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 const PetscScalar *u; 31 32 PetscFunctionBegin; 33 PetscCall(VecGetArrayRead(U, &u)); 34 if (actx->mode == 1) { 35 fvalue[0] = u[1] - actx->lambda1 * u[0]; 36 } else if (actx->mode == 2) { 37 fvalue[0] = u[1] - actx->lambda2 * u[0]; 38 } 39 PetscCall(VecRestoreArrayRead(U, &u)); 40 PetscFunctionReturn(0); 41 } 42 43 PetscErrorCode ShiftGradients(TS ts, Vec U, AppCtx *actx) 44 { 45 Vec *lambda, *mu; 46 PetscScalar *x, *y; 47 const PetscScalar *u; 48 PetscScalar tmp[2], A1[2][2], A2[2], denorm; 49 PetscInt numcost; 50 51 PetscFunctionBegin; 52 PetscCall(TSGetCostGradients(ts, &numcost, &lambda, &mu)); 53 PetscCall(VecGetArrayRead(U, &u)); 54 55 if (actx->mode == 2) { 56 denorm = -actx->lambda1 * (u[0] - 100. * u[1]) + 1. * (10. * u[0] + u[1]); 57 A1[0][0] = 110. * u[1] * (-actx->lambda1) / denorm + 1.; 58 A1[0][1] = -110. * u[0] * (-actx->lambda1) / denorm; 59 A1[1][0] = 110. * u[1] * 1. / denorm; 60 A1[1][1] = -110. * u[0] * 1. / denorm + 1.; 61 62 A2[0] = 110. * u[1] * (-u[0]) / denorm; 63 A2[1] = -110. * u[0] * (-u[0]) / denorm; 64 } else { 65 denorm = -actx->lambda2 * (u[0] + 10. * u[1]) + 1. * (-100. * u[0] + u[1]); 66 A1[0][0] = 110. * u[1] * (actx->lambda2) / denorm + 1; 67 A1[0][1] = -110. * u[0] * (actx->lambda2) / denorm; 68 A1[1][0] = -110. * u[1] * 1. / denorm; 69 A1[1][1] = 110. * u[0] * 1. / denorm + 1.; 70 71 A2[0] = 0; 72 A2[1] = 0; 73 } 74 75 PetscCall(VecRestoreArrayRead(U, &u)); 76 77 PetscCall(VecGetArray(lambda[0], &x)); 78 PetscCall(VecGetArray(mu[0], &y)); 79 tmp[0] = A1[0][0] * x[0] + A1[0][1] * x[1]; 80 tmp[1] = A1[1][0] * x[0] + A1[1][1] * x[1]; 81 y[0] = y[0] + A2[0] * x[0] + A2[1] * x[1]; 82 x[0] = tmp[0]; 83 x[1] = tmp[1]; 84 PetscCall(VecRestoreArray(mu[0], &y)); 85 PetscCall(VecRestoreArray(lambda[0], &x)); 86 87 PetscCall(VecGetArray(lambda[1], &x)); 88 PetscCall(VecGetArray(mu[1], &y)); 89 tmp[0] = A1[0][0] * x[0] + A1[0][1] * x[1]; 90 tmp[1] = A1[1][0] * x[0] + A1[1][1] * x[1]; 91 y[0] = y[0] + A2[0] * x[0] + A2[1] * x[1]; 92 x[0] = tmp[0]; 93 x[1] = tmp[1]; 94 PetscCall(VecRestoreArray(mu[1], &y)); 95 PetscCall(VecRestoreArray(lambda[1], &x)); 96 PetscFunctionReturn(0); 97 } 98 99 PetscErrorCode PostEventFunction(TS ts, PetscInt nevents, PetscInt event_list[], PetscReal t, Vec U, PetscBool forwardsolve, void *ctx) 100 { 101 AppCtx *actx = (AppCtx *)ctx; 102 103 PetscFunctionBegin; 104 /* PetscCall(VecView(U,PETSC_VIEWER_STDOUT_WORLD)); */ 105 if (!forwardsolve) PetscCall(ShiftGradients(ts, U, actx)); 106 if (actx->mode == 1) { 107 actx->mode = 2; 108 /* PetscCall(PetscPrintf(PETSC_COMM_SELF,"Change from mode 1 to 2 at t = %f \n",(double)t)); */ 109 } else if (actx->mode == 2) { 110 actx->mode = 1; 111 /* PetscCall(PetscPrintf(PETSC_COMM_SELF,"Change from mode 2 to 1 at t = %f \n",(double)t)); */ 112 } 113 PetscFunctionReturn(0); 114 } 115 116 /* 117 Defines the ODE passed to the ODE solver 118 */ 119 static PetscErrorCode IFunction(TS ts, PetscReal t, Vec U, Vec Udot, Vec F, void *ctx) 120 { 121 AppCtx *actx = (AppCtx *)ctx; 122 PetscScalar *f; 123 const PetscScalar *u, *udot; 124 125 PetscFunctionBegin; 126 /* The next three lines allow us to access the entries of the vectors directly */ 127 PetscCall(VecGetArrayRead(U, &u)); 128 PetscCall(VecGetArrayRead(Udot, &udot)); 129 PetscCall(VecGetArray(F, &f)); 130 131 if (actx->mode == 1) { 132 f[0] = udot[0] - u[0] + 100 * u[1]; 133 f[1] = udot[1] - 10 * u[0] - u[1]; 134 } else if (actx->mode == 2) { 135 f[0] = udot[0] - u[0] - 10 * u[1]; 136 f[1] = udot[1] + 100 * u[0] - u[1]; 137 } 138 139 PetscCall(VecRestoreArrayRead(U, &u)); 140 