Logarithmic and Exponential Functions

Functions
double	itpp::logb (double b, double x)
	Base-b logarithm.
int	itpp::pow2i (int x)
	Calculate two to the power of x (2^x); x is integer.
double	itpp::pow2 (double x)
	Calculate two to the power of x (2^x)
double	itpp::pow2 (int x)
	Calculate two to the power of x (2^x) for large integer x.
double	itpp::pow10 (double x)
	Calculate ten to the power of x (10^x)
double	itpp::dB (double x)
	Decibel of x (10*log10(x))
double	itpp::inv_dB (double x)
	Inverse of decibel of x.
int	itpp::int2bits (int n)
	Calculate the number of bits needed to represent an integer n.
int	itpp::levels2bits (int n)
	Calculate the number of bits needed to represent n different values (levels).
double	itpp::trunc_log (double x)
	Truncated natural logarithm function.
double	itpp::trunc_exp (double x)
	Truncated exponential function.
double	itpp::log_add (double log_a, double log_b)
	Safe substitute for log(exp(log_a) + exp(log_b))
vec	itpp::exp (const vec &x)
	Exp of the elements of a vector x.
cvec	itpp::exp (const cvec &x)
	Exp of the elements of a complex vector x.
mat	itpp::exp (const mat &m)
	Exp of the elements of a matrix m.
cmat	itpp::exp (const cmat &m)
	Exp of the elements of a complex matrix m.
vec	itpp::pow (const double x, const vec &y)
	Calculates x to the power of y (x^y)
mat	itpp::pow (const double x, const mat &y)
	Calculates x to the power of y (x^y)
vec	itpp::pow (const vec &x, const double y)
	Calculates x to the power of y (x^y)
mat	itpp::pow (const mat &x, const double y)
	Calculates x to the power of y (x^y)
vec	itpp::pow2 (const vec &x)
	Calculates two to the power of x (2^x)
vec	itpp::pow2 (const ivec &x)
	Calculates two to the power of x (2^x) for integer x.
mat	itpp::pow2 (const mat &x)
	Calculates two to the power of x (2^x)
mat	itpp::pow2 (const imat &x)
	Calculates two to the power of x (2^x) for integer x.
vec	itpp::pow10 (const vec &x)
	Calculates ten to the power of x (10^x)
mat	itpp::pow10 (const mat &x)
	Calculates ten to the power of x (10^x)
vec	itpp::log (const vec &x)
	The natural logarithm of the elements.
mat	itpp::log (const mat &x)
	The natural logarithm of the elements.
cvec	itpp::log (const cvec &x)
	The natural logarithm of the elements.
cmat	itpp::log (const cmat &x)
	The natural logarithm of the elements.
vec	itpp::log2 (const vec &x)
	log-2 of the elements
mat	itpp::log2 (const mat &x)
	log-2 of the elements
vec	itpp::log10 (const vec &x)
	log-10 of the elements
mat	itpp::log10 (const mat &x)
	log-10 of the elements
vec	itpp::logb (double b, const vec &x)
	log-b of x
mat	itpp::logb (double b, const mat &x)
	log-b of x
vec	itpp::dB (const vec &x)
	Calculates 10*log10(x)
mat	itpp::dB (const mat &x)
	Calculates 10*log10(x)
vec	itpp::inv_dB (const vec &x)
	Calulates the inverse of dB, 10^(x/10)
mat	itpp::inv_dB (const mat &x)
	Calculates the inverse of dB, 10^(x/10)
ivec	itpp::int2bits (const ivec &v)
	Calculate the number of bits needed to represent each integer in a vector.
ivec	itpp::levels2bits (const ivec &v)
	Calculate the number of bits needed to represent a numer of levels saved in a vector.

Variables
const double	itpp::log_double_max = std::log(std::numeric_limits<double>::max())
	Constant definition to speed up trunc_log() and trunc_exp()
const double	itpp::log_double_min = std::log(std::numeric_limits<double>::min())
	Constant definition to speed up trunc_log(), trunc_exp() and log_add()

Detailed Description

Function Documentation

double itpp::trunc_log ( double  x )

inline

Truncated natural logarithm function.

This truncated function provides a solution in the cases when the logarithm argument is less or equal to zero or infinity. The function checks for such extreme values and use some kind of truncation (saturation) before calculating the logarithm.

The truncated logarithm function can be used for calculation of log-likelihood in soft demodulators, when numerical instability problem might occur.

Definition at line 115 of file log_exp.h.

References itpp::log(), itpp::log_double_max, and itpp::log_double_min.

Referenced by itpp::Modulator< T >::demodulate_soft_bits(), itpp::PAM_c::demodulate_soft_bits(), and itpp::Rec_Syst_Conv_Code::map_decode().

double itpp::trunc_exp ( double  x )

inline

Truncated exponential function.

This truncated function provides a solution in the case when the exponent function results in infinity. The function checks for an extreme value and use truncation (saturation) before calculating the result.

The truncated exponential function can be used when numerical instability problem occurs for a standard exp function.

Definition at line 137 of file log_exp.h.

References itpp::exp(), itpp::log_double_max, and itpp::max().

Referenced by itpp::MOG_diag::lhood_internal(), itpp::MOG_generic::lhood_internal(), itpp::Rec_Syst_Conv_Code::map_decode(), and itpp::MOG_diag_EM_sup::ml_update_params().