Actual source code: rosenbrock1.c
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: /*
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: KSP ksp;
38: PC pc;
39: Mat M;
40: Vec in, out, out2;
41: PetscReal mult_solve_dist;
43: /* Initialize TAO and PETSc */
44: PetscFunctionBeginUser;
45: PetscCall(PetscInitialize(&argc, &argv, (char *)0, help));
46: PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
47: PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Incorrect number of processors");
49: /* Initialize problem parameters */
50: user.n = 2;
51: user.alpha = 99.0;
52: user.chained = PETSC_FALSE;
53: /* Check for command line arguments to override defaults */
54: PetscCall(PetscOptionsGetInt(NULL, NULL, "-n", &user.n, &flg));
55: PetscCall(PetscOptionsGetReal(NULL, NULL, "-alpha", &user.alpha, &flg));
56: PetscCall(PetscOptionsGetBool(NULL, NULL, "-chained", &user.chained, &flg));
57: PetscCall(PetscOptionsGetBool(NULL, NULL, "-test_lmvm", &test_lmvm, &flg));
59: /* Allocate vectors for the solution and gradient */
60: PetscCall(VecCreateSeq(PETSC_COMM_SELF, user.n, &x));
61: PetscCall(MatCreateSeqBAIJ(PETSC_COMM_SELF, 2, user.n, user.n, 1, NULL, &H));
63: /* The TAO code begins here */
65: /* Create TAO solver with desired solution method */
66: PetscCall(TaoCreate(PETSC_COMM_SELF, &tao));
67: PetscCall(TaoSetType(tao, TAOLMVM));
69: /* Set solution vec and an initial guess */
70: PetscCall(VecSet(x, zero));
71: PetscCall(TaoSetSolution(tao, x));
73: /* Set routines for function, gradient, hessian evaluation */
74: PetscCall(TaoSetObjectiveAndGradient(tao, NULL, FormFunctionGradient, &user));
75: PetscCall(TaoSetHessian(tao, H, H, FormHessian, &user));
77: /* Test the LMVM matrix */
78: if (test_lmvm) PetscCall(PetscOptionsSetValue(NULL, "-tao_type", "bqnktr"));
80: /* Check for TAO command line options */
81: PetscCall(TaoSetFromOptions(tao));
83: /* SOLVE THE APPLICATION */
84: PetscCall(TaoSolve(tao));
86: /* Test the LMVM matrix */
87: if (test_lmvm) {
88: PetscCall(TaoGetKSP(tao, &ksp));
89: PetscCall(KSPGetPC(ksp, &pc));
90: PetscCall(PCLMVMGetMatLMVM(pc, &M));
91: PetscCall(VecDuplicate(x, &in));
92: PetscCall(VecDuplicate(x, &out));
93: PetscCall(VecDuplicate(x, &out2));
94: PetscCall(VecSet(in, 1.0));
95: PetscCall(MatMult(M, in, out));
96: PetscCall(MatSolve(M, out, out2));
97: PetscCall(VecAXPY(out2, -1.0, in));
98: PetscCall(VecNorm(out2, NORM_2, &mult_solve_dist));
99: if (mult_solve_dist < 1.e-11) {
100: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)tao), "error between LMVM MatMult and MatSolve: < 1.e-11\n"));
101: } else if (mult_solve_dist < 1.e-6) {
102: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)tao), "error between LMVM MatMult and MatSolve: < 1.e-6\n"));
103: } else {
104: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)tao), "error between LMVM MatMult and MatSolve: %e\n", (double)mult_solve_dist));
105: }
106: PetscCall(VecDestroy(&in));
107: PetscCall(VecDestroy(&out));
108: PetscCall(VecDestroy(&out2));
109: }
111: PetscCall(TaoDestroy(&tao));
112: PetscCall(VecDestroy(&x));
113: PetscCall(MatDestroy(&H));
115: PetscCall(PetscFinalize());
116: return 0;
117: }
119: /* -------------------------------------------------------------------- */
120: /*
121: FormFunctionGradient - Evaluates the function, f(X), and gradient, G(X).
123: Input Parameters:
124: . tao - the Tao context
125: . X - input vector
126: . ptr - optional user-defined context, as set by TaoSetFunctionGradient()
128: Output Parameters:
129: . G - vector containing the newly evaluated gradient
130: . f - function value
132: Note:
133: Some optimization methods ask for the function and the gradient evaluation
134: at the same time. Evaluating both at once may be more efficient that
135: evaluating each separately.
