Actual source code: ex58.c


  2: static char help[] = "Solves a tridiagonal linear system with KSP.\n\n";

  4: /*
  5:   Modified from ex1.c for testing matrix operations when matrix structure is changed.
  6:   Contributed by Jose E. Roman, Feb. 2012.
  7: */
  8: #include <petscksp.h>

 10: int main(int argc,char **args)
 11: {
 12:   Vec            x, b, u;      /* approx solution, RHS, exact solution */
 13:   Mat            A,B,C;        /* linear system matrix */
 14:   KSP            ksp;          /* linear solver context */
 15:   PC             pc;           /* preconditioner context */
 16:   PetscReal      norm;         /* norm of solution error */
 17:   PetscInt       i,n = 20,col[3],its;
 18:   PetscMPIInt    size;
 19:   PetscScalar    one = 1.0,value[3];
 20:   PetscBool      nonzeroguess = PETSC_FALSE;

 22:   PetscInitialize(&argc,&args,(char*)0,help);
 23:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
 25:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 26:   PetscOptionsGetBool(NULL,NULL,"-nonzero_guess",&nonzeroguess,NULL);

 28:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 29:          Compute the matrix and right-hand-side vector that define
 30:          the linear system, Ax = b.
 31:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 33:   /*
 34:      Create vectors.  Note that we form 1 vector from scratch and
 35:      then duplicate as needed.
 36:   */
 37:   VecCreate(PETSC_COMM_WORLD,&x);
 38:   PetscObjectSetName((PetscObject) x, "Solution");
 39:   VecSetSizes(x,PETSC_DECIDE,n);
 40:   VecSetFromOptions(x);
 41:   VecDuplicate(x,&b);
 42:   VecDuplicate(x,&u);

 44:   /*
 45:      Create matrix.  When using MatCreate(), the matrix format can
 46:      be specified at runtime.

 48:      Performance tuning note:  For problems of substantial size,
 49:      preallocation of matrix memory is crucial for attaining good
 50:      performance. See the matrix chapter of the users manual for details.
 51:   */
 52:   MatCreate(PETSC_COMM_WORLD,&A);
 53:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
 54:   MatSetFromOptions(A);
 55:   MatSetUp(A);

 57:   /*
 58:      Assemble matrix
 59:   */
 60:   value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
 61:   for (i=1; i<n-1; i++) {
 62:     col[0] = i-1; col[1] = i; col[2] = i+1;
 63:     MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
 64:   }
 65:   i    = n - 1; col[0] = n - 2; col[1] = n - 1;
 66:   MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
 67:   i    = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
 68:   MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
 69:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 70:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

 72:   /*
 73:      jroman: added matrices
 74:   */
 75:   MatCreate(PETSC_COMM_WORLD,&B);
 76:   MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);
 77:   MatSetFromOptions(B);
 78:   MatSetUp(B);
 79:   for (i=0; i<n; i++) {
 80:     MatSetValue(B,i,i,value[1],INSERT_VALUES);
 81:     if (n-i+n/3<n) {
 82:       MatSetValue(B,n-i+n/3,i,value[0],INSERT_VALUES);
 83:       MatSetValue(B,i,n-i+n/3,value[0],INSERT_VALUES);
 84:     }
 85:   }
 86:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
 87:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
 88:   MatDuplicate(A,MAT_COPY_VALUES,&C);
 89:   MatAXPY(C,2.0,B,DIFFERENT_NONZERO_PATTERN);

 91:   /*
 92:      Set exact solution; then compute right-hand-side vector.
 93:   */
 94:   VecSet(u,one);
 95:   MatMult(C,u,b);

 97:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 98:                 Create the linear solver and set various options
 99:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
100:   /*
101:      Create linear solver context
102:   */
103:   KSPCreate(PETSC_COMM_WORLD,&ksp);

105:   /*
106:      Set operators. Here the matrix that defines the linear system
107:      also serves as the preconditioning matrix.
108:   */
109:   KSPSetOperators(ksp,C,C);

111:   /*
112:      Set linear solver defaults for this problem (optional).
113:      - By extracting the KSP and PC contexts from the KSP context,
114:        we can then directly call any KSP and PC routines to set
115:        various options.
116:      - The following four statements are optional; all of these
117:        parameters could alternatively be specified at runtime via
118:        KSPSetFromOptions();
119:   */
120:   KSPGetPC(ksp,&pc);
121:   PCSetType(pc,PCJACOBI);
122:   KSPSetTolerances(ksp,1.e-5,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);

124:   /*
125:     Set runtime options, e.g.,
126:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
127:     These options will override those specified above as long as
128:     KSPSetFromOptions() is called _after_ any other customization
129:     routines.
130:   */
131:   KSPSetFromOptions(ksp);

133:   if (nonzeroguess) {
134:     PetscScalar p = .5;
135:     VecSet(x,p);
136:     KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
137:   }

139:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
140:                       Solve the linear system
141:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
142:   /*
143:      Solve linear system
144:   */
145:   KSPSolve(ksp,b,x);

147:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
148:                       Check solution and clean up
149:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
150:   /*
151:      Check the error
152:   */
153:   VecAXPY(x,-1.0,u);
154:   VecNorm(x,NORM_2,&norm);
155:   KSPGetIterationNumber(ksp,&its);
156:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);

158:   /*
159:      Free work space.  All PETSc objects should be destroyed when they
160:      are no longer needed.
161:   */
162:   VecDestroy(&x)); PetscCall(VecDestroy(&u);
163:   VecDestroy(&b)); PetscCall(MatDestroy(&A);
164:   MatDestroy(&B);
165:   MatDestroy(&C);
166:   KSPDestroy(&ksp);

168:   /*
169:      Always call PetscFinalize() before exiting a program.  This routine
170:        - finalizes the PETSc libraries as well as MPI
171:        - provides summary and diagnostic information if certain runtime
172:          options are chosen (e.g., -log_view).
173:   */
174:   PetscFinalize();
175:   return 0;
176: }

178: /*TEST

180:    test:
181:       args: -mat_type aij
182:       output_file: output/ex58.out

184:    test:
185:       suffix: baij
186:       args: -mat_type baij
187:       output_file: output/ex58.out

189:    test:
190:       suffix: sbaij
191:       args: -mat_type sbaij
192:       output_file: output/ex58.out

194: TEST*/