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</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Numeric-RootFinding.html">Source</a></li><li><a href="index.html">Contents</a></li><li><a href="doc-index.html">Index</a></li></ul><p class="caption">math-functions-0.2.1.0: Special functions and Chebyshev polynomials</p></div><div id="content"><div id="module-header"><table class="info"><tr><th valign="top">Copyright</th><td>(c) 2011 Bryan O'Sullivan</td></tr><tr><th>License</th><td>BSD3</td></tr><tr><th>Maintainer</th><td>bos@serpentine.com</td></tr><tr><th>Stability</th><td>experimental</td></tr><tr><th>Portability</th><td>portable</td></tr><tr><th>Safe Haskell</th><td>None</td></tr><tr><th>Language</th><td>Haskell2010</td></tr></table><p class="caption">Numeric.RootFinding</p></div><div id="table-of-contents"><p class="caption">Contents</p><ul><li><a href="#g:1">References</a></li></ul></div><div id="description"><p class="caption">Description</p><div class="doc"><p>Haskell functions for finding the roots of real functions of real arguments.</p></div></div><div id="synopsis"><p id="control.syn" class="caption expander" onclick="toggleSection('syn')">Synopsis</p><ul id="section.syn" class="hide" onclick="toggleSection('syn')"><li class="src short"><span class="keyword">data</span> <a href="#t:Root">Root</a> a<ul class="subs"><li>= <a href="#v:NotBracketed">NotBracketed</a></li><li>| <a href="#v:SearchFailed">SearchFailed</a></li><li>| <a href="#v:Root">Root</a> a</li></ul></li><li class="src short"><a href="#v:fromRoot">fromRoot</a> :: a -> <a href="Numeric-RootFinding.html#t:Root">Root</a> a -> a</li><li class="src short"><a href="#v:ridders">ridders</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Double">Double</a> -> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Double">Double</a>, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Double">Double</a>) -> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Double">Double</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Double">Double</a>) -> <a href="Numeric-RootFinding.html#t:Root">Root</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Double">Double</a></li><li class="src short"><a href="#v:newtonRaphson">newtonRaphson</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Double">Double</a> -> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Double">Double</a>, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Double">Double</a>, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Double">Double</a>) -> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Double">Double</a> -> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Double">Double</a>, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Double">Double</a>)) -> <a href="Numeric-RootFinding.html#t:Root">Root</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Double">Double</a></li></ul></div><div id="interface"><h1>Documentation</h1><div class="top"><p class="src"><span class="keyword">data</span> <a id="t:Root" class="def">Root</a> a <a href="src/Numeric-RootFinding.html#Root" class="link">Source</a> <a href="#t:Root" class="selflink">#</a></p><div class="doc"><p>The result of searching for a root of a mathematical function.</p></div><div class="subs constructors"><p class="caption">Constructors</p><table><tr><td class="src"><a id="v:NotBracketed" class="def">NotBracketed</a></td><td class="doc"><p>The function does not have opposite signs when
evaluated at the lower and upper bounds of the search.</p></td></tr><tr><td class="src"><a id="v:SearchFailed" class="def">SearchFailed</a></td><td class="doc"><p>The search failed to converge to within the given
error tolerance after the given number of iterations.</p></td></tr><tr><td class="src"><a id="v:Root" class="def">Root</a> a</td><td class="doc"><p>A root was successfully found.</p></td></tr></table></div><div class="subs instances"><p id="control.i:Root" class="caption collapser" onclick="toggleSection('i:Root')">Instances</p><div id="section.i:Root" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Root:Monad:1" class="instance expander" onclick="toggleSection('i:id:Root:Monad:1')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Control-Monad.html#t:Monad">Monad</a> <a href="Numeric-RootFinding.html#t:Root">Root</a></span> <a href="src/Numeric-RootFinding.html#line-52" class="link">Source</a> <a href="#t:Root" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Root:Monad:1" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:-62--62--61-">(>>=)</a> :: <a href="Numeric-RootFinding.html#t:Root">Root</a> a -> (a -> <a href="Numeric-RootFinding.html#t:Root">Root</a> b) -> <a href="Numeric-RootFinding.html#t:Root">Root</a> b <a href="#v:-62--62--61-" class="selflink">#</a></p><p class="src"><a href="#v:-62--62-">(>>)</a> :: <a