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