lagrange


lagrange, a Fortran90 code which evaluates any Lagrange basis polynomial L(i)(x), its antiderivative, or its first or second derivatives. Sample plots are made.

Licensing:

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

Languages:

lagrange 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:

lagrange_test

dirichlet, a Fortran90 code which evaluates the Dirichlet kernel function, sometimes called the periodic sinc function. The function includes a parameter n, normally taken to be an integer. The function is defined by diric(x,n)=sin(0.5*n*x)/n/sin(0.5*x). Sample plots of these functions are made.

fresnel, a Fortran90 code which evaluates the Fresnel cosine and sine integrals.

gaussian, a Fortran90 code which evaluates the Gaussian function for arbitrary mu and sigma, its antiderivative, and derivatives of arbitrary order.

humps, a Fortran90 code which evaluates the humps() function, its first and second derivatives, and its antiderivative. The functions are plotted.

r8poly, a Fortran90 code which operates on real polynomials, including evaluation, differentiation, integration, multiplication, synthetic division, shifting the base, computing a power, taking the norm. It also defines Chebyshev, Lagrange and Legendre polynomials.

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]. The functions are plotted.

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.

Source Code:


Last revised on 05 August 2025.