OOPSE/libmdtools/Minimizer1D.cpp

#include "Minimizer1D.hpp"
#include "math.h"
#include "Utility.hpp"
GoldenSectionMinimizer::GoldenSectionMinimizer(NLModel* nlp)
                               :Minimizer1D(nlp){
  setName("GoldenSection");
}

int GoldenSectionMinimizer::checkConvergence(){

  if ((rightVar - leftVar) < stepTol)
    return 1;
  else
    return -1;
}

void GoldenSectionMinimizer::minimize(){
  vector<double> tempX;
  vector <double> currentX;
  double curF;
  const double goldenRatio = 0.618034;
  
  tempX = currentX =  model->getX();
  model->calcF();
  curF = model->getF();
  
  alpha = leftVar + (1 - goldenRatio) * (rightVar  - leftVar);
  beta = leftVar + goldenRatio * (rightVar - leftVar);

  for (int i = 0; i < tempX.size(); i ++)
    tempX[i] = currentX[i] + direction[i] * alpha;

  fAlpha = model->calcF(tempX);

  for (int i = 0; i < tempX.size(); i ++)
    tempX[i] = currentX[i] + direction[i] * beta;

  fBeta = model->calcF(tempX);

  for(currentIter = 0; currentIter < maxIteration; currentIter++){

     if (checkConvergence() > 0){

      //quick hack
      if (fMinVar > curF) {
        fMinVar = curF;
        minVar = 0;
        minStatus = MINSTATUS_ERROR;
      }
      
       minStatus = MINSTATUS_CONVERGE;
       return;
     }
    
    if (fAlpha > fBeta){
      leftVar = alpha;
      alpha = beta;
      
      beta =  leftVar + goldenRatio * (rightVar - leftVar);

      for (int i = 0; i < tempX.size(); i ++)
        tempX[i] = currentX[i] + direction[i] * beta;
      fAlpha = fBeta;
      fBeta  = model->calcF(tempX);
      
      prevMinVar = alpha;
      fPrevMinVar = fAlpha;      
      minVar = beta;
      fMinVar = fBeta;      
    }
    else{
      rightVar = beta;
      beta = alpha;

      alpha = leftVar + (1 - goldenRatio) * (rightVar  - leftVar);

      for (int i = 0; i < tempX.size(); i ++)
        tempX[i] = currentX[i] + direction[i] * alpha;

      fBeta = fAlpha;
      fAlpha = model->calcF(tempX);

      prevMinVar = beta;
      fPrevMinVar = fBeta;

      minVar = alpha;
      fMinVar = fAlpha;       
    }
     
  }

  cerr << "GoldenSectionMinimizer Warning : can not reach tolerance" << endl;
  minStatus = MINSTATUS_MAXITER;
    
}

/**
 * Brent's method is a root-finding algorithm which combines root bracketing, interval bisection,
 * and inverse quadratic interpolation.
 */
BrentMinimizer::BrentMinimizer(NLModel* nlp)
                   :Minimizer1D(nlp){
  setName("Brent");
}

void BrentMinimizer::minimize(vector<double>& direction, double left, double right){

  //brent algorithm ascending order

  if (left > right)
      setRange(right, left);
  else    
    setRange(left, right);
  
  setDirection(direction);
  
  minimize();
}
void BrentMinimizer::minimize(){

  double fu, fv, fw;
  double p, q, r;
  double u, v, w;
  double d;
  double e;
  double etemp;
  double stepTol2;
  double fLeftVar, fRightVar;
  const double goldenRatio = 0.3819660;
  vector<double> tempX, currentX;
  
  stepTol2 = 2 * stepTol;

  e = 0;
  d = 0;

  currentX = model->getX();
  tempX.resize(currentX.size());

  
  for (int i = 0; i < tempX.size(); i ++)
    tempX[i] = currentX[i] + direction[i] * leftVar;
  
  fLeftVar = model->calcF(tempX);

  for (int i = 0; i < tempX.size(); i ++)
    tempX[i] = currentX[i] + direction[i] * rightVar;  
  
  fRightVar = model->calcF(tempX);

