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 information on this web page is 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, a MATLAB code which supplies test values of various mathematical functions, including Abramowitz, AGM, Airy, Bell, Bernoulli, Bessel, Beta, Binomial, Bivariate Normal, Catalan, Cauchy, Chebyshev, Chi Square, Clausen, Clebsch Gordan, Collatz, Cosine integral, Dawson, Debye, Dedekind, dilogarithm, Exponential integral, Elliptic, Error, Euler, Exponential integral, F probability, Fresnel, Frobenius, Gamma, Gegenbauer, Goodwin, Gudermannian, Harmonic, Hermite, Hypergeometric, inverse trigonometic, Jacobi, Julian Ephemeris Date, Kelvin, Laguerre, Lambert W, Laplace, Legendre, Lerch, Lobachevsky, Lobatto, Logarithmic integral, Log normal, McNugget numbers, Mertens, Mittag-Leffler, Moebius, Multinomial, Negative binomial, Nine J, Normal, Omega, Owen, Partition, Phi, Pi, Poisson, Polylogarithm, Polyomino, Prime, Psi, Rayleigh, Hyperbolic Sine integral, Sigma, Sine Power integral, Sine integral, Six J, Sphere area, Sphere volume, Spherical harmonic, Stirling, Stromgen, Struve, Student, Subfactorial, Student probability, Three J, Transport, Trigamma, Truncated normal, van der Corput, von Mises, Weibull, Wright omega, Zeta.

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.