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;       
    }
     
  }

  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:	1057
Committed:	Tue Feb 17 19:23:44 2004 UTC (21 years, 2 months ago) by tim
File size:	8935 byte(s)
Log Message:	adding function shakeF in order to remove the constraint force along bond direction
#	User	Rev	Content
1	tim	1002	#include "Minimizer1D.hpp"
2	tim	1005	#include "math.h"
3	tim	1023	#include "Utility.hpp"
4	tim	1005	GoldenSectionMinimizer::GoldenSectionMinimizer(NLModel* nlp)
5			:Minimizer1D(nlp){
6			setName("GoldenSection");
7			}
8	tim	1002
9	tim	1005	int GoldenSectionMinimizer::checkConvergence(){
10
11	tim	1002	if ((rightVar - leftVar) < stepTol)
12	tim	1010	return 1;
13	tim	1002	else
14			return -1;
15			}
16	tim	1031
17	tim	1002	void GoldenSectionMinimizer::minimize(){
18			vector<double> tempX;
19			vector <double> currentX;
20
21			const double goldenRatio = 0.618034;
22
23	tim	1015	tempX = currentX = model->getX();
24	tim	1002
25			alpha = leftVar + (1 - goldenRatio) * (rightVar - leftVar);
26			beta = leftVar + goldenRatio * (rightVar - leftVar);
27
28	tim	1015	for (int i = 0; i < tempX.size(); i ++)
29			tempX[i] = currentX[i] + direction[i] * alpha;
30
31	tim	1002	fAlpha = model->calcF(tempX);
32
33	tim	1015	for (int i = 0; i < tempX.size(); i ++)
34			tempX[i] = currentX[i] + direction[i] * beta;
35
36	tim	1002	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	tim	1023
49	tim	1002	beta = leftVar + goldenRatio * (rightVar - leftVar);
50
51	tim	1015	for (int i = 0; i < tempX.size(); i ++)
52			tempX[i] = currentX[i] + direction[i] * beta;
53	tim	1023	fAlpha = fBeta;
54			fBeta = model->calcF(tempX);
55	tim	1002
56	tim	1023	prevMinVar = alpha;
57			fPrevMinVar = fAlpha;
58	tim	1002	minVar = beta;
59	tim	1023	fMinVar = fBeta;
60	tim	1002	}
61			else{
62			rightVar = beta;
63			beta = alpha;
64	tim	1023
65	tim	1002	alpha = leftVar + (1 - goldenRatio) * (rightVar - leftVar);
66
67	tim	1015	for (int i = 0; i < tempX.size(); i ++)
68			tempX[i] = currentX[i] + direction[i] * alpha;
69	tim	1002
70	tim	1023	fBeta = fAlpha;
71			fAlpha = model->calcF(tempX);
72
73			prevMinVar = beta;
74			fPrevMinVar = fBeta;
75
76	tim	1002	minVar = alpha;
77	tim	1023	fMinVar = fAlpha;
78	tim	1002	}
79
80			}
81
82	tim	1057	cerr << "GoldenSectionMinimizer Warning : can not reach tolerance" << endl;
83	tim	1002	minStatus = MINSTATUS_MAXITER;
84
85			}
86
87	tim	1005	/**
88			* Brent's method is a root-finding algorithm which combines root bracketing, interval bisection,
89			* and inverse quadratic interpolation.
