Actual source code: ex58.c


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

  4: /*T
  5:    Concepts: KSP^solving a system of linear equations
  6:    Processors: 1
  7: T*/

  9: /*
 10:   Modified from ex1.c for testing matrix operations when matrix structure is changed.
 11:   Contributed by Jose E. Roman, Feb. 2012.
 12: */
 13: #include <petscksp.h>

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

 27:   PetscInitialize(&argc,&args,(char*)0,help);
 28:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
 30:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 31:   PetscOptionsGetBool(NULL,NULL,"-nonzero_guess",&nonzeroguess,NULL);

 33:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 34:          Compute the matrix and right-hand-side vector that define
 35:          the linear system, Ax = b.
 36:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

 49:   /*
 50:      Create matrix.  When using MatCreate(), the matrix format can
 51:      be specified at runtime.

 53:      Performance tuning note:  For problems of substantial size,
 54:      preallocation of matrix memory is crucial for attaining good
 55:      performance. See the matrix chapter of the users manual for details.
 56:   */
 57:   MatCreate(PETSC_COMM_WORLD,&A);
 58:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
 59:   MatSetFromOptions(A);
 60:   MatSetUp(A);

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

 77:   /*
 78:      jroman: added matrices
 79:   */
 80:   MatCreate(PETSC_COMM_WORLD,&B);
 81:   MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);
 82:   MatSetFromOptions(B);
 83:   MatSetUp(B);
 84:   for (i=0; i<n; i++) {
 85:     MatSetValue(B,i,i,value[1],INSERT_VALUES);
 86:     if (n-i+n/3<n) {
 87:       MatSetValue(B,n-i+n/3,i,value[0],INSERT_VALUES);
 88:       MatSetValue(B,i,n-i+n/3,value[0],INSERT_VALUES);
 89:     }
 90:   }
 91:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
 92:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
 93:   MatDuplicate(A,MAT_COPY_VALUES,&C);
 94:   MatAXPY(C,2.0,B,DIFFERENT_NONZERO_PATTERN);

 96:   /*
 97:      Set exact solution; then compute right-hand-side vector.
 98:   */
 99:   VecSet(u,one);
100:   MatMult(C,u,b);

102:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
103:                 Create the linear solver and set various options
104:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
105:   /*
106:      Create linear solver context
107:   */
108:   KSPCreate(PETSC_COMM_WORLD,&ksp);

110:   /*
111:      Set operators. Here the matrix that defines the linear system
112:      also serves as the preconditioning matrix.
113:   */
114:   KSPSetOperators(ksp,C,C);

116:   /*
117:      Set linear solver defaults for this problem (optional).
118:      - By extracting the KSP and PC contexts from the KSP context,
119:        we can then directly call any KSP and PC routines to set
120:        various options.
121:      - The following four statements are optional; all of these
122:        parameters could alternatively be specified at runtime via
123:        KSPSetFromOptions();
124:   */
125:   KSPGetPC(ksp,&pc);
126:   PCSetType(pc,PCJACOBI);
127:   KSPSetTolerances(ksp,1.e-5,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);

129:   /*
130:     Set runtime options, e.g.,
131:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
132:     These options will override those specified above as long as
133:     KSPSetFromOptions() is called _after_ any other customization
134:     routines.
135:   */
136:   KSPSetFromOptions(ksp);

138:   if (nonzeroguess) {
139:     PetscScalar p = .5;
140:     VecSet(x,p);
141:     KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
142:   }

144:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
145:                       Solve the linear system
146:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
147:   /*
148:      Solve linear system
149:   */
150:   KSPSolve(ksp,b,x);

152:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
153:                       Check solution and clean up
154:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
155:   /*
156:      Check the error
157:   */
158:   VecAXPY(x,-1.0,u);
159:   VecNorm(x,NORM_2,&norm);
160:   KSPGetIterationNumber(ksp,&its);
161:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);

163:   /*
164:      Free work space.  All PETSc objects should be destroyed when they
165:      are no longer needed.
166:   */
167:   VecDestroy(&x)); PetscCall(VecDestroy(&u);
168:   VecDestroy(&b)); PetscCall(MatDestroy(&A);
169:   MatDestroy(&B);
170:   MatDestroy(&C);
171:   KSPDestroy(&ksp);

173:   /*
174:      Always call PetscFinalize() before exiting a program.  This routine
175:        - finalizes the PETSc libraries as well as MPI
176:        - provides summary and diagnostic information if certain runtime
177:          options are chosen (e.g., -log_view).
178:   */
179:   PetscFinalize();
180:   return 0;
181: }

183: /*TEST

185:    test:
186:       args: -mat_type aij
187:       output_file: output/ex58.out

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

194:    test:
195:       suffix: sbaij
196:       args: -mat_type sbaij
197:       output_file: output/ex58.out

199: TEST*/