1 2 static char help[] = "Newton's method to solve a two-variable system that comes from the Rosenbrock function.\n\n"; 3 4 /* 5 Include "petscsnes.h" so that we can use SNES solvers. Note that this 6 file automatically includes: 7 petscsys.h - base PETSc routines petscvec.h - vectors 8 petscmat.h - matrices 9 petscis.h - index sets petscksp.h - Krylov subspace methods 10 petscviewer.h - viewers petscpc.h - preconditioners 11 petscksp.h - linear solvers 12 */ 13 #include <petscsnes.h> 14 15 extern PetscErrorCode FormJacobian1(SNES, Vec, Mat, Mat, void *); 16 extern PetscErrorCode FormFunction1(SNES, Vec, Vec, void *); 17 18 int main(int argc, char **argv) 19 { 20 SNES snes; /* nonlinear solver context */ 21 Vec x, r; /* solution, residual vectors */ 22 Mat J; /* Jacobian matrix */ 23 PetscInt its; 24 PetscScalar *xx; 25 SNESConvergedReason reason; 26 27 PetscFunctionBeginUser; 28 PetscCall(PetscInitialize(&argc, &argv, (char *)0, help)); 29 30 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 31 Create nonlinear solver context 32 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 33 PetscCall(SNESCreate(PETSC_COMM_WORLD, &snes)); 34 35 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 36 Create matrix and vector data structures; set corresponding routines 37 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 38 /* 39 Create vectors for solution and nonlinear function 40 */ 41 PetscCall(VecCreate(PETSC_COMM_WORLD, &x)); 42 PetscCall(VecSetSizes(x, PETSC_DECIDE, 2)); 43 PetscCall(VecSetFromOptions(x)); 44 PetscCall(VecDuplicate(x, &r)); 45 46 /* 47 Create Jacobian matrix data structure 48 */ 49 PetscCall(MatCreate(PETSC_COMM_WORLD, &J)); 50 PetscCall(MatSetSizes(J, PETSC_DECIDE, PETSC_DECIDE, 2, 2)); 51 PetscCall(MatSetFromOptions(J)); 52 PetscCall(MatSetUp(J)); 53 54 /* 55 Set function evaluation routine and vector. 56 */ 57 PetscCall(SNESSetFunction(snes, r, FormFunction1, NULL)); 58 59 /* 60 Set Jacobian matrix data structure and Jacobian evaluation routine 61 */ 62 PetscCall(SNESSetJacobian(snes, J, J, FormJacobian1, NULL)); 63 64 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 65 Customize nonlinear solver; set runtime options 66 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 67 PetscCall(SNESSetFromOptions(snes)); 68 69 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 70 Evaluate initial guess; then solve nonlinear system 71 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 72 PetscCall(VecGetArray(x, &xx)); 73 xx[0] = -1.2; 74 xx[1] = 1.0; 75 PetscCall(VecRestoreArray(x, &xx)); 76 77 /* 78 Note: The user should initialize the vector, x, with the initial guess 79 for the nonlinear solver prior to calling SNESSolve(). In particular, 80 to employ an initial guess of zero, the user should explicitly set 81 this vector to zero by calling VecSet(). 82 */ 83 84 PetscCall(SNESSolve(snes, NULL, x)); 85 PetscCall(VecView(x, PETSC_VIEWER_STDOUT_WORLD)); 86 PetscCall(SNESGetIterationNumber(snes, &its)); 87 PetscCall(SNESGetConvergedReason(snes, &reason)); 88 /* 89 Some systems computes a residual that is identically zero, thus converging 90 due to FNORM_ABS, others converge due to FNORM_RELATIVE. Here, we only 91 report the reason if the iteration did not converge so that the tests are 92 reproducible. 