Actual source code: rosenbrock1.c
petsc-3.6.4 2016-04-12
1: /* Program usage: mpirun -np 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";
11: /*T
12: Concepts: TAO^Solving an unconstrained minimization problem
13: Routines: TaoCreate();
14: Routines: TaoSetType(); TaoSetObjectiveAndGradientRoutine();
15: Routines: TaoSetHessianRoutine();
16: Routines: TaoSetInitialVector();
17: Routines: TaoSetFromOptions();
18: Routines: TaoSolve();
19: Routines: TaoGetConvergedReason(); TaoDestroy();
20: Processors: 1
21: T*/
24: /*
25: User-defined application context - contains data needed by the
26: application-provided call-back routines that evaluate the function,
27: gradient, and hessian.
28: */
29: typedef struct {
30: PetscInt n; /* dimension */
31: PetscReal alpha; /* condition parameter */
32: } AppCtx;
34: /* -------------- User-defined routines ---------- */
35: PetscErrorCode FormFunctionGradient(Tao,Vec,PetscReal*,Vec,void*);
36: 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;
48: PetscMPIInt size,rank; /* number of processes running */
49: TaoConvergedReason reason;
50: AppCtx user; /* user-defined application context */
52: /* Initialize TAO and PETSc */
53: PetscInitialize(&argc,&argv,(char*)0,help);
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;
60: /* Check for command line arguments to override defaults */
61: PetscOptionsGetInt(NULL,"-n",&user.n,&flg);
62: PetscOptionsGetReal(NULL,"-alpha",&user.alpha,&flg);
64: /* Allocate vectors for the solution and gradient */
65: VecCreateSeq(PETSC_COMM_SELF,user.n,&x);
66: MatCreateSeqBAIJ(PETSC_COMM_SELF,2,user.n,user.n,1,NULL,&H);
68: /* The TAO code begins here */
70: /* Create TAO solver with desired solution method */
71: TaoCreate(PETSC_COMM_SELF,&tao);
72: TaoSetType(tao,TAOLMVM);
74: /* Set solution vec and an initial guess */
75: VecSet(x, zero);
76: TaoSetInitialVector(tao,x);
78: /* Set routines for function, gradient, hessian evaluation */
79: TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,&user);
80: TaoSetHessianRoutine(tao,H,H,FormHessian,&user);
82: /* Check for TAO command line options */
83: TaoSetFromOptions(tao);
85: /* SOLVE THE APPLICATION */
86: TaoSolve(tao);
88: /* Get termination information */
89: TaoGetConvergedReason(tao,&reason);
90: if (reason <= 0) {
91: PetscPrintf(MPI_COMM_WORLD,"Try a different TAO type, adjust some parameters, or check the function evaluation routines\n");
92: }
94: TaoDestroy(&tao);
95: VecDestroy(&x);
96: MatDestroy(&H);
98: PetscFinalize();
99: return 0;
100: }
102: /* -------------------------------------------------------------------- */
105: /*
106: FormFunctionGradient - Evaluates the function, f(X), and gradient, G(X).
108: Input Parameters:
109: . tao - the Tao context
110: . X - input vector
111: . ptr - optional user-defined context, as set by TaoSetFunctionGradient()
113: Output Parameters:
114: . G - vector containing the newly evaluated gradient
115: . f - function value
117: Note:
118: Some optimization methods ask for the function and the gradient evaluation
119: at the same time. Evaluating both at once may be more efficient that
120: evaluating each separately.
121: */
122: PetscErrorCode FormFunctionGradient(Tao tao,Vec X,PetscReal *f, Vec G,void *ptr)
123: {
124: AppCtx *user = (AppCtx *) ptr;
125: PetscInt i,nn=user->n/2;
127: PetscReal ff=0,t1,t2,alpha=user->alpha;
128: PetscReal *x,*g;
130: /* Get pointers to vector data */
131: VecGetArray(X,&x);
132: VecGetArray(G,&g);
134: /* Compute G(X) */
135: for (i=0; i<nn; i++){
136: t1 = x[2*i+1]-x[2*i]*x[2*i]; t2= 1-x[2*i];
137: ff += alpha*t1*t1 + t2*t2;
138: g[2*i] = -4*alpha*t1*x[2*i]-2.0*t2;
139: g[2*i+1] = 2*alpha*t1;
140: }
142: /* Restore vectors */
143: VecRestoreArray(X,&x);
144: VecRestoreArray(G,&g);
145: *f=ff;
147: PetscLogFlops(nn*15);
148: return 0;
149: }
151: /* ------------------------------------------------------------------- */
154: /*
155: FormHessian - Evaluates Hessian matrix.
157: Input Parameters:
158: . tao - the Tao context
159: . x - input vector
160: . ptr - optional user-defined context, as set by TaoSetHessian()
162: Output Parameters:
163: . H - Hessian matrix
165: Note: Providing the Hessian may not be necessary. Only some solvers
166: require this matrix.
167: */
168: PetscErrorCode FormHessian(Tao tao,Vec X,Mat H, Mat Hpre, void *ptr)
169: {
170: AppCtx *user = (AppCtx*)ptr;
172: PetscInt i, nn=user->n/2, ind[2];
173: PetscReal alpha=user->alpha;
174: PetscReal v[2][2],*x;
175: PetscBool assembled;
177: /* Zero existing matrix entries */
178: MatAssembled(H,&assembled);
179: if (assembled){MatZeroEntries(H); }
181: /* Get a pointer to vector data */
182: VecGetArray(X,&x);
184: /* Compute H(X) entries */
185: for (i=0; i<user->n/2; i++){
186: v[1][1] = 2*alpha;
187: v[0][0] = -4*alpha*(x[2*i+1]-3*x[2*i]*x[2*i]) + 2;
188: v[1][0] = v[0][1] = -4.0*alpha*x[2*i];
189: ind[0]=2*i; ind[1]=2*i+1;
190: MatSetValues(H,2,ind,2,ind,v[0],INSERT_VALUES);
191: }
192: VecRestoreArray(X,&x);
194: /* Assemble matrix */
195: MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY);
196: MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY);
197: PetscLogFlops(nn*9);
198: return 0;
199: }