AERN-Real 0.9.3.1 → 0.9.4

raw patch · 6 files changed

+169/−48 lines, 6 filesPVP: major bump suggested

API removals or changes: PVP suggests a major version bump

API changes (from Hackage documentation)

Files

• AERN-Real.cabal +3/−2
• ChangeLog +23/−0
• HISTORY +0/−19
• src/Data/Number/ER/BasicTypes.hs +0/−7
• src/Data/Number/ER/Real/Arithmetic/LinearSolver.hs +118/−0
• src/Data/Number/ER/Real/Base/Float.hs +25/−20

@@ -1,5 +1,5 @@ Name:           AERN-Real-Version:        0.9.3.1+Version:        0.9.4 Cabal-Version:  >= 1.2 Build-Type:     Simple License:        BSD3@@ -47,7 +47,7 @@     and simple numerical integration.  Extra-source-files:-    HISTORY tests/Test1.hs+    ChangeLog tests/Test1.hs  Flag containers-in-base     Default: False@@ -71,6 +71,7 @@     Data.Number.ER.Real.Base,     Data.Number.ER.Real.Arithmetic.Elementary,     Data.Number.ER.Real.Arithmetic.Integration,+    Data.Number.ER.Real.Arithmetic.LinearSolver,     Data.Number.ER.Real.Arithmetic.Taylor,     Data.Number.ER.Real.Arithmetic.Newton,     Data.Number.ER.Real.Approx.Sequence,

@@ -0,0 +1,23 @@+0.9.4:+    * fixed buggy formatting of floating point numbers+    * added a simple although inefficient linear solver++0.9.3.1: 12 July 2008+    * fixed email in cabal maintainer field++0.9.3: 12 July 2008+    * Fixed Data.Number.ER.Real so that it is usable as a single import+      for the library and its documentation links are more useful.+    * Added a module with some tests, which can also serve as an example.+    * Improved formatting of floating point numbers.++0.9.2: 11 July 2008+    * declared dependency on haskell98 in cabal file (thanks to Don Stewart)++0.9.1: 11 July 2008+    * fixed licence specification within modules++0.9.0: 11 July 2008+    * initial release of AERN-Real+    +    

@@ -1,19 +0,0 @@-0.9.3.1: 12 July 2008-    * fixed email in cabal maintainer field--0.9.3: 12 July 2008-    * Fixed Data.Number.ER.Real so that it is usable as a single import-      for the library and its documentation links are more useful.-    * Added a module with some tests, which can also serve as an example.-    * Improved formatting of floating point numbers.--0.9.2: 11 July 2008-    * declared dependency on haskell98 in cabal file (thanks to Don Stewart)--0.9.1: 11 July 2008-    * fixed licence specification within modules--0.9.0: 11 July 2008-    * initial release of AERN-Real-    -    

@@ -82,11 +82,4 @@     A many-dimensional point or interval. -} type Box ira = Map.Map VarID ira--{-| using 'defaultVar' -}-unaryDom :: ira -> Box ira-unaryDom r = Map.singleton defaultVar r--noinfoDom :: Box ira-noinfoDom = Map.empty  

