<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> <html> <head> <!-- Generated by HsColour, http://www.cs.york.ac.uk/fp/darcs/hscolour/ --> <title>Data/Colour/Matrix.hs</title> <link type='text/css' rel='stylesheet' href='hscolour.css' /> </head> <body> <pre><a name="line-1"></a><span class='hs-comment'>{- <a name="line-2"></a>Copyright (c) 2008 <a name="line-3"></a>Russell O'Connor <a name="line-4"></a> <a name="line-5"></a>Permission is hereby granted, free of charge, to any person obtaining a copy <a name="line-6"></a>of this software and associated documentation files (the "Software"), to deal <a name="line-7"></a>in the Software without restriction, including without limitation the rights <a name="line-8"></a>to use, copy, modify, merge, publish, distribute, sublicense, and/or sell <a name="line-9"></a>copies of the Software, and to permit persons to whom the Software is <a name="line-10"></a>furnished to do so, subject to the following conditions: <a name="line-11"></a> <a name="line-12"></a>The above copyright notice and this permission notice shall be included in <a name="line-13"></a>all copies or substantial portions of the Software. <a name="line-14"></a> <a name="line-15"></a>THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR <a name="line-16"></a>IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, <a name="line-17"></a>FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE <a name="line-18"></a>AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER <a name="line-19"></a>LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, <a name="line-20"></a>OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN <a name="line-21"></a>THE SOFTWARE. <a name="line-22"></a>-}</span> <a name="line-23"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Colour</span><span class='hs-varop'>.</span><span class='hs-conid'>Matrix</span> <span class='hs-keyword'>where</span> <a name="line-24"></a> <a name="line-25"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>List</span> <a name="line-26"></a> <a name="line-27"></a><span class='hs-keyword'>default</span> <span class='hs-layout'>(</span><span class='hs-conid'>Rational</span><span class='hs-layout'>)</span> <a name="line-28"></a> <a name="line-29"></a><a name="inverse"></a><span class='hs-definition'>inverse</span> <span class='hs-varid'>m</span><span class='hs-keyglyph'>@</span><span class='hs-keyglyph'>[</span><span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span><span class='hs-varid'>b</span><span class='hs-layout'>,</span><span class='hs-varid'>c</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>,</span><span class='hs-keyglyph'>[</span><span class='hs-varid'>d</span><span class='hs-layout'>,</span><span class='hs-varid'>e</span><span class='hs-layout'>,</span><span class='hs-varid'>f</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>,</span><span class='hs-keyglyph'>[</span><span class='hs-varid'>g</span><span class='hs-layout'>,</span><span class='hs-varid'>h</span><span class='hs-layout'>,</span><span class='hs-varid'>i</span><span class='hs-keyglyph'>]</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>=</span> <a name="line-30"></a> <span class='hs-keyglyph'>[</span><span class='hs-keyglyph'>[</span><span class='hs-layout'>(</span><span class='hs-varid'>e</span><span class='hs-varop'>*</span><span class='hs-varid'>i</span><span class='hs-comment'>-</span><span class='hs-varid'>f</span><span class='hs-varop'>*</span><span class='hs-varid'>h</span><span class='hs-layout'>)</span><span class='hs-varop'>/</span><span class='hs-varid'>det</span><span class='hs-layout'>,</span> <span class='hs-comment'>-</span><span class='hs-layout'>(</span><span class='hs-varid'>b</span><span class='hs-varop'>*</span><span class='hs-varid'>i</span><span class='hs-comment'>-</span><span class='hs-varid'>c</span><span class='hs-varop'>*</span><span class='hs-varid'>h</span><span class='hs-layout'>)</span><span class='hs-varop'>/</span><span class='hs-varid'>det</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>b</span><span class='hs-varop'>*</span><span class='hs-varid'>f</span><span class='hs-comment'>-</span><span class='hs-varid'>c</span><span class='hs-varop'>*</span><span class='hs-varid'>e</span><span class='hs-layout'>)</span><span class='hs-varop'>/</span><span class='hs-varid'>det</span><span class='hs-keyglyph'>]</span> <a name="line-31"></a> <span class='hs-layout'>,</span><span class='hs-keyglyph'>[</span><span class='hs-comment'>-</span><span class='hs-layout'>(</span><span class='hs-varid'>d</span><span class='hs-varop'>*</span><span class='hs-varid'>i</span><span class='hs-comment'>-</span><span class='hs-varid'>f</span><span class='hs-varop'>*</span><span class='hs-varid'>g</span><span class='hs-layout'>)</span><span class='hs-varop'>/</span><span class='hs-varid'>det</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-varop'>*</span><span class='hs-varid'>i</span><span class='hs-comment'>-</span><span class='hs-varid'>c</span><span