1 static char help[] = "Demonstrates automatic Jacobian generation using ADOL-C for an adjoint sensitivity analysis of the van der Pol equation.\n\ 2 Input parameters include:\n\ 3 -mu : stiffness parameter\n\n"; 4 5 /* 6 REQUIRES configuration of PETSc with option --download-adolc. 7 8 For documentation on ADOL-C, see 9 $PETSC_ARCH/externalpackages/ADOL-C-2.6.0/ADOL-C/doc/adolc-manual.pdf 10 */ 11 /* ------------------------------------------------------------------------ 12 See ex16adj for a description of the problem being solved. 13 ------------------------------------------------------------------------- */ 14 15 #include <petscts.h> 16 #include <petscmat.h> 17 #include "adolc-utils/drivers.cxx" 18 #include <adolc/adolc.h> 19 20 typedef struct _n_User *User; 21 struct _n_User { 22 PetscReal mu; 23 PetscReal next_output; 24 PetscReal tprev; 25 26 /* Automatic differentiation support */ 27 AdolcCtx *adctx; 28 }; 29 30 /* 31 'Passive' RHS function, used in residual evaluations during the time integration. 32 */ 33 static PetscErrorCode RHSFunctionPassive(TS ts,PetscReal t,Vec X,Vec F,void *ctx) 34 { 35 User user = (User)ctx; 36 PetscScalar *f; 37 const PetscScalar *x; 38 39 PetscFunctionBeginUser; 40 PetscCall(VecGetArrayRead(X,&x)); 41 PetscCall(VecGetArray(F,&f)); 42 f[0] = x[1]; 43 f[1] = user->mu*(1.-x[0]*x[0])*x[1]-x[0]; 44 PetscCall(VecRestoreArrayRead(X,&x)); 45 PetscCall(VecRestoreArray(F,&f)); 46 PetscFunctionReturn(0); 47 } 48 49 /* 50 Trace RHS to mark on tape 1 the dependence of f upon x. This tape is used in generating the 51 Jacobian transform. 52 */ 53 static PetscErrorCode RHSFunctionActive(TS ts,PetscReal t,Vec X,Vec F,void *ctx) 54 { 55 User user = (User)ctx; 56 PetscScalar *f; 57 const PetscScalar *x; 58 59 adouble f_a[2]; /* 'active' double for dependent variables */ 60 adouble x_a[2]; /* 'active' double for independent variables */ 61 62 PetscFunctionBeginUser; 63 PetscCall(VecGetArrayRead(X,&x)); 64 PetscCall(VecGetArray(F,&f)); 65 66 /* Start of active section */ 67 trace_on(1); 68 x_a[0] <<= x[0];x_a[1] <<= x[1]; /* Mark independence */ 69 f_a[0] = x_a[1]; 70 f_a[1] = user->mu*(1.-x_a[0]*x_a[0])*x_a[1]-x_a[0]; 71 f_a[0] >>= f[0];f_a[1] >>= f[1]; /* Mark dependence */ 72 trace_off(); 73 /* End of active section */ 74 75 PetscCall(VecRestoreArrayRead(X,&x)); 76 PetscCall(VecRestoreArray(F,&f)); 77 PetscFunctionReturn(0); 78 } 79 80 /* 81 Trace RHS again to mark on tape 2 the dependence of f upon the parameter mu. This tape is used in 82 generating JacobianP. 83 */ 84 static PetscErrorCode RHSFunctionActiveP(TS ts,PetscReal t,Vec X,Vec F,void *ctx) 85 { 86 User user = (User)ctx; 87 PetscScalar *f; 88 const PetscScalar *x; 89 90 adouble f_a[2]; /* 'active' double for dependent variables */ 91 adouble x_a[2],mu_a; /* 'active' double for independent variables */ 92 93 PetscFunctionBeginUser; 94 PetscCall(VecGetArrayRead(X,&x)); 95 PetscCall(VecGetArray(F,&f)); 96 97 /* Start of active section */ 98 trace_on(3); 99 x_a[0] <<= x[0];x_a[1] <<= x[1];mu_a <<= user->mu; /* Mark independence */ 100 f_a[0] = x_a[1]; 101 f_a[1] = mu_a*(1.-x_a[0]*x_a[0])*x_a[1]-x_a[0]; 102 f_a[0] >>= f[0];f_a[1] >>= f[1]; /* Mark dependence */ 103 trace_off(); 104 /* End of active section */ 105 106 PetscCall(VecRestoreArrayRead(X,&x)); 107 PetscCall(VecRestoreArray(F,&f)); 108 PetscFunctionReturn(0); 109 } 110 111 /* 112 Compute the Jacobian w.r.t. x using PETSc-ADOL-C driver for explicit TS. 113 */ 114 static PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec X,Mat A,Mat B,void *ctx) 115 { 116 User user = (User)ctx; 117 const PetscScalar *x; 118 119 PetscFunctionBeginUser; 120 PetscCall(VecGetArrayRead(X,&x)); 121 PetscCall(PetscAdolcComputeRHSJacobian(1,A,x,user->adctx)); 122 PetscCall(VecRestoreArrayRead(X,&x)); 123 PetscFunctionReturn(0); 124 } 125 126 /* 127 Compute the Jacobian w.r.t. mu using PETSc-ADOL-C