Actual source code: ex3sa.c
petsc-3.9.2 2018-05-20
2: static char help[] = "Adjoint and tangent linear sensitivity analysis of the basic equation for generator stability analysis.\n";
\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}
13: /*
14: This code demonstrate the sensitivity analysis interface to a system of ordinary differential equations with discontinuities.
15: It computes the sensitivities of an integral cost function
16: \int c*max(0,\theta(t)-u_s)^beta dt
17: w.r.t. initial conditions and the parameter P_m.
18: Backward Euler method is used for time integration.
19: The discontinuities are detected with TSEvent.
20: */
22: #include <petscts.h>
24: typedef struct {
25: PetscScalar H,D,omega_b,omega_s,Pmax,Pmax_ini,Pm,E,V,X,u_s,c;
26: PetscInt beta;
27: PetscReal tf,tcl;
28: } AppCtx;
30: typedef enum {SA_ADJ, SA_TLM} SAMethod;
31: static const char *const SAMethods[] = {"ADJ","TLM","SAMethod","SA_",0};
33: /* Event check */
34: PetscErrorCode EventFunction(TS ts,PetscReal t,Vec X,PetscScalar *fvalue,void *ctx)
35: {
36: AppCtx *user=(AppCtx*)ctx;
39: /* Event for fault-on time */
40: fvalue[0] = t - user->tf;
41: /* Event for fault-off time */
42: fvalue[1] = t - user->tcl;
44: return(0);
45: }
47: PetscErrorCode PostEventFunction(TS ts,PetscInt nevents,PetscInt event_list[],PetscReal t,Vec X,PetscBool forwardsolve,void* ctx)
48: {
49: AppCtx *user=(AppCtx*)ctx;
53: if (event_list[0] == 0) {
54: if (forwardsolve) user->Pmax = 0.0; /* Apply disturbance - this is done by setting Pmax = 0 */
55: else user->Pmax = user->Pmax_ini; /* Going backward, reversal of event */
56: } else if(event_list[0] == 1) {
57: if (forwardsolve) user->Pmax = user->Pmax_ini; /* Remove the fault - this is done by setting Pmax = Pmax_ini */
58: else user->Pmax = 0.0; /* Going backward, reversal of event */
59: }
60: return(0);
61: }
63: PetscErrorCode PostStepFunction(TS ts)
64: {
65: PetscErrorCode ierr;
66: Vec U;
67: PetscReal t;
68: const PetscScalar *u;
71: TSGetTime(ts,&t);
72: TSGetSolution(ts,&U);
73: VecGetArrayRead(U,&u);
74: PetscPrintf(PETSC_COMM_SELF,"delta(%3.2f) = %8.7f\n",(double)t,(double)u[0]);
75: VecRestoreArrayRead(U,&u);
77: return(0);
78: }
80: /*
81: Defines the ODE passed to the ODE solver
82: */
83: static PetscErrorCode IFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,AppCtx *ctx)
84: {
85: PetscErrorCode ierr;
86: PetscScalar *f,Pmax;
87: const PetscScalar *u,*udot;
90: /* The next three lines allow us to access the entries of the vectors directly */
91: VecGetArrayRead(U,&u);
92: VecGetArrayRead(Udot,&udot);
93: VecGetArray(F,&f);
94: Pmax = ctx->Pmax;
95: f[0] = udot[0] - ctx->omega_b*(u[1] - ctx->omega_s);
96: f[1] = 2.0*ctx->H/ctx->omega_s*udot[1] + Pmax*PetscSinScalar(u[0]) + ctx->D*(u[1] - ctx->omega_s)- ctx->Pm;
98: VecRestoreArrayRead(U,&u);
99: VecRestoreArrayRead(Udot,&udot);
100: VecRestoreArray(F,&f);
101: return(0);
102: }
104: /*
105: Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
106: */
107: static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat A,Mat B,AppCtx *ctx)
108: {
109: PetscErrorCode ierr;
110: PetscInt rowcol[] = {0,1};
111: PetscScalar J[2][2],Pmax;
112: const PetscScalar *u,*udot;
115: VecGetArrayRead(U,&u);
116: VecGetArrayRead(Udot,&udot);
117: Pmax = ctx->Pmax;
119: J[0][0] = a; J[0][1] = -ctx->omega_b;
120: J[1][1] = 2.0*ctx->H/ctx->omega_s*a + ctx->D; J[1][0] = Pmax*PetscCosScalar(u[0]);
122: MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);
123: VecRestoreArrayRead(U,&u);
124: VecRestoreArrayRead(Udot,&udot);
126: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
