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