Actual source code: ex3sa.c

petsc-3.12.0 2019-09-29
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  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>
 23: #include "ex3.h"

 25: int main(int argc,char **argv)
 26: {
 27:   TS             ts,quadts;     /* ODE integrator */
 28:   Vec            U;             /* solution will be stored here */
 30:   PetscMPIInt    size;
 31:   PetscInt       n = 2;
 32:   AppCtx         ctx;
 33:   PetscScalar    *u;
 34:   PetscReal      du[2] = {0.0,0.0};
 35:   PetscBool      ensemble = PETSC_FALSE,flg1,flg2;
 36:   PetscReal      ftime;
 37:   PetscInt       steps;
 38:   PetscScalar    *x_ptr,*y_ptr,*s_ptr;
 39:   Vec            lambda[1],q,mu[1];
 40:   PetscInt       direction[2];
 41:   PetscBool      terminate[2];
 42:   Mat            qgrad;
 43:   Mat            sp;            /* Forward sensitivity matrix */
 44:   SAMethod       sa;

 46:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 47:      Initialize program
 48:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 49:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
 50:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
 51:   if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");

 53:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 54:     Create necessary matrix and vectors
 55:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 56:   MatCreate(PETSC_COMM_WORLD,&ctx.Jac);
 57:   MatSetSizes(ctx.Jac,n,n,PETSC_DETERMINE,PETSC_DETERMINE);
 58:   MatSetType(ctx.Jac,MATDENSE);
 59:   MatSetFromOptions(ctx.Jac);
 60:   MatSetUp(ctx.Jac);
 61:   MatCreateVecs(ctx.Jac,&U,NULL);
 62:   MatCreate(PETSC_COMM_WORLD,&ctx.Jacp);
 63:   MatSetSizes(ctx.Jacp,PETSC_DECIDE,PETSC_DECIDE,2,1);
 64:   MatSetFromOptions(ctx.Jacp);
 65:   MatSetUp(ctx.Jacp);
 66:   MatCreateDense(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,&ctx.DRDP);
 67:   MatSetUp(ctx.DRDP);
 68:   MatCreateDense(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,2,1,NULL,&ctx.DRDU);
 69:   MatSetUp(ctx.DRDU);

 71:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 72:     Set runtime options
 73:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 74:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Swing equation options","");
 75:   {
 76:     ctx.beta    = 2;
 77:     ctx.c       = 10000.0;
 78:     ctx.u_s     = 1.0;
 79:     ctx.omega_s = 1.0;
 80:     ctx.omega_b = 120.0*PETSC_PI;
 81:     ctx.H       = 5.0;
 82:     PetscOptionsScalar("-Inertia","","",ctx.H,&ctx.H,NULL);
 83:     ctx.D       = 5.0;
 84:     PetscOptionsScalar("-D","","",ctx.D,&ctx.D,NULL);
 85:     ctx.E       = 1.1378;
 86:     ctx.V       = 1.0;
 87:     ctx.X       = 0.545;
 88:     ctx.Pmax    = ctx.E*ctx.V/ctx.X;
 89:     ctx.Pmax_ini = ctx.Pmax;
 90:     PetscOptionsScalar("-Pmax","","",ctx.Pmax,&ctx.Pmax,NULL);
 91:     ctx.Pm      = 1.1;
 92:     PetscOptionsScalar("-Pm","","",ctx.Pm,&ctx.Pm,NULL);
 93:     ctx.tf      = 0.1;
 94:     ctx.tcl     = 0.2;
 95:     PetscOptionsReal("-tf","Time to start fault","",ctx.tf,&ctx.tf,NULL);
 96:     PetscOptionsReal("-tcl","Time to end fault","",ctx.tcl,&ctx.tcl,NULL);
 97:     PetscOptionsBool("-ensemble","Run ensemble of different initial conditions","",ensemble,&ensemble,NULL);
 98:     if (ensemble) {
 99:       ctx.tf      = -1;
100:       ctx.tcl     = -1;
101:     }

