1 static char help[] = "Trajectory 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 PetscReal print_time; 26 } AppCtx; 27 28 PetscErrorCode MyMonitor(TS ts, PetscInt stepnum, PetscReal time, Vec U, void *ctx) { 29 AppCtx *actx = (AppCtx *)ctx; 30 Mat sp; 31 PetscScalar *u; 32 PetscInt nump; 33 FILE *f; 34 35 PetscFunctionBegin; 36 if (time >= actx->print_time) { 37 actx->print_time += 1. / 256.; 38 PetscCall(TSForwardGetSensitivities(ts, &nump, &sp)); 39 PetscCall(MatDenseGetColumn(sp, 2, &u)); 40 f = fopen("fwd_sp.out", "a"); 41 PetscCall(PetscFPrintf(PETSC_COMM_WORLD, f, "%20.15lf %20.15lf %20.15lf\n", (double)time, (double)PetscRealPart(u[0]), (double)PetscRealPart(u[1]))); 42 PetscCall(MatDenseRestoreColumn(sp, &u)); 43 fclose(f); 44 } 45 PetscFunctionReturn(0); 46 } 47 48 PetscErrorCode EventFunction(TS ts, PetscReal t, Vec U, PetscScalar *fvalue, void *ctx) { 49 AppCtx *actx = (AppCtx *)ctx; 50 const PetscScalar *u; 51 52 PetscFunctionBegin; 53 PetscCall(VecGetArrayRead(U, &u)); 54 if (actx->mode == 1) { 55 fvalue[0] = u[1] - actx->lambda1 * u[0]; 56 } else if (actx->mode == 2) { 57 fvalue[0] = u[1] - actx->lambda2 * u[0]; 58 } 59 PetscCall(VecRestoreArrayRead(U, &u)); 60 PetscFunctionReturn(0); 61 } 62 63 PetscErrorCode ShiftGradients(TS ts, Vec U, AppCtx *actx) { 64 Mat sp; 65 PetscScalar *x; 66 PetscScalar *u; 67 PetscScalar tmp[2], A1[2][2], A2[2], denorm; 68 PetscInt nump; 69 70 PetscFunctionBegin; 71 PetscCall(TSForwardGetSensitivities(ts, &nump, &sp)); 72 PetscCall(VecGetArray(U, &u)); 73 74 if (actx->mode == 1) { 75 denorm = -actx->lambda1 * (u[0] - 100. * u[1]) + 1. * (10. * u[0] + u[1]); 76 A1[0][0] = 110. * u[1] * (-actx->lambda1) / denorm + 1.; 77 A1[1][0] = -110. * u[0] * (-actx->lambda1) / denorm; 78 A1[0][1] = 110. * u[1] * 1. / denorm; 79 A1[1][1] = -110. * u[0] * 1. / denorm + 1.; 80 81 A2[0] = 110. * u[1] * (-u[0]) / denorm; 82 A2[1] = -110. * u[0] * (-u[0]) / denorm; 83 } else { 84 denorm = -actx->lambda2 * (u[0] + 10. * u[1]) + 1. * (-100. * u[0] + u[1]); 85 A1[0][0] = 110. * u[1] * (actx->lambda2) / denorm + 1; 86 A1[1][0] = -110. * u[0] * (actx->lambda2) / denorm; 87 A1[0][1] = -110. * u[1] * 1. / denorm; 88 A1[1][1] = 110. * u[0] * 1. / denorm + 1.; 89 90 A2[0] = 0; 91 A2[1] = 0; 92 } 93 94 PetscCall(VecRestoreArray(U, &u)); 95 96 PetscCall(MatDenseGetColumn(sp, 0, &x)); 97 tmp[0] = A1[0][0] * x[0] + A1[0][1] * x[1]; 98 tmp[1] = A1[1][0] * x[0] + A1[1][1] * x[1]; 99 x[0] = tmp[0]; 100 x[1] = tmp[1]; 101 PetscCall(MatDenseRestoreColumn(sp, &x)); 102 103 PetscCall(MatDenseGetColumn(sp, 1, &x)); 104 tmp[0] = A1[0][0] * x[0] + A1[0][1] * x[1]; 105 tmp[1] = A1[1][0] * x[0] + A1[1][1] * x[1]; 106 x[0] = tmp[0]; 107 x[1] = tmp[1]; 108 PetscCall(MatDenseRestoreColumn(sp, &x)); 109 110 PetscCall(MatDenseGetColumn(sp, 2, &x)); 111 tmp[0] = A1[0][0] * x[0] + A1[0][1] * x[1]; 112 tmp[1] = A1[1][0] * x[0] + A1[1][1] * x[1]; 113 x[0] = tmp[0] + A2[0]; 114 x[1] = tmp[1] + A2[1]; 115 PetscCall(MatDenseRestoreColumn(sp, &x)); 116 117 PetscFunctionReturn(0); 118 } 119 120 PetscErrorCode PostEventFunction(TS ts, PetscInt nevents, PetscInt event_list[], PetscReal t, Vec U, PetscBool forwardsolve, void *ctx) { 121 AppCtx *actx = (AppCtx *)ctx; 122 123 PetscFunctionBegin; 124 /* PetscCall(VecView(U,PETSC_VIEWER_STDOUT_WORLD)); */ 125 PetscCall(ShiftGradients(ts, U, actx)); 126 if (actx->mode == 1) { 127 actx->mode = 2; 