Actual source code: rosenbrock3.c
1: /* Program usage: mpiexec -n 1 rosenbrock2 [-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*/
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: PetscBool chained;
34: } AppCtx;
36: /* -------------- User-defined routines ---------- */
37: PetscErrorCode FormFunctionGradient(Tao,Vec,PetscReal*,Vec,void*);
38: PetscErrorCode FormHessian(Tao,Vec,Mat,Mat,void*);
40: int main(int argc,char **argv)
41: {
42: PetscErrorCode ierr; /* used to check for functions returning nonzeros */
43: PetscReal zero=0.0;
44: Vec x; /* solution vector */
45: Mat H;
46: Tao tao; /* Tao solver context */
47: PetscBool flg, test_lmvm = PETSC_FALSE;
48: PetscMPIInt size; /* number of processes running */
49: AppCtx user; /* user-defined application context */
50: TaoConvergedReason reason;
51: PetscInt its, recycled_its=0, oneshot_its=0;
53: /* Initialize TAO and PETSc */
54: PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
55: MPI_Comm_size(PETSC_COMM_WORLD,&size);
56: if (size >1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"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);
64: PetscOptionsGetBool(NULL,NULL,"-test_lmvm",&test_lmvm,&flg);
66: /* Allocate vectors for the solution and gradient */
67: VecCreateSeq(PETSC_COMM_SELF,user.n,&x);
68: MatCreateSeqBAIJ(PETSC_COMM_SELF,2,user.n,user.n,1,NULL,&H);
70: /* The TAO code begins here */
72: /* Create TAO solver with desired solution method */
73: TaoCreate(PETSC_COMM_SELF,&tao);
74: TaoSetType(tao,TAOBQNLS);
76: /* Set solution vec and an initial guess */
77: VecSet(x, zero);
78: TaoSetInitialVector(tao,x);
80: /* Set routines for function, gradient, hessian evaluation */
81: TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,&user);
82: TaoSetHessianRoutine(tao,H,H,FormHessian,&user);
84: /* Check for TAO command line options */
85: TaoSetFromOptions(tao);
87: /* Solve the problem */
88: TaoSetTolerances(tao, 1.e-5, 0.0, 0.0);
89: TaoSetMaximumIterations(tao, 5);
90: TaoSetRecycleHistory(tao, PETSC_TRUE);
91: reason = TAO_CONTINUE_ITERATING;
92: flg = PETSC_FALSE;
93: TaoGetRecycleHistory(tao, &flg);
94: if (flg) PetscPrintf(PETSC_COMM_SELF, "Recycle: enabled\n");
95: while (reason != TAO_CONVERGED_GATOL) {
96: TaoSolve(tao);
97: TaoGetConvergedReason(tao, &reason);
98: TaoGetIterationNumber(tao, &its);
99: recycled_its += its;
100: PetscPrintf(PETSC_COMM_SELF, "-----------------------\n");
101: }
103: /* Disable recycling and solve again! */
104: TaoSetMaximumIterations(tao, 100);
105: TaoSetRecycleHistory(tao, PETSC_FALSE);
106: VecSet(x, zero);
107: TaoGetRecycleHistory(tao, &flg);
108: if (!flg) PetscPrintf(PETSC_COMM_SELF, "Recycle: disabled\n");
109: TaoSolve(tao);
110: TaoGetConvergedReason(tao, &reason);
111: if (reason != TAO_CONVERGED_GATOL) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "Solution failed to converge!");
112: TaoGetIterationNumber(tao, &oneshot_its);
113: PetscPrintf(PETSC_COMM_SELF, "-----------------------\n");
114: PetscPrintf(PETSC_COMM_SELF, "recycled its: %D | oneshot its: %D\n", recycled_its, oneshot_its);
115: if (recycled_its != oneshot_its) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "Recycled solution does not match oneshot solution!");
117: TaoDestroy(&tao);
118: VecDestroy(&x);
119: MatDestroy(&H);
121: PetscFinalize();
122: return ierr;
123: }
125: /* -------------------------------------------------------------------- */
126: /*
127: FormFunctionGradient - Evaluates the function, f(X), and gradient, G(X).
129: Input Parameters:
130: . tao - the Tao context
131: . X - input vector
132: . ptr - optional user-defined context, as set by TaoSetFunctionGradient()
134: Output Parameters:
135: . G - vector containing the newly evaluated gradient
136: . f - function value
138: Note:
139: Some optimization methods ask for the function and the gradient evaluation
140: at the same time. Evaluating both at once may be more efficient than
141: evaluating each separately.
