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SparseDiff.h
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1//# SparseDiff.h: An automatic differentiating class for functions
2//# Copyright (C) 2007,2008
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
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25//#
26//#
27//# $Id: SparseDiff.h,v 1.3 2008/01/10 12:00:42 wbrouw Exp $
28
29#ifndef SCIMATH_SPARSEDIFF_H
30#define SCIMATH_SPARSEDIFF_H
31
32//# Includes
33#include <casacore/casa/aips.h>
34#include <casacore/scimath/Mathematics/AutoDiff.h>
35#include <casacore/scimath/Mathematics/SparseDiffRep.h>
36#include <casacore/casa/vector.h>
37#include <utility>
38
39// Using
40using std::pair;
41
42namespace casacore { //# NAMESPACE CASACORE - BEGIN
43
44 //# Forward declarations
45 template <class T> class SparseDiff;
46
47 // <summary>
48 // Class that computes partial derivatives by automatic differentiation.
49 // </summary>
50 //
51 // <use visibility=export>
52 //
53 // <reviewed reviewer="UNKNOWN" date="" tests="tSparseDiff.cc" demos="dSparseDiff.cc">
54 // </reviewed>
55 //
56 // <prerequisite>
57 // <li> <linkto class=AutoDiff>AutoDiff</linkto> class
58 // </prerequisite>
59 //
60 // <etymology>
61 // Class that computes partial derivatives for some parameters by automatic
62 // differentiation, thus SparseDiff.
63 // </etymology>
64 //
65 // <synopsis>
66 // Class that computes partial derivatives by automatic differentiation.
67 // It does this by storing the value of a function and the values of its first
68 // derivatives with respect to some of its independent parameters.
69 // When a mathematical
70 // operation is applied to a SparseDiff object, the derivative values of the
71 // resulting new object are computed according to the chain rules
72 // of differentiation. SparseDiff operates like the
73 // <linkto class=AutoDiff>AutoDiff</linkto> class, but only determines the
74 // derivatives with respect to the actual dependent variables.
75 //
76 // Suppose we have a function f(x0,x1,...,xn) and its differential is
77 // <srcblock>
78 // df = (df/dx0)*dx0 + (df/dx1)*dx1 + ... + (df/dxn)*dxn
79 // </srcblock>
80 // We can build a class that has the value of the function,
81 // f(x0,x1,...,xn), and the values of the derivatives, (df/dx0), (df/dx1),
82 // ..., (df/dxn) at (x0,x1,...,xn), as class members.
83 //
84 // Now if we have another function, g(x0,x1,...,xn) and its differential is
85 // dg = (dg/dx0)*dx0 + (dg/dx1)*dx1 + ... + (dg/dxn)*dxn,
86 // since
87 // <srcblock>
88 // d(f+g) = df + dg,
89 // d(f*g) = g*df + f*dg,
90 // d(f/g) = df/g - fdg/g^2,
91 // dsin(f) = cos(f)df,
92 // ...,
93 // </srcblock>
94 // we can calculate
95 // <srcblock>
96 // d(f+g), d(f*g), ...,
97 // </srcblock> based on our information on
98 // <srcblock>
99 // df/dx0, df/dx1, ..., dg/dx0, dg/dx1, ..., dg/dxn.
100 // </srcblock>
101 // All we need to do is to define the operators and derivatives of common
102 // mathematical functions.
103 //
104 // To be able to use the class as an automatic differentiator of a function
105 // object, we need a templated function object, i.e. an object with:
106 // <ul>
107 // <li> a <src> template <class T> T operator()(const T)</src>
108 // <li> or multiple variable input like:
109 // <src> template <class T> T operator()(const Vector<T> &)</src>
110 // <li> all dependent variables used in the calculation of the function
111 // value should have been typed with T.
112 // </ul>
113 // A simple example of such a function object could be:
114 // <srcblock>
115 // template <class T> f {
116 // public:
117 // T operator()(const T &x, const T &a, const T &b) {
118 // return a*b*x; }
119 // };
120 // // Instantiate the following versions:
121 // template class f<Double>;
122 // template class f<SparseDiff<Double> >;
123 // </srcblock>
124 // A call with values will produce the function value:
125 // <srcblock>
126 // cout << f(7.0, 2.0, 3.0) << endl;
127 // // will produce the value at x=7 for a=2; b=3:
128 // 42
129 // // But a call indicating that we want derivatives to a and b:
130 // cout << f(SparseDiff<Double>(7.0), SparseDiff<Double>(2.0, 0),
131 // SparseDiff<Double>(3.0, 1)) << endl;
132 // // will produce the value at x=7 for a=2; b=3:
133 // // and the partial derivatives wrt a and b at x=7:
134 // (42, [21, 14])
135 // // The following will calculate the derivate wrt x:
136 // cout << f(SparseDiff<Double>(7.0, 0), SparseDiff<Double>(2.0),
137 // SparseDiff<Double>(3.0)) << endl;
138 // (42,[6])
139 // </srcblock>
140 // Note that in practice constants may be given as Double constants.
