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Interpolate1D.h
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//# Interpolate1D.h: Interpolate in one dimension
//# Copyright (C) 1996,1997,1999,2002,2005
//# Associated Universities, Inc. Washington DC, USA.
//#
//# This library is free software; you can redistribute it and/or modify it
//# under the terms of the GNU Library General Public License as published by
//# the Free Software Foundation; either version 2 of the License, or (at your
//# option) any later version.
//#
//# This library 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 Library General Public
//# License for more details.
//#
//# You should have received a copy of the GNU Library General Public License
//# along with this library; if not, write to the Free Software Foundation,
//# Inc., 675 Massachusetts Ave, Cambridge, MA 02139, USA.
//#
//# Correspondence concerning AIPS++ should be addressed as follows:
//# Internet email: casa-feedback@nrao.edu.
//# Postal address: AIPS++ Project Office
//# National Radio Astronomy Observatory
//# 520 Edgemont Road
//# Charlottesville, VA 22903-2475 USA
#ifndef SCIMATH_INTERPOLATE1D_H
#define SCIMATH_INTERPOLATE1D_H
#include <casacore/casa/aips.h>
#include <casacore/scimath/Functionals/Function1D.h>
#include <casacore/casa/Containers/Block.h>
namespace casacore { //# NAMESPACE CASACORE - BEGIN
template<class Range> class SampledFunctional;
// <summary> Interpolate in one dimension </summary>
// <use visibility=export>
// <reviewed reviewer="wyoung" date="1996/10/18" tests="tInterpolate1D" demos="dInterpolate1D">
// </reviewed>
// <prerequisite>
// <li> <linkto class=SampledFunctional>SampledFunctional</linkto>
// <li> <linkto class=Function1D>Function1D</linkto>
// </prerequisite>
// <etymology>
// The Interpolate1D class does interpolation in one dimension only.
// </etymology>
// <synopsis>
// This class will, given the abscissa and ordinates of a set of one
// dimensional data, interpolate on this data set giving the value at any
// specified ordinate. It will extrapolate if necessary, but this is will
// usually give a poor result. There is no requirement for the ordinates to
// be regularly spaced, or even sorted in any numerical order. However each
// abscissa should have a unique value.
//
// Interpolation can be done using the following methods:
// <ul>
// <li> Nearest Neighbour (default if there is one data point)
// <li> Linear (default unless there is only one data point)
// <li> Cubic Polynomial
// <li> Natural Cubic Spline
// </ul>
//
// The restriction that each abcissus has a unique value can be lifted
// by setting the <src>uniq=True </src> option in the appropriate
// functions. This imposes the following additional restrictions on
// interpolation.
// <ul>
// <li> You cannot use cubic spline interpolation.
// <li> You cannot cannot interpolate within two data points of a repeated
// x-value when using cubic interpolation.
// <li> You cannot interpolate within one data point of a repeated
// x-value when using linear or nearest neighbour interpolation.
// </ul>
//
// The abscissa must be a SampledFunctional that returns a scalar value that
// can be ordered. ie. an uInt, Int, Float or Double (not Complex). The
// ordinate can be any data type that has addition, and subtraction defined
// as well as multiplication by a scalar. So the ordinate can be complex
// numbers, where the interpolation is done separately on the real and
// imaginary components, or an array, where the interpolation is done
// separately on an element by element basis.
//
// This class will curently make an internal copy of the data supplied to
// it, and sort the data if it is not told it is already sorted, by using
// the <src> sorted=True </src> flag.
// </synopsis>
// <example>
// This code fragment sets the interpolation method to cubic before
// interpolating on the supplied (x,y) vectors.
