gaussian, a Fortran90 code which evaluates the Gaussian function for arbitrary mu and sigma, its antiderivative, and derivatives of arbitrary order.
A formula for the Gaussian function at the point x is:
g(x,mu,sigma) = 1/sigma/sqrt(2*pi) * exp ( -(x-mu)^2/2/sigma^2)
where mu is the mean value, and sigma is the standard deviation.
The information on this web page is distributed under the MIT license.
gaussian is available in a Fortran90 version and a MATLAB version and an Octave version and a Python version.
hermite_polynomial, a Fortran90 code which evaluates the physicist's Hermite polynomial, the probabilist's Hermite polynomial, the Hermite function, and related functions.
humps, a Fortran90 code which evaluates the humps() function, its first and second derivatives, and its antiderivative. The functions are plotted.
runge, a Fortran90 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]. Plots of these functions are made.
sigmoid, a Fortran90 code which evaluates the sigmoid function s(x)=1/(1+exp(-x)) or its derivatives of any order. The test code creates graphic images.
sinc, a Fortran90 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.
steinerberger, a Fortran90 code which evaluates the Steinerberger function, a continuous function with discontinuous derivative, which is very hard to accurately plot, integrate, minimize, or interpolate. Plots of these functions are made.