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Functionals.h
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1//# Functionals.h: A module that represents various function-like classes.
2//# Copyright (C) 1995,1996,1998,1999,2001,2002
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
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25//#
26//# $Id$
27
28
29#ifndef SCIMATH_FUNCTIONALS_H
30#define SCIMATH_FUNCTIONALS_H
31
32//# Base classes
33#include <casacore/casa/aips.h>
34#include <casacore/casa/BasicMath/Functional.h>
35#include <casacore/scimath/Functionals/FunctionTraits.h>
36#include <casacore/scimath/Functionals/FunctionParam.h>
37#include <casacore/scimath/Functionals/Function.h>
38#include <casacore/scimath/Functionals/Function1D.h>
39
40//# Combination methods
41#include <casacore/scimath/Functionals/FunctionWrapper.h>
42#include <casacore/scimath/Functionals/CombiFunction.h>
43#include <casacore/scimath/Functionals/CompoundFunction.h>
44
45//# remainder will be removed
46#include <casacore/scimath/Functionals/SampledFunctional.h>
47
48//# 1-D Functions
49#include <casacore/scimath/Functionals/Interpolate1D.h>
50#include <casacore/scimath/Functionals/ArraySampledFunctional.h>
51#include <casacore/scimath/Functionals/ScalarSampledFunctional.h>
52
53namespace casacore { //# NAMESPACE CASACORE - BEGIN
54
55// <module>
56//
57// <summary>A module that represents various function-like classes.</summary>
58
59// <reviewed reviewer="tcornwel" date="1996/02/13" demos=""></reviewed>
60
61// <etymology>
62// The term <src>Functional</src> was chosen to roughly follow the usage in
63// Barton and Nackman's <em>Scientific and Engineering C++</em>.
64// Functional classes map a Domain object into a Range object, rather like a
65// mathematical <src>function</src>. They use <src>operator()</src>,
66// so they look much like single argument C++ <src>functions</src>.
67// </etymology>
68//
69// <synopsis>
70// <src>Functionals</src> and their derived classes map an input
71// <src>Domain</src> object into an output <src>Range</src> object using the
72// <src>operator()</src>.
73// Often the input and output types are numeric, but it can be of any type.
74// <srcblock>
75// class Offspring : public Functional<List<Parents>, List<Children> > {
76// public:
77// List<Children> operator()(List<Parents>);
78// };
79// </srcblock>
80// would be a legal Functional.
81//
82// The <src>Functions</src> and their derived classes map, again using the
83// <src>operator()</src>, numeric value(s) into a numeric value. Since they are
84// numeric, the <src>Domain</src> and <src>Range</src> base type can be of type
85// <src>AutoDiff<T></src> (where <src>T</src> is numeric base type) or one
86// of its derivations, in which case the value and its derivatives will be
87// calculated.
88//
89// <note role=warning> In the current version the <src>Domain</src> and
90// <src>Range</src> are the same for Functions </note>
91//
92// The basic classes are:
93// <dl>
94// <dt> <linkto class=Functional><src>Functional<Domain, Range></src></linkto>
95// <dd>
96// A base class that maps a <src>Domain</src> object into a <src>Range</src>
97// object using the <src>Range operator(const Domain &)</src>. All
98// information necessary to convert the <src>Domain</src> into a
99// <src>Range</src> will be available in the class
100// or in the input information. No variable class state (<em>parameters</em>)
101// are available.
102//
103// <dt> <linkto class=FunctionParam><src>FunctionParam<T></src></linkto>
104// <dd> A helper base class that acts as a container for <em>parameters</em>
105// (<em>state</em>) used in <src>Function</src> classes. The class contains
106// a list of parameters, and a list of flags associated with the parameters.
107// Methods to set and obtain the parameters (using <src>operator[]</src>)
108// and their flags (using methods <src>mask()</src>) are available. The flags
109// can e.g. be used to indicate to <src>Fitting</src> routines if a certain
110// parameter has to be updated ('fitted') or not.
