text: // Copyright (C) 2006  Davis E. King (davis@dlib.net)
  // License: Boost Software License   See LICENSE.txt for the full license.
  #ifndef DLIB_MATRIx_MATH_FUNCTIONS
  #define DLIB_MATRIx_MATH_FUNCTIONS 
  
  #include "matrix_math_functions_abstract.h"
  #include "matrix_op.h"
  #include "matrix_utilities.h"
  #include "matrix.h"
  #include "../algs.h"
  #include <cmath>
  #include <complex>
  #include <limits>
  
  
  namespace dlib
  {
  
  // ----------------------------------------------------------------------------------------
  
      DLIB_DEFINE_FUNCTION_M(op_sqrt, sqrt, std::sqrt ,7);
      DLIB_DEFINE_FUNCTION_M(op_log, log, std::log ,7);
      DLIB_DEFINE_FUNCTION_M(op_log10, log10, std::log10 ,7);
      DLIB_DEFINE_FUNCTION_M(op_exp, exp, std::exp ,7);
  
      DLIB_DEFINE_FUNCTION_M(op_conj, conj, std::conj ,2);
  
      DLIB_DEFINE_FUNCTION_M(op_ceil, ceil, std::ceil ,7);
      DLIB_DEFINE_FUNCTION_M(op_floor, floor, std::floor ,7);
  
      DLIB_DEFINE_FUNCTION_M(op_sin, sin, std::sin ,7);
      DLIB_DEFINE_FUNCTION_M(op_cos, cos, std::cos ,7);
      DLIB_DEFINE_FUNCTION_M(op_tan, tan, std::tan ,7);
      DLIB_DEFINE_FUNCTION_M(op_sinh, sinh, std::sinh ,7);
      DLIB_DEFINE_FUNCTION_M(op_cosh, cosh, std::cosh ,7);
      DLIB_DEFINE_FUNCTION_M(op_tanh, tanh, std::tanh ,7);
      DLIB_DEFINE_FUNCTION_M(op_asin, asin, std::asin ,7);
      DLIB_DEFINE_FUNCTION_M(op_acos, acos, std::acos ,7);
      DLIB_DEFINE_FUNCTION_M(op_atan, atan, std::atan ,7);
  
  // ----------------------------------------------------------------------------------------
  
      namespace impl
      {
          template <typename type>
          inline type sigmoid (const type& val)
          {
              return static_cast<type>(1/(1 + std::exp(-val)));
          }
  
          template <typename type, typename S>
          inline type round_zeros_eps (const type& val, const S& eps)
          {
              // you can only round matrices that contain built in scalar types like double, long, float, etc.
              COMPILE_TIME_ASSERT(is_built_in_scalar_type<type>::value);
  
              if (val >= eps || val <= -eps)
                  return val;
              else
                  return 0;
          }
  
          template <typename type>
          inline type round_zeros (const type& val)
          {
              // you can only round matrices that contain built in scalar types like double, long, float, etc.
              COMPILE_TIME_ASSERT(is_built_in_scalar_type<type>::value);
  
              const type eps = 10*std::numeric_limits<type>::epsilon();
              if (val >= eps || val <= -eps)
                  return val;
              else
                  return 0;
          }
  
          template <typename type>
          inline type squared (const type& val)
          {
              return val*val;
          }
  
          template <typename type>
          inline type sign (const type& val)
          {
              if (val >= 0)
                  return +1;
              else
                  return -1;
          }
  
          template <typename type>
          type cubed (const type& val)
          {
              return val*val*val;
          }
  
          template <typename type, typename S>
          inline type pow1 (const type& val, const S& s)
          {
              // you can only call pow() on matrices that contain floats, doubles or long doubles.
              COMPILE_TIME_ASSERT((
                      is_same_type<type,float>::value == true || 
                      is_same_type<type,double>::value == true || 
                      is_same_type<type,long double>::value == true 
              ));
  
              return std::pow(val,static_cast<type>(s));
          }
  
          template <typename type, typename S>
          inline type pow2 (const S& s, const type& val)
          {
              // you can only call pow() on matrices that contain floats, doubles or long doubles.
              COMPILE_TIME_ASSERT((
                      is_same_type<type,float>::value == true || 
                      is_same_type<type,double>::value == true || 
                      is_same_type<type,long double>::value == true 
              ));
  
              return std::pow(static_cast<type>(s),val);
          }
  
          template <typename type>
          inline type reciprocal (const type& val)
          {
              // you can only compute reciprocal matrices that contain floats, doubles or long doubles.
              COMPILE_TIME_ASSERT((
                      is_same_type<type,float>::value == true || 
                      is_same_type<type,double>::value == true || 
                      is_same_type<type,long double>::value == true  ||
                      is_same_type<type,std::complex<float> >::value == true || 
                      is_same_type<type,std::complex<double> >::value == true || 
                      is_same_type<type,std::complex<long double> >::value == true 
              ));
  
              if (val != static_cast<type>(0))
                  return static_cast<type>((type)1.0/val);
              else
                  return 0;
          }
  
          template <typename type>
          inline type reciprocal_max (const type& val)
          {
              // you can only compute reciprocal_max matrices that contain floats, doubles or long doubles.
              COMPILE_TIME_ASSERT((
                      is_same_type<type,float>::value == true || 
                      is_same_type<type,double>::value == true || 
                      is_same_type<type,long double>::value == true 
              ));
  
              if (val != static_cast<type>(0))
                  return static_cast<type>((type)1.0/val);
              else
                  return std::numeric_limits<type>::max();
          }
  