driver for explicit TS. 128 */ 129 static PetscErrorCode RHSJacobianP(TS ts,PetscReal t,Vec X,Mat A,void *ctx) 130 { 131 User user = (User)ctx; 132 const PetscScalar *x; 133 134 PetscFunctionBeginUser; 135 PetscCall(VecGetArrayRead(X,&x)); 136 PetscCall(PetscAdolcComputeRHSJacobianP(3,A,x,&user->mu,user->adctx)); 137 PetscCall(VecRestoreArrayRead(X,&x)); 138 PetscFunctionReturn(0); 139 } 140 141 /* 142 Monitor timesteps and use interpolation to output at integer multiples of 0.1 143 */ 144 static PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal t,Vec X,void *ctx) 145 { 146 const PetscScalar *x; 147 PetscReal tfinal, dt, tprev; 148 User user = (User)ctx; 149 150 PetscFunctionBeginUser; 151 PetscCall(TSGetTimeStep(ts,&dt)); 152 PetscCall(TSGetMaxTime(ts,&tfinal)); 153 PetscCall(TSGetPrevTime(ts,&tprev)); 154 PetscCall(VecGetArrayRead(X,&x)); 155 PetscCall(PetscPrintf(PETSC_COMM_WORLD,"[%.1f] %" PetscInt_FMT " TS %.6f (dt = %.6f) X % 12.6e % 12.6e\n",(double)user->next_output,step,(double)t,(double)dt,(double)PetscRealPart(x[0]),(double)PetscRealPart(x[1]))); 156 PetscCall(PetscPrintf(PETSC_COMM_WORLD,"t %.6f (tprev = %.6f) \n",(double)t,(double)tprev)); 157 PetscCall(VecRestoreArrayRead(X,&x)); 158 PetscFunctionReturn(0); 159 } 160 161 int main(int argc,char **argv) 162 { 163 TS ts; /* nonlinear solver */ 164 Vec x; /* solution, residual vectors */ 165 Mat A; /* Jacobian matrix */ 166 Mat Jacp; /* JacobianP matrix */ 167 PetscInt steps; 168 PetscReal ftime = 0.5; 169 PetscBool monitor = PETSC_FALSE; 170 PetscScalar *x_ptr; 171 PetscMPIInt size; 172 struct _n_User user; 173 AdolcCtx *adctx; 174 Vec lambda[2],mu[2],r; 175 176 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 177 Initialize program 178 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 179 PetscFunctionBeginUser; 180 PetscCall(PetscInitialize(&argc,&argv,NULL,help)); 181 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD,&size)); 182 PetscCheck(size == 1,PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only!"); 183 184 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 185 Set runtime options and create AdolcCtx 186 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 187 PetscCall(PetscNew(&adctx)); 188 user.mu = 1; 189 user.next_output = 0.0; 190 adctx->m = 2;adctx->n = 2;adctx->p = 2;adctx->num_params = 1; 191 user.adctx = adctx; 192 193 PetscCall(PetscOptionsGetReal(NULL,NULL,"-mu",&user.mu,NULL)); 194 PetscCall(PetscOptionsGetBool(NULL,NULL,"-monitor",&monitor,NULL)); 195 196 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 197 Create necessary matrix and vectors, solve same ODE on every process 198 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 199 PetscCall(MatCreate(PETSC_COMM_WORLD,&A)); 200 PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,2,2)); 201 PetscCall(MatSetFromOptions(A)); 202 PetscCall(MatSetUp(A)); 203 PetscCall(MatCreateVecs(A,&x,NULL)); 204 205 PetscCall(MatCreate(PETSC_COMM_WORLD,&Jacp)); 206 PetscCall(MatSetSizes(Jacp,PETSC_DECIDE,PETSC_DECIDE,2,1)); 207 PetscCall(MatSetFromOptions(Jacp)); 208 PetscCall(MatSetUp(Jacp)); 209 210 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 211 Create timestepping solver context 212 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 213 PetscCall(TSCreate(PETSC_COMM_WORLD,&ts)); 214 PetscCall(TSSetType(ts,TSRK)); 215 PetscCall(TSSetRHSFunction(ts,NULL,RHSFunctionPassive,&user)); 216 217 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 218 Set initial conditions 219 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 220 PetscCall(VecGetArray(x,&x_ptr)); 221 x_ptr[0] = 2; x_ptr[1] = 0.66666654321; 222 PetscCall(VecRestoreArray(x,&x_ptr)); 223 224 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 225 Trace just once on each tape and put zeros on Jacobian diagonal 226 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 227 