Actual source code: ex2.c

  2: /* Program usage:  mpiexec -n <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:      petscsys.h       - base PETSc routines   petscvec.h - vectors
 22:      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 = PETSC_FALSE;
 40:   PetscScalar    v,one = 1.0,neg_one = -1.0;
 41: #if defined(PETSC_USE_LOG)
 42:   PetscLogStage  stage;
 43: #endif

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

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

 68:   /* 
 69:      Currently, all PETSc parallel matrix formats are partitioned by
 70:      contiguous chunks of rows across the processors.  Determine which
 71:      rows of the matrix are locally owned. 
 72:   */
 73:   MatGetOwnershipRange(A,&Istart,&Iend);

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

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

 87:    */
 88:   PetscLogStageRegister("Assembly", &stage);
 89:   PetscLogStagePush(stage);
 90:   for (Ii=Istart; Ii<Iend; Ii++) {
 91:     v = -1.0; i = Ii/n; j = Ii - i*n;
 92:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 93:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 94:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 95:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 96:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
 97:   }

 99:   /* 
100:      Assemble matrix, using the 2-step process:
101:        MatAssemblyBegin(), MatAssemblyEnd()
102:      Computations can be done while messages are in transition
103:      by placing code between these two statements.
104:   */
105:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
106:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
107:   PetscLogStagePop();

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

131:   /* 
132:      Set exact solution; then compute right-hand-side vector.
133:      By default we use an exact solution of a vector with all
134:      elements of 1.0;  Alternatively, using the runtime option
135:      -random_sol forms a solution vector with random components.
136:   */
137:   PetscOptionsGetTruth(PETSC_NULL,"-random_exact_sol",&flg,PETSC_NULL);
138:   if (flg) {
139:     PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
140:     PetscRandomSetFromOptions(rctx);
141:     VecSetRandom(u,rctx);
142:     PetscRandomDestroy(rctx);
143:   } else