1 static char help[] = "Demonstrates tapeless 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 18 #define ADOLC_TAPELESS 19 #define NUMBER_DIRECTIONS 3 20 #include "adolc-utils/drivers.cxx" 21 #include <adolc/adtl.h> 22 using namespace adtl; 23 24 typedef struct _n_User *User; 25 struct _n_User { 26 PetscReal mu; 27 PetscReal next_output; 28 PetscReal tprev; 29 30 /* Automatic differentiation support */ 31 AdolcCtx *adctx; 32 Vec F; 33 }; 34 35 /* 36 Residual evaluation templated, so as to allow for PetscScalar or adouble 37 arguments. 38 */ 39 template <class T> PetscErrorCode EvaluateResidual(const T *x,T mu,T *f) 40 { 41 PetscFunctionBegin; 42 f[0] = x[1]; 43 f[1] = mu*(1.-x[0]*x[0])*x[1]-x[0]; 44 PetscFunctionReturn(0); 45 } 46 47 /* 48 'Passive' RHS function, used in residual evaluations during the time integration. 49 */ 50 static PetscErrorCode RHSFunctionPassive(TS ts,PetscReal t,Vec X,Vec F,void *ctx) 51 { 52 User user = (User)ctx; 53 PetscScalar *f; 54 const PetscScalar *x; 55 56 PetscFunctionBeginUser; 57 PetscCall(VecGetArrayRead(X,&x)); 58 PetscCall(VecGetArray(F,&f)); 59 PetscCall(EvaluateResidual(x,user->mu,f)); 60 PetscCall(VecRestoreArrayRead(X,&x)); 61 PetscCall(VecRestoreArray(F,&f)); 62 PetscFunctionReturn(0); 63 } 64 65 /* 66 Compute the Jacobian w.r.t. x using tapeless mode of ADOL-C. 67 */ 68 static PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec X,Mat A,Mat B,void *ctx) 69 { 70 User user = (User)ctx; 71 PetscScalar **J; 72 const PetscScalar *x; 73 adouble f_a[2]; /* 'active' double for dependent variables */ 74 adouble x_a[2],mu_a; /* 'active' doubles for independent variables */ 75 PetscInt i,j; 76 77 PetscFunctionBeginUser; 78 /* Set values for independent variables and parameters */ 79 PetscCall(VecGetArrayRead(X,&x)); 80 x_a[0].setValue(x[0]); 81 x_a[1].setValue(x[1]); 82 mu_a.setValue(user->mu); 83 PetscCall(VecRestoreArrayRead(X,&x)); 84 85 /* Set seed matrix as 3x3 identity matrix */ 86 x_a[0].setADValue(0,1.);x_a[0].setADValue(1,0.);x_a[0].setADValue(2,0.); 87 x_a[1].setADValue(0,0.);x_a[1].setADValue(1,1.);x_a[1].setADValue(2,0.); 88 mu_a.setADValue(0,0.);mu_a.setADValue(1,0.);mu_a.setADValue(2,1.); 89 90 /* Evaluate residual (on active variables) */ 91 PetscCall(EvaluateResidual(x_a,mu_a,f_a)); 92 93 /* Extract derivatives */ 94 PetscCall(PetscMalloc1(user->adctx->n,&J)); 95 J[0] = (PetscScalar*) f_a[0].getADValue(); 96 J[1] = (PetscScalar*) f_a[1].getADValue(); 97 98 /* Set matrix values */ 99 for (i=0; i<user->adctx->m; i++) { 100 for (j=0; j<user->adctx->n; j++) { 101 PetscCall(MatSetValues(A,1,&i,1,&j,&J[i][j],INSERT_VALUES)); 102 } 103 } 104 PetscCall(PetscFree(J)); 105 PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY)); 106 PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY)); 107 if (A != B) { 108 PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY)); 109 PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY)); 110 } 111 PetscFunctionReturn(0); 112 } 113 114 /* 115 Compute the Jacobian w.r.t. mu using tapeless mode of ADOL-C. 116 */ 117 static PetscErrorCode RHSJacobianP(TS ts,PetscReal t,Vec X,Mat A,void *ctx) 118 { 119 User user = (User)ctx; 120 PetscScalar **J; 121 PetscScalar *x; 122 adouble f_a[2]; /* 'active' double for dependent variables */ 123 adouble x_a[2],mu_a; /* 'active' doubles for independent variables */ 124 PetscInt i,j = 0; 125 126 PetscFunctionBeginUser; 127 128 /* Set values for independent variables and parameters */ 129 PetscCall(VecGetArray(X,&x)); 130 x_a[0].setValue(x[0]); 131 x_a[1].setValue(x[1]); 132 mu_a.setValue(user->mu); 133 PetscCall(VecRestoreArray(X,&x)); 134 135 /* Set seed matrix as 3x3 identity matrix */ 136 x_a[0].setADValue(0,1.);x_a[0].setADValue(1,0.);x_a[0].setADValue(2,0.); 137 