1 
2 static char help[] = "Basic equation for generator stability analysis.\n";
3 
4 /*F
5 
6 \begin{eqnarray}
7                  \frac{d \theta}{dt} = \omega_b (\omega - \omega_s)
8                  \frac{2 H}{\omega_s}\frac{d \omega}{dt} & = & P_m - P_max \sin(\theta) -D(\omega - \omega_s)\\
9 \end{eqnarray}
10 
11 
12 
13   Ensemble of initial conditions
14    ./ex2 -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
15 
16   Fault at .1 seconds
17    ./ex2           -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
18 
19   Initial conditions same as when fault is ended
20    ./ex2 -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
21 
22 
23 F*/
24 
25 /*
26    Include "petscts.h" so that we can use TS solvers.  Note that this
27    file automatically includes:
28      petscsys.h       - base PETSc routines   petscvec.h - vectors
29      petscmat.h - matrices
30      petscis.h     - index sets            petscksp.h - Krylov subspace methods
31      petscviewer.h - viewers               petscpc.h  - preconditioners
32      petscksp.h   - linear solvers
33 */
34 
35 #include <petsctao.h>
36 #include <petscts.h>
37 
38 typedef struct {
39   TS          ts;
40   PetscScalar H,D,omega_b,omega_s,Pmax,Pm,E,V,X,u_s,c;
41   PetscInt    beta;
42   PetscReal   tf,tcl,dt;
43 } AppCtx;
44 
45 PetscErrorCode FormFunction(Tao,Vec,PetscReal*,void*);
46 PetscErrorCode FormGradient(Tao,Vec,Vec,void*);
47 
48 /*
49      Defines the ODE passed to the ODE solver
50 */
RHSFunction(TS ts,PetscReal t,Vec U,Vec F,AppCtx * ctx)51 static PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec U,Vec F,AppCtx *ctx)
52 {
53   PetscErrorCode    ierr;
54   PetscScalar       *f,Pmax;
55   const PetscScalar *u;
56 
57   PetscFunctionBegin;
58   /*  The next three lines allow us to access the entries of the vectors directly */
59   ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr);
60   ierr = VecGetArray(F,&f);CHKERRQ(ierr);
61   if ((t > ctx->tf) && (t < ctx->tcl)) Pmax = 0.0; /* A short-circuit on the generator terminal that drives the electrical power output (Pmax*sin(delta)) to 0 */
62   else Pmax = ctx->Pmax;
63 
64   f[0] = ctx->omega_b*(u[1] - ctx->omega_s);
65   f[1] = (-Pmax*PetscSinScalar(u[0]) - ctx->D*(u[1] - ctx->omega_s) + ctx->Pm)*ctx->omega_s/(2.0*ctx->H);
66 
67   ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr);
68   ierr = VecRestoreArray(F,&f);CHKERRQ(ierr);
69   PetscFunctionReturn(0);
70 }
71 
72 /*
73      Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
74 */
RHSJacobian(TS ts,PetscReal t,Vec U,Mat A,Mat B,AppCtx * ctx)75 static PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec U,Mat A,Mat B,AppCtx *ctx)
76 {
77   PetscErrorCode    ierr;
78   PetscInt          rowcol[] = {0,1};
79   PetscScalar       J[2][2],Pmax;
80   const PetscScalar *u;
81 
82   PetscFunctionBegin;
83   ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr);
84   if ((t > ctx->tf) && (t < ctx->tcl)) Pmax = 0.0; /* A short-circuit on the generator terminal that drives the electrical power output (Pmax*sin(delta)) to 0 */
85   else Pmax = ctx->Pmax;
86 
87   J[0][0] = 0;                                  J[0][1] = ctx->omega_b;
88   J[1][1] = -ctx->D*ctx->omega_s/(2.0*ctx->H);  J[1][0] = -Pmax*PetscCosScalar(u[0])*ctx->omega_s/(2.0*ctx->H);
89 
90   ierr    = MatSetValues(A,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);CHKERRQ(ierr);