class='hs-varop'>*</span><span class='hs-varid'>g</span><span class='hs-layout'>)</span><span class='hs-varop'>/</span><span class='hs-varid'>det</span><span class='hs-layout'>,</span> <span class='hs-comment'>-</span><span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-varop'>*</span><span class='hs-varid'>f</span><span class='hs-comment'>-</span><span class='hs-varid'>c</span><span class='hs-varop'>*</span><span class='hs-varid'>d</span><span class='hs-layout'>)</span><span class='hs-varop'>/</span><span class='hs-varid'>det</span><span class='hs-keyglyph'>]</span> <a name="line-32"></a> <span class='hs-layout'>,</span><span class='hs-keyglyph'>[</span><span class='hs-layout'>(</span><span class='hs-varid'>d</span><span class='hs-varop'>*</span><span class='hs-varid'>h</span><span class='hs-comment'>-</span><span class='hs-varid'>e</span><span class='hs-varop'>*</span><span class='hs-varid'>g</span><span class='hs-layout'>)</span><span class='hs-varop'>/</span><span class='hs-varid'>det</span><span class='hs-layout'>,</span> <span class='hs-comment'>-</span><span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-varop'>*</span><span class='hs-varid'>h</span><span class='hs-comment'>-</span><span class='hs-varid'>b</span><span class='hs-varop'>*</span><span class='hs-varid'>g</span><span class='hs-layout'>)</span><span class='hs-varop'>/</span><span class='hs-varid'>det</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-varop'>*</span><span class='hs-varid'>e</span><span class='hs-comment'>-</span><span class='hs-varid'>b</span><span class='hs-varop'>*</span><span class='hs-varid'>d</span><span class='hs-layout'>)</span><span class='hs-varop'>/</span><span class='hs-varid'>det</span><span class='hs-keyglyph'>]</span><span class='hs-keyglyph'>]</span> <a name="line-33"></a> <span class='hs-keyword'>where</span> <a name="line-34"></a> <span class='hs-varid'>det</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>determinant</span> <span class='hs-varid'>m</span> <a name="line-35"></a><a name="determinant"></a><span class='hs-definition'>determinant</span> <span class='hs-keyglyph'>[</span><span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span><span class='hs-varid'>b</span><span class='hs-layout'>,</span><span class='hs-varid'>c</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>,</span><span class='hs-keyglyph'>[</span><span class='hs-varid'>d</span><span class='hs-layout'>,</span><span class='hs-varid'>e</span><span class='hs-layout'>,</span><span class='hs-varid'>f</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>,</span><span class='hs-keyglyph'>[</span><span class='hs-varid'>g</span><span class='hs-layout'>,</span><span class='hs-varid'>h</span><span class='hs-layout'>,</span><span class='hs-varid'>i</span><span class='hs-keyglyph'>]</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>=</span> <a name="line-36"></a> <span class='hs-varid'>a</span><span class='hs-varop'>*</span><span class='hs-layout'>(</span><span class='hs-varid'>e</span><span class='hs-varop'>*</span><span class='hs-varid'>i</span><span class='hs-comment'>-</span><span class='hs-varid'>f</span><span class='hs-varop'>*</span><span class='hs-varid'>h</span><span class='hs-layout'>)</span> <span class='hs-comment'>-</span> <span class='hs-varid'>b</span><span class='hs-varop'>*</span><span class='hs-layout'>(</span><span class='hs-varid'>d</span><span class='hs-varop'>*</span><span class='hs-varid'>i</span><span class='hs-comment'>-</span><span class='hs-varid'>f</span><span class='hs-varop'>*</span><span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-varop'>+</span> <span class='hs-varid'>c</span><span class='hs-varop'>*</span><span class='hs-layout'>(</span><span class='hs-varid'>d</span><span class='hs-varop'>*</span><span class='hs-varid'>h</span><span class='hs-comment'>-</span><span class='hs-varid'>e</span><span class='hs-varop'>*</span><span class='hs-varid'>g</span><span class='hs-layout'>)</span> <a name="line-37"></a> <a name="line-38"></a><a name="mult"></a><span class='hs-definition'>mult</span> <span class='hs-varid'>l</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>map</span> <span class='hs-layout'>(</span><span class='hs-varid'>sum</span> <span class='hs-varop'>.</span> <span class='hs-layout'>(</span><span class='hs-varid'>zipWith</span> <span class='hs-layout'>(</span><span class='hs-varop'>*</span><span class='hs-layout'>)</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-varid'>l</span> <a name="line-39"></a> <a name="line-40"></a><a name="matrixMult"></a><span class='hs-definition'>matrixMult</span> <span class='hs-varid'>l</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>transpose</span> <span class='hs-layout'>(</span><span class='hs-varid'>map</span> <span class='hs-layout'>(</span><span class='hs-varid'>mult</span> <span class='hs-varid'>l</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>transpose</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> </pre></body> </html>