111// <note role=tip>
112// The FunctionParam class does not assume anything about the uses of the
113// class, but leaves that to the final users. This means that a lot of
114// copying between intermediate and final users is not necessary
115// (like between a Gaussian fitter with fixed parameters
116// and the Fitting routines: the Gaussian fitter just sets a flag to False, and
117// let the Fitting worry about what to do internally).
118// </note>
119//
120// <dt> <linkto class=Function><src>Function<T></src></linkto>
121// <dd> Base class for function objects with zero or more parameters (i.e.
122// Functionals with state).
123// All parameters should be of the same type <em>T</em> as the <src>
124// Function<T></src>. <src>Function</src> objects are specifically geared
125// towards use in the <linkto module=Fitting>Fitting</linkto> classes, but
126// can be used anywhere where the value (and/or derivatives) of functions
127// are needed.
128//
129// The <src>Function<T></src> class is derived from <src>Functional</src>
130// and contains a <src>FunctionParam<T></src> object.
131// The parameters act as state for the function
132// (e.g. a width for a Gaussian). A function object is called using the
133// <src>T operator(const T&)</src> (<em>ndim=1</em>), or the
134// <src>T operator(const Vector<T>&)</src> (all values of <em>ndim</em>), or
135// <src>T operator(const T&, const T&)</src> (for <em>ndim=2</em> only).
136// If the template argument is <src>AutoDiff<T></src>, the parameters and the
137// returned value will be <src>AutoDiff<T></src>; the arguments of the
138// <src>operator()</src> will be of type <src>T</src>. The returned value
139// of the function will be the function value at <em>x</em> (and the
140// derivatives w.r.t. the non-masked parameters) Using <src>AutoDiffA<T></src>
141// the derivatives can be calculated w.r.t. parameters and/or arguments, see
142// <linkto class=AutoDiff>AutoDiff</linkto> and <linkto class=FunctionTraits>
143// FunctionTraits</linkto> for details.
144//
145// <note role=tip>
146// A <src>Function1D</src> is provided for 1-dimensional function objects
147// </note>
148// </dl>
149//
150// Actual functional classes:
151// <dl>
152// <dt> e.g. <linkto
153// class=Gaussian1D><src>Gaussian1D<T></src></linkto>
154// <dd> An actual function object will be derived from
155// <src>Function<T></src>. The minimum functionality of a Function
156// object will be support for the <src>operator()</src> methods (through a
157// single, hidden, <src>eval()</src> method); for the manipulation of the
158// associated parameters (using <src>operator[index]</src> and
159// <src>mask(index)</src>) and some administrative aids (<src>ndim()</src>,
160// <src>nparameters()</src> and the like.
161//
162// In most cases it is advantageous to have a special parameter handling
163// class (e.g. <src>Gaussian1DParam</src>), to separate the (template
164// independent) parameter handling from the possible specialization of
165// the <src>eval()</src> method, and to more easily incorporate
166// special parameter handling (e.g. using <em>flux</em> rather than amplitude
167// of a Gaussian). All of this is transparent to the end-user.
168// </dl>
169// Combinatory Function objects are provided to easily combine and create
170// function objects:
171// <dl>
172// <dt> <linkto class=CompoundFunction>CompoundFunction</linkto>
173// <dd> creates
174// a new, compound, function object from one or more other function objects
175// (including compounds...). The new function will have the sum of the
176// parameters of the input functions as the new parameters (i.e. the compound
177// function created from a 1-dimensional Gaussian (with 3 parameters) and a
178// third-order polynomial (with 4 parameters) will have 7 parameters).
179// <dt> <linkto class=CombiFunction>CombiFunction</linkto>
180// <dd> creates
181// a (linear) combination of a number of input functions. The number of
182// parameters of the newly created function will be equal to the number of
183// input functions (i.e. the combi
184// function created from a 1-dimensional Gaussian (with 3 parameters) and a
185// third-order polynomial (with 4 parameters) will have 2 parameters). The
186// function will be <src>param0*gauss(x) + param1*poly(x)</src>
187// <dt> <linkto class=FunctionWrapper>FunctionWrapper</linkto>
188// <dd> will take
189// a global function (or by the use of the <em>STL</em> function adapters
190// <src>mem_fun*</src> also member functions) of any dimension, and with
191// any number of parameters. The function is assumed to be called as
192// <src>f(x, p)</src>, and is wrapped like
193// <src>FunctionWrapper(&func, param&, ndim)</src> (see example).
