1 static char help[] = "A toy example for testing forward and adjoint sensitivity analysis of an implicit ODE with a parametrized mass matrice.\n"; 2 3 /* 4 This example solves the simple ODE 5 c x' = b x, x(0) = a, 6 whose analytical solution is x(T)=a*exp(b/c*T), and calculates the derivative of x(T) w.r.t. c (by default) or w.r.t. b (can be enabled with command line option -der 2). 7 8 */ 9 10 #include <petscts.h> 11 12 typedef struct _n_User *User; 13 struct _n_User { 14 PetscReal a; 15 PetscReal b; 16 PetscReal c; 17 /* Sensitivity analysis support */ 18 PetscInt steps; 19 PetscReal ftime; 20 Mat Jac; /* Jacobian matrix */ 21 Mat Jacp; /* JacobianP matrix */ 22 Vec x; 23 Mat sp; /* forward sensitivity variables */ 24 Vec lambda[1]; /* adjoint sensitivity variables */ 25 Vec mup[1]; /* adjoint sensitivity variables */ 26 PetscInt der; 27 }; 28 29 static PetscErrorCode IFunction(TS ts, PetscReal t, Vec X, Vec Xdot, Vec F, PetscCtx ctx) 30 { 31 User user = (User)ctx; 32 const PetscScalar *x, *xdot; 33 PetscScalar *f; 34 35 PetscFunctionBeginUser; 36 PetscCall(VecGetArrayRead(X, &x)); 37 PetscCall(VecGetArrayRead(Xdot, &xdot)); 38 PetscCall(VecGetArrayWrite(F, &f)); 39 f[0] = user->c * xdot[0] - user->b * x[0]; 40 PetscCall(VecRestoreArrayRead(X, &x)); 41 PetscCall(VecRestoreArrayRead(Xdot, &xdot)); 42 PetscCall(VecRestoreArrayWrite(F, &f)); 43 PetscFunctionReturn(PETSC_SUCCESS); 44 } 45 46 static PetscErrorCode IJacobian(TS ts, PetscReal t, Vec X, Vec Xdot, PetscReal a, Mat A, Mat B, PetscCtx ctx) 47 { 48 User user = (User)ctx; 49 PetscInt rowcol[] = {0}; 50 PetscScalar J[1][1]; 51 const PetscScalar *x; 52 53 PetscFunctionBeginUser; 54 PetscCall(VecGetArrayRead(X, &x)); 55 J[0][0] = user->c * a - user->b * 1.0; 56 PetscCall(MatSetValues(B, 1, rowcol, 1, rowcol, &J[0][0], INSERT_VALUES)); 57 PetscCall(VecRestoreArrayRead(X, &x)); 58 59 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY)); 60 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY)); 61 if (A != B) { 62 PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY)); 63 PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY)); 64 } 65 PetscFunctionReturn(PETSC_SUCCESS); 66 } 67 68 static PetscErrorCode IJacobianP(TS ts, PetscReal t, Vec X, Vec Xdot, PetscReal shift, Mat A, PetscCtx ctx) 69 { 70 User user = (User)ctx; 71 PetscInt row[] = {0}, col[] = {0}; 72 PetscScalar J[1][1]; 73 const PetscScalar *x, *xdot; 74 PetscReal dt; 75 76 PetscFunctionBeginUser; 77 PetscCall(VecGetArrayRead(X, &x)); 78 PetscCall(VecGetArrayRead(Xdot, &xdot)); 79 PetscCall(TSGetTimeStep(ts, &dt)); 80 if (user->der == 1) J[0][0] = xdot[0]; 81 if (user->der == 2) J[0][0] = -x[0]; 82 PetscCall(MatSetValues(A, 1, row, 1, col, &J[0][0], INSERT_VALUES)); 83 PetscCall(VecRestoreArrayRead(X, &x)); 84 85 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY)); 86 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY)); 87 PetscFunctionReturn(PETSC_SUCCESS); 88 } 89 90 int main(int argc, char **argv) 91 { 92 TS ts; 93 PetscScalar *x_ptr; 94 PetscMPIInt size; 95 struct _n_User user; 96 PetscInt rows, cols; 97 98 PetscFunctionBeginUser; 99 PetscCall(PetscInitialize(&argc, &argv, NULL, help)); 100 101 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); 102 PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!"); 103 104 user.a = 2.0; 105 user.b = 4.0; 106 user.c = 3.0; 107 user.steps = 0; 108 user.ftime = 1.0; 109 user.der = 1; 110 PetscCall(PetscOptionsGetInt(NULL, NULL, "-der", &user.der, NULL)); 111 112 rows = 1; 113 cols = 1; 114 PetscCall(MatCreate(PETSC_COMM_WORLD, &user.Jac)); 