1 static char help[] = "Adjoint and tangent linear sensitivity analysis of the basic equation for generator stability analysis.\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 demonstrate the sensitivity analysis interface to a system of ordinary differential equations with discontinuities. 14 It computes the sensitivities of an integral cost function 15 \int c*max(0,\theta(t)-u_s)^beta dt 16 w.r.t. initial conditions and the parameter P_m. 17 Backward Euler method is used for time integration. 18 The discontinuities are detected with TSEvent. 19 */ 20 21 #include <petscts.h> 22 #include "ex3.h" 23 24 int main(int argc, char **argv) 25 { 26 TS ts, quadts; /* ODE integrator */ 27 Vec U; /* solution will be stored here */ 28 PetscMPIInt size; 29 PetscInt n = 2; 30 AppCtx ctx; 31 PetscScalar *u; 32 PetscReal du[2] = {0.0, 0.0}; 33 PetscBool ensemble = PETSC_FALSE, flg1, flg2; 34 PetscReal ftime; 35 PetscInt steps; 36 PetscScalar *x_ptr, *y_ptr, *s_ptr; 37 Vec lambda[1], q, mu[1]; 38 PetscInt direction[2]; 39 PetscBool terminate[2]; 40 Mat qgrad; 41 Mat sp; /* Forward sensitivity matrix */ 42 SAMethod sa; 43 44 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 45 Initialize program 46 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 47 PetscFunctionBeginUser; 48 PetscCall(PetscInitialize(&argc, &argv, NULL, help)); 49 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); 50 PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs"); 51 52 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 53 Create necessary matrix and vectors 54 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 55 PetscCall(MatCreate(PETSC_COMM_WORLD, &ctx.Jac)); 56 PetscCall(MatSetSizes(ctx.Jac, n, n, PETSC_DETERMINE, PETSC_DETERMINE)); 57 PetscCall(MatSetType(ctx.Jac, MATDENSE)); 58 PetscCall(MatSetFromOptions(ctx.Jac)); 59 PetscCall(MatSetUp(ctx.Jac)); 60 PetscCall(MatCreateVecs(ctx.Jac, &U, NULL)); 61 PetscCall(MatCreate(PETSC_COMM_WORLD, &ctx.Jacp)); 62 PetscCall(MatSetSizes(ctx.Jacp, PETSC_DECIDE, PETSC_DECIDE, 2, 1)); 63 PetscCall(MatSetFromOptions(ctx.Jacp)); 64 PetscCall(MatSetUp(ctx.Jacp)); 65 PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 1, 1, NULL, &ctx.DRDP)); 66 PetscCall(MatSetUp(ctx.DRDP)); 67 PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 2, 1, NULL, &ctx.DRDU)); 68 PetscCall(MatSetUp(ctx.DRDU)); 69 70 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 71 Set runtime options 72 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 73 PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Swing equation options", ""); 74 { 75 ctx.beta = 2; 76 ctx.c = 10000.0; 77 ctx.u_s = 1.0; 78 ctx.omega_s = 1.0; 79 ctx.omega_b = 120.0 * PETSC_PI; 80 ctx.H = 5.0; 81 PetscCall(PetscOptionsScalar("-Inertia", "", "", ctx.H, &ctx.H, NULL)); 82 ctx.D = 5.0; 83 PetscCall(PetscOptionsScalar("-D", "", "", ctx.D, &ctx.D, NULL)); 84 ctx.E = 1.1378; 85 ctx.V = 1.0; 86 ctx.X = 0.545; 87 ctx.Pmax = ctx.E * ctx.V / ctx.X; 88 ctx.Pmax_ini = ctx.Pmax; 89 PetscCall(PetscOptionsScalar("-Pmax", "", "", ctx.Pmax, &ctx.Pmax, NULL)); 90 ctx.Pm = 1.1; 91 PetscCall(PetscOptionsScalar("-Pm", "", "", ctx.Pm, &ctx.Pm, NULL)); 92 ctx.tf = 0.1; 93 ctx.tcl = 0.2; 94 PetscCall(PetscOptionsReal("-tf", "Time to start fault", "", ctx.tf, &ctx.tf, NULL)); 95 PetscCall(PetscOptionsReal("-tcl", "Time to end fault", "", ctx.tcl, &ctx.tcl, NULL)); 96 PetscCall(PetscOptionsBool("-ensemble", "Run ensemble of different initial conditions", "", ensemble, &ensemble, NULL)); 