      }
  
      DLIB_DEFINE_FUNCTION_M(op_sigmoid, sigmoid, impl::sigmoid, 7);
      DLIB_DEFINE_FUNCTION_MS(op_round_zeros, round_zeros, impl::round_zeros_eps, 7);
      DLIB_DEFINE_FUNCTION_M(op_round_zeros2, round_zeros, impl::round_zeros, 7);
      DLIB_DEFINE_FUNCTION_M(op_cubed, cubed, impl::cubed, 7);
      DLIB_DEFINE_FUNCTION_M(op_squared, squared, impl::squared, 6);
      DLIB_DEFINE_FUNCTION_M(op_sign, sign, impl::sign, 6);
      DLIB_DEFINE_FUNCTION_MS(op_pow1, pow, impl::pow1, 7);
      DLIB_DEFINE_FUNCTION_SM(op_pow2, pow, impl::pow2, 7);
      DLIB_DEFINE_FUNCTION_M(op_reciprocal, reciprocal, impl::reciprocal, 6);
      DLIB_DEFINE_FUNCTION_M(op_reciprocal_max, reciprocal_max, impl::reciprocal_max, 6);
  
  // ----------------------------------------------------------------------------------------
  
      template <typename M, typename enabled = void>
      struct op_round : basic_op_m<M> 
      {
          op_round( const M& m_) : basic_op_m<M>(m_){}
  
          const static long cost = M::cost+7;
          typedef typename M::type type;
          typedef const typename M::type const_ret_type;
          const_ret_type apply (long r, long c) const
          { 
              return static_cast<type>(std::floor(this->m(r,c)+0.5)); 
          }
      };
  
      template <typename M>
      struct op_round<M,typename enable_if_c<std::numeric_limits<typename M::type>::is_integer>::type > 
      : basic_op_m<M>
      {
          op_round( const M& m_) : basic_op_m<M>(m_){}
  
          const static long cost = M::cost;
          typedef typename M::type type;
          typedef typename M::const_ret_type const_ret_type;
          const_ret_type apply (long r, long c) const
          { 
              return this->m(r,c);
          }
      };
  
      template <
          typename EXP
          >
      const matrix_op<op_round<EXP> > round (
          const matrix_exp<EXP>& m
      )
      {
          // you can only round matrices that contain built in scalar types like double, long, float, etc.
          COMPILE_TIME_ASSERT(is_built_in_scalar_type<typename EXP::type>::value);
  
          typedef op_round<EXP> op;
          return matrix_op<op>(op(m.ref()));
      }
  
  // ----------------------------------------------------------------------------------------
  
      template <typename M>
      struct op_normalize : basic_op_m<M> 
      {
          typedef typename M::type type;
  
          op_normalize( const M& m_, const type& s_) : basic_op_m<M>(m_), s(s_){}
  
          const type s;
  
          const static long cost = M::cost+5;
          typedef const typename M::type const_ret_type;
          const_ret_type apply (long r, long c) const
          { 
              return this->m(r,c)*s;
          }
      };
  
      template <
          typename EXP
          >
      const matrix_op<op_normalize<EXP> > normalize (
          const matrix_exp<EXP>& m
      )
      {
          // you can only compute normalized matrices that contain floats, doubles or long doubles.
          COMPILE_TIME_ASSERT((
                  is_same_type<typename EXP::type,float>::value == true || 
                  is_same_type<typename EXP::type,double>::value == true || 
                  is_same_type<typename EXP::type,long double>::value == true 
          ));
  
  
          typedef op_normalize<EXP> op;
          typename EXP::type temp = std::sqrt(sum(squared(m)));
          if (temp != 0.0)
              temp = 1.0/temp;
  
          return matrix_op<op>(op(m.ref(),temp));
      }
  
  // ----------------------------------------------------------------------------------------
  
      template <typename M, typename return_type = typename M::type>
      struct op_abs : basic_op_m<M>
      {
          op_abs( const M& m_) : basic_op_m<M>(m_){}
  
          const static long cost = M::cost+7;
          typedef typename M::type type;
          typedef const typename M::type const_ret_type;
          const_ret_type apply ( long r, long c) const
          { 
              return static_cast<type>(std::abs(this->m(r,c))); 
          }
      };
  
      template <typename M, typename T>
      struct op_abs<M, std::complex<T> > : basic_op_m<M>
      {
          op_abs( const M& m_) : basic_op_m<M>(m_){}
  
          const static long cost = M::cost;
          typedef T type;
          typedef const T const_ret_type;
          const_ret_type apply ( long r, long c) const
          { 
              return static_cast<type>(std::abs(this->m(r,c))); 
          }
      };
  
      template <
          typename EXP
          >
      const matrix_op<op_abs<EXP> > abs (
          const matrix_exp<EXP>& m
      )
      {
          typedef op_abs<EXP> op;
          return matrix_op<op>(op(m.ref()));
      }
  
