Actual source code: toy.c
petsc-3.14.6 2021-03-30
1: /* Program usage: mpiexec -n 1 toy[-help] [all TAO options] */
3: /* ----------------------------------------------------------------------
4: min f=(x1-x2)^2 + (x2-2)^2 -2*x1-2*x2
5: s.t. x1^2 + x2 = 2
6: 0 <= x1^2 - x2 <= 1
7: -1 <= x1,x2 <= 2
8: ---------------------------------------------------------------------- */
10: #include <petsctao.h>
12: static char help[]="";
14: /*
15: User-defined application context - contains data needed by the
16: application-provided call-back routines, FormFunction(),
17: FormGradient(), and FormHessian().
18: */
20: /*
21: x,d in R^n
22: f in R
23: bin in R^mi
24: beq in R^me
25: Aeq in R^(me x n)
26: Ain in R^(mi x n)
27: H in R^(n x n)
28: min f=(1/2)*x'*H*x + d'*x
29: s.t. Aeq*x == beq
30: Ain*x >= bin
31: */
32: typedef struct {
33: PetscInt n; /* Length x */
34: PetscInt ne; /* number of equality constraints */
35: PetscInt ni; /* number of inequality constraints */
36: Vec x,xl,xu;
37: Vec ce,ci,bl,bu;
38: Mat Ae,Ai,H;
39: } AppCtx;
41: /* -------- User-defined Routines --------- */
43: PetscErrorCode InitializeProblem(AppCtx *);
44: PetscErrorCode DestroyProblem(AppCtx *);
45: PetscErrorCode FormFunctionGradient(Tao,Vec,PetscReal *,Vec,void *);
46: PetscErrorCode FormHessian(Tao,Vec,Mat,Mat, void*);
47: PetscErrorCode FormInequalityConstraints(Tao,Vec,Vec,void*);
48: PetscErrorCode FormEqualityConstraints(Tao,Vec,Vec,void*);
49: PetscErrorCode FormInequalityJacobian(Tao,Vec,Mat,Mat, void*);
50: PetscErrorCode FormEqualityJacobian(Tao,Vec,Mat,Mat, void*);
54: PetscErrorCode main(int argc,char **argv)
55: {
56: PetscErrorCode ierr; /* used to check for functions returning nonzeros */
57: Tao tao;
58: KSP ksp;
59: PC pc;
60: AppCtx user; /* application context */
62: PetscInitialize(&argc,&argv,(char *)0,help);if (ierr) return ierr;
63: PetscPrintf(PETSC_COMM_WORLD,"\n---- TOY Problem -----\n");
64: PetscPrintf(PETSC_COMM_WORLD,"Solution should be f(1,1)=-2\n");
65: InitializeProblem(&user);
66: TaoCreate(PETSC_COMM_WORLD,&tao);
67: TaoSetType(tao,TAOIPM);
68: TaoSetInitialVector(tao,user.x);
69: TaoSetVariableBounds(tao,user.xl,user.xu);
70: TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,(void*)&user);
72: TaoSetEqualityConstraintsRoutine(tao,user.ce,FormEqualityConstraints,(void*)&user);
73: TaoSetInequalityConstraintsRoutine(tao,user.ci,FormInequalityConstraints,(void*)&user);
75: TaoSetJacobianEqualityRoutine(tao,user.Ae,user.Ae,FormEqualityJacobian,(void*)&user);
76: TaoSetJacobianInequalityRoutine(tao,user.Ai,user.Ai,FormInequalityJacobian,(void*)&user);
77: TaoSetHessianRoutine(tao,user.H,user.H,FormHessian,(void*)&user);
78: /* TaoSetTolerances(tao,0,0,0); */
80: TaoGetKSP(tao,&ksp);
81: KSPGetPC(ksp,&pc);
82: PCSetType(pc,PCLU);
83: /*
84: This algorithm produces matrices with zeros along the diagonal therefore we need to use
85: SuperLU which does partial pivoting
86: */
87: PCFactorSetMatSolverType(pc,MATSOLVERSUPERLU);
88: KSPSetType(ksp,KSPPREONLY);
89: KSPSetFromOptions(ksp);
91: TaoSetFromOptions(tao);
92: /* TaoSetTolerances(tao,0,0,0); */
93: TaoSolve(tao);
95: DestroyProblem(&user);
96: TaoDestroy(&tao);
97: PetscFinalize();
98: return ierr;
99: }
101: PetscErrorCode InitializeProblem(AppCtx *user)
102: {
106: user->n = 2;
107: VecCreateSeq(PETSC_COMM_SELF,user->n,&user->x);
108: VecDuplicate(user->x,&user->xl);
109: VecDuplicate(user->x,&user->xu);
110: VecSet(user->x,0.0);
111: VecSet(user->xl,-1.0);
112: VecSet(user->xu,2.0);
114: user->ne = 1;
115: VecCreateSeq(PETSC_COMM_SELF,user->ne,&user->ce);
117: user->ni = 2;
118: VecCreateSeq(PETSC_COMM_SELF,user->ni,&user->ci);
