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/usr/include/spline3.h is in libalglib-dev 2.6.0-3.

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/*************************************************************************
Copyright (c) 2007, Sergey Bochkanov (ALGLIB project).

>>> SOURCE LICENSE >>>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation (www.fsf.org); either version 2 of the 
License, or (at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

A copy of the GNU General Public License is available at
http://www.fsf.org/licensing/licenses

>>> END OF LICENSE >>>
*************************************************************************/

#ifndef _spline3_h
#define _spline3_h

#include "ap.h"
#include "ialglib.h"

void buildlinearspline(ap::real_1d_array x,
     ap::real_1d_array y,
     int n,
     ap::real_1d_array& c);


void buildcubicspline(ap::real_1d_array x,
     ap::real_1d_array y,
     int n,
     int boundltype,
     double boundl,
     int boundrtype,
     double boundr,
     ap::real_1d_array& c);


void buildhermitespline(ap::real_1d_array x,
     ap::real_1d_array y,
     ap::real_1d_array d,
     int n,
     ap::real_1d_array& c);


void buildakimaspline(ap::real_1d_array x,
     ap::real_1d_array y,
     int n,
     ap::real_1d_array& c);


double splineinterpolation(const ap::real_1d_array& c, double x);


void splinedifferentiation(const ap::real_1d_array& c,
     double x,
     double& s,
     double& ds,
     double& d2s);


void splinecopy(const ap::real_1d_array& c, ap::real_1d_array& cc);


void splineunpack(const ap::real_1d_array& c, int& n, ap::real_2d_array& tbl);


void splinelintransx(ap::real_1d_array& c, double a, double b);


void splinelintransy(ap::real_1d_array& c, double a, double b);


double splineintegration(const ap::real_1d_array& c, double x);


void spline3buildtable(int n,
     const int& diffn,
     ap::real_1d_array x,
     ap::real_1d_array y,
     const double& boundl,
     const double& boundr,
     ap::real_2d_array& ctbl);


double spline3interpolate(int n, const ap::real_2d_array& c, const double& x);


#endif