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/*
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 * $Id: cumd_cau.cpp 542 2012-07-10 21:04:06Z johnoel $
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 *
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 * Author: David Fournier
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 * Copyright (c) 2008-2012 Regents of the University of California 
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 */
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/**
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 * \file
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 * Description not yet available.
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 */
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#include <fvar.hpp>
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/**
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 * Description not yet available.
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 * \param
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 */
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double cumd_cauchy(const double& x)
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{
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  double t=0.0;
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  const double r2=sqrt(2.0);
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  t=atan(x/r2);
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  return (0.5 + t/PI);
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}
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/**
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 * Description not yet available.
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 * \param
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 */
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double density_cauchy(const double& x)
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{
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  const double r2=PI*sqrt(2.0);
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  return 1./(r2*(1+0.5*x*x)); 
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}
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/**
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 * Description not yet available.
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 * \param
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 */
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double log_density_cauchy(const double& x)
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{
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  const double r2=PI*sqrt(2.0);
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  return -log(r2*(1+0.5*x*x)); 
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}
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/**
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 * Description not yet available.
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 * \param
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 */
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double inv_cumd_cauchy(const double& x)
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{
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  const double r2=sqrt(2.0);
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  return (r2*tan(PI*(x-0.5)));
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}