TOMS443
Solution of the Transcendental Equation W*EXP(W)=X

TOMS443 is a FORTRAN77 library which implements ACM TOMS algorithm 443, for evaluating Lambert's W function.

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.

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.

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.

Reference:

1. Fred Fritsch, R Shafer, W Crowley,
   Algorithm 443: Calculation of Optimum Parameters for Alternating Direction Implicit Procedures,
   Communications of the ACM,
   October 1973, Volume 16, Number 2, pages 123-124.

Source Code:

• toms443.f, the source code.
• toms443.sh, commands to compile the source code.

Examples and Tests:

• toms443_prb.f, a sample calling program.
• toms443_prb.sh, commands to compile and run the sample program.
• toms443_prb_output.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 FORTRAN77 source codes.