136: */
137: PetscErrorCode FormFunctionGradient(Tao tao, Vec X, PetscReal *f, Vec G, void *ptr)
138: {
139: AppCtx *user = (AppCtx *)ptr;
140: PetscInt i, nn = user->n / 2;
141: PetscReal ff = 0, t1, t2, alpha = user->alpha;
142: PetscScalar *g;
143: const PetscScalar *x;
145: PetscFunctionBeginUser;
146: /* Get pointers to vector data */
147: PetscCall(VecGetArrayRead(X, &x));
148: PetscCall(VecGetArray(G, &g));
150: /* Compute G(X) */
151: if (user->chained) {
152: g[0] = 0;
153: for (i = 0; i < user->n - 1; i++) {
154: t1 = x[i + 1] - x[i] * x[i];
155: ff += PetscSqr(1 - x[i]) + alpha * t1 * t1;
156: g[i] += -2 * (1 - x[i]) + 2 * alpha * t1 * (-2 * x[i]);
157: g[i + 1] = 2 * alpha * t1;
158: }
159: } else {
160: for (i = 0; i < nn; i++) {
161: t1 = x[2 * i + 1] - x[2 * i] * x[2 * i];
162: t2 = 1 - x[2 * i];
163: ff += alpha * t1 * t1 + t2 * t2;
164: g[2 * i] = -4 * alpha * t1 * x[2 * i] - 2.0 * t2;
165: g[2 * i + 1] = 2 * alpha * t1;
166: }
167: }
169: /* Restore vectors */
170: PetscCall(VecRestoreArrayRead(X, &x));
171: PetscCall(VecRestoreArray(G, &g));
172: *f = ff;
174: PetscCall(PetscLogFlops(15.0 * nn));
175: PetscFunctionReturn(PETSC_SUCCESS);
176: }
178: /* ------------------------------------------------------------------- */
179: /*
180: FormHessian - Evaluates Hessian matrix.
182: Input Parameters:
183: . tao - the Tao context
184: . x - input vector
185: . ptr - optional user-defined context, as set by TaoSetHessian()
187: Output Parameters:
188: . H - Hessian matrix
190: Note: Providing the Hessian may not be necessary. Only some solvers
191: require this matrix.
192: */
193: PetscErrorCode FormHessian(Tao tao, Vec X, Mat H, Mat Hpre, void *ptr)
194: {
195: AppCtx *user = (AppCtx *)ptr;
196: PetscInt i, ind[2];
197: PetscReal alpha = user->alpha;
198: PetscReal v[2][2];
199: const PetscScalar *x;
200: PetscBool assembled;
202: PetscFunctionBeginUser;
203: /* Zero existing matrix entries */
204: PetscCall(MatAssembled(H, &assembled));
205: if (assembled) PetscCall(MatZeroEntries(H));
207: /* Get a pointer to vector data */
208: PetscCall(VecGetArrayRead(X, &x));
210: /* Compute H(X) entries */
211: if (user->chained) {
212: PetscCall(MatZeroEntries(H));
213: for (i = 0; i < user->n - 1; i++) {
214: PetscScalar t1 = x[i + 1] - x[i] * x[i];
215: v[0][0] = 2 + 2 * alpha * (t1 * (-2) - 2 * x[i]);
216: v[0][1] = 2 * alpha * (-2 * x[i]);
217: v[1][0] = 2 * alpha * (-2 * x[i]);
218: v[1][1] = 2 * alpha * t1;
219: ind[0] = i;
220: ind[1] = i + 1;
221: PetscCall(MatSetValues(H, 2, ind, 2, ind, v[0], ADD_VALUES));
222: }
223: } else {
224: for (i = 0; i < user->n / 2; i++) {
225: v[1][1] = 2 * alpha;
226: v[0][0] = -4 * alpha * (x[2 * i + 1] - 3 * x[2 * i] * x[2 * i]) + 2;
227: v[1][0] = v[0][1] = -4.0 * alpha * x[2 * i];
228: ind[0] = 2 * i;
229: ind[1] = 2 * i + 1;
230: PetscCall(MatSetValues(H, 2, ind, 2, ind, v[0], INSERT_VALUES));
231: }
232: }
233: PetscCall(VecRestoreArrayRead(X, &x));
235: /* Assemble matrix */
236: PetscCall(MatAssemblyBegin(H, MAT_FINAL_ASSEMBLY));
237: PetscCall(MatAssemblyEnd(H, MAT_FINAL_ASSEMBLY));
238: PetscCall(PetscLogFlops(9.0 * user->n / 2.0));
239: PetscFunctionReturn(PETSC_SUCCESS);
240: }
242: /*TEST
244: build:
