static char help[] = "Performs adjoint sensitivity analysis for the van der Pol equation.\n"; /* ------------------------------------------------------------------------ This program solves the van der Pol DAE ODE equivalent [ u_1' ] = [ u_2 ] (2) [ u_2' ] [ \mu ((1 - u_1^2) u_2 - u_1) ] on the domain 0 <= x <= 1, with the boundary conditions u_1(0) = 2, u_2(0) = - 2/3 +10/(81*\mu) - 292/(2187*\mu^2), and \mu = 10^6 ( y'(0) ~ -0.6666665432100101)., and computes the sensitivities of the final solution w.r.t. initial conditions and parameter \mu with the implicit theta method and its discrete adjoint. Notes: This code demonstrates the TSAdjoint interface to a DAE system. The user provides the implicit right-hand-side function [ F(u',u,t) ] = [u' - f(u,t)] = [ u_1'] - [ u_2 ] [ u_2'] [ \mu ((1-u_1^2)u_2-u_1) ] and the Jacobian of F (from the PETSc user manual) dF dF J(F) = a * -- + -- du' du and the JacobianP of the explicit right-hand side of (2) f(u,t) ( which is equivalent to -F(0,u,t)). df [ 0 ] -- = [ ] dp [ (1 - u_1^2) u_2 - u_1 ]. See ex20.c for more details on the Jacobian. ------------------------------------------------------------------------- */ #include #include typedef struct _n_User *User; struct _n_User { PetscReal mu; PetscReal next_output; /* Sensitivity analysis support */ PetscInt steps; PetscReal ftime; Mat A; /* Jacobian matrix */ Mat Jacp; /* JacobianP matrix */ Vec U,lambda[2],mup[2]; /* adjoint variables */ }; /* ----------------------- Explicit form of the ODE -------------------- */ static PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec U,Vec F,void *ctx) { User user = (User)ctx; PetscScalar *f; const PetscScalar *u; PetscFunctionBeginUser; PetscCall(VecGetArrayRead(U,&u)); PetscCall(VecGetArray(F,&f)); f[0] = u[1]; f[1] = user->mu*((1.-u[0]*u[0])*u[1]-u[0]); PetscCall(VecRestoreArrayRead(U,&u)); PetscCall(VecRestoreArray(F,&f)); PetscFunctionReturn(0); } static PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec U,Mat A,Mat B,void *ctx) { User user = (User)ctx; PetscReal mu = user->mu; PetscInt rowcol[] = {0,1}; PetscScalar J[2][2]; const PetscScalar *u; PetscFunctionBeginUser; PetscCall(VecGetArrayRead(U,&u)); J[0][0] = 0; J[1][0] = -mu*(2.0*u[1]*u[0]+1.); J[0][1] = 1.0; J[1][1] = mu*(1.0-u[0]*u[0]); PetscCall(MatSetValues(A,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES)); PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY)); PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY)); if (A != B) { PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY)); PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY)); } PetscCall(VecRestoreArrayRead(U,&u)); PetscFunctionReturn(0); } /* ----------------------- Implicit form of the ODE -------------------- */ static PetscErrorCode IFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,void *ctx) { User user = (User)ctx; const PetscScalar *u,*udot; PetscScalar *f; PetscFunctionBeginUser; PetscCall(VecGetArrayRead(U,&u)); PetscCall(VecGetArrayRead(Udot,&udot)); PetscCall(VecGetArray(F,&f)); f[0] = udot[0] - u[1]; f[1] = udot[1] - user->mu*((1.0-u[0]*u[0])*u[1] - u[0]); PetscCall(VecRestoreArrayRead(U,&u)); PetscCall(VecRestoreArrayRead(Udot,&udot)); PetscCall(VecRestoreArray(F,&f)); PetscFunctionReturn(0); } static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat A,Mat B,void *ctx) { User user = (User)ctx; PetscInt rowcol[] = {0,1}; PetscScalar J[2][2]; const PetscScalar *u; PetscFunctionBeginUser; PetscCall(VecGetArrayRead(U,&u)); J[0][0] = a; J[0][1] = -1.0; J[1][0] = user->mu*(2.0*u[0]*u[1] + 1.0); J[1][1] = a - user->mu*(1.0-u[0]*u[0]); PetscCall(MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES)); PetscCall(VecRestoreArrayRead(U,&u)); PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY)); PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY)); if (B && A != B) { PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY)); PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY)); } PetscFunctionReturn(0); } static PetscErrorCode RHSJacobianP(TS ts,PetscReal t,Vec U,Mat A,void *ctx) { PetscInt row[] = {0,1},col[]={0}; PetscScalar J[2][1]; const PetscScalar *u; PetscFunctionBeginUser; PetscCall(VecGetArrayRead(U,&u)); J[0][0] = 0; J[1][0] = (1.