91   ierr    = VecRestoreArrayRead(U,&u);CHKERRQ(ierr);
92 
93   ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
94   ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
95   if (A != B) {
96     ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
97     ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
98   }
99   PetscFunctionReturn(0);
100 }
101 
RHSJacobianP(TS ts,PetscReal t,Vec X,Mat A,void * ctx0)102 static PetscErrorCode RHSJacobianP(TS ts,PetscReal t,Vec X,Mat A,void *ctx0)
103 {
104   PetscErrorCode ierr;
105   PetscInt       row[] = {0,1},col[]={0};
106   PetscScalar    J[2][1];
107   AppCtx         *ctx=(AppCtx*)ctx0;
108 
109   PetscFunctionBeginUser;
110   J[0][0] = 0;
111   J[1][0] = ctx->omega_s/(2.0*ctx->H);
112   ierr    = MatSetValues(A,2,row,1,col,&J[0][0],INSERT_VALUES);CHKERRQ(ierr);
113   ierr    = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
114   ierr    = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
115   PetscFunctionReturn(0);
116 }
117 
CostIntegrand(TS ts,PetscReal t,Vec U,Vec R,AppCtx * ctx)118 static PetscErrorCode CostIntegrand(TS ts,PetscReal t,Vec U,Vec R,AppCtx *ctx)
119 {
120   PetscErrorCode    ierr;
121   PetscScalar       *r;
122   const PetscScalar *u;
123 
124   PetscFunctionBegin;
125   ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr);
126   ierr = VecGetArray(R,&r);CHKERRQ(ierr);
127   r[0] = ctx->c*PetscPowScalarInt(PetscMax(0., u[0]-ctx->u_s),ctx->beta);CHKERRQ(ierr);
128   ierr = VecRestoreArray(R,&r);CHKERRQ(ierr);
129   ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr);
130   PetscFunctionReturn(0);
131 }
132 
DRDUJacobianTranspose(TS ts,PetscReal t,Vec U,Mat DRDU,Mat B,AppCtx * ctx)133 static PetscErrorCode DRDUJacobianTranspose(TS ts,PetscReal t,Vec U,Mat DRDU,Mat B,AppCtx *ctx)
134 {
135   PetscErrorCode    ierr;
136   PetscScalar       ru[1];
137   const PetscScalar *u;
138   PetscInt          row[] = {0},col[] = {0};
139 
140   PetscFunctionBegin;
141   ierr  = VecGetArrayRead(U,&u);CHKERRQ(ierr);
142   ru[0] = ctx->c*ctx->beta*PetscPowScalarInt(PetscMax(0., u[0]-ctx->u_s),ctx->beta-1);CHKERRQ(ierr);
143   ierr  = VecRestoreArrayRead(U,&u);CHKERRQ(ierr);
144   ierr  = MatSetValues(DRDU,1,row,1,col,ru,INSERT_VALUES);CHKERRQ(ierr);
145   ierr  = MatAssemblyBegin(DRDU,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
146   ierr  = MatAssemblyEnd(DRDU,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
147   PetscFunctionReturn(0);
148 }
149 
DRDPJacobianTranspose(TS ts,PetscReal t,Vec U,Mat DRDP,AppCtx * ctx)150 static PetscErrorCode DRDPJacobianTranspose(TS ts,PetscReal t,Vec U,Mat DRDP,AppCtx *ctx)
151 {
152   PetscErrorCode ierr;
153 
154   PetscFunctionBegin;
155   ierr = MatZeroEntries(DRDP);CHKERRQ(ierr);
156   ierr = MatAssemblyBegin(DRDP,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
157   ierr = MatAssemblyEnd(DRDP,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
158   PetscFunctionReturn(0);
159 }
160 
ComputeSensiP(Vec lambda,Vec mu,AppCtx * ctx)161 PetscErrorCode ComputeSensiP(Vec lambda,Vec mu,AppCtx *ctx)
162 {
163   PetscErrorCode    ierr;
164   PetscScalar       *y,sensip;
165   const PetscScalar *x;
166 
167   PetscFunctionBegin;
168   ierr = VecGetArrayRead(lambda,&x);CHKERRQ(ierr);
169   ierr = VecGetArray(mu,&y);CHKERRQ(ierr);