  // find an interior point  left < interior < right which satisfy f(left) > f(interior) and f(right) > f(interior)
   
  bracket(minVar, fMinVar, leftVar, fLeftVar, rightVar, fRightVar);

  if(fRightVar < fLeftVar) {
    prevMinVar = rightVar;
    fPrevMinVar = fRightVar;
    v  = leftVar;
    fv = fLeftVar;
  }
  else {
    prevMinVar = leftVar;
    fPrevMinVar = fLeftVar;
    v  = rightVar;
    fv = fRightVar;
  }
    
  minVar =  rightVar+ goldenRatio * (rightVar - leftVar);

  for (int i = 0; i < tempX.size(); i ++)
    tempX[i] = currentX[i] + direction[i] * minVar; 

  fMinVar = model->calcF(tempX);
  
  prevMinVar = v = minVar;
  fPrevMinVar = fv = fMinVar;
  midVar = (leftVar + rightVar) / 2;
  
  for(currentIter = 0; currentIter < maxIteration; currentIter++){

     //construct a trial parabolic fit
     if (fabs(e) > stepTol){

       r = (minVar - prevMinVar) * (fMinVar - fv);
       q = (minVar - v) * (fMinVar - fPrevMinVar);
       p = (minVar - v) *q -(minVar - prevMinVar)*r;
       q = 2.0 *(q-r);

       if (q > 0.0)
         p = -p;

       q = fabs(q);

       etemp = e;
       e  = d;

       if(fabs(p) >= fabs(0.5*q*etemp) || p <= q*(leftVar - minVar) || p >= q*(rightVar - minVar)){
         //reject parabolic fit and use golden section step instead
         e =  minVar >= midVar ? leftVar - minVar : rightVar - minVar;
         d = goldenRatio * e;
       }
       else{

        //take the parabolic step
         d = p/q;
         u = minVar + d;
         if ( u - leftVar < stepTol2 || rightVar - u  < stepTol2)
           d = midVar > minVar ? stepTol : - stepTol;
       }
       
     }
     else{
       e = minVar >= midVar ? leftVar -minVar : rightVar-minVar;
       d = goldenRatio * e;        
     }

     u = fabs(d) >= stepTol ? minVar + d : minVar + copysign(stepTol, d);

     for (int i = 0; i < tempX.size(); i ++)
       tempX[i] = currentX[i] + direction[i] * u;  
    
     fu = model->calcF(tempX);   

     if(fu <= fMinVar){

       if(u >= minVar)
         leftVar = minVar;
       else
         rightVar = minVar;

       v  = prevMinVar;
       prevMinVar = minVar;
       minVar = u;
       
       fv = fPrevMinVar;
       fPrevMinVar = fMinVar;
       fMinVar = fu;
       
     }
     else{
       if (u < minVar) leftVar = u;
         else rightVar= u;
         
       if(fu <= fPrevMinVar || prevMinVar == minVar) {
         v  = prevMinVar;
         fv = fPrevMinVar;
         prevMinVar = u;
         fPrevMinVar = fu;
      }
      else if ( fu <= fv || v == minVar || v == prevMinVar ) {
        v  = u;
         fv = fu;
      }   
    }    

    midVar = (leftVar + rightVar) /2;

     if (checkConvergence() > 0){
       minStatus = MINSTATUS_CONVERGE;
       return;
     }
    
  }


  minStatus = MINSTATUS_MAXITER;
  return;  
}

int BrentMinimizer::checkConvergence(){
  
  if (fabs(minVar - midVar) <  stepTol)
    return 1;
  else
    return -1;
}

/*******************************************************
*    Bracketing a minimum of a real function Y=F(X)    *
*             using MNBRAK subroutine                  *
* ---------------------------------------------------- *
* REFERENCE: "Numerical recipes, The Art of Scientific *
*             Computing by W.H. Press, B.P. Flannery,  *
*             S.A. Teukolsky and W.T. Vetterling,      *
*             Cambridge university Press, 1986".       *
* ---------------------------------------------------- *
* We have different situation here, we want to limit the 
********************************************************/
void BrentMinimizer::bracket(double& cx, double& fc, double& ax, double& fa, double& bx, double& fb){
  vector<double> currentX;
  vector<double> tempX;
  double u, r, q;
  double fu;
  double ulim;  
  const double TINY = 1.0e-20;
  const double GLIMIT = 100.0;
  const double GoldenRatio = 0.618034;
  const int MAXBRACKETITER = 100; 
  currentX = model->getX();
  tempX.resize(currentX.size());

   if (fb > fa){
     swap(fa, fb);
     swap(ax, bx);
   }

   cx = bx + GoldenRatio * (bx - ax);

   fc = model->calcF(tempX);

