1 static char help[] = "An example of hybrid system using TS event.\n"; 2 3 /* 4 The dynamics is described by the ODE 5 u_t = A_i u 6 7 where A_1 = [ 1 -100 8 10 1 ], 9 A_2 = [ 1 10 10 -100 1 ]. 11 The index i changes from 1 to 2 when u[1]=2.75u[0] and from 2 to 1 when u[1]=0.36u[0]. 12 Initially u=[0 1]^T and i=1. 13 14 Reference: 15 I. A. Hiskens, M.A. Pai, Trajectory Sensitivity Analysis of Hybrid Systems, IEEE Transactions on Circuits and Systems, Vol 47, No 2, February 2000 16 */ 17 18 #include <petscts.h> 19 20 typedef struct { 21 PetscReal lambda1; 22 PetscReal lambda2; 23 PetscInt mode; /* mode flag*/ 24 } AppCtx; 25 26 PetscErrorCode FWDRun(TS, Vec, void *); 27 28 PetscErrorCode EventFunction(TS ts,PetscReal t,Vec U,PetscScalar *fvalue,void *ctx) 29 { 30 AppCtx *actx=(AppCtx*)ctx; 31 PetscErrorCode ierr; 32 const PetscScalar *u; 33 34 PetscFunctionBegin; 35 ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr); 36 if (actx->mode == 1) { 37 fvalue[0] = u[1]-actx->lambda1*u[0]; 38 } else if (actx->mode == 2) { 39 fvalue[0] = u[1]-actx->lambda2*u[0]; 40 } 41 ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr); 42 PetscFunctionReturn(0); 43 } 44 45 PetscErrorCode ShiftGradients(TS ts,Vec U,AppCtx *actx) 46 { 47 Vec *lambda,*mu; 48 PetscScalar *x,*y; 49 const PetscScalar *u; 50 PetscErrorCode ierr; 51 PetscScalar tmp[2],A1[2][2],A2[2],denorm1,denorm2; 52 PetscInt numcost; 53 54 PetscFunctionBegin; 55 ierr = TSGetCostGradients(ts,&numcost,&lambda,&mu);CHKERRQ(ierr); 56 ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr); 57 58 if (actx->mode==2) { 59 denorm1 = -actx->lambda1*(u[0]-100.*u[1])+1.*(10.*u[0]+u[1]); 60 denorm2 = -actx->lambda1*(u[0]+10.*u[1])+1.*(-100.*u[0]+u[1]); 61 A1[0][0] = 110.*u[1]*(-actx->lambda1)/denorm1+1.; 62 A1[0][1] = -110.*u[0]*(-actx->lambda1)/denorm1; 63 A1[1][0] = 110.*u[1]*1./denorm1; 64 A1[1][1] = -110.*u[0]*1./denorm1+1.; 65 66 A2[0] = 110.*u[1]*(-u[0])/denorm2; 67 A2[1] = -110.*u[0]*(-u[0])/denorm2; 68 } else { 69 denorm2 = -actx->lambda2*(u[0]+10.*u[1])+1.*(-100.*u[0]+u[1]); 70 A1[0][0] = 110.*u[1]*(-actx->lambda1)/denorm2+1; 71 A1[0][1] = -110.*u[0]*(-actx->lambda1)/denorm2; 72 A1[1][0] = 110.*u[1]*1./denorm2; 73 A1[1][1] = -110.*u[0]*1./denorm2+1.; 74 75 A2[0] = 0; 76 A2[1] = 0; 77 } 78 79 ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr); 80 81 ierr = VecGetArray(lambda[0],&x);CHKERRQ(ierr); 82 ierr = VecGetArray(mu[0],&y);CHKERRQ(ierr); 83 tmp[0] = A1[0][0]*x[0]+A1[0][1]*x[1]; 84 tmp[1] = A1[1][0]*x[0]+A1[1][1]*x[1]; 85 y[0] = y[0] + A2[0]*x[0]+A2[1]*x[1]; 86 x[0] = tmp[0]; 87 x[1] = tmp[1]; 88 ierr = VecRestoreArray(mu[0],&y);CHKERRQ(ierr); 89 ierr = VecRestoreArray(lambda[0],&x);CHKERRQ(ierr); 90 91 ierr = VecGetArray(lambda[1],&x);CHKERRQ(ierr); 92 ierr = VecGetArray(mu[1],&y);CHKERRQ(ierr); 93 tmp[0] = A1[0][0]*x[0]+A1[0][1]*x[1]; 94 tmp[1] = A1[1][0]*x[0]+A1[1][1]*x[1]; 95 y[0] = y[0] + A2[0]*x[0]+A2[1]*x[1]; 96 x[0] = tmp[0]; 97 x[1] = tmp[1]; 98 ierr = VecRestoreArray(mu[1],&y);CHKERRQ(ierr); 99 ierr = VecRestoreArray(lambda[1],&x);CHKERRQ(ierr); 100 PetscFunctionReturn(0); 101 } 102 103 PetscErrorCode PostEventFunction(TS ts,PetscInt nevents,PetscInt event_list[],PetscReal t,Vec U,PetscBool forwardsolve,void* ctx) 104 { 105 AppCtx *actx=(AppCtx*)ctx; 106 PetscErrorCode ierr; 107 108 PetscFunctionBegin; 109 if (!forwardsolve) { 110 ierr = ShiftGradients(ts,U,actx);CHKERRQ(ierr); 111 } 112 if (actx->mode == 1) { 113 actx->mode = 2; 114 ierr = PetscPrintf(PETSC_COMM_SELF,"Change from mode 1 to 2 at t = %f \n",(double)t);CHKERRQ(ierr); 115 } else if (actx->mode == 2) { 116 actx->mode = 1; 117 ierr = PetscPrintf(PETSC_COMM_SELF,"Change from mode 2 to 1 at t = %f \n",(double)t);CHKERRQ(ierr); 118 } 119 PetscFunctionReturn(0); 120 } 121 122 /* 123 Defines the ODE passed to the ODE solver 124 */ 125 static PetscErrorCode IFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,void *ctx) 126 { 127 AppCtx *actx=(AppCtx*)ctx; 128 PetscErrorCode ierr; 129 PetscScalar *f; 130 const PetscScalar *u,*udot; 131 132 PetscFunctionBegin; 133 /* The next three lines allow us to access the entries of the vectors directly */ 134 ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr); 135 ierr = VecGetArrayRead(Udot,&udot);CHKERRQ(ierr); 136 ierr = VecGetArray(F,&f);CHKERRQ(ierr); 137 138 if (actx->mode == 1) { 139 f[0] = udot[0]-u[0]+100*u[1]; 140 f[1] = udot[1]-10*u[0]-u[1]; 141 } else if (actx->mode == 2) { 142 f[0] = udot[0]-u[0]-10*u[1]; 143 f[1] = udot[1]+100*u[0]-u[1]; 144 } 145 146 ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr); 147 ierr = VecRestoreArrayRead(Udot,&udot);CHKERRQ(ierr); 148 ierr = VecRestoreArray(F,&f);CHKERRQ(ierr); 149 PetscFunctionReturn(0); 150 } 151 152 /* 153 Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian. 154 */ 155 static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat A,Mat B,void *ctx) 156 { 157 AppCtx *actx=(AppCtx*)ctx; 158 PetscErrorCode ierr; 159 PetscInt rowcol[] = {0,1}; 160 PetscScalar J[2][2]; 161 const PetscScalar *u,*udot; 162 163 PetscFunctionBegin; 164 ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr); 165 ierr = VecGetArrayRead(Udot,&udot);CHKERRQ(ierr); 166 167 if (actx->mode == 1) { 168 J[0][0] = a-1; J[0][1] = 100; 169 J[1][0] = -10; J[1][1] = a-1; 170 } else if (actx->mode == 2) { 171 J[0][0] = a-1; J[0][1] = -10; 172 J[1][0] = 100; J[1][1] = a-1; 173 } 174 ierr = MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);CHKERRQ(ierr); 175 176 ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr); 177 ierr = VecRestoreArrayRead(Udot,&udot);CHKERRQ(ierr); 178 179 ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 180 ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 181 if (A != B) { 182 ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 183 ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 184 } 185 PetscFunctionReturn(0); 186 } 187 188 int main(int argc,char **argv) 189 { 190 TS ts; /* ODE integrator */ 191 Vec U; /* solution