358 lines
12 KiB
C++
358 lines
12 KiB
C++
// ____ ______ __
|
|
// / __ \ / ____// /
|
|
// / /_/ // / / /
|
|
// / ____// /___ / /___ PixInsight Class Library
|
|
// /_/ \____//_____/ PCL 2.4.23
|
|
// ----------------------------------------------------------------------------
|
|
// pcl/CubicSplineInterpolation.h - Released 2022-03-12T18:59:29Z
|
|
// ----------------------------------------------------------------------------
|
|
// This file is part of the PixInsight Class Library (PCL).
|
|
// PCL is a multiplatform C++ framework for development of PixInsight modules.
|
|
//
|
|
// Copyright (c) 2003-2022 Pleiades Astrophoto S.L. All Rights Reserved.
|
|
//
|
|
// Redistribution and use in both source and binary forms, with or without
|
|
// modification, is permitted provided that the following conditions are met:
|
|
//
|
|
// 1. All redistributions of source code must retain the above copyright
|
|
// notice, this list of conditions and the following disclaimer.
|
|
//
|
|
// 2. All redistributions in binary form must reproduce the above copyright
|
|
// notice, this list of conditions and the following disclaimer in the
|
|
// documentation and/or other materials provided with the distribution.
|
|
//
|
|
// 3. Neither the names "PixInsight" and "Pleiades Astrophoto", nor the names
|
|
// of their contributors, may be used to endorse or promote products derived
|
|
// from this software without specific prior written permission. For written
|
|
// permission, please contact info@pixinsight.com.
|
|
//
|
|
// 4. All products derived from this software, in any form whatsoever, must
|
|
// reproduce the following acknowledgment in the end-user documentation
|
|
// and/or other materials provided with the product:
|
|
//
|
|
// "This product is based on software from the PixInsight project, developed
|
|
// by Pleiades Astrophoto and its contributors (https://pixinsight.com/)."
|
|
//
|
|
// Alternatively, if that is where third-party acknowledgments normally
|
|
// appear, this acknowledgment must be reproduced in the product itself.
|
|
//
|
|
// THIS SOFTWARE IS PROVIDED BY PLEIADES ASTROPHOTO AND ITS CONTRIBUTORS
|
|
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
|
|
// TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
|
|
// PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL PLEIADES ASTROPHOTO OR ITS
|
|
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
|
|
// EXEMPLARY OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, BUSINESS
|
|
// INTERRUPTION; PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; AND LOSS OF USE,
|
|
// DATA OR PROFITS) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
|
|
// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
|
|
// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
|
|
// POSSIBILITY OF SUCH DAMAGE.
|
|
// ----------------------------------------------------------------------------
|
|
|
|
#ifndef __PCL_CubicSplineInterpolation_h
|
|
#define __PCL_CubicSplineInterpolation_h
|
|
|
|
/// \file pcl/CubicSplineInterpolation.h
|
|
|
|
#include <pcl/Defs.h>
|
|
#include <pcl/Diagnostics.h>
|
|
|
|
#include <pcl/UnidimensionalInterpolation.h>
|
|
|
|
namespace pcl
|
|
{
|
|
|
|
// ----------------------------------------------------------------------------
|
|
|
|
#define m_x this->m_x
|
|
#define m_y this->m_y
|
|
|
|
/*!
|
|
* \class CubicSplineInterpolation
|
|
* \brief Generic interpolating cubic spline
|
|
*
|
|
* Interpolation with piecewise cubic polynomials. Spline interpolation is
|
|
* usually preferred to interpolation with high-degree polynomials, which are
|
|
* subject to oscillations caused by the Runge's phenomenon.
|
|
*
|
|
* \sa AkimaInterpolation, LinearInterpolation
|
|
*/
|
|
template <typename T = double>
|
|
class PCL_CLASS CubicSplineInterpolation : public UnidimensionalInterpolation<T>
|
|
{
|
|
public:
|
|
|
|
typedef typename UnidimensionalInterpolation<T>::vector_type vector_type;
|
|
|
|
/*!