   for(int k = 0; k < MAXBRACKETITER && (fb < fc); k++){
    
     r = (bx  - ax) * (fb -fc);
     q = (bx - cx) * (fb - fa);
     u = bx -((bx - cx)*q - (bx-ax)*r)/(2.0 * copysign(max(fabs(q-r), TINY) ,q-r));
     ulim = bx + GLIMIT *(cx - bx);
     
     for (int i = 0; i < tempX.size(); i ++)
       tempX[i] = currentX[i] + direction[i] * u;  
     
     if ((bx -u) * (u -cx) > 0){ 
       fu = model->calcF(tempX);

       if (fu < fc){
         ax = bx;
         bx = u;
         fa = fb;
         fb = fu;
       }
       else if (fu > fb){
         cx = u;
         fc = fu;
         return;
       }       
     }
     else if ((cx - u)* (u - ulim) > 0.0){

       fu = model->calcF(tempX); 

       if (fu < fc){
         bx = cx;
         cx = u;
         u = cx + GoldenRatio * (cx - bx);

         fb = fc;
         fc = fu;

         for (int i = 0; i < tempX.size(); i ++)
           tempX[i] = currentX[i] + direction[i] * u;    

         fu = model->calcF(tempX);
       }
     }
     else if ((u-ulim) * (ulim - cx) >= 0.0){
       u = ulim;
       
       fu =  model->calcF(tempX);
     
     }
     else {
       u = cx + GoldenRatio * (cx -bx);
       
       fu = model->calcF(tempX);
     }

     ax = bx;
     bx = cx;
     cx = u;
     
     fa = fb;
     fb = fc;
     fc = fu;

