Actual source code: rosenbrock1.c
petsc-3.9.4 2018-09-11
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*/
28: /*
29: User-defined application context - contains data needed by the
30: application-provided call-back routines that evaluate the function,
31: gradient, and hessian.
32: */
33: typedef struct {
34: PetscInt n; /* dimension */
35: PetscReal alpha; /* condition parameter */
36: PetscBool chained;
37: } AppCtx;
39: /* -------------- User-defined routines ---------- */
40: PetscErrorCode FormFunctionGradient(Tao,Vec,PetscReal*,Vec,void*);
41: PetscErrorCode FormHessian(Tao,Vec,Mat,Mat,void*);
43: int main(int argc,char **argv)
44: {
45: PetscErrorCode ierr; /* used to check for functions returning nonzeros */
46: PetscReal zero=0.0;
47: Vec x; /* solution vector */
48: Mat H;
49: Tao tao; /* Tao solver context */
50: PetscBool flg;
51: PetscMPIInt size,rank; /* number of processes running */
52: AppCtx user; /* user-defined application context */
54: /* Initialize TAO and PETSc */
55: PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
56: MPI_Comm_size(PETSC_COMM_WORLD,&size);
57: MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
58: if (size >1) SETERRQ(PETSC_COMM_SELF,1,"Incorrect number of processors");
60: /* Initialize problem parameters */
61: user.n = 2; user.alpha = 99.0; user.chained = PETSC_FALSE;
62: /* Check for command line arguments to override defaults */
63: PetscOptionsGetInt(NULL,NULL,"-n",&user.n,&flg);
64: PetscOptionsGetReal(NULL,NULL,"-alpha",&user.alpha,&flg);
65: PetscOptionsGetBool(NULL,NULL,"-chained",&user.chained,&flg);
67: /* Allocate vectors for the solution and gradient */
68: VecCreateSeq(PETSC_COMM_SELF,user.n,&x);
69: MatCreateSeqBAIJ(PETSC_COMM_SELF,2,user.n,user.n,1,NULL,&H);
71: /* The TAO code begins here */
73: /* Create TAO solver with desired solution method */
74: TaoCreate(PETSC_COMM_SELF,&tao);
75: TaoSetType(tao,TAOLMVM);
77: /* Set solution vec and an initial guess */
78: VecSet(x, zero);
79: TaoSetInitialVector(tao,x);
81: /* Set routines for function, gradient, hessian evaluation */
82: TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,&user);
83: TaoSetHessianRoutine(tao,H,H,FormHessian,&user);
85: /* Check for TAO command line options */
86: TaoSetFromOptions(tao);
88: /* SOLVE THE APPLICATION */
89: TaoSolve(tao);
91: TaoDestroy(&tao);
92: VecDestroy(&x);
93: MatDestroy(&H);
95: PetscFinalize();
96: return ierr;
97: }
99: /* -------------------------------------------------------------------- */
100: /*
101: FormFunctionGradient - Evaluates the function, f(X), and gradient, G(X).
103: Input Parameters:
104: . tao - the Tao context
105: . X - input vector
106: . ptr - optional user-defined context, as set by TaoSetFunctionGradient()
108: Output Parameters:
109: . G - vector containing the newly evaluated gradient
110: . f - function value
112: Note:
113: Some optimization methods ask for the function and the gradient evaluation
114: at the same time. Evaluating both at once may be more efficient that
115: evaluating each separately.