170   sensip = 1./PetscSqrtScalar(1.-(ctx->Pm/ctx->Pmax)*(ctx->Pm/ctx->Pmax))/ctx->Pmax*x[0]+y[0];
171   y[0] = sensip;
172   ierr = VecRestoreArray(mu,&y);CHKERRQ(ierr);
173   ierr = VecRestoreArrayRead(lambda,&x);CHKERRQ(ierr);
174   PetscFunctionReturn(0);
175 }
176 
main(int argc,char ** argv)177 int main(int argc,char **argv)
178 {
179   Vec            p;
180   PetscScalar    *x_ptr;
181   PetscErrorCode ierr;
182   PetscMPIInt    size;
183   AppCtx         ctx;
184   Vec            lowerb,upperb;
185   Tao            tao;
186   KSP            ksp;
187   PC             pc;
188   Vec            U,lambda[1],mu[1];
189   Mat            A;             /* Jacobian matrix */
190   Mat            Jacp;          /* Jacobian matrix */
191   Mat            DRDU,DRDP;
192   PetscInt       n = 2;
193   TS             quadts;
194 
195   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
196      Initialize program
197      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
198   ierr = PetscInitialize(&argc,&argv,NULL,help);if (ierr) return ierr;
199   PetscFunctionBeginUser;
200   ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
201   if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only!");
202 
203   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
204     Set runtime options
205     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
206   ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Swing equation options","");CHKERRQ(ierr);
207   {
208     ctx.beta    = 2;
209     ctx.c       = PetscRealConstant(10000.0);
210     ctx.u_s     = PetscRealConstant(1.0);
211     ctx.omega_s = PetscRealConstant(1.0);
212     ctx.omega_b = PetscRealConstant(120.0)*PETSC_PI;
213     ctx.H       = PetscRealConstant(5.0);
214     ierr        = PetscOptionsScalar("-Inertia","","",ctx.H,&ctx.H,NULL);CHKERRQ(ierr);
215     ctx.D       = PetscRealConstant(5.0);
216     ierr        = PetscOptionsScalar("-D","","",ctx.D,&ctx.D,NULL);CHKERRQ(ierr);
217     ctx.E       = PetscRealConstant(1.1378);
218     ctx.V       = PetscRealConstant(1.0);
219     ctx.X       = PetscRealConstant(0.545);
220     ctx.Pmax    = ctx.E*ctx.V/ctx.X;
221     ierr        = PetscOptionsScalar("-Pmax","","",ctx.Pmax,&ctx.Pmax,NULL);CHKERRQ(ierr);
222     ctx.Pm      = PetscRealConstant(1.0194);
223     ierr        = PetscOptionsScalar("-Pm","","",ctx.Pm,&ctx.Pm,NULL);CHKERRQ(ierr);
224     ctx.tf      = PetscRealConstant(0.1);
225     ctx.tcl     = PetscRealConstant(0.2);
226     ierr        = PetscOptionsReal("-tf","Time to start fault","",ctx.tf,&ctx.tf,NULL);CHKERRQ(ierr);
227     ierr        = PetscOptionsReal("-tcl","Time to end fault","",ctx.tcl,&ctx.tcl,NULL);CHKERRQ(ierr);
228 
229   }
230   ierr = PetscOptionsEnd();CHKERRQ(ierr);
231 
232   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
233     Create necessary matrix and vectors
234     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
235   ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
236   ierr = MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
237   ierr = MatSetType(A,MATDENSE);CHKERRQ(ierr);
238   ierr = MatSetFromOptions(A);CHKERRQ(ierr);
239   ierr = MatSetUp(A);CHKERRQ(ierr);
240 
241   ierr = MatCreateVecs(A,&U,NULL);CHKERRQ(ierr);
242 
243   ierr = MatCreate(PETSC_COMM_WORLD,&Jacp);CHKERRQ(ierr);
244   ierr = MatSetSizes(Jacp,PETSC_DECIDE,PETSC_DECIDE,2,1);CHKERRQ(ierr);
245   ierr = MatSetFromOptions(Jacp);CHKERRQ(ierr);
