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Interpolate1D.h
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1//# Interpolate1D.h: Interpolate in one dimension
2//# Copyright (C) 1996,1997,1999,2002,2005
3//# Associated Universities, Inc. Washington DC, USA.
4//#
5//# This library is free software; you can redistribute it and/or modify it
6//# under the terms of the GNU Library General Public License as published by
7//# the Free Software Foundation; either version 2 of the License, or (at your
8//# option) any later version.
9//#
10//# This library is distributed in the hope that it will be useful, but WITHOUT
11//# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
12//# FITNESS FOR A PARTICULAR PURPOSE. See the GNU Library General Public
13//# License for more details.
14//#
15//# You should have received a copy of the GNU Library General Public License
16//# along with this library; if not, write to the Free Software Foundation,
17//# Inc., 675 Massachusetts Ave, Cambridge, MA 02139, USA.
18//#
19//# Correspondence concerning AIPS++ should be addressed as follows:
20//# Internet email: aips2-request@nrao.edu.
21//# Postal address: AIPS++ Project Office
22//# National Radio Astronomy Observatory
23//# 520 Edgemont Road
24//# Charlottesville, VA 22903-2475 USA
25//# $Id$
26
27#ifndef SCIMATH_INTERPOLATE1D_H
28#define SCIMATH_INTERPOLATE1D_H
29
30#include <casacore/casa/aips.h>
31#include <casacore/scimath/Functionals/Function1D.h>
32#include <casacore/casa/Containers/Block.h>
33
34namespace casacore { //# NAMESPACE CASACORE - BEGIN
35
36template<class Range> class SampledFunctional;
37
38// <summary> Interpolate in one dimension </summary>
39
40// <use visibility=export>
41
42// <reviewed reviewer="wyoung" date="1996/10/18" tests="tInterpolate1D" demos="dInterpolate1D">
43// </reviewed>
44
45// <prerequisite>
46// <li> <linkto class=SampledFunctional>SampledFunctional</linkto>
47// <li> <linkto class=Function1D>Function1D</linkto>
48// </prerequisite>
49
50// <etymology>
51// The Interpolate1D class does interpolation in one dimension only.
52// </etymology>
53
54// <synopsis>
55// This class will, given the abscissa and ordinates of a set of one
56// dimensional data, interpolate on this data set giving the value at any
57// specified ordinate. It will extrapolate if necessary, but this is will
58// usually give a poor result. There is no requirement for the ordinates to
59// be regularly spaced, or even sorted in any numerical order. However each
60// abscissa should have a unique value.
61//
62// Interpolation can be done using the following methods:
63// <ul>
64// <li> Nearest Neighbour (default if there is one data point)
65// <li> Linear (default unless there is only one data point)
66// <li> Cubic Polynomial
67// <li> Natural Cubic Spline
68// </ul>
69//
70// The restriction that each abcissus has a unique value can be lifted
71// by setting the <src>uniq=True </src> option in the appropriate
72// functions. This imposes the following additional restrictions on
73// interpolation.
74// <ul>
75// <li> You cannot use cubic spline interpolation.
76// <li> You cannot cannot interpolate within two data points of a repeated
77// x-value when using cubic interpolation.
78// <li> You cannot interpolate within one data point of a repeated
79// x-value when using linear or nearest neighbour interpolation.
80// </ul>
81//
82// The abscissa must be a SampledFunctional that returns a scalar value that
83// can be ordered. ie. an uInt, Int, Float or Double (not Complex). The
84// ordinate can be any data type that has addition, and subtraction defined
85// as well as multiplication by a scalar. So the ordinate can be complex
86// numbers, where the interpolation is done separately on the real and
87// imaginary components, or an array, where the interpolation is done
88// separately on an element by element basis.
89//
90// This class will curently make an internal copy of the data supplied to
91// it, and sort the data if it is not told it is already sorted, by using
92// the <src> sorted=True </src> flag.
93// </synopsis>
94
95// <example>
96// This code fragment sets the interpolation method to cubic before
97// interpolating on the supplied (x,y) vectors.
98// <srcblock>
99// Vector<Float> x(4); indgen(x);
100// Vector<Double> y(4); indgen(y); y = y*y*y;
101// ScalarSampledFunctional<Float> fx(x)
102// ScalarSampledFunctional<Double> fy(y);
103// Interpolate1D<Float, Double> gain(fx, fy);
104// gain.setMethod(Interpolate1D<Float,Double>::cubic);
105// for (Float xs = -1; xs < 5; xs += 0.1)
106// cout << "gain(" << xs << "):" << gain(xs) << endl;
107// </srcblock>
108// </example>
109
110// <motivation>
111// This class is motivated by the need to interpolate over the gain
112// solutions obtained from calibrator observations, in order to get the gain
113// at arbitrary times.
114// </motivation>
115
116// <templating arg=Domain>
117// <li> The Domain class must be a type that can be ordered in a mathematical
118// sense. This includes uInt, Int, Float, Double, but not Complex.
