Actual source code: rosenbrock1.c

petsc-master 2017-04-26
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  1: /* Program usage: mpiexec -n 1 rosenbrock1 [-help] [all TAO options] */

  3: /*  Include "petsctao.h" so we can use TAO solvers.  */
  4:  #include <petsctao.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\
 10: or the chained Rosenbrock function:\n\
 11:    sum_{i=0}^{n-1} alpha*(x_{i+1} - x_i^2)^2 + (1 - x_i)^2\n";

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


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

 37: /* -------------- User-defined routines ---------- */
 38: PetscErrorCode FormFunctionGradient(Tao,Vec,PetscReal*,Vec,void*);
 39: PetscErrorCode FormHessian(Tao,Vec,Mat,Mat,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:   Tao                tao;                   /* Tao solver context */
 48:   PetscBool          flg;
 49:   PetscMPIInt        size,rank;                  /* number of processes running */
 50:   AppCtx             user;                  /* user-defined application context */

 52:   /* Initialize TAO and PETSc */
 53:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
 54:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
 55:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
 56:   if (size >1) SETERRQ(PETSC_COMM_SELF,1,"Incorrect number of processors");

 58:   /* Initialize problem parameters */
 59:   user.n = 2; user.alpha = 99.0; user.chained = PETSC_FALSE;
 60:   /* Check for command line arguments to override defaults */
 61:   PetscOptionsGetInt(NULL,NULL,"-n",&user.n,&flg);
 62:   PetscOptionsGetReal(NULL,NULL,"-alpha",&user.alpha,&flg);
 63:   PetscOptionsGetBool(NULL,NULL,"-chained",&user.chained,&flg);

 65:   /* Allocate vectors for the solution and gradient */
 66:   VecCreateSeq(PETSC_COMM_SELF,user.n,&x);
 67:   MatCreateSeqBAIJ(PETSC_COMM_SELF,2,user.n,user.n,1,NULL,&H);

 69:   /* The TAO code begins here */

 71:   /* Create TAO solver with desired solution method */
 72:   TaoCreate(PETSC_COMM_SELF,&tao);
 73:   TaoSetType(tao,TAOLMVM);

 75:   /* Set solution vec and an initial guess */
 76:   VecSet(x, zero);
 77:   TaoSetInitialVector(tao,x);

 79:   /* Set routines for function, gradient, hessian evaluation */
 80:   TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,&user);
 81:   TaoSetHessianRoutine(tao,H,H,FormHessian,&user);

 83:   /* Check for TAO command line options */
 84:   TaoSetFromOptions(tao);

 86:   /* SOLVE THE APPLICATION */
 87:   TaoSolve(tao);

 89:   TaoDestroy(&tao);
 90:   VecDestroy(&x);
 91:   MatDestroy(&H);

 93:   PetscFinalize();
 94:   return ierr;
 95: }

 97: /* -------------------------------------------------------------------- */
 98: /*
 99:     FormFunctionGradient - Evaluates the function, f(X), and gradient, G(X).

101:     Input Parameters:
102: .   tao  - the Tao context
103: .   X    - input vector
104: .   ptr  - optional user-defined context, as set by TaoSetFunctionGradient()

106:     Output Parameters:
107: .   G - vector containing the newly evaluated gradient
108: .   f - function value

110:     Note:
111:     Some optimization methods ask for the function and the gradient evaluation
112:     at the same time.  Evaluating both at once may be more efficient that
113:     evaluating each separately.
114: */
115: PetscErrorCode FormFunctionGradient(Tao tao,Vec X,PetscReal *f, Vec G,void *ptr)
116: {
117:   AppCtx         *user = (AppCtx *) ptr;
118:   PetscInt       i,nn=user->n/2;
120:   PetscReal      ff=0,t1,t2,alpha=user->alpha;
121:   PetscReal      *x,*g;

123:   /* Get pointers to vector data */
124:   VecGetArray(X,&x);
125:   VecGetArray(G,&g);

127:   /* Compute G(X) */
128:   if (user->chained) {
129:     g[0] = 0;
130:     for (i=0; i<user->n-1; i++) {
131:       t1 = x[i+1] - x[i]*x[i];
132:       ff += PetscSqr(1 - x[i]) + alpha*t1*t1;
133:       g[i] += -2*(1 - x[i]) + 2*alpha*t1*(-2*x[i]);
134:       g[i+1] = 2*alpha*t1;
135:     }
136:   } else {
137:     for (i=0; i<nn; i++){
138:       t1 = x[2*i+1]-x[2*i]*x[2*i]; t2= 1-x[2*i];
139:       ff += alpha*t1*t1 + t2*t2;
140:       g[2*i] = -4*alpha*t1*x[2*i]-2.0*t2;
141:       g[2*i+1] = 2*alpha*t1;
142:     }
143:   }

145:   /* Restore vectors */
146:   VecRestoreArray(X,&x);
147:   VecRestoreArray(G,&g);
148:   *f=ff;

150:   PetscLogFlops(nn*15);
151:   return 0;
152: }

154: /* ------------------------------------------------------------------- */
155: /*
156:    FormHessian - Evaluates Hessian matrix.

158:    Input Parameters:
159: .  tao   - the Tao context
160: .  x     - input vector
161: .  ptr   - optional user-defined context, as set by TaoSetHessian()

163:    Output Parameters:
164: .  H     - Hessian matrix

166:    Note:  Providing the Hessian may not be necessary.  Only some solvers
167:    require this matrix.
168: */
169: PetscErrorCode FormHessian(Tao tao,Vec X,Mat H, Mat Hpre, void *ptr)
170: {
171:   AppCtx         *user = (AppCtx*)ptr;
173:   PetscInt       i, ind[2];
174:   PetscReal      alpha=user->alpha;
175:   PetscReal      v[2][2],*x;
176:   PetscBool      assembled;

178:   /* Zero existing matrix entries */
179:   MatAssembled(H,&assembled);
180:   if (assembled){MatZeroEntries(H); }

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

185:   /* Compute H(X) entries */
186:   if (user->chained) {
187:     MatZeroEntries(H);
188:     for (i=0; i<user->n-1; i++) {
189:       PetscScalar t1 = x[i+1] - x[i]*x[i];
190:       v[0][0] = 2 + 2*alpha*(t1*(-2) - 2*x[i]);
191:       v[0][1] = 2*alpha*(-2*x[i]);
192:       v[1][0] = 2*alpha*(-2*x[i]);
193:       v[1][1] = 2*alpha*t1;
194:       ind[0] = i; ind[1] = i+1;
195:       MatSetValues(H,2,ind,2,ind,v[0],ADD_VALUES);
196:     }
197:   } else {
198:     for (i=0; i<user->n/2; i++){
199:       v[1][1] = 2*alpha;
200:       v[0][0] = -4*alpha*(x[2*i+1]-3*x[2*i]*x[2*i]) + 2;
201:       v[1][0] = v[0][1] = -4.0*alpha*x[2*i];
202:       ind[0]=2*i; ind[1]=2*i+1;
203:       MatSetValues(H,2,ind,2,ind,v[0],INSERT_VALUES);
204:     }
205:   }
206:   VecRestoreArray(X,&x);

208:   /* Assemble matrix */
209:   MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY);
210:   MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY);
211:   PetscLogFlops(9.0*user->n/2.0);
212:   return 0;
213: }