Actual source code: ex1.c

  1: /*$Id: ex1.c,v 1.90 2001/08/07 21:30:54 bsmith Exp $*/

  3: /* Program usage:  mpirun ex1 [-help] [all PETSc options] */

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

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

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

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

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

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

 41:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 42:          Compute the matrix and right-hand-side vector that define
 43:          the linear system, Ax = b.
 44:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 46:   /* 
 47:      Create vectors.  Note that we form 1 vector from scratch and
 48:      then duplicate as needed.
 49:   */
 50:   VecCreate(PETSC_COMM_WORLD,&x);
 51:   PetscObjectSetName((PetscObject) x, "Solution");
 52:   VecSetSizes(x,PETSC_DECIDE,n);
 53:   VecSetFromOptions(x);
 54:   VecDuplicate(x,&b);
 55:   VecDuplicate(x,&u);

 57:   /* 
 58:      Create matrix.  When using MatCreate(), the matrix format can
 59:      be specified at runtime.

 61:      Performance tuning note:  For problems of substantial size,
 62:      preallocation of matrix memory is crucial for attaining good 
 63:      performance.  Since preallocation is not possible via the generic
 64:      matrix creation routine MatCreate(), we recommend for practical 
 65:      problems instead to use the creation routine for a particular matrix
 66:      format, e.g.,
 67:          MatCreateSeqAIJ() - sequential AIJ (compressed sparse row)
 68:          MatCreateSeqBAIJ() - block AIJ
 69:      See the matrix chapter of the users manual for details.
 70:   */
 71:   MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,&A);
 72:   MatSetFromOptions(A);

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

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

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

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

109:   /* 
110:      Set linear solver defaults for this problem (optional).
111:      - By extracting the KSP and PC contexts from the KSP context,
112:        we can then directly call any KSP and PC routines to set
113:        various options.
114:      - The following four statements are optional; all of these
115:        parameters could alternatively be specified at runtime via
116:        KSPSetFromOptions();
117:   */
118:   KSPGetPC(ksp,&pc);
119:   PCSetType(pc,PCJACOBI);
120:   KSPSetTolerances(ksp,1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);

122:   /* 
123:     Set runtime options, e.g.,
124:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
125:     These options will override those specified above as long as
126:     KSPSetFromOptions() is called _after_ any other customization
127:     routines.
128:   */
129:   KSPSetFromOptions(ksp);
130: 
131:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
132:                       Solve the linear system
133:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
134:   /* 
135:      Solve linear system
136:   */
137:   KSPSetRhs(ksp,b);
138:   KSPSetSolution(ksp,x);
139:   KSPSolve(ksp);

141:   /* 
142:      View solver info; we could instead use the option -ksp_view to
143:      print this info to the screen at the conclusion of KSPSolve().
144:   */
145:   KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD);

147:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
148:                       Check solution and clean up
149:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
150:   /* 
151:      Check the error
152:   */
153:   VecAXPY(&neg_one,u,x);
154:   VecNorm(x,NORM_2,&norm);
155:   KSPGetIterationNumber(ksp,&its);
156:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A, Iterations %d\n",
157:                      norm,its);
158:   /* 
159:      Free work space.  All PETSc objects should be destroyed when they
160:      are no longer needed.
161:   */
162:   VecDestroy(x); VecDestroy(u);
163:   VecDestroy(b); MatDestroy(A);
164:   KSPDestroy(ksp);

166:   /*
167:      Always call PetscFinalize() before exiting a program.  This routine
168:        - finalizes the PETSc libraries as well as MPI
169:        - provides summary and diagnostic information if certain runtime
170:          options are chosen (e.g., -log_summary).
171:   */
172:   PetscFinalize();
173:   return 0;
174: }