|
|
* Constructs an empty %CubicSplineInterpolation instance, which cannot be
|
|
* used for interpolation prior to initialization.
|
|
*/
|
|
CubicSplineInterpolation() = default;
|
|
|
|
/*!
|
|
* Copy constructor.
|
|
*/
|
|
CubicSplineInterpolation( const CubicSplineInterpolation& ) = default;
|
|
|
|
/*!
|
|
* Move constructor.
|
|
*/
|
|
CubicSplineInterpolation( CubicSplineInterpolation&& ) = default;
|
|
|
|
/*!
|
|
* Virtual destructor.
|
|
*/
|
|
virtual ~CubicSplineInterpolation()
|
|
{
|
|
}
|
|
|
|
/*!
|
|
* Gets the boundary conditions of this interpolating cubic spline.
|
|
*
|
|
* \param[out] y1 First derivative of the interpolating cubic spline at
|
|
* the first data point x[0].
|
|
*
|
|
* \param[out] yn First derivative of the interpolating cubic spline at
|
|
* the last data point x[n-1].
|
|
*/
|
|
void GetBoundaryConditions( double& y1, double& yn ) const
|
|
{
|
|
y1 = m_dy1;
|
|
yn = m_dyn;
|
|
}
|
|
|
|
/*!
|
|
* Sets the boundary conditions of this interpolating cubic spline.
|
|
*
|
|
* \param y1 First derivative of the interpolating cubic spline at the
|
|
* first data point x[0].
|
|
*
|
|
* \param yn First derivative of the interpolating cubic spline at the
|
|
* last data point x[n-1].
|
|
*/
|
|
void SetBoundaryConditions( double y1, double yn )
|
|
{
|
|
Clear();
|
|
m_dy1 = y1;
|
|
m_dyn = yn;
|
|
}
|
|
|
|
/*!
|
|
* Generation of an interpolating cubic spline.
|
|
*
|
|
* \param x %Vector of x-values:\n
|
|
* \n
|
|
* \li If \a x is not empty: Must be a vector of monotonically
|
|
* increasing, distinct values: x[0] < x[1] < ... < x[n-1].\n
|
|
* \li If \a x is empty: This function will generate a natural cubic
|
|
* spline with implicit x[i] = i for i = {0,1,...,n-1}.
|
|
*
|
|
* \param y %Vector of function values for i = {0,1,...,n-1}.
|
|
*
|
|
* When \a x is an empty vector, a <em>natural spline</em> is always
|
|
* generated: boundary conditions are ignored and taken as zero at both ends
|
|
* of the data sequence.
|
|
*
|
|
* The length of the \a y vector (and also the length of a nonempty \a x
|
|
* vector) must be \e n >= 2.
|
|
*/
|
|
void Initialize( const vector_type& x, const vector_type& y ) override
|
|
{
|
|
if ( y.Length() < 2 )
|
|
throw Error( "CubicSplineInterpolation::Initialize(): Less than two data points specified." );
|
|
|
|
try
|
|
{
|
|
Clear();
|
|
UnidimensionalInterpolation<T>::Initialize( x, y );
|
|
|
|
int n = this->Length();
|
|
m_dy2 = DVector( n );
|
|
m_current = -1; // prepare for 1st interpolation
|
|
DVector w( n ); // working vector
|
|
|
|
if ( m_x )
|
|
{
|
|
/*
|
|
* Cubic splines with explicit x[i] for i = {0,...,n-1}.
|
|
*/
|
|
if ( m_dy1 == 0 && m_dyn == 0 )
|
|
{
|
|
/*
|
|
* Natural cubic spline.