115 PetscCall(MatSetSizes(user.Jac, PETSC_DECIDE, PETSC_DECIDE, 1, 1)); 116 PetscCall(MatSetFromOptions(user.Jac)); 117 PetscCall(MatSetUp(user.Jac)); 118 PetscCall(MatCreateVecs(user.Jac, &user.x, NULL)); 119 120 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 121 PetscCall(TSSetType(ts, TSBEULER)); 122 PetscCall(TSSetIFunction(ts, NULL, IFunction, &user)); 123 PetscCall(TSSetIJacobian(ts, user.Jac, user.Jac, IJacobian, &user)); 124 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP)); 125 PetscCall(TSSetMaxTime(ts, user.ftime)); 126 127 PetscCall(VecGetArrayWrite(user.x, &x_ptr)); 128 x_ptr[0] = user.a; 129 PetscCall(VecRestoreArrayWrite(user.x, &x_ptr)); 130 PetscCall(TSSetTimeStep(ts, 0.001)); 131 132 /* Set up forward sensitivity */ 133 PetscCall(MatCreate(PETSC_COMM_WORLD, &user.Jacp)); 134 PetscCall(MatSetSizes(user.Jacp, PETSC_DECIDE, PETSC_DECIDE, rows, cols)); 135 PetscCall(MatSetFromOptions(user.Jacp)); 136 PetscCall(MatSetUp(user.Jacp)); 137 PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, rows, cols, NULL, &user.sp)); 138 PetscCall(MatZeroEntries(user.sp)); 139 PetscCall(TSForwardSetSensitivities(ts, cols, user.sp)); 140 PetscCall(TSSetIJacobianP(ts, user.Jacp, IJacobianP, &user)); 141 142 PetscCall(TSSetSaveTrajectory(ts)); 143 PetscCall(TSSetFromOptions(ts)); 144 145 PetscCall(TSSolve(ts, user.x)); 146 PetscCall(TSGetSolveTime(ts, &user.ftime)); 147 PetscCall(TSGetStepNumber(ts, &user.steps)); 148 PetscCall(VecGetArray(user.x, &x_ptr)); 149 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n ode solution %g\n", (double)PetscRealPart(x_ptr[0]))); 150 PetscCall(VecRestoreArray(user.x, &x_ptr)); 151 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n analytical solution %g\n", (double)(user.a * PetscExpReal(user.b / user.c * user.ftime)))); 152 153 if (user.der == 1) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n analytical derivative w.r.t. c %g\n", (double)(-user.a * user.ftime * user.b / (user.c * user.c) * PetscExpReal(user.b / user.c * user.ftime)))); 154 if (user.der == 2) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n analytical derivative w.r.t. b %g\n", (double)(user.a * user.ftime / user.c * PetscExpReal(user.b / user.c * user.ftime)))); 155 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n forward sensitivity:\n")); 156 PetscCall(MatView(user.sp, PETSC_VIEWER_STDOUT_WORLD)); 157 158 PetscCall(MatCreateVecs(user.Jac, &user.lambda[0], NULL)); 159 /* Set initial conditions for the adjoint integration */ 160 PetscCall(VecGetArrayWrite(user.lambda[0], &x_ptr)); 161 x_ptr[0] = 1.0; 162 PetscCall(VecRestoreArrayWrite(user.lambda[0], &x_ptr)); 163 PetscCall(MatCreateVecs(user.Jacp, &user.mup[0], NULL)); 164 PetscCall(VecGetArrayWrite(user.mup[0], &x_ptr)); 165 x_ptr[0] = 0.0; 166 PetscCall(VecRestoreArrayWrite(user.mup[0], &x_ptr)); 167 168 PetscCall(TSSetCostGradients(ts, 1, user.lambda, user.mup)); 169 PetscCall(TSAdjointSolve(ts)); 170 171 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\n adjoint sensitivity:\n")); 172 PetscCall(VecView(user.mup[0], PETSC_VIEWER_STDOUT_WORLD)); 173 174 PetscCall(MatDestroy(&user.Jac)); 175 PetscCall(MatDestroy(&user.sp)); 176 PetscCall(MatDestroy(&user.Jacp)); 177 PetscCall(VecDestroy(&user.x)); 178 PetscCall(VecDestroy(&user.lambda[0])); 179 PetscCall(VecDestroy(&user.mup[0])); 180 PetscCall(TSDestroy(&ts)); 181 182 PetscCall(PetscFinalize()); 183 return 0; 184 } 185 186 /*TEST 187 188 test: 189 args: -ts_type beuler 190 191 test: 192 suffix: 2 193 args: -ts_type cn 194 output_file: output/ex23fwdadj_1.out 195 196 TEST*/ 197