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