-u[0]*u[0])*u[1]-u[0]; PetscCall(MatSetValues(A,2,row,1,col,&J[0][0],INSERT_VALUES)); PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY)); PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY)); PetscCall(VecRestoreArrayRead(U,&u)); PetscFunctionReturn(0); } /* Monitor timesteps and use interpolation to output at integer multiples of 0.1 */ static PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal t,Vec U,void *ctx) { const PetscScalar *u; PetscReal tfinal, dt; User user = (User)ctx; Vec interpolatedU; PetscFunctionBeginUser; PetscCall(TSGetTimeStep(ts,&dt)); PetscCall(TSGetMaxTime(ts,&tfinal)); while (user->next_output <= t && user->next_output <= tfinal) { PetscCall(VecDuplicate(U,&interpolatedU)); PetscCall(TSInterpolate(ts,user->next_output,interpolatedU)); PetscCall(VecGetArrayRead(interpolatedU,&u)); PetscCall(PetscPrintf(PETSC_COMM_WORLD,"[%g] %D TS %g (dt = %g) X %g %g\n", (double)user->next_output,step,(double)t,(double)dt,(double)PetscRealPart(u[0]), (double)PetscRealPart(u[1]))); PetscCall(VecRestoreArrayRead(interpolatedU,&u)); PetscCall(VecDestroy(&interpolatedU)); user->next_output += 0.1; } PetscFunctionReturn(0); } int main(int argc,char **argv) { TS ts; PetscBool monitor = PETSC_FALSE,implicitform = PETSC_TRUE; PetscScalar *x_ptr,*y_ptr,derp; PetscMPIInt size; struct _n_User user; /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Initialize program - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(PetscInitialize(&argc,&argv,NULL,help)); PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD,&size)); PetscCheck(size == 1,PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only!"); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Set runtime options - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ user.next_output = 0.0; user.mu = 1.0e3; user.steps = 0; user.ftime = 0.5; PetscCall(PetscOptionsGetBool(NULL,NULL,"-monitor",&monitor,NULL)); PetscCall(PetscOptionsGetReal(NULL,NULL,"-mu",&user.mu,NULL)); PetscCall(PetscOptionsGetBool(NULL,NULL,"-implicitform",&implicitform,NULL)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create necessary matrix and vectors, solve same ODE on every process - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(MatCreate(PETSC_COMM_WORLD,&user.A)); PetscCall(MatSetSizes(user.A,PETSC_DECIDE,PETSC_DECIDE,2,2)); PetscCall(MatSetFromOptions(user.A)); PetscCall(MatSetUp(user.A)); PetscCall(MatCreateVecs(user.A,&user.U,NULL)); PetscCall(MatCreate(PETSC_COMM_WORLD,&user.Jacp)); PetscCall(MatSetSizes(user.Jacp,PETSC_DECIDE,PETSC_DECIDE,2,1)); PetscCall(MatSetFromOptions(user.Jacp)); PetscCall(MatSetUp(user.Jacp)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create timestepping solver context - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(TSCreate(PETSC_COMM_WORLD,&ts)); PetscCall(TSSetEquationType(ts,TS_EQ_ODE_EXPLICIT)); /* less Jacobian evaluations when adjoint BEuler is used, otherwise no effect */ if (implicitform) { PetscCall(TSSetIFunction(ts,NULL,IFunction,&user)); PetscCall(TSSetIJacobian(ts,user.A,user.A,IJacobian,&user)); PetscCall(TSSetType(ts,TSCN)); } else { PetscCall(TSSetRHSFunction(ts,NULL,RHSFunction,&user)); PetscCall(TSSetRHSJacobian(ts,user.A,user.A,RHSJacobian,&user)); PetscCall(TSSetType(ts,TSRK)); } PetscCall(TSSetRHSJacobianP(ts,user.Jacp,RHSJacobianP,&user)); PetscCall(TSSetMaxTime(ts,user.ftime)); PetscCall(TSSetTimeStep(ts,0.001)); PetscCall(TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP)); if (monitor) PetscCall(TSMonitorSet(ts,Monitor,&user,NULL)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Set initial conditions - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(VecGetArray(user.U,&x_ptr)); x_ptr[0] = 2.0; x_ptr[1] = -2.0/3.0 + 