93 */ 94 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%s number of SNES iterations = %" PetscInt_FMT "\n", reason > 0 ? "CONVERGED" : SNESConvergedReasons[reason], its)); 95 96 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 97 Free work space. All PETSc objects should be destroyed when they 98 are no longer needed. 99 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 100 101 PetscCall(VecDestroy(&x)); 102 PetscCall(VecDestroy(&r)); 103 PetscCall(MatDestroy(&J)); 104 PetscCall(SNESDestroy(&snes)); 105 PetscCall(PetscFinalize()); 106 return 0; 107 } 108 /* ------------------------------------------------------------------- */ 109 /* 110 FormFunction1 - Evaluates nonlinear function, F(x). 111 112 Input Parameters: 113 . snes - the SNES context 114 . x - input vector 115 . ctx - optional user-defined context 116 117 Output Parameter: 118 . f - function vector 119 */ 120 PetscErrorCode FormFunction1(SNES snes, Vec x, Vec f, void *ctx) 121 { 122 PetscScalar *ff; 123 const PetscScalar *xx; 124 125 /* 126 Get pointers to vector data. 127 - For default PETSc vectors, VecGetArray() returns a pointer to 128 the data array. Otherwise, the routine is implementation dependent. 129 - You MUST call VecRestoreArray() when you no longer need access to 130 the array. 131 */ 132 PetscCall(VecGetArrayRead(x, &xx)); 133 PetscCall(VecGetArray(f, &ff)); 134 135 /* Compute function */ 136 ff[0] = -2.0 + 2.0 * xx[0] + 400.0 * xx[0] * xx[0] * xx[0] - 400.0 * xx[0] * xx[1]; 137 ff[1] = -200.0 * xx[0] * xx[0] + 200.0 * xx[1]; 138 139 /* Restore vectors */ 140 PetscCall(VecRestoreArrayRead(x, &xx)); 141 PetscCall(VecRestoreArray(f, &ff)); 142 return 0; 143 } 144 /* ------------------------------------------------------------------- */ 145 /* 146 FormJacobian1 - Evaluates Jacobian matrix. 147 148 Input Parameters: 149 . snes - the SNES context 150 . x - input vector 151 . dummy - optional user-defined context (not used here) 152 153 Output Parameters: 154 . jac - Jacobian matrix 155 . B - optionally different preconditioning matrix 156 . flag - flag indicating matrix structure 157 */ 158 PetscErrorCode FormJacobian1(SNES snes, Vec x, Mat jac, Mat B, void *dummy) 159 { 160 const PetscScalar *xx; 161 PetscScalar A[4]; 162 PetscInt idx[2] = {0, 1}; 163 164 /* 165 Get pointer to vector data 166 */ 167 PetscCall(VecGetArrayRead(x, &xx)); 168 169 /* 170 Compute Jacobian entries and insert into matrix. 171 - Since this is such a small problem, we set all entries for 172 the matrix at once. 173 */ 174 A[0] = 2.0 + 1200.0 * xx[0] * xx[0] - 400.0 * xx[1]; 175 A[1] = -400.0 * xx[0]; 176 A[2] = -400.0 * xx[0]; 177 A[3] = 200; 178 PetscCall(MatSetValues(B, 2, idx, 2, idx, A, INSERT_VALUES)); 179 180 /* 181 Restore vector 182 */ 183 PetscCall(VecRestoreArrayRead(x, &xx)); 184 185 /* 186 Assemble matrix 187 */ 188 PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY)); 189 PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY)); 190 if (jac != B) { 191 PetscCall(MatAssemblyBegin(jac, MAT_FINAL_ASSEMBLY)); 192 PetscCall(MatAssemblyEnd(jac, MAT_FINAL_ASSEMBLY)); 193 } 194 return 0; 195 } 196 197 /*TEST 198 199 test: 200 suffix: 1 201 args: -snes_monitor_short -snes_max_it 1000 202 requires: !single 203 204 test: 205 suffix: 2 206 args: -snes_monitor_short -snes_max_it 1000 -snes_type newtontrdc -snes_trdc_use_cauchy false 207 requires: !single 208 209 TEST*/ 210