/usr/include/votca/tools/akimaspline.h is in libvotca-tools-dev 1.4.1-2.
This file is owned by root:root, with mode 0o644.
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* Copyright 2009-2011 The VOTCA Development Team (http://www.votca.org)
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
*/
#ifndef _AKIMASPLINE_H
#define _AKIMASPLINE_H
#include "spline.h"
#include <boost/numeric/ublas/vector.hpp>
#include <boost/numeric/ublas/vector_proxy.hpp>
#include <boost/numeric/ublas/vector_expression.hpp>
#include <iostream>
namespace votca { namespace tools {
namespace ub = boost::numeric::ublas;
/**
*
* \brief An Akima Spline Class
*
* does Akima interpolation based on the paper
* "A new method of interpolation and smooth curve fitting based on local procedures"
*
* Fitting is not supported. In order to fit data, do linear fitting and interpolate
* the linear fitted values by Akima interpolation.
*/
class AkimaSpline : public Spline
{
public:
// default constructor
AkimaSpline() {};
//AkimaSpline() :
// _boundaries(splineNormal) {}
// destructor
~AkimaSpline() {};
/**
* \brief Calculate the slope according to the original Akima paper ("A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures")
* \param slopes m1 to m4 of line segments connecting the five data points
* \return slope
* handles all special cases to determine the slope t based on slopes m1,m2,m3,m4
*/
double getSlope(double m1, double m2, double m3, double m4);
// construct an interpolation spline
// x, y are the the points to construct interpolation, both vectors must be of same size
void Interpolate(ub::vector<double> &x, ub::vector<double> &y);
// fit spline through noisy data
// x,y are arrays with noisy data, both vectors must be of same size
void Fit(ub::vector<double> &x, ub::vector<double> &y);
// Calculate the function value
double Calculate(const double &x);
// Calculate the function derivative
double CalculateDerivative(const double &x);
// Calculate the function value for a whole array, story it in y
template<typename vector_type1, typename vector_type2>
void Calculate(vector_type1 &x, vector_type2 &y);
// Calculate the derivative value for a whole array, story it in y
template<typename vector_type1, typename vector_type2>
void CalculateDerivative(vector_type1 &x, vector_type2 &y);
protected:
// p1,p2,p3,p4 and t1,t2 (same identifiers as in Akima paper, page 591)
ub::vector<double> p0;
ub::vector<double> p1;
ub::vector<double> p2;
ub::vector<double> p3;
ub::vector<double> t;
};
inline double AkimaSpline::Calculate(const double &r)
{
int interval = getInterval(r);
double z = r-_r[interval];
return p0(interval)
+ p1(interval)*z
+ p2(interval)*z*z
+ p3(interval)*z*z*z;
}
inline double AkimaSpline::CalculateDerivative(const double &r)
{
int interval = getInterval(r);
double z = r-_r[interval];
return + p1(interval)
+ 2.0*p2(interval)*z
+ 3.0*p3(interval)*z*z;
}
inline double AkimaSpline::getSlope(double m1, double m2, double m3, double m4)
{
if ((m1==m2) && (m3==m4)) {
return (m2+m3)/2.0;
} else {
return (fabs(m4-m3)*m2 + fabs(m2-m1)*m3) / (fabs(m4-m3) + fabs(m2-m1));
}
}
}}
#endif /* _AKIMASPLINE_H */
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