will be stored here */ 192 Mat A; /* Jacobian matrix */ 193 Mat Ap; /* dfdp */ 194 PetscErrorCode ierr; 195 PetscMPIInt size; 196 PetscInt n = 2; 197 PetscScalar *u; 198 AppCtx app; 199 PetscInt direction[1]; 200 PetscBool terminate[1]; 201 PetscReal delta,tmp[2],sensi[2]; 202 203 delta = 1e-8; 204 205 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 206 Initialize program 207 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 208 ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr; 209 ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRMPI(ierr); 210 if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs"); 211 app.mode = 1; 212 app.lambda1 = 2.75; 213 app.lambda2 = 0.36; 214 ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"ex1 options","");CHKERRQ(ierr); 215 { 216 ierr = PetscOptionsReal("-lambda1","","",app.lambda1,&app.lambda1,NULL);CHKERRQ(ierr); 217 ierr = PetscOptionsReal("-lambda2","","",app.lambda2,&app.lambda2,NULL);CHKERRQ(ierr); 218 } 219 ierr = PetscOptionsEnd();CHKERRQ(ierr); 220 221 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 222 Create necessary matrix and vectors 223 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 224 ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr); 225 ierr = MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr); 226 ierr = MatSetType(A,MATDENSE);CHKERRQ(ierr); 227 ierr = MatSetFromOptions(A);CHKERRQ(ierr); 228 ierr = MatSetUp(A);CHKERRQ(ierr); 229 230 ierr = MatCreateVecs(A,&U,NULL);CHKERRQ(ierr); 231 232 ierr = MatCreate(PETSC_COMM_WORLD,&Ap);CHKERRQ(ierr); 233 ierr = MatSetSizes(Ap,n,1,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr); 234 ierr = MatSetType(Ap,MATDENSE);CHKERRQ(ierr); 235 ierr = MatSetFromOptions(Ap);CHKERRQ(ierr); 236 ierr = MatSetUp(Ap);CHKERRQ(ierr); 237 ierr = MatZeroEntries(Ap);CHKERRQ(ierr); /* initialize to zeros */ 238 239 ierr = VecGetArray(U,&u);CHKERRQ(ierr); 240 u[0] = 0; 241 u[1] = 1; 242 ierr = VecRestoreArray(U,&u);CHKERRQ(ierr); 243 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 244 Create timestepping solver context 245 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 246 ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr); 247 ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr); 248 ierr = TSSetType(ts,TSCN);CHKERRQ(ierr); 249 ierr = TSSetIFunction(ts,NULL,(TSIFunction)IFunction,&app);CHKERRQ(ierr); 250 ierr = TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&app);CHKERRQ(ierr); 251 252 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 253 Set initial conditions 254 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 255 ierr = TSSetSolution(ts,U);CHKERRQ(ierr); 256 257 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 258 Set solver options 259 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 260 ierr = TSSetMaxTime(ts,0.125);CHKERRQ(ierr); 261 ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);CHKERRQ(ierr); 262 ierr = TSSetTimeStep(ts,1./256.);CHKERRQ(ierr); 