1 static char help[] = "Finds optimal parameter P_m for the generator system while maintaining generator stability.\n"; 2 3 /*F 4 5 \begin{eqnarray} 6 \frac{d \theta}{dt} = \omega_b (\omega - \omega_s) 7 \frac{2 H}{\omega_s}\frac{d \omega}{dt} & = & P_m - P_max \sin(\theta) -D(\omega - \omega_s)\\ 8 \end{eqnarray} 9 10 F*/ 11 12 /* 13 This code demonstrates how to solve a ODE-constrained optimization problem with TAO, TSEvent, TSAdjoint and TS. 14 The problem features discontinuities and a cost function in integral form. 15 The gradient is computed with the discrete adjoint of an implicit theta method, see ex3adj.c for details. 16 */ 17 18 #include <petsctao.h> 19 #include <petscts.h> 20 #include "ex3.h" 21 22 PetscErrorCode FormFunctionGradient(Tao, Vec, PetscReal *, Vec, void *); 23 24 PetscErrorCode monitor(Tao tao, AppCtx *ctx) 25 { 26 FILE *fp; 27 PetscInt iterate; 28 PetscReal f, gnorm, cnorm, xdiff; 29 TaoConvergedReason reason; 30 31 PetscFunctionBeginUser; 32 PetscCall(TaoGetSolutionStatus(tao, &iterate, &f, &gnorm, &cnorm, &xdiff, &reason)); 33 34 fp = fopen("ex3opt_conv.out", "a"); 35 PetscCall(PetscFPrintf(PETSC_COMM_WORLD, fp, "%" PetscInt_FMT " %g\n", iterate, (double)gnorm)); 36 fclose(fp); 37 PetscFunctionReturn(PETSC_SUCCESS); 38 } 39 40 int main(int argc, char **argv) 41 { 42 Vec p; 43 PetscScalar *x_ptr; 44 PetscMPIInt size; 45 AppCtx ctx; 46 Tao tao; 47 KSP ksp; 48 PC pc; 49 Vec lambda[1], mu[1], lowerb, upperb; 50 PetscBool printtofile; 51 PetscInt direction[2]; 52 PetscBool terminate[2]; 53 Mat qgrad; /* Forward sesivitiy */ 54 Mat sp; /* Forward sensitivity matrix */ 55 56 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 57 Initialize program 58 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 59 PetscFunctionBeginUser; 60 PetscCall(PetscInitialize(&argc, &argv, NULL, help)); 61 PetscFunctionBeginUser; 62 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); 63 PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!"); 64 65 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 66 Set runtime options 67 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 68 PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Swing equation options", ""); 69 { 70 ctx.beta = 2; 71 ctx.c = 10000.0; 72 ctx.u_s = 1.0; 73 ctx.omega_s = 1.0; 74 ctx.omega_b = 120.0 * PETSC_PI; 75 ctx.H = 5.0; 76 PetscCall(PetscOptionsScalar("-Inertia", "", "", ctx.H, &ctx.H, NULL)); 77 ctx.D = 5.0; 78 PetscCall(PetscOptionsScalar("-D", "", "", ctx.D, &ctx.D, NULL)); 79 ctx.E = 1.1378; 80 ctx.V = 1.0; 81 ctx.X = 0.545; 82 ctx.Pmax = ctx.E * ctx.V / ctx.X; 83 ctx.Pmax_ini = ctx.Pmax; 84 PetscCall(PetscOptionsScalar("-Pmax", "", "", ctx.Pmax, &ctx.Pmax, NULL)); 85 ctx.Pm = 1.06; 86 PetscCall(PetscOptionsScalar("-Pm", "", "", ctx.Pm, &ctx.Pm, NULL)); 87 ctx.tf = 0.1; 88 ctx.tcl = 0.2; 89 PetscCall(PetscOptionsReal("-tf", "Time to start fault", "", ctx.tf, &ctx.tf, NULL)); 90 PetscCall(PetscOptionsReal("-tcl", "Time to end fault", "", ctx.tcl, &ctx.tcl, NULL)); 91 printtofile = PETSC_FALSE; 92 PetscCall(PetscOptionsBool("-printtofile", "Print convergence results to file", "", printtofile, &printtofile, NULL)); 93 ctx.sa = SA_ADJ; 94 