static char help[] = "Trajectory sensitivity of a hybrid system with state-dependent switchings.\n"; /* The dynamics is described by the ODE u_t = A_i u where A_1 = [ 1 -100 10 1 ], A_2 = [ 1 10 -100 1 ]. 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]. Initially u=[0 1]^T and i=1. References: + * - 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 - * - I. A. Hiskens, M.A. Pai, Trajectory Sensitivity Analysis of Hybrid Systems, IEEE Transactions on Circuits and Systems, Vol 47, No 2, February 2000 */ #include typedef struct { PetscScalar lambda1; PetscScalar lambda2; PetscInt mode; /* mode flag*/ PetscReal print_time; } AppCtx; PetscErrorCode MyMonitor(TS ts, PetscInt stepnum, PetscReal time, Vec U, PetscCtx ctx) { AppCtx *actx = (AppCtx *)ctx; Mat sp; PetscScalar *u; PetscInt nump; FILE *f; PetscFunctionBegin; if (time >= actx->print_time) { actx->print_time += 1. / 256.; PetscCall(TSForwardGetSensitivities(ts, &nump, &sp)); PetscCall(MatDenseGetColumn(sp, 2, &u)); f = fopen("fwd_sp.out", "a"); PetscCall(PetscFPrintf(PETSC_COMM_WORLD, f, "%20.15lf %20.15lf %20.15lf\n", (double)time, (double)PetscRealPart(u[0]), (double)PetscRealPart(u[1]))); PetscCall(MatDenseRestoreColumn(sp, &u)); fclose(f); } PetscFunctionReturn(PETSC_SUCCESS); } PetscErrorCode EventFunction(TS ts, PetscReal t, Vec U, PetscReal *fvalue, PetscCtx ctx) { AppCtx *actx = (AppCtx *)ctx; const PetscScalar *u; PetscFunctionBegin; PetscCall(VecGetArrayRead(U, &u)); if (actx->mode == 1) { fvalue[0] = PetscRealPart(u[1] - actx->lambda1 * u[0]); } else if (actx->mode == 2) { fvalue[0] = PetscRealPart(u[1] - actx->lambda2 * u[0]); } PetscCall(VecRestoreArrayRead(U, &u)); PetscFunctionReturn(PETSC_SUCCESS); } PetscErrorCode ShiftGradients(TS ts, Vec U, AppCtx *actx) { Mat sp; PetscScalar *x; PetscScalar *u; PetscScalar tmp[2], A1[2][2], A2[2], denorm; PetscInt nump; PetscFunctionBegin; PetscCall(TSForwardGetSensitivities(ts, &nump, &sp)); PetscCall(VecGetArray(U, &u)); if (actx->mode == 1) { denorm = -actx->lambda1 * (u[0] - 100. * u[1]) + 1. * (10. * u[0] + u[1]); A1[0][0] = 110. * u[1] * (-actx->lambda1) / denorm + 1.; A1[1][0] = -110. * u[0] * (-actx->lambda1) / denorm; A1[0][1] = 110. * u[1] * 1. / denorm; A1[1][1] = -110. * u[0] * 1. / denorm + 1.; A2[0] = 110. * u[1] * (-u[0]) / denorm; A2[1] = -110. * u[0] * (-u[0]) / denorm; } else { denorm = -actx->lambda2 * (u[0] + 10. * u[1]) + 1. * (-100. * u[0] + u[1]); A1[0][0] = 110. * u[1] * (actx->lambda2) / denorm + 1; A1[1][0] = -110. * u[0] * (actx->lambda2) / denorm; A1[0][1] = -110. * u[1] * 1. / denorm; A1[1][1] = 110. * u[0] * 1. / denorm + 1.; A2[0] = 0; A2[1] = 0; } PetscCall(VecRestoreArray(U, &u)); PetscCall(MatDenseGetColumn(sp, 0, &x)); tmp[0] = A1[0][0] * x[0] + A1[0][1] * x[1]; tmp[1] = A1[1][0] * x[0] + A1[1][1] * x[1]; x[0] = tmp[0]; x[1] = tmp[1]; PetscCall(MatDenseRestoreColumn(sp, &x)); PetscCall(MatDenseGetColumn(sp, 1, &x)); tmp[0] = A1[0][0] * x[0] + A1[0][1] * x[1]; tmp[1] = A1[1][0] * x[0] + A1[1][1] * x[1]; x[0] = tmp[0]; x[1] = tmp[1]; PetscCall(MatDenseRestoreColumn(sp, &x)); PetscCall(MatDenseGetColumn(sp, 