href="Numeric-RootFinding.html#t:Root">Root</a> a -> <a href="Numeric-RootFinding.html#t:Root">Root</a> b -> <a href="Numeric-RootFinding.html#t:Root">Root</a> b <a href="#v:-62--62-" class="selflink">#</a></p><p class="src"><a href="#v:return">return</a> :: a -> <a href="Numeric-RootFinding.html#t:Root">Root</a> a <a href="#v:return" class="selflink">#</a></p><p class="src"><a href="#v:fail">fail</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-String.html#t:String">String</a> -> <a href="Numeric-RootFinding.html#t:Root">Root</a> a <a href="#v:fail" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Root:Functor:2" class="instance expander" onclick="toggleSection('i:id:Root:Functor:2')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Functor.html#t:Functor">Functor</a> <a href="Numeric-RootFinding.html#t:Root">Root</a></span> <a href="src/Numeric-RootFinding.html#line-47" class="link">Source</a> <a href="#t:Root" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Root:Functor:2" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:fmap">fmap</a> :: (a -> b) -> <a href="Numeric-RootFinding.html#t:Root">Root</a> a -> <a href="Numeric-RootFinding.html#t:Root">Root</a> b <a href="#v:fmap" class="selflink">#</a></p><p class="src"><a href="#v:-60--36-">(<$)</a> :: a -> <a href="Numeric-RootFinding.html#t:Root">Root</a> b -> <a href="Numeric-RootFinding.html#t:Root">Root</a> a <a href="#v:-60--36-" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Root:Applicative:3" class="instance expander" onclick="toggleSection('i:id:Root:Applicative:3')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Control-Applicative.html#t:Applicative">Applicative</a> <a href="Numeric-RootFinding.html#t:Root">Root</a></span> <a href="src/Numeric-RootFinding.html#line-65" class="link">Source</a> <a href="#t:Root" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Root:Applicative:3" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:pure">pure</a> :: a -> <a href="Numeric-RootFinding.html#t:Root">Root</a> a <a href="#v:pure" class="selflink">#</a></p><p class="src"><a href="#v:-60--42--62-">(<*>)</a> :: <a href="Numeric-RootFinding.html#t:Root">Root</a> (a -> b) -> <a href="Numeric-RootFinding.html#t:Root">Root</a> a -> <a href="Numeric-RootFinding.html#t:Root">Root</a> b <a href="#v:-60--42--62-" class="selflink">#</a></p><p class="src"><a href="#v:-42--62-">(*>)</a> :: <a href="Numeric-RootFinding.html#t:Root">Root</a> a -> <a href="Numeric-RootFinding.html#t:Root">Root</a> b -> <a href="Numeric-RootFinding.html#t:Root">Root</a> b <a href="#v:-42--62-" class="selflink">#</a></p><p class="src"><a href="#v:-60--42-">(<*)</a> :: <a href="Numeric-RootFinding.html#t:Root">Root</a> a -> <a href="Numeric-RootFinding.html#t:Root">Root</a> b -> <a href="Numeric-RootFinding.html#t:Root">Root</a> a <a href="#v:-60--42-" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Root:Alternative:4" class="instance expander" onclick="toggleSection('i:id:Root:Alternative:4')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Control-Applicative.html#t:Alternative">Alternative</a> <a href="Numeric-RootFinding.html#t:Root">Root</a></span> <a href="src/Numeric-RootFinding.html#line-69" class="link">Source</a> <a href="#t:Root" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Root:Alternative:4" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:empty">empty</a> :: <a href="Numeric-RootFinding.html#t:Root">Root</a> a <a href="#v:empty" class="selflink">#</a></p><p class="src"><a href="#v:-60--124--62-">(<|>)</a> :: <a href="Numeric-RootFinding.html#t:Root">Root</a> a -> <a href="Numeric-RootFinding.html#t:Root">Root</a> a -> <a href="Numeric-RootFinding.html#t:Root">Root</a> a <a href="#v:-60--124--62-" class="selflink">#</a></p><p class="src"><a href="#v:some">some</a> :: <a href="Numeric-RootFinding.html#t:Root">Root</a> a -> <a href="Numeric-RootFinding.html#t:Root">Root</a> [a] <a href="#v:some" class="selflink">#</a></p><p class="src"><a href="#v:many">many</a> :: <a href="Numeric-RootFinding.html#t:Root">Root</a> a -> <a href="Numeric-RootFinding.html#t:Root">Root</a> [a] <a href="#v:many" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Root:MonadPlus:5" class="instance expander" onclick="toggleSection('i:id:Root:MonadPlus:5')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Control-Monad.html#t:MonadPlus">MonadPlus</a> <a href="Numeric-RootFinding.html#t:Root">Root</a></span> <a href="src/Numeric-RootFinding.html#line-59" class="link">Source</a> <a href="#t:Root" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Root:MonadPlus:5" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:mzero">mzero</a> :: <a href="Numeric-RootFinding.html#t:Root">Root</a> a <a href="#v:mzero" class="selflink">#</a></p><p class="src"><a href="#v:mplus">mplus</a> :: <a