PetscCall(PetscOptionsEnum("-sa_method", "Sensitivity analysis method (adj or tlm)", "", SAMethods, (PetscEnum)ctx.sa, (PetscEnum *)&ctx.sa, NULL)); 95 } 96 PetscOptionsEnd(); 97 98 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 99 Create necessary matrix and vectors 100 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 101 PetscCall(MatCreate(PETSC_COMM_WORLD, &ctx.Jac)); 102 PetscCall(MatSetSizes(ctx.Jac, 2, 2, PETSC_DETERMINE, PETSC_DETERMINE)); 103 PetscCall(MatSetType(ctx.Jac, MATDENSE)); 104 PetscCall(MatSetFromOptions(ctx.Jac)); 105 PetscCall(MatSetUp(ctx.Jac)); 106 PetscCall(MatCreate(PETSC_COMM_WORLD, &ctx.Jacp)); 107 PetscCall(MatSetSizes(ctx.Jacp, PETSC_DECIDE, PETSC_DECIDE, 2, 1)); 108 PetscCall(MatSetFromOptions(ctx.Jacp)); 109 PetscCall(MatSetUp(ctx.Jacp)); 110 PetscCall(MatCreateVecs(ctx.Jac, &ctx.U, NULL)); 111 PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 1, 1, NULL, &ctx.DRDP)); 112 PetscCall(MatSetUp(ctx.DRDP)); 113 PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 2, 1, NULL, &ctx.DRDU)); 114 PetscCall(MatSetUp(ctx.DRDU)); 115 116 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 117 Create timestepping solver context 118 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 119 PetscCall(TSCreate(PETSC_COMM_WORLD, &ctx.ts)); 120 PetscCall(TSSetProblemType(ctx.ts, TS_NONLINEAR)); 121 PetscCall(TSSetType(ctx.ts, TSCN)); 122 PetscCall(TSSetRHSFunction(ctx.ts, NULL, (TSRHSFunction)RHSFunction, &ctx)); 123 PetscCall(TSSetRHSJacobian(ctx.ts, ctx.Jac, ctx.Jac, (TSRHSJacobian)RHSJacobian, &ctx)); 124 PetscCall(TSSetRHSJacobianP(ctx.ts, ctx.Jacp, RHSJacobianP, &ctx)); 125 126 if (ctx.sa == SA_ADJ) { 127 PetscCall(MatCreateVecs(ctx.Jac, &lambda[0], NULL)); 128 PetscCall(MatCreateVecs(ctx.Jacp, &mu[0], NULL)); 129 PetscCall(TSSetSaveTrajectory(ctx.ts)); 130 PetscCall(TSSetCostGradients(ctx.ts, 1, lambda, mu)); 131 PetscCall(TSCreateQuadratureTS(ctx.ts, PETSC_FALSE, &ctx.quadts)); 132 PetscCall(TSSetRHSFunction(ctx.quadts, NULL, (TSRHSFunction)CostIntegrand, &ctx)); 133 PetscCall(TSSetRHSJacobian(ctx.quadts, ctx.DRDU, ctx.DRDU, (TSRHSJacobian)DRDUJacobianTranspose, &ctx)); 134 PetscCall(TSSetRHSJacobianP(ctx.quadts, ctx.DRDP, DRDPJacobianTranspose, &ctx)); 135 } 136 if (ctx.sa == SA_TLM) { 137 PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 1, 1, NULL, &qgrad)); 138 PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 2, 1, NULL, &sp)); 139 PetscCall(TSForwardSetSensitivities(ctx.ts, 1, sp)); 140 PetscCall(TSCreateQuadratureTS(ctx.ts, PETSC_TRUE, &ctx.quadts)); 141 PetscCall(TSForwardSetSensitivities(ctx.quadts, 1, qgrad)); 142 PetscCall(TSSetRHSFunction(ctx.quadts, NULL, (TSRHSFunction)CostIntegrand, &ctx)); 143 PetscCall(TSSetRHSJacobian(ctx.quadts, ctx.DRDU, ctx.DRDU, (TSRHSJacobian)DRDUJacobianTranspose, &ctx)); 144 PetscCall(TSSetRHSJacobianP(ctx.quadts, ctx.DRDP, DRDPJacobianTranspose, &ctx)); 145 } 146 147 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 148 Set solver options 149 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 150 PetscCall(TSSetMaxTime(ctx.ts, 1.0)); 151 PetscCall(TSSetExactFinalTime(ctx.ts, TS_EXACTFINALTIME_MATCHSTEP)); 152 PetscCall(TSSetTimeStep(ctx.ts, 