Actual source code: ex2.c

  2: /* Program usage:  mpiexec -np <procs> ex2 [-help] [all PETSc options] */

  4: static char help[] = "Solves a linear system in parallel with KSP.\n\
  5: Input parameters include:\n\
  6:   -random_exact_sol : use a random exact solution vector\n\
  7:   -view_exact_sol   : write exact solution vector to stdout\n\
  8:   -m <mesh_x>       : number of mesh points in x-direction\n\
  9:   -n <mesh_n>       : number of mesh points in y-direction\n\n";

 11: /*T
 12:    Concepts: KSP^basic parallel example;
 13:    Concepts: KSP^Laplacian, 2d
 14:    Concepts: Laplacian, 2d
 15:    Processors: n
 16: T*/

 18: /* 
 19:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
 20:   automatically includes:
 21:      petsc.h       - base PETSc routines   petscvec.h - vectors
 22:      petscsys.h    - system routines       petscmat.h - matrices
 23:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 24:      petscviewer.h - viewers               petscpc.h  - preconditioners
 25: */
 26:  #include petscksp.h

 30: int main(int argc,char **args)
 31: {
 32:   Vec            x,b,u;  /* approx solution, RHS, exact solution */
 33:   Mat            A;        /* linear system matrix */
 34:   KSP            ksp;     /* linear solver context */
 35:   PetscRandom    rctx;     /* random number generator context */
 36:   PetscReal      norm;     /* norm of solution error */
 37:   PetscInt       i,j,Ii,J,Istart,Iend,m = 8,n = 7,its;
 39:   PetscTruth     flg;
 40:   PetscScalar    v,one = 1.0,neg_one = -1.0;

 42:   PetscInitialize(&argc,&args,(char *)0,help);
 43:   PetscOptionsGetInt(PETSC_NULL,"-m",&m,PETSC_NULL);
 44:   PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);
 45:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 46:          Compute the matrix and right-hand-side vector that define
 47:          the linear system, Ax = b.
 48:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 49:   /* 
 50:      Create parallel matrix, specifying only its global dimensions.
 51:      When using MatCreate(), the matrix format can be specified at
 52:      runtime. Also, the parallel partitioning of the matrix is
 53:      determined by PETSc at runtime.

 55:      Performance tuning note:  For problems of substantial size,
 56:      preallocation of matrix memory is crucial for attaining good 
 57:      performance. See the matrix chapter of the users manual for details.
 58:   */
 59:   MatCreate(PETSC_COMM_WORLD,&A);
 60:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
 61:   MatSetType(A, MATAIJ);
 62:   MatSetFromOptions(A);
 63:   MatMPIAIJSetPreallocation(A,5,PETSC_NULL,5,PETSC_NULL);
 64:   MatSeqAIJSetPreallocation(A,5,PETSC_NULL);

 66:   /* 
 67:      Currently, all PETSc parallel matrix formats are partitioned by
 68:      contiguous chunks of rows across the processors.  Determine which
 69:      rows of the matrix are locally owned. 
 70:   */
 71:   MatGetOwnershipRange(A,&Istart,&Iend);

 73:   /* 
 74:      Set matrix elements for the 2-D, five-point stencil in parallel.
 75:       - Each processor needs to insert only elements that it owns
 76:         locally (but any non-local elements will be sent to the
 77:         appropriate processor during matrix assembly). 
 78:       - Always specify global rows and columns of matrix entries.

 80:      Note: this uses the less common natural ordering that orders first
 81:      all the unknowns for x = h then for x = 2h etc; Hence you see J = Ii +- n
 82:      instead of J = I +- m as you might expect. The more standard ordering
 83:      would first do all variables for y = h, then y = 2h etc.