142: */
143: PetscErrorCode FormFunctionGradient(Tao tao,Vec X,PetscReal *f, Vec G,void *ptr)
144: {
145: AppCtx *user = (AppCtx *) ptr;
146: PetscInt i,nn=user->n/2;
147: PetscErrorCode ierr;
148: PetscReal ff=0,t1,t2,alpha=user->alpha;
149: PetscScalar *g;
150: const PetscScalar *x;
153: /* Get pointers to vector data */
154: VecGetArrayRead(X,&x);
155: VecGetArrayWrite(G,&g);
157: /* Compute G(X) */
158: if (user->chained) {
159: g[0] = 0;
160: for (i=0; i<user->n-1; i++) {
161: t1 = x[i+1] - x[i]*x[i];
162: ff += PetscSqr(1 - x[i]) + alpha*t1*t1;
163: g[i] += -2*(1 - x[i]) + 2*alpha*t1*(-2*x[i]);
164: g[i+1] = 2*alpha*t1;
165: }
166: } else {
167: for (i=0; i<nn; i++){
168: t1 = x[2*i+1]-x[2*i]*x[2*i]; t2= 1-x[2*i];
169: ff += alpha*t1*t1 + t2*t2;
170: g[2*i] = -4*alpha*t1*x[2*i]-2.0*t2;
171: g[2*i+1] = 2*alpha*t1;
172: }
173: }
175: /* Restore vectors */
176: VecRestoreArrayRead(X,&x);
177: VecRestoreArrayWrite(G,&g);
178: *f = ff;
180: PetscLogFlops(15.0*nn);
181: return(0);
182: }
184: /* ------------------------------------------------------------------- */
185: /*
186: FormHessian - Evaluates Hessian matrix.
188: Input Parameters:
189: . tao - the Tao context
190: . x - input vector
191: . ptr - optional user-defined context, as set by TaoSetHessian()
193: Output Parameters:
194: . H - Hessian matrix
196: Note: Providing the Hessian may not be necessary. Only some solvers
197: require this matrix.
198: */
199: PetscErrorCode FormHessian(Tao tao,Vec X,Mat H, Mat Hpre, void *ptr)
200: {
201: AppCtx *user = (AppCtx*)ptr;
202: PetscErrorCode ierr;
203: PetscInt i, ind[2];
204: PetscReal alpha=user->alpha;
205: PetscReal v[2][2];
206: const PetscScalar *x;
207: PetscBool assembled;
210: /* Zero existing matrix entries */
211: MatAssembled(H,&assembled);
212: if (assembled || user->chained){MatZeroEntries(H);}
214: /* Get a pointer to vector data */
215: VecGetArrayRead(X,&x);
217: /* Compute H(X) entries */
218: if (user->chained) {
219: for (i=0; i<user->n-1; i++) {
220: PetscScalar t1 = x[i+1] - x[i]*x[i];
221: v[0][0] = 2 + 2*alpha*(t1*(-2) - 2*x[i]);
222: v[0][1] = 2*alpha*(-2*x[i]);
223: v[1][0] = 2*alpha*(-2*x[i]);
224: v[1][1] = 2*alpha*t1;
225: ind[0] = i; ind[1] = i+1;
226: MatSetValues(H,2,ind,2,ind,v[0],ADD_VALUES);
227: }
228: } else {
229: for (i=0; i<user->n/2; i++){
230: v[1][1] = 2*alpha;
231: v[0][0] = -4*alpha*(x[2*i+1]-3*x[2*i]*x[2*i]) + 2;
232: v[1][0] = v[0][1] = -4.0*alpha*x[2*i];
233: ind[0]=2*i; ind[1]=2*i+1;
234: MatSetValues(H,2,ind,2,ind,v[0],INSERT_VALUES);
235: }
236: }
237: VecRestoreArrayRead(X,&x);
239: /* Assemble matrix */
240: MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY);
241: MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY);
242: PetscLogFlops(9.0*user->n/2.0);
243: return(0);
244: }
247: /*TEST
249: build:
250: requires: !complex
252: test:
253: args: -tao_type bqnls -tao_monitor
254: requires: !single
256: TEST*/