0.03125)); 153 PetscCall(TSSetFromOptions(ctx.ts)); 154 155 direction[0] = direction[1] = 1; 156 terminate[0] = terminate[1] = PETSC_FALSE; 157 PetscCall(TSSetEventHandler(ctx.ts, 2, direction, terminate, EventFunction, PostEventFunction, &ctx)); 158 159 /* Create TAO solver and set desired solution method */ 160 PetscCall(TaoCreate(PETSC_COMM_WORLD, &tao)); 161 PetscCall(TaoSetType(tao, TAOBLMVM)); 162 if (printtofile) PetscCall(TaoSetMonitor(tao, (PetscErrorCode(*)(Tao, void *))monitor, (void *)&ctx, NULL)); 163 /* 164 Optimization starts 165 */ 166 /* Set initial solution guess */ 167 PetscCall(VecCreateSeq(PETSC_COMM_WORLD, 1, &p)); 168 PetscCall(VecGetArray(p, &x_ptr)); 169 x_ptr[0] = ctx.Pm; 170 PetscCall(VecRestoreArray(p, &x_ptr)); 171 172 PetscCall(TaoSetSolution(tao, p)); 173 /* Set routine for function and gradient evaluation */ 174 PetscCall(TaoSetObjectiveAndGradient(tao, NULL, FormFunctionGradient, (void *)&ctx)); 175 176 /* Set bounds for the optimization */ 177 PetscCall(VecDuplicate(p, &lowerb)); 178 PetscCall(VecDuplicate(p, &upperb)); 179 PetscCall(VecGetArray(lowerb, &x_ptr)); 180 x_ptr[0] = 0.; 181 PetscCall(VecRestoreArray(lowerb, &x_ptr)); 182 PetscCall(VecGetArray(upperb, &x_ptr)); 183 x_ptr[0] = 1.1; 184 PetscCall(VecRestoreArray(upperb, &x_ptr)); 185 PetscCall(TaoSetVariableBounds(tao, lowerb, upperb)); 186 187 /* Check for any TAO command line options */ 188 PetscCall(TaoSetFromOptions(tao)); 189 PetscCall(TaoGetKSP(tao, &ksp)); 190 if (ksp) { 191 PetscCall(KSPGetPC(ksp, &pc)); 192 PetscCall(PCSetType(pc, PCNONE)); 193 } 194 195 /* SOLVE THE APPLICATION */ 196 PetscCall(TaoSolve(tao)); 197 198 PetscCall(VecView(p, PETSC_VIEWER_STDOUT_WORLD)); 199 200 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 201 Free work space. All PETSc objects should be destroyed when they are no longer needed. 202 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 203 PetscCall(MatDestroy(&ctx.Jac)); 204 PetscCall(MatDestroy(&ctx.Jacp)); 205 PetscCall(MatDestroy(&ctx.DRDU)); 206 PetscCall(MatDestroy(&ctx.DRDP)); 207 PetscCall(VecDestroy(&ctx.U)); 208 if (ctx.sa == SA_ADJ) { 209 PetscCall(VecDestroy(&lambda[0])); 210 PetscCall(VecDestroy(&mu[0])); 211 } 212 if (ctx.sa == SA_TLM) { 213 PetscCall(MatDestroy(&qgrad)); 214 PetscCall(MatDestroy(&sp)); 215 } 216 PetscCall(TSDestroy(&ctx.ts)); 217 PetscCall(VecDestroy(&p)); 218 PetscCall(VecDestroy(&lowerb)); 219 PetscCall(VecDestroy(&upperb)); 220 PetscCall(TaoDestroy(&tao)); 221 PetscCall(PetscFinalize()); 222 return 0; 223 } 224 225 /* ------------------------------------------------------------------ */ 226 /* 227 FormFunctionGradient - Evaluates the function and corresponding gradient. 228 229 Input Parameters: 230 tao - the Tao context 231 X - the input vector 232 ptr - optional user-defined context, as set by TaoSetObjectiveAndGradient() 233 234 Output Parameters: 235 f - the newly evaluated function 236 G - the newly evaluated gradient 237 */ 238 PetscErrorCode FormFunctionGradient(Tao tao, Vec P, PetscReal *f, Vec G, void *ctx0) 239 { 240 AppCtx *ctx = (AppCtx *)ctx0; 241 PetscInt nadj; 242 PetscReal ftime; 243 PetscInt steps; 244 PetscScalar *u; 245 