141 // In actual practice, there are a few rules to obey for the structure of
142 // the function object if you want to use the function object and its
143 // derivatives in least squares fitting procedures in the Fitting
144 // module. The major one is to view the function object having 'fixed' and
145 // 'variable' parameters. I.e., rather than viewing the function as
146 // depending on parameters <em>a, b, x</em> (<src>f(a,b,x)</src>), the
147 // function is considered to be <src>f(x; a,b)</src>, where <em>a, b</em>
148 // are 'fixed' parameters, and <em>x</em> a variable parameter.
149 // Fixed parameters should be contained in a
150 // <linkto class=FunctionParam>FunctionParam</linkto> container object;
151 // while the variable parameter(s) are given in the function
152 // <src>operator()</src>. See <linkto class=Function>Function</linkto> class
153 // for details.
154 //
155 // A Gaussian spectral profile would in general have the center frequency,
156 // the width and the amplitude as fixed parameters, and the frequency as
157 // a variable. Given a spectrum, you would solve for the fixed parameters,
158 // given spectrum values. However, in other cases the role of the
159 // parameters could be reversed. An example could be a whole stack of
160 // observed (in the laboratory) spectra at different temperatures at
161 // one frequency. In that case the width would be the variable parameter,
162 // and the frequency one of the fixed (and to be solved for)parameters.
163 //
164 // Since the calculation of the derivatives is done with simple overloading,
165 // the calculation of second (and higher) derivatives is easy. It should be
166 // noted that higher deivatives are inefficient in the current incarnation
167 // (there is no knowledge e.g. about symmetry in the Jacobian). However,
168 // it is a very good way to get the correct answers of the derivatives. In
169 // practice actual production code will be better off with specialization
170 // of the <src>f<SparseDiff<> ></src> implementation.
171 //
172 // The <src>SparseDiff</src> class is the class the user communicates with.
173 // Alias classes (<linkto class=SparseDiffA>SparseDiffA</linkto> and
174 // <linkto class=SparseDiffA>SparseDiffX</linkto>) exist
175 // to make it possible to have different incarnations of a templated
176 // method (e.g. a generic one and a specialized one). See the
177 // <src>dSparseDiff</src> demo for an example of its use.
178 //
179 // All operators and functions are declared in <linkto file=SparseDiffMath.h>
180 // SparseDiffMath</linkto>. The output operator in
181 // <linkto file=SparseDiffIO.h>SparseDiffIO</linkto>.
182 // The actual structure of the
183 // data block used by <src>SparseDiff</src> is described in
184 // <linkto class=SparseDiffRep>SparseDiffRep</linkto>.
185 //
186 // A SparseDiff can be constructed from an AutoDiff.
187 // <em>toAutoDiff(n)</em> can convert it to an AutoDiff.
188 // </synopsis>
189 //
190 // <example>
191 // <srcblock>
192 // // First a simple example.
193 // // We have a function of the form f(x,y,z); and want to know the
194 // // value of the function for x=10; y=20; z=30; and for
195 // // the derivatives at those points.
196 // // Specify the values; and indicate the parameter dependence:
197 // SparseDiff<Double> x(10.0, 0);
198 // SparseDiff<Double> y(20.0, 1);
199 // SparseDiff<Double> z(30.0, 2);
200 // // The result will be:
201 // SparseDiff<Double> result = x*y + sin(z);
202 // cout << result.value() << endl;
203 // // 199.012
204 // cout << result.derivatives() << endl;
205 // // [20, 10, 0.154251]
206 // // Note: sin(30) = -0.988; cos(30) = 0.154251;
207 // </srcblock>
208 //
209 // See for an extensive example the demo program dSparseDiff. It is
210 // based on the example given above, and shows also the use of second
211 // derivatives (which is just using <src>SparseDiff<SparseDiff<Double> ></src>
212 // as template argument).
