TOMS443
Evaluation of Lambert's W function.

TOMS443 is a FORTRAN90 library 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: http://www.acm.org/pubs/calgo or NETLIB: http://www.netlib.org/toms/index.html.

Usage:

w = wew ( x, en )

where X, is the argument, EN is the last correction to the output value made by the Newton iteration, and the value of W(X)) is returned in WEW.

Languages:

TOMS443 is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

TEST_VALUES, a FORTRAN90 library which contains routines which return sample values of various functions, including the modified beta function, and the logarithm of the gamma function.

TOMS743, a FORTRAN90 library 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:

• toms443.f, the source code.

Examples and Tests:

• toms443_test.f, a sample calling program.
• toms443_test.txt, the output file.

List of Routines:

• WEW_A evaluates Lambert's W function using code appropriate for a CDC 6600 (default 64 bit precision).
• WEW_B evaluates Lambert's W function using code appropriate for a computer with precision of about 3.0E-07.

You can go up one level to the FORTRAN90 source codes.