  // ----------------------------------------------------------------------------------------
  
      template <typename M>
      struct op_complex_matrix : basic_op_m<M>
      {
          op_complex_matrix( const M& m_) : basic_op_m<M>(m_){}
  
          const static long cost = M::cost+1;
          typedef std::complex<typename M::type> type;
          typedef const std::complex<typename M::type> const_ret_type;
          const_ret_type apply ( long r, long c) const
          { 
              return type(this->m(r,c));
          }
      };
  
      template <
          typename EXP
          >
      const matrix_op<op_complex_matrix<EXP> > complex_matrix (
          const matrix_exp<EXP>& m
      )
      {
          typedef op_complex_matrix<EXP> op;
          return matrix_op<op>(op(m.ref()));
      }
  
  // ----------------------------------------------------------------------------------------
  
      template <typename M1, typename M2>
      struct op_complex_matrix2 : basic_op_mm<M1,M2>
      {
          op_complex_matrix2( const M1& m1_, const M2& m2_) : basic_op_mm<M1,M2>(m1_,m2_){}
  
          const static long cost = M1::cost+M2::cost+1;
          typedef std::complex<typename M1::type> type;
          typedef const std::complex<typename M1::type> const_ret_type;
  
          const_ret_type apply ( long r, long c) const
          { return type(this->m1(r,c), this->m2(r,c)); }
      };
  
      template <
          typename EXP1,
          typename EXP2
          >
      const matrix_op<op_complex_matrix2<EXP1,EXP2> > complex_matrix (
          const matrix_exp<EXP1>& real_part,
          const matrix_exp<EXP2>& imag_part 
      )
      {
          COMPILE_TIME_ASSERT((is_same_type<typename EXP1::type,typename EXP2::type>::value == true));
          COMPILE_TIME_ASSERT(EXP1::NR == EXP2::NR || EXP1::NR == 0 || EXP2::NR == 0);
          COMPILE_TIME_ASSERT(EXP1::NC == EXP2::NC || EXP1::NC == 0 || EXP2::NC == 0);
  
          DLIB_ASSERT(real_part.nr() == imag_part.nr() &&
                 real_part.nc() == imag_part.nc(), 
              "\tconst matrix_exp::type complex_matrix(real_part, imag_part)"
              << "\n\tYou can only make a complex matrix from two equally sized matrices"
              << "\n\treal_part.nr(): " << real_part.nr()
              << "\n\treal_part.nc(): " << real_part.nc() 
              << "\n\timag_part.nr(): " << imag_part.nr()
              << "\n\timag_part.nc(): " << imag_part.nc() 
              );
  
          typedef op_complex_matrix2<EXP1,EXP2> op;
          return matrix_op<op>(op(real_part.ref(),imag_part.ref()));
      }
  
  // ----------------------------------------------------------------------------------------
  
      template <typename M>
      struct op_norm : basic_op_m<M>
      {
          op_norm( const M& m_) : basic_op_m<M>(m_){}
  
          const static long cost = M::cost+6;
          typedef typename M::type::value_type type;
          typedef const typename M::type::value_type const_ret_type;
          const_ret_type apply ( long r, long c) const
          { return std::norm(this->m(r,c)); }
      };
  
      template <
          typename EXP
          >
      const matrix_op<op_norm<EXP> > norm (
          const matrix_exp<EXP>& m
      )
      {
          typedef op_norm<EXP> op;
          return matrix_op<op>(op(m.ref()));
      }
  
  // ----------------------------------------------------------------------------------------
  
      template <typename M>
      struct op_real : basic_op_m<M>
      {
          op_real( const M& m_) : basic_op_m<M>(m_){}
  
          const static long cost = M::cost;
          typedef typename M::type::value_type type;
          typedef const typename M::type::value_type const_ret_type;
          const_ret_type apply ( long r, long c) const
          { return std::real(this->m(r,c)); }
      };
  
      template <
          typename EXP
          >
      const matrix_op<op_real<EXP> > real (
          const matrix_exp<EXP>& m
      )
      {
          typedef op_real<EXP> op;
          return matrix_op<op>(op(m.ref()));
      }
  
  // ----------------------------------------------------------------------------------------
  
      template <typename M>
      struct op_imag : basic_op_m<M>
      {
          op_imag( const M& m_) : basic_op_m<M>(m_){}
  
          const static long cost = M::cost;
          typedef typename M::type::value_type type;
          typedef const typename M::type::value_type const_ret_type;
          const_ret_type apply (long r, long c) const
          { return std::imag(this->m(r,c)); }
      };
  
      template <
          typename EXP
          >
      const matrix_op<op_imag<EXP> > imag (
          const matrix_exp<EXP>& m
      )
      {
          typedef op_imag<EXP> op;
          return matrix_op<op>(op(m.ref()));
      }
  
  // ----------------------------------------------------------------------------------------
  
  }
  
  #endif // DLIB_MATRIx_MATH_FUNCTIONS
  
  