PetscScalar *x_ptr, *y_ptr; 246 Vec q; 247 Mat qgrad; 248 249 PetscFunctionBeginUser; 250 PetscCall(VecGetArrayRead(P, (const PetscScalar **)&x_ptr)); 251 ctx->Pm = x_ptr[0]; 252 PetscCall(VecRestoreArrayRead(P, (const PetscScalar **)&x_ptr)); 253 254 /* reinitialize the solution vector */ 255 PetscCall(VecGetArray(ctx->U, &u)); 256 u[0] = PetscAsinScalar(ctx->Pm / ctx->Pmax); 257 u[1] = 1.0; 258 PetscCall(VecRestoreArray(ctx->U, &u)); 259 PetscCall(TSSetSolution(ctx->ts, ctx->U)); 260 261 /* reset time */ 262 PetscCall(TSSetTime(ctx->ts, 0.0)); 263 264 /* reset step counter, this is critical for adjoint solver */ 265 PetscCall(TSSetStepNumber(ctx->ts, 0)); 266 267 /* reset step size, the step size becomes negative after TSAdjointSolve */ 268 PetscCall(TSSetTimeStep(ctx->ts, 0.03125)); 269 270 /* reinitialize the integral value */ 271 PetscCall(TSGetQuadratureTS(ctx->ts, NULL, &ctx->quadts)); 272 PetscCall(TSGetSolution(ctx->quadts, &q)); 273 PetscCall(VecSet(q, 0.0)); 274 275 if (ctx->sa == SA_TLM) { /* reset the forward sensitivities */ 276 TS quadts; 277 Mat sp; 278 PetscScalar val[2]; 279 const PetscInt row[] = {0, 1}, col[] = {0}; 280 281 PetscCall(TSGetQuadratureTS(ctx->ts, NULL, &quadts)); 282 PetscCall(TSForwardGetSensitivities(quadts, NULL, &qgrad)); 283 PetscCall(MatZeroEntries(qgrad)); 284 PetscCall(TSForwardGetSensitivities(ctx->ts, NULL, &sp)); 285 val[0] = 1. / PetscSqrtScalar(1. - (ctx->Pm / ctx->Pmax) * (ctx->Pm / ctx->Pmax)) / ctx->Pmax; 286 val[1] = 0.0; 287 PetscCall(MatSetValues(sp, 2, row, 1, col, val, INSERT_VALUES)); 288 PetscCall(MatAssemblyBegin(sp, MAT_FINAL_ASSEMBLY)); 289 PetscCall(MatAssemblyEnd(sp, MAT_FINAL_ASSEMBLY)); 290 } 291 292 /* solve the ODE */ 293 PetscCall(TSSolve(ctx->ts, ctx->U)); 294 PetscCall(TSGetSolveTime(ctx->ts, &ftime)); 295 PetscCall(TSGetStepNumber(ctx->ts, &steps)); 296 297 if (ctx->sa == SA_ADJ) { 298 Vec *lambda, *mu; 299 /* reset the terminal condition for adjoint */ 300 PetscCall(TSGetCostGradients(ctx->ts, &nadj, &lambda, &mu)); 301 PetscCall(VecGetArray(lambda[0], &y_ptr)); 302 y_ptr[0] = 0.0; 303 y_ptr[1] = 0.0; 304 PetscCall(VecRestoreArray(lambda[0], &y_ptr)); 305 PetscCall(VecGetArray(mu[0], &x_ptr)); 306 x_ptr[0] = -1.0; 307 PetscCall(VecRestoreArray(mu[0], &x_ptr)); 308 309 /* solve the adjont */ 310 PetscCall(TSAdjointSolve(ctx->ts)); 311 312 PetscCall(ComputeSensiP(lambda[0], mu[0], ctx)); 313 PetscCall(VecCopy(mu[0], G)); 314 } 315 316 if (ctx->sa == SA_TLM) { 317 PetscCall(VecGetArray(G, &x_ptr)); 318 PetscCall(MatDenseGetArray(qgrad, &y_ptr)); 319 x_ptr[0] = y_ptr[0] - 1.; 320 PetscCall(MatDenseRestoreArray(qgrad, &y_ptr)); 321 PetscCall(VecRestoreArray(G, &x_ptr)); 322 } 323 324 PetscCall(TSGetSolution(ctx->quadts, &q)); 325 PetscCall(VecGetArray(q, &x_ptr)); 326 *f = -ctx->Pm + x_ptr[0]; 327 PetscCall(VecRestoreArray(q, &x_ptr)); 328 PetscFunctionReturn(PETSC_SUCCESS); 329 } 330 331 /*TEST 332 333 build: 334 requires: !complex !single 335 336 test: 337 args: -viewer_binary_skip_info -ts_type cn -pc_type lu -tao_monitor 338 339 test: 340 suffix: 2 341 output_file: output/ex3opt_1.out 342 args: -sa_method tlm -ts_type cn -pc_type lu -tao_monitor 343 TEST*/ 344