href="Numeric-RootFinding.html#t:Root">Root</a> a -> <a href="Numeric-RootFinding.html#t:Root">Root</a> a -> <a href="Numeric-RootFinding.html#t:Root">Root</a> a <a href="#v:mplus" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Root:Eq:6" class="instance expander" onclick="toggleSection('i:id:Root:Eq:6')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> a => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Eq.html#t:Eq">Eq</a> (<a href="Numeric-RootFinding.html#t:Root">Root</a> a)</span> <a href="src/Numeric-RootFinding.html#line-40" class="link">Source</a> <a href="#t:Root" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Root:Eq:6" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:-61--61-">(==)</a> :: <a href="Numeric-RootFinding.html#t:Root">Root</a> a -> <a href="Numeric-RootFinding.html#t:Root">Root</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-61--61-" class="selflink">#</a></p><p class="src"><a href="#v:-47--61-">(/=)</a> :: <a href="Numeric-RootFinding.html#t:Root">Root</a> a -> <a href="Numeric-RootFinding.html#t:Root">Root</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Bool.html#t:Bool">Bool</a> <a href="#v:-47--61-" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Root:Data:7" class="instance expander" onclick="toggleSection('i:id:Root:Data:7')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Data.html#t:Data">Data</a> a => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Data.html#t:Data">Data</a> (<a href="Numeric-RootFinding.html#t:Root">Root</a> a)</span> <a href="src/Numeric-RootFinding.html#line-40" class="link">Source</a> <a href="#t:Root" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Root:Data:7" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:gfoldl">gfoldl</a> :: (<span class="keyword">forall</span> d b. <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Data.html#t:Data">Data</a> d => c (d -> b) -> d -> c b) -> (<span class="keyword">forall</span> g. g -> c g) -> <a href="Numeric-RootFinding.html#t:Root">Root</a> a -> c (<a href="Numeric-RootFinding.html#t:Root">Root</a> a) <a href="#v:gfoldl" class="selflink">#</a></p><p class="src"><a href="#v:gunfold">gunfold</a> :: (<span class="keyword">forall</span> b r. <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Data.html#t:Data">Data</a> b => c (b -> r) -> c r) -> (<span class="keyword">forall</span> r. r -> c r) -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Data.html#t:Constr">Constr</a> -> c (<a href="Numeric-RootFinding.html#t:Root">Root</a> a) <a href="#v:gunfold" class="selflink">#</a></p><p class="src"><a href="#v:toConstr">toConstr</a> :: <a href="Numeric-RootFinding.html#t:Root">Root</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Data.html#t:Constr">Constr</a> <a href="#v:toConstr" class="selflink">#</a></p><p class="src"><a href="#v:dataTypeOf">dataTypeOf</a> :: <a href="Numeric-RootFinding.html#t:Root">Root</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Data.html#t:DataType">DataType</a> <a href="#v:dataTypeOf" class="selflink">#</a></p><p class="src"><a href="#v:dataCast1">dataCast1</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Typeable-Internal.html#t:Typeable">Typeable</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Kind.html#t:-42-">*</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Kind.html#t:-42-">*</a>) t => (<span class="keyword">forall</span> d. <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Data.html#t:Data">Data</a> d => c (t d)) -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Maybe.html#t:Maybe">Maybe</a> (c (<a href="Numeric-RootFinding.html#t:Root">Root</a> a)) <a href="#v:dataCast1" class="selflink">#</a></p><p class="src"><a href="#v:dataCast2">dataCast2</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Typeable-Internal.html#t:Typeable">Typeable</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Kind.html#t:-42-">*</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Kind.html#t:-42-">*</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Kind.html#t:-42-">*</a>) t => (<span class="keyword">forall</span> d e. (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Data.html#t:Data">Data</a> d, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Data.html#t:Data">Data</a> e) => c (t d e)) -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Maybe.html#t:Maybe">Maybe</a> (c (<a href="Numeric-RootFinding.html#t:Root">Root</a> a)) <a href="#v:dataCast2" class="selflink">#</a></p><p class="src"><a href="#v:gmapT">gmapT</a> :: (<span class="keyword">forall</span> b. <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Data.html#t:Data">Data</a> b => b -> b) -> <a href="Numeric-RootFinding.html#t:Root">Root</a> a -> <a href="Numeric-RootFinding.html#t:Root">Root</a> a <a href="#v:gmapT" class="selflink">#</a></p><p