213 // <srcblock>
214 // // The function, with fixed parameters a,b:
215 // template <class T> class f {
216 // public:
217 // T operator()(const T& x) { return a_p*a_p*a_p*b_p*b_p*x; }
218 // void set(const T& a, const T& b) { a_p = a; b_p = b; }
219 // private:
220 // T a_p;
221 // T b_p;
222 // };
223 // // Call it with different template arguments:
224 // Double a0(2), b0(3), x0(7);
225 // f<Double> f0; f0.set(a0, b0);
226 // cout << "Value: " << f0(x0) << endl;
227 //
228 // SparseDiff<Double> a1(2,0), b1(3,1), x1(7);
229 // f<SparseDiff<Double> > f1; f1.set(a1, b1);
230 // cout << "Diff a,b: " << f1(x1) << endl;
231 //
232 // SparseDiff<Double> a2(2), b2(3), x2(7,0);
233 // f<SparseDiff<Double> > f2; f2.set(a2, b2);
234 // cout << "Diff x: " << f2(x2) << endl;
235 //
236 // SparseDiff<SparseDiff<Double> > a3(SparseDiff<Double>(2,0),0),
237 // b3(SparseDiff<Double>(3,1),1), x3(SparseDiff<Double>(7));
238 // f<SparseDiff<SparseDiff<Double> > > f3; f3.set(a3, b3);
239 // cout << "Diff2 a,b: " << f3(x3) << endl;
240 //
241 // SparseDiff<SparseDiff<Double> > a4(SparseDiff<Double>(2)),
242 // b4(SparseDiff<Double>(3)),
243 // x4(SparseDiff<Double>(7,0),0);
244 // f<SparseDiff<SparseDiff<Double> > > f4; f4.set(a4, b4);
245 // cout << "Diff2 x: " << f4(x4) << endl;
246 //
247 // // Result will be:
248 // // Value: 504
249 // // Diff a,b: (504, [756, 336])
250 // // Diff x: (504, [72])
251 // // Diff2 a,b: ((504, [756, 336]), [(756, [756, 504]), (336, [504, 112])])
252 // // Diff2 x: ((504, [72]), [(72, [0])])
253 //
254 // // It needed the template instantiations definitions:
255 // template class f<Double>;
256 // template class f<SparseDiff<Double> >;
257 // template class f<SparseDiff<SparseDiff<Double> > >;
258 // </srcblock>
259 // </example>
260 //
261 // <motivation>
262 // The creation of the class was motivated by least-squares non-linear fits
263 // in cases where each individual condition equation depends only on a
264 // fraction of the fixed parameters (e.g. self-calibration where only pairs
265 // of antennas are present per equation), and hence only a few
266 // partial derivatives of a fitted function are needed. It would be tedious
267 // to create functionals for all partial derivatives of a function.
268 // </motivation>
269 //
270 // <templating arg=T>
271 // <li> any class that has the standard mathematical and comparison
272 // operators and functions defined.
273 // </templating>
274 //
275 // <todo asof="2007/11/27">
276 // <li> Nothing I know of.
277 // </todo>
278
279 template <class T> class SparseDiff {
280 public:
281 //# Typedefs
282 typedef T value_type;
287
288 //# Constructors
289 // Construct a constant with a value of zero. Zero derivatives.
291
292 // Construct a constant with a value of v. Zero derivatives.
293 SparseDiff(const T &v);
294
295 // A function f(x0,x1,...,xn,...) with a value of v. The
296 // nth derivative is one, and all other derivatives are zero.
297 SparseDiff(const T &v, const uInt n);
298
299 // A function f(x0,x1,...,xn,...) with a value of v. The
300 // nth derivative is der, and all other derivatives are zero.
301 SparseDiff(const T &v, const uInt n, const T &der);
302
303 // Construct from an AutoDiff
304 SparseDiff(const AutoDiff<T> &other);
305
306 // Construct one from another (deep copy)
308
309 // Destructor
311
312 // Assignment operator. Assign a constant to variable.
314
315 // Assignment operator. Add a gradient to variable.
316 SparseDiff<T> &operator=(const pair<uInt, T> &der);
317
318 // Assignment operator. Assign gradients to variable.
319 SparseDiff<T> &operator=(const vector<pair<uInt, T> > &der);
320
321 // Assign from an Autodiff
323
324 // Assign one to another (deep copy)
326
327 // Assignment operators
328 // <group>
329 void operator*=(const SparseDiff<T> &other);
330 void operator/=(const SparseDiff<T> &other);
331 void operator+=(const SparseDiff<T> &other);
332 void operator-=(const SparseDiff<T> &other);
333 void operator*=(const T other) { rep_p->operator*=(other);
334 value() *= other; }
335 void operator/=(const T other) { rep_p->operator/=(other);
336 value() /= other; }
337 void operator+=(const T other) { value() += other; }
338 void operator-=(const T other) { value() -= other; }
339 // </group>
340
341 // Convert to an AutoDiff of length <em>n</em>
343
344 // Returns the pointer to the structure of value and derivatives.
345 // <group>
347 const SparseDiffRep<T> *theRep() const { return rep_p; }
348 // </group>
349
350 // Returns the value of the function
351 // <group>
352 T &value() { return rep_p->val_p; }
353 const T &value() const { return rep_p->val_p; }
354 // </group>
355
356 // Returns a vector of the derivatives of a SparseDiff
357 // <group>
358 vector<pair<uInt, T> > &derivatives() const;
359 void derivatives(vector<pair<uInt, T> > &res) const;
360 const vector<pair<uInt, T> > &grad() const { return rep_p->grad_p; }
361 vector<pair<uInt, T> > &grad() { return rep_p->grad_p; }
362 // </group>
363
364 // Returns a specific derivative. No check for a valid which.