PetscCall(VecRestoreArrayRead(Udot, &udot)); 141 PetscCall(VecRestoreArray(F, &f)); 142 PetscFunctionReturn(0); 143 } 144 145 /* 146 Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian. 147 */ 148 static PetscErrorCode IJacobian(TS ts, PetscReal t, Vec U, Vec Udot, PetscReal a, Mat A, Mat B, void *ctx) 149 { 150 AppCtx *actx = (AppCtx *)ctx; 151 PetscInt rowcol[] = {0, 1}; 152 PetscScalar J[2][2]; 153 const PetscScalar *u, *udot; 154 155 PetscFunctionBegin; 156 PetscCall(VecGetArrayRead(U, &u)); 157 PetscCall(VecGetArrayRead(Udot, &udot)); 158 159 if (actx->mode == 1) { 160 J[0][0] = a - 1; 161 J[0][1] = 100; 162 J[1][0] = -10; 163 J[1][1] = a - 1; 164 } else if (actx->mode == 2) { 165 J[0][0] = a - 1; 166 J[0][1] = -10; 167 J[1][0] = 100; 168 J[1][1] = a - 1; 169 } 170 PetscCall(MatSetValues(B, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES)); 171 172 PetscCall(VecRestoreArrayRead(U, &u)); 173 PetscCall(VecRestoreArrayRead(Udot, &udot)); 174 175 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY)); 176 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY)); 177 if (A != B) { 178 PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY)); 179 PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY)); 180 } 181 PetscFunctionReturn(0); 182 } 183 184 /* Matrix JacobianP is constant so that it only needs to be evaluated once */ 185 static PetscErrorCode RHSJacobianP(TS ts, PetscReal t, Vec X, Mat A, void *ctx) 186 { 187 PetscFunctionBeginUser; 188 PetscFunctionReturn(0); 189 } 190 191 int main(int argc, char **argv) 192 { 193 TS ts; /* ODE integrator */ 194 Vec U; /* solution will be stored here */ 195 Mat A; /* Jacobian matrix */ 196 Mat Ap; /* dfdp */ 197 PetscMPIInt size; 198 PetscInt n = 2; 199 PetscScalar *u, *v; 200 AppCtx app; 201 PetscInt direction[1]; 202 PetscBool terminate[1]; 203 Vec lambda[2], mu[2]; 204 PetscReal tend; 205 206 FILE *f; 207 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 208 Initialize program 209 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 210 PetscFunctionBeginUser; 211 PetscCall(PetscInitialize(&argc, &argv, (char *)0, help)); 212 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); 213 PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs"); 214 app.mode = 1; 215 app.lambda1 = 2.75; 216 app.lambda2 = 0.36; 217 tend = 0.125; 218 PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "ex1adj options", ""); 219 { 220 PetscCall(PetscOptionsReal("-lambda1", "", "", app.lambda1, &app.lambda1, NULL)); 221 PetscCall(PetscOptionsReal("-lambda2", "", "", app.lambda2, &app.lambda2, NULL)); 222 PetscCall(PetscOptionsReal("-tend", "", "", tend, &tend, NULL)); 223 } 224 PetscOptionsEnd(); 225 226 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 227 Create necessary matrix and vectors 228 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 229 PetscCall(MatCreate(PETSC_COMM_WORLD, &A)); 230 PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE)); 231 PetscCall(MatSetType(A, MATDENSE)); 232 PetscCall(MatSetFromOptions(A)); 233 PetscCall(MatSetUp(A)); 234 235 PetscCall(MatCreateVecs(A, &U, NULL)); 236 237 PetscCall(MatCreate(PETSC_COMM_WORLD, &Ap)); 238 PetscCall(MatSetSizes(Ap, n, 1, PETSC_DETERMINE, PETSC_DETERMINE)); 239 PetscCall(MatSetType(Ap, MATDENSE)); 240 PetscCall(MatSetFromOptions(Ap)); 241 PetscCall(MatSetUp(Ap)); 242 PetscCall(MatZeroEntries(Ap)); /* initialize to zeros */ 243 244 PetscCall(VecGetArray(U, &u)); 245 u[0] = 0; 246 u[1] = 1; 247 PetscCall(VecRestoreArray(U, &u)); 248 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 249 Create timestepping solver context 250 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 251 