@@ -0,0 +1,118 @@+{-|+    Module      :  Data.Number.ER.Real.LinearSolver+    Description :  arbitrary precision piece-wise something function enclosures+    Copyright   :  (c) Jan Duracz, Michal Konecny+    License     :  BSD3++    Maintainer  :  mik@konecny.aow.cz+    Stability   :  experimental+    Portability :  portable++    A simple validated solver for systems of linear equations with+    interval coefficients.  It uses a naive splitting approach and is+    therefore very slow.+-}+module Data.Number.ER.Real.Arithmetic.LinearSolver +(+    linearSolver+)+where++import qualified Data.Number.ER.Real.Approx as RA +import Data.Number.ER.BasicTypes++import Data.List+import Data.Maybe+import qualified Data.Map as Map++{-+import Data.Number.ER.Real.DefaultRepr ++eq1 :: (Box IRA, IRA)+eq1 = (mkBox [1,2,1], 2)+eq2 = (mkBox [2,4,2], 4)+eq3 = (mkBox [2,4,4], 5)+eqs = [eq1,eq2,eq3]++box = mkBox $ replicate 3 $ (-1)RA.\/1  +x1 = (-13/16)RA.\/(-3/4) :: IRA+x2 = (5/16)RA.\/(3/8) :: IRA+tol = 2^^(-20) :: IRA++mkBox :: [IRA] -> Box IRA+mkBox iras = Map.fromList $ zip [1..] iras+-}++linearSolver ::+    (RA.ERIntApprox ira) =>+    [(Map.Map VarID ira, ira)] +        {-^ the equations; +            each equation has coefficients of linear terms +              + constant term -} ->+    Box ira {-^ the domain of the variables -} ->+    ira {-^ an upper bound on the size of an acceptable solution box -} ->+    Maybe (Box ira) +        {-^ +            A box containing at least one solution within the domain; +            Nothing if there is no solution. +        -}+linearSolver eqns domBox tolerance =+    linearSolver' eqns [domBox] tolerance+    +linearSolver' eqns [] tolerance = +    Nothing+linearSolver' eqns (b:bs) tolerance+    | not $ evalEqns b eqns = -- no solutions in the box+        linearSolver' eqns bs tolerance+    | width (b Map.! (widestVar b)) < tolerance = +        Just b+    | otherwise = +        linearSolver' eqns (splitBox b ++ bs) tolerance               ++evalEqns box eqns =+    and $ map (evalEqn box) eqns+            +{-|+    returns true iff there exists a solution to the equation in the box+-}+evalEqn box (expr,cons) = +    cons `RA.refines` (evalExpr expr box)+    where+    evalExpr expr box = Map.fold (+) 0 $ Map.unionWith (*) expr box++{-|+    returns the list of (two) boxes resulting from splitting the widest edge +    of the box in half+-}+splitBox box =+    [Map.insert k (iLg RA.\/ iMg) box, Map.insert k (iMg RA.\/ iRg) box]+    where+    iMg = (iLg+iRg)/2+    iLg = incrementGranularity iL+    iRg = incrementGranularity iR+    (iL,iR) = RA.bounds i+    i = box Map.! k+    k = widestVar box+    incrementGranularity x =+        RA.setMinGranularity (RA.getGranularity x + 1) x++widestVar box =+    fst $ maxm (head widthMap) $ tail widthMap+    where+    widthMap = +        Map.assocs $ Map.map width box+    maxm m [] = m+    maxm m (x:xs) = +        if mW < xW then +            maxm x xs +        else +            maxm m xs+        where+        mW = snd m+        xW = snd x++width i =+    snd $ RA.bounds (iR-iL)+    where+    (iL,iR) = RA.bounds i+

@@ -213,41 +213,46 @@     maybeGran gr         | showGran = "{g=" ++ show gr ++ "}"         | otherwise = ""+    showPM Plus = ""+    showPM Minus = "-"     showERF (ERFloatNaN gr) = "NaN" ++ (maybeGran gr)  -    showERF (ERFloatZero gr pm) = show pm ++ "0" ++ (maybeGran gr)-    showERF (ERFloatInfty gr pm) = show pm ++ "oo" ++ (maybeGran gr)+    showERF (ERFloatZero gr pm) = showPM pm ++ "0.0" ++ (maybeGran gr)+    showERF (ERFloatInfty gr pm) = showPM pm ++ "oo" ++ (maybeGran gr)     showERF f@(ERFloat gr s m e) =         decimal ++ (maybeGran gr) ++ maybeComps         where         maybeComps             | showComponents = "{val="++ show (s,m,e) ++ "}"             | otherwise = ""-        decimal = -            (case s of Plus -> ""; Minus -> "-")+        decimal =+            showPM s             ++ show digit1 ++ "." ++ (concat $ map show $ take numDigits digits)             ++ (if dexp == 0 then "" else "e" ++ show dexp)-        dexp = dexpBound - zerosCount-        digit1 : digits =-            drop zerosCount preDigits+        (dexp, digit1 : digits) +            | noLeadingZerosDexp == -1 =+                (0, 0 : noLeadingZeroDigits)+            | otherwise =+                (noLeadingZerosDexp, noLeadingZeroDigits)+        noLeadingZerosDexp = dexpBound - zerosCount+        (zerosCount, noLeadingZeroDigits) = +            stripCountZeros 0 preDigits+        stripCountZeros prevZeros ds@(d : dsRest) +            | d == 0 = stripCountZeros (prevZeros + 1) dsRest+            | otherwise = (prevZeros, ds)         dexpBound -- upper bound of dexp: f/10^dexpBound < 1-            | e > 0 = intLog 10 (2^e)-            | e <= 0 = 2 - (intLog 10 (2^(-e)))-        (zerosCount, preDigits) =-            getDigits 0 $ (abs $ setERFloatGranularity gran f) / (ten ^^ dexpBound)+            | e >= 0 = intLog 10 (2^e)+            | e < 0 = 2 - (intLog 10 (2^(-e)))+        preDigits =+            getDigits $ (abs $ setERFloatGranularity gran f) / (ten ^^ dexpBound)         ten = setERFloatGranularity gran 10         gran = 10 + (max (4 * numDigits) gr)-        getDigits prevZeros ff -            | digit > 0 = (prevZeros, digit : digits)-            | zerosCount == 1 = (0, (digit : digits))-            | otherwise = (zerosCount, digit : digits)+        getDigits ff =+            digit : digits             where             digit :: Integer             digit = truncate ff-            (zerosCount, digits) =-                getDigits zerosNow ((ff - (fromInteger digit)) * ten)-            zerosNow-                | digit == 0 = prevZeros + 1-                | otherwise = 0+            digits =+                getDigits ((ff - (fromInteger digit)) * ten)               {-