x_a[1].setADValue(0,0.);x_a[1].setADValue(1,1.);x_a[1].setADValue(2,0.); 138 mu_a.setADValue(0,0.);mu_a.setADValue(1,0.);mu_a.setADValue(2,1.); 139 140 /* Evaluate residual (on active variables) */ 141 PetscCall(EvaluateResidual(x_a,mu_a,f_a)); 142 143 /* Extract derivatives */ 144 PetscCall(PetscMalloc1(2,&J)); 145 J[0] = (PetscScalar*) f_a[0].getADValue(); 146 J[1] = (PetscScalar*) f_a[1].getADValue(); 147 148 /* Set matrix values */ 149 for (i=0; i<user->adctx->m; i++) { 150 PetscCall(MatSetValues(A,1,&i,1,&j,&J[i][user->adctx->n],INSERT_VALUES)); 151 } 152 PetscCall(PetscFree(J)); 153 PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY)); 154 PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY)); 155 PetscFunctionReturn(0); 156 } 157 158 /* 159 Monitor timesteps and use interpolation to output at integer multiples of 0.1 160 */ 161 static PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal t,Vec X,void *ctx) 162 { 163 const PetscScalar *x; 164 PetscReal tfinal, dt, tprev; 165 User user = (User)ctx; 166 167 PetscFunctionBeginUser; 168 PetscCall(TSGetTimeStep(ts,&dt)); 169 PetscCall(TSGetMaxTime(ts,&tfinal)); 170 PetscCall(TSGetPrevTime(ts,&tprev)); 171 PetscCall(VecGetArrayRead(X,&x)); 172 PetscCall(PetscPrintf(PETSC_COMM_WORLD,"[%.1f] %D 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]))); 173 PetscCall(PetscPrintf(PETSC_COMM_WORLD,"t %.6f (tprev = %.6f) \n",(double)t,(double)tprev)); 174 PetscCall(VecRestoreArrayRead(X,&x)); 175 PetscFunctionReturn(0); 176 } 177 178 int main(int argc,char **argv) 179 { 180 TS ts; /* nonlinear solver */ 181 Vec x; /* solution, residual vectors */ 182 Mat A; /* Jacobian matrix */ 183 Mat Jacp; /* JacobianP matrix */ 184 PetscInt steps; 185 PetscReal ftime = 0.5; 186 PetscBool monitor = PETSC_FALSE; 187 PetscScalar *x_ptr; 188 PetscMPIInt size; 189 struct _n_User user; 190 AdolcCtx *adctx; 191 Vec lambda[2],mu[2]; 192 193 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 194 Initialize program 195 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 196 PetscCall(PetscInitialize(&argc,&argv,NULL,help)); 197 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD,&size)); 198 PetscCheckFalse(size != 1,PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only!"); 199 200 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 201 Set runtime options and create AdolcCtx 202 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 203 PetscCall(PetscNew(&adctx)); 204 user.mu = 1; 205 user.next_output = 0.0; 206 adctx->m = 2;adctx->n = 2;adctx->p = 2; 207 user.adctx = adctx; 208 adtl::setNumDir(adctx->n+1); /* #indep. variables, plus parameters */ 209 210 PetscCall(PetscOptionsGetReal(NULL,NULL,"-mu",&user.mu,NULL)); 211 PetscCall(PetscOptionsGetBool(NULL,NULL,"-monitor",&monitor,NULL)); 212 213 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 214 Create necessary matrix and vectors, solve same ODE on every process 215 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 216 PetscCall(MatCreate(PETSC_COMM_WORLD,&A)); 217 PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,2,2)); 218 PetscCall(MatSetFromOptions(A)); 219 PetscCall(MatSetUp(A)); 220 PetscCall(MatCreateVecs(A,&x,NULL)); 221 222 PetscCall(MatCreate(PETSC_COMM_WORLD,&Jacp)); 223 PetscCall(MatSetSizes(Jacp,PETSC_DECIDE,PETSC_DECIDE,2,1)); 224 PetscCall(MatSetFromOptions(Jacp)); 225 PetscCall(MatSetUp(Jacp)); 226 227 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 228 Create timestepping solver context 229 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 230 PetscCall(TSCreate(PETSC_COMM_WORLD,&ts)); 231 PetscCall(TSSetType(ts,TSRK)); 232 PetscCall(TSSetRHSFunction(ts,NULL,RHSFunctionPassive,&user)); 233 234 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 235 Set initial conditions 236 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 