toms443

toms443, a MATLAB 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.

Related Data and Programs:

toms443_test

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

toms743, a MATLAB 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.