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: /*
14: User-defined application context - contains data needed by the
15: application-provided call-back routines that evaluate the function,
16: gradient, and hessian.
17: */
18: typedef struct {
19: PetscInt n; /* dimension */
20: PetscReal alpha; /* condition parameter */
21: PetscBool chained;
22: } AppCtx;
24: /* -------------- User-defined routines ---------- */
25: PetscErrorCode FormFunctionGradient(Tao,Vec,PetscReal*,Vec,void*);
26: PetscErrorCode FormHessian(Tao,Vec,Mat,Mat,void*);
28: int main(int argc,char **argv)
29: {
30: PetscReal zero=0.0;
31: Vec x; /* solution vector */
32: Mat H;
33: Tao tao; /* Tao solver context */
34: PetscBool flg, test_lmvm = PETSC_FALSE;
35: PetscMPIInt size; /* number of processes running */
36: AppCtx user; /* user-defined application context */
37: TaoConvergedReason reason;
38: PetscInt its, recycled_its=0, oneshot_its=0;
40: /* Initialize TAO and PETSc */
41: PetscInitialize(&argc,&argv,(char*)0,help);
42: MPI_Comm_size(PETSC_COMM_WORLD,&size);
45: /* Initialize problem parameters */
46: user.n = 2; user.alpha = 99.0; user.chained = PETSC_FALSE;
47: /* Check for command line arguments to override defaults */
48: PetscOptionsGetInt(NULL,NULL,"-n",&user.n,&flg);
49: PetscOptionsGetReal(NULL,NULL,"-alpha",&user.alpha,&flg);
50: PetscOptionsGetBool(NULL,NULL,"-chained",&user.chained,&flg);
51: PetscOptionsGetBool(NULL,NULL,"-test_lmvm",&test_lmvm,&flg);
53: /* Allocate vectors for the solution and gradient */
54: VecCreateSeq(PETSC_COMM_SELF,user.n,&x);
55: MatCreateSeqBAIJ(PETSC_COMM_SELF,2,user.n,user.n,1,NULL,&H);
57: /* The TAO code begins here */
59: /* Create TAO solver with desired solution method */
60: TaoCreate(PETSC_COMM_SELF,&tao);
61: TaoSetType(tao,TAOLMVM);
63: /* Set solution vec and an initial guess */
64: VecSet(x, zero);
65: TaoSetSolution(tao,x);
67: /* Set routines for function, gradient, hessian evaluation */
68: TaoSetObjectiveAndGradient(tao,NULL,FormFunctionGradient,&user);
69: TaoSetHessian(tao,H,H,FormHessian,&user);
71: /* Check for TAO command line options */
72: TaoSetFromOptions(tao);
74: /* Solve the problem */
75: TaoSetTolerances(tao, 1.e-5, 0.0, 0.0);
76: TaoSetMaximumIterations(tao, 5);
77: TaoLMVMRecycle(tao, PETSC_TRUE);
78: reason = TAO_CONTINUE_ITERATING;
79: while (reason != TAO_CONVERGED_GATOL) {
80: TaoSolve(tao);
81: TaoGetConvergedReason(tao, &reason);
82: TaoGetIterationNumber(tao, &its);
83: recycled_its += its;
84: PetscPrintf(PETSC_COMM_SELF, "-----------------------\n");
85: }
87: /* Disable recycling and solve again! */
88: TaoSetMaximumIterations(tao, 100);
89: TaoLMVMRecycle(tao, PETSC_FALSE);
90: VecSet(x, zero);
91: TaoSolve(tao);
92: TaoGetConvergedReason(tao, &reason);
94: TaoGetIterationNumber(tao, &oneshot_its);
95: PetscPrintf(PETSC_COMM_SELF, "-----------------------\n");
96: PetscPrintf(PETSC_COMM_SELF, "recycled its: %D | oneshot its: %D\n", recycled_its, oneshot_its);
99: TaoDestroy(&tao);
100: VecDestroy(&x);
101: MatDestroy(&H);
103: PetscFinalize();
104: return 0;
105: }
107: /* -------------------------------------------------------------------- */
108: /*
109: FormFunctionGradient - Evaluates the function, f(X), and gradient, G(X).
