 ++++ numerical-analysis.cabal | 74 +++++ src/Roots.hs | 97 ++++++ test/Doctests.hs | 7 + 6 files changed, 848 insertions(+) create mode 100644 Setup.hs create mode 100644 doc/LICENSE create mode 100644 makefile create mode 100644 numerical-analysis.cabal create mode 100644 src/Roots.hs create mode 100644 test/Doctests.hs diff --git a/Setup.hs b/Setup.hs new file mode 100644 index 0000000..9a994af --- /dev/null +++ b/Setup.hs @@ -0,0 +1,2 @@ +import Distribution.Simple +main = defaultMain diff --git a/doc/LICENSE b/doc/LICENSE new file mode 100644 index 0000000..bc08fe2 --- /dev/null +++ b/doc/LICENSE @@ -0,0 +1,619 @@ + GNU GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The GNU General Public License is a free, copyleft license for +software and other kinds of works. + + The licenses for most software and other practical works are designed +to take away your freedom to share and change the works. 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Interpretation of Sections 15 and 16. + + If the disclaimer of warranty and limitation of liability provided +above cannot be given local legal effect according to their terms, +reviewing courts shall apply local law that most closely approximates +an absolute waiver of all civil liability in connection with the +Program, unless a warranty or assumption of liability accompanies a +copy of the Program in return for a fee. diff --git a/makefile b/makefile new file mode 100644 index 0000000..8b9c250 --- /dev/null +++ b/makefile @@ -0,0 +1,49 @@ +BIN = dist/build/numerical-analysis/numerical-analysis +DOCTESTS_BIN = dist/build/doctests/doctests + +.PHONY : test publish_doc doc dist hlint + +$(BIN): src/*.hs + runghc Setup.hs clean + runghc Setup.hs configure --user --flags=${FLAGS} + runghc Setup.hs build + +$(DOCTESTS_BIN): src/*.hs test/Doctests.hs + runghc Setup.hs configure --user --flags=${FLAGS} --enable-tests + runghc Setup.hs build + + +profile: src/*.hs + runghc Setup.hs configure --user --enable-executable-profiling + runghc Setup.hs build + +hpc: src/*.hs + FLAGS="hpc" make + +clean: + runghc Setup.hs clean + rm -f dist/ + rm -f *.prof + rm -rf .hpc + + +test: $(BIN) $(DOCTESTS_BIN) + runghc Setup.hs test + +dist: + runghc Setup.hs configure + runghc Setup.hs sdist + +# Neither 'haddock' nor 'hscolour' seem to work properly. +doc: src/*.hs + runghc Setup.hs configure --user --flags=${FLAGS} + runghc Setup.hs hscolour --executables + runghc Setup.hs haddock --internal \ + --executables \ + --hyperlink-source + +hlint: + hlint --ignore="Use camelCase" \ + --ignore="Redundant bracket" \ + --color \ + src diff --git a/numerical-analysis.cabal b/numerical-analysis.cabal new file mode 100644 index 0000000..708644f --- /dev/null +++ b/numerical-analysis.cabal @@ -0,0 +1,74 @@ +name: numerical-analysis +version: 0.0.0 +cabal-version: >= 1.8 +author: Michael Orlitzky +maintainer: Michael Orlitzky +license: GPL-3 +license-file: doc/LICENSE +bug-reports: mailto:michael@orlitzky.com +build-type: Simple +category: Text +synopsis: + A library of numerical analysis functions for UMBC's MATH620. +description: + Haskell implementations of algorithms from UMBC's Numerical + Analysis course, MATH620. +data-files: makefile + +library + exposed-modules: Roots + + build-depends: + base == 4.5.*, + HUnit == 1.2.*, + QuickCheck == 2.*, + test-framework == 0.6.*, + test-framework-hunit == 0.2.*, + test-framework-quickcheck2 == 0.2.* + + hs-source-dirs: + src/ + + ghc-options: + -Wall + -fwarn-hi-shadowing + -fwarn-missing-signatures + -fwarn-name-shadowing + -fwarn-orphans + -fwarn-type-defaults + -fwarn-tabs + -fwarn-incomplete-record-updates + -fwarn-monomorphism-restriction + -fwarn-unused-do-bind + -rtsopts + -threaded + -O2 + -optc-O3 + -optc-march=native + + +test-suite doctests + type: exitcode-stdio-1.0 + hs-source-dirs: test + main-is: Doctests.hs + build-depends: + base == 4.5.