PetscCall(VecDuplicate(x,&r)); 228 PetscCall(RHSFunctionActive(ts,0.,x,r,&user)); 229 PetscCall(RHSFunctionActiveP(ts,0.,x,r,&user)); 230 PetscCall(VecSet(r,0)); 231 PetscCall(MatDiagonalSet(A,r,INSERT_VALUES)); 232 PetscCall(VecDestroy(&r)); 233 234 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 235 Set RHS Jacobian for the adjoint integration 236 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 237 PetscCall(TSSetRHSJacobian(ts,A,A,RHSJacobian,&user)); 238 PetscCall(TSSetMaxTime(ts,ftime)); 239 PetscCall(TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP)); 240 if (monitor) { 241 PetscCall(TSMonitorSet(ts,Monitor,&user,NULL)); 242 } 243 PetscCall(TSSetTimeStep(ts,.001)); 244 245 /* 246 Have the TS save its trajectory so that TSAdjointSolve() may be used 247 */ 248 PetscCall(TSSetSaveTrajectory(ts)); 249 250 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 251 Set runtime options 252 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 253 PetscCall(TSSetFromOptions(ts)); 254 255 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 256 Solve nonlinear system 257 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 258 PetscCall(TSSolve(ts,x)); 259 PetscCall(TSGetSolveTime(ts,&ftime)); 260 PetscCall(TSGetStepNumber(ts,&steps)); 261 PetscCall(PetscPrintf(PETSC_COMM_WORLD,"mu %g, steps %" PetscInt_FMT ", ftime %g\n",(double)user.mu,steps,(double)ftime)); 262 PetscCall(VecView(x,PETSC_VIEWER_STDOUT_WORLD)); 263 264 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 265 Start the Adjoint model 266 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 267 PetscCall(MatCreateVecs(A,&lambda[0],NULL)); 268 PetscCall(MatCreateVecs(A,&lambda[1],NULL)); 269 /* Reset initial conditions for the adjoint integration */ 270 PetscCall(VecGetArray(lambda[0],&x_ptr)); 271 x_ptr[0] = 1.0; x_ptr[1] = 0.0; 272 PetscCall(VecRestoreArray(lambda[0],&x_ptr)); 273 PetscCall(VecGetArray(lambda[1],&x_ptr)); 274 x_ptr[0] = 0.0; x_ptr[1] = 1.0; 275 PetscCall(VecRestoreArray(lambda[1],&x_ptr)); 276 277 PetscCall(MatCreateVecs(Jacp,&mu[0],NULL)); 278 PetscCall(MatCreateVecs(Jacp,&mu[1],NULL)); 279 PetscCall(VecGetArray(mu[0],&x_ptr)); 280 x_ptr[0] = 0.0; 281 PetscCall(VecRestoreArray(mu[0],&x_ptr)); 282 PetscCall(VecGetArray(mu[1],&x_ptr)); 283 x_ptr[0] = 0.0; 284 PetscCall(VecRestoreArray(mu[1],&x_ptr)); 285 PetscCall(TSSetCostGradients(ts,2,lambda,mu)); 286 287 /* Set RHS JacobianP */ 288 PetscCall(TSSetRHSJacobianP(ts,Jacp,RHSJacobianP,&user)); 289 290 PetscCall(TSAdjointSolve(ts)); 291 292 PetscCall(VecView(lambda[0],PETSC_VIEWER_STDOUT_WORLD)); 293 PetscCall(VecView(lambda[1],PETSC_VIEWER_STDOUT_WORLD)); 294 PetscCall(VecView(mu[0],PETSC_VIEWER_STDOUT_WORLD)); 295 PetscCall(VecView(mu[1],PETSC_VIEWER_STDOUT_WORLD)); 296 297 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 298 Free work space. All PETSc objects should be destroyed when they 299 are no longer needed. 300 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 301 PetscCall(MatDestroy(&A)); 302 PetscCall(MatDestroy(&Jacp)); 303 PetscCall(VecDestroy(&x)); 304 PetscCall(VecDestroy(&lambda[0])); 305 PetscCall(VecDestroy(&lambda[1])); 306 PetscCall(VecDestroy(&mu[0])); 307 PetscCall(VecDestroy(&mu[1])); 308 PetscCall(TSDestroy(&ts)); 309 PetscCall(PetscFree(adctx)); 310 PetscCall(PetscFinalize()); 311 return 0; 312 } 313 314 /*TEST 315 316 build: 317 requires: double !complex adolc 318 319 test: 320 suffix: 1 321 args: -ts_max_steps 10 -ts_monitor -ts_adjoint_monitor 322 output_file: output/ex16adj_1.out 323 324 test: 325 suffix: 2 326 args: -ts_max_steps 10 -ts_monitor -ts_adjoint_monitor -mu 5 327 output_file: output/ex16adj_2.out 328 329 test: 330 suffix: 3 331 args: -ts_max_steps 10 -monitor 332 output_file: output/ex16adj_3.out 333 334 test: 335 suffix: 4 336 args: -ts_max_steps 10 -monitor -mu 5 337 output_file: output/ex16adj_4.out 338 339 TEST*/ 340