toms443

toms443, an Octave code which evaluates Lambert's W function. This is a version of ACM TOMS algorithm 443, by Fritsch, Shafer and Crowley.

Lambert's W function W(X) satisfies the equation

        W(x) * exp ( W(x) ) = x
      

The text of many ACM TOMS algorithms is available online through ACM: https://calgo.acm.org/ or NETLIB: https://www.netlib.org/toms/index.html.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

toms443 is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

toms443_test

test_values, an Octave code which contains routines which return sample values of various functions, including the modified beta function, and the logarithm of the gamma function.

toms743, an Octave code which evaluates lambert's w function. this is a version of acm toms algorithm 743, by barry, barry and culligan-hensley.

Reference:

1. Fred Fritsch, RE Shafer, WP Crowley,
   Algorithm 443: Solution of the Transcendental Equation W*exp(W)=X,
   Communications of the ACM,
   Volume 16, Number 1, February 1973, pages 123-124.
2. Andrew Barry, S. J. Barry, Patricia Culligan-Hensley,
   Algorithm 743: WAPR - A Fortran routine for calculating real values of the W-function,
   ACM Transactions on Mathematical Software,
   Volume 21, Number 2, June 1995, pages 172-181.

Source Code:

• lambert_w_values.m, returns selected values of the Lambert W function.
• wew_a.m, evaluates Lambert's W function using code appropriate for a CDC 6600 (default 64 bit precision).
• wew_b.m, evaluates Lambert's W function using code appropriate for a computer with precision of about 3.0E-07.