sigmoid

sigmoid, a MATLAB code which evaluates the sigmoid function s(x)=1/(1+exp(-x)) or a derivative of any order. The test code creates graphic images.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

sigmoid is available in a C version and a C++ version and a Fortran77 version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

sigmoid_test

humps, a MATLAB code which evaluates the humps() function, its first and second derivatives, and its antiderivative. The functions are plotted.

polpak, a MATLAB code which evaluates a variety of mathematical functions, polynomials, and sequences, including Bell, Benford, Bernoulli, Bernstein, Cardan, Catalan, Charlier, Chebyshev, Collatz, Delannoy, Euler, Fibonacci, Gegenbauer, Gudermannian, Harmonic, Hermite, Hofstadter, Hypergeometric 2F1, Jacobi, Krawtchouk, Laguerre, Lambert W, Legendre, Lerch, Meixner, Mertens, Moebius, Motzkin, Phi, Stirling Numbers, Tau, Tribonacci, Zernike.

runge, a MATLAB code which evaluates the Runge() function, its first and second derivatives, and its antiderivative. This function causes a breakdown for polynomial interpolation over equally spaced nodes in [-1,+1]. The functions are plotted using gnuplot().

sinc, a MATLAB code which evaluates the sinc() function, its first and second derivative and its antiderivative. The normalized function is defined by sincn=sin(pi*x)/(pi*x), the unnormalized function is sincu=sin(x)/x. Plots of these functions are made.

Reference:

1. Joe McKenna,
   Derivatives of the sigmoid function,
   https://joepatmckenna.github.io/calculus/derivative/sigmoid%20function/linear%20albegra/2018/01/20/sigmoid-derivs/

Source Code:

• sigmoid_coef.m returns the coefficients in an expansion of the n-th derivative of the sigmoid function in terms of a polynomial in the value of the sigmoid function itself.
• sigmoid_value.m evaluates the n-th derivative of the sigmoid function at a point x.