Actual source code: rosenbrock2.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,TAOLMVM);
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: TaoLMVMRecycle(tao, PETSC_TRUE);
91: reason = TAO_CONTINUE_ITERATING;
92: while (reason != TAO_CONVERGED_GATOL) {
93: TaoSolve(tao);
94: TaoGetConvergedReason(tao, &reason);
95: TaoGetIterationNumber(tao, &its);
96: recycled_its += its;
97: PetscPrintf(PETSC_COMM_SELF, "-----------------------\n");
98: }
100: /* Disable recycling and solve again! */
101: TaoSetMaximumIterations(tao, 100);
102: TaoLMVMRecycle(tao, PETSC_FALSE);
103: VecSet(x, zero);
104: TaoSolve(tao);
105: TaoGetConvergedReason(tao, &reason);
106: if (reason != TAO_CONVERGED_GATOL) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "Solution failed to converge!");
107: TaoGetIterationNumber(tao, &oneshot_its);
108: PetscPrintf(PETSC_COMM_SELF, "-----------------------\n");
109: PetscPrintf(PETSC_COMM_SELF, "recycled its: %D | oneshot its: %D\n", recycled_its, oneshot_its);
110: if (recycled_its != oneshot_its) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "LMVM recycling does not work!");
112: TaoDestroy(&tao);
113: VecDestroy(&x);
114: MatDestroy(&H);
116: PetscFinalize();
117: return ierr;
118: }
120: /* -------------------------------------------------------------------- */
121: /*
122: FormFunctionGradient - Evaluates the function, f(X), and gradient, G(X).
124: Input Parameters:
125: . tao - the Tao context
126: . X - input vector
127: . ptr - optional user-defined context, as set by TaoSetFunctionGradient()
129: Output Parameters:
130: . G - vector containing the newly evaluated gradient
131: . f - function value
133: Note:
134: Some optimization methods ask for the function and the gradient evaluation
135: at the same time. Evaluating both at once may be more efficient that
136: evaluating each separately.
137: */
138: PetscErrorCode FormFunctionGradient(Tao tao,Vec X,PetscReal *f, Vec G,void *ptr)
139: {
140: AppCtx *user = (AppCtx *) ptr;
141: PetscInt i,nn=user->n/2;
142: PetscErrorCode ierr;
143: PetscReal ff=0,t1,t2,alpha=user->alpha;
144: PetscScalar *g;
145: const PetscScalar *x;
148: /* Get pointers to vector data */
149: VecGetArrayRead(X,&x);
150: VecGetArray(G,&g);
152: /* Compute G(X) */
153: if (user->chained) {
154: g[0] = 0;
155: for (i=0; i<user->n-1; i++) {
156: t1 = x[i+1] - x[i]*x[i];
157: ff += PetscSqr(1 - x[i]) + alpha*t1*t1;
158: g[i] += -2*(1 - x[i]) + 2*alpha*t1*(-2*x[i]);
159: g[i+1] = 2*alpha*t1;
160: }
161: } else {
162: for (i=0; i<nn; i++) {
163: t1 = x[2*i+1]-x[2*i]*x[2*i]; t2= 1-x[2*i];
164: ff += alpha*t1*t1 + t2*t2;
165: g[2*i] = -4*alpha*t1*x[2*i]-2.0*t2;
166: g[2*i+1] = 2*alpha*t1;
167: }
168: }
170: /* Restore vectors */
171: VecRestoreArrayRead(X,&x);
172: VecRestoreArray(G,&g);
173: *f = ff;
175: PetscLogFlops(15.0*nn);
176: return(0);
177: }
179: /* ------------------------------------------------------------------- */
180: /*
181: FormHessian - Evaluates Hessian matrix.
183: Input Parameters:
184: . tao - the Tao context
185: . x - input vector
186: . ptr - optional user-defined context, as set by TaoSetHessian()
188: Output Parameters:
189: . H - Hessian matrix
191: Note: Providing the Hessian may not be necessary. Only some solvers
192: require this matrix.
193: */
194: PetscErrorCode FormHessian(Tao tao,Vec X,Mat H, Mat Hpre, void *ptr)
195: {
196: AppCtx *user = (AppCtx*)ptr;
197: PetscErrorCode ierr;
198: PetscInt i, ind[2];
199: PetscReal alpha=user->alpha;
200: PetscReal v[2][2];
201: const PetscScalar *x;
202: PetscBool assembled;
205: /* Zero existing matrix entries */
206: MatAssembled(H,&assembled);
207: if (assembled) {MatZeroEntries(H);}
209: /* Get a pointer to vector data */
210: VecGetArrayRead(X,&x);
212: /* Compute H(X) entries */
213: if (user->chained) {
214: MatZeroEntries(H);
215: for (i=0; i<user->n-1; i++) {
216: PetscScalar t1 = x[i+1] - x[i]*x[i];
217: v[0][0] = 2 + 2*alpha*(t1*(-2) - 2*x[i]);
218: v[0][1] = 2*alpha*(-2*x[i]);
219: v[1][0] = 2*alpha*(-2*x[i]);
220: v[1][1] = 2*alpha*t1;
221: ind[0] = i; ind[1] = i+1;
222: MatSetValues(H,2,ind,2,ind,v[0],ADD_VALUES);
223: }
224: } else {
225: for (i=0; i<user->n/2; i++) {
226: v[1][1] = 2*alpha;
227: v[0][0] = -4*alpha*(x[2*i+1]-3*x[2*i]*x[2*i]) + 2;
228: v[1][0] = v[0][1] = -4.0*alpha*x[2*i];
229: ind[0]=2*i; ind[1]=2*i+1;
230: MatSetValues(H,2,ind,2,ind,v[0],INSERT_VALUES);
231: }
232: }
233: VecRestoreArrayRead(X,&x);
235: /* Assemble matrix */
236: MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY);
237: MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY);
238: PetscLogFlops(9.0*user->n/2.0);
239: return(0);
240: }
242: /*TEST
244: build:
245: requires: !complex
247: test:
248: args: -tao_type lmvm -tao_monitor
249: requires: !single
251: TEST*/