Actual source code: ex42.c


  2: static char help[] = "Newton's method to solve a two-variable system that comes from the Rosenbrock function.\n\n";

  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>

 15: extern PetscErrorCode FormJacobian1(SNES,Vec,Mat,Mat,void*);
 16: extern PetscErrorCode FormFunction1(SNES,Vec,Vec,void*);

 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;

 27:   PetscInitialize(&argc,&argv,(char*)0,help);

 29:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 30:      Create nonlinear solver context
 31:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 32:   SNESCreate(PETSC_COMM_WORLD,&snes);

 34:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 35:      Create matrix and vector data structures; set corresponding routines
 36:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 37:   /*
 38:      Create vectors for solution and nonlinear function
 39:   */
 40:   VecCreate(PETSC_COMM_WORLD,&x);
 41:   VecSetSizes(x,PETSC_DECIDE,2);
 42:   VecSetFromOptions(x);
 43:   VecDuplicate(x,&r);

 45:   /*
 46:      Create Jacobian matrix data structure
 47:   */
 48:   MatCreate(PETSC_COMM_WORLD,&J);
 49:   MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,2,2);
 50:   MatSetFromOptions(J);
 51:   MatSetUp(J);

 53:   /*
 54:      Set function evaluation routine and vector.
 55:   */
 56:   SNESSetFunction(snes,r,FormFunction1,NULL);

 58:   /*
 59:      Set Jacobian matrix data structure and Jacobian evaluation routine
 60:   */
 61:   SNESSetJacobian(snes,J,J,FormJacobian1,NULL);

 63:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 64:      Customize nonlinear solver; set runtime options
 65:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 66:   SNESSetFromOptions(snes);

 68:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 69:      Evaluate initial guess; then solve nonlinear system
 70:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 71:   VecGetArray(x,&xx);
 72:   xx[0] = -1.2; xx[1] = 1.0;
 73:   VecRestoreArray(x,&xx);

 75:   /*
 76:      Note: The user should initialize the vector, x, with the initial guess
 77:      for the nonlinear solver prior to calling SNESSolve().  In particular,
 78:      to employ an initial guess of zero, the user should explicitly set
 79:      this vector to zero by calling VecSet().
 80:   */

 82:   SNESSolve(snes,NULL,x);
 83:   VecView(x,PETSC_VIEWER_STDOUT_WORLD);
 84:   SNESGetIterationNumber(snes,&its);
 85:   SNESGetConvergedReason(snes,&reason);
 86:   /*
 87:      Some systems computes a residual that is identically zero, thus converging
 88:      due to FNORM_ABS, others converge due to FNORM_RELATIVE.  Here, we only
 89:      report the reason if the iteration did not converge so that the tests are
 90:      reproducible.
 91:   */
 92:   PetscPrintf(PETSC_COMM_WORLD,"%s number of SNES iterations = %D\n",reason>0 ? "CONVERGED" : SNESConvergedReasons[reason],its);

 94:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 95:      Free work space.  All PETSc objects should be destroyed when they
 96:      are no longer needed.
 97:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 99:   VecDestroy(&x)); PetscCall(VecDestroy(&r);
100:   MatDestroy(&J)); PetscCall(SNESDestroy(&snes);
101:   PetscFinalize();
102:   return 0;
103: }
104: /* ------------------------------------------------------------------- */
105: /*
106:    FormFunction1 - Evaluates nonlinear function, F(x).

108:    Input Parameters:
109: .  snes - the SNES context
110: .  x    - input vector
111: .  ctx  - optional user-defined context

113:    Output Parameter:
114: .  f - function vector
115:  */
116: PetscErrorCode FormFunction1(SNES snes,Vec x,Vec f,void *ctx)
117: {
118:   PetscScalar       *ff;
119:   const PetscScalar *xx;

121:   /*
122:     Get pointers to vector data.
123:     - For default PETSc vectors, VecGetArray() returns a pointer to
124:     the data array.  Otherwise, the routine is implementation dependent.
125:     - You MUST call VecRestoreArray() when you no longer need access to
126:     the array.
127:   */
128:   VecGetArrayRead(x,&xx);
129:   VecGetArray(f,&ff);

131:   /* Compute function */
132:   ff[0] = -2.0 + 2.0*xx[0] + 400.0*xx[0]*xx[0]*xx[0] - 400.0*xx[0]*xx[1];
133:   ff[1] = -200.0*xx[0]*xx[0] + 200.0*xx[1];

135:   /* Restore vectors */
136:   VecRestoreArrayRead(x,&xx);
137:   VecRestoreArray(f,&ff);
138:   return 0;
139: }
140: /* ------------------------------------------------------------------- */
141: /*
142:    FormJacobian1 - Evaluates Jacobian matrix.

144:    Input Parameters:
145: .  snes - the SNES context
146: .  x - input vector
147: .  dummy - optional user-defined context (not used here)

149:    Output Parameters:
150: .  jac - Jacobian matrix
151: .  B - optionally different preconditioning matrix
152: .  flag - flag indicating matrix structure
153: */
154: PetscErrorCode FormJacobian1(SNES snes,Vec x,Mat jac,Mat B,void *dummy)
155: {
156:   const PetscScalar *xx;
157:   PetscScalar       A[4];
158:   PetscInt          idx[2] = {0,1};

160:   /*
161:      Get pointer to vector data
162:   */
163:   VecGetArrayRead(x,&xx);

165:   /*
166:      Compute Jacobian entries and insert into matrix.
167:       - Since this is such a small problem, we set all entries for
168:         the matrix at once.
169:   */
170:   A[0]  = 2.0 + 1200.0*xx[0]*xx[0] - 400.0*xx[1];
171:   A[1]  = -400.0*xx[0];
172:   A[2]  = -400.0*xx[0];
173:   A[3]  = 200;
174:   MatSetValues(B,2,idx,2,idx,A,INSERT_VALUES);

176:   /*
177:      Restore vector
178:   */
179:   VecRestoreArrayRead(x,&xx);

181:   /*
182:      Assemble matrix
183:   */
184:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
185:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
186:   if (jac != B) {
187:     MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
188:     MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
189:   }
190:   return 0;
191: }

193: /*TEST

195:    test:
196:       suffix: 1
197:       args: -snes_monitor_short -snes_max_it 1000
198:       requires: !single

200:    test:
201:       suffix: 2
202:       args: -snes_monitor_short -snes_max_it 1000 -snes_type newtontrdc -snes_trdc_use_cauchy false
203:       requires: !single

205: TEST*/