97 if (ensemble) { 98 ctx.tf = -1; 99 ctx.tcl = -1; 100 } 101 102 PetscCall(VecGetArray(U, &u)); 103 u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax); 104 u[1] = 1.0; 105 PetscCall(PetscOptionsRealArray("-u", "Initial solution", "", u, &n, &flg1)); 106 n = 2; 107 PetscCall(PetscOptionsRealArray("-du", "Perturbation in initial solution", "", du, &n, &flg2)); 108 u[0] += du[0]; 109 u[1] += du[1]; 110 PetscCall(VecRestoreArray(U, &u)); 111 if (flg1 || flg2) { 112 ctx.tf = -1; 113 ctx.tcl = -1; 114 } 115 sa = SA_ADJ; 116 PetscCall(PetscOptionsEnum("-sa_method", "Sensitivity analysis method (adj or tlm)", "", SAMethods, (PetscEnum)sa, (PetscEnum *)&sa, NULL)); 117 } 118 PetscOptionsEnd(); 119 120 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 121 Create timestepping solver context 122 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 123 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 124 PetscCall(TSSetProblemType(ts, TS_NONLINEAR)); 125 PetscCall(TSSetType(ts, TSBEULER)); 126 PetscCall(TSSetRHSFunction(ts, NULL, (TSRHSFunctionFn *)RHSFunction, &ctx)); 127 PetscCall(TSSetRHSJacobian(ts, ctx.Jac, ctx.Jac, (TSRHSJacobianFn *)RHSJacobian, &ctx)); 128 129 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 130 Set initial conditions 131 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 132 PetscCall(TSSetSolution(ts, U)); 133 134 /* Set RHS JacobianP */ 135 PetscCall(TSSetRHSJacobianP(ts, ctx.Jacp, RHSJacobianP, &ctx)); 136 137 PetscCall(TSCreateQuadratureTS(ts, PETSC_FALSE, &quadts)); 138 PetscCall(TSSetRHSFunction(quadts, NULL, (TSRHSFunctionFn *)CostIntegrand, &ctx)); 139 PetscCall(TSSetRHSJacobian(quadts, ctx.DRDU, ctx.DRDU, (TSRHSJacobianFn *)DRDUJacobianTranspose, &ctx)); 140 PetscCall(TSSetRHSJacobianP(quadts, ctx.DRDP, DRDPJacobianTranspose, &ctx)); 141 if (sa == SA_ADJ) { 142 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 143 Save trajectory of solution so that TSAdjointSolve() may be used 144 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 145 PetscCall(TSSetSaveTrajectory(ts)); 146 PetscCall(MatCreateVecs(ctx.Jac, &lambda[0], NULL)); 147 PetscCall(MatCreateVecs(ctx.Jacp, &mu[0], NULL)); 148 PetscCall(TSSetCostGradients(ts, 1, lambda, mu)); 149 } 150 151 if (sa == SA_TLM) { 152 PetscScalar val[2]; 153 PetscInt row[] = {0, 1}, col[] = {0}; 154 155 PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 1, 1, NULL, &qgrad)); 156 PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, 2, 1, NULL, &sp)); 157 PetscCall(TSForwardSetSensitivities(ts, 1, sp)); 158 PetscCall(TSForwardSetSensitivities(quadts, 1, qgrad)); 159 val[0] = 1. / PetscSqrtScalar(1. - (ctx.Pm / ctx.Pmax) * (ctx.Pm / ctx.Pmax)) / ctx.Pmax; 160 val[1] = 0.0; 161 PetscCall(MatSetValues(sp, 2, row, 1, col, val, INSERT_VALUES)); 162 PetscCall(MatAssemblyBegin(sp, MAT_FINAL_ASSEMBLY)); 163 PetscCall(MatAssemblyEnd(sp, MAT_FINAL_ASSEMBLY)); 164 } 165 166 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 167 Set solver options 168 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 169 PetscCall(TSSetMaxTime(ts, 1.0)); 170 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP)); 171 PetscCall(TSSetTimeStep(ts, 0.03125)); 172 PetscCall(TSSetFromOptions(ts)); 173 174 direction[0] = direction[1] = 1; 175 terminate[0] = terminate[1] = PETSC_FALSE; 176 177 PetscCall(TSSetEventHandler(ts, 2, direction, terminate, EventFunction, PostEventFunction, (void *)&ctx)); 178 179 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 