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 252 PetscCall(TSSetProblemType(ts, TS_NONLINEAR)); 253 PetscCall(TSSetType(ts, TSCN)); 254 PetscCall(TSSetIFunction(ts, NULL, (TSIFunction)IFunction, &app)); 255 PetscCall(TSSetIJacobian(ts, A, A, (TSIJacobian)IJacobian, &app)); 256 PetscCall(TSSetRHSJacobianP(ts, Ap, RHSJacobianP, &app)); 257 258 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 259 Set initial conditions 260 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 261 PetscCall(TSSetSolution(ts, U)); 262 263 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 264 Save trajectory of solution so that TSAdjointSolve() may be used 265 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 266 PetscCall(TSSetSaveTrajectory(ts)); 267 268 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 269 Set solver options 270 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 271 PetscCall(TSSetMaxTime(ts, tend)); 272 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP)); 273 PetscCall(TSSetTimeStep(ts, 1. / 256.)); 274 PetscCall(TSSetFromOptions(ts)); 275 276 /* Set directions and terminate flags for the two events */ 277 direction[0] = 0; 278 terminate[0] = PETSC_FALSE; 279 PetscCall(TSSetEventHandler(ts, 1, direction, terminate, EventFunction, PostEventFunction, (void *)&app)); 280 281 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 282 Run timestepping solver 283 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 284 PetscCall(TSSolve(ts, U)); 285 286 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 287 Adjoint model starts here 288 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 289 PetscCall(MatCreateVecs(A, &lambda[0], NULL)); 290 PetscCall(MatCreateVecs(A, &lambda[1], NULL)); 291 /* Set initial conditions for the adjoint integration */ 292 PetscCall(VecZeroEntries(lambda[0])); 293 PetscCall(VecZeroEntries(lambda[1])); 294 PetscCall(VecGetArray(lambda[0], &u)); 295 u[0] = 1.; 296 PetscCall(VecRestoreArray(lambda[0], &u)); 297 PetscCall(VecGetArray(lambda[1], &u)); 298 u[1] = 1.; 299 PetscCall(VecRestoreArray(lambda[1], &u)); 300 301 PetscCall(MatCreateVecs(Ap, &mu[0], NULL)); 302 PetscCall(MatCreateVecs(Ap, &mu[1], NULL)); 303 PetscCall(VecZeroEntries(mu[0])); 304 PetscCall(VecZeroEntries(mu[1])); 305 PetscCall(TSSetCostGradients(ts, 2, lambda, mu)); 306 307 PetscCall(TSAdjointSolve(ts)); 308 309 /* 310 PetscCall(VecView(lambda[0],PETSC_VIEWER_STDOUT_WORLD)); 311 PetscCall(VecView(lambda[1],PETSC_VIEWER_STDOUT_WORLD)); 312 PetscCall(VecView(mu[0],PETSC_VIEWER_STDOUT_WORLD)); 313 PetscCall(VecView(mu[1],PETSC_VIEWER_STDOUT_WORLD)); 314 */ 315 PetscCall(VecGetArray(mu[0], &u)); 316 PetscCall(VecGetArray(mu[1], &v)); 317 f = fopen("adj_mu.out", "a"); 318 PetscCall(PetscFPrintf(PETSC_COMM_WORLD, f, "%20.15lf %20.15lf %20.15lf\n", (double)tend, (double)PetscRealPart(u[0]), (double)PetscRealPart(v[0]))); 319 PetscCall(VecRestoreArray(mu[0], &u)); 320 PetscCall(VecRestoreArray(mu[1], &v)); 321 fclose(f); 322 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 323 Free work space. All PETSc objects should be destroyed when they are no longer needed. 324 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 325 PetscCall(MatDestroy(&A)); 326 PetscCall(VecDestroy(&U)); 327 PetscCall(TSDestroy(&ts)); 328 329 PetscCall(MatDestroy(&Ap)); 330 PetscCall(VecDestroy(&lambda[0])); 331 PetscCall(VecDestroy(&lambda[1])); 332 PetscCall(VecDestroy(&mu[0])); 333 PetscCall(VecDestroy(&mu[1])); 334 PetscCall(PetscFinalize()); 335 return 0; 336 } 337 338 /*TEST 339 340 build: 341 requires: !complex 342 343 test: 344 args: -ts_monitor -ts_adjoint_monitor 345 346 TEST*/ 347