103:     VecGetArray(U,&u);
104:     u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
105:     u[1] = 1.0;
106:     PetscOptionsRealArray("-u","Initial solution","",u,&n,&flg1);
107:     n    = 2;
108:     PetscOptionsRealArray("-du","Perturbation in initial solution","",du,&n,&flg2);
109:     u[0] += du[0];
110:     u[1] += du[1];
111:     VecRestoreArray(U,&u);
112:     if (flg1 || flg2) {
113:       ctx.tf      = -1;
114:       ctx.tcl     = -1;
115:     }
116:     sa = SA_ADJ;
117:     PetscOptionsEnum("-sa_method","Sensitivity analysis method (adj or tlm)","",SAMethods,(PetscEnum)sa,(PetscEnum*)&sa,NULL);
118:   }
119:   PetscOptionsEnd();

121:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
122:      Create timestepping solver context
123:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
124:   TSCreate(PETSC_COMM_WORLD,&ts);
125:   TSSetProblemType(ts,TS_NONLINEAR);
126:   TSSetType(ts,TSBEULER);
127:   TSSetRHSFunction(ts,NULL,(TSRHSFunction)RHSFunction,&ctx);
128:   TSSetRHSJacobian(ts,ctx.Jac,ctx.Jac,(TSRHSJacobian)RHSJacobian,&ctx);

130:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
131:      Set initial conditions
132:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
133:   TSSetSolution(ts,U);

135:   /*   Set RHS JacobianP */
136:   TSSetRHSJacobianP(ts,ctx.Jacp,RHSJacobianP,&ctx);

138:   TSCreateQuadratureTS(ts,PETSC_FALSE,&quadts);
139:   TSSetRHSFunction(quadts,NULL,(TSRHSFunction)CostIntegrand,&ctx);
140:   TSSetRHSJacobian(quadts,ctx.DRDU,ctx.DRDU,(TSRHSJacobian)DRDUJacobianTranspose,&ctx);
141:   TSSetRHSJacobianP(quadts,ctx.DRDP,DRDPJacobianTranspose,&ctx);
142:   if (sa == SA_ADJ) {
143:     /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
144:       Save trajectory of solution so that TSAdjointSolve() may be used
145:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
146:     TSSetSaveTrajectory(ts);
147:     MatCreateVecs(ctx.Jac,&lambda[0],NULL);
148:     MatCreateVecs(ctx.Jacp,&mu[0],NULL);
149:     TSSetCostGradients(ts,1,lambda,mu);
150:   }

152:   if (sa == SA_TLM) {
153:     PetscScalar val[2];
154:     PetscInt    row[]={0,1},col[]={0};

156:     MatCreateDense(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,&qgrad);
157:     MatCreateDense(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,2,1,NULL,&sp);
158:     TSForwardSetSensitivities(ts,1,sp);
159:     TSForwardSetSensitivities(quadts,1,qgrad);
160:     val[0] = 1./PetscSqrtScalar(1.-(ctx.Pm/ctx.Pmax)*(ctx.Pm/ctx.Pmax))/ctx.Pmax;
161:     val[1] = 0.0;
162:     MatSetValues(sp,2,row,1,col,val,INSERT_VALUES);
163:     MatAssemblyBegin(sp,MAT_FINAL_ASSEMBLY);
164:     MatAssemblyEnd(sp,MAT_FINAL_ASSEMBLY);
165:   }

167:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
168:      Set solver options
169:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
170:   TSSetMaxTime(ts,1.0);
171:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);
172:   TSSetTimeStep(ts,0.03125);
173:   TSSetFromOptions(ts);

175:   direction[0] = direction[1] = 1;
176:   terminate[0] = terminate[1] = PETSC_FALSE;