116: */
117: PetscErrorCode FormFunctionGradient(Tao tao,Vec X,PetscReal *f, Vec G,void *ptr)
118: {
119: AppCtx *user = (AppCtx *) ptr;
120: PetscInt i,nn=user->n/2;
121: PetscErrorCode ierr;
122: PetscReal ff=0,t1,t2,alpha=user->alpha;
123: PetscScalar *g;
124: const PetscScalar *x;
127: /* Get pointers to vector data */
128: VecGetArrayRead(X,&x);
129: VecGetArray(G,&g);
131: /* Compute G(X) */
132: if (user->chained) {
133: g[0] = 0;
134: for (i=0; i<user->n-1; i++) {
135: t1 = x[i+1] - x[i]*x[i];
136: ff += PetscSqr(1 - x[i]) + alpha*t1*t1;
137: g[i] += -2*(1 - x[i]) + 2*alpha*t1*(-2*x[i]);
138: g[i+1] = 2*alpha*t1;
139: }
140: } else {
141: for (i=0; i<nn; i++){
142: t1 = x[2*i+1]-x[2*i]*x[2*i]; t2= 1-x[2*i];
143: ff += alpha*t1*t1 + t2*t2;
144: g[2*i] = -4*alpha*t1*x[2*i]-2.0*t2;
145: g[2*i+1] = 2*alpha*t1;
146: }
147: }
149: /* Restore vectors */
150: VecRestoreArrayRead(X,&x);
151: VecRestoreArray(G,&g);
152: *f = ff;
154: PetscLogFlops(nn*15);
155: return(0);
156: }
158: /* ------------------------------------------------------------------- */
159: /*
160: FormHessian - Evaluates Hessian matrix.
162: Input Parameters:
163: . tao - the Tao context
164: . x - input vector
165: . ptr - optional user-defined context, as set by TaoSetHessian()
167: Output Parameters:
168: . H - Hessian matrix
170: Note: Providing the Hessian may not be necessary. Only some solvers
171: require this matrix.
172: */
173: PetscErrorCode FormHessian(Tao tao,Vec X,Mat H, Mat Hpre, void *ptr)
174: {
175: AppCtx *user = (AppCtx*)ptr;
176: PetscErrorCode ierr;
177: PetscInt i, ind[2];
178: PetscReal alpha=user->alpha;
179: PetscReal v[2][2];
180: const PetscScalar *x;
181: PetscBool assembled;
184: /* Zero existing matrix entries */
185: MatAssembled(H,&assembled);
186: if (assembled){MatZeroEntries(H); }
188: /* Get a pointer to vector data */
189: VecGetArrayRead(X,&x);
191: /* Compute H(X) entries */
192: if (user->chained) {
193: MatZeroEntries(H);
194: for (i=0; i<user->n-1; i++) {
195: PetscScalar t1 = x[i+1] - x[i]*x[i];
196: v[0][0] = 2 + 2*alpha*(t1*(-2) - 2*x[i]);
197: v[0][1] = 2*alpha*(-2*x[i]);
198: v[1][0] = 2*alpha*(-2*x[i]);
199: v[1][1] = 2*alpha*t1;
200: ind[0] = i; ind[1] = i+1;
201: MatSetValues(H,2,ind,2,ind,v[0],ADD_VALUES);
202: }
203: } else {
204: for (i=0; i<user->n/2; i++){
205: v[1][1] = 2*alpha;
206: v[0][0] = -4*alpha*(x[2*i+1]-3*x[2*i]*x[2*i]) + 2;
207: v[1][0] = v[0][1] = -4.0*alpha*x[2*i];
208: ind[0]=2*i; ind[1]=2*i+1;
209: MatSetValues(H,2,ind,2,ind,v[0],INSERT_VALUES);
210: }
211: }
212: VecRestoreArrayRead(X,&x);
214: /* Assemble matrix */
215: MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY);
216: MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY);
217: PetscLogFlops(9.0*user->n/2.0);
218: return(0);
219: }
222: /*TEST
224: build:
225: requires: !complex
227: test:
228: args: -tao_smonitor -tao_type nls
229: requires: !single
231: test:
232: suffix: 2
233: args: -tao_smonitor -tao_type lmvm -tao_gttol 1.e-2
235: test:
236: suffix: 3
237: args: -tao_smonitor -tao_type ntr
238: requires: !single
240: test:
241: suffix: 4
242: args: -tao_smonitor -tao_type ntr -tao_mf_hessian -tao_ntr_pc_type none
244: TEST*/