127: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
128: if (A != B) {
129: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
130: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
131: }
132: return(0);
133: }
135: static PetscErrorCode RHSJacobianP(TS ts,PetscReal t,Vec X,Mat A,void *ctx0)
136: {
138: PetscInt row[] = {0,1},col[]={0};
139: PetscScalar *x,J[2][1];
142: VecGetArray(X,&x);
144: J[0][0] = 0;
145: J[1][0] = 1.;
146: MatSetValues(A,2,row,1,col,&J[0][0],INSERT_VALUES);
148: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
149: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
150: return(0);
151: }
153: static PetscErrorCode CostIntegrand(TS ts,PetscReal t,Vec U,Vec R,AppCtx *ctx)
154: {
155: PetscErrorCode ierr;
156: PetscScalar *r;
157: const PetscScalar *u;
160: VecGetArrayRead(U,&u);
161: VecGetArray(R,&r);
162: r[0] = ctx->c*PetscPowScalarInt(PetscMax(0., u[0]-ctx->u_s),ctx->beta);
163: VecRestoreArray(R,&r);
164: VecRestoreArrayRead(U,&u);
165: return(0);
166: }
168: static PetscErrorCode DRDYFunction(TS ts,PetscReal t,Vec U,Vec *drdy,AppCtx *ctx)
169: {
170: PetscErrorCode ierr;
171: PetscScalar *ry;
172: const PetscScalar *u;
175: VecGetArrayRead(U,&u);
176: VecGetArray(drdy[0],&ry);
177: ry[0] = ctx->c*ctx->beta*PetscPowScalarInt(PetscMax(0., u[0]-ctx->u_s),ctx->beta-1);
178: VecRestoreArray(drdy[0],&ry);
179: VecRestoreArrayRead(U,&u);
180: return(0);
181: }
183: static PetscErrorCode DRDPFunction(TS ts,PetscReal t,Vec U,Vec *drdp,AppCtx *ctx)
184: {
185: PetscErrorCode ierr;
186: PetscScalar *rp;
187: const PetscScalar *u;
190: VecGetArrayRead(U,&u);
191: VecGetArray(drdp[0],&rp);
192: rp[0] = 0.;
193: VecRestoreArray(drdp[0],&rp);
194: VecGetArrayRead(U,&u);
195: return(0);
196: }
198: PetscErrorCode ComputeSensiP(Vec lambda,Vec mu,PetscScalar *val,AppCtx *ctx)
199: {
200: PetscErrorCode ierr;
201: const PetscScalar *x,*y;
204: VecGetArrayRead(lambda,&x);
205: VecGetArrayRead(mu,&y);
206: val[0] = 1./PetscSqrtScalar(1.-(ctx->Pm/ctx->Pmax)*(ctx->Pm/ctx->Pmax))/ctx->Pmax*x[0]+y[0];
207: VecRestoreArrayRead(lambda,&x);
208: VecRestoreArrayRead(mu,&y);
209: return(0);
210: }
212: int main(int argc,char **argv)
213: {
214: TS ts; /* ODE integrator */
215: Vec U; /* solution will be stored here */
216: Mat A; /* Jacobian matrix */
217: Mat Jacp; /* JacobianP matrix */
219: PetscMPIInt size;
220: PetscInt n = 2;
221: AppCtx ctx;
222: PetscScalar *u;
223: PetscReal du[2] = {0.0,0.0};
224: PetscBool ensemble = PETSC_FALSE,flg1,flg2;
225: PetscReal ftime;
226: PetscInt steps;
227: PetscScalar *x_ptr,*y_ptr,*s_ptr;
228: Vec lambda[1],q,mu[1];
229: PetscInt direction[2];
230: PetscBool terminate[2];
231: Vec qgrad[1]; /* Forward sesivitiy */
232: Mat sp; /* Forward sensitivity matrix */
233: SAMethod sa;
235: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
236: Initialize program
237: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
238: PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
239: MPI_Comm_size(PETSC_COMM_WORLD,&size);
240: if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");
242: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
243: Create necessary matrix and vectors
244: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
245: MatCreate(PETSC_COMM_WORLD,&A);
246: MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);
247: MatSetType(A,MATDENSE);
248: MatSetFromOptions(A);
249: MatSetUp(A);
251: MatCreateVecs(A,&U,NULL);
253: MatCreate(PETSC_COMM_WORLD,&Jacp);
254: MatSetSizes(Jacp,PETSC_DECIDE,PETSC_DECIDE,2,1);