class="src"><a href="#v:gmapQl">gmapQl</a> :: (r -> r' -> r) -> r -> (<span class="keyword">forall</span> d. <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Data.html#t:Data">Data</a> d => d -> r') -> <a href="Numeric-RootFinding.html#t:Root">Root</a> a -> r <a href="#v:gmapQl" class="selflink">#</a></p><p class="src"><a href="#v:gmapQr">gmapQr</a> :: (r' -> r -> r) -> r -> (<span class="keyword">forall</span> d. <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Data.html#t:Data">Data</a> d => d -> r') -> <a href="Numeric-RootFinding.html#t:Root">Root</a> a -> r <a href="#v:gmapQr" class="selflink">#</a></p><p class="src"><a href="#v:gmapQ">gmapQ</a> :: (<span class="keyword">forall</span> d. <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Data.html#t:Data">Data</a> d => d -> u) -> <a href="Numeric-RootFinding.html#t:Root">Root</a> a -> [u] <a href="#v:gmapQ" class="selflink">#</a></p><p class="src"><a href="#v:gmapQi">gmapQi</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -> (<span class="keyword">forall</span> d. <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Data.html#t:Data">Data</a> d => d -> u) -> <a href="Numeric-RootFinding.html#t:Root">Root</a> a -> u <a href="#v:gmapQi" class="selflink">#</a></p><p class="src"><a href="#v:gmapM">gmapM</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Control-Monad.html#t:Monad">Monad</a> m => (<span class="keyword">forall</span> d. <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Data.html#t:Data">Data</a> d => d -> m d) -> <a href="Numeric-RootFinding.html#t:Root">Root</a> a -> m (<a href="Numeric-RootFinding.html#t:Root">Root</a> a) <a href="#v:gmapM" class="selflink">#</a></p><p class="src"><a href="#v:gmapMp">gmapMp</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Control-Monad.html#t:MonadPlus">MonadPlus</a> m => (<span class="keyword">forall</span> d. <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Data.html#t:Data">Data</a> d => d -> m d) -> <a href="Numeric-RootFinding.html#t:Root">Root</a> a -> m (<a href="Numeric-RootFinding.html#t:Root">Root</a> a) <a href="#v:gmapMp" class="selflink">#</a></p><p class="src"><a href="#v:gmapMo">gmapMo</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Control-Monad.html#t:MonadPlus">MonadPlus</a> m => (<span class="keyword">forall</span> d. <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Data.html#t:Data">Data</a> d => d -> m d) -> <a href="Numeric-RootFinding.html#t:Root">Root</a> a -> m (<a href="Numeric-RootFinding.html#t:Root">Root</a> a) <a href="#v:gmapMo" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Root:Read:8" class="instance expander" onclick="toggleSection('i:id:Root:Read:8')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Text-Read.html#t:Read">Read</a> a => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Text-Read.html#t:Read">Read</a> (<a href="Numeric-RootFinding.html#t:Root">Root</a> a)</span> <a href="src/Numeric-RootFinding.html#line-40" class="link">Source</a> <a href="#t:Root" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Root:Read:8" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:readsPrec">readsPrec</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Text-ParserCombinators-ReadP.html#t:ReadS">ReadS</a> (<a href="Numeric-RootFinding.html#t:Root">Root</a> a) <a href="#v:readsPrec" class="selflink">#</a></p><p class="src"><a href="#v:readList">readList</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Text-ParserCombinators-ReadP.html#t:ReadS">ReadS</a> [<a href="Numeric-RootFinding.html#t:Root">Root</a> a] <a href="#v:readList" class="selflink">#</a></p><p class="src"><a href="#v:readPrec">readPrec</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Text-ParserCombinators-ReadPrec.html#t:ReadPrec">ReadPrec</a> (<a href="Numeric-RootFinding.html#t:Root">Root</a> a) <a href="#v:readPrec" class="selflink">#</a></p><p class="src"><a href="#v:readListPrec">readListPrec</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Text-ParserCombinators-ReadPrec.html#t:ReadPrec">ReadPrec</a> [<a href="Numeric-RootFinding.html#t:Root">Root</a> a] <a href="#v:readListPrec" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Root:Show:9" class="instance expander" onclick="toggleSection('i:id:Root:Show:9')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Text-Show.html#t:Show">Show</a> a => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Text-Show.html#t:Show">Show</a> (<a href="Numeric-RootFinding.html#t:Root">Root</a> a)</span> <a href="src/Numeric-RootFinding.html#line-40" class="link">Source</a> <a href="#t:Root" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Root:Show:9" class="inst-details hide"><div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:showsPrec">showsPrec</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Int.html#t:Int">Int</a> -> <a