Actual source code: ex1.c

  2: /* Program usage:  mpiexec ex1 [-help] [all PETSc options] */

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

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

 11: /* 
 12:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
 13:   automatically includes:
 14:      petscsys.h       - base PETSc routines   petscvec.h - vectors
 15:      petscmat.h - matrices
 16:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 17:      petscviewer.h - viewers               petscpc.h  - preconditioners

 19:   Note:  The corresponding parallel example is ex23.c
 20: */
 21: #include <petscksp.h>

 25: int main(int argc,char **args)
 26: {
 27:   Vec            x, b, u;      /* approx solution, RHS, exact solution */
 28:   Mat            A;            /* linear system matrix */
 29:   KSP            ksp;         /* linear solver context */
 30:   PC             pc;           /* preconditioner context */
 31:   PetscReal      norm;         /* norm of solution error */
 33:   PetscInt       i,n = 10,col[3],its;
 34:   PetscMPIInt    size;
 35:   PetscScalar    neg_one = -1.0,one = 1.0,value[3];
 36:   PetscBool      nonzeroguess = PETSC_FALSE;

 38:   PetscInitialize(&argc,&args,(char *)0,help);
 39:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
 40:   if (size != 1) SETERRQ(PETSC_COMM_WORLD,1,"This is a uniprocessor example only!");
 41:   PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);
 42:   PetscOptionsGetBool(PETSC_NULL,"-nonzero_guess",&nonzeroguess,PETSC_NULL);


 45:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 46:          Compute the matrix and right-hand-side vector that define
 47:          the linear system, Ax = b.
 48:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 50:   /* 
 51:      Create vectors.  Note that we form 1 vector from scratch and
 52:      then duplicate as needed.
 53:   */
 54:   VecCreate(PETSC_COMM_WORLD,&x);
 55:   PetscObjectSetName((PetscObject) x, "Solution");
 56:   VecSetSizes(x,PETSC_DECIDE,n);
 57:   VecSetFromOptions(x);
 58:   VecDuplicate(x,&b);
 59:   VecDuplicate(x,&u);

 61:   /* 
 62:      Create matrix.  When using MatCreate(), the matrix format can
 63:      be specified at runtime.

 65:      Performance tuning note:  For problems of substantial size,
 66:      preallocation of matrix memory is crucial for attaining good 
 67:      performance. See the matrix chapter of the users manual for details.
 68:   */
 69:   MatCreate(PETSC_COMM_WORLD,&A);
 70:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
 71:   MatSetFromOptions(A);

 73:   /* 
 74:      Assemble matrix
 75:   */
 76:   value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
 77:   for (i=1; i<n-1; i++) {
 78:     col[0] = i-1; col[1] = i; col[2] = i+1;
 79:     MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
 80:   }
 81:   i = n - 1; col[0] = n - 2; col[1] = n - 1;
 82:   MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
 83:   i = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
 84:   MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
 85:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 86:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

 88:   /* 
 89:      Set exact solution; then compute right-hand-side vector.
 90:   */
 91:   VecSet(u,one);
 92:   MatMult(A,u,b);

 94:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 95:                 Create the linear solver and set various options
 96:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 97:   /* 
 98:      Create linear solver context
 99:   */
100:   KSPCreate(PETSC_COMM_WORLD,&ksp);

102:   /* 
103:      Set operators. Here the matrix that defines the linear system
104:      also serves as the preconditioning matrix.
105:   */
106:   KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);

108:   /* 
109:      Set linear solver defaults for this problem (optional).
110:      - By extracting the KSP and PC contexts from the KSP context,
111:        we can then directly call any KSP and PC routines to set
112:        various options.
113:      - The following four statements are optional; all of these
114:        parameters could alternatively be specified at runtime via
115:        KSPSetFromOptions();
116:   */
117:   KSPGetPC(ksp,&pc);
118:   PCSetType(pc,PCJACOBI);
119:   KSPSetTolerances(ksp,1.e-5,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);

121:   /* 
122:     Set runtime options, e.g.,
123:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
124:     These options will override those specified above as long as
125:     KSPSetFromOptions() is called _after_ any other customization
126:     routines.
127:   */
128:   KSPSetFromOptions(ksp);

130:   if (nonzeroguess) {
131:     PetscScalar p = .5;
132:     VecSet(x,p);
133:     KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
134:   }
135: 
136:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
137:                       Solve the linear system
138:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
139:   /* 
140:      Solve linear system
141:   */
142:   KSPSolve(ksp,b,x);

144:   /* 
145:      View solver info; we could instead use the option -ksp_view to
146:      print this info to the screen at the conclusion of KSPSolve().
147:   */
148:   KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD);

150:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
151:                       Check solution and clean up
152:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
153:   /* 
154:      Check the error
155:   */
156:   VecAXPY(x,neg_one,u);
157:   VecNorm(x,NORM_2,&norm);
158:   KSPGetIterationNumber(ksp,&its);
159:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A, Iterations %D\n",
160:                      norm,its);

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

170:   /*
171:      Always call PetscFinalize() before exiting a program.  This routine
172:        - finalizes the PETSc libraries as well as MPI
173:        - provides summary and diagnostic information if certain runtime
174:          options are chosen (e.g., -log_summary).
175:   */
176:   PetscFinalize();
177:   return 0;
178: }