255: MatSetFromOptions(Jacp);
256: MatSetUp(Jacp);
258: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
259: Set runtime options
260: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
261: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Swing equation options","");
262: {
263: ctx.beta = 2;
264: ctx.c = 10000.0;
265: ctx.u_s = 1.0;
266: ctx.omega_s = 1.0;
267: ctx.omega_b = 120.0*PETSC_PI;
268: ctx.H = 5.0;
269: PetscOptionsScalar("-Inertia","","",ctx.H,&ctx.H,NULL);
270: ctx.D = 5.0;
271: PetscOptionsScalar("-D","","",ctx.D,&ctx.D,NULL);
272: ctx.E = 1.1378;
273: ctx.V = 1.0;
274: ctx.X = 0.545;
275: ctx.Pmax = ctx.E*ctx.V/ctx.X;
276: ctx.Pmax_ini = ctx.Pmax;
277: PetscOptionsScalar("-Pmax","","",ctx.Pmax,&ctx.Pmax,NULL);
278: ctx.Pm = 1.1;
279: PetscOptionsScalar("-Pm","","",ctx.Pm,&ctx.Pm,NULL);
280: ctx.tf = 0.1;
281: ctx.tcl = 0.2;
282: PetscOptionsReal("-tf","Time to start fault","",ctx.tf,&ctx.tf,NULL);
283: PetscOptionsReal("-tcl","Time to end fault","",ctx.tcl,&ctx.tcl,NULL);
284: PetscOptionsBool("-ensemble","Run ensemble of different initial conditions","",ensemble,&ensemble,NULL);
285: if (ensemble) {
286: ctx.tf = -1;
287: ctx.tcl = -1;
288: }
290: VecGetArray(U,&u);
291: u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
292: u[1] = 1.0;
293: PetscOptionsRealArray("-u","Initial solution","",u,&n,&flg1);
294: n = 2;
295: PetscOptionsRealArray("-du","Perturbation in initial solution","",du,&n,&flg2);
296: u[0] += du[0];
297: u[1] += du[1];
298: VecRestoreArray(U,&u);
299: if (flg1 || flg2) {
300: ctx.tf = -1;
301: ctx.tcl = -1;
302: }
303: sa = SA_ADJ;
304: PetscOptionsEnum("-sa_method","Sensitivity analysis method (adj or tlm)","",SAMethods,(PetscEnum)sa,(PetscEnum*)&sa,NULL);
305: }
306: PetscOptionsEnd();
308: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
309: Create timestepping solver context
310: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
311: TSCreate(PETSC_COMM_WORLD,&ts);
312: TSSetProblemType(ts,TS_NONLINEAR);
313: TSSetType(ts,TSBEULER);
314: TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&ctx);
315: TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&ctx);
317: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
318: Set initial conditions
319: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
320: TSSetSolution(ts,U);
322: /* Set RHS JacobianP */
323: TSSetRHSJacobianP(ts,Jacp,RHSJacobianP,&ctx);
324: if (sa == SA_ADJ) {
325: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
326: Save trajectory of solution so that TSAdjointSolve() may be used
327: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
328: TSSetSaveTrajectory(ts);
330: MatCreateVecs(A,&lambda[0],NULL);
331: MatCreateVecs(Jacp,&mu[0],NULL);
332: TSSetCostGradients(ts,1,lambda,mu);
333: TSSetCostIntegrand(ts,1,NULL,(PetscErrorCode (*)(TS,PetscReal,Vec,Vec,void*))CostIntegrand,
334: (PetscErrorCode (*)(TS,PetscReal,Vec,Vec*,void*))DRDYFunction,
335: (PetscErrorCode (*)(TS,PetscReal,Vec,Vec*,void*))DRDPFunction,PETSC_TRUE,&ctx);
336: }
338: if (sa == SA_TLM) {
339: PetscScalar val[2];
340: PetscInt row[]={0,1},col[]={0};
342: VecCreate(PETSC_COMM_WORLD,&qgrad[0]);
343: VecSetSizes(qgrad[0],PETSC_DECIDE,1);
344: VecSetFromOptions(qgrad[0]);
346: MatCreateDense(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,2,1,NULL,&sp);
347: TSForwardSetSensitivities(ts,1,sp);
348: TSForwardSetIntegralGradients(ts,1,qgrad);
349: TSSetCostIntegrand(ts,1,NULL,(PetscErrorCode (*)(TS,PetscReal,Vec,Vec,void*))CostIntegrand,
350: (PetscErrorCode (*)(TS,PetscReal,Vec,Vec*,void*))DRDYFunction,