*, + -- Additional test dependencies. + doctest == 0.7.* + + -- It's not entirely clear to me why I have to reproduce all of this. + ghc-options: + -rtsopts + -threaded + -funbox-strict-fields + -fexcess-precision + -fno-spec-constr-count + -O2 + -optc-O3 + -optc-march=native + + +source-repository head + type: git + location: http://git.michael.orlitzky.com/umbc/math620.git + branch: master diff --git a/src/Roots.hs b/src/Roots.hs new file mode 100644 index 0000000..a8c3c76 --- /dev/null +++ b/src/Roots.hs @@ -0,0 +1,97 @@ +-- | The Roots module contains root-finding algorithms. That is, +-- procedures to (numerically) find solutions to the equation, +-- +-- > f(x) = 0 +-- +-- where f is assumed to be continuous on the interval of interest. +-- + +module Roots +where + + +-- | Does the (continuous) function @f@ have a root on the interval +-- [a,b]? If f(a) <] 0 and f(b) ]> 0, we know that there's a root in +-- [a,b] by the intermediate value theorem. Likewise when f(a) >= 0 +-- and f(b) <= 0. +-- +-- Examples: +-- +-- >>> let f x = x**3 +-- >>> has_root f (-1) 1 Nothing +-- True +-- +-- This fails if we don't specify an @epsilon@, because cos(-2) == +-- cos(2) doesn't imply that there's a root on [-2,2]. +-- +-- >>> has_root cos (-2) 2 Nothing +-- False +-- >>> has_root cos (-2) 2 (Just 0.001) +-- True +-- +has_root :: (Fractional a, Ord a, Ord b, Num b) + => (a -> b) -- ^ The function @f@ + -> a -- ^ The \"left\" endpoint, @a@ + -> a -- ^ The \"right\" endpoint, @b@ + -> Maybe a -- ^ The size of the smallest subinterval + -- we'll examine, @epsilon@ + -> Bool +has_root f a b epsilon = + if not ((signum (f a)) * (signum (f b)) == 1) then + -- We don't care about epsilon here, there's definitely a root! + True + else + if (b - a) <= epsilon' then + -- Give up, return false. + False + else + -- If either [a,c] or [c,b] have roots, we do too. + (has_root f a c (Just epsilon')) || (has_root f c b (Just epsilon')) + where + -- If the size of the smallest subinterval is not specified, + -- assume we just want to check once on all of [a,b]. + epsilon' = case epsilon of + Nothing -> (b-a) + Just eps -> eps + c = (a + b)/2 + + + +-- | We are given a function @f@ and an interval [a,b]. The bisection +-- method checks finds a root by splitting [a,b] in half repeatedly. +-- +-- If one is found within some prescribed tolerance @epsilon@, it is +-- returned. Otherwise, the interval [a,b] is split into two +-- subintervals [a,c] and [c,b] of equal length which are then both +-- checked via the same process. +-- +-- Returns 'Just' the value x for which f(x) == 0 if one is found, +-- or Nothing if one of the preconditions is violated. +-- +-- Examples: +-- +-- >>> bisect cos 1 2 0.001 +-- Just 1.5712890625 +-- +-- >>> bisect sin (-1) 1 0.001 +-- Just 0.0 +-- +bisect :: (Fractional a, Ord a, Num b, Ord b) + => (a -> b) -- ^ The function @f@ whose root we seek + -> a -- ^ The \"left\" endpoint of the interval, @a@ + -> a -- ^ The \"right\" endpoint of the interval, @b@ + -> a -- ^ The tolerance, @epsilon@ + -> Maybe a +bisect f a b epsilon + -- We pass @epsilon@ to the 'has_root' function because if we want a + -- result within epsilon of the true root, we need to know that + -- there *is* a root within an interval of length epsilon. + | not (has_root f a b (Just epsilon)) = Nothing + | f a == 0 = Just a + | f b == 0 = Just b + | (b - c) < epsilon = Just c + | otherwise = + if (has_root f a c (Just epsilon)) then bisect f a c epsilon + else bisect f c b epsilon + where + c = (a + b) / 2 diff --git a/test/Doctests.hs b/test/Doctests.hs new file mode 100644 index 0000000..f9bacc5 --- /dev/null +++ b/test/Doctests.hs @@ -0,0 +1,7 @@ +module Main +where + +import Test.DocTest + +main :: IO () +main = doctest ["--optghc=-isrc", "src/Root.hs"] -- 2.44.2