1 static char help[] = "Adjoint sensitivity of a hybrid system with state-dependent switchings.\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 References: 15 H. Zhang, S. Abhyankar, E. Constantinescu, M. Mihai, Discrete Adjoint Sensitivity Analysis of Hybrid Dynamical Systems With Switching, IEEE Transactions on Circuits and Systems I: Regular Papers, 64(5), May 2017 16 I. A. Hiskens, M.A. Pai, Trajectory Sensitivity Analysis of Hybrid Systems, IEEE Transactions on Circuits and Systems, Vol 47, No 2, February 2000 17 */ 18 19 #include <petscts.h> 20 21 typedef struct { 22 PetscScalar lambda1; 23 PetscScalar lambda2; 24 PetscInt mode; /* mode flag*/ 25 } AppCtx; 26 27 PetscErrorCode EventFunction(TS ts,PetscReal t,Vec U,PetscScalar *fvalue,void *ctx) 28 { 29 AppCtx *actx=(AppCtx*)ctx; 30 PetscErrorCode ierr; 31 const PetscScalar *u; 32 33 PetscFunctionBegin; 34 ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr); 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 ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr); 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 PetscErrorCode ierr; 50 PetscScalar tmp[2],A1[2][2],A2[2],denorm; 51 PetscInt numcost; 52 53 PetscFunctionBegin; 54 ierr = TSGetCostGradients(ts,&numcost,&lambda,&mu);CHKERRQ(ierr); 55 ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr); 56 57 if (actx->mode==2) { 58 denorm = -actx->lambda1*(u[0]-100.*u[1])+1.*(10.*u[0]+u[1]); 59 A1[0][0] = 110.*u[1]*(-actx->lambda1)/denorm+1.; 60 A1[0][1] = -110.*u[0]*(-actx->lambda1)/denorm; 61 A1[1][0] = 110.*u[1]*1./denorm; 62 A1[1][1] = -110.*u[0]*1./denorm+1.; 63 64 A2[0] = 110.*u[1]*(-u[0])/denorm; 65 A2[1] = -110.*u[0]*(-u[0])/denorm; 66 } else { 67 denorm = -actx->lambda2*(u[0]+10.*u[1])+1.*(-100.*u[0]+u[1]); 68 A1[0][0] = 110.*u[1]*(actx->lambda2)/denorm+1; 69 A1[0][1] = -110.*u[0]*(actx->lambda2)/denorm; 70 A1[1][0] = -110.*u[1]*1./denorm; 71 A1[1][1] = 110.*u[0]*1./denorm+1.; 72 73 A2[0] = 0; 74 A2[1] = 0; 75 } 76 77 ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr); 78 79 ierr = VecGetArray(lambda[0],&x);CHKERRQ(ierr); 80 ierr = VecGetArray(mu[0],&y);CHKERRQ(ierr); 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 ierr = VecRestoreArray(mu[0],&y);CHKERRQ(ierr); 87 ierr = VecRestoreArray(lambda[0],&x);CHKERRQ(ierr); 88 89 ierr = VecGetArray(lambda[1],&x);CHKERRQ(ierr); 90 ierr = VecGetArray(mu[1],&y);CHKERRQ(ierr); 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 ierr = VecRestoreArray(mu[1],&y);CHKERRQ(ierr); 97 ierr = VecRestoreArray(lambda[1],&x);CHKERRQ(ierr); 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 PetscErrorCode ierr; 105 106 PetscFunctionBegin; 107 /* ierr = VecView(U,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); */ 108 if (!forwardsolve) { 109 ierr = ShiftGradients(ts,U,actx);CHKERRQ(ierr); 110 } 111 if (actx->mode == 1) { 112 actx->mode = 2; 113 /* ierr = PetscPrintf(PETSC_COMM_SELF,"Change from mode 1 to 2 at t = %f \n",(double)t);CHKERRQ(ierr); */ 114 } else if (actx->mode == 2) { 115 actx->mode = 1; 116 /* ierr = PetscPrintf(PETSC_COMM_SELF,"Change from mode 2 to 1 at t = %f \n",(double)t);CHKERRQ(ierr); */ 117 } 118 PetscFunctionReturn(0); 119 } 120 121 /* 122 Defines the ODE passed to the ODE solver 123 */ 124 static PetscErrorCode IFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,void *ctx) 125 { 126 AppCtx *actx=(AppCtx*)ctx; 127 PetscErrorCode ierr; 128 PetscScalar *f; 129 const PetscScalar *u,*udot; 130 131 PetscFunctionBegin; 132 /* The next three lines allow us to access the entries of the vectors directly */ 133 ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr); 134 ierr = VecGetArrayRead(Udot,&udot);CHKERRQ(ierr); 135 ierr = VecGetArray(F,&f);CHKERRQ(ierr); 136 137 if (actx->mode == 1) { 138 f[0] = udot[0]-u[0]+100*u[1]; 139 f[1] = udot[1]-10*u[0]-u[1]; 140 } else if (actx->mode == 2) { 141 f[0] = udot[0]-u[0]-10*u[1]; 142 f[1] = udot[1]+100*u[0]-u[1]; 143 } 144 145 ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr); 