351: (PetscErrorCode (*)(TS,PetscReal,Vec,Vec*,void*))DRDPFunction,PETSC_TRUE,&ctx);
352: val[0] = 1./PetscSqrtScalar(1.-(ctx.Pm/ctx.Pmax)*(ctx.Pm/ctx.Pmax))/ctx.Pmax;
353: val[1] = 0.0;
354: MatSetValues(sp,2,row,1,col,val,INSERT_VALUES);
355: MatAssemblyBegin(sp,MAT_FINAL_ASSEMBLY);
356: MatAssemblyEnd(sp,MAT_FINAL_ASSEMBLY);
357: }
359: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
360: Set solver options
361: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
362: TSSetMaxTime(ts,1.0);
363: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
364: TSSetTimeStep(ts,0.03125);
365: TSSetFromOptions(ts);
367: direction[0] = direction[1] = 1;
368: terminate[0] = terminate[1] = PETSC_FALSE;
370: TSSetEventHandler(ts,2,direction,terminate,EventFunction,PostEventFunction,(void*)&ctx);
372: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
373: Solve nonlinear system
374: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
375: if (ensemble) {
376: for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
377: VecGetArray(U,&u);
378: u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
379: u[1] = ctx.omega_s;
380: u[0] += du[0];
381: u[1] += du[1];
382: VecRestoreArray(U,&u);
383: TSSetTimeStep(ts,0.03125);
384: TSSolve(ts,U);
385: }
386: } else {
387: TSSolve(ts,U);
388: }
389: TSGetSolveTime(ts,&ftime);
390: TSGetStepNumber(ts,&steps);
392: if (sa == SA_ADJ) {
393: PetscScalar grad[1];
394: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
395: Adjoint model starts here
396: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
397: /* Set initial conditions for the adjoint integration */
398: VecGetArray(lambda[0],&y_ptr);
399: y_ptr[0] = 0.0; y_ptr[1] = 0.0;
400: VecRestoreArray(lambda[0],&y_ptr);
402: VecGetArray(mu[0],&x_ptr);
403: x_ptr[0] = 0.0;
404: VecRestoreArray(mu[0],&x_ptr);
406: TSAdjointSolve(ts);
408: PetscPrintf(PETSC_COMM_WORLD,"\n lambda: d[Psi(tf)]/d[phi0] d[Psi(tf)]/d[omega0]\n");
409: VecView(lambda[0],PETSC_VIEWER_STDOUT_WORLD);
410: PetscPrintf(PETSC_COMM_WORLD,"\n mu: d[Psi(tf)]/d[pm] d[Psi(tf)]/d[pm]\n");
411: VecView(mu[0],PETSC_VIEWER_STDOUT_WORLD);
412: TSGetCostIntegral(ts,&q);
413: VecGetArray(q,&x_ptr);
414: PetscPrintf(PETSC_COMM_WORLD,"\n cost function=%g\n",(double)(x_ptr[0]-ctx.Pm));
415: VecRestoreArray(q,&x_ptr);
416: ComputeSensiP(lambda[0],mu[0],grad,&ctx);
417: PetscPrintf(PETSC_COMM_WORLD,"\n gradient=%g\n",(double)grad[0]);
418: VecDestroy(&lambda[0]);
419: VecDestroy(&mu[0]);
420: }
422: if (sa == SA_TLM) {
423: PetscPrintf(PETSC_COMM_WORLD,"\n trajectory sensitivity: d[Psi(tf)]/d[pm] d[Psi(tf)]/d[pm]\n");
424: MatView(sp,PETSC_VIEWER_STDOUT_WORLD);
425: TSGetCostIntegral(ts,&q);
426: VecGetArray(q,&s_ptr);
427: PetscPrintf(PETSC_COMM_WORLD,"\n cost function=%g\n",(double)(s_ptr[0]-ctx.Pm));
428: VecRestoreArray(q,&s_ptr);
429: VecGetArray(qgrad[0],&s_ptr);
430: PetscPrintf(PETSC_COMM_WORLD,"\n gradient=%g\n",(double)s_ptr[0]);
431: VecRestoreArray(qgrad[0],&s_ptr);
432: VecDestroy(&qgrad[0]);
433: MatDestroy(&sp);
434: }
435: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
436: Free work space. All PETSc objects should be destroyed when they are no longer needed.
437: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
438: MatDestroy(&A);
439: MatDestroy(&Jacp);
440: VecDestroy(&U);
441: TSDestroy(&ts);
442: PetscFinalize();
443: return ierr;
444: }
447: /*TEST
449: build:
450: requires: !complex !single
452: test:
453: args: -sa_method adj -viewer_binary_skip_info -ts_type cn -pc_type lu
455: test:
456: suffix: 2
457: args: -sa_method tlm -ts_type cn -pc_type lu
459: TEST*/