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, 16 IEEE Transactions on Circuits and Systems I: Regular Papers, 64(5), May 2017 17 - * - I. A. Hiskens, M.A. Pai, Trajectory Sensitivity Analysis of Hybrid Systems, IEEE Transactions on Circuits and Systems, Vol 47, No 2, February 2000 18 */ 19 20 #include <petscts.h> 21 22 typedef struct { 23 PetscScalar lambda1; 24 PetscScalar lambda2; 25 PetscInt mode; /* mode flag*/ 26 } AppCtx; 27 28 PetscErrorCode EventFunction(TS ts, PetscReal t, Vec U, PetscReal *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] = PetscRealPart(u[1] - actx->lambda1 * u[0]); 37 } else if (actx->mode == 2) { 38 fvalue[0] = PetscRealPart(u[1] - actx->lambda2 * u[0]); 39 } 40 PetscCall(VecRestoreArrayRead(U, &u)); 41 PetscFunctionReturn(PETSC_SUCCESS); 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], denorm; 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 denorm = -actx->lambda1 * (u[0] - 100. * u[1]) + 1. * (10. * u[0] + u[1]); 58 A1[0][0] = 110. * u[1] * (-actx->lambda1) / denorm + 1.; 59 A1[0][1] = -110. * u[0] * (-actx->lambda1) / denorm; 60 A1[1][0] = 110. * u[1] * 1. / denorm; 61 A1[1][1] = -110. * u[0] * 1. / denorm + 1.; 62 63 A2[0] = 110. * u[1] * (-u[0]) / denorm; 64 A2[1] = -110. * u[0] * (-u[0]) / denorm; 65 } else { 66 denorm = -actx->lambda2 * (u[0] + 10. * u[1]) + 1. * (-100. * u[0] + u[1]); 67 A1[0][0] = 110. * u[1] * (actx->lambda2) / denorm + 1; 68 A1[0][1] = -110. * u[0] * (actx->lambda2) / denorm; 69 A1[1][0] = -110. * u[1] * 1. / denorm; 70 A1[1][1] = 110. * u[0] * 1. / denorm + 1.; 71 72 A2[0] = 0; 73 A2[1] = 0; 74 } 75 76 PetscCall(VecRestoreArrayRead(U, &u)); 77 78 PetscCall(VecGetArray(lambda[0], &x)); 79 PetscCall(VecGetArray(mu[0], &y)); 80 tmp[0] = A1[0][0] * x[0] + A1[0][1] * x[1]; 81 tmp[1] = A1[1][0] * x[0] + A1[1][1] * x[1]; 82 y[0] = y[0] + A2[0] * x[0] + A2[1] * x[1]; 83 x[0] = tmp[0]; 84 x[1] = tmp[1]; 85 PetscCall(VecRestoreArray(mu[0], &y)); 86 PetscCall(VecRestoreArray(lambda[0], &x)); 87 88 PetscCall(VecGetArray(lambda[1], &x)); 89 PetscCall(VecGetArray(mu[1], &y)); 90 tmp[0] = A1[0][0] * x[0] + A1[0][1] * x[1]; 91 tmp[1] = A1[1][0] * x[0] + A1[1][1] * x[1]; 92 y[0] = y[0] + A2[0] * x[0] + A2[1] * x[1]; 93 x[0] = tmp[0]; 94 x[1] = tmp[1]; 95 PetscCall(VecRestoreArray(mu[1], &y)); 96 PetscCall(VecRestoreArray(lambda[1], &x)); 97 PetscFunctionReturn(PETSC_SUCCESS); 98 } 99 100 PetscErrorCode PostEventFunction(TS ts, PetscInt nevents, PetscInt event_list[], PetscReal t, Vec U, PetscBool forwardsolve, void *ctx) 101 { 102 AppCtx *actx = (AppCtx *)ctx; 103 104 PetscFunctionBegin; 105 /* PetscCall(VecView(U,PETSC_VIEWER_STDOUT_WORLD)); */ 106 if (!forwardsolve) PetscCall(ShiftGradients(ts, U, actx)); 107 if (actx->mode == 1) { 108 actx->mode = 2; 109 /* PetscCall(PetscPrintf(PETSC_COMM_SELF,"Change from mode 1 to 2 at t = %f \n",(double)t)); */ 110 } else if (actx->mode == 2) { 111 actx->mode = 1; 112 /* PetscCall(PetscPrintf(PETSC_COMM_SELF,"Change from mode 2 to 1 at t = %f \n",(double)t)); */ 113 } 114 PetscFunctionReturn(PETSC_SUCCESS); 115 } 116 117 /* 118 Defines the ODE passed to the ODE solver 119 */ 120 static PetscErrorCode IFunction(TS ts, PetscReal t, Vec U, Vec Udot, Vec F, void *ctx) 121 { 122 AppCtx *actx = (AppCtx *)ctx; 123 PetscScalar *f; 124 const PetscScalar *u, *udot; 125 126 PetscFunctionBegin; 127 /* The next three lines allow us to access the entries of the vectors directly */ 128 PetscCall(VecGetArrayRead(U, &u)); 129 PetscCall(VecGetArrayRead(Udot, &udot)); 130 PetscCall(VecGetArray(F, &f)); 131 132 if (actx->mode == 1) { 133 f[0] = udot[0] - u[0] + 100 * u[1]; 134 f[1] = udot[1] - 10 * u[0] - u[1]; 135 } else if (actx->mode == 2) { 136 f[0] = udot[0] - u[0] - 10 * u[1]; 