<?xml version="1.0" encoding="UTF-8"?> <!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>src/ForSyDe/Shallow/Gaussian.hs</title> <link type='text/css' rel='stylesheet' href='hscolour.css' /> </head> <body> <pre><a name="line-1"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span> <a name="line-2"></a><span class='hs-comment'>-- |</span> <a name="line-3"></a><span class='hs-comment'>-- Module : ForSyDe.Shallow.Gaussian</span> <a name="line-4"></a><span class='hs-comment'>-- Copyright : (c) SAM Group, KTH/ICT/ECS 2007-2008</span> <a name="line-5"></a><span class='hs-comment'>-- License : BSD-style (see the file LICENSE)</span> <a name="line-6"></a><span class='hs-comment'>-- </span> <a name="line-7"></a><span class='hs-comment'>-- Maintainer : forsyde-dev@ict.kth.se</span> <a name="line-8"></a><span class='hs-comment'>-- Stability : experimental</span> <a name="line-9"></a><span class='hs-comment'>-- Portability : portable</span> <a name="line-10"></a><span class='hs-comment'>--</span> <a name="line-11"></a><span class='hs-comment'>-- We follow the Box-Muller method to generate white gaussian noise, </span> <a name="line-12"></a><span class='hs-comment'>-- described at: <<a href="http://www.dspguru.com/howto/tech/wgn.htm">http://www.dspguru.com/howto/tech/wgn.htm</a>></span> <a name="line-13"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span> <a name="line-14"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>ForSyDe</span><span class='hs-varop'>.</span><span class='hs-conid'>Shallow</span><span class='hs-varop'>.</span><span class='hs-conid'>Gaussian</span> <span class='hs-layout'>(</span> <a name="line-15"></a> <span class='hs-varid'>pGaussianNoise</span> <a name="line-16"></a> <span class='hs-layout'>)</span> <a name="line-17"></a><span class='hs-keyword'>where</span> <a name="line-18"></a> <a name="line-19"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>ForSyDe</span><span class='hs-varop'>.</span><span class='hs-conid'>Shallow</span><span class='hs-varop'>.</span><span class='hs-conid'>UntimedLib</span> <a name="line-20"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>ForSyDe</span><span class='hs-varop'>.</span><span class='hs-conid'>Shallow</span><span class='hs-varop'>.</span><span class='hs-conid'>Signal</span> <a name="line-21"></a> <a name="line-22"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>System</span><span class='hs-varop'>.</span><span class='hs-conid'>Random</span> <a name="line-23"></a> <a name="line-24"></a><a name="pGaussianNoise"></a><span class='hs-comment'>-- |To generate an infinite Signal of Gaussian values</span> <a name="line-25"></a><span class='hs-definition'>pGaussianNoise</span><span class='hs-keyglyph'>::</span> <span class='hs-conid'>Double</span> <span class='hs-comment'>-- Mean value of the Gaussian noise</span> <a name="line-26"></a> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Double</span> <span class='hs-comment'>-- Variance of the Gaussian noise</span> <a name="line-27"></a> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Int</span> <span class='hs-comment'>-- The seed</span> <a name="line-28"></a> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Signal</span> <span class='hs-conid'>Double</span> <span class='hs-comment'>-- Output gaussian noise signal</span> <a name="line-29"></a><span class='hs-definition'>pGaussianNoise</span> <span class='hs-varid'>mean</span> <span class='hs-varid'>variance</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mapU</span> <span class='hs-num'>2</span> <span class='hs-varid'>gaussianXY</span> <span class='hs-varop'>.</span> <span class='hs-varid'>pUnitNormXY</span> <a name="line-30"></a> <span class='hs-keyword'>where</span> <a name="line-31"></a> <span class='hs-varid'>gaussianXY</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>x</span><span class='hs-layout'>,</span> <span class='hs-varid'>y</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>mean</span> <span class='hs-varop'>+</span> <span class='hs-varid'>sqrt</span><span class='hs-layout'>(</span><span class='hs-varid'>variance</span><span class='hs-layout'>)</span> <span class='hs-varop'>*</span> <span class='hs-varid'>x</span><span class='hs-layout'>,</span> <a name="line-32"></a> <span class='hs-varid'>mean</span> <span class='hs-varop'>+</span> <span class='hs-varid'>sqrt</span><span class='hs-layout'>(</span><span class='hs-varid'>variance</span><span class='hs-layout'>)</span> <span class='hs-varop'>*</span> <span class='hs-varid'>y</span><span class='hs-keyglyph'>]</span> <a name="line-33"></a> <span class='hs-varid'>gaussianXY</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>error</span> <span class='hs-str'>"gaussianXY: unexpected pattern."</span> <a name="line-34"></a> <a name="line-35"></a><a name="uniform"></a><span class='hs-comment'>-- |To get a uniform random variable in the range [0, 1]</span> <a name="line-36"></a><span class='hs-definition'>uniform</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Fractional</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>RandomGen</span> <span class='hs-varid'>g</span><span class='hs-layout'>,</span> <span class='hs-conid'>Random</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <a name="line-37"></a> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <a name="line-38"></a><span class='hs-definition'>uniform</span> <span class='hs-varid'>rGen</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>randomR</span> <span class='hs-layout'>(</span><span class='hs-num'>0.0</span><span class='hs-layout'>,</span><span class='hs-num'>1.0</span><span class='hs-layout'>)</span> <span class='hs-varid'>rGen</span> <a name="line-39"></a> <a name="line-40"></a><a name="pUnitNormXY"></a><span class='hs-comment'>-- |To generate an infinite signal of unit normal random variables,</span> <a name="line-41"></a><span class='hs-comment'>-- with the specified seed</span> <a name="line-42"></a><span class='hs-definition'>pUnitNormXY</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Int</span> <span class='hs-comment'>-- The seed</span> <a name="line-43"></a> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Signal</span> <span class='hs-conid'>Double</span> <span class='hs-comment'>-- The infinite ouput signal</span> <a name="line-44"></a><span class='hs-definition'>pUnitNormXY</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mapU</span> <span class='hs-num'>3</span> <span class='hs-varid'>unitNormXY</span> <span class='hs-varop'>.