href="Numeric-RootFinding.html#t:Root">Root</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Text-Show.html#t:ShowS">ShowS</a> <a href="#v:showsPrec" class="selflink">#</a></p><p class="src"><a href="#v:show">show</a> :: <a href="Numeric-RootFinding.html#t:Root">Root</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-String.html#t:String">String</a> <a href="#v:show" class="selflink">#</a></p><p class="src"><a href="#v:showList">showList</a> :: [<a href="Numeric-RootFinding.html#t:Root">Root</a> a] -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Text-Show.html#t:ShowS">ShowS</a> <a href="#v:showList" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Root:Generic:10" class="instance expander" onclick="toggleSection('i:id:Root:Generic:10')"></span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/GHC-Generics.html#t:Generic">Generic</a> (<a href="Numeric-RootFinding.html#t:Root">Root</a> a)</span> <a href="src/Numeric-RootFinding.html#line-42" class="link">Source</a> <a href="#t:Root" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Root:Generic:10" class="inst-details hide"><div class="subs associated-types"><p class="caption">Associated Types</p><p class="src"><span class="keyword">type</span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/GHC-Generics.html#t:Rep">Rep</a> (<a href="Numeric-RootFinding.html#t:Root">Root</a> a) :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Kind.html#t:-42-">*</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Kind.html#t:-42-">*</a> <a href="#t:Rep" class="selflink">#</a></p></div> <div class="subs methods"><p class="caption">Methods</p><p class="src"><a href="#v:from">from</a> :: <a href="Numeric-RootFinding.html#t:Root">Root</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/GHC-Generics.html#t:Rep">Rep</a> (<a href="Numeric-RootFinding.html#t:Root">Root</a> a) x <a href="#v:from" class="selflink">#</a></p><p class="src"><a href="#v:to">to</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/GHC-Generics.html#t:Rep">Rep</a> (<a href="Numeric-RootFinding.html#t:Root">Root</a> a) x -> <a href="Numeric-RootFinding.html#t:Root">Root</a> a <a href="#v:to" class="selflink">#</a></p></div></div></td></tr><tr><td class="src clearfix"><span class="inst-left"><span id="control.i:id:Root:Rep:11" class="instance expander" onclick="toggleSection('i:id:Root:Rep:11')"></span> <span class="keyword">type</span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/GHC-Generics.html#t:Rep">Rep</a> (<a href="Numeric-RootFinding.html#t:Root">Root</a> a)</span> <a href="src/Numeric-RootFinding.html#line-32" class="link">Source</a> <a href="#t:Root" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div id="section.i:id:Root:Rep:11" class="inst-details hide"><div class="src"><span class="keyword">type</span> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/GHC-Generics.html#t:Rep">Rep</a> (<a href="Numeric-RootFinding.html#t:Root">Root</a> a) = <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/GHC-Generics.html#t:D1">D1</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/GHC-Generics.html#v:MetaData">MetaData</a> "Root" "Numeric.RootFinding" "math-functions-0.2.1.0-KPr6PZcLbtiGnQNnW2g0oV" <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Bool.html#v:False">False</a>) (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/GHC-Generics.html#t::-43-:">(:+:)</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/GHC-Generics.html#t:C1">C1</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/GHC-Generics.html#v:MetaCons">MetaCons</a> "NotBracketed" <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/GHC-Generics.html#v:PrefixI">PrefixI</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Bool.html#v:False">False</a>) <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/GHC-Generics.html#t:U1">U1</a>) (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/GHC-Generics.html#t::-43-:">(:+:)</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/GHC-Generics.html#t:C1">C1</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/GHC-Generics.html#v:MetaCons">MetaCons</a> "SearchFailed" <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/GHC-Generics.html#v:PrefixI">PrefixI</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Bool.html#v:False">False</a>) <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/GHC-Generics.html#t:U1">U1</a>) (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/GHC-Generics.html#t:C1">C1</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/GHC-Generics.html#v:MetaCons">MetaCons</a> "Root" <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/GHC-Generics.html#v:PrefixI">PrefixI</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Bool.html#v:False">False</a>) (