// <srcblock>
// Vector<Float> x(4); indgen(x);
// Vector<Double> y(4); indgen(y); y = y*y*y;
// ScalarSampledFunctional<Float> fx(x)
// ScalarSampledFunctional<Double> fy(y);
// Interpolate1D<Float, Double> gain(fx, fy);
// gain.setMethod(Interpolate1D<Float,Double>::cubic);
// for (Float xs = -1; xs < 5; xs += 0.1)
// cout << "gain(" << xs << "):" << gain(xs) << endl;
// </srcblock>
// </example>
// <motivation>
// This class is motivated by the need to interpolate over the gain
// solutions obtained from calibrator observations, in order to get the gain
// at arbitrary times.
// </motivation>
// <templating arg=Domain>
// <li> The Domain class must be a type that can be ordered in a mathematical
// sense. This includes uInt, Int, Float, Double, but not Complex.
// </templating>
// <templating arg=Range>
// <li> The Range class must have addition and subtraction of Range objects with
// each other as well as multiplication by a scalar defined. Besides the
// scalar types listed above this includes Complex, DComplex, and Arrays of
// any of these types.
// </templating>
// <thrown>
// <li> AipsError
// </thrown>
// <todo asof="1996/10/22">
// <li> avoid an internal copy of the data and have an index array as the
// only private data (plus the interpolation method and pointers to
// the actual data).
// <li> Review the use of copy semantics in the copy constructor &
// assignment operator after making the above change.
// </todo>
template <class Domain, class Range> class Interpolate1D :
public Function1D<Domain, Range> {
public:
// The different interpolation methods are enumerated here
enum Method {
// Crude but sometimes useful
nearestNeighbour,
// The most common method and the Default
linear,
// Fits a third order polynomial to 4 pts
cubic,
// Natural Cubic Splines
spline
};
// The default constructor generates a useless object until the setData
// function has been called.
Interpolate1D();
// Construct an object with the specified data
Interpolate1D(const SampledFunctional<Domain> &x,
const SampledFunctional<Range> &y,
const Bool sorted=False,
const Bool uniq=False);
// Define a new data set for the class to operate on. Equivalent in many
// aspects to creating a new object.
void setData(const SampledFunctional<Domain> &x,
const SampledFunctional<Range> &y,
const Bool sorted=False,
const Bool uniq=False);
// The standard copy constructor, assignment operator and
// destructor. Internal data is copied in both cases (copy semantics)
// <group>
Interpolate1D(const Interpolate1D<Domain, Range>& other);
Interpolate1D<Domain, Range> &
operator=(const Interpolate1D<Domain, Range> & other);
~Interpolate1D();
// </group>
// Name of function
virtual const String &name() const { static String x("interpolate1d");
return x; }
// Interpolation is done using the () operator (see example above). Actual
// use is through the virtual <src>eval()</src> function.
virtual Range eval(typename Function1D<Domain, Range>::FunctionArg x)
const;
// inquire/set the current interpolation method. uInts are used as
// arguments instead of the Interpolate1D::Method enumerator due to
// compiler limitations. See the example above (or the demo code) for the
// recommended way to call these functions.
// <group>
uInt getMethod() const {return curMethod;}
void setMethod(uInt method);
// </group>
// Access the data set that interpolation is done over. This will usually be
// sorted.
// <group>
Vector<Domain> getX() const;
Vector<Range> getY() const;
// </group>
// A function to copy the Interpolate1D object
// <group>
virtual Function<Domain, Range> *clone() const;
// </group>
private:
// A private function for doing polynomial interpolation
Range polynomialInterpolation(const Domain x, uInt n, uInt offset) const;
uInt curMethod; // interpolation method to use
uInt nElements; // how many elements in the data set
Block<Domain> xValues; // the abscissa of the data set (sorted)
Block<Range> yValues; // The corresponding ordinate of the data set
Block<Range> y2Values; // The numerical second derivates (only for splines)
};
} //# NAMESPACE CASACORE - END
#ifndef CASACORE_NO_AUTO_TEMPLATES
#include <casacore/scimath/Functionals/Interpolate1D.tcc>
#endif //# CASACORE_NO_AUTO_TEMPLATES
#endif
casacore::Block
Definition Block.h:140
casacore::Function1D::FunctionArg
const T * FunctionArg
Definition Function1D.h:76
casacore::Function1D< Domain, Range >::Function1D
Function1D()
Definition Function1D.h:81
casacore::Function
Definition Function.h:200
casacore::Interpolate1D::polynomialInterpolation
Range polynomialInterpolation(const Domain x, uInt n, uInt offset) const
A private function for doing polynomial interpolation.
