Actual source code: rosenbrock1.c

tao-2.1-p0 2012-07-24
  1: /* Program usage: mpirun -np 1 rosenbrock1 [-help] [all TAO options] */

  3: /*  Include "tao.h" so we can use TAO solvers.  */
  4: #include "tao.h"

  6: static  char help[] = "This example demonstrates use of the TAO package to \n\
  7: solve an unconstrained minimization problem on a single processor.  We \n\
  8: minimize the extended Rosenbrock function: \n\
  9:    sum_{i=0}^{n/2-1} ( alpha*(x_{2i+1}-x_{2i}^2)^2 + (1-x_{2i})^2 ) \n";

 11: /*T 
 12:    Concepts: TAO - Solving an unconstrained minimization problem
 13:    Routines: TaoInitialize(); TaoFinalize();
 14:    Routines: TaoCreate();
 15:    Routines: TaoSetType(); TaoSetObjectiveAndGradientRoutine();
 16:    Routines: TaoSetHessianRoutine();
 17:    Routines: TaoSetInitialVector();
 18:    Routines: TaoSetFromOptions();
 19:    Routines: TaoSolve();
 20:    Routines: TaoGetTerminationReason(); TaoDestroy(); 
 21:    Processors: 1
 22: T*/ 


 25: /* 
 26:    User-defined application context - contains data needed by the 
 27:    application-provided call-back routines that evaluate the function,
 28:    gradient, and hessian.
 29: */
 30: typedef struct {
 31:   PetscInt n;          /* dimension */
 32:   PetscReal alpha;   /* condition parameter */
 33: } AppCtx;

 35: /* -------------- User-defined routines ---------- */
 36: PetscErrorCode FormFunctionGradient(TaoSolver,Vec,PetscReal*,Vec,void*);
 37: PetscErrorCode FormHessian(TaoSolver,Vec,Mat*,Mat*,MatStructure*,void*);

 41: int main(int argc,char **argv)
 42: {
 43:   PetscErrorCode  ierr;                  /* used to check for functions returning nonzeros */
 44:   PetscReal zero=0.0;
 45:   Vec        x;                     /* solution vector */
 46:   Mat        H;
 47:   TaoSolver  tao;                   /* TaoSolver solver context */
 48:   PetscBool  flg;
 49:   int        size,rank;                  /* number of processes running */
 50:   TaoSolverTerminationReason reason;
 51:   AppCtx     user;                  /* user-defined application context */

 53:   /* Initialize TAO and PETSc */
 54:   TaoInitialize(&argc,&argv,(char*)0,help);
 55:   MPI_Comm_size(PETSC_COMM_WORLD,&size); 
 56:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank); 

 58:   if (size >1) {
 59:       if (rank == 0) {
 60:           PetscPrintf(PETSC_COMM_SELF,"This example is intended for single processor use!\n"); 
 61:           SETERRQ(PETSC_COMM_SELF,1,"Incorrect number of processors");
 62:       }
 63:   }


 66:   /* Initialize problem parameters */
 67:   user.n = 2; user.alpha = 99.0;
 68:   /* Check for command line arguments to override defaults */
 69:   PetscOptionsGetInt(PETSC_NULL,"-n",&user.n,&flg); 
 70:   PetscOptionsGetReal(PETSC_NULL,"-alpha",&user.alpha,&flg); 

 72:   /* Allocate vectors for the solution and gradient */
 73:   VecCreateSeq(PETSC_COMM_SELF,user.n,&x); 
 74:   MatCreateSeqBAIJ(PETSC_COMM_SELF,2,user.n,user.n,1,PETSC_NULL,&H); 

 76:   /* The TAO code begins here */

 78:   /* Create TAO solver with desired solution method */
 79:   TaoCreate(PETSC_COMM_SELF,&tao); 
 80:   TaoSetType(tao,"tao_lmvm"); 

 82:   /* Set solution vec and an initial guess */
 83:   VecSet(x, zero); 
 84:   TaoSetInitialVector(tao,x);  

 86:   /* Set routines for function, gradient, hessian evaluation */
 87:   TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,&user); 
 88:   TaoSetHessianRoutine(tao,H,H,FormHessian,&user); 
 89:     
 90:   /* Check for TAO command line options */
 91:   TaoSetFromOptions(tao); 