246   ierr = MatSetUp(Jacp);CHKERRQ(ierr);
247   ierr = MatCreateDense(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,&DRDP);CHKERRQ(ierr);
248   ierr = MatSetUp(DRDP);CHKERRQ(ierr);
249   ierr = MatCreateDense(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,1,2,NULL,&DRDU);CHKERRQ(ierr);
250   ierr = MatSetUp(DRDU);CHKERRQ(ierr);
251 
252   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
253      Create timestepping solver context
254      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
255   ierr = TSCreate(PETSC_COMM_WORLD,&ctx.ts);CHKERRQ(ierr);
256   ierr = TSSetProblemType(ctx.ts,TS_NONLINEAR);CHKERRQ(ierr);
257   ierr = TSSetEquationType(ctx.ts,TS_EQ_ODE_EXPLICIT);CHKERRQ(ierr); /* less Jacobian evaluations when adjoint BEuler is used, otherwise no effect */
258   ierr = TSSetType(ctx.ts,TSRK);CHKERRQ(ierr);
259   ierr = TSSetRHSFunction(ctx.ts,NULL,(TSRHSFunction)RHSFunction,&ctx);CHKERRQ(ierr);
260   ierr = TSSetRHSJacobian(ctx.ts,A,A,(TSRHSJacobian)RHSJacobian,&ctx);CHKERRQ(ierr);
261   ierr = TSSetExactFinalTime(ctx.ts,TS_EXACTFINALTIME_MATCHSTEP);CHKERRQ(ierr);
262 
263   ierr = MatCreateVecs(A,&lambda[0],NULL);CHKERRQ(ierr);
264   ierr = MatCreateVecs(Jacp,&mu[0],NULL);CHKERRQ(ierr);
265   ierr = TSSetCostGradients(ctx.ts,1,lambda,mu);CHKERRQ(ierr);
266   ierr = TSSetRHSJacobianP(ctx.ts,Jacp,RHSJacobianP,&ctx);CHKERRQ(ierr);
267 
268   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
269      Set solver options
270    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
271   ierr = TSSetMaxTime(ctx.ts,PetscRealConstant(1.0));CHKERRQ(ierr);
272   ierr = TSSetTimeStep(ctx.ts,PetscRealConstant(0.01));CHKERRQ(ierr);
273   ierr = TSSetFromOptions(ctx.ts);CHKERRQ(ierr);
274 
275   ierr = TSGetTimeStep(ctx.ts,&ctx.dt);CHKERRQ(ierr); /* save the stepsize */
276 
277   ierr = TSCreateQuadratureTS(ctx.ts,PETSC_TRUE,&quadts);CHKERRQ(ierr);
278   ierr = TSSetRHSFunction(quadts,NULL,(TSRHSFunction)CostIntegrand,&ctx);CHKERRQ(ierr);
279   ierr = TSSetRHSJacobian(quadts,DRDU,DRDU,(TSRHSJacobian)DRDUJacobianTranspose,&ctx);CHKERRQ(ierr);
280   ierr = TSSetRHSJacobianP(quadts,DRDP,(TSRHSJacobianP)DRDPJacobianTranspose,&ctx);CHKERRQ(ierr);
281   ierr = TSSetSolution(ctx.ts,U);CHKERRQ(ierr);
282 
283   /* Create TAO solver and set desired solution method */
284   ierr = TaoCreate(PETSC_COMM_WORLD,&tao);CHKERRQ(ierr);
285   ierr = TaoSetType(tao,TAOBLMVM);CHKERRQ(ierr);
286 
287   /*
288      Optimization starts
289   */
290   /* Set initial solution guess */
291   ierr = VecCreateSeq(PETSC_COMM_WORLD,1,&p);CHKERRQ(ierr);
292   ierr = VecGetArray(p,&x_ptr);CHKERRQ(ierr);
293   x_ptr[0]   = ctx.Pm;
294   ierr = VecRestoreArray(p,&x_ptr);CHKERRQ(ierr);
295 
296   ierr = TaoSetInitialVector(tao,p);CHKERRQ(ierr);
297   /* Set routine for function and gradient evaluation */
298   ierr = TaoSetObjectiveRoutine(tao,FormFunction,(void *)&ctx);CHKERRQ(ierr);
299   ierr = TaoSetGradientRoutine(tao,FormGradient,(void *)&ctx);CHKERRQ(ierr);
300 
301   /* Set bounds for the optimization */
302   ierr = VecDuplicate(p,&lowerb);CHKERRQ(ierr);
303   ierr = VecDuplicate(p,&upperb);CHKERRQ(ierr);
304   ierr = VecGetArray(lowerb,&x_ptr);CHKERRQ(ierr);
305   x_ptr[0] = 0.;
306   ierr = VecRestoreArray(lowerb,&x_ptr);CHKERRQ(ierr);
307   ierr = VecGetArray(upperb,&x_ptr);CHKERRQ(ierr);
