toms743

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.

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 made available on this web page are distributed under the MIT license

Languages:

toms743 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:

toms743_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.

toms443, an Octave code which evaluates lambert's w function. this is a version of acm toms algorithm 443.

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:

• bisect.m, approximates the W function using bisection.
• crude.m, returns a crude approximation for the W function.
• nbits_compute.m, computes the mantissa length minus one.
• wapr.m, approximates the W function.