137 f[1] = udot[1] + 100 * u[0] - u[1]; 138 } 139 140 PetscCall(VecRestoreArrayRead(U, &u)); 141 PetscCall(VecRestoreArrayRead(Udot, &udot)); 142 PetscCall(VecRestoreArray(F, &f)); 143 PetscFunctionReturn(PETSC_SUCCESS); 144 } 145 146 /* 147 Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian. 148 */ 149 static PetscErrorCode IJacobian(TS ts, PetscReal t, Vec U, Vec Udot, PetscReal a, Mat A, Mat B, void *ctx) 150 { 151 AppCtx *actx = (AppCtx *)ctx; 152 PetscInt rowcol[] = {0, 1}; 153 PetscScalar J[2][2]; 154 const PetscScalar *u, *udot; 155 156 PetscFunctionBegin; 157 PetscCall(VecGetArrayRead(U, &u)); 158 PetscCall(VecGetArrayRead(Udot, &udot)); 159 160 if (actx->mode == 1) { 161 J[0][0] = a - 1; 162 J[0][1] = 100; 163 J[1][0] = -10; 164 J[1][1] = a - 1; 165 } else if (actx->mode == 2) { 166 J[0][0] = a - 1; 167 J[0][1] = -10; 168 J[1][0] = 100; 169 J[1][1] = a - 1; 170 } 171 PetscCall(MatSetValues(B, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES)); 172 173 PetscCall(VecRestoreArrayRead(U, &u)); 174 PetscCall(VecRestoreArrayRead(Udot, &udot)); 175 176 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY)); 177 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY)); 178 if (A != B) { 179 PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY)); 180 PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY)); 181 } 182 PetscFunctionReturn(PETSC_SUCCESS); 183 } 184 185 /* Matrix JacobianP is constant so that it only needs to be evaluated once */ 186 static PetscErrorCode RHSJacobianP(TS ts, PetscReal t, Vec X, Mat A, void *ctx) 187 { 188 PetscFunctionBeginUser; 189 PetscFunctionReturn(PETSC_SUCCESS); 190 } 191 192 int main(int argc, char **argv) 193 { 194 TS ts; /* ODE integrator */ 195 Vec U; /* solution will be stored here */ 196 Mat A; /* Jacobian matrix */ 197 Mat Ap; /* dfdp */ 198 PetscMPIInt size; 199 PetscInt n = 2; 200 PetscScalar *u, *v; 201 AppCtx app; 202 PetscInt direction[1]; 203 PetscBool terminate[1]; 204 Vec lambda[2], mu[2]; 205 PetscReal tend; 206 207 FILE *f; 208 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 209 Initialize program 210 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 211 PetscFunctionBeginUser; 212 PetscCall(PetscInitialize(&argc, &argv, (char *)0, help)); 213 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); 214 PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs"); 215 app.mode = 1; 216 app.lambda1 = 2.75; 217 app.lambda2 = 0.36; 218 tend = 0.125; 219 PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "ex1adj options", ""); 220 { 221 PetscCall(PetscOptionsReal("-lambda1", "", "", app.lambda1, &app.lambda1, NULL)); 222 PetscCall(PetscOptionsReal("-lambda2", "", "", app.lambda2, &app.lambda2, NULL)); 223 PetscCall(PetscOptionsReal("-tend", "", "", tend, &tend, NULL)); 224 } 225 PetscOptionsEnd(); 226 227 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 228 Create necessary matrix and vectors 229 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 230 PetscCall(MatCreate(PETSC_COMM_WORLD, &A)); 231 PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE)); 232 PetscCall(MatSetType(A, MATDENSE)); 233 PetscCall(MatSetFromOptions(A)); 234 PetscCall(MatSetUp(A)); 235 236 PetscCall(MatCreateVecs(A, &U, NULL)); 237 238 PetscCall(MatCreate(PETSC_COMM_WORLD, &Ap)); 239 PetscCall(MatSetSizes(Ap, n, 1, PETSC_DETERMINE, PETSC_DETERMINE)); 240 PetscCall(MatSetType(Ap, MATDENSE)); 241 PetscCall(MatSetFromOptions(Ap)); 242 PetscCall(MatSetUp(Ap)); 243 PetscCall(MatZeroEntries(Ap)); /* initialize to zeros */ 244 245 PetscCall(VecGetArray(U, &u)); 246 u[0] = 0; 247 u[1] = 1; 248 PetscCall(VecRestoreArray(U, &u)); 249 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 250 Create timestepping solver