// 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()));
}
// ----------------------------------------------------------------------------------------
template <typename M>
struct op_softmax : basic_op_m<M>
{
typedef typename M::type type;
op_softmax(const M& m_, const type& s_, const type& v_) : basic_op_m<M>(m_), s(s_), v(v_){}
const type s;
const type v;
const static long cost = M::cost + 9;
typedef type const_ret_type;
const_ret_type apply(long r, long c) const { return std::exp(this->m(r, c) - v) * s; }
};
template <
typename EXP
>
const matrix_op<op_softmax<EXP> > soft_max (
const matrix_exp<EXP>& m
)
{
// you can only compute softmax on 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_softmax<EXP> op;
typename EXP::type max_val = max(m);
typename EXP::type temp = static_cast<typename EXP::type>(1) / sum(exp(m - max_val));
return matrix_op<op>(op(m.ref(), temp, max_val));
}
}
#endif // DLIB_MATRIx_MATH_FUNCTIONS