Actual source code: rosenbrock1.c
petsc-3.10.5 2019-03-28
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, test_lmvm = PETSC_FALSE;
51: PetscMPIInt size,rank; /* number of processes running */
52: AppCtx user; /* user-defined application context */
53: KSP ksp;
54: PC pc;
55: Mat M;
56: Vec in, out, out2;
57: PetscReal mult_solve_dist;
59: /* Initialize TAO and PETSc */
60: PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
61: MPI_Comm_size(PETSC_COMM_WORLD,&size);
62: MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
63: if (size >1) SETERRQ(PETSC_COMM_SELF,1,"Incorrect number of processors");
65: /* Initialize problem parameters */
66: user.n = 2; user.alpha = 99.0; user.chained = PETSC_FALSE;
67: /* Check for command line arguments to override defaults */
68: PetscOptionsGetInt(NULL,NULL,"-n",&user.n,&flg);
69: PetscOptionsGetReal(NULL,NULL,"-alpha",&user.alpha,&flg);
70: PetscOptionsGetBool(NULL,NULL,"-chained",&user.chained,&flg);
71: PetscOptionsGetBool(NULL,NULL,"-test_lmvm",&test_lmvm,&flg);
73: /* Allocate vectors for the solution and gradient */
74: VecCreateSeq(PETSC_COMM_SELF,user.n,&x);
75: MatCreateSeqBAIJ(PETSC_COMM_SELF,2,user.n,user.n,1,NULL,&H);
77: /* The TAO code begins here */
79: /* Create TAO solver with desired solution method */
80: TaoCreate(PETSC_COMM_SELF,&tao);
81: TaoSetType(tao,TAOLMVM);
83: /* Set solution vec and an initial guess */
84: VecSet(x, zero);
85: TaoSetInitialVector(tao,x);
87: /* Set routines for function, gradient, hessian evaluation */
88: TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,&user);
89: TaoSetHessianRoutine(tao,H,H,FormHessian,&user);
90:
91: /* Test the LMVM matrix */
92: if (test_lmvm) {
93: PetscOptionsSetValue(NULL, "-tao_type", "bqnktr");
94: }
96: /* Check for TAO command line options */
97: TaoSetFromOptions(tao);
99: /* SOLVE THE APPLICATION */
100: TaoSolve(tao);
101:
102: /* Test the LMVM matrix */
103: if (test_lmvm) {
104: TaoGetKSP(tao, &ksp);
105: KSPGetPC(ksp, &pc);
106: PCLMVMGetMatLMVM(pc, &M);
107: VecDuplicate(x, &in);
108: VecDuplicate(x, &out);
109: VecDuplicate(x, &out2);
110: VecSet(in, 1.0);
111: MatMult(M, in, out);
112: MatSolve(M, out, out2);
113: VecAXPY(out2, -1.0, in);
114: VecNorm(out2, NORM_2, &mult_solve_dist);
115: if (mult_solve_dist < 1.e-11) {
116: PetscPrintf(PetscObjectComm((PetscObject)tao), "error between LMVM MatMult and MatSolve: < 1.e-11\n");
117: } else if(mult_solve_dist < 1.e-6) {
118: PetscPrintf(PetscObjectComm((PetscObject)tao), "error between LMVM MatMult and MatSolve: < 1.e-6\n");
119: } else {
120: PetscPrintf(PetscObjectComm((PetscObject)tao), "error between LMVM MatMult and MatSolve: %e\n", (double)mult_solve_dist);
121: }
122: VecDestroy(&in);
123: VecDestroy(&out);
124: VecDestroy(&out2);
125: }
127: TaoDestroy(&tao);
128: VecDestroy(&x);
129: MatDestroy(&H);
131: PetscFinalize();
132: return ierr;
133: }
135: /* -------------------------------------------------------------------- */
136: /*
137: FormFunctionGradient - Evaluates the function, f(X), and gradient, G(X).
139: Input Parameters:
140: . tao - the Tao context
141: . X - input vector
142: . ptr - optional user-defined context, as set by TaoSetFunctionGradient()
144: Output Parameters:
145: . G - vector containing the newly evaluated gradient
146: . f - function value
148: Note:
149: Some optimization methods ask for the function and the gradient evaluation
150: at the same time. Evaluating both at once may be more efficient that
151: evaluating each separately.
152: */
153: PetscErrorCode FormFunctionGradient(Tao tao,Vec X,PetscReal *f, Vec G,void *ptr)
154: {
155: AppCtx *user = (AppCtx *) ptr;
156: PetscInt i,nn=user->n/2;
157: PetscErrorCode ierr;
158: PetscReal ff=0,t1,t2,alpha=user->alpha;
159: PetscScalar *g;
160: const PetscScalar *x;
163: /* Get pointers to vector data */
164: VecGetArrayRead(X,&x);
165: VecGetArray(G,&g);
167: /* Compute G(X) */
168: if (user->chained) {
169: g[0] = 0;
170: for (i=0; i<user->n-1; i++) {
171: t1 = x[i+1] - x[i]*x[i];
172: ff += PetscSqr(1 - x[i]) + alpha*t1*t1;
173: g[i] += -2*(1 - x[i]) + 2*alpha*t1*(-2*x[i]);
174: g[i+1] = 2*alpha*t1;
175: }
176: } else {
177: for (i=0; i<nn; i++){
178: t1 = x[2*i+1]-x[2*i]*x[2*i]; t2= 1-x[2*i];
179: ff += alpha*t1*t1 + t2*t2;
180: g[2*i] = -4*alpha*t1*x[2*i]-2.0*t2;
181: g[2*i+1] = 2*alpha*t1;
182: }
183: }
185: /* Restore vectors */
186: VecRestoreArrayRead(X,&x);
187: VecRestoreArray(G,&g);
188: *f = ff;
190: PetscLogFlops(nn*15);
191: return(0);
192: }
194: /* ------------------------------------------------------------------- */
195: /*
196: FormHessian - Evaluates Hessian matrix.