</span> <span class='hs-varid'>signal</span> <span class='hs-varop'>.</span> <span class='hs-varid'>svGenerator</span> <span class='hs-varop'>.</span> <span class='hs-varid'>mkStdGen</span> <a name="line-45"></a> <span class='hs-keyword'>where</span> <a name="line-46"></a> <span class='hs-varid'>unitNormXY</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>s</span><span class='hs-layout'>,</span> <span class='hs-varid'>v1</span><span class='hs-layout'>,</span> <span class='hs-varid'>v2</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>sqrt</span><span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-num'>2</span> <span class='hs-varop'>*</span> <span class='hs-varid'>log</span><span class='hs-layout'>(</span><span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-varop'>/</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-varop'>*</span> <span class='hs-varid'>v1</span><span class='hs-layout'>,</span> <a name="line-47"></a> <span class='hs-varid'>sqrt</span><span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-num'>2</span> <span class='hs-varop'>*</span> <span class='hs-varid'>log</span><span class='hs-layout'>(</span><span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-varop'>/</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-varop'>*</span> <span class='hs-varid'>v2</span><span class='hs-keyglyph'>]</span> <a name="line-48"></a> <span class='hs-varid'>unitNormXY</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>error</span> <span class='hs-str'>"pUnitNormXY: Unexpected pattern."</span> <a name="line-49"></a> <a name="line-50"></a> <a name="line-51"></a><a name="svGenerator"></a><span class='hs-comment'>-- |To generate the s, v1, v2 value</span> <a name="line-52"></a><span class='hs-definition'>svGenerator</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>StdGen</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Double</span><span class='hs-keyglyph'>]</span> <a name="line-53"></a><span class='hs-definition'>svGenerator</span> <span class='hs-varid'>s</span> <a name="line-54"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>sVal</span> <span class='hs-varop'>>=</span><span class='hs-num'>1</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>[]</span><span class='hs-varop'>++</span> <span class='hs-varid'>svGenerator</span> <span class='hs-varid'>newStdG</span> <a name="line-55"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>svVal</span> <span class='hs-varop'>++</span> <span class='hs-varid'>svGenerator</span> <span class='hs-varid'>newStdG</span> <a name="line-56"></a> <span class='hs-keyword'>where</span> <a name="line-57"></a> <span class='hs-varid'>svGen1</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>svHelper</span> <span class='hs-varid'>s</span> <a name="line-58"></a> <span class='hs-varid'>svVal</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fst</span> <span class='hs-varid'>svGen1</span> <a name="line-59"></a> <span class='hs-varid'>sVal</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>head</span> <span class='hs-varid'>svVal</span> <a name="line-60"></a> <span class='hs-varid'>newStdG</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>snd</span> <span class='hs-varid'>svGen1</span> <a name="line-61"></a> <span class='hs-varid'>svHelper</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>StdGen</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>[</span><span class='hs-conid'>Double</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>,</span> <span class='hs-conid'>StdGen</span><span class='hs-layout'>)</span> <a name="line-62"></a> <span class='hs-varid'>svHelper</span> <span class='hs-varid'>stdG</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>[</span><span class='hs-varid'>s</span><span class='hs-layout'>,</span> <span class='hs-varid'>v1</span><span class='hs-layout'>,</span> <span class='hs-varid'>v2</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>,</span> <span class='hs-varid'>sNew2</span><span class='hs-layout'>)</span> <a name="line-63"></a> <span class='hs-keyword'>where</span> <a name="line-64"></a> <span class='hs-layout'>(</span><span class='hs-varid'>u1</span><span class='hs-layout'>,</span> <span class='hs-varid'>sNew1</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>uniform</span> <span class='hs-varid'>stdG</span> <a name="line-65"></a> <span class='hs-layout'>(</span><span class='hs-varid'>u2</span><span class='hs-layout'>,</span> <span class='hs-varid'>sNew2</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>uniform</span> <span class='hs-varid'>sNew1</span> <a name="line-66"></a> <span class='hs-varid'>v1</span><span class='hs-keyglyph'>=</span><span class='hs-num'>2</span> <span class='hs-varop'>*</span> <span class='hs-varid'>u1</span> <span class='hs-comment'>-</span><span class='hs-num'>1</span> <a name="line-67"></a> <span class='hs-varid'>v2</span><span class='hs-keyglyph'>=</span><span class='hs-num'>2</span> <span class='hs-varop'>*</span> <span class='hs-varid'>u2</span> <span class='hs-comment'>-</span><span class='hs-num'>1</span> <a name="line-68"></a> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>v1</span><span class='hs-varop'>*</span><span class='hs-varid'>v1</span> <span class='hs-varop'>+</span> <span class='hs-varid'>v2</span><span class='hs-varop'>*</span><span class='hs-varid'>v2</span> </pre></body> </html>
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