90	tim	1002	*/
91	tim	1005	BrentMinimizer::BrentMinimizer(NLModel* nlp)
92			:Minimizer1D(nlp){
93			setName("Brent");
94			}
95	tim	1002
96	tim	1031	void BrentMinimizer::minimize(vector<double>& direction, double left, double right){
97
98			//brent algorithm ascending order
99
100			if (left > right)
101			setRange(right, left);
102			else
103			setRange(left, right);
104
105			setDirection(direction);
106
107			minimize();
108			}
109	tim	1002	void BrentMinimizer::minimize(){
110
111	tim	1005	double fu, fv, fw;
112			double p, q, r;
113			double u, v, w;
114			double d;
115			double e;
116			double etemp;
117			double stepTol2;
118	tim	1010	double fLeftVar, fRightVar;
119	tim	1005	const double goldenRatio = 0.3819660;
120			vector<double> tempX, currentX;
121
122			stepTol2 = 2 * stepTol;
123	tim	1031
124	tim	1005	e = 0;
125			d = 0;
126
127	tim	1031	currentX = model->getX();
128			tempX.resize(currentX.size());
129	tim	1005
130	tim	1031
131
132
133	tim	1015	for (int i = 0; i < tempX.size(); i ++)
134			tempX[i] = currentX[i] + direction[i] * leftVar;
135
136	tim	1010	fLeftVar = model->calcF(tempX);
137	tim	1015
138			for (int i = 0; i < tempX.size(); i ++)
139			tempX[i] = currentX[i] + direction[i] * rightVar;
140	tim	1005
141	tim	1010	fRightVar = model->calcF(tempX);
142	tim	1005
143	tim	1031	// find an interior point left < interior < right which satisfy f(left) > f(interior) and f(right) > f(interior)
144
145			bracket(minVar, fMinVar, leftVar, fLeftVar, rightVar, fRightVar);
146
147	tim	1010	if(fRightVar < fLeftVar) {
148			prevMinVar = rightVar;
149			fPrevMinVar = fRightVar;
150	tim	1005	v = leftVar;
151			fv = fLeftVar;
152			}
153			else {
154			prevMinVar = leftVar;
155	tim	1010	fPrevMinVar = fLeftVar;
156	tim	1005	v = rightVar;
157	tim	1010	fv = fRightVar;
158	tim	1005	}
159	tim	1031
160			minVar = rightVar+ goldenRatio * (rightVar - leftVar);
161	tim	1010
162	tim	1031	for (int i = 0; i < tempX.size(); i ++)
163			tempX[i] = currentX[i] + direction[i] * minVar;
164
165			fMinVar = model->calcF(tempX);
166
167			prevMinVar = v = minVar;
168			fPrevMinVar = fv = fMinVar;
169	tim	1023	midVar = (leftVar + rightVar) / 2;
170	tim	1005
171	tim	1023	for(currentIter = 0; currentIter < maxIteration; currentIter++){
172	tim	1002
173	tim	1031	//construct a trial parabolic fit
174	tim	1005	if (fabs(e) > stepTol){
175	tim	1002
176	tim	1005	r = (minVar - prevMinVar) * (fMinVar - fv);
177			q = (minVar - v) * (fMinVar - fPrevMinVar);
178			p = (minVar - v) q -(minVar - prevMinVar)r;
179			q = 2.0 *(q-r);
180	tim	1002
181	tim	1005	if (q > 0.0)
182			p = -p;
183	tim	1002
184	tim	1005	q = fabs(q);
185
186			etemp = e;
187			e = d;
188
189	tim	1010	if(fabs(p) >= fabs(0.5qetemp) \|\| p <= q(leftVar - minVar) \|\| p >= q(rightVar - minVar)){
190	tim	1031	//reject parabolic fit and use golden section step instead
191	tim	1005	e = minVar >= midVar ? leftVar - minVar : rightVar - minVar;
192			d = goldenRatio * e;
193			}
194			else{
195	tim	1031
196			//take the parabolic step
197	tim	1005	d = p/q;
198			u = minVar + d;
199			if ( u - leftVar < stepTol2 \|\| rightVar - u < stepTol2)
200			d = midVar > minVar ? stepTol : - stepTol;
201			}
202	tim	1031
203	tim	1005	}
204			else{
205	tim	1031	e = minVar >= midVar ? leftVar -minVar : rightVar-minVar;
206			d = goldenRatio * e;
207	tim	1005	}
208
209	tim	1031	u = fabs(d) >= stepTol ? minVar + d : minVar + copysign(stepTol, d);
210	tim	1005
211	tim	1015	for (int i = 0; i < tempX.size(); i ++)
212			tempX[i] = currentX[i] + direction[i] * u;
213
214	tim	1023	fu = model->calcF(tempX);
