Actual source code: rosenbrock1.c
petsc-3.7.5 2017-01-01
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";
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: 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: AppCtx user; /* user-defined application context */
51: /* Initialize TAO and PETSc */
52: PetscInitialize(&argc,&argv,(char*)0,help);
53: MPI_Comm_size(PETSC_COMM_WORLD,&size);
54: MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
55: if (size >1) SETERRQ(PETSC_COMM_SELF,1,"Incorrect number of processors");
57: /* Initialize problem parameters */
58: user.n = 2; user.alpha = 99.0;
59: /* Check for command line arguments to override defaults */
60: PetscOptionsGetInt(NULL,NULL,"-n",&user.n,&flg);
61: PetscOptionsGetReal(NULL,NULL,"-alpha",&user.alpha,&flg);
63: /* Allocate vectors for the solution and gradient */
64: VecCreateSeq(PETSC_COMM_SELF,user.n,&x);
65: MatCreateSeqBAIJ(PETSC_COMM_SELF,2,user.n,user.n,1,NULL,&H);
67: /* The TAO code begins here */
69: /* Create TAO solver with desired solution method */
70: TaoCreate(PETSC_COMM_SELF,&tao);
71: TaoSetType(tao,TAOLMVM);
73: /* Set solution vec and an initial guess */
74: VecSet(x, zero);
75: TaoSetInitialVector(tao,x);
77: /* Set routines for function, gradient, hessian evaluation */
78: TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,&user);
79: TaoSetHessianRoutine(tao,H,H,FormHessian,&user);
81: /* Check for TAO command line options */
82: TaoSetFromOptions(tao);
84: /* SOLVE THE APPLICATION */
85: TaoSolve(tao);
87: TaoDestroy(&tao);
88: VecDestroy(&x);
89: MatDestroy(&H);
91: PetscFinalize();
92: return 0;
93: }
95: /* -------------------------------------------------------------------- */
98: /*
99: FormFunctionGradient - Evaluates the function, f(X), and gradient, G(X).
101: Input Parameters:
102: . tao - the Tao context
103: . X - input vector
104: . ptr - optional user-defined context, as set by TaoSetFunctionGradient()
106: Output Parameters:
107: . G - vector containing the newly evaluated gradient
108: . f - function value
110: Note:
111: Some optimization methods ask for the function and the gradient evaluation
112: at the same time. Evaluating both at once may be more efficient that
113: evaluating each separately.
114: */
115: PetscErrorCode FormFunctionGradient(Tao tao,Vec X,PetscReal *f, Vec G,void *ptr)
116: {
117: AppCtx *user = (AppCtx *) ptr;
118: PetscInt i,nn=user->n/2;
120: PetscReal ff=0,t1,t2,alpha=user->alpha;
121: PetscReal *x,*g;
123: /* Get pointers to vector data */
124: VecGetArray(X,&x);
125: VecGetArray(G,&g);
127: /* Compute G(X) */
128: for (i=0; i<nn; i++){
129: t1 = x[2*i+1]-x[2*i]*x[2*i]; t2= 1-x[2*i];
130: ff += alpha*t1*t1 + t2*t2;
131: g[2*i] = -4*alpha*t1*x[2*i]-2.0*t2;
132: g[2*i+1] = 2*alpha*t1;
133: }
135: /* Restore vectors */
136: VecRestoreArray(X,&x);
137: VecRestoreArray(G,&g);
138: *f=ff;
140: PetscLogFlops(nn*15);
141: return 0;
142: }
144: /* ------------------------------------------------------------------- */
147: /*
148: FormHessian - Evaluates Hessian matrix.
150: Input Parameters:
151: . tao - the Tao context
152: . x - input vector
153: . ptr - optional user-defined context, as set by TaoSetHessian()
155: Output Parameters:
156: . H - Hessian matrix
158: Note: Providing the Hessian may not be necessary. Only some solvers
159: require this matrix.
160: */
161: PetscErrorCode FormHessian(Tao tao,Vec X,Mat H, Mat Hpre, void *ptr)
162: {
163: AppCtx *user = (AppCtx*)ptr;
165: PetscInt i, ind[2];
166: PetscReal alpha=user->alpha;
167: PetscReal v[2][2],*x;
168: PetscBool assembled;
170: /* Zero existing matrix entries */
171: MatAssembled(H,&assembled);
172: if (assembled){MatZeroEntries(H); }
174: /* Get a pointer to vector data */
175: VecGetArray(X,&x);
177: /* Compute H(X) entries */
178: for (i=0; i<user->n/2; i++){
179: v[1][1] = 2*alpha;
180: v[0][0] = -4*alpha*(x[2*i+1]-3*x[2*i]*x[2*i]) + 2;
181: v[1][0] = v[0][1] = -4.0*alpha*x[2*i];
182: ind[0]=2*i; ind[1]=2*i+1;
183: MatSetValues(H,2,ind,2,ind,v[0],INSERT_VALUES);
184: }
185: VecRestoreArray(X,&x);
187: /* Assemble matrix */
188: MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY);
189: MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY);
190: PetscLogFlops(9.0*user->n/2.0);
191: return 0;
192: }