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/GHC-Generics.html#t:S1">S1</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/GHC-Generics.html#v:MetaSel">MetaSel</a> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Data-Maybe.html#v:Nothing">Nothing</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/GHC-TypeLits.html#t:Symbol">Symbol</a>) <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/GHC-Generics.html#v:NoSourceUnpackedness">NoSourceUnpackedness</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/GHC-Generics.html#v:NoSourceStrictness">NoSourceStrictness</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/GHC-Generics.html#v:DecidedLazy">DecidedLazy</a>) (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/GHC-Generics.html#t:Rec0">Rec0</a> a)))))</div></div></td></tr></table></div></div></div><div class="top"><p class="src"><a id="v:fromRoot" class="def">fromRoot</a> <a href="src/Numeric-RootFinding.html#fromRoot" class="link">Source</a> <a href="#v:fromRoot" class="selflink">#</a></p><div class="subs arguments"><p class="caption">Arguments</p><table><tr><td class="src">:: a</td><td class="doc"><p>Default value.</p></td></tr><tr><td class="src">-> <a href="Numeric-RootFinding.html#t:Root">Root</a> a</td><td class="doc"><p>Result of search for a root.</p></td></tr><tr><td class="src">-> a</td><td class="doc empty"> </td></tr></table></div><div class="doc"><p>Returns either the result of a search for a root, or the default
value if the search failed.</p></div></div><div class="top"><p class="src"><a id="v:ridders" class="def">ridders</a> <a href="src/Numeric-RootFinding.html#ridders" class="link">Source</a> <a href="#v:ridders" class="selflink">#</a></p><div class="subs arguments"><p class="caption">Arguments</p><table><tr><td class="src">:: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Double">Double</a></td><td class="doc"><p>Absolute error tolerance.</p></td></tr><tr><td class="src">-> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Double">Double</a>, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Double">Double</a>)</td><td class="doc"><p>Lower and upper bounds for the search.</p></td></tr><tr><td class="src">-> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Double">Double</a> -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Double">Double</a>)</td><td class="doc"><p>Function to find the roots of.</p></td></tr><tr><td class="src">-> <a href="Numeric-RootFinding.html#t:Root">Root</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Double">Double</a></td><td class="doc empty"> </td></tr></table></div><div class="doc"><p>Use the method of Ridders to compute a root of a function.</p><p>The function must have opposite signs when evaluated at the lower
and upper bounds of the search (i.e. the root must be bracketed).</p></div></div><div class="top"><p class="src"><a id="v:newtonRaphson" class="def">newtonRaphson</a> <a href="src/Numeric-RootFinding.html#newtonRaphson" class="link">Source</a> <a href="#v:newtonRaphson" class="selflink">#</a></p><div class="subs arguments"><p class="caption">Arguments</p><table><tr><td class="src">:: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Double">Double</a></td><td class="doc"><p>Required precision</p></td></tr><tr><td class="src">-> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Double">Double</a>, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Double">Double</a>, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Double">Double</a>)</td><td class="doc"><p>(lower bound, initial guess, upper bound). Iterations will no
go outside of the interval</p></td></tr><tr><td class="src">-> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Double">Double</a> -> (<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Double">Double</a>, <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Double">Double</a>))</td><td class="doc"><p>Function to finds roots. It returns pair of function value and
its derivative</p></td></tr><tr><td class="src">-> <a href="Numeric-RootFinding.html#t:Root">Root</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.9.1.0/Prelude.html#t:Double">Double</a></td><td class="doc empty"> </td></tr></table></div><div class="doc"><p>Solve equation using Newton-Raphson iterations.</p><p>This method require both initial guess and bounds for root. If
Newton step takes us out of bounds on root function reverts to
bisection.</p></div></div><h1 id="g:1">References</h1><div class="doc"><ul><li>Ridders, C.F.J. (1979) A new algorithm for computing a single
root of a real continuous function.
<em>IEEE Transactions on Circuits and Systems</em> 26:979–980.</li></ul></div></div></div><div id="footer"><p>Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.17.3</p></div></body></html>
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