194//
195// </dl>
196//
197// </synopsis>
198
199// <example>
200// A function to find a bracketed root by bisection could be written
201// as follows:
202// <srcblock>
203// template <class Domain, class Range>
204// Domain findRoot(const Functional<Domain,Range> &func, Domain left,
205// Domain right, Domain tol) {
206// Range fr = func(right);
207// Range fl = func(left);
208// Range sign = fr > 0 ? 1 : -1 ;
209// AlwaysAssertExit(fl*fr < 0.0 && right > left);
210// while (right - left > tol) {
211// Domain mid = (left + right) / 2;
212// Range fmid = func(mid);
213// if (sign*fmid > 0.0) right = mid;
214// else left = mid;
215// };
216// return (left + right)/2;
217// }
218// </srcblock>
219// Since Function1D is derived from Functional, the
220// above function will also work with classes derived from Function1D. To
221// behave sensibly, the Domain and Range types should be real, <em>i.e.</em>,
222// Float or Double.
223//
224// To calculate the value of a polynomial
225// <srcblock>2 + 4x<sup>2</sup> + 6x<sup>4</sup></srcblock>
226// at <src>x=5.1</src>:
227// <srcblock>
228// Polynomial<Double> pol(4);
229// pol[0] = 2; pol[2] = 4; pol[4] = 6;
230// cout << "Polynomial value at 5.1: " << pol(5.1) << endl;
231// </srcblock>
232//
233// Create a simple function (1-dimensional) with 2 parameters (A and B):
234// <srcblock>
235// Double myf(const Double x, const Vector<Double> p) {
236// return p[0]*sin(p[1]*x); }
237// </srcblock>
238// make it into a function object for initial parameters 2 and pi:
239// <srcblock>
240// Vector<Double> p(2);
241// p[0] = 2; p[1] = C::pi;
242// FunctionWrapper<Double> f0(myf, p, 2);
243// </srcblock>
244// Make the first parameter 3:
245// <srcblock>
246// f0[0] = 3;
247// </srcblock>
248// (for the global function you have to change <src>p[0]</src>).
249// Calculate the value of the function:
250// <srcblock>
251// cout << "The value " << f0(3) << " should be 1.5 times the value " <<
252// myf(3) << endl;
253// </srcblock>
254// A function object could be created as:
255// <srcblock>
256// template<class T> class objf : public Function<T> {
257// public:
258// objf() : Function<T>(2) {}; // 2 parameters
259// objf(const objf<T> &other) : Function<T>(other) {};
260// virtual ~objf() {};
261// // The actual method called for the evaluation operator():
262// virtual T eval(typename Function<T>::FunctionArg x) const {
263// return param_p[0] * sin(param_p[1] * x[0]); };
264// // Return a copy of function (used for combination e.g.)
265// virtual Function<T> *clone() const {
266// return new objf<T>(*this); };
267// };
268// </srcblock>
269// Which can be called as:
270// <srcblock>
271// objf<Double> f1;
272// f1[0] = 2; f1[1] = C::pi;
273// cout << "The value " << myf(3) << " should be equal to the value " <<
274// f1(3) << endl;
275// </srcblock>
276// </example>
277
278// <motivation>
279// The immediate motivations for this module were:
280// <ol>
281// <li> To represent functions which are used in linear and non-linear least
282// squares fitting
283// </ol>
284// </motivation>
285
286// <todo asof="2001/12/30">
287// <li> It could be convenient to have a letter/envelope class, and to
288// define ``function arithmetic.''
289// </todo>
290
291// </module>
292
293
294} //# NAMESPACE CASACORE - END
295
296#endif
297
this file contains all the compiler specific defines
Definition: mainpage.dox:28