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

180:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
181:      Solve nonlinear system
182:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
183:   if (ensemble) {
184:     for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
185:       VecGetArray(U,&u);
186:       u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
187:       u[1] = ctx.omega_s;
188:       u[0] += du[0];
189:       u[1] += du[1];
190:       VecRestoreArray(U,&u);
191:       TSSetTimeStep(ts,0.03125);
192:       TSSolve(ts,U);
193:     }
194:   } else {
195:     TSSolve(ts,U);
196:   }
197:   TSGetSolveTime(ts,&ftime);
198:   TSGetStepNumber(ts,&steps);

200:   if (sa == SA_ADJ) {
201:     /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
202:        Adjoint model starts here
203:        - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
204:     /*   Set initial conditions for the adjoint integration */
205:     VecGetArray(lambda[0],&y_ptr);
206:     y_ptr[0] = 0.0; y_ptr[1] = 0.0;
207:     VecRestoreArray(lambda[0],&y_ptr);

209:     VecGetArray(mu[0],&x_ptr);
210:     x_ptr[0] = 0.0;
211:     VecRestoreArray(mu[0],&x_ptr);

213:     TSAdjointSolve(ts);

215:     PetscPrintf(PETSC_COMM_WORLD,"\n lambda: d[Psi(tf)]/d[phi0]  d[Psi(tf)]/d[omega0]\n");
216:     VecView(lambda[0],PETSC_VIEWER_STDOUT_WORLD);
217:     PetscPrintf(PETSC_COMM_WORLD,"\n mu: d[Psi(tf)]/d[pm]\n");
218:     VecView(mu[0],PETSC_VIEWER_STDOUT_WORLD);
219:     TSGetCostIntegral(ts,&q);
220:     VecGetArray(q,&x_ptr);
221:     PetscPrintf(PETSC_COMM_WORLD,"\n cost function=%g\n",(double)(x_ptr[0]-ctx.Pm));
222:     VecRestoreArray(q,&x_ptr);
223:     ComputeSensiP(lambda[0],mu[0],&ctx);
224:     VecGetArray(mu[0],&x_ptr);
225:     PetscPrintf(PETSC_COMM_WORLD,"\n gradient=%g\n",(double)x_ptr[0]);
226:     VecRestoreArray(mu[0],&x_ptr);
227:     VecDestroy(&lambda[0]);
228:     VecDestroy(&mu[0]);
229:   }
230:   if (sa == SA_TLM) {
231:     PetscPrintf(PETSC_COMM_WORLD,"\n trajectory sensitivity: d[phi(tf)]/d[pm]  d[omega(tf)]/d[pm]\n");
232:     MatView(sp,PETSC_VIEWER_STDOUT_WORLD);
233:     TSGetCostIntegral(ts,&q);
234:     VecGetArray(q,&s_ptr);
235:     PetscPrintf(PETSC_COMM_WORLD,"\n cost function=%g\n",(double)(s_ptr[0]-ctx.Pm));
236:     VecRestoreArray(q,&s_ptr);
237:     MatDenseGetArray(qgrad,&s_ptr);
238:     PetscPrintf(PETSC_COMM_WORLD,"\n gradient=%g\n",(double)s_ptr[0]);
239:     MatDenseRestoreArray(qgrad,&s_ptr);
240:     MatDestroy(&qgrad);
241:     MatDestroy(&sp);
242:   }
243:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
244:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
245:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
246:   MatDestroy(&ctx.Jac);
247:   MatDestroy(&ctx.Jacp);
248:   MatDestroy(&ctx.DRDU);
249:   MatDestroy(&ctx.DRDP);
250:   VecDestroy(&U);
251:   TSDestroy(&ts);
252:   PetscFinalize();
253:   return ierr;
254: }


257: /*TEST

259:    build:
260:       requires: !complex !single

262:    test:
263:       args: -sa_method adj -viewer_binary_skip_info -ts_type cn -pc_type lu

265:    test:
266:       suffix: 2
267:       args: -sa_method tlm -ts_type cn -pc_type lu

269:    test:
270:       suffix: 3
271:       args: -sa_method adj -ts_type rk -ts_rk_type 2a -ts_adapt_type dsp

273: TEST*/