static char help[] = "An example of hybrid system using TS event.\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. Reference: 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*/ } AppCtx; PetscErrorCode EventFunction(TS ts,PetscReal t,Vec U,PetscScalar *fvalue,void *ctx) { AppCtx *actx=(AppCtx*)ctx; PetscErrorCode ierr; const PetscScalar *u; PetscFunctionBegin; ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr); if (actx->mode == 1) { fvalue[0] = u[1]-actx->lambda1*u[0]; }else if (actx->mode == 2) { fvalue[0] = u[1]-actx->lambda2*u[0]; } ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr); PetscFunctionReturn(0); } PetscErrorCode PostEventFunction(TS ts,PetscInt nevents,PetscInt event_list[],PetscReal t,Vec U,PetscBool forwardsolve,void* ctx) { AppCtx *actx=(AppCtx*)ctx; PetscErrorCode ierr; PetscFunctionBegin; if (actx->mode == 1) { actx->mode = 2; ierr = PetscPrintf(PETSC_COMM_SELF,"Change from mode 1 to 2 at t = %f \n",(double)t);CHKERRQ(ierr); } else if (actx->mode == 2) { actx->mode = 1; ierr = PetscPrintf(PETSC_COMM_SELF,"Change from mode 2 to 1 at t = %f \n",(double)t);CHKERRQ(ierr); } PetscFunctionReturn(0); } /* Defines the ODE passed to the ODE solver */ static PetscErrorCode IFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,void *ctx) { AppCtx *actx=(AppCtx*)ctx; PetscErrorCode ierr; PetscScalar *f; const PetscScalar *u,*udot; PetscFunctionBegin; /* The next three lines allow us to access the entries of the vectors directly */ ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr); ierr = VecGetArrayRead(Udot,&udot);CHKERRQ(ierr); ierr = VecGetArray(F,&f);CHKERRQ(ierr); 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]; } ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr); ierr = VecRestoreArrayRead(Udot,&udot);CHKERRQ(ierr); ierr = VecRestoreArray(F,&f);CHKERRQ(ierr); PetscFunctionReturn(0); } /* 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,void *ctx) { AppCtx *actx=(AppCtx*)ctx; PetscErrorCode ierr; PetscInt rowcol[] = {0,1}; PetscScalar J[2][2]; const PetscScalar *u,*udot; PetscFunctionBegin; ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr); ierr = VecGetArrayRead(Udot,&udot);CHKERRQ(ierr); 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; } ierr = MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);CHKERRQ(ierr); ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr); ierr = VecRestoreArrayRead(Udot,&udot);CHKERRQ(ierr); ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); if (A != B) { ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); } PetscFunctionReturn(0); } int main(int argc,char **argv) { TS ts; /* ODE integrator */ Vec U; /* solution will be stored here */ Mat A; /* Jacobian matrix */ PetscErrorCode ierr; PetscMPIInt size; PetscInt n = 2; PetscScalar *u; AppCtx app; PetscInt direction[1]; PetscBool terminate[1]; /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Initialize program - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr; ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRMPI(ierr); if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs"); app.mode = 1; app.lambda1 = 2.75; app.lambda2 = 0.36; ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"ex1 options","");CHKERRQ(ierr); { ierr = PetscOptionsReal("-lambda1","","",app.lambda1,&app.lambda1,NULL);CHKERRQ(ierr); ierr = PetscOptionsReal("-lambda2","","",app.lambda2,&app.lambda2,NULL);CHKERRQ(ierr); } ierr = PetscOptionsEnd();CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create necessary matrix and vectors - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr); ierr = MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr); ierr = MatSetType(A,MATDENSE);CHKERRQ(ierr); ierr = MatSetFromOptions(A);CHKERRQ(ierr); ierr = MatSetUp(A);CHKERRQ(ierr); ierr = MatCreateVecs(A,&U,NULL);CHKERRQ(ierr); ierr = VecGetArray(U,&u);CHKERRQ(ierr); u[0] = 0; u[1] = 1; ierr = VecRestoreArray(U,&u);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create timestepping solver context - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr); ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr); ierr = TSSetType(ts,TSCN);CHKERRQ(ierr); ierr = TSSetIFunction(ts,NULL,(TSIFunction)IFunction,&app);CHKERRQ(ierr); ierr = TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&app);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Set initial conditions - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = TSSetSolution(ts,U);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Set solver options - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = TSSetMaxTime(ts,0.125);CHKERRQ(ierr); ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);CHKERRQ(ierr); ierr = TSSetTimeStep(ts,1./256.);CHKERRQ(ierr); ierr = TSSetFromOptions(ts);CHKERRQ(ierr); /* Set directions and terminate flags for the two events */ direction[0] = 0; terminate[0] = PETSC_FALSE; ierr = TSSetEventHandler(ts,1,direction,terminate,EventFunction,PostEventFunction,(void*)&app);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Run timestepping solver - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = TSSolve(ts,U);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Free work space. All PETSc objects should be destroyed when they are no longer needed. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = MatDestroy(&A);CHKERRQ(ierr); ierr = VecDestroy(&U);CHKERRQ(ierr); ierr = TSDestroy(&ts);CHKERRQ(ierr); ierr = PetscFinalize(); return(ierr); } /*TEST build: requires: !complex test: args: -ts_monitor test: suffix: 2 args: -ts_monitor_lg_solution -1 requires: x TEST*/