263 ierr = TSSetFromOptions(ts);CHKERRQ(ierr); 264 265 /* Set directions and terminate flags for the two events */ 266 direction[0] = 0; 267 terminate[0] = PETSC_FALSE; 268 ierr = TSSetEventHandler(ts,1,direction,terminate,EventFunction,PostEventFunction,(void*)&app);CHKERRQ(ierr); 269 270 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 271 Run timestepping solver 272 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 273 ierr = TSSolve(ts,U);CHKERRQ(ierr); 274 275 ierr = VecGetArray(U,&u);CHKERRQ(ierr); 276 tmp[0] = u[0]; 277 tmp[1] = u[1]; 278 279 u[0] = 0+delta; 280 u[1] = 1; 281 ierr = VecRestoreArray(U,&u);CHKERRQ(ierr); 282 283 ierr = FWDRun(ts,U,(void*)&app);CHKERRQ(ierr); 284 285 ierr = VecGetArray(U,&u);CHKERRQ(ierr); 286 sensi[0] = (u[0]-tmp[0])/delta; 287 sensi[1] = (u[1]-tmp[1])/delta; 288 ierr = PetscPrintf(PETSC_COMM_SELF,"d x1(tf) /d x1(t0) = %f d x2(tf) / d x1(t0) = %f \n",sensi[0],sensi[1]);CHKERRQ(ierr); 289 u[0] = 0; 290 u[1] = 1+delta; 291 ierr = VecRestoreArray(U,&u);CHKERRQ(ierr); 292 293 ierr = FWDRun(ts,U,(void*)&app);CHKERRQ(ierr); 294 295 ierr = VecGetArray(U,&u);CHKERRQ(ierr); 296 sensi[0] = (u[0]-tmp[0])/delta; 297 sensi[1] = (u[1]-tmp[1])/delta; 298 ierr = PetscPrintf(PETSC_COMM_SELF,"d x1(tf) /d x2(t0) = %f d x2(tf) / d x2(t0) = %f \n",sensi[0],sensi[1]);CHKERRQ(ierr); 299 u[0] = 0; 300 u[1] = 1; 301 app.lambda1 = app.lambda1+delta; 302 ierr = VecRestoreArray(U,&u);CHKERRQ(ierr); 303 304 ierr = FWDRun(ts,U,(void*)&app);CHKERRQ(ierr); 305 306 ierr = VecGetArray(U,&u);CHKERRQ(ierr); 307 sensi[0] = (u[0]-tmp[0])/delta; 308 sensi[1] = (u[1]-tmp[1])/delta; 309 ierr = PetscPrintf(PETSC_COMM_SELF,"Final gradients: d x1(tf) /d p = %f d x2(tf) / d p = %f \n",sensi[0],sensi[1]);CHKERRQ(ierr); 310 ierr = VecRestoreArray(U,&u);CHKERRQ(ierr); 311 312 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 313 Free work space. All PETSc objects should be destroyed when they are no longer needed. 314 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 315 ierr = MatDestroy(&A);CHKERRQ(ierr); 316 ierr = VecDestroy(&U);CHKERRQ(ierr); 317 ierr = TSDestroy(&ts);CHKERRQ(ierr); 318 319 ierr = MatDestroy(&Ap);CHKERRQ(ierr); 320 ierr = PetscFinalize(); 321 return ierr; 322 } 323 324 PetscErrorCode FWDRun(TS ts, Vec U0, void *ctx0) 325 { 326 Vec U; /* solution will be stored here */ 327 PetscErrorCode ierr; 328 AppCtx *ctx=(AppCtx*)ctx0; 329 330 PetscFunctionBeginUser; 331 ierr = TSGetSolution(ts,&U);CHKERRQ(ierr); 332 ierr = VecCopy(U0,U);CHKERRQ(ierr); 333 334 ctx->mode = 1; 335 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 336 Run timestepping solver 337 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 338 ierr = TSSetTime(ts, 0.0);CHKERRQ(ierr); 339 340 ierr = TSSolve(ts,U);CHKERRQ(ierr); 341 342 PetscFunctionReturn(0); 343 } 344 345 /*TEST 346 347 build: 348 requires: !defined(PETSC_USE_CXXCOMPLEX) 349 350 test: 351 args: -ts_event_tol 1e-9 352 timeoutfactor: 18 353 requires: !single 354 355 TEST*/ 356