146 ierr = VecRestoreArrayRead(Udot,&udot);CHKERRQ(ierr); 147 ierr = VecRestoreArray(F,&f);CHKERRQ(ierr); 148 PetscFunctionReturn(0); 149 } 150 151 /* 152 Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian. 153 */ 154 static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat A,Mat B,void *ctx) 155 { 156 AppCtx *actx=(AppCtx*)ctx; 157 PetscErrorCode ierr; 158 PetscInt rowcol[] = {0,1}; 159 PetscScalar J[2][2]; 160 const PetscScalar *u,*udot; 161 162 PetscFunctionBegin; 163 ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr); 164 ierr = VecGetArrayRead(Udot,&udot);CHKERRQ(ierr); 165 166 if (actx->mode == 1) { 167 J[0][0] = a-1; J[0][1] = 100; 168 J[1][0] = -10; J[1][1] = a-1; 169 } else if (actx->mode == 2) { 170 J[0][0] = a-1; J[0][1] = -10; 171 J[1][0] = 100; J[1][1] = a-1; 172 } 173 ierr = MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);CHKERRQ(ierr); 174 175 ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr); 176 ierr = VecRestoreArrayRead(Udot,&udot);CHKERRQ(ierr); 177 178 ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 179 ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 180 if (A != B) { 181 ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 182 ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 183 } 184 PetscFunctionReturn(0); 185 } 186 187 /* Matrix JacobianP is constant so that it only needs to be evaluated once */ 188 static PetscErrorCode RHSJacobianP(TS ts,PetscReal t,Vec X,Mat A, void *ctx) 189 { 190 PetscFunctionBeginUser; 191 PetscFunctionReturn(0); 192 } 193 194 int main(int argc,char **argv) 195 { 196 TS ts; /* ODE integrator */ 197 Vec U; /* solution will be stored here */ 198 Mat A; /* Jacobian matrix */ 199 Mat Ap; /* dfdp */ 200 PetscErrorCode ierr; 201 PetscMPIInt size; 202 PetscInt n = 2; 203 PetscScalar *u,*v; 204 AppCtx app; 205 PetscInt direction[1]; 206 PetscBool terminate[1]; 207 Vec lambda[2],mu[2]; 208 PetscReal tend; 209 210 FILE *f; 211 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 212 Initialize program 213 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 214 ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr; 215 ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRMPI(ierr); 216 if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs"); 217 app.mode = 1; 218 app.lambda1 = 2.75; 219 app.lambda2 = 0.36; 220 tend = 0.125; 221 ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"ex1adj options","");CHKERRQ(ierr); 222 { 223 ierr = PetscOptionsReal("-lambda1","","",app.lambda1,&app.lambda1,NULL);CHKERRQ(ierr); 224 ierr = PetscOptionsReal("-lambda2","","",app.lambda2,&app.lambda2,NULL);CHKERRQ(ierr); 225 ierr = PetscOptionsReal("-tend","","",tend,&tend,NULL);CHKERRQ(ierr); 226 } 227 ierr = PetscOptionsEnd();CHKERRQ(ierr); 228 229 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 230 Create necessary matrix and vectors 231 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 232 ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr); 233 ierr = MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr); 234 ierr = MatSetType(A,MATDENSE);CHKERRQ(ierr); 235 ierr = MatSetFromOptions(A);CHKERRQ(ierr); 236 ierr = MatSetUp(A);CHKERRQ(ierr); 237 238 ierr = MatCreateVecs(A,&U,NULL);CHKERRQ(ierr); 239 240 ierr = MatCreate(PETSC_COMM_WORLD,&Ap);CHKERRQ(ierr); 241 ierr = MatSetSizes(Ap,n,1,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr); 242 ierr = MatSetType(Ap,MATDENSE);CHKERRQ(ierr); 243 ierr = MatSetFromOptions(Ap);CHKERRQ(ierr); 244 ierr = MatSetUp(Ap);CHKERRQ(ierr); 245 ierr = MatZeroEntries(Ap);CHKERRQ(ierr); /* initialize to zeros */ 246 247 ierr = VecGetArray(U,&u);CHKERRQ(ierr); 248 u[0] = 0; 249 u[1] = 1; 250 ierr = VecRestoreArray(U,&u);CHKERRQ(ierr); 251 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 252 Create timestepping solver context 253 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 254 ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr); 255 ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr); 256 ierr = TSSetType(ts,TSCN);CHKERRQ(ierr); 257 ierr = TSSetIFunction(ts,NULL,(TSIFunction)IFunction,&app);CHKERRQ(ierr); 258 ierr = TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&app);CHKERRQ(ierr); 259 ierr = TSSetRHSJacobianP(ts,Ap,RHSJacobianP,&app);CHKERRQ(ierr); 260 261 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 262 Set initial conditions 263 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 264 ierr = TSSetSolution(ts,U);CHKERRQ(ierr); 265 266 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 267 Save trajectory of solution so that TSAdjointSolve() may be used 268 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 269 ierr = TSSetSaveTrajectory(ts);CHKERRQ(ierr); 270 271 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 272 Set solver options 273 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 274 ierr = TSSetMaxTime(ts,tend);CHKERRQ(ierr); 275 ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);CHKERRQ(ierr); 276 ierr = TSSetTimeStep(ts,1./256.);CHKERRQ(ierr); 277 ierr = TSSetFromOptions(ts);CHKERRQ(ierr); 278 279 /* Set directions and terminate flags for the two events */ 280 direction[0] = 0; 281 terminate[0] = PETSC_FALSE; 282 ierr = TSSetEventHandler(ts,1,direction,terminate,EventFunction,PostEventFunction,(void*)&app);CHKERRQ(ierr); 283 284 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 285 Run timestepping solver 286 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 287 ierr = TSSolve(ts,U);CHKERRQ(ierr); 288 289 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 290 Adjoint model starts here 291 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 292 ierr = MatCreateVecs(A,&lambda[0],NULL);CHKERRQ(ierr); 293 ierr = MatCreateVecs(A,&lambda[1],NULL);CHKERRQ(ierr); 294 /* Set initial conditions for the adjoint integration */ 295 ierr = VecZeroEntries(lambda[0]);CHKERRQ(ierr); 296 ierr = VecZeroEntries(lambda[1]);CHKERRQ(ierr); 297 ierr = VecGetArray(lambda[0],&u);CHKERRQ(ierr); 298 u[0] = 1.; 299 ierr = VecRestoreArray(lambda[0],&u);CHKERRQ(ierr); 300 ierr = VecGetArray(lambda[1],&u);CHKERRQ(ierr); 301 u[1] = 1.; 302 ierr = VecRestoreArray(lambda[1],&u);CHKERRQ(ierr); 303 304 ierr = MatCreateVecs(Ap,&mu[0],NULL);CHKERRQ(ierr); 305 ierr = MatCreateVecs(Ap,&mu[1],NULL);CHKERRQ(ierr); 306 ierr = VecZeroEntries(mu[0]);CHKERRQ(ierr); 307 ierr = VecZeroEntries(mu[1]);CHKERRQ(ierr); 308 ierr = TSSetCostGradients(ts,2,lambda,mu);CHKERRQ(ierr); 309 310 ierr = TSAdjointSolve(ts);CHKERRQ(ierr); 311 312 /* 313 ierr = VecView(lambda[0],PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); 314 ierr = VecView(lambda[1],PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); 315 ierr = VecView(mu[0],PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); 316 ierr = VecView(mu[1],PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); 317 */ 318 ierr = VecGetArray(mu[0],&u);CHKERRQ(ierr); 319 ierr = VecGetArray(mu[1],&v);CHKERRQ(ierr); 320 f = fopen("adj_mu.out", "a"); 321 ierr = PetscFPrintf(PETSC_COMM_WORLD,f,"%20.15lf %20.15lf %20.15lf\n",tend,u[0],v[0]);CHKERRQ(ierr); 322 ierr = VecRestoreArray(mu[0],&u);CHKERRQ(ierr); 323 ierr = VecRestoreArray(mu[1],&v);CHKERRQ(ierr); 324 fclose(f); 325 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 326 Free work space. All PETSc objects should be destroyed when they are no longer needed. 327 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 328 ierr = MatDestroy(&A);CHKERRQ(ierr); 329 ierr = VecDestroy(&U);CHKERRQ(ierr); 330 ierr = TSDestroy(&ts);CHKERRQ(ierr); 331 332 ierr = MatDestroy(&Ap);CHKERRQ(ierr); 333 ierr = VecDestroy(&lambda[0]);CHKERRQ(ierr); 334 ierr = VecDestroy(&lambda[1]);CHKERRQ(ierr); 335 ierr = VecDestroy(&mu[0]);CHKERRQ(ierr); 336 ierr = VecDestroy(&mu[1]);CHKERRQ(ierr); 337 ierr = PetscFinalize(); 338 return ierr; 339 } 340 341 /*TEST 342 343 build: 344 requires: !complex 345 346 test: 347 args: -ts_monitor -ts_adjoint_monitor 348 349 TEST*/ 350