|
|
*/
|
|
m_dy2[0] = m_dy2[n-1] = w[0] = 0;
|
|
|
|
for ( int i = 1; i < n-1; ++i )
|
|
{
|
|
double s = (double( m_x[i] ) - double( m_x[i-1] )) / (double( m_x[i+1] ) - double( m_x[i-1] ));
|
|
double p = s*m_dy2[i-1] + 2;
|
|
m_dy2[i] = (s - 1)/p;
|
|
w[i] = (double( m_y[i+1] ) - double( m_y[i ] )) / (double( m_x[i+1] ) - double( m_x[i ] ))
|
|
- (double( m_y[i ] ) - double( m_y[i-1] )) / (double( m_x[i ] ) - double( m_x[i-1] ));
|
|
w[i] = (6*w[i]/(double( m_x[i+1] ) - double( m_x[i-1] )) - s*w[i-1])/p;
|
|
}
|
|
|
|
for ( int i = n-2; i > 0; --i ) // N.B. w[0] is not defined
|
|
m_dy2[i] = m_dy2[i]*m_dy2[i+1] + w[i];
|
|
}
|
|
else
|
|
{
|
|
/*
|
|
* Cubic spline with prescribed end point derivatives.
|
|
*/
|
|
w[0] = 3/(double( m_x[1] ) - double( m_x[0] ))
|
|
* ((double( m_y[1] ) - double( m_y[0] ))/(double( m_x[1] ) - double( m_x[0] )) - m_dy1);
|
|
|
|
m_dy2[0] = -0.5;
|
|
|
|
for ( int i = 1; i < n-1; ++i )
|
|
{
|
|
double s = (double( m_x[i] ) - double( m_x[i-1] )) / (double( m_x[i+1] ) - double( m_x[i-1] ));
|
|
double p = s*m_dy2[i-1] + 2;
|
|
m_dy2[i] = (s - 1)/p;
|
|
w[i] = (double( m_y[i+1] ) - double( m_y[i ] )) / (double( m_x[i+1] ) - double( m_x[i ] ))
|
|
- (double( m_y[i ] ) - double( m_y[i-1] )) / (double( m_x[i ] ) - double( m_x[i-1] ));
|
|
w[i] = (6*w[i]/(double( m_x[i+1] ) - double( m_x[i-1] )) - s*w[i-1])/p;
|
|
}
|
|
|
|
m_dy2[n-1] = (3/(double( m_x[n-1] ) - double( m_x[n-2] ))
|
|
* (m_dyn - (double( m_y[n-1] ) - double( m_y[n-2] ))/(double( m_x[n-1] ) - double( m_x[n-2] ))) - w[n-2]/2)
|
|
/ (1 + m_dy2[n-2]/2);
|
|
|
|
for ( int i = n-2; i >= 0; --i )
|
|
m_dy2[i] = m_dy2[i]*m_dy2[i+1] + w[i];
|
|
}
|
|
}
|
|
else
|
|
{
|
|
/*
|
|
* Natural cubic spline with
|
|
* implicit x[i] = i for i = {0,1,...,n-1}.
|
|
*/
|
|
m_dy2[0] = m_dy2[n-1] = w[0] = 0;
|
|
|
|
for ( int i = 1; i < n-1; ++i )
|
|
{
|
|
double p = m_dy2[i-1]/2 + 2;
|
|
m_dy2[i] = -0.5/p;
|
|
w[i] = double( m_y[i+1] ) - 2*double( m_y[i] ) + double( m_y[i-1] );
|
|
w[i] = (3*w[i] - w[i-1]/2)/p;
|
|
}
|
|
|
|
for ( int i = n-2; i > 0; --i ) // N.B. w[0] is not defined
|
|
m_dy2[i] = m_dy2[i]*m_dy2[i+1] + w[i];
|
|
}
|
|
}
|
|
catch ( ... )
|
|
{
|
|
Clear();
|
|
throw;
|
|
}
|
|
}
|
|
|
|
/*!
|
|
* Cubic spline interpolation. Returns an interpolated value at the
|
|
* specified point \a x.