10.0/(81.0*user.mu) - 292.0/(2187.0*user.mu*user.mu); PetscCall(VecRestoreArray(user.U,&x_ptr)); PetscCall(TSSetTimeStep(ts,0.001)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Save trajectory of solution so that TSAdjointSolve() may be used - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(TSSetSaveTrajectory(ts)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Set runtime options - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(TSSetFromOptions(ts)); PetscCall(TSSolve(ts,user.U)); PetscCall(TSGetSolveTime(ts,&user.ftime)); PetscCall(TSGetStepNumber(ts,&user.steps)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Adjoint model starts here - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(MatCreateVecs(user.A,&user.lambda[0],NULL)); /* Set initial conditions for the adjoint integration */ PetscCall(VecGetArray(user.lambda[0],&y_ptr)); y_ptr[0] = 1.0; y_ptr[1] = 0.0; PetscCall(VecRestoreArray(user.lambda[0],&y_ptr)); PetscCall(MatCreateVecs(user.A,&user.lambda[1],NULL)); PetscCall(VecGetArray(user.lambda[1],&y_ptr)); y_ptr[0] = 0.0; y_ptr[1] = 1.0; PetscCall(VecRestoreArray(user.lambda[1],&y_ptr)); PetscCall(MatCreateVecs(user.Jacp,&user.mup[0],NULL)); PetscCall(VecGetArray(user.mup[0],&x_ptr)); x_ptr[0] = 0.0; PetscCall(VecRestoreArray(user.mup[0],&x_ptr)); PetscCall(MatCreateVecs(user.Jacp,&user.mup[1],NULL)); PetscCall(VecGetArray(user.mup[1],&x_ptr)); x_ptr[0] = 0.0; PetscCall(VecRestoreArray(user.mup[1],&x_ptr)); PetscCall(TSSetCostGradients(ts,2,user.lambda,user.mup)); PetscCall(TSAdjointSolve(ts)); PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n sensitivity wrt initial conditions: d[y(tf)]/d[y0] d[y(tf)]/d[z0]\n")); PetscCall(VecView(user.lambda[0],PETSC_VIEWER_STDOUT_WORLD)); PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n sensitivity wrt initial conditions: d[z(tf)]/d[y0] d[z(tf)]/d[z0]\n")); PetscCall(VecView(user.lambda[1],PETSC_VIEWER_STDOUT_WORLD)); PetscCall(VecGetArray(user.mup[0],&x_ptr)); PetscCall(VecGetArray(user.lambda[0],&y_ptr)); derp = y_ptr[1]*(-10.0/(81.0*user.mu*user.mu)+2.0*292.0/(2187.0*user.mu*user.mu*user.mu))+x_ptr[0]; PetscCall(VecRestoreArray(user.mup[0],&x_ptr)); PetscCall(VecRestoreArray(user.lambda[0],&y_ptr)); PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n sensitivity wrt parameters: d[y(tf)]/d[mu]\n%g\n",(double)PetscRealPart(derp))); PetscCall(VecGetArray(user.mup[1],&x_ptr)); PetscCall(VecGetArray(user.lambda[1],&y_ptr)); derp = y_ptr[1]*(-10.0/(81.0*user.mu*user.mu)+2.0*292.0/(2187.0*user.mu*user.mu*user.mu))+x_ptr[0]; PetscCall(VecRestoreArray(user.mup[1],&x_ptr)); PetscCall(VecRestoreArray(user.lambda[1],&y_ptr)); PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n sensivitity wrt parameters: d[z(tf)]/d[mu]\n%g\n",(double)PetscRealPart(derp))); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Free work space. All PETSc objects should be destroyed when they are no longer needed. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(MatDestroy(&user.A)); PetscCall(MatDestroy(&user.Jacp)); PetscCall(VecDestroy(&user.U)); PetscCall(VecDestroy(&user.lambda[0])); PetscCall(VecDestroy(&user.lambda[1])); PetscCall(VecDestroy(&user.mup[0])); PetscCall(VecDestroy(&user.mup[1])); PetscCall(TSDestroy(&ts)); PetscCall(PetscFinalize()); return 0; } /*TEST test: requires: revolve args: -monitor 0 -ts_type theta -ts_theta_endpoint -ts_theta_theta 0.5 -viewer_binary_skip_info -ts_dt 0.001 -mu 100000 test: suffix: 2 args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_solution_only test: suffix: 3 args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_solution_only 0 output_file: output/ex20adj_2.out test: suffix: 4 args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_stride 5 -ts_trajectory_solution_only -ts_trajectory_save_stack output_file: output/ex20adj_2.out test: suffix: 5 args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_stride 5 -ts_trajectory_solution_only 0 -ts_trajectory_save_stack output_file: output/ex20adj_2.out test: suffix: 6 args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_stride 5 -ts_trajectory_solution_only -ts_trajectory_save_stack 0 output_file: output/ex20adj_2.out test: suffix: 7 args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_stride 5 -ts_trajectory_solution_only 0 -ts_trajectory_save_stack 0 output_file: output/ex20adj_2.out test: suffix: 8 requires: revolve !cams args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_cps_ram 5 -ts_trajectory_solution_only -ts_trajectory_monitor output_file: output/ex20adj_3.out test: suffix: 9 requires: revolve !cams args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_cps_ram 5 -ts_trajectory_solution_only 0 -ts_trajectory_monitor output_file: output/ex20adj_4.out test: requires: revolve suffix: 10 args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_cps_ram 5 -ts_trajectory_revolve_online -ts_trajectory_solution_only output_file: output/ex20adj_2.out test: requires: revolve suffix: 11 args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_cps_ram 5 -ts_trajectory_revolve_online -ts_trajectory_solution_only 0 output_file: output/ex20adj_2.out test: suffix: 12 requires: revolve args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_cps_ram 3 -ts_trajectory_max_cps_disk 8 -ts_trajectory_solution_only output_file: output/ex20adj_2.out test: suffix: 13 requires: revolve args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_cps_ram 3 -ts_trajectory_max_cps_disk 8 -ts_trajectory_solution_only 0 output_file: output/ex20adj_2.out test: suffix: 14 requires: revolve args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_cps_ram 3 -ts_trajectory_stride 5 -ts_trajectory_solution_only -ts_trajectory_save_stack output_file: output/ex20adj_2.out test: suffix: 15 requires: revolve args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_cps_ram 3 -ts_trajectory_stride 5 -ts_trajectory_solution_only -ts_trajectory_save_stack 0 output_file: output/ex20adj_2.out test: suffix: 16 requires: revolve args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_cps_ram 3 -ts_trajectory_stride 5 -ts_trajectory_solution_only 0 -ts_trajectory_save_stack output_file: output/ex20adj_2.out test: suffix: 17 requires: revolve args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_cps_ram 3 -ts_trajectory_stride 5 -ts_trajectory_solution_only 0 -ts_trajectory_save_stack 0 output_file: output/ex20adj_2.out test: suffix: 18 requires: revolve args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_cps_ram 3 -ts_trajectory_max_cps_disk 8 -ts_trajectory_stride 5 -ts_trajectory_solution_only -ts_trajectory_save_stack output_file: output/ex20adj_2.out test: suffix: 19 requires: revolve args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_cps_ram 3 -ts_trajectory_max_cps_disk 8 -ts_trajectory_stride 5 -ts_trajectory_solution_only 0 -ts_trajectory_save_stack output_file: output/ex20adj_2.out test: suffix: 20 requires: revolve args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_cps_ram 3 -ts_trajectory_max_cps_disk 8 -ts_trajectory_solution_only 0 output_file: output/ex20adj_2.out test: suffix: 21 requires: revolve args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_cps_ram 3 -ts_trajectory_max_cps_disk 8 -ts_trajectory_stride 5 -ts_trajectory_solution_only 0 -ts_trajectory_save_stack 0 output_file: output/ex20adj_2.out test: suffix: 22 args: -ts_type beuler -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_solution_only output_file: output/ex20adj_2.out test: suffix: 23 requires: cams args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_units_ram 5 -ts_trajectory_solution_only -ts_trajectory_monitor -ts_trajectory_memory_type cams output_file: output/ex20adj_5.out test: suffix: 24 requires: cams args: -ts_type cn -ts_dt 0.001 -mu 100000 -ts_max_steps 15 -ts_trajectory_type memory -ts_trajectory_max_units_ram 5 -ts_trajectory_solution_only 0 -ts_trajectory_monitor -ts_trajectory_memory_type cams output_file: output/ex20adj_6.out TEST*/