119// </templating>
120
121// <templating arg=Range>
122// <li> The Range class must have addition and subtraction of Range objects with
123// each other as well as multiplication by a scalar defined. Besides the
124// scalar types listed above this includes Complex, DComplex, and Arrays of
125// any of these types.
126// </templating>
127
128// <thrown>
129// <li> AipsError
130// </thrown>
131
132// <todo asof="1996/10/22">
133// <li> avoid an internal copy of the data and have an index array as the
134// only private data (plus the interpolation method and pointers to
135// the actual data).
136// <li> Review the use of copy semantics in the copy constructor &
137// assignment operator after making the above change.
138// </todo>
139
140template <class Domain, class Range> class Interpolate1D :
141public Function1D<Domain, Range> {
142public:
143 // The different interpolation methods are enumerated here
144 enum Method {
145 // Crude but sometimes useful
147 // The most common method and the Default
149 // Fits a third order polynomial to 4 pts
151 // Natural Cubic Splines
152 spline
153 };
154
155 // The default constructor generates a useless object until the setData
156 // function has been called.
158
159 // Construct an object with the specified data
161 const SampledFunctional<Range> &y,
162 const Bool sorted=False,
163 const Bool uniq=False);
164
165 // Define a new data set for the class to operate on. Equivalent in many
166 // aspects to creating a new object.
168 const SampledFunctional<Range> &y,
169 const Bool sorted=False,
170 const Bool uniq=False);
171
172 // The standard copy constructor, assignment operator and
173 // destructor. Internal data is copied in both cases (copy semantics)
174 // <group>
179 // </group>
180
181 // Name of function
182 virtual const String &name() const { static String x("interpolate1d");
183 return x; }
184
185 // Interpolation is done using the () operator (see example above). Actual
186 // use is through the virtual <src>eval()</src> function.
188 const;
189
190 // inquire/set the current interpolation method. uInts are used as
191 // arguments instead of the Interpolate1D::Method enumerator due to
192 // compiler limitations. See the example above (or the demo code) for the
193 // recommended way to call these functions.
194 // <group>
195 uInt getMethod() const {return curMethod;}
196 void setMethod(uInt method);
197 // </group>
198
199 // Access the data set that interpolation is done over. This will usually be
200 // sorted.
201 // <group>
204 // </group>
205
206 // A function to copy the Interpolate1D object
207 // <group>
209 // </group>
210
211private:
212 // A private function for doing polynomial interpolation
213 Range polynomialInterpolation(const Domain x, uInt n, uInt offset) const;
214
215 uInt curMethod; // interpolation method to use
216 uInt nElements; // how many elements in the data set
217 Block<Domain> xValues; // the abscissa of the data set (sorted)
218 Block<Range> yValues; // The corresponding ordinate of the data set
219 Block<Range> y2Values; // The numerical second derivates (only for splines)
220
221};
222
223
224} //# NAMESPACE CASACORE - END
225
226#ifndef CASACORE_NO_AUTO_TEMPLATES
227#include <casacore/scimath/Functionals/Interpolate1D.tcc>
228#endif //# CASACORE_NO_AUTO_TEMPLATES
229#endif
simple 1-D array
Definition Block.h:200
const T * FunctionArg
Definition Function1D.h:78
Range polynomialInterpolation(const Domain x, uInt n, uInt offset) const
A private function for doing polynomial interpolation.
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.
Interpolate1D(const SampledFunctional< Domain > &x, const SampledFunctional< Range > &y, const Bool sorted=False, const Bool uniq=False)
Construct an object with the specified data.
Method
The different interpolation methods are enumerated here.
@ nearestNeighbour
Crude but sometimes useful.
@ linear
The most common method and the Default.
@ cubic
Fits a third order polynomial to 4 pts
@ spline
Natural Cubic Splines.
Vector< Range > getY() const
virtual Function< Domain, Range > * clone() const
A function to copy the Interpolate1D object.
Interpolate1D(const Interpolate1D< Domain, Range > &other)
The standard copy constructor, assignment operator and destructor.
Block< Domain > xValues
uInt getMethod() const
inquire/set the current interpolation method.
Interpolate1D()
The default constructor generates a useless object until the setData function has been called.
void setMethod(uInt method)
virtual const String & name() const
Name of function.
Interpolate1D< Domain, Range > & operator=(const Interpolate1D< Domain, Range > &other)
virtual Range eval(typename Function1D< Domain, Range >::FunctionArg x) const
Interpolation is done using the () operator (see example above).
Vector< Domain > getX() const
Access the data set that interpolation is done over.
String: the storage and methods of handling collections of characters.
Definition String.h:225
this file contains all the compiler specific defines
Definition mainpage.dox:28
const Bool False
Definition aipstype.h:44
unsigned int uInt
Definition aipstype.h:51
bool Bool
Define the standard types used by Casacore.
Definition aipstype.h:42