context 251 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 252 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 253 PetscCall(TSSetProblemType(ts, TS_NONLINEAR)); 254 PetscCall(TSSetType(ts, TSCN)); 255 PetscCall(TSSetIFunction(ts, NULL, (TSIFunctionFn *)IFunction, &app)); 256 PetscCall(TSSetIJacobian(ts, A, A, (TSIJacobianFn *)IJacobian, &app)); 257 PetscCall(TSSetRHSJacobianP(ts, Ap, RHSJacobianP, &app)); 258 259 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 260 Set initial conditions 261 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 262 PetscCall(TSSetSolution(ts, U)); 263 264 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 265 Save trajectory of solution so that TSAdjointSolve() may be used 266 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 267 PetscCall(TSSetSaveTrajectory(ts)); 268 269 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 270 Set solver options 271 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 272 PetscCall(TSSetMaxTime(ts, tend)); 273 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP)); 274 PetscCall(TSSetTimeStep(ts, 1. / 256.)); 275 PetscCall(TSSetFromOptions(ts)); 276 277 /* Set directions and terminate flags for the two events */ 278 direction[0] = 0; 279 terminate[0] = PETSC_FALSE; 280 PetscCall(TSSetEventHandler(ts, 1, direction, terminate, EventFunction, PostEventFunction, (void *)&app)); 281 282 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 283 Run timestepping solver 284 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 285 PetscCall(TSSolve(ts, U)); 286 287 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 288 Adjoint model starts here 289 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 290 PetscCall(MatCreateVecs(A, &lambda[0], NULL)); 291 PetscCall(MatCreateVecs(A, &lambda[1], NULL)); 292 /* Set initial conditions for the adjoint integration */ 293 PetscCall(VecZeroEntries(lambda[0])); 294 PetscCall(VecZeroEntries(lambda[1])); 295 PetscCall(VecGetArray(lambda[0], &u)); 296 u[0] = 1.; 297 PetscCall(VecRestoreArray(lambda[0], &u)); 298 PetscCall(VecGetArray(lambda[1], &u)); 299 u[1] = 1.; 300 PetscCall(VecRestoreArray(lambda[1], &u)); 301 302 PetscCall(MatCreateVecs(Ap, &mu[0], NULL)); 303 PetscCall(MatCreateVecs(Ap, &mu[1], NULL)); 304 PetscCall(VecZeroEntries(mu[0])); 305 PetscCall(VecZeroEntries(mu[1])); 306 PetscCall(TSSetCostGradients(ts, 2, lambda, mu)); 307 308 PetscCall(TSAdjointSolve(ts)); 309 310 /* 311 PetscCall(VecView(lambda[0],PETSC_VIEWER_STDOUT_WORLD)); 312 PetscCall(VecView(lambda[1],PETSC_VIEWER_STDOUT_WORLD)); 313 PetscCall(VecView(mu[0],PETSC_VIEWER_STDOUT_WORLD)); 314 PetscCall(VecView(mu[1],PETSC_VIEWER_STDOUT_WORLD)); 315 */ 316 PetscCall(VecGetArray(mu[0], &u)); 317 PetscCall(VecGetArray(mu[1], &v)); 318 f = fopen("adj_mu.out", "a"); 319 PetscCall(PetscFPrintf(PETSC_COMM_WORLD, f, "%20.15lf %20.15lf %20.15lf\n", (double)tend, (double)PetscRealPart(u[0]), (double)PetscRealPart(v[0]))); 320 PetscCall(VecRestoreArray(mu[0], &u)); 321 PetscCall(VecRestoreArray(mu[1], &v)); 322 fclose(f); 323 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 324 Free work space. All PETSc objects should be destroyed when they are no longer needed. 325 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 326 PetscCall(MatDestroy(&A)); 327 PetscCall(VecDestroy(&U)); 328 PetscCall(TSDestroy(&ts)); 329 330 PetscCall(MatDestroy(&Ap)); 331 PetscCall(VecDestroy(&lambda[0])); 332 PetscCall(VecDestroy(&lambda[1])); 333 PetscCall(VecDestroy(&mu[0])); 334 PetscCall(VecDestroy(&mu[1])); 335 PetscCall(PetscFinalize()); 336 return 0; 337 } 338 339 /*TEST 340 341 build: 342 requires: !complex 343 344 test: 345 args: -ts_monitor -ts_adjoint_monitor 346 347 TEST*/ 348