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] %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]))); 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 PetscCall(PetscInitialize(&argc,&argv,NULL,help)); 180 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD,&size)); 181 PetscCheckFalse(size != 1,PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only!"); 182 183 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 184 Set runtime options and create AdolcCtx 185 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 186 PetscCall(PetscNew(&adctx)); 187 user.mu = 1; 188 user.next_output = 0.0; 189 adctx->m = 2;adctx->n = 2;adctx->p = 2;adctx->num_params = 1; 190 user.adctx = adctx; 191 192 PetscCall(PetscOptionsGetReal(NULL,NULL,"-mu",&user.mu,NULL)); 193 PetscCall(PetscOptionsGetBool(NULL,NULL,"-monitor",&monitor,NULL)); 194 195 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 196 Create necessary matrix and vectors, solve same ODE on every process 197 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 198 PetscCall(MatCreate(PETSC_COMM_WORLD,&A)); 199 PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,2,2)); 200 PetscCall(MatSetFromOptions(A)); 201 PetscCall(MatSetUp(A)); 202 PetscCall(MatCreateVecs(A,&x,NULL)); 203 204 PetscCall(MatCreate(PETSC_COMM_WORLD,&Jacp)); 205 PetscCall(MatSetSizes(Jacp,PETSC_DECIDE,PETSC_DECIDE,2,1)); 206 PetscCall(MatSetFromOptions(Jacp)); 207 PetscCall(MatSetUp(Jacp)); 208 209 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 210 Create timestepping solver context 211 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 212 PetscCall(TSCreate(PETSC_COMM_WORLD,&ts)); 213 PetscCall(TSSetType(ts,TSRK)); 214 PetscCall(TSSetRHSFunction(ts,NULL,RHSFunctionPassive,&user)); 215 216 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 217 Set initial conditions 218 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 219 PetscCall(VecGetArray(x,&x_ptr)); 220 x_ptr[0] = 2; x_ptr[1] = 0.66666654321; 221 PetscCall(VecRestoreArray(x,&x_ptr)); 222 223 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 224 Trace just once on each tape and put zeros on Jacobian diagonal 225 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 226 PetscCall(VecDuplicate(x,&r)); 227 PetscCall(RHSFunctionActive(ts,0.,x,r,&user)); 228 PetscCall(RHSFunctionActiveP(ts,0.,x,r,&user)); 229 PetscCall(VecSet(r,0)); 230 PetscCall(MatDiagonalSet(A,r,INSERT_VALUES)); 231 PetscCall(VecDestroy(&r)); 232 233 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 234 Set RHS Jacobian for the adjoint integration 235 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 236 PetscCall(TSSetRHSJacobian(ts,A,A,RHSJacobian,&user)); 237 PetscCall(TSSetMaxTime(ts,ftime)); 238 PetscCall(TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP)); 239 if (monitor) { 240 PetscCall(TSMonitorSet(ts,Monitor,&user,NULL)); 241 } 242 PetscCall(TSSetTimeStep(ts,.001)); 243 244 /* 245 Have the TS save its trajectory so that TSAdjointSolve() may be used 246 */ 247 PetscCall(TSSetSaveTrajectory(ts)); 248 249 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 250 Set runtime options 251 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 252 PetscCall(TSSetFromOptions(ts)); 253 254 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 255 Solve nonlinear system 256 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 257 PetscCall(TSSolve(ts,x)); 258 PetscCall(TSGetSolveTime(ts,&ftime)); 259 PetscCall(TSGetStepNumber(ts,&steps)); 260 PetscCall(PetscPrintf(PETSC_COMM_WORLD,"mu %g, steps %D, ftime %g\n",(double)user.mu,steps,(double)ftime)); 261 PetscCall(VecView(x,PETSC_VIEWER_STDOUT_WORLD)); 262 263 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 264 Start the Adjoint model 265 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 266 PetscCall(MatCreateVecs(A,&lambda[0],NULL)); 267 PetscCall(MatCreateVecs(A,&lambda[1],NULL)); 268 /* Reset initial conditions for the adjoint integration */ 269 PetscCall(VecGetArray(lambda[0],&x_ptr)); 270 x_ptr[0] = 1.0; x_ptr[1] = 0.0; 271 PetscCall(VecRestoreArray(lambda[0],&x_ptr)); 272 PetscCall(VecGetArray(lambda[1],&x_ptr)); 273 x_ptr[0] = 0.0; x_ptr[1] = 1.0; 274 PetscCall(VecRestoreArray(lambda[1],&x_ptr)); 275 276 PetscCall(MatCreateVecs(Jacp,&mu[0],NULL)); 277 PetscCall(MatCreateVecs(Jacp,&mu[1],NULL)); 278 PetscCall(VecGetArray(mu[0],&x_ptr)); 279 x_ptr[0] = 0.0; 280 PetscCall(VecRestoreArray(mu[0],&x_ptr)); 281 PetscCall(VecGetArray(mu[1],&x_ptr)); 282 x_ptr[0] = 0.0; 283 PetscCall(VecRestoreArray(mu[1],&x_ptr)); 284 PetscCall(TSSetCostGradients(ts,2,lambda,mu)); 285 286 /* Set RHS JacobianP */ 287 PetscCall(TSSetRHSJacobianP(ts,Jacp,RHSJacobianP,&user)); 288 289 PetscCall(TSAdjointSolve(ts)); 290 291 PetscCall(VecView(lambda[0],PETSC_VIEWER_STDOUT_WORLD)); 292 PetscCall(VecView(lambda[1],PETSC_VIEWER_STDOUT_WORLD)); 293 PetscCall(VecView(mu[0],PETSC_VIEWER_STDOUT_WORLD)); 294 PetscCall(VecView(mu[1],PETSC_VIEWER_STDOUT_WORLD)); 295 296 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 297 Free work space. All PETSc objects should be destroyed when they 298 are no longer needed. 299 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 300 PetscCall(MatDestroy(&A)); 301 PetscCall(MatDestroy(&Jacp)); 302 PetscCall(VecDestroy(&x)); 303 PetscCall(VecDestroy(&lambda[0])); 304 PetscCall(VecDestroy(&lambda[1])); 305 PetscCall(VecDestroy(&mu[0])); 306 PetscCall(VecDestroy(&mu[1])); 307 PetscCall(TSDestroy(&ts)); 308 PetscCall(PetscFree(adctx)); 309 PetscCall(PetscFinalize()); 310 return 0; 311 } 312 313 /*TEST 314 315 build: 316 requires: double !complex adolc 317 318 test: 319 suffix: 1 320 args: -ts_max_steps 10 -ts_monitor -ts_adjoint_monitor 321 output_file: output/ex16adj_1.out 322 323 test: 324 suffix: 2 325 args: -ts_max_steps 10 -ts_monitor -ts_adjoint_monitor -mu 5 326 output_file: output/ex16adj_2.out 327 328 test: 329 suffix: 3 330 args: -ts_max_steps 10 -monitor 331 output_file: output/ex16adj_3.out 332 333 test: 334 suffix: 4 335 args: -ts_max_steps 10 -monitor -mu 5 336 output_file: output/ex16adj_4.out 337 338 TEST*/ 339