static char help[] = "Basic equation for generator stability analysis.\n";

/*F

\begin{eqnarray}
                 \frac{d \theta}{dt} = \omega_b (\omega - \omega_s)
                 \frac{2 H}{\omega_s}\frac{d \omega}{dt} & = & P_m - P_max \sin(\theta) -D(\omega - \omega_s)\\
\end{eqnarray}

  Ensemble of initial conditions
   ./ex3 -ensemble -ts_monitor_draw_solution_phase -1,-3,3,3      -ts_adapt_dt_max .01  -ts_monitor -ts_type rosw -pc_type lu -ksp_type preonly

  Fault at .1 seconds
   ./ex3           -ts_monitor_draw_solution_phase .42,.95,.6,1.05 -ts_adapt_dt_max .01  -ts_monitor -ts_type rosw -pc_type lu -ksp_type preonly

  Initial conditions same as when fault is ended
   ./ex3 -u 0.496792,1.00932 -ts_monitor_draw_solution_phase .42,.95,.6,1.05  -ts_adapt_dt_max .01  -ts_monitor -ts_type rosw -pc_type lu -ksp_type preonly

F*/

/*
   Include "petscts.h" so that we can use TS solvers.  Note that this
   file automatically includes:
     petscsys.h       - base PETSc routines   petscvec.h - vectors
     petscmat.h - matrices
     petscis.h     - index sets            petscksp.h - Krylov subspace methods
     petscviewer.h - viewers               petscpc.h  - preconditioners
     petscksp.h   - linear solvers
*/
/*T

T*/

#include <petscts.h>
#include "ex3.h"

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;
  AppCtx         ctx;
  PetscScalar    *u;
  PetscReal      du[2] = {0.0,0.0};
  PetscBool      ensemble = PETSC_FALSE,flg1,flg2;
  PetscInt       direction[2];
  PetscBool      terminate[2];

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Initialize program
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
  CHKERRMPI(MPI_Comm_size(PETSC_COMM_WORLD,&size));
  PetscCheck(size == 1,PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"Only for sequential runs");

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    Create necessary matrix and vectors
    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  CHKERRQ(MatCreate(PETSC_COMM_WORLD,&A));
  CHKERRQ(MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE));
  CHKERRQ(MatSetType(A,MATDENSE));
  CHKERRQ(MatSetFromOptions(A));
  CHKERRQ(MatSetUp(A));

  CHKERRQ(MatCreateVecs(A,&U,NULL));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    Set runtime options
    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Swing equation options","");CHKERRQ(ierr);
  {
    ctx.omega_b = 1.0;
    ctx.omega_s = 2.0*PETSC_PI*60.0;
    ctx.H       = 5.0;
    CHKERRQ(PetscOptionsScalar("-Inertia","","",ctx.H,&ctx.H,NULL));
    ctx.D       = 5.0;
    CHKERRQ(PetscOptionsScalar("-D","","",ctx.D,&ctx.D,NULL));
    ctx.E       = 1.1378;
    ctx.V       = 1.0;
    ctx.X       = 0.545;
    ctx.Pmax    = ctx.E*ctx.V/ctx.X;
    ctx.Pmax_ini = ctx.Pmax;
    CHKERRQ(PetscOptionsScalar("-Pmax","","",ctx.Pmax,&ctx.Pmax,NULL));
    ctx.Pm      = 0.9;
    CHKERRQ(PetscOptionsScalar("-Pm","","",ctx.Pm,&ctx.Pm,NULL));
    ctx.tf      = 1.0;
    ctx.tcl     = 1.05;
    CHKERRQ(PetscOptionsReal("-tf","Time to start fault","",ctx.tf,&ctx.tf,NULL));
    CHKERRQ(PetscOptionsReal("-tcl","Time to end fault","",ctx.tcl,&ctx.tcl,NULL));
    CHKERRQ(PetscOptionsBool("-ensemble","Run ensemble of different initial conditions","",ensemble,&ensemble,NULL));
    if (ensemble) {
      ctx.tf      = -1;
      ctx.tcl     = -1;
    }

    CHKERRQ(VecGetArray(U,&u));
    u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
    u[1] = 1.0;
    CHKERRQ(PetscOptionsRealArray("-u","Initial solution","",u,&n,&flg1));
    n    = 2;
    CHKERRQ(PetscOptionsRealArray("-du","Perturbation in initial solution","",du,&n,&flg2));
    u[0] += du[0];
    u[1] += du[1];
    CHKERRQ(VecRestoreArray(U,&u));
    if (flg1 || flg2) {
      ctx.tf      = -1;
      ctx.tcl     = -1;
    }
  }
  ierr = PetscOptionsEnd();CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Create timestepping solver context
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  CHKERRQ(TSCreate(PETSC_COMM_WORLD,&ts));
  CHKERRQ(TSSetProblemType(ts,TS_NONLINEAR));
  CHKERRQ(TSSetType(ts,TSTHETA));
  CHKERRQ(TSSetEquationType(ts,TS_EQ_IMPLICIT));
  CHKERRQ(TSARKIMEXSetFullyImplicit(ts,PETSC_TRUE));
  CHKERRQ(TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&ctx));
  CHKERRQ(TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&ctx));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set initial conditions
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  CHKERRQ(TSSetSolution(ts,U));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set solver options
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  CHKERRQ(TSSetMaxTime(ts,35.0));
  CHKERRQ(TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP));
  CHKERRQ(TSSetTimeStep(ts,.1));
  CHKERRQ(TSSetFromOptions(ts));

  direction[0] = direction[1] = 1;
  terminate[0] = terminate[1] = PETSC_FALSE;

  CHKERRQ(TSSetEventHandler(ts,2,direction,terminate,EventFunction,PostEventFunction,(void*)&ctx));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Solve nonlinear system
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  if (ensemble) {
    for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
      CHKERRQ(VecGetArray(U,&u));
      u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
      u[1] = ctx.omega_s;
      u[0] += du[0];
      u[1] += du[1];
      CHKERRQ(VecRestoreArray(U,&u));
      CHKERRQ(TSSetTimeStep(ts,.01));
      CHKERRQ(TSSolve(ts,U));
    }
  } else {
    CHKERRQ(TSSolve(ts,U));
  }
  CHKERRQ(VecView(U,PETSC_VIEWER_STDOUT_WORLD));
  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Free work space.  All PETSc objects should be destroyed when they are no longer needed.
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  CHKERRQ(MatDestroy(&A));
  CHKERRQ(VecDestroy(&U));
  CHKERRQ(TSDestroy(&ts));
  ierr = PetscFinalize();
  return ierr;
}

/*TEST

   build:
     requires: !complex !single

   test:
      args: -nox

TEST*/