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 PetscScalar lambda1; 22 PetscScalar lambda2; 23 PetscInt mode; /* mode flag*/ 24 } AppCtx; 25 26 PetscErrorCode EventFunction(TS ts, PetscReal t, Vec U, PetscReal *fvalue, PetscCtx ctx) 27 { 28 AppCtx *actx = (AppCtx *)ctx; 29 const PetscScalar *u; 30 31 PetscFunctionBegin; 32 PetscCall(VecGetArrayRead(U, &u)); 33 if (actx->mode == 1) { 34 fvalue[0] = PetscRealPart(u[1] - actx->lambda1 * u[0]); 35 } else if (actx->mode == 2) { 36 fvalue[0] = PetscRealPart(u[1] - actx->lambda2 * u[0]); 37 } 38 PetscCall(VecRestoreArrayRead(U, &u)); 39 PetscFunctionReturn(PETSC_SUCCESS); 40 } 41 42 PetscErrorCode PostEventFunction(TS ts, PetscInt nevents, PetscInt event_list[], PetscReal t, Vec U, PetscBool forwardsolve, PetscCtx ctx) 43 { 44 AppCtx *actx = (AppCtx *)ctx; 45 46 PetscFunctionBegin; 47 if (actx->mode == 1) { 48 actx->mode = 2; 49 PetscCall(PetscPrintf(PETSC_COMM_SELF, "Change from mode 1 to 2 at t = %f \n", (double)t)); 50 } else if (actx->mode == 2) { 51 actx->mode = 1; 52 PetscCall(PetscPrintf(PETSC_COMM_SELF, "Change from mode 2 to 1 at t = %f \n", (double)t)); 53 } 54 PetscFunctionReturn(PETSC_SUCCESS); 55 } 56 57 /* 58 Defines the ODE passed to the ODE solver 59 */ 60 static PetscErrorCode IFunction(TS ts, PetscReal t, Vec U, Vec Udot, Vec F, PetscCtx ctx) 61 { 62 AppCtx *actx = (AppCtx *)ctx; 63 PetscScalar *f; 64 const PetscScalar *u, *udot; 65 66 PetscFunctionBegin; 67 /* The next three lines allow us to access the entries of the vectors directly */ 68 PetscCall(VecGetArrayRead(U, &u)); 69 PetscCall(VecGetArrayRead(Udot, &udot)); 70 PetscCall(VecGetArray(F, &f)); 71 72 if (actx->mode == 1) { 73 f[0] = udot[0] - u[0] + 100 * u[1]; 74 f[1] = udot[1] - 10 * u[0] - u[1]; 75 } else if (actx->mode == 2) { 76 f[0] = udot[0] - u[0] - 10 * u[1]; 77 f[1] = udot[1] + 100 * u[0] - u[1]; 78 } 79 80 PetscCall(VecRestoreArrayRead(U, &u)); 81 PetscCall(VecRestoreArrayRead(Udot, &udot)); 82 PetscCall(VecRestoreArray(F, &f)); 83 PetscFunctionReturn(PETSC_SUCCESS); 84 } 85 86 /* 87 Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian. 88 */ 89 static PetscErrorCode IJacobian(TS ts, PetscReal t, Vec U, Vec Udot, PetscReal a, Mat A, Mat B, PetscCtx ctx) 90 { 91 AppCtx *actx = (AppCtx *)ctx; 92 PetscInt rowcol[] = {0, 1}; 93 PetscScalar J[2][2]; 94 const PetscScalar *u, *udot; 95 96 PetscFunctionBegin; 97 PetscCall(VecGetArrayRead(U, &u)); 98 PetscCall(VecGetArrayRead(Udot, &udot)); 99 100 if (actx->mode == 1) { 101 J[0][0] = a - 1; 102 J[0][1] = 100; 103 J[1][0] = -10; 104 J[1][1] = a - 1; 105 } else if (actx->mode == 2) { 106 J[0][0] = a - 1; 107 J[0][1] = -10; 108 J[1][0] = 100; 109 J[1][1] = a - 1; 110 } 111 PetscCall(MatSetValues(B, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES)); 112 113 PetscCall(VecRestoreArrayRead(U, &u)); 114 PetscCall(VecRestoreArrayRead(Udot, &udot)); 115 116 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY)); 117 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY)); 118 if (A != B) { 119 PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY)); 120 PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY)); 121 } 122 PetscFunctionReturn(PETSC_SUCCESS); 123 } 124 125 int main(int argc, char **argv) 126 { 127 TS ts; /* ODE integrator */ 128 Vec U; /* solution will be stored