198: Input Parameters:
199: . tao - the Tao context
200: . x - input vector
201: . ptr - optional user-defined context, as set by TaoSetHessian()
203: Output Parameters:
204: . H - Hessian matrix
206: Note: Providing the Hessian may not be necessary. Only some solvers
207: require this matrix.
208: */
209: PetscErrorCode FormHessian(Tao tao,Vec X,Mat H, Mat Hpre, void *ptr)
210: {
211: AppCtx *user = (AppCtx*)ptr;
212: PetscErrorCode ierr;
213: PetscInt i, ind[2];
214: PetscReal alpha=user->alpha;
215: PetscReal v[2][2];
216: const PetscScalar *x;
217: PetscBool assembled;
220: /* Zero existing matrix entries */
221: MatAssembled(H,&assembled);
222: if (assembled){MatZeroEntries(H); }
224: /* Get a pointer to vector data */
225: VecGetArrayRead(X,&x);
227: /* Compute H(X) entries */
228: if (user->chained) {
229: MatZeroEntries(H);
230: for (i=0; i<user->n-1; i++) {
231: PetscScalar t1 = x[i+1] - x[i]*x[i];
232: v[0][0] = 2 + 2*alpha*(t1*(-2) - 2*x[i]);
233: v[0][1] = 2*alpha*(-2*x[i]);
234: v[1][0] = 2*alpha*(-2*x[i]);
235: v[1][1] = 2*alpha*t1;
236: ind[0] = i; ind[1] = i+1;
237: MatSetValues(H,2,ind,2,ind,v[0],ADD_VALUES);
238: }
239: } else {
240: for (i=0; i<user->n/2; i++){
241: v[1][1] = 2*alpha;
242: v[0][0] = -4*alpha*(x[2*i+1]-3*x[2*i]*x[2*i]) + 2;
243: v[1][0] = v[0][1] = -4.0*alpha*x[2*i];
244: ind[0]=2*i; ind[1]=2*i+1;
245: MatSetValues(H,2,ind,2,ind,v[0],INSERT_VALUES);
246: }
247: }
248: VecRestoreArrayRead(X,&x);
250: /* Assemble matrix */
251: MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY);
252: MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY);
253: PetscLogFlops(9.0*user->n/2.0);
254: return(0);
255: }
258: /*TEST
260: build:
261: requires: !complex
263: test:
264: args: -tao_smonitor -tao_type nls -tao_gatol 1.e-4
265: requires: !single
267: test:
268: suffix: 2
269: args: -tao_smonitor -tao_type lmvm -tao_gatol 1.e-3
271: test:
272: suffix: 3
273: args: -tao_smonitor -tao_type ntr -tao_gatol 1.e-4
274: requires: !single
276: test:
277: suffix: 4
278: args: -tao_smonitor -tao_type ntr -tao_mf_hessian -tao_ntr_pc_type none -tao_gatol 1.e-4
279:
280: test:
281: suffix: 5
282: args: -tao_smonitor -tao_type bntr -tao_gatol 1.e-4
283:
284: test:
285: suffix: 6
286: args: -tao_smonitor -tao_type bntl -tao_gatol 1.e-4
287:
288: test:
289: suffix: 7
290: args: -tao_smonitor -tao_type bnls -tao_gatol 1.e-4
291:
292: test:
293: suffix: 8
294: args: -tao_smonitor -tao_type bntr -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4
295:
296: test:
297: suffix: 9
298: args: -tao_smonitor -tao_type bntl -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4
299:
300: test:
301: suffix: 10
302: args: -tao_smonitor -tao_type bnls -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4
303:
304: test:
305: suffix: 11
306: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbrdn
307:
308: test:
309: suffix: 12
310: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbadbrdn
311:
312: test:
313: suffix: 13
314: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsymbrdn
316: test:
317: suffix: 14
318: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbfgs
319:
320: test:
321: suffix: 15
322: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmdfp
323:
324: test:
325: suffix: 16
326: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsr1
327:
328: test:
329: suffix: 17
330: args: -tao_smonitor -tao_gatol 1e-4 -tao_type bqnls
331:
332: test:
333: suffix: 18
334: args: -tao_smonitor -tao_gatol 1e-4 -tao_type blmvm
335:
336: test:
337: suffix: 19
338: args: -tao_smonitor -tao_gatol 1e-4 -tao_type bqnktr -tao_bqnk_mat_type lmvmsr1
339:
340: test:
341: suffix: 20
342: args: -tao_monitor -tao_gatol 1e-4 -tao_type blmvm -tao_ls_monitor
343:
344: test:
345: suffix: 21
346: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsymbadbrdn
348: TEST*/