Actual source code: ex42.c
petsc-3.7.5 2017-01-01
2: static char help[] = "Newton's method to solve a two-variable system that comes from the Rosenbrock function.\n\n";
4: /*T
5: Concepts: SNES^basic example
6: T*/
8: /*
9: Include "petscsnes.h" so that we can use SNES solvers. Note that this
10: file automatically includes:
11: petscsys.h - base PETSc routines petscvec.h - vectors
12: petscmat.h - matrices
13: petscis.h - index sets petscksp.h - Krylov subspace methods
14: petscviewer.h - viewers petscpc.h - preconditioners
15: petscksp.h - linear solvers
16: */
17: #include <petscsnes.h>
19: extern PetscErrorCode FormJacobian1(SNES,Vec,Mat,Mat,void*);
20: extern PetscErrorCode FormFunction1(SNES,Vec,Vec,void*);
24: int main(int argc,char **argv)
25: {
26: SNES snes; /* nonlinear solver context */
27: Vec x,r; /* solution, residual vectors */
28: Mat J; /* Jacobian matrix */
29: PetscErrorCode ierr;
30: PetscInt its;
31: PetscScalar *xx;
32: SNESConvergedReason reason;
34: PetscInitialize(&argc,&argv,(char*)0,help);
36: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
37: Create nonlinear solver context
38: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
39: SNESCreate(PETSC_COMM_WORLD,&snes);
41: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
42: Create matrix and vector data structures; set corresponding routines
43: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
44: /*
45: Create vectors for solution and nonlinear function
46: */
47: VecCreate(PETSC_COMM_WORLD,&x);
48: VecSetSizes(x,PETSC_DECIDE,2);
49: VecSetFromOptions(x);
50: VecDuplicate(x,&r);
52: /*
53: Create Jacobian matrix data structure
54: */
55: MatCreate(PETSC_COMM_WORLD,&J);
56: MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,2,2);
57: MatSetFromOptions(J);
58: MatSetUp(J);
60: /*
61: Set function evaluation routine and vector.
62: */
63: SNESSetFunction(snes,r,FormFunction1,NULL);
65: /*
66: Set Jacobian matrix data structure and Jacobian evaluation routine
67: */
68: SNESSetJacobian(snes,J,J,FormJacobian1,NULL);
70: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
71: Customize nonlinear solver; set runtime options
72: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
73: SNESSetFromOptions(snes);
75: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
76: Evaluate initial guess; then solve nonlinear system
77: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
78: VecGetArray(x,&xx);
79: xx[0] = -1.2; xx[1] = 1.0;
80: VecRestoreArray(x,&xx);
82: /*
83: Note: The user should initialize the vector, x, with the initial guess
84: for the nonlinear solver prior to calling SNESSolve(). In particular,
85: to employ an initial guess of zero, the user should explicitly set
86: this vector to zero by calling VecSet().
87: */
89: SNESSolve(snes,NULL,x);
90: VecView(x,PETSC_VIEWER_STDOUT_WORLD);
91: SNESGetIterationNumber(snes,&its);
92: SNESGetConvergedReason(snes,&reason);
93: /*
94: Some systems computes a residual that is identically zero, thus converging
95: due to FNORM_ABS, others converge due to FNORM_RELATIVE. Here, we only
96: report the reason if the iteration did not converge so that the tests are
97: reproducible.
98: */
99: PetscPrintf(PETSC_COMM_WORLD,"%s number of SNES iterations = %D\n",reason>0 ? "CONVERGED" : (char*) SNESConvergedReasons[reason],its);
101: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
102: Free work space. All PETSc objects should be destroyed when they
103: are no longer needed.
104: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
106: VecDestroy(&x); VecDestroy(&r);
107: MatDestroy(&J); SNESDestroy(&snes);
108: PetscFinalize();
109: return 0;
110: }
111: /* ------------------------------------------------------------------- */
114: /*
115: FormFunction1 - Evaluates nonlinear function, F(x).
117: Input Parameters:
118: . snes - the SNES context
119: . x - input vector
120: . ctx - optional user-defined context
122: Output Parameter:
123: . f - function vector
124: */
125: PetscErrorCode FormFunction1(SNES snes,Vec x,Vec f,void *ctx)
126: {
127: PetscErrorCode ierr;
128: PetscScalar *ff;
129: const PetscScalar *xx;
131: /*
132: Get pointers to vector data.
133: - For default PETSc vectors, VecGetArray() returns a pointer to
134: the data array. Otherwise, the routine is implementation dependent.
135: - You MUST call VecRestoreArray() when you no longer need access to
136: the array.
137: */
138: VecGetArrayRead(x,&xx);
139: VecGetArray(f,&ff);
141: /* Compute function */
142: ff[0] = -2.0 + 2.0*xx[0] + 400.0*xx[0]*xx[0]*xx[0] - 400.0*xx[0]*xx[1];
143: ff[1] = -200.0*xx[0]*xx[0] + 200.0*xx[1];
145: /* Restore vectors */
146: VecRestoreArrayRead(x,&xx);
147: VecRestoreArray(f,&ff);
148: return 0;
149: }
150: /* ------------------------------------------------------------------- */
153: /*
154: FormJacobian1 - Evaluates Jacobian matrix.
156: Input Parameters:
157: . snes - the SNES context
158: . x - input vector
159: . dummy - optional user-defined context (not used here)
161: Output Parameters:
162: . jac - Jacobian matrix
163: . B - optionally different preconditioning matrix
164: . flag - flag indicating matrix structure
165: */
166: PetscErrorCode FormJacobian1(SNES snes,Vec x,Mat jac,Mat B,void *dummy)
167: {
168: const PetscScalar *xx;
169: PetscScalar A[4];
170: PetscErrorCode ierr;
171: PetscInt idx[2] = {0,1};
173: /*
174: Get pointer to vector data
175: */
176: VecGetArrayRead(x,&xx);
178: /*
179: Compute Jacobian entries and insert into matrix.
180: - Since this is such a small problem, we set all entries for
181: the matrix at once.
182: */
183: A[0] = 2.0 + 1200.0*xx[0]*xx[0] - 400.0*xx[1];
184: A[1] = -400.0*xx[0];
185: A[2] = -400.0*xx[0];
186: A[3] = 200;
187: MatSetValues(B,2,idx,2,idx,A,INSERT_VALUES);
189: /*
190: Restore vector
191: */
192: VecRestoreArrayRead(x,&xx);
194: /*
195: Assemble matrix
196: */
197: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
198: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
199: if (jac != B) {
200: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
201: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
202: }
203: return 0;
204: }