Actual source code: ex3sa.c


  2: static char help[] = "Adjoint and tangent linear sensitivity analysis of the basic equation for generator stability analysis.\n";

  4: /*F

  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}

 11: F*/

 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 */
 29:   PetscMPIInt  size;
 30:   PetscInt     n = 2;
 31:   AppCtx       ctx;
 32:   PetscScalar *u;
 33:   PetscReal    du[2]    = {0.0, 0.0};
 34:   PetscBool    ensemble = PETSC_FALSE, flg1, flg2;
 35:   PetscReal    ftime;
 36:   PetscInt     steps;
 37:   PetscScalar *x_ptr, *y_ptr, *s_ptr;
 38:   Vec          lambda[1], q, mu[1];
 39:   PetscInt     direction[2];
 40:   PetscBool    terminate[2];
 41:   Mat          qgrad;
 42:   Mat          sp; /* Forward sensitivity matrix */
 43:   SAMethod     sa;

 45:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 46:      Initialize program
 47:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 48:   PetscFunctionBeginUser;
 49:   PetscCall(PetscInitialize(&argc, &argv, (char *)0, help));
 50:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
 51:   PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs");

 53:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 54:     Create necessary matrix and vectors
 55:     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 56:   PetscCall(MatCreate(PETSC_COMM_WORLD, &ctx.Jac));
 57:   PetscCall(MatSetSizes(ctx.Jac, n, n, PETSC_DETERMINE, PETSC_DETERMINE));
 58:   PetscCall(MatSetType(ctx.Jac, MATDENSE));
 59:   PetscCall(MatSetFromOptions(ctx.Jac));
 60:   PetscCall(MatSetUp(ctx.Jac));
 61:   PetscCall(MatCreateVecs(ctx.Jac, &U, NULL));
 62:   PetscCall(MatCreate(PETSC_COMM_WORLD, &ctx.Jacp));
 63:   PetscCall(MatSetSizes(ctx.Jacp, PETSC_DECIDE, PETSC_DECIDE, 2, 1));
 64:   PetscCall(MatSetFromOptions(ctx.Jacp));
 65:   PetscCall(MatSetUp(ctx.Jacp));
 66:   PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 1, 1, NULL, &ctx.DRDP));
 67:   PetscCall(MatSetUp(ctx.DRDP));
 68:   PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 2, 1, NULL, &ctx.DRDU));
 69:   PetscCall(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:     PetscCall(PetscOptionsScalar("-Inertia", "", "", ctx.H, &ctx.H, NULL));
 83:     ctx.D = 5.0;
 84:     PetscCall(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:     PetscCall(PetscOptionsScalar("-Pmax", "", "", ctx.Pmax, &ctx.Pmax, NULL));
 91:     ctx.Pm = 1.1;
 92:     PetscCall(PetscOptionsScalar("-Pm", "", "", ctx.Pm, &ctx.Pm, NULL));
 93:     ctx.tf  = 0.1;
 94:     ctx.tcl = 0.2;
 95:     PetscCall(PetscOptionsReal("-tf", "Time to start fault", "", ctx.tf, &ctx.tf, NULL));
 96:     PetscCall(PetscOptionsReal("-tcl", "Time to end fault", "", ctx.tcl, &ctx.tcl, NULL));
 97:     PetscCall(PetscOptionsBool("-ensemble", "Run ensemble of different initial conditions", "", ensemble, &ensemble, NULL));
 98:     if (ensemble) {
 99:       ctx.tf  = -1;
100:       ctx.tcl = -1;
101:     }

103:     PetscCall(VecGetArray(U, &u));
104:     u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax);
105:     u[1] = 1.0;
106:     PetscCall(PetscOptionsRealArray("-u", "Initial solution", "", u, &n, &flg1));
107:     n = 2;
108:     PetscCall(PetscOptionsRealArray("-du", "Perturbation in initial solution", "", du, &n, &flg2));
109:     u[0] += du[0];
110:     u[1] += du[1];
111:     PetscCall(VecRestoreArray(U, &u));
112:     if (flg1 || flg2) {
113:       ctx.tf  = -1;
114:       ctx.tcl = -1;
115:     }
116:     sa = SA_ADJ;
117:     PetscCall(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:   PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
125:   PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
126:   PetscCall(TSSetType(ts, TSBEULER));
127:   PetscCall(TSSetRHSFunction(ts, NULL, (TSRHSFunction)RHSFunction, &ctx));
128:   PetscCall(TSSetRHSJacobian(ts, ctx.Jac, ctx.Jac, (TSRHSJacobian)RHSJacobian, &ctx));

