Actual source code: ex2.c

  2: /* Program usage:  mpirun -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);

 46:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 47:          Compute the matrix and right-hand-side vector that define
 48:          the linear system, Ax = b.
 49:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 50:   /* 
 51:      Create parallel matrix, specifying only its global dimensions.
 52:      When using MatCreate(), the matrix format can be specified at
 53:      runtime. Also, the parallel partitioning of the matrix is
 54:      determined by PETSc at runtime.

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

 64:   /* 
 65:      Currently, all PETSc parallel matrix formats are partitioned by
 66:      contiguous chunks of rows across the processors.  Determine which
 67:      rows of the matrix are locally owned. 
 68:   */
 69:   MatGetOwnershipRange(A,&Istart,&Iend);

 71:   /* 
 72:      Set matrix elements for the 2-D, five-point stencil in parallel.
 73:       - Each processor needs to insert only elements that it owns
 74:         locally (but any non-local elements will be sent to the
 75:         appropriate processor during matrix assembly). 
 76:       - Always specify global rows and columns of matrix entries.

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

 83:    */
 84:   for (Ii=Istart; Ii<Iend; Ii++) {
 85:     v = -1.0; i = Ii/n; j = Ii - i*n;
 86:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 87:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 88:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 89:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 90:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
 91:   }

 93:   /* 
 94:      Assemble matrix, using the 2-step process:
 95:        MatAssemblyBegin(), MatAssemblyEnd()
 96:      Computations can be done while messages are in transition
 97:      by placing code between these two statements.
 98:   */
 99:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
100:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

102:   /* 
103:      Create parallel vectors.
104:       - We form 1 vector from scratch and then duplicate as needed.
105:       - When using VecCreate(), VecSetSizes and VecSetFromOptions()
106:         in this example, we specify only the
107:         vector's global dimension; the parallel partitioning is determined
108:         at runtime. 
109:       - When solving a linear system, the vectors and matrices MUST
110:         be partitioned accordingly.  PETSc automatically generates
111:         appropriately partitioned matrices and vectors when MatCreate()
112:         and VecCreate() are used with the same communicator.  
113:       - The user can alternatively specify the local vector and matrix
114:         dimensions when more sophisticated partitioning is needed
115:         (replacing the PETSC_DECIDE argument in the VecSetSizes() statement
116:         below).
117:   */
118:   VecCreate(PETSC_COMM_WORLD,&u);
119:   VecSetSizes(u,PETSC_DECIDE,m*n);
120:   VecSetFromOptions(u);
121:   VecDuplicate(u,&b);
122:   VecDuplicate(b,&x);

124:   /* 
125:      Set exact solution; then compute right-hand-side vector.
126:      By default we use an exact solution of a vector with all
127:      elements of 1.0;  Alternatively, using the runtime option
128:      -random_sol forms a solution vector with random components.
129:   */
130:   PetscOptionsHasName(PETSC_NULL,"-random_exact_sol",&flg);
131:   if (flg) {
132:     PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
133:     PetscRandomSetFromOptions(rctx);
134:     VecSetRandom(u,rctx);
135:     PetscRandomDestroy(rctx);
136:   } else {
137:     VecSet(u,one);
138:   }
139:   MatMult(A,u,b);

141:   /*
142:      View the exact solution vector if desired
143:   */
144:   PetscOptionsHasName(PETSC_NULL,"-view_exact_sol",&flg);
145:   if (flg) {VecView(u,PETSC_VIEWER_STDOUT_WORLD);}

147:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
148:                 Create the linear solver and set various options
149:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

151:   /* 
152:      Create linear solver context
153:   */
154:   KSPCreate(PETSC_COMM_WORLD,&ksp);

156:   /* 
157:      Set operators. Here the matrix that defines the linear system
158:      also serves as the preconditioning matrix.
159:   */
160:   KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);

162:   /* 
163:      Set linear solver defaults for this problem (optional).
164:      - By extracting the KSP and PC contexts from the KSP context,
165:        we can then directly call any KSP and PC routines to set
166:        various options.
167:      - The following two statements are optional; all of these
168:        parameters could alternatively be specified at runtime via
169:        KSPSetFromOptions().  All of these defaults can be
170:        overridden at runtime, as indicated below.
171:   */

173:   KSPSetTolerances(ksp,1.e-2/((m+1)*(n+1)),1.e-50,PETSC_DEFAULT,
174:                           PETSC_DEFAULT);

176:   /* 
177:     Set runtime options, e.g.,
178:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
179:     These options will override those specified above as long as
180:     KSPSetFromOptions() is called _after_ any other customization
181:     routines.
182:   */
183:   KSPSetFromOptions(ksp);

185:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
186:                       Solve the linear system
187:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

189:   KSPSolve(ksp,b,x);

191:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
192:                       Check solution and clean up
193:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

195:   /* 
196:      Check the error
197:   */
198:   VecAXPY(x,neg_one,u);
199:   VecNorm(x,NORM_2,&norm);
200:   KSPGetIterationNumber(ksp,&its);
201:   /* Scale the norm */
202:   /*  norm *= sqrt(1.0/((m+1)*(n+1))); */

204:   /*
205:      Print convergence information.  PetscPrintf() produces a single 
206:      print statement from all processes that share a communicator.
207:      An alternative is PetscFPrintf(), which prints to a file.
208:   */
209:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A iterations %D\n",
210:                      norm,its);

212:   /*
213:      Free work space.  All PETSc objects should be destroyed when they
214:      are no longer needed.
215:   */
216:   KSPDestroy(ksp);
217:   VecDestroy(u);  VecDestroy(x);
218:   VecDestroy(b);  MatDestroy(A);

220:   /*
221:      Always call PetscFinalize() before exiting a program.  This routine
222:        - finalizes the PETSc libraries as well as MPI
223:        - provides summary and diagnostic information if certain runtime
224:          options are chosen (e.g., -log_summary). 
225:   */
226:   PetscFinalize();
227:   return 0;
228: }