here */ 129 Mat A; /* Jacobian matrix */ 130 PetscMPIInt size; 131 PetscInt n = 2; 132 PetscScalar *u; 133 AppCtx app; 134 PetscInt direction[1]; 135 PetscBool terminate[1]; 136 137 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 138 Initialize program 139 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 140 PetscFunctionBeginUser; 141 PetscCall(PetscInitialize(&argc, &argv, NULL, help)); 142 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); 143 PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs"); 144 app.mode = 1; 145 app.lambda1 = 2.75; 146 app.lambda2 = 0.36; 147 PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "ex1 options", ""); 148 { 149 PetscCall(PetscOptionsReal("-lambda1", "", "", app.lambda1, &app.lambda1, NULL)); 150 PetscCall(PetscOptionsReal("-lambda2", "", "", app.lambda2, &app.lambda2, NULL)); 151 } 152 PetscOptionsEnd(); 153 154 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 155 Create necessary matrix and vectors 156 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 157 PetscCall(MatCreate(PETSC_COMM_WORLD, &A)); 158 PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE)); 159 PetscCall(MatSetType(A, MATDENSE)); 160 PetscCall(MatSetFromOptions(A)); 161 PetscCall(MatSetUp(A)); 162 163 PetscCall(MatCreateVecs(A, &U, NULL)); 164 165 PetscCall(VecGetArray(U, &u)); 166 u[0] = 0; 167 u[1] = 1; 168 PetscCall(VecRestoreArray(U, &u)); 169 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 170 Create timestepping solver context 171 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 172 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 173 PetscCall(TSSetProblemType(ts, TS_NONLINEAR)); 174 PetscCall(TSSetType(ts, TSCN)); 175 PetscCall(TSSetIFunction(ts, NULL, (TSIFunctionFn *)IFunction, &app)); 176 PetscCall(TSSetIJacobian(ts, A, A, (TSIJacobianFn *)IJacobian, &app)); 177 178 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 179 Set initial conditions 180 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 181 PetscCall(TSSetSolution(ts, U)); 182 183 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 184 Set solver options 185 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 186 PetscCall(TSSetMaxTime(ts, 0.125)); 187 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP)); 188 PetscCall(TSSetTimeStep(ts, 1. / 256.)); 189 PetscCall(TSSetFromOptions(ts)); 190 191 /* Set directions and terminate flags for the two events */ 192 direction[0] = 0; 193 terminate[0] = PETSC_FALSE; 194 PetscCall(TSSetEventHandler(ts, 1, direction, terminate, EventFunction, PostEventFunction, (void *)&app)); 195 196 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 197 Run timestepping solver 198 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 199 PetscCall(TSSolve(ts, U)); 200 201 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 202 Free work space. All PETSc objects should be destroyed when they are no longer needed. 203 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 204 PetscCall(MatDestroy(&A)); 205 PetscCall(VecDestroy(&U)); 206 PetscCall(TSDestroy(&ts)); 207 208 PetscCall(PetscFinalize()); 209 return 0; 210 } 211 212 /*TEST 213 214 build: 215 requires: !complex 216 test: 217 args: -ts_monitor 218 219 test: 220 suffix: 2 221 args: -ts_monitor_lg_solution -1 222 requires: x 223 224 TEST*/ 225