245: requires: !complex
247: test:
248: args: -tao_smonitor -tao_type nls -tao_gatol 1.e-4
249: requires: !single
251: test:
252: suffix: 2
253: args: -tao_smonitor -tao_type lmvm -tao_gatol 1.e-3
255: test:
256: suffix: 3
257: args: -tao_smonitor -tao_type ntr -tao_gatol 1.e-4
258: requires: !single
260: test:
261: suffix: 4
262: args: -tao_smonitor -tao_type ntr -tao_mf_hessian -tao_ntr_pc_type none -tao_gatol 1.e-4
264: test:
265: suffix: 5
266: args: -tao_smonitor -tao_type bntr -tao_gatol 1.e-4
268: test:
269: suffix: 6
270: args: -tao_smonitor -tao_type bntl -tao_gatol 1.e-4
272: test:
273: suffix: 7
274: args: -tao_smonitor -tao_type bnls -tao_gatol 1.e-4
276: test:
277: suffix: 8
278: args: -tao_smonitor -tao_type bntr -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4
280: test:
281: suffix: 9
282: args: -tao_smonitor -tao_type bntl -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4
284: test:
285: suffix: 10
286: args: -tao_smonitor -tao_type bnls -tao_bnk_max_cg_its 3 -tao_gatol 1.e-4
288: test:
289: suffix: 11
290: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbroyden
292: test:
293: suffix: 12
294: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbadbroyden
296: test:
297: suffix: 13
298: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsymbroyden
300: test:
301: suffix: 14
302: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmbfgs
304: test:
305: suffix: 15
306: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmdfp
308: test:
309: suffix: 16
310: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsr1
312: test:
313: suffix: 17
314: args: -tao_smonitor -tao_gatol 1e-4 -tao_type bqnls
316: test:
317: suffix: 18
318: args: -tao_smonitor -tao_gatol 1e-4 -tao_type blmvm
320: test:
321: suffix: 19
322: args: -tao_smonitor -tao_gatol 1e-4 -tao_type bqnktr -tao_bqnk_mat_type lmvmsr1
324: test:
325: suffix: 20
326: args: -tao_monitor -tao_gatol 1e-4 -tao_type blmvm -tao_ls_monitor
328: test:
329: suffix: 21
330: args: -test_lmvm -tao_max_it 10 -tao_bqnk_mat_type lmvmsymbadbroyden
332: test:
333: suffix: 22
334: args: -tao_max_it 1 -tao_converged_reason
336: test:
337: suffix: 23
338: args: -tao_max_funcs 0 -tao_converged_reason
340: test:
341: suffix: 24
342: args: -tao_gatol 10 -tao_converged_reason
344: test:
345: suffix: 25
346: args: -tao_grtol 10 -tao_converged_reason
348: test:
349: suffix: 26
350: args: -tao_gttol 10 -tao_converged_reason
352: test:
353: suffix: 27
354: args: -tao_steptol 10 -tao_converged_reason
356: test:
357: suffix: 28
358: args: -tao_fmin 10 -tao_converged_reason
360: test:
361: suffix: snes
362: args: -snes_monitor ::ascii_info_detail -tao_type snes -snes_type newtontr -snes_atol 1.e-4 -pc_type none -tao_mf_hessian -ksp_type cg
364: test:
365: suffix: snes_ls_armijo
366: args: -snes_monitor ::ascii_info_detail -tao_type snes -snes_type newtonls -snes_atol 1.e-4 -pc_type none -tao_mf_hessian -snes_linesearch_monitor -snes_linesearch_order 1
368: test:
369: suffix: snes_tr_cgnegcurve_kmdc
370: args: -snes_monitor ::ascii_info_detail -tao_type snes -snes_type newtontr -snes_atol 1.e-4 -pc_type none -ksp_type cg -snes_tr_kmdc 0.01 -ksp_converged_neg_curve -ksp_converged_reason
371: requires: !single
373: TEST*/