111: Input Parameters:
112: . tao - the Tao context
113: . X - input vector
114: . ptr - optional user-defined context, as set by TaoSetFunctionGradient()
116: Output Parameters:
117: . G - vector containing the newly evaluated gradient
118: . f - function value
120: Note:
121: Some optimization methods ask for the function and the gradient evaluation
122: at the same time. Evaluating both at once may be more efficient that
123: evaluating each separately.
124: */
125: PetscErrorCode FormFunctionGradient(Tao tao,Vec X,PetscReal *f, Vec G,void *ptr)
126: {
127: AppCtx *user = (AppCtx *) ptr;
128: PetscInt i,nn=user->n/2;
129: PetscReal ff=0,t1,t2,alpha=user->alpha;
130: PetscScalar *g;
131: const PetscScalar *x;
134: /* Get pointers to vector data */
135: VecGetArrayRead(X,&x);
136: VecGetArray(G,&g);
138: /* Compute G(X) */
139: if (user->chained) {
140: g[0] = 0;
141: for (i=0; i<user->n-1; i++) {
142: t1 = x[i+1] - x[i]*x[i];
143: ff += PetscSqr(1 - x[i]) + alpha*t1*t1;
144: g[i] += -2*(1 - x[i]) + 2*alpha*t1*(-2*x[i]);
145: g[i+1] = 2*alpha*t1;
146: }
147: } else {
148: for (i=0; i<nn; i++) {
149: t1 = x[2*i+1]-x[2*i]*x[2*i]; t2= 1-x[2*i];
150: ff += alpha*t1*t1 + t2*t2;
151: g[2*i] = -4*alpha*t1*x[2*i]-2.0*t2;
152: g[2*i+1] = 2*alpha*t1;
153: }
154: }
156: /* Restore vectors */
157: VecRestoreArrayRead(X,&x);
158: VecRestoreArray(G,&g);
159: *f = ff;
161: PetscLogFlops(15.0*nn);
162: return 0;
163: }
165: /* ------------------------------------------------------------------- */
166: /*
167: FormHessian - Evaluates Hessian matrix.
169: Input Parameters:
170: . tao - the Tao 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(Tao tao,Vec X,Mat H, Mat Hpre, void *ptr)
181: {
182: AppCtx *user = (AppCtx*)ptr;
183: PetscInt i, ind[2];
184: PetscReal alpha=user->alpha;
185: PetscReal v[2][2];
186: const PetscScalar *x;
187: PetscBool assembled;
190: /* Zero existing matrix entries */
191: MatAssembled(H,&assembled);
192: if (assembled) MatZeroEntries(H);
194: /* Get a pointer to vector data */
195: VecGetArrayRead(X,&x);
197: /* Compute H(X) entries */
198: if (user->chained) {
199: MatZeroEntries(H);
200: for (i=0; i<user->n-1; i++) {
201: PetscScalar t1 = x[i+1] - x[i]*x[i];
202: v[0][0] = 2 + 2*alpha*(t1*(-2) - 2*x[i]);
203: v[0][1] = 2*alpha*(-2*x[i]);
204: v[1][0] = 2*alpha*(-2*x[i]);
205: v[1][1] = 2*alpha*t1;
206: ind[0] = i; ind[1] = i+1;
207: MatSetValues(H,2,ind,2,ind,v[0],ADD_VALUES);
208: }
209: } else {
210: for (i=0; i<user->n/2; i++) {
211: v[1][1] = 2*alpha;
212: v[0][0] = -4*alpha*(x[2*i+1]-3*x[2*i]*x[2*i]) + 2;
213: v[1][0] = v[0][1] = -4.0*alpha*x[2*i];
214: ind[0]=2*i; ind[1]=2*i+1;
215: MatSetValues(H,2,ind,2,ind,v[0],INSERT_VALUES);
216: }
217: }
218: VecRestoreArrayRead(X,&x);
220: /* Assemble matrix */
221: MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY);
222: MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY);
223: PetscLogFlops(9.0*user->n/2.0);
224: return 0;
225: }
227: /*TEST
229: build:
230: requires: !complex
232: test:
233: args: -tao_type lmvm -tao_monitor
234: requires: !single
236: TEST*/