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Error Functions


Functions

vec itpp::erf (const vec &x)
 Error function.
mat itpp::erf (const mat &x)
 Error function.
cvec itpp::erf (const cvec &x)
 Error function.
cmat itpp::erf (const cmat &x)
 Error function.
vec itpp::erfinv (const vec &x)
 Inverse of error function.
mat itpp::erfinv (const mat &x)
 Inverse of error function.
vec itpp::erfc (const vec &x)
 Complementary error function.
mat itpp::erfc (const mat &x)
 Complementary error function.
vec itpp::Qfunc (const vec &x)
 Q-function.
mat itpp::Qfunc (const mat &x)
 Q-function.
double itpp::Qfunc (double x)
 Q-function.
double itpp::erfinv (double x)
 Inverse of error function.
std::complex< double > itpp::erf (const std::complex< double > &z)
 Error function for complex argument.

Detailed Description


Function Documentation

vec itpp::erf ( const vec x  )  [inline]

Error function.

Definition at line 132 of file elmatfunc.h.

References itpp::vec_function().

Referenced by itpp::erf().

mat itpp::erf ( const mat x  )  [inline]

Error function.

Definition at line 134 of file elmatfunc.h.

References itpp::erf(), and itpp::mat_function().

cvec itpp::erf ( const cvec x  )  [inline]

Error function.

Definition at line 136 of file elmatfunc.h.

References itpp::cvec_function(), and itpp::erf().

cmat itpp::erf ( const cmat x  )  [inline]

Error function.

Definition at line 138 of file elmatfunc.h.

References itpp::cmat_function(), and itpp::erf().

vec itpp::erfinv ( const vec x  )  [inline]

Inverse of error function.

Definition at line 140 of file elmatfunc.h.

References itpp::vec_function().

Referenced by itpp::erfinv().

mat itpp::erfinv ( const mat x  )  [inline]

Inverse of error function.

Definition at line 142 of file elmatfunc.h.

References itpp::erfinv(), and itpp::mat_function().

vec itpp::erfc ( const vec x  )  [inline]

Complementary error function.

Definition at line 144 of file elmatfunc.h.

References itpp::vec_function().

Referenced by itpp::erfc(), and itpp::Qfunc().

mat itpp::erfc ( const mat x  )  [inline]

Complementary error function.

Definition at line 146 of file elmatfunc.h.

References itpp::erfc(), and itpp::mat_function().

vec itpp::Qfunc ( const vec x  )  [inline]

Q-function.

Definition at line 148 of file elmatfunc.h.

References itpp::vec_function().

Referenced by itpp::Qfunc().

mat itpp::Qfunc ( const mat x  )  [inline]

Q-function.

Definition at line 150 of file elmatfunc.h.

References itpp::mat_function(), and itpp::Qfunc().

double itpp::Qfunc ( double  x  ) 

Q-function.

Definition at line 186 of file scalfunc.cpp.

References itpp::erfc().

double itpp::erfinv ( double  P  ) 

Inverse of error function.

Definition at line 191 of file scalfunc.cpp.

References itpp::G1, itpp::G2, it_error_if, itpp::log(), itpp::sgn(), and itpp::sqrt().

std::complex< double > itpp::erf ( const std::complex< double > &  z  ) 

Error function for complex argument.

Author:
Adam Piatyszek
This function calculates a well known error function erf(z) for complex z. The implementation is based on unofficial implementation for Octave. Here is a part of the author's note from original sources:

Put together by John Smith john at arrows dot demon dot co dot uk, using ideas by others.

Calculate erf(z) for complex z. Three methods are implemented; which one is used depends on z.

The code includes some hard coded constants that are intended to give about 14 decimal places of accuracy. This is appropriate for 64-bit floating point numbers.

Definition at line 352 of file scalfunc.cpp.

References itpp::abs(), itpp::cerf_continued_fraction(), itpp::cerf_rybicki(), and itpp::cerf_series().

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