MathFunctions.h

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//                   OpenMS -- Open-Source Mass Spectrometry
// --------------------------------------------------------------------------
// Copyright The OpenMS Team -- Eberhard Karls University Tuebingen,
// ETH Zurich, and Freie Universitaet Berlin 2002-2020.
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// $Maintainer: Timo Sachsenberg$
// $Authors: Marc Sturm $
// --------------------------------------------------------------------------
 
#pragma once
 
#include <OpenMS/CONCEPT/Types.h>
 
#include <boost/math/special_functions/gamma.hpp>
#include <cmath>
#include <utility>
 
namespace OpenMS
{
  namespace Math
  {
    inline static double ceilDecimal(double x, int decPow)
    {
      return (ceil(x / pow(10.0, decPow))) * pow(10.0, decPow); // decimal shift right, ceiling, decimal shift left
    }
 
    inline static double roundDecimal(double x, int decPow)
    {
      if (x > 0)
        return (floor(0.5 + x / pow(10.0, decPow))) * pow(10.0, decPow);
 
      return -((floor(0.5 + fabs(x) / pow(10.0, decPow))) * pow(10.0, decPow));
    }
 
    inline static double intervalTransformation(double x, double left1, double right1, double left2, double right2)
    {
      return left2 + (x - left1) * (right2 - left2) / (right1 - left1);
    }
 
    inline double linear2log(double x)
    {
      return log10(x + 1);     //+1 to avoid negative logarithms
    }
 
    inline double log2linear(double x)
    {
      return pow(10, x) - 1;
    }
 
    inline bool isOdd(UInt x)
    {
      return (x & 1) != 0;
    }
 
    template <typename T>
    T round(T x)
    {
      if (x >= T(0))
      {
        return T(floor(x + T(0.5)));
      }
      else
      {
        return T(ceil(x - T(0.5)));
      }
    }
 
    inline static bool approximatelyEqual(double a, double b, double tol)
    {
      return std::fabs(a - b) <= tol;
    }
 
    template <typename T>
    T gcd(T a, T b)
    {
      T c;
      while (b != 0)
      {
        c = a % b;
        a = b;
        b = c;
      }
      return a;
    }
 
    template <typename T>
    T gcd(T a, T b, T & u1, T & u2)
    {
      u1 = 1;
      u2 = 0;
      T u3 = a;
 
      T v1 = 0;
      T v2 = 1;
      T v3 = b;
 
      while (v3 != 0)
      {
        T q = u3 / v3;
        T t1 = u1 - v1 * q;
        T t2 = u2 - v2 * q;
        T t3 = u3 - v3 * q;
 
        u1 = v1;
        u2 = v2;
        u3 = v3;
 
        v1 = t1;
        v2 = t2;
        v3 = t3;
      }
 
      return u3;
    }
 
    template <typename T>
    T getPPM(T mz_obs, T mz_ref)
    {
      return (mz_obs - mz_ref) / mz_ref * 1e6;
    }
    
    template <typename T>
    T getPPMAbs(T mz_obs, T mz_ref)
    {
      return std::fabs(getPPM(mz_obs, mz_ref));
    }
 
    template <typename T>
    T ppmToMass(T ppm, T mz_ref)
    {
      return (ppm / 1e6) * mz_ref;
    }
    
    /*
      @brief Compute the absolute mass diff in [Th], given a ppm value and a reference point.
 
      The returned mass diff is always positive!
 
      @param ppm Parts-per-million error
      @param mz_ref Reference m/z
      @return The absolute mass diff in [Th]
    */
    template <typename T>
    T ppmToMassAbs(T ppm, T mz_ref)
    {
      return std::fabs(ppmToMass(ppm, mz_ref));
    }
 
    inline static std::pair<double, double> getTolWindow(double val, double tol, bool ppm)
    {
      double left, right;
 
      if (ppm)
      {
        left = val - val * tol * 1e-6;
        right = val / (1.0 - tol * 1e-6);
      }
      else
      {
        left = val - tol;
        right = val + tol;
      }
 
      return std::make_pair(left, right);
    }
    
    inline double factLn(UInt x)
    {
      return lgamma(double(x+1));
    }
 
  } // namespace Math
} // namespace OpenMS