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