 93:   /* SOLVE THE APPLICATION */
 94:   TaoSolve(tao); 

 96:   /* Get termination information */
 97:   TaoGetTerminationReason(tao,&reason); 
 98:   if (reason <= 0)
 99:     PetscPrintf(MPI_COMM_WORLD,"Try a different TAO type, adjust some parameters, or check the function evaluation routines\n");


102:   /* Free TAO data structures */
103:   TaoDestroy(&tao); 

105:   /* Free PETSc data structures */
106:   VecDestroy(&x); 
107:   MatDestroy(&H); 

109:   TaoFinalize();

111:   return 0;
112: }

114: /* -------------------------------------------------------------------- */
117: /*  
118:     FormFunctionGradient - Evaluates the function, f(X), and gradient, G(X). 

120:     Input Parameters:
121: .   tao  - the TaoSolver context
122: .   X    - input vector
123: .   ptr  - optional user-defined context, as set by TaoSetFunctionGradient()
124:     
125:     Output Parameters:
126: .   G - vector containing the newly evaluated gradient
127: .   f - function value

129:     Note:
130:     Some optimization methods ask for the function and the gradient evaluation
131:     at the same time.  Evaluating both at once may be more efficient that
132:     evaluating each separately. 
133: */
134: PetscErrorCode FormFunctionGradient(TaoSolver tao,Vec X,PetscReal *f, Vec G,void *ptr)
135: {
136:   AppCtx *user = (AppCtx *) ptr;  
137:   PetscInt    i,nn=user->n/2;
139:   PetscReal ff=0,t1,t2,alpha=user->alpha;
140:   PetscReal *x,*g;

142:   /* Get pointers to vector data */
143:   VecGetArray(X,&x); 
144:   VecGetArray(G,&g); 

146:   /* Compute G(X) */
147:   for (i=0; i<nn; i++){
148:     t1 = x[2*i+1]-x[2*i]*x[2*i]; t2= 1-x[2*i];
149:     ff += alpha*t1*t1 + t2*t2;
150:     g[2*i] = -4*alpha*t1*x[2*i]-2.0*t2;
151:     g[2*i+1] = 2*alpha*t1;
152:   }

154:   /* Restore vectors */
155:   VecRestoreArray(X,&x); 
156:   VecRestoreArray(G,&g); 
157:   *f=ff;

159:   PetscLogFlops(nn*15); 
160:   return 0;
161: }

163: /* ------------------------------------------------------------------- */
166: /*
167:    FormHessian - Evaluates Hessian matrix.

169:    Input Parameters:
170: .  tao   - the TaoSolver context
171: .  x     - input vector
172: .  ptr   - optional user-defined context, as set by TaoSetHessian()

174:    Output Parameters:
175: .  H     - Hessian matrix

177:    Note:  Providing the Hessian may not be necessary.  Only some solvers
178:    require this matrix.
179: */
180: PetscErrorCode FormHessian(TaoSolver tao,Vec X,Mat *HH, Mat *Hpre, MatStructure *flag,void *ptr)
181: {
182:   AppCtx  *user = (AppCtx*)ptr;
184:   PetscInt     i, nn=user->n/2, ind[2];
185:   PetscReal  alpha=user->alpha;
186:   PetscReal  v[2][2],*x;
187:   Mat H=*HH;
188:   PetscBool assembled;

190:   /* Zero existing matrix entries */
191:   MatAssembled(H,&assembled); 
192:   if (assembled){MatZeroEntries(H);  }


195:   /* Get a pointer to vector data */
196:   VecGetArray(X,&x); 

198:   /* Compute H(X) entries */
199:   for (i=0; i<user->n/2; i++){
200:     v[1][1] = 2*alpha;
201:     v[0][0] = -4*alpha*(x[2*i+1]-3*x[2*i]*x[2*i]) + 2;
202:     v[1][0] = v[0][1] = -4.0*alpha*x[2*i];
203:     ind[0]=2*i; ind[1]=2*i+1;
204:     MatSetValues(H,2,ind,2,ind,v[0],INSERT_VALUES); 
205:   }
206:   VecRestoreArray(X,&x); 

208:   /* Assemble matrix */
209:   MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY); 
210:   MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY); 
211:   *flag=SAME_NONZERO_PATTERN;
212:   
213:   PetscLogFlops(nn*9); 
214:   return 0;
215: }