215	tim	1005
216			if(fu <= fMinVar){
217
218			if(u >= minVar)
219			leftVar = minVar;
220			else
221			rightVar = minVar;
222
223			v = prevMinVar;
224	tim	1031	prevMinVar = minVar;
225			minVar = u;
226
227	tim	1005	fv = fPrevMinVar;
228			fPrevMinVar = fMinVar;
229			fMinVar = fu;
230
231			}
232			else{
233			if (u < minVar) leftVar = u;
234	tim	1031	else rightVar= u;
235
236	tim	1005	if(fu <= fPrevMinVar \|\| prevMinVar == minVar) {
237			v = prevMinVar;
238			fv = fPrevMinVar;
239			prevMinVar = u;
240			fPrevMinVar = fu;
241			}
242			else if ( fu <= fv \|\| v == minVar \|\| v == prevMinVar ) {
243			v = u;
244			fv = fu;
245			}
246			}
247
248	tim	1023	midVar = (leftVar + rightVar) /2;
249	tim	1005
250			if (checkConvergence() > 0){
251			minStatus = MINSTATUS_CONVERGE;
252			return;
253			}
254
255	tim	1002	}
256
257
258			minStatus = MINSTATUS_MAXITER;
259	tim	1010	return;
260	tim	1002	}
261	tim	1005
262	tim	1010	int BrentMinimizer::checkConvergence(){
263	tim	1005
264			if (fabs(minVar - midVar) < stepTol)
265			return 1;
266			else
267			return -1;
268			}
269	tim	1031
270			/*******************************************************
271			* Bracketing a minimum of a real function Y=F(X) *
272			* using MNBRAK subroutine *
273			* ---------------------------------------------------- *
274			* REFERENCE: "Numerical recipes, The Art of Scientific *
275			* Computing by W.H. Press, B.P. Flannery, *
276			* S.A. Teukolsky and W.T. Vetterling, *
277			* Cambridge university Press, 1986". *
278			* ---------------------------------------------------- *
279			* We have different situation here, we want to limit the
280			********************************************************/
281			void BrentMinimizer::bracket(double& cx, double& fc, double& ax, double& fa, double& bx, double& fb){
282			vector<double> currentX;
283			vector<double> tempX;
284			double u, r, q;
285			double fu;
286			double ulim;
287			const double TINY = 1.0e-20;
288			const double GLIMIT = 100.0;
289			const double GoldenRatio = 0.618034;
290			const int MAXBRACKETITER = 100;
291			currentX = model->getX();
292			tempX.resize(currentX.size());
293
294			if (fb > fa){
295			swap(fa, fb);
296			swap(ax, bx);
297			}
298
299			cx = bx + GoldenRatio * (bx - ax);
300
301			fc = model->calcF(tempX);
302
303			for(int k = 0; k < MAXBRACKETITER && (fb < fc); k++){
304
305			r = (bx - ax) * (fb -fc);
306			q = (bx - cx) * (fb - fa);
307			u = bx -((bx - cx)q - (bx-ax)r)/(2.0 * copysign(max(fabs(q-r), TINY) ,q-r));
308			ulim = bx + GLIMIT *(cx - bx);
309
310			for (int i = 0; i < tempX.size(); i ++)
311			tempX[i] = currentX[i] + direction[i] * u;
312
313			if ((bx -u) * (u -cx) > 0){
314			fu = model->calcF(tempX);
315
316			if (fu < fc){
317			ax = bx;
318			bx = u;
319			fa = fb;
320			fb = fu;
321			}
322			else if (fu > fb){
323			cx = u;
324			fc = fu;
325			return;
326			}
327			}
328			else if ((cx - u)* (u - ulim) > 0.0){
329
330			fu = model->calcF(tempX);
331
332			if (fu < fc){
333			bx = cx;
334			cx = u;
335			u = cx + GoldenRatio * (cx - bx);
336
337			fb = fc;
338			fc = fu;
339
340			for (int i = 0; i < tempX.size(); i ++)
341			tempX[i] = currentX[i] + direction[i] * u;
342
343			fu = model->calcF(tempX);
344			}
345			}
346			else if ((u-ulim) * (ulim - cx) >= 0.0){
347			u = ulim;
348
349			fu = model->calcF(tempX);
350
351			}
352			else {
353			u = cx + GoldenRatio * (cx -bx);
354
355			fu = model->calcF(tempX);
356			}
357
358			ax = bx;
359			bx = cx;
360			cx = u;
361
362			fa = fb;
363			fb = fc;
364			fc = fu;
365
366			}
367
368			}
369