casacore
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.
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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 
53 namespace 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