perazz / fitpack

A Modern Fortran translation of the FITPACK package for curve and surface fitting

fortran-fitpack

This is a Modern Fortran translation of the FITPACK package for curve and surface fitting. The functions are modernized and translated from the original Fortran77 code FITPACK by Paul Dierckx. The starting code used the double precision version of FITPACK distributed with scipy.

An object-oriented interface wrapper was also built. A C/C++ interface is also being built.

1D Spline interpolators:

Class	Description	Degree
fitpack_curve	1D spline interpolation of scattered data, $y = s(x)$	up to 5
fitpack_periodic_curve	1D spline interpolation of scattered data on a periodic domain, $y = s(x), s(0) = s(x_{per})$	up to 5
fitpack_parametric_curve	Parametric 1D curves in N dimensions, $x_i = s_i(u)$, $i=1,\ldots,n$	up to 5
fitpack_closed_curve	Closed parametric 1D curves in N dimensions, $x_i = s_i(u)$, $i=1,\ldots,n$, $x_i(0)=x_i(1)$	up to 5
fitpack_constrained_curve	Parametric 1D curves in N dimensions with value/derivative constraints at the endpoints $x_i = s_i(u)$, $i=1,\ldots,n$, $x_{i}^{(j)}(0)=u_{L,i}^{(j)}$ , $x_{i}^{(j)}(1)=u_{R,i}^{(j)}$, $0\le j \le 2$	up to 5

2D Spline interpolators:

Class	Description	Degree
fitpack_surface	2D spline interpolation of scattered data, $z = s(x,y)$	up to 5
fitpack_polar	2D spline interpolation of scattered data in a user-defined polar domain $z = s(u,v)$, $u\in[0,1]$, $v\in[-\pi,\pi]$, user-defined domain radius as a function of polar angle $r=r(v)$	3
fitpack_sphere	2D spline interpolation of scattered data on a sphere domain $z = s(u,v)$ with latitude $u \in [0,\pi]$, longitude $v \in [-\pi,\pi]$	3
fitpack_grid_surface	2D spline interpolation of rectangular 2D data $z = s(x,y)$ with gridded fitting coordinates $x_i, i=1,\ldots,n_x$, $y_j, j=1,\ldots,n_y$	up to 5
fitpack_grid_polar	2D spline interpolation of polar data $z = s(u,v)$ in the fixed-radius circular polar domain $u\in[0,r]$, $v\in[-\pi,\pi]$, with user-control of function and derivatives at the origin and the boundaries	3

C, C++ interfaces

The C and C++ header-only interfaces are found in the include folder. The following scheme shows a comparison between the Fortran, C++ and C struct names for the currently available classes:

Fortran	C	C++
fitpack_curve	fitpack_curve_c	fpCurve
fitpack_periodic_curve	fitpack_periodic_curve_c	fpPeriodicCurve
fitpack_parametric_curve	fitpack_parametric_curve_c	fpParametricCurve
fitpack_closed_curve	fitpack_closed_curve_c	fpClosedCurve
fitpack_constrained_curve	fitpack_constrained_curve_c	fpConstrainedCurve

The choice to provide a header-only C++ implementation is motivated by the need to keep the library C-ABI compatible whatever compiler is being used to build it. For example, on macOS, one may build the library with g++/gfortran, that is not ABI-compatible with clang++. So, it is important that no C++ code is compiled together with the Fortran code in the library.

Building, using

An automated build is available via the Fortran Package Manager. To use FITPACK within your FPM project, add the following to your fpm.toml file:

[dependencies]
fitpack = { git="https://github.com/perazz/fitpack.git" }

Otherwise, a simple command line build script that builds all modules in the src/ folder is possible.

Several test programs are available through the Fortran Package manager. To run them, just type

fpm test

References

Fitpack contains very robust algorithms for curve interpolation and fitting, based on algorithms described by Paul Dierckx in Ref [1-4]:

[1] P. Dierckx, "An algorithm for smoothing, differentiation and integration of experimental data using spline functions", J.Comp.Appl.Maths 1 (1975) 165-184.

[2] P. Dierckx, "A fast algorithm for smoothing data on a rectangular grid while using spline functions", SIAM J.Numer.Anal. 19 (1982) 1286-1304.

[3] P. Dierckx, "An improved algorithm for curve fitting with spline functions", report tw54, Dept. Computer Science,K.U. Leuven, 1981.

[4] P. Dierckx, "Curve and surface fitting with splines", Monographs on Numerical Analysis, Oxford University Press, 1993.

[5] P. Dierckx, R. Piessens, "Calculation of Fourier coefficients of discrete functions using cubic splines", Journal of Computational and Applied Mathematics 3(3), 207-209, 1977.

See also

• Dierckx.jl, a Julia interface to FITPACK
• scipy.interpolate, which includes interfaces to FITPACK