308   x_ptr[0] = PetscRealConstant(1.1);
309   ierr = VecRestoreArray(upperb,&x_ptr);CHKERRQ(ierr);
310   ierr = TaoSetVariableBounds(tao,lowerb,upperb);CHKERRQ(ierr);
311 
312   /* Check for any TAO command line options */
313   ierr = TaoSetFromOptions(tao);CHKERRQ(ierr);
314   ierr = TaoGetKSP(tao,&ksp);CHKERRQ(ierr);
315   if (ksp) {
316     ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
317     ierr = PCSetType(pc,PCNONE);CHKERRQ(ierr);
318   }
319 
320   /* SOLVE THE APPLICATION */
321   ierr = TaoSolve(tao);CHKERRQ(ierr);
322 
323   ierr = VecView(p,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
324   /* Free TAO data structures */
325   ierr = TaoDestroy(&tao);CHKERRQ(ierr);
326   ierr = VecDestroy(&p);CHKERRQ(ierr);
327   ierr = VecDestroy(&lowerb);CHKERRQ(ierr);
328   ierr = VecDestroy(&upperb);CHKERRQ(ierr);
329 
330   ierr = TSDestroy(&ctx.ts);CHKERRQ(ierr);
331   ierr = VecDestroy(&U);CHKERRQ(ierr);
332   ierr = MatDestroy(&A);CHKERRQ(ierr);
333   ierr = MatDestroy(&Jacp);CHKERRQ(ierr);
334   ierr = MatDestroy(&DRDU);CHKERRQ(ierr);
335   ierr = MatDestroy(&DRDP);CHKERRQ(ierr);
336   ierr = VecDestroy(&lambda[0]);CHKERRQ(ierr);
337   ierr = VecDestroy(&mu[0]);CHKERRQ(ierr);
338   ierr = PetscFinalize();
339   return ierr;
340 }
341 
342 /* ------------------------------------------------------------------ */
343 /*
344    FormFunction - Evaluates the function
345 
346    Input Parameters:
347    tao - the Tao context
348    X   - the input vector
349    ptr - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()
350 
351    Output Parameters:
352    f   - the newly evaluated function
353 */
FormFunction(Tao tao,Vec P,PetscReal * f,void * ctx0)354 PetscErrorCode FormFunction(Tao tao,Vec P,PetscReal *f,void *ctx0)
355 {
356   AppCtx         *ctx = (AppCtx*)ctx0;
357   TS             ts = ctx->ts;
358   Vec            U;             /* solution will be stored here */
359   PetscErrorCode ierr;
360   PetscScalar    *u;
361   PetscScalar    *x_ptr;
362   Vec            q;
363 
364   ierr = VecGetArrayRead(P,(const PetscScalar**)&x_ptr);CHKERRQ(ierr);
365   ctx->Pm = x_ptr[0];
366   ierr = VecRestoreArrayRead(P,(const PetscScalar**)&x_ptr);CHKERRQ(ierr);
367 
368   /* reset time */
369   ierr = TSSetTime(ts,0.0);CHKERRQ(ierr);
370   /* reset step counter, this is critical for adjoint solver */
371   ierr = TSSetStepNumber(ts,0);CHKERRQ(ierr);
372   /* reset step size, the step size becomes negative after TSAdjointSolve */
373   ierr = TSSetTimeStep(ts,ctx->dt);CHKERRQ(ierr);
374   /* reinitialize the integral value */
375   ierr = TSGetCostIntegral(ts,&q);CHKERRQ(ierr);
376   ierr = VecSet(q,0.0);CHKERRQ(ierr);
377 
378   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
379      Set initial conditions
380    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
381   ierr = TSGetSolution(ts,&U);CHKERRQ(ierr);
382   ierr = VecGetArray(U,&u);CHKERRQ(ierr);
383   u[0] = PetscAsinScalar(ctx->Pm/ctx->Pmax);
384   u[1] = PetscRealConstant(1.0);
385   ierr = VecRestoreArray(U,&u);CHKERRQ(ierr);
386 
387   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
388      Solve nonlinear system
389      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
390   ierr = TSSolve(ts,U);CHKERRQ(ierr);
391   ierr = TSGetCostIntegral(ts,&q);CHKERRQ(ierr);
392   ierr = VecGetArray(q,&x_ptr);CHKERRQ(ierr);
393   *f   = -ctx->Pm + x_ptr[0];