180 Solve nonlinear system 181 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 182 if (ensemble) { 183 for (du[1] = -2.5; du[1] <= .01; du[1] += .1) { 184 PetscCall(VecGetArray(U, &u)); 185 u[0] = PetscAsinScalar(ctx.Pm / ctx.Pmax); 186 u[1] = ctx.omega_s; 187 u[0] += du[0]; 188 u[1] += du[1]; 189 PetscCall(VecRestoreArray(U, &u)); 190 PetscCall(TSSetTimeStep(ts, 0.03125)); 191 PetscCall(TSSolve(ts, U)); 192 } 193 } else { 194 PetscCall(TSSolve(ts, U)); 195 } 196 PetscCall(TSGetSolveTime(ts, &ftime)); 197 PetscCall(TSGetStepNumber(ts, &steps)); 198 199 if (sa == SA_ADJ) { 200 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 201 Adjoint model starts here 202 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 203 /* Set initial conditions for the adjoint integration */ 204 PetscCall(VecGetArray(lambda[0], &y_ptr)); 205 y_ptr[0] = 0.0; 206 y_ptr[1] = 0.0; 207 PetscCall(VecRestoreArray(lambda[0], &y_ptr)); 208 209 PetscCall(VecGetArray(mu[0], &x_ptr)); 210 x_ptr[0] = 0.0; 211 PetscCall(VecRestoreArray(mu[0], &x_ptr)); 212 213 PetscCall(TSAdjointSolve(ts)); 214 215 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n lambda: d[Psi(tf)]/d[phi0] d[Psi(tf)]/d[omega0]\n")); 216 PetscCall(VecView(lambda[0], PETSC_VIEWER_STDOUT_WORLD)); 217 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n mu: d[Psi(tf)]/d[pm]\n")); 218 PetscCall(VecView(mu[0], PETSC_VIEWER_STDOUT_WORLD)); 219 PetscCall(TSGetCostIntegral(ts, &q)); 220 PetscCall(VecGetArray(q, &x_ptr)); 221 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n cost function=%g\n", (double)(x_ptr[0] - ctx.Pm))); 222 PetscCall(VecRestoreArray(q, &x_ptr)); 223 PetscCall(ComputeSensiP(lambda[0], mu[0], &ctx)); 224 PetscCall(VecGetArray(mu[0], &x_ptr)); 225 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n gradient=%g\n", (double)x_ptr[0])); 226 PetscCall(VecRestoreArray(mu[0], &x_ptr)); 227 PetscCall(VecDestroy(&lambda[0])); 228 PetscCall(VecDestroy(&mu[0])); 229 } 230 if (sa == SA_TLM) { 231 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n trajectory sensitivity: d[phi(tf)]/d[pm] d[omega(tf)]/d[pm]\n")); 232 PetscCall(MatView(sp, PETSC_VIEWER_STDOUT_WORLD)); 233 PetscCall(TSGetCostIntegral(ts, &q)); 234 PetscCall(VecGetArray(q, &s_ptr)); 235 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n cost function=%g\n", (double)(s_ptr[0] - ctx.Pm))); 236 PetscCall(VecRestoreArray(q, &s_ptr)); 237 PetscCall(MatDenseGetArray(qgrad, &s_ptr)); 238 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n gradient=%g\n", (double)s_ptr[0])); 239 PetscCall(MatDenseRestoreArray(qgrad, &s_ptr)); 240 PetscCall(MatDestroy(&qgrad)); 241 PetscCall(MatDestroy(&sp)); 242 } 243 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 244 Free work space. All PETSc objects should be destroyed when they are no longer needed. 245 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 246 PetscCall(MatDestroy(&ctx.Jac)); 247 PetscCall(MatDestroy(&ctx.Jacp)); 248 PetscCall(MatDestroy(&ctx.DRDU)); 249 PetscCall(MatDestroy(&ctx.DRDP)); 250 PetscCall(VecDestroy(&U)); 251 PetscCall(TSDestroy(&ts)); 252 PetscCall(PetscFinalize()); 253 return 0; 254 } 255 256 /*TEST 257 258 build: 259 requires: !complex !single 260 261 test: 262 args: -sa_method adj -viewer_binary_skip_info -ts_type cn -pc_type lu 263 264 test: 265 suffix: 2 266 args: -sa_method tlm -ts_type cn -pc_type lu 267 268 test: 269 suffix: 3 270 args: -sa_method adj -ts_type rk -ts_rk_type 2a -ts_adapt_type dsp 271 272 TEST*/ 273