|
|
*/
|
|
double operator()( double x ) const override
|
|
{
|
|
PCL_PRECONDITION( IsValid() )
|
|
|
|
int n = this->Length();
|
|
|
|
if ( m_x )
|
|
{
|
|
/*
|
|
* Cubic spline with explicit x[i] for i = {0,...,n-1}.
|
|
*/
|
|
|
|
/*
|
|
* Bracket the evaluation point x by binary search of the closest
|
|
* pair of data points, if needed. m_current < 0 signals first-time
|
|
* evaluation since initialization.
|
|
*/
|
|
int j0 = m_current, j1;
|
|
if ( j0 < 0 || x < m_x[j0] || m_x[j0+1] < x )
|
|
for ( j0 = 0, j1 = n-1; j1-j0 > 1; )
|
|
{
|
|
int m = (j0 + j1) >> 1;
|
|
if ( x < m_x[m] )
|
|
j1 = m;
|
|
else
|
|
j0 = m;
|
|
}
|
|
else
|
|
j1 = j0 + 1;
|
|
m_current = j0;
|
|
|
|
/*
|
|
* Distance h between the closest neighbors. Will be zero (or
|
|
* insignificant) if two or more x values are equal with respect to
|
|
* the machine epsilon for type T.
|
|
*/
|
|
double h = double( m_x[j1] ) - double( m_x[j0] );
|
|
if ( 1 + h == 1 )
|
|
return 0.5*(double( m_y[j0] ) + double( m_y[j1] ));
|
|
|
|
double a = (double( m_x[j1] ) - x)/h;
|
|
double b = (x - double( m_x[j0] ))/h;
|
|
return a*double( m_y[j0] )
|
|
+ b*double( m_y[j1] )
|
|
+ ((a*a*a - a)*m_dy2[j0] + (b*b*b - b)*m_dy2[j1])*h*h/6;
|
|
}
|
|
else
|
|
{
|
|
/*
|
|
* Natural cubic spline with implicit x[i] = i for i = {0,1,...,n-1}.
|
|
*/
|
|
int j0 = pcl::Range( pcl::TruncInt( x ), 0, n-1 );
|
|
int j1 = pcl::Min( n-1, j0+1 );
|
|
double a = j1 - x;
|
|
double b = x - j0;
|
|
return a*double( m_y[j0] )
|
|
+ b*double( m_y[j1] )
|
|
+ ((a*a*a - a)*m_dy2[j0] + (b*b*b - b)*m_dy2[j1])/6;
|
|
}
|
|
}
|
|
|
|
/*!
|
|
* Resets this cubic spline interpolation, deallocating all internal
|
|
* working structures.
|
|
*/
|
|
void Clear() override
|
|
{
|
|
UnidimensionalInterpolation<T>::Clear();
|
|
m_dy2.Clear();
|
|
}
|
|
|
|
/*!
|
|
* Returns true iff this interpolation is valid, i.e. if it has been
|
|
* correctly initialized and is ready to interpolate function values.
|
|
*/
|
|
bool IsValid() const override
|
|
{
|
|
return m_dy2;
|
|
}
|
|
|
|
private:
|
|
|
|
double m_dy1 = 0; // 1st derivative of spline at the first data point
|
|
double m_dyn = 0; // 1st derivative of spline at the last data point
|
|
DVector m_dy2; // second derivatives of the interpolating function at x[i]
|
|
mutable int m_current = -1; // index of the current interpolation segment
|
|
};
|
|
|
|
#undef m_x
|
|
#undef m_y
|
|
|
|
// ----------------------------------------------------------------------------
|
|
|
|
} // pcl
|
|
|
|
#endif // __PCL_CubicSplineInterpolation_h
|
|
|
|
// ----------------------------------------------------------------------------
|
|
// EOF pcl/CubicSplineInterpolation.h - Released 2022-03-12T18:59:29Z
|