2, &x)); tmp[0] = A1[0][0] * x[0] + A1[0][1] * x[1]; tmp[1] = A1[1][0] * x[0] + A1[1][1] * x[1]; x[0] = tmp[0] + A2[0]; x[1] = tmp[1] + A2[1]; PetscCall(MatDenseRestoreColumn(sp, &x)); PetscFunctionReturn(PETSC_SUCCESS); } PetscErrorCode PostEventFunction(TS ts, PetscInt nevents, PetscInt event_list[], PetscReal t, Vec U, PetscBool forwardsolve, PetscCtx ctx) { AppCtx *actx = (AppCtx *)ctx; PetscFunctionBegin; /* PetscCall(VecView(U,PETSC_VIEWER_STDOUT_WORLD)); */ PetscCall(ShiftGradients(ts, U, actx)); if (actx->mode == 1) { actx->mode = 2; /* PetscCall(PetscPrintf(PETSC_COMM_SELF,"Change from mode 1 to 2 at t = %f \n",(double)t)); */ } else if (actx->mode == 2) { actx->mode = 1; /* PetscCall(PetscPrintf(PETSC_COMM_SELF,"Change from mode 2 to 1 at t = %f \n",(double)t)); */ } PetscFunctionReturn(PETSC_SUCCESS); } /* Defines the ODE passed to the ODE solver */ static PetscErrorCode IFunction(TS ts, PetscReal t, Vec U, Vec Udot, Vec F, PetscCtx ctx) { AppCtx *actx = (AppCtx *)ctx; PetscScalar *f; const PetscScalar *u, *udot; PetscFunctionBegin; /* The next three lines allow us to access the entries of the vectors directly */ PetscCall(VecGetArrayRead(U, &u)); PetscCall(VecGetArrayRead(Udot, &udot)); PetscCall(VecGetArray(F, &f)); if (actx->mode == 1) { f[0] = udot[0] - u[0] + 100 * u[1]; f[1] = udot[1] - 10 * u[0] - u[1]; } else if (actx->mode == 2) { f[0] = udot[0] - u[0] - 10 * u[1]; f[1] = udot[1] + 100 * u[0] - u[1]; } PetscCall(VecRestoreArrayRead(U, &u)); PetscCall(VecRestoreArrayRead(Udot, &udot)); PetscCall(VecRestoreArray(F, &f)); PetscFunctionReturn(PETSC_SUCCESS); } /* Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian. */ static PetscErrorCode IJacobian(TS ts, PetscReal t, Vec U, Vec Udot, PetscReal a, Mat A, Mat B, PetscCtx ctx) { AppCtx *actx = (AppCtx *)ctx; PetscInt rowcol[] = {0, 1}; PetscScalar J[2][2]; const PetscScalar *u, *udot; PetscFunctionBegin; PetscCall(VecGetArrayRead(U, &u)); PetscCall(VecGetArrayRead(Udot, &udot)); if (actx->mode == 1) { J[0][0] = a - 1; J[0][1] = 100; J[1][0] = -10; J[1][1] = a - 1; } else if (actx->mode == 2) { J[0][0] = a - 1; J[0][1] = -10; J[1][0] = 100; J[1][1] = a - 1; } PetscCall(MatSetValues(B, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES)); PetscCall(VecRestoreArrayRead(U, &u)); PetscCall(VecRestoreArrayRead(Udot, &udot)); PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY)); PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY)); if (A != B) { PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY)); PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY)); } PetscFunctionReturn(PETSC_SUCCESS); } /* Matrix JacobianP is constant so that it only needs to be evaluated once */ static PetscErrorCode RHSJacobianP(TS ts, PetscReal t, Vec X, Mat Ap, PetscCtx ctx) { PetscFunctionBeginUser; PetscFunctionReturn(PETSC_SUCCESS); } int main(int argc, char **argv) { TS ts; /* ODE integrator */ Vec U; /* solution will be stored here */ Mat A; /* Jacobian matrix */ Mat Ap; /* Jacobian dfdp */ PetscMPIInt size; PetscInt n = 2; PetscScalar *u; AppCtx app; PetscInt direction[1]; PetscBool terminate[1]; Mat sp; PetscReal tend; /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Initialize program - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscFunctionBeginUser; PetscCall(PetscInitialize(&argc, &argv, NULL, help)); PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs"); app.mode = 1; app.lambda1 = 2.75; app.lambda2 = 0.36; app.print_time = 1. / 256.; tend = 0.125; PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "ex1fwd options", ""); { PetscCall(PetscOptionsReal("-lambda1", "", "", app.lambda1, &app.lambda1, NULL)); PetscCall(PetscOptionsReal("-lambda2", "", "", app.lambda2, &app.lambda2, NULL)); PetscCall(PetscOptionsReal("-tend", "", "", tend, &tend, NULL)); } PetscOptionsEnd(); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create necessary matrix and vectors - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(MatCreate(PETSC_COMM_WORLD, &A)); PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE)); PetscCall(MatSetType(A, MATDENSE)); PetscCall(MatSetFromOptions(A)); PetscCall(MatSetUp(A)); PetscCall(MatCreateVecs(A, &U, NULL)); PetscCall(MatCreate(PETSC_COMM_WORLD, &Ap)); PetscCall(MatSetSizes(Ap, n, 3, PETSC_DETERMINE, PETSC_DETERMINE)); PetscCall(MatSetType(Ap, MATDENSE)); PetscCall(MatSetFromOptions(Ap)); PetscCall(MatSetUp(Ap)); PetscCall(MatZeroEntries(Ap)); PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, n, 3, NULL, &sp)); PetscCall(MatZeroEntries(sp)); PetscCall(MatShift(sp, 1.0)); PetscCall(VecGetArray(U, &u)); u[0] = 0; u[1] = 1; PetscCall(VecRestoreArray(U, &u)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create timestepping solver context - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); PetscCall(TSSetProblemType(ts, TS_NONLINEAR)); PetscCall(TSSetType(ts, TSCN)); PetscCall(TSSetIFunction(ts, NULL, (TSIFunctionFn *)IFunction, &app)); PetscCall(TSSetIJacobian(ts, A, A, (TSIJacobianFn *)IJacobian, &app)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Set initial conditions - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(TSSetSolution(ts, U)); PetscCall(TSForwardSetSensitivities(ts, 3, sp)); /* Set RHS JacobianP */ PetscCall(TSSetRHSJacobianP(ts, Ap, RHSJacobianP, &app)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Set solver options - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(TSSetMaxTime(ts, tend)); PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP)); PetscCall(TSSetTimeStep(ts, 1. / 256.)); PetscCall(TSMonitorSet(ts, MyMonitor, &app, NULL)); PetscCall(TSSetFromOptions(ts)); /* Set directions and terminate flags for the two events */ direction[0] = 0; terminate[0] = PETSC_FALSE; PetscCall(TSSetEventHandler(ts, 1, direction, terminate, EventFunction, PostEventFunction, (void *)&app)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Run timestepping solver - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(TSSolve(ts, U)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Free work space. All PETSc objects should be destroyed when they are no longer needed. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(MatDestroy(&A)); PetscCall(VecDestroy(&U)); PetscCall(TSDestroy(&ts)); PetscCall(MatDestroy(&Ap)); PetscCall(MatDestroy(&sp)); PetscCall(PetscFinalize()); return 0; } /*TEST build: requires: !complex test: args: -ts_monitor TEST*/