etl/include/etl/correlation.h

///\file

/******************************************************************************
The MIT License(MIT)

Embedded Template Library.
https://github.com/ETLCPP/etl
https://www.etlcpp.com

Copyright(c) 2021 John Wellbelove

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******************************************************************************/

#ifndef ETL_CORRELATION_INCLUDED
#define ETL_CORRELATION_INCLUDED

#include "platform.h"
#include "functional.h"
#include "type_traits.h"

#include <math.h>
#include <stdint.h>

namespace etl
{
  namespace private_correlation
  {
    //***************************************************************************
    /// Types for generic correlation.
    //***************************************************************************
    template <typename TInput, typename TCalc>
    struct correlation_traits
    {
      typedef TCalc calc_t;
    };

    //***************************************************************************
    /// Types for float correlation.
    //***************************************************************************
    template <typename TCalc>
    struct correlation_traits<float, TCalc>
    {
      typedef float calc_t;
    };

    //***************************************************************************
    /// Types for double correlation.
    //***************************************************************************
    template <typename TCalc>
    struct correlation_traits<double, TCalc>
    {
      typedef double calc_t;
    };
  }

  //***************************************************************************
  /// Correlation Type.
  //***************************************************************************
  struct correlation_type
  {
    static ETL_CONSTANT bool Sample     = false;
    static ETL_CONSTANT bool Population = true;
  };

  //***************************************************************************
  /// Correlation.
  //***************************************************************************
  template <bool Correlation_Type, typename TInput, typename TCalc = TInput>
  class correlation 
    : public private_correlation::correlation_traits<TInput, TCalc>
    , public etl::binary_function<TInput, TInput, void>
  {
  private:

    static ETL_CONSTANT int Adjustment = (Correlation_Type == correlation_type::Population) ? 0 : 1;

    typedef typename private_correlation::correlation_traits<TInput, TCalc>::calc_t calc_t;

  public:

    //*********************************
    /// Constructor.
    //*********************************
    correlation()
    {
      clear();
    }

    //*********************************
    /// Constructor.
    //*********************************
    template <typename TIterator>
    correlation(TIterator first1, TIterator last1, TIterator first2)
    {
      clear();
      add(first1, last1, first2);
    }

    //*********************************
    /// Add a pair of values.
    //*********************************
    void add(TInput value1, TInput value2)
    {
      inner_product   += TCalc(value1 * value2);
      sum_of_squares1 += TCalc(value1 * value1);
      sum_of_squares2 += TCalc(value2 * value2);
      sum1            += TCalc(value1);
      sum2            += TCalc(value2);
      ++counter;
      recalculate = true;
    }

    //*********************************
    /// Add a range.
    //*********************************
    template <typename TIterator>
    void add(TIterator first1, TIterator last1, TIterator first2)
    {
      while (first1 != last1)
      {
        add(*first1, *first2);
        ++first1;
        ++first2;
      }
    }

    //*********************************
    /// operator ()
    /// Add a pair of values.
    //*********************************
    void operator ()(TInput value1, TInput value2)
    {
      add(value1, value2);
    }

    //*********************************
    /// operator ()
    /// Add a range.
    //*********************************
    template <typename TIterator>
    void operator ()(TIterator first1, TIterator last1, TIterator first2)
    {
      add(first1, last1, first2);
    }

    //*********************************
    /// Get the correlation.
    //*********************************
    double get_covariance() const
    {
      calculate();

      return covariance_value;
    }

    //*********************************
    /// Get the correlation.
    //*********************************
    double get_correlation() const
    {
      calculate();

      return correlation_value;
    }

    //*********************************
    /// Get the correlation.
    //*********************************
    operator double() const
    {
      return get_correlation();
    }

    //*********************************
    /// Get the total number added entries.
    //*********************************
    size_t count() const
    {
      return size_t(counter);
    }

    //*********************************
    /// Clear the correlation.
    //*********************************
    void clear()
    {
      inner_product     = calc_t(0);
      sum_of_squares1   = calc_t(0);
      sum_of_squares2   = calc_t(0);
      sum1              = calc_t(0);
      sum2              = calc_t(0);
      counter           = 0U;
      covariance_value  = 0.0;
      correlation_value = 0.0;
      recalculate       = true;
    }

  private:
  
    //*********************************
    /// Do the calculation.
    //*********************************
    void calculate() const
    {
      if (recalculate)
      {
        correlation_value = 0.0;
        covariance_value  = 0.0;

        if (counter != 0)
        {
          double n = double(counter);
          double adjustment = 1.0 / (n * (n - Adjustment));

          double square_of_sum1 = (sum1 * sum1);
          double square_of_sum2 = (sum2 * sum2);

          double variance1 = ((n * sum_of_squares1) - square_of_sum1) * adjustment;
          double variance2 = ((n * sum_of_squares2) - square_of_sum2) * adjustment;

          double stddev1 = 0.0;
          double stddev2 = 0.0;

          if (variance1 > 0)
          {
            stddev1 = sqrt(variance1);
          }

          if (variance2 > 0)
          {
            stddev2 = sqrt(variance2);
          }

          covariance_value = ((n * inner_product) - (sum1 * sum2)) * adjustment;

          if ((stddev1 > 0.0) && (stddev2 > 0.0))
          {            
            correlation_value = covariance_value / (stddev1 * stddev2);
          }
        }

        recalculate = false;
      }
    }

    calc_t   inner_product;
    calc_t   sum_of_squares1;
    calc_t   sum_of_squares2;
    calc_t   sum1;
    calc_t   sum2;
    uint32_t counter;
    mutable double covariance_value;
    mutable double correlation_value;
    mutable bool   recalculate;
  };
}

#endif