394   ierr = VecRestoreArray(q,&x_ptr);CHKERRQ(ierr);
395   return 0;
396 }
397 
FormGradient(Tao tao,Vec P,Vec G,void * ctx0)398 PetscErrorCode FormGradient(Tao tao,Vec P,Vec G,void *ctx0)
399 {
400   AppCtx         *ctx = (AppCtx*)ctx0;
401   TS             ts = ctx->ts;
402   Vec            U;             /* solution will be stored here */
403   PetscErrorCode ierr;
404   PetscReal      ftime;
405   PetscInt       steps;
406   PetscScalar    *u;
407   PetscScalar    *x_ptr,*y_ptr;
408   Vec            *lambda,q,*mu;
409 
410   ierr = VecGetArrayRead(P,(const PetscScalar**)&x_ptr);CHKERRQ(ierr);
411   ctx->Pm = x_ptr[0];
412   ierr = VecRestoreArrayRead(P,(const PetscScalar**)&x_ptr);CHKERRQ(ierr);
413 
414   /* reset time */
415   ierr = TSSetTime(ts,0.0);CHKERRQ(ierr);
416   /* reset step counter, this is critical for adjoint solver */
417   ierr = TSSetStepNumber(ts,0);CHKERRQ(ierr);
418   /* reset step size, the step size becomes negative after TSAdjointSolve */
419   ierr = TSSetTimeStep(ts,ctx->dt);CHKERRQ(ierr);
420   /* reinitialize the integral value */
421   ierr = TSGetCostIntegral(ts,&q);CHKERRQ(ierr);
422   ierr = VecSet(q,0.0);CHKERRQ(ierr);
423 
424   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
425      Set initial conditions
426    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
427   ierr = TSGetSolution(ts,&U);CHKERRQ(ierr);
428   ierr = VecGetArray(U,&u);CHKERRQ(ierr);
429   u[0] = PetscAsinScalar(ctx->Pm/ctx->Pmax);
430   u[1] = PetscRealConstant(1.0);
431   ierr = VecRestoreArray(U,&u);CHKERRQ(ierr);
432 
433   /* Set up to save trajectory before TSSetFromOptions() so that TSTrajectory options can be captured */
434   ierr = TSSetSaveTrajectory(ts);CHKERRQ(ierr);
435   ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
436 
437   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
438      Solve nonlinear system
439      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
440   ierr = TSSolve(ts,U);CHKERRQ(ierr);
441 
442   ierr = TSGetSolveTime(ts,&ftime);CHKERRQ(ierr);
443   ierr = TSGetStepNumber(ts,&steps);CHKERRQ(ierr);
444 
445   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
446      Adjoint model starts here
447      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
448   ierr = TSGetCostGradients(ts,NULL,&lambda,&mu);CHKERRQ(ierr);
449   /*   Set initial conditions for the adjoint integration */
450   ierr = VecGetArray(lambda[0],&y_ptr);CHKERRQ(ierr);
451   y_ptr[0] = 0.0; y_ptr[1] = 0.0;
452   ierr = VecRestoreArray(lambda[0],&y_ptr);CHKERRQ(ierr);
453   ierr = VecGetArray(mu[0],&x_ptr);CHKERRQ(ierr);
454   x_ptr[0] = PetscRealConstant(-1.0);
455   ierr = VecRestoreArray(mu[0],&x_ptr);CHKERRQ(ierr);
456 
457   ierr = TSAdjointSolve(ts);CHKERRQ(ierr);
458   ierr = TSGetCostIntegral(ts,&q);CHKERRQ(ierr);
459   ierr = ComputeSensiP(lambda[0],mu[0],ctx);CHKERRQ(ierr);
460   ierr = VecCopy(mu[0],G);CHKERRQ(ierr);
461   return 0;
462 }
463 
464 
465 /*TEST
466 
467    build:
468       requires: !complex
469 
470    test:
471       args: -viewer_binary_skip_info -ts_adapt_type none -tao_monitor -tao_gatol 0.0 -tao_grtol 1.e-3 -tao_converged_reason
472 
473    test:
474       suffix: 2
475       args: -viewer_binary_skip_info -ts_adapt_type none -tao_monitor -tao_gatol 0.0 -tao_grtol 1.e-3 -tao_converged_reason -tao_test_gradient
476 
477 TEST*/
478