Actual source code: ex42.c

petsc-master 2017-01-20
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  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*);

 22: int main(int argc,char **argv)
 23: {
 24:   SNES                snes;    /* nonlinear solver context */
 25:   Vec                 x,r;     /* solution, residual vectors */
 26:   Mat                 J;       /* Jacobian matrix */
 27:   PetscErrorCode      ierr;
 28:   PetscInt            its;
 29:   PetscScalar         *xx;
 30:   SNESConvergedReason reason;

 32:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;

 34:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 35:      Create nonlinear solver context
 36:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 37:   SNESCreate(PETSC_COMM_WORLD,&snes);

 39:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 40:      Create matrix and vector data structures; set corresponding routines
 41:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 42:   /*
 43:      Create vectors for solution and nonlinear function
 44:   */
 45:   VecCreate(PETSC_COMM_WORLD,&x);
 46:   VecSetSizes(x,PETSC_DECIDE,2);
 47:   VecSetFromOptions(x);
 48:   VecDuplicate(x,&r);

 50:   /*
 51:      Create Jacobian matrix data structure
 52:   */
 53:   MatCreate(PETSC_COMM_WORLD,&J);
 54:   MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,2,2);
 55:   MatSetFromOptions(J);
 56:   MatSetUp(J);

 58:   /*
 59:      Set function evaluation routine and vector.
 60:   */
 61:   SNESSetFunction(snes,r,FormFunction1,NULL);

 63:   /*
 64:      Set Jacobian matrix data structure and Jacobian evaluation routine
 65:   */
 66:   SNESSetJacobian(snes,J,J,FormJacobian1,NULL);

 68:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 69:      Customize nonlinear solver; set runtime options
 70:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 71:   SNESSetFromOptions(snes);

 73:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 74:      Evaluate initial guess; then solve nonlinear system
 75:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 76:   VecGetArray(x,&xx);
 77:   xx[0] = -1.2; xx[1] = 1.0;
 78:   VecRestoreArray(x,&xx);

 80:   /*
 81:      Note: The user should initialize the vector, x, with the initial guess
 82:      for the nonlinear solver prior to calling SNESSolve().  In particular,
 83:      to employ an initial guess of zero, the user should explicitly set
 84:      this vector to zero by calling VecSet().
 85:   */

 87:   SNESSolve(snes,NULL,x);
 88:   VecView(x,PETSC_VIEWER_STDOUT_WORLD);
 89:   SNESGetIterationNumber(snes,&its);
 90:   SNESGetConvergedReason(snes,&reason);
 91:   /*
 92:      Some systems computes a residual that is identically zero, thus converging
 93:      due to FNORM_ABS, others converge due to FNORM_RELATIVE.  Here, we only
 94:      report the reason if the iteration did not converge so that the tests are
 95:      reproducible.
 96:   */
 97:   PetscPrintf(PETSC_COMM_WORLD,"%s number of SNES iterations = %D\n",reason>0 ? "CONVERGED" : (char*) SNESConvergedReasons[reason],its);

 99:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
100:      Free work space.  All PETSc objects should be destroyed when they
101:      are no longer needed.
102:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

104:   VecDestroy(&x); VecDestroy(&r);
105:   MatDestroy(&J); SNESDestroy(&snes);
106:   PetscFinalize();
107:   return ierr;
108: }
109: /* ------------------------------------------------------------------- */
110: /*
111:    FormFunction1 - Evaluates nonlinear function, F(x).

113:    Input Parameters:
114: .  snes - the SNES context
115: .  x    - input vector
116: .  ctx  - optional user-defined context

118:    Output Parameter:
119: .  f - function vector
120:  */
121: PetscErrorCode FormFunction1(SNES snes,Vec x,Vec f,void *ctx)
122: {
123:   PetscErrorCode    ierr;
124:   PetscScalar       *ff;
125:   const PetscScalar *xx;

127:   /*
128:     Get pointers to vector data.
129:     - For default PETSc vectors, VecGetArray() returns a pointer to
130:     the data array.  Otherwise, the routine is implementation dependent.
131:     - You MUST call VecRestoreArray() when you no longer need access to
132:     the array.
133:   */
134:   VecGetArrayRead(x,&xx);
135:   VecGetArray(f,&ff);

137:   /* Compute function */
138:   ff[0] = -2.0 + 2.0*xx[0] + 400.0*xx[0]*xx[0]*xx[0] - 400.0*xx[0]*xx[1];
139:   ff[1] = -200.0*xx[0]*xx[0] + 200.0*xx[1];

141:   /* Restore vectors */
142:   VecRestoreArrayRead(x,&xx);
143:   VecRestoreArray(f,&ff);
144:   return 0;
145: }
146: /* ------------------------------------------------------------------- */
147: /*
148:    FormJacobian1 - Evaluates Jacobian matrix.

150:    Input Parameters:
151: .  snes - the SNES context
152: .  x - input vector
153: .  dummy - optional user-defined context (not used here)

155:    Output Parameters:
156: .  jac - Jacobian matrix
157: .  B - optionally different preconditioning matrix
158: .  flag - flag indicating matrix structure
159: */
160: PetscErrorCode FormJacobian1(SNES snes,Vec x,Mat jac,Mat B,void *dummy)
161: {
162:   const PetscScalar *xx;
163:   PetscScalar       A[4];
164:   PetscErrorCode    ierr;
165:   PetscInt          idx[2] = {0,1};

167:   /*
168:      Get pointer to vector data
169:   */
170:   VecGetArrayRead(x,&xx);

172:   /*
173:      Compute Jacobian entries and insert into matrix.
174:       - Since this is such a small problem, we set all entries for
175:         the matrix at once.
176:   */
177:   A[0]  = 2.0 + 1200.0*xx[0]*xx[0] - 400.0*xx[1];
178:   A[1]  = -400.0*xx[0];
179:   A[2]  = -400.0*xx[0];
180:   A[3]  = 200;
181:   MatSetValues(B,2,idx,2,idx,A,INSERT_VALUES);

183:   /*
184:      Restore vector
185:   */
186:   VecRestoreArrayRead(x,&xx);

188:   /*
189:      Assemble matrix
190:   */
191:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
192:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
193:   if (jac != B) {
194:     MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
195:     MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
196:   }
197:   return 0;
198: }