120: MatCreateSeqAIJ(PETSC_COMM_SELF,user->ne,user->n,user->n,NULL,&user->Ae);
121: MatCreateSeqAIJ(PETSC_COMM_SELF,user->ni,user->n,user->n,NULL,&user->Ai);
122: MatSetFromOptions(user->Ae);
123: MatSetFromOptions(user->Ai);
126: MatCreateSeqAIJ(PETSC_COMM_SELF,user->n,user->n,1,NULL,&user->H);
127: MatSetFromOptions(user->H);
129: return(0);
130: }
132: PetscErrorCode DestroyProblem(AppCtx *user)
133: {
137: MatDestroy(&user->Ae);
138: MatDestroy(&user->Ai);
139: MatDestroy(&user->H);
141: VecDestroy(&user->x);
142: VecDestroy(&user->ce);
143: VecDestroy(&user->ci);
144: VecDestroy(&user->xl);
145: VecDestroy(&user->xu);
146: return(0);
147: }
149: PetscErrorCode FormFunctionGradient(Tao tao, Vec X, PetscReal *f, Vec G, void *ctx)
150: {
151: PetscScalar *g;
152: const PetscScalar *x;
153: PetscErrorCode ierr;
156: VecGetArrayRead(X,&x);
157: VecGetArray(G,&g);
158: *f = (x[0]-2.0)*(x[0]-2.0) + (x[1]-2.0)*(x[1]-2.0) - 2.0*(x[0]+x[1]);
159: g[0] = 2.0*(x[0]-2.0) - 2.0;
160: g[1] = 2.0*(x[1]-2.0) - 2.0;
161: VecRestoreArrayRead(X,&x);
162: VecRestoreArray(G,&g);
163: return(0);
164: }
166: PetscErrorCode FormHessian(Tao tao, Vec x, Mat H, Mat Hpre, void *ctx)
167: {
168: Vec DE,DI;
169: const PetscScalar *de, *di;
170: PetscInt zero=0,one=1;
171: PetscScalar two=2.0;
172: PetscScalar val;
173: PetscErrorCode ierr;
176: TaoGetDualVariables(tao,&DE,&DI);
178: VecGetArrayRead(DE,&de);
179: VecGetArrayRead(DI,&di);
180: val=2.0 * (1 + de[0] + di[0] - di[1]);
181: VecRestoreArrayRead(DE,&de);
182: VecRestoreArrayRead(DI,&di);
184: MatSetValues(H,1,&zero,1,&zero,&val,INSERT_VALUES);
185: MatSetValues(H,1,&one,1,&one,&two,INSERT_VALUES);
187: MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY);
188: MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY);
189: return(0);
190: }
192: PetscErrorCode FormInequalityConstraints(Tao tao, Vec X, Vec CI, void *ctx)
193: {
194: const PetscScalar *x;
195: PetscScalar *c;
196: PetscErrorCode ierr;
199: VecGetArrayRead(X,&x);
200: VecGetArray(CI,&c);
201: c[0] = x[0]*x[0] - x[1];
202: c[1] = -x[0]*x[0] + x[1] + 1.0;
203: VecRestoreArrayRead(X,&x);
204: VecRestoreArray(CI,&c);
205: return(0);
206: }
208: PetscErrorCode FormEqualityConstraints(Tao tao, Vec X, Vec CE,void *ctx)
209: {
210: PetscScalar *x,*c;
214: VecGetArray(X,&x);
215: VecGetArray(CE,&c);
216: c[0] = x[0]*x[0] + x[1] - 2.0;
217: VecRestoreArray(X,&x);
218: VecRestoreArray(CE,&c);
219: return(0);
220: }
222: PetscErrorCode FormInequalityJacobian(Tao tao, Vec X, Mat JI, Mat JIpre, void *ctx)
223: {
224: PetscInt rows[2];
225: PetscInt cols[2];
226: PetscScalar vals[4];
227: const PetscScalar *x;
228: PetscErrorCode ierr;
231: VecGetArrayRead(X,&x);
232: rows[0] = 0; rows[1] = 1;
233: cols[0] = 0; cols[1] = 1;
234: vals[0] = +2*x[0]; vals[1] = -1.0;
235: vals[2] = -2*x[0]; vals[3] = +1.0;
236: VecRestoreArrayRead(X,&x);
237: MatSetValues(JI,2,rows,2,cols,vals,INSERT_VALUES);
238: MatAssemblyBegin(JI,MAT_FINAL_ASSEMBLY);
239: MatAssemblyEnd(JI,MAT_FINAL_ASSEMBLY);
241: return(0);
242: }
244: PetscErrorCode FormEqualityJacobian(Tao tao, Vec X, Mat JE, Mat JEpre, void *ctx)
245: {
246: PetscInt rows[2];
247: PetscScalar vals[2];
248: const PetscScalar *x;
249: PetscErrorCode ierr;
252: VecGetArrayRead(X,&x);
253: rows[0] = 0; rows[1] = 1;
254: vals[0] = 2*x[0]; vals[1] = 1.0;
255: VecRestoreArrayRead(X,&x);
256: MatSetValues(JE,1,rows,2,rows,vals,INSERT_VALUES);
257: MatAssemblyBegin(JE,MAT_FINAL_ASSEMBLY);
258: MatAssemblyEnd(JE,MAT_FINAL_ASSEMBLY);
259: return(0);
260: }
263: /*TEST
265: build:
266: requires: !complex !define(PETSC_USE_CXX)
268: test:
269: requires: superlu
270: args: -tao_smonitor -tao_view -tao_gatol 1.e-5
272: TEST*/