237 PetscCall(VecGetArray(x,&x_ptr)); 238 x_ptr[0] = 2; x_ptr[1] = 0.66666654321; 239 PetscCall(VecRestoreArray(x,&x_ptr)); 240 241 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 242 Set RHS Jacobian for the adjoint integration 243 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 244 PetscCall(TSSetRHSJacobian(ts,A,A,RHSJacobian,&user)); 245 PetscCall(TSSetMaxTime(ts,ftime)); 246 PetscCall(TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP)); 247 if (monitor) { 248 PetscCall(TSMonitorSet(ts,Monitor,&user,NULL)); 249 } 250 PetscCall(TSSetTimeStep(ts,.001)); 251 252 /* 253 Have the TS save its trajectory so that TSAdjointSolve() may be used 254 */ 255 PetscCall(TSSetSaveTrajectory(ts)); 256 257 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 258 Set runtime options 259 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 260 PetscCall(TSSetFromOptions(ts)); 261 262 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 263 Solve nonlinear system 264 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 265 PetscCall(TSSolve(ts,x)); 266 PetscCall(TSGetSolveTime(ts,&ftime)); 267 PetscCall(TSGetStepNumber(ts,&steps)); 268 PetscCall(PetscPrintf(PETSC_COMM_WORLD,"mu %g, steps %D, ftime %g\n",(double)user.mu,steps,(double)ftime)); 269 PetscCall(VecView(x,PETSC_VIEWER_STDOUT_WORLD)); 270 271 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 272 Start the Adjoint model 273 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 274 PetscCall(MatCreateVecs(A,&lambda[0],NULL)); 275 PetscCall(MatCreateVecs(A,&lambda[1],NULL)); 276 /* Reset initial conditions for the adjoint integration */ 277 PetscCall(VecGetArray(lambda[0],&x_ptr)); 278 x_ptr[0] = 1.0; x_ptr[1] = 0.0; 279 PetscCall(VecRestoreArray(lambda[0],&x_ptr)); 280 PetscCall(VecGetArray(lambda[1],&x_ptr)); 281 x_ptr[0] = 0.0; x_ptr[1] = 1.0; 282 PetscCall(VecRestoreArray(lambda[1],&x_ptr)); 283 284 PetscCall(MatCreateVecs(Jacp,&mu[0],NULL)); 285 PetscCall(MatCreateVecs(Jacp,&mu[1],NULL)); 286 PetscCall(VecGetArray(mu[0],&x_ptr)); 287 x_ptr[0] = 0.0; 288 PetscCall(VecRestoreArray(mu[0],&x_ptr)); 289 PetscCall(VecGetArray(mu[1],&x_ptr)); 290 x_ptr[0] = 0.0; 291 PetscCall(VecRestoreArray(mu[1],&x_ptr)); 292 PetscCall(TSSetCostGradients(ts,2,lambda,mu)); 293 294 /* Set RHS JacobianP */ 295 PetscCall(TSSetRHSJacobianP(ts,Jacp,RHSJacobianP,&user)); 296 297 PetscCall(TSAdjointSolve(ts)); 298 299 PetscCall(VecView(lambda[0],PETSC_VIEWER_STDOUT_WORLD)); 300 PetscCall(VecView(lambda[1],PETSC_VIEWER_STDOUT_WORLD)); 301 PetscCall(VecView(mu[0],PETSC_VIEWER_STDOUT_WORLD)); 302 PetscCall(VecView(mu[1],PETSC_VIEWER_STDOUT_WORLD)); 303 304 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 305 Free work space. All PETSc objects should be destroyed when they 306 are no longer needed. 307 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 308 PetscCall(MatDestroy(&A)); 309 PetscCall(MatDestroy(&Jacp)); 310 PetscCall(VecDestroy(&x)); 311 PetscCall(VecDestroy(&lambda[0])); 312 PetscCall(VecDestroy(&lambda[1])); 313 PetscCall(VecDestroy(&mu[0])); 314 PetscCall(VecDestroy(&mu[1])); 315 PetscCall(TSDestroy(&ts)); 316 PetscCall(PetscFree(adctx)); 317 PetscCall(PetscFinalize()); 318 return 0; 319 } 320 321 /*TEST 322 323 build: 324 requires: double !complex adolc 325 326 test: 327 suffix: 1 328 args: -ts_max_steps 10 -ts_monitor -ts_adjoint_monitor 329 output_file: output/ex16adj_tl_1.out 330 331 test: 332 suffix: 2 333 args: -ts_max_steps 10 -ts_monitor -ts_adjoint_monitor -mu 5 334 output_file: output/ex16adj_tl_2.out 335 336 test: 337 suffix: 3 338 args: -ts_max_steps 10 -monitor 339 output_file: output/ex16adj_tl_3.out 340 341 test: 342 suffix: 4 343 args: -ts_max_steps 10 -monitor -mu 5 344 output_file: output/ex16adj_tl_4.out 345 346 TEST*/ 347