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

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

138:   PetscCall(TSCreateQuadratureTS(ts, PETSC_FALSE, &quadts));
139:   PetscCall(TSSetRHSFunction(quadts, NULL, (TSRHSFunction)CostIntegrand, &ctx));
140:   PetscCall(TSSetRHSJacobian(quadts, ctx.DRDU, ctx.DRDU, (TSRHSJacobian)DRDUJacobianTranspose, &ctx));
141:   PetscCall(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:     PetscCall(TSSetSaveTrajectory(ts));
147:     PetscCall(MatCreateVecs(ctx.Jac, &lambda[0], NULL));
148:     PetscCall(MatCreateVecs(ctx.Jacp, &mu[0], NULL));
149:     PetscCall(TSSetCostGradients(ts, 1, lambda, mu));
150:   }

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

156:     PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 1, 1, NULL, &qgrad));
157:     PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 2, 1, NULL, &sp));
158:     PetscCall(TSForwardSetSensitivities(ts, 1, sp));
159:     PetscCall(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:     PetscCall(MatSetValues(sp, 2, row, 1, col, val, INSERT_VALUES));
163:     PetscCall(MatAssemblyBegin(sp, MAT_FINAL_ASSEMBLY));
164:     PetscCall(MatAssemblyEnd(sp, MAT_FINAL_ASSEMBLY));
165:   }

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

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

178:   PetscCall(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:       PetscCall(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:       PetscCall(VecRestoreArray(U, &u));
191:       PetscCall(TSSetTimeStep(ts, 0.03125));
192:       PetscCall(TSSolve(ts, U));
193:     }
194:   } else {
195:     PetscCall(TSSolve(ts, U));
196:   }
197:   PetscCall(TSGetSolveTime(ts, &ftime));
198:   PetscCall(TSGetStepNumber(ts, &steps));

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

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

214:     PetscCall(TSAdjointSolve(ts));

216:     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n lambda: d[Psi(tf)]/d[phi0]  d[Psi(tf)]/d[omega0]\n"));
217:     PetscCall(VecView(lambda[0], PETSC_VIEWER_STDOUT_WORLD));
218:     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n mu: d[Psi(tf)]/d[pm]\n"));
219:     PetscCall(VecView(mu[0], PETSC_VIEWER_STDOUT_WORLD));
220:     PetscCall(TSGetCostIntegral(ts, &q));
221:     PetscCall(VecGetArray(q, &x_ptr));
222:     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n cost function=%g\n", (double)(x_ptr[0] - ctx.Pm)));
223:     PetscCall(VecRestoreArray(q, &x_ptr));
224:     PetscCall(ComputeSensiP(lambda[0], mu[0], &ctx));
225:     PetscCall(VecGetArray(mu[0], &x_ptr));
226:     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n gradient=%g\n", (double)x_ptr[0]));
227:     PetscCall(VecRestoreArray(mu[0], &x_ptr));
228:     PetscCall(VecDestroy(&lambda[0]));
229:     PetscCall(VecDestroy(&mu[0]));
230:   }
231:   if (sa == SA_TLM) {
232:     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n trajectory sensitivity: d[phi(tf)]/d[pm]  d[omega(tf)]/d[pm]\n"));
233:     PetscCall(MatView(sp, PETSC_VIEWER_STDOUT_WORLD));
234:     PetscCall(TSGetCostIntegral(ts, &q));
235:     PetscCall(VecGetArray(q, &s_ptr));
236:     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n cost function=%g\n", (double)(s_ptr[0] - ctx.Pm)));
237:     PetscCall(VecRestoreArray(q, &s_ptr));
238:     PetscCall(MatDenseGetArray(qgrad, &s_ptr));
239:     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n gradient=%g\n", (double)s_ptr[0]));
240:     PetscCall(MatDenseRestoreArray(qgrad, &s_ptr));
241:     PetscCall(MatDestroy(&qgrad));
242:     PetscCall(MatDestroy(&sp));
243:   }
244:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
245:      Free work space.  All PETSc objects should be destroyed when they are no longer needed.
246:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
247:   PetscCall(MatDestroy(&ctx.Jac));
248:   PetscCall(MatDestroy(&ctx.Jacp));
249:   PetscCall(MatDestroy(&ctx.DRDU));
250:   PetscCall(MatDestroy(&ctx.DRDP));
251:   PetscCall(VecDestroy(&U));
252:   PetscCall(TSDestroy(&ts));
253:   PetscCall(PetscFinalize());
254:   return 0;
255: }

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*/