casacore::Interpolate1D::setData
void setData(const SampledFunctional< Domain > &x, const SampledFunctional< Range > &y, const Bool sorted=False, const Bool uniq=False)
Define a new data set for the class to operate on.
casacore::Interpolate1D::Interpolate1D
Interpolate1D(const SampledFunctional< Domain > &x, const SampledFunctional< Range > &y, const Bool sorted=False, const Bool uniq=False)
Construct an object with the specified data.
casacore::Interpolate1D::Method
Method
The different interpolation methods are enumerated here.
Definition Interpolate1D.h:143
casacore::Interpolate1D::nearestNeighbour
@ nearestNeighbour
Crude but sometimes useful.
Definition Interpolate1D.h:145
casacore::Interpolate1D::linear
@ linear
The most common method and the Default.
Definition Interpolate1D.h:147
casacore::Interpolate1D::cubic
@ cubic
Fits a third order polynomial to 4 pts.
Definition Interpolate1D.h:149
casacore::Interpolate1D::spline
@ spline
Natural Cubic Splines.
Definition Interpolate1D.h:151
casacore::Interpolate1D::getY
Vector< Range > getY() const
casacore::Interpolate1D::curMethod
uInt curMethod
Definition Interpolate1D.h:214
casacore::Interpolate1D::clone
virtual Function< Domain, Range > * clone() const
A function to copy the Interpolate1D object.
casacore::Interpolate1D::Interpolate1D
Interpolate1D(const Interpolate1D< Domain, Range > &other)
The standard copy constructor, assignment operator and destructor.
casacore::Interpolate1D::nElements
uInt nElements
Definition Interpolate1D.h:215
casacore::Interpolate1D::xValues
Block< Domain > xValues
Definition Interpolate1D.h:216
casacore::Interpolate1D::getMethod
uInt getMethod() const
inquire/set the current interpolation method.
Definition Interpolate1D.h:194
casacore::Interpolate1D::~Interpolate1D
~Interpolate1D()
casacore::Interpolate1D::Interpolate1D
Interpolate1D()
The default constructor generates a useless object until the setData function has been called.
casacore::Interpolate1D::y2Values
Block< Range > y2Values
Definition Interpolate1D.h:218
casacore::Interpolate1D::setMethod
void setMethod(uInt method)
casacore::Interpolate1D::name
virtual const String & name() const
Name of function.
Definition Interpolate1D.h:181
casacore::Interpolate1D::operator=
Interpolate1D< Domain, Range > & operator=(const Interpolate1D< Domain, Range > &other)
casacore::Interpolate1D::yValues
Block< Range > yValues
Definition Interpolate1D.h:217
casacore::Interpolate1D::eval
virtual Range eval(typename Function1D< Domain, Range >::FunctionArg x) const
Interpolation is done using the () operator (see example above).
casacore::Interpolate1D::getX
Vector< Domain > getX() const
Access the data set that interpolation is done over.
casacore::SampledFunctional
Definition SampledFunctional.h:101
casacore::String
String: the storage and methods of handling collections of characters.
Definition String.h:223
casacore::Vector
Definition Vector.h:82
casacore
this file contains all the compiler specific defines
Definition mainpage.dox:28
casacore::False
const Bool False
Definition aipstype.h:42
casacore::offset
int offset(int, int) const
compute a linear offset from array indicies
casacore::uInt
unsigned int uInt
Definition aipstype.h:49
casacore::Bool
bool Bool
Define the standard types used by Casacore.
Definition aipstype.h:40