   }
      
}

Revision:	1064
Committed:	Tue Feb 24 15:44:45 2004 UTC (21 years, 2 months ago) by tim
File size:	9147 byte(s)
Log Message:	Using inherit instead of compose to implement Minimizer both versions are working
#	Content
1	#include "Minimizer1D.hpp"
2	#include "math.h"
3	#include "Utility.hpp"
4	GoldenSectionMinimizer::GoldenSectionMinimizer(NLModel* nlp)
5	:Minimizer1D(nlp){
6	setName("GoldenSection");
7	}
8
9	int GoldenSectionMinimizer::checkConvergence(){
10
11	if ((rightVar - leftVar) < stepTol)
12	return 1;
13	else
14	return -1;
15	}
16
17	void GoldenSectionMinimizer::minimize(){
18	vector<double> tempX;
19	vector <double> currentX;
20	double curF;
21	const double goldenRatio = 0.618034;
22
23	tempX = currentX = model->getX();
24	model->calcF();
25	curF = model->getF();
26
27	alpha = leftVar + (1 - goldenRatio) * (rightVar - leftVar);
28	beta = leftVar + goldenRatio * (rightVar - leftVar);
29
30	for (int i = 0; i < tempX.size(); i ++)
31	tempX[i] = currentX[i] + direction[i] * alpha;
32
33	fAlpha = model->calcF(tempX);
34
35	for (int i = 0; i < tempX.size(); i ++)
36	tempX[i] = currentX[i] + direction[i] * beta;
37
38	fBeta = model->calcF(tempX);
39
40	for(currentIter = 0; currentIter < maxIteration; currentIter++){
41
42	if (checkConvergence() > 0){
43
44	//quick hack
45	if (fMinVar > curF) {
46	fMinVar = curF;
47	minVar = 0;
48	minStatus = MINSTATUS_ERROR;
49	}
50
51	minStatus = MINSTATUS_CONVERGE;
52	return;
53	}
54
55	if (fAlpha > fBeta){
56	leftVar = alpha;
57	alpha = beta;
58
59	beta = leftVar + goldenRatio * (rightVar - leftVar);
60
61	for (int i = 0; i < tempX.size(); i ++)
62	tempX[i] = currentX[i] + direction[i] * beta;
63	fAlpha = fBeta;
64	fBeta = model->calcF(tempX);
65
66	prevMinVar = alpha;
67	fPrevMinVar = fAlpha;
68	minVar = beta;
69	fMinVar = fBeta;
70	}
71	else{
72	rightVar = beta;
73	beta = alpha;
74
75	alpha = leftVar + (1 - goldenRatio) * (rightVar - leftVar);
76
77	for (int i = 0; i < tempX.size(); i ++)
78	tempX[i] = currentX[i] + direction[i] * alpha;
79
80	fBeta = fAlpha;
81	fAlpha = model->calcF(tempX);
82
83	prevMinVar = beta;
84	fPrevMinVar = fBeta;
85
86	minVar = alpha;
87	fMinVar = fAlpha;
88	}
89
90	}
91
92	cerr << "GoldenSectionMinimizer Warning : can not reach tolerance" << endl;
93	minStatus = MINSTATUS_MAXITER;
94
95	}
96
97	/**
98	* Brent's method is a root-finding algorithm which combines root bracketing, interval bisection,
99	* and inverse quadratic interpolation.
100	*/
101	BrentMinimizer::BrentMinimizer(NLModel* nlp)
102	:Minimizer1D(nlp){
103	setName("Brent");
104	}
105
106	void BrentMinimizer::minimize(vector<double>& direction, double left, double right){
107
108	//brent algorithm ascending order
109
110	if (left > right)
111	setRange(right, left);
112	else
113	setRange(left, right);
114
115	setDirection(direction);
116
117	minimize();
118	}
119	void BrentMinimizer::minimize(){
120
121	double fu, fv, fw;
122	double p, q, r;
123	double u, v, w;
124	double d;
125	double e;
126	double etemp;
127	double stepTol2;
128	double fLeftVar, fRightVar;
129	const double goldenRatio = 0.3819660;
130	vector<double> tempX, currentX;
131
132	stepTol2 = 2 * stepTol;
133
134	e = 0;
135	d = 0;
136
137	currentX = model->getX();
138	tempX.resize(currentX.size());
139
140
141
142
143	for (int i = 0; i < tempX.size(); i ++)
144	tempX[i] = currentX[i] + direction[i] * leftVar;
145
146	fLeftVar = model->calcF(tempX);
147
148	for (int i = 0; i < tempX.size(); i ++)
149	tempX[i] = currentX[i] + direction[i] * rightVar;
150
151	fRightVar = model->calcF(tempX);
152
153	// find an interior point left < interior < right which satisfy f(left) > f(interior) and f(right) > f(interior)
154
155	bracket(minVar, fMinVar, leftVar, fLeftVar, rightVar, fRightVar);
156
157	if(fRightVar < fLeftVar) {
158	prevMinVar = rightVar;
159	fPrevMinVar = fRightVar;
160	v = leftVar;
161	fv = fLeftVar;
162	}
163	else {
164	prevMinVar = leftVar;
165	fPrevMinVar = fLeftVar;
166	v = rightVar;
167	fv = fRightVar;
168	}
169
170	minVar = rightVar+ goldenRatio * (rightVar - leftVar);
171
172	for (int i = 0; i < tempX.size(); i ++)
173	tempX[i] = currentX[i] + direction[i] * minVar;
174
175	fMinVar = model->calcF(tempX);
176
177	prevMinVar = v = minVar;
178	fPrevMinVar = fv = fMinVar;
179	midVar = (leftVar + rightVar) / 2;
180
181	for(currentIter = 0; currentIter < maxIteration; currentIter++){
182
183	//construct a trial parabolic fit
184	if (fabs(e) > stepTol){
185
186	r = (minVar - prevMinVar) * (fMinVar - fv);
187	q = (minVar - v) * (fMinVar - fPrevMinVar);
188	p = (minVar - v) q -(minVar - prevMinVar)r;
189	q = 2.0 *(q-r);
190
191	if (q > 0.0)
192	p = -p;
193
194	q = fabs(q);
195
196	etemp = e;
197	e = d;
198
199	if(fabs(p) >= fabs(0.5qetemp) \|\| p <= q(leftVar - minVar) \|\| p >= q(rightVar - minVar)){
200	//reject parabolic fit and use golden section step instead
201	e = minVar >= midVar ? leftVar - minVar : rightVar - minVar;
202	d = goldenRatio * e;
203	}
204	else{
205
206	//take the parabolic step
207	d = p/q;
208	u = minVar + d;
209	if ( u - leftVar < stepTol2 \|\| rightVar - u < stepTol2)
210	d = midVar > minVar ? stepTol : - stepTol;
211	}
212
213	}
214	else{
215	e = minVar >= midVar ? leftVar -minVar : rightVar-minVar;
216	d = goldenRatio * e;
217	}
218
219	u = fabs(d) >= stepTol ? minVar + d : minVar + copysign(stepTol, d);
220
221	for (int i = 0; i < tempX.size(); i ++)
222	tempX[i] = currentX[i] + direction[i] * u;
223
224	fu = model->calcF(tempX);
225
226	if(fu <= fMinVar){
227
228	if(u >= minVar)
229	leftVar = minVar;
230	else
231	rightVar = minVar;
232
233	v = prevMinVar;
234	prevMinVar = minVar;
235	minVar = u;
236
237	fv = fPrevMinVar;
238	fPrevMinVar = fMinVar;
239	fMinVar = fu;
240
241	}
242	else{
243	if (u < minVar) leftVar = u;
244	else rightVar= u;
245
246	if(fu <= fPrevMinVar \|\| prevMinVar == minVar) {
247	v = prevMinVar;
248	fv = fPrevMinVar;
249	prevMinVar = u;
250	fPrevMinVar = fu;
251	}
252	else if ( fu <= fv \|\| v == minVar \|\| v == prevMinVar ) {
253	v = u;
254	fv = fu;
255	}
256	}
257
258	midVar = (leftVar + rightVar) /2;
259
260	if (checkConvergence() > 0){
261	minStatus = MINSTATUS_CONVERGE;
262	return;
263	}
264
265	}
266
267
268	minStatus = MINSTATUS_MAXITER;
269	return;
270	}
271
272	int BrentMinimizer::checkConvergence(){
273
274	if (fabs(minVar - midVar) < stepTol)
275	return 1;
276	else
277	return -1;
278	}
279
280	/*******************************************************
281	* Bracketing a minimum of a real function Y=F(X) *
282	* using MNBRAK subroutine *
283	* ---------------------------------------------------- *
284	* REFERENCE: "Numerical recipes, The Art of Scientific *
285	* Computing by W.H. Press, B.P. Flannery, *
286	* S.A. Teukolsky and W.T. Vetterling, *
287	* Cambridge university Press, 1986". *
288	* ---------------------------------------------------- *
289	* We have different situation here, we want to limit the
290	********************************************************/
291	void BrentMinimizer::bracket(double& cx, double& fc, double& ax, double& fa, double& bx, double& fb){
292	vector<double> currentX;
293	vector<double> tempX;
294	double u, r, q;
295	double fu;
296	double ulim;
297	const double TINY = 1.0e-20;
298	const double GLIMIT = 100.0;
299	const double GoldenRatio = 0.618034;
300	const int MAXBRACKETITER = 100;
301	currentX = model->getX();
302	tempX.resize(currentX.size());
303
304	if (fb > fa){
305	swap(fa, fb);
306	swap(ax, bx);
307	}
308
309	cx = bx + GoldenRatio * (bx - ax);
310
311	fc = model->calcF(tempX);
312
313	for(int k = 0; k < MAXBRACKETITER && (fb < fc); k++){
314
315	r = (bx - ax) * (fb -fc);
316	q = (bx - cx) * (fb - fa);
317	u = bx -((bx - cx)q - (bx-ax)r)/(2.0 * copysign(max(fabs(q-r), TINY) ,q-r));
318	ulim = bx + GLIMIT *(cx - bx);
319
320	for (int i = 0; i < tempX.size(); i ++)
321	tempX[i] = currentX[i] + direction[i] * u;
322
323	if ((bx -u) * (u -cx) > 0){
324	fu = model->calcF(tempX);
325
326	if (fu < fc){
327	ax = bx;
328	bx = u;
329	fa = fb;
330	fb = fu;
331	}
332	else if (fu > fb){
333	cx = u;
334	fc = fu;
335	return;
336	}
337	}
338	else if ((cx - u)* (u - ulim) > 0.0){
339
340	fu = model->calcF(tempX);
341
342	if (fu < fc){
343	bx = cx;
344	cx = u;
345	u = cx + GoldenRatio * (cx - bx);
346
347	fb = fc;
348	fc = fu;
349
350	for (int i = 0; i < tempX.size(); i ++)
351	tempX[i] = currentX[i] + direction[i] * u;
352
353	fu = model->calcF(tempX);
354	}
355	}
356	else if ((u-ulim) * (ulim - cx) >= 0.0){
357	u = ulim;
358
359	fu = model->calcF(tempX);
360
361	}
362	else {
363	u = cx + GoldenRatio * (cx -bx);
364
365	fu = model->calcF(tempX);
366	}
367
368	ax = bx;
369	bx = cx;
370	cx = u;
371
372	fa = fb;
373	fb = fc;
374	fc = fu;
375
376	}
377
378	}
379