365 // <group>
366 pair<uInt, T> &derivative(uInt which) { return rep_p->grad_p[which]; }
367 const pair<uInt, T> &derivative(uInt which) const {
368 return rep_p->grad_p[which]; }
369 // </group>
370
371 // Return total number of derivatives
372 uInt nDerivatives() const { return rep_p->grad_p.size(); }
373
374 // Is it a constant, i.e., with zero derivatives?
375 Bool isConstant() const { return rep_p->grad_p.empty(); }
376
377 // Sort criterium
378 static Bool ltSort(pair<uInt, T> &lhs, pair<uInt, T> &rhs);
379
380 // Sort derivative list; cater for doubles and zeroes
381 void sort();
382
383 private:
384 //# Data
385 // Value representation
387
388 };
389
390
391} //# NAMESPACE CASACORE - END
392
393#ifndef CASACORE_NO_AUTO_TEMPLATES
394#include <casacore/scimath/Mathematics/SparseDiff.tcc>
395#endif //# CASACORE_NO_AUTO_TEMPLATES
396#endif
static Bool ltSort(pair< uInt, T > &lhs, pair< uInt, T > &rhs)
Sort criterium.
void sort()
Sort derivative list; cater for doubles and zeroes.
vector< pair< uInt, T > > & derivatives() const
Returns a vector of the derivatives of a SparseDiff.
const T & value() const
Definition: SparseDiff.h:353
SparseDiff< T > & operator=(const vector< pair< uInt, T > > &der)
Assignment operator.
void operator*=(const SparseDiff< T > &other)
Assignment operators.
SparseDiff(const T &v, const uInt n)
A function f(x0,x1,...,xn,...) with a value of v.
SparseDiff(const T &v, const uInt n, const T &der)
A function f(x0,x1,...,xn,...) with a value of v.
SparseDiffRep< T > * theRep()
Returns the pointer to the structure of value and derivatives.
Definition: SparseDiff.h:346
void operator/=(const SparseDiff< T > &other)
uInt nDerivatives() const
Return total number of derivatives.
Definition: SparseDiff.h:372
void operator+=(const SparseDiff< T > &other)
SparseDiff< T > & operator=(const AutoDiff< T > &other)
Assign from an Autodiff.
void operator-=(const SparseDiff< T > &other)
pair< uInt, T > & derivative(uInt which)
Returns a specific derivative.
Definition: SparseDiff.h:366
SparseDiff()
Construct a constant with a value of zero.
SparseDiff(const AutoDiff< T > &other)
Construct from an AutoDiff.
value_type & reference
Definition: SparseDiff.h:283
const vector< pair< uInt, T > > & grad() const
Definition: SparseDiff.h:360
~SparseDiff()
Destructor.
void operator-=(const T other)
Definition: SparseDiff.h:338
const value_type & const_reference
Definition: SparseDiff.h:284
SparseDiffRep< T > * rep_p
Value representation.
Definition: SparseDiff.h:386
AutoDiff< T > toAutoDiff(uInt n) const
Convert to an AutoDiff of length n
SparseDiff< T > & operator=(const T &v)
Assignment operator.
const SparseDiffRep< T > * theRep() const
Definition: SparseDiff.h:347
SparseDiff(const T &v)
Construct a constant with a value of v.
Bool isConstant() const
Is it a constant, i.e., with zero derivatives?
Definition: SparseDiff.h:375
value_type * iterator
Definition: SparseDiff.h:285
const pair< uInt, T > & derivative(uInt which) const
Definition: SparseDiff.h:367
T & value()
Returns the value of the function.
Definition: SparseDiff.h:352
SparseDiff(const SparseDiff< T > &other)
Construct one from another (deep copy)
SparseDiff< T > & operator=(const SparseDiff< T > &other)
Assign one to another (deep copy)
SparseDiff< T > & operator=(const pair< uInt, T > &der)
Assignment operator.
vector< pair< uInt, T > > & grad()
Definition: SparseDiff.h:361
void operator+=(const T other)
Definition: SparseDiff.h:337
void operator/=(const T other)
Definition: SparseDiff.h:335
const value_type * const_iterator
Definition: SparseDiff.h:286
void operator*=(const T other)
Definition: SparseDiff.h:333
void derivatives(vector< pair< uInt, T > > &res) const
this file contains all the compiler specific defines
Definition: mainpage.dox:28
unsigned int uInt
Definition: aipstype.h:51
bool Bool
Define the standard types used by Casacore.
Definition: aipstype.h:42