128 /* PetscCall(PetscPrintf(PETSC_COMM_SELF,"Change from mode 1 to 2 at t = %f \n",(double)t)); */ 129 } else if (actx->mode == 2) { 130 actx->mode = 1; 131 /* PetscCall(PetscPrintf(PETSC_COMM_SELF,"Change from mode 2 to 1 at t = %f \n",(double)t)); */ 132 } 133 PetscFunctionReturn(0); 134 } 135 136 /* 137 Defines the ODE passed to the ODE solver 138 */ 139 static PetscErrorCode IFunction(TS ts, PetscReal t, Vec U, Vec Udot, Vec F, void *ctx) { 140 AppCtx *actx = (AppCtx *)ctx; 141 PetscScalar *f; 142 const PetscScalar *u, *udot; 143 144 PetscFunctionBegin; 145 /* The next three lines allow us to access the entries of the vectors directly */ 146 PetscCall(VecGetArrayRead(U, &u)); 147 PetscCall(VecGetArrayRead(Udot, &udot)); 148 PetscCall(VecGetArray(F, &f)); 149 150 if (actx->mode == 1) { 151 f[0] = udot[0] - u[0] + 100 * u[1]; 152 f[1] = udot[1] - 10 * u[0] - u[1]; 153 } else if (actx->mode == 2) { 154 f[0] = udot[0] - u[0] - 10 * u[1]; 155 f[1] = udot[1] + 100 * u[0] - u[1]; 156 } 157 158 PetscCall(VecRestoreArrayRead(U, &u)); 159 PetscCall(VecRestoreArrayRead(Udot, &udot)); 160 PetscCall(VecRestoreArray(F, &f)); 161 PetscFunctionReturn(0); 162 } 163 164 /* 165 Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian. 166 */ 167 static PetscErrorCode IJacobian(TS ts, PetscReal t, Vec U, Vec Udot, PetscReal a, Mat A, Mat B, void *ctx) { 168 AppCtx *actx = (AppCtx *)ctx; 169 PetscInt rowcol[] = {0, 1}; 170 PetscScalar J[2][2]; 171 const PetscScalar *u, *udot; 172 173 PetscFunctionBegin; 174 PetscCall(VecGetArrayRead(U, &u)); 175 PetscCall(VecGetArrayRead(Udot, &udot)); 176 177 if (actx->mode == 1) { 178 J[0][0] = a - 1; 179 J[0][1] = 100; 180 J[1][0] = -10; 181 J[1][1] = a - 1; 182 } else if (actx->mode == 2) { 183 J[0][0] = a - 1; 184 J[0][1] = -10; 185 J[1][0] = 100; 186 J[1][1] = a - 1; 187 } 188 PetscCall(MatSetValues(B, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES)); 189 190 PetscCall(VecRestoreArrayRead(U, &u)); 191 PetscCall(VecRestoreArrayRead(Udot, &udot)); 192 193 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY)); 194 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY)); 195 if (A != B) { 196 PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY)); 197 PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY)); 198 } 199 PetscFunctionReturn(0); 200 } 201 202 /* Matrix JacobianP is constant so that it only needs to be evaluated once */ 203 static PetscErrorCode RHSJacobianP(TS ts, PetscReal t, Vec X, Mat Ap, void *ctx) { 204 PetscFunctionBeginUser; 205 PetscFunctionReturn(0); 206 } 207 208 int main(int argc, char **argv) { 209 TS ts; /* ODE integrator */ 210 Vec U; /* solution will be stored here */ 211 Mat A; /* Jacobian matrix */ 212 Mat Ap; /* Jacobian dfdp */ 213 PetscMPIInt size; 214 PetscInt n = 2; 215 PetscScalar *u; 216 AppCtx app; 217 PetscInt direction[1]; 218 PetscBool terminate[1]; 219 Mat sp; 220 PetscReal tend; 221 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 222 Initialize program 223 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 224 PetscFunctionBeginUser; 225 PetscCall(PetscInitialize(&argc, &argv, (char *)0, help)); 226 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); 227 PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs"); 228 app.mode = 1; 229 app.lambda1 = 2.75; 230 app.lambda2 = 0.36; 231 app.print_time = 1. / 256.; 232 tend = 0.125; 233 PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "ex1fwd options", ""); 234 { 235 PetscCall(PetscOptionsReal("-lambda1", "", "", app.lambda1, &app.lambda1, NULL)); 236 PetscCall(PetscOptionsReal("-lambda2", "", "", app.lambda2, &app.lambda2, NULL)); 237 PetscCall(PetscOptionsReal("-tend", "", "", tend, &tend, NULL)); 238 } 239 PetscOptionsEnd(); 240 241 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 242 Create necessary matrix and vectors 243 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 244 PetscCall(MatCreate(PETSC_COMM_WORLD, &A)); 245 PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE)); 246 PetscCall(MatSetType(A, MATDENSE)); 247 PetscCall(MatSetFromOptions(A)); 248 PetscCall(MatSetUp(A)); 249 250 PetscCall(MatCreateVecs(A, &U, NULL)); 251 252 PetscCall(MatCreate(PETSC_COMM_WORLD, &Ap)); 253 PetscCall(MatSetSizes(Ap, n, 3, PETSC_DETERMINE, PETSC_DETERMINE)); 254 PetscCall(MatSetType(Ap, MATDENSE)); 255 PetscCall(MatSetFromOptions(Ap)); 256 PetscCall(MatSetUp(Ap)); 257 PetscCall(MatZeroEntries(Ap)); 258 259 PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, n, 3, NULL, &sp)); 260 PetscCall(MatZeroEntries(sp)); 261 PetscCall(MatShift(sp, 1.0)); 262 263 PetscCall(VecGetArray(U, &u)); 264 u[0] = 0; 265 u[1] = 1; 266 PetscCall(VecRestoreArray(U, &u)); 267 268 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 269 Create timestepping solver context 270 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 271 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 272 PetscCall(TSSetProblemType(ts, TS_NONLINEAR)); 273 PetscCall(TSSetType(ts, TSCN)); 274 PetscCall(TSSetIFunction(ts, NULL, (TSIFunction)IFunction, &app)); 275 PetscCall(TSSetIJacobian(ts, A, A, (TSIJacobian)IJacobian, &app)); 276 277 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 278 Set initial conditions 279 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 280 PetscCall(TSSetSolution(ts, U)); 281 282 PetscCall(TSForwardSetSensitivities(ts, 3, sp)); 283 /* Set RHS JacobianP */ 284 PetscCall(TSSetRHSJacobianP(ts, Ap, RHSJacobianP, &app)); 285 286 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 287 Set solver options 288 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 289 PetscCall(TSSetMaxTime(ts, tend)); 290 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP)); 291 PetscCall(TSSetTimeStep(ts, 1. / 256.)); 292 PetscCall(TSMonitorSet(ts, MyMonitor, &app, PETSC_NULL)); 293 PetscCall(TSSetFromOptions(ts)); 294 295 /* Set directions and terminate flags for the two events */ 296 direction[0] = 0; 297 terminate[0] = PETSC_FALSE; 298 PetscCall(TSSetEventHandler(ts, 1, direction, terminate, EventFunction, PostEventFunction, (void *)&app)); 299 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 300 Run timestepping solver 301 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 302 PetscCall(TSSolve(ts, U)); 303 304 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 305 Free work space. All PETSc objects should be destroyed when they are no longer needed. 306 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 307 PetscCall(MatDestroy(&A)); 308 PetscCall(VecDestroy(&U)); 309 PetscCall(TSDestroy(&ts)); 310 311 PetscCall(MatDestroy(&Ap)); 312 PetscCall(MatDestroy(&sp)); 313 PetscCall(PetscFinalize()); 314 return (0); 315 } 316 317 /*TEST 318 319 build: 320 requires: !complex 321 322 test: 323 args: -ts_monitor 324 325 TEST*/ 326