 85:    */
 86:   for (Ii=Istart; Ii<Iend; Ii++) {
 87:     v = -1.0; i = Ii/n; j = Ii - i*n;
 88:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 89:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 90:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 91:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 92:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
 93:   }

 95:   /* 
 96:      Assemble matrix, using the 2-step process:
 97:        MatAssemblyBegin(), MatAssemblyEnd()
 98:      Computations can be done while messages are in transition
 99:      by placing code between these two statements.
100:   */
101:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
102:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

104:   /* 
105:      Create parallel vectors.
106:       - We form 1 vector from scratch and then duplicate as needed.
107:       - When using VecCreate(), VecSetSizes and VecSetFromOptions()
108:         in this example, we specify only the
109:         vector's global dimension; the parallel partitioning is determined
110:         at runtime. 
111:       - When solving a linear system, the vectors and matrices MUST
112:         be partitioned accordingly.  PETSc automatically generates
113:         appropriately partitioned matrices and vectors when MatCreate()
114:         and VecCreate() are used with the same communicator.  
115:       - The user can alternatively specify the local vector and matrix
116:         dimensions when more sophisticated partitioning is needed
117:         (replacing the PETSC_DECIDE argument in the VecSetSizes() statement
118:         below).
119:   */
120:   VecCreate(PETSC_COMM_WORLD,&u);
121:   VecSetSizes(u,PETSC_DECIDE,m*n);
122:   VecSetFromOptions(u);
123:   VecDuplicate(u,&b);
124:   VecDuplicate(b,&x);

126:   /* 
127:      Set exact solution; then compute right-hand-side vector.
128:      By default we use an exact solution of a vector with all
129:      elements of 1.0;  Alternatively, using the runtime option
130:      -random_sol forms a solution vector with random components.
131:   */
132:   PetscOptionsHasName(PETSC_NULL,"-random_exact_sol",&flg);
133:   if (flg) {
134:     PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
135:     PetscRandomSetFromOptions(rctx);
136:     VecSetRandom(u,rctx);
137:     PetscRandomDestroy(rctx);
138:   } else {
139:     VecSet(u,one);
140:   }
141:   MatMult(A,u,b);

143:   /*
144:      View the exact solution vector if desired
145:   */
146:   PetscOptionsHasName(PETSC_NULL,"-view_exact_sol",&flg);
147:   if (flg) {VecView(u,PETSC_VIEWER_STDOUT_WORLD);}

149:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
150:                 Create the linear solver and set various options
151:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

153:   /* 
154:      Create linear solver context
155:   */
156:   KSPCreate(PETSC_COMM_WORLD,&ksp);

158:   /* 
159:      Set operators. Here the matrix that defines the linear system
160:      also serves as the preconditioning matrix.
161:   */
162:   KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);

164:   /* 
165:      Set linear solver defaults for this problem (optional).
166:      - By extracting the KSP and PC contexts from the KSP context,
167:        we can then directly call any KSP and PC routines to set
168:        various options.
169:      - The following two statements are optional; all of these
170:        parameters could alternatively be specified at runtime via
171:        KSPSetFromOptions().  All of these defaults can be
172:        overridden at runtime, as indicated below.
173:   */
174:   KSPSetTolerances(ksp,1.e-2/((m+1)*(n+1)),1.e-50,PETSC_DEFAULT,
175:                           PETSC_DEFAULT);

177:   /* 
178:     Set runtime options, e.g.,
179:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
180:     These options will override those specified above as long as
181:     KSPSetFromOptions() is called _after_ any other customization
182:     routines.
183:   */
184:   KSPSetFromOptions(ksp);

186:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
187:                       Solve the linear system
188:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

190:   KSPSolve(ksp,b,x);

192:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
193:                       Check solution and clean up
194:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

196:   /* 
197:      Check the error
198:   */
199:   VecAXPY(x,neg_one,u);
200:   VecNorm(x,NORM_2,&norm);
201:   KSPGetIterationNumber(ksp,&its);
202:   /* Scale the norm */
203:   /*  norm *= sqrt(1.0/((m+1)*(n+1))); */

205:   /*
206:      Print convergence information.  PetscPrintf() produces a single 
207:      print statement from all processes that share a communicator.
208:      An alternative is PetscFPrintf(), which prints to a file.
209:   */
210:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A iterations %D\n",
211:                      norm,its);

213:   /*
214:      Free work space.  All PETSc objects should be destroyed when they
215:      are no longer needed.
216:   */
217:   KSPDestroy(ksp);
218:   VecDestroy(u);  VecDestroy(x);
219:   VecDestroy(b);  MatDestroy(A);

221:   /*
222:      Always call PetscFinalize() before exiting a program.  This routine
223:        - finalizes the PETSc libraries as well as MPI
224:        - provides summary and diagnostic information if certain runtime
225:          options are chosen (e.g., -log_summary). 
226:   */
227:   PetscFinalize();
228:   return 0;
229: }