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;

  const double goldenRatio = 0.618034;
  
  tempX = currentX =  model->getX();

  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){
       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;       
    }
     
  }

  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:	1031
Committed:	Fri Feb 6 18:58:06 2004 UTC (20 years, 5 months ago) by tim
File size:	8856 byte(s)
Log Message:	Add some lines into global.cpp to make it work with energy minimization
#	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
21	const double goldenRatio = 0.618034;
22
23	tempX = currentX = model->getX();
24
25	alpha = leftVar + (1 - goldenRatio) * (rightVar - leftVar);
26	beta = leftVar + goldenRatio * (rightVar - leftVar);
27
28	for (int i = 0; i < tempX.size(); i ++)
29	tempX[i] = currentX[i] + direction[i] * alpha;
30
31	fAlpha = model->calcF(tempX);
32
33	for (int i = 0; i < tempX.size(); i ++)
34	tempX[i] = currentX[i] + direction[i] * beta;
35
36	fBeta = model->calcF(tempX);
37
38	for(currentIter = 0; currentIter < maxIteration; currentIter++){
39
40	if (checkConvergence() > 0){
41	minStatus = MINSTATUS_CONVERGE;
42	return;
43	}
44
45	if (fAlpha > fBeta){
46	leftVar = alpha;
47	alpha = beta;
48
49	beta = leftVar + goldenRatio * (rightVar - leftVar);
50
51	for (int i = 0; i < tempX.size(); i ++)
52	tempX[i] = currentX[i] + direction[i] * beta;
53	fAlpha = fBeta;
54	fBeta = model->calcF(tempX);
55
56	prevMinVar = alpha;
57	fPrevMinVar = fAlpha;
58	minVar = beta;
59	fMinVar = fBeta;
60	}
61	else{
62	rightVar = beta;
63	beta = alpha;
64
65	alpha = leftVar + (1 - goldenRatio) * (rightVar - leftVar);
66
67	for (int i = 0; i < tempX.size(); i ++)
68	tempX[i] = currentX[i] + direction[i] * alpha;
69
70	fBeta = fAlpha;
71	fAlpha = model->calcF(tempX);
72
73	prevMinVar = beta;
74	fPrevMinVar = fBeta;
75
76	minVar = alpha;
77	fMinVar = fAlpha;
78	}
79
80	}
81
82	minStatus = MINSTATUS_MAXITER;
83
84	}
85
86	/**
87	* Brent's method is a root-finding algorithm which combines root bracketing, interval bisection,
88	* and inverse quadratic interpolation.
89	*/
90	BrentMinimizer::BrentMinimizer(NLModel* nlp)
91	:Minimizer1D(nlp){
92	setName("Brent");
93	}
94
95	void BrentMinimizer::minimize(vector<double>& direction, double left, double right){
96
97	//brent algorithm ascending order
98
99	if (left > right)
100	setRange(right, left);
101	else
102	setRange(left, right);
103
104	setDirection(direction);
105
106	minimize();
107	}
108	void BrentMinimizer::minimize(){
109
110	double fu, fv, fw;
111	double p, q, r;
112	double u, v, w;
113	double d;
114	double e;
115	double etemp;
116	double stepTol2;
117	double fLeftVar, fRightVar;
118	const double goldenRatio = 0.3819660;
119	vector<double> tempX, currentX;
120
121	stepTol2 = 2 * stepTol;
122
123	e = 0;
124	d = 0;
125
126	currentX = model->getX();
127	tempX.resize(currentX.size());
128
129
130
131
132	for (int i = 0; i < tempX.size(); i ++)
133	tempX[i] = currentX[i] + direction[i] * leftVar;
134
135	fLeftVar = model->calcF(tempX);
136
137	for (int i = 0; i < tempX.size(); i ++)
138	tempX[i] = currentX[i] + direction[i] * rightVar;
139
140	fRightVar = model->calcF(tempX);
141
142	// find an interior point left < interior < right which satisfy f(left) > f(interior) and f(right) > f(interior)
143
144	bracket(minVar, fMinVar, leftVar, fLeftVar, rightVar, fRightVar);
145
146	if(fRightVar < fLeftVar) {
147	prevMinVar = rightVar;
148	fPrevMinVar = fRightVar;
149	v = leftVar;
150	fv = fLeftVar;
151	}
152	else {
153	prevMinVar = leftVar;
154	fPrevMinVar = fLeftVar;
155	v = rightVar;
156	fv = fRightVar;
157	}
158
159	minVar = rightVar+ goldenRatio * (rightVar - leftVar);
160
161	for (int i = 0; i < tempX.size(); i ++)
162	tempX[i] = currentX[i] + direction[i] * minVar;
163
164	fMinVar = model->calcF(tempX);
165
166	prevMinVar = v = minVar;
167	fPrevMinVar = fv = fMinVar;
168	midVar = (leftVar + rightVar) / 2;
169
170	for(currentIter = 0; currentIter < maxIteration; currentIter++){
171
172	//construct a trial parabolic fit
173	if (fabs(e) > stepTol){
174
175	r = (minVar - prevMinVar) * (fMinVar - fv);
176	q = (minVar - v) * (fMinVar - fPrevMinVar);
177	p = (minVar - v) q -(minVar - prevMinVar)r;
178	q = 2.0 *(q-r);
179
180	if (q > 0.0)
181	p = -p;
182
183	q = fabs(q);
184
185	etemp = e;
186	e = d;
187
188	if(fabs(p) >= fabs(0.5qetemp) \|\| p <= q(leftVar - minVar) \|\| p >= q(rightVar - minVar)){
189	//reject parabolic fit and use golden section step instead
190	e = minVar >= midVar ? leftVar - minVar : rightVar - minVar;
191	d = goldenRatio * e;
192	}
193	else{
194
195	//take the parabolic step
196	d = p/q;
197	u = minVar + d;
198	if ( u - leftVar < stepTol2 \|\| rightVar - u < stepTol2)
199	d = midVar > minVar ? stepTol : - stepTol;
200	}
201
202	}
203	else{
204	e = minVar >= midVar ? leftVar -minVar : rightVar-minVar;
205	d = goldenRatio * e;
206	}
207
208	u = fabs(d) >= stepTol ? minVar + d : minVar + copysign(stepTol, d);
209
210	for (int i = 0; i < tempX.size(); i ++)
211	tempX[i] = currentX[i] + direction[i] * u;
212
213	fu = model->calcF(tempX);
214
215	if(fu <= fMinVar){
216
217	if(u >= minVar)
218	leftVar = minVar;
219	else
220	rightVar = minVar;
221
222	v = prevMinVar;
223	prevMinVar = minVar;
224	minVar = u;
225
226	fv = fPrevMinVar;
227	fPrevMinVar = fMinVar;
228	fMinVar = fu;
229
230	}
231	else{
232	if (u < minVar) leftVar = u;
233	else rightVar= u;
234
235	if(fu <= fPrevMinVar \|\| prevMinVar == minVar) {
236	v = prevMinVar;
237	fv = fPrevMinVar;
238	prevMinVar = u;
239	fPrevMinVar = fu;
240	}
241	else if ( fu <= fv \|\| v == minVar \|\| v == prevMinVar ) {
242	v = u;
243	fv = fu;
244	}
245	}
246
247	midVar = (leftVar + rightVar) /2;
248
249	if (checkConvergence() > 0){
250	minStatus = MINSTATUS_CONVERGE;
251	return;
252	}
253
254	}
255
256
257	minStatus = MINSTATUS_MAXITER;
258	return;
259	}
260
261	int BrentMinimizer::checkConvergence(){
262
263	if (fabs(minVar - midVar) < stepTol)
264	return 1;
265	else
266	return -1;
267	}
268
269	/*******************************************************
270	* Bracketing a minimum of a real function Y=F(X) *
271	* using MNBRAK subroutine *
272	* ---------------------------------------------------- *
273	* REFERENCE: "Numerical recipes, The Art of Scientific *
274	* Computing by W.H. Press, B.P. Flannery, *
275	* S.A. Teukolsky and W.T. Vetterling, *
276	* Cambridge university Press, 1986". *
277	* ---------------------------------------------------- *
278	* We have different situation here, we want to limit the
279	********************************************************/
280	void BrentMinimizer::bracket(double& cx, double& fc, double& ax, double& fa, double& bx, double& fb){
281	vector<double> currentX;
282	vector<double> tempX;
283	double u, r, q;
284	double fu;
285	double ulim;
286	const double TINY = 1.0e-20;
287	const double GLIMIT = 100.0;
288	const double GoldenRatio = 0.618034;
289	const int MAXBRACKETITER = 100;
290	currentX = model->getX();
291	tempX.resize(currentX.size());
292
293	if (fb > fa){
294	swap(fa, fb);
295	swap(ax, bx);
296	}
297
298	cx = bx + GoldenRatio * (bx - ax);
299
300	fc = model->calcF(tempX);
301
302	for(int k = 0; k < MAXBRACKETITER && (fb < fc); k++){
303
304	r = (bx - ax) * (fb -fc);
305	q = (bx - cx) * (fb - fa);
306	u = bx -((bx - cx)q - (bx-ax)r)/(2.0 * copysign(max(fabs(q-r), TINY) ,q-r));
307	ulim = bx + GLIMIT *(cx - bx);
308
309	for (int i = 0; i < tempX.size(); i ++)
310	tempX[i] = currentX[i] + direction[i] * u;
311
312	if ((bx -u) * (u -cx) > 0){
313	fu = model->calcF(tempX);
314
315	if (fu < fc){
316	ax = bx;
317	bx = u;
318	fa = fb;
319	fb = fu;
320	}
321	else if (fu > fb){
322	cx = u;
323	fc = fu;
324	return;
325	}
326	}
327	else if ((cx - u)* (u - ulim) > 0.0){
328
329	fu = model->calcF(tempX);
330
331	if (fu < fc){
332	bx = cx;
333	cx = u;
334	u = cx + GoldenRatio * (cx - bx);
335
336	fb = fc;
337	fc = fu;
338
339	for (int i = 0; i < tempX.size(); i ++)
340	tempX[i] = currentX[i] + direction[i] * u;
341
342	fu = model->calcF(tempX);
343	}
344	}
345	else if ((u-ulim) * (ulim - cx) >= 0.0){
346	u = ulim;
347
348	fu = model->calcF(tempX);
349
350	}
351	else {
352	u = cx + GoldenRatio * (cx -bx);
353
354	fu = model->calcF(tempX);
355	}
356
357	ax = bx;
358	bx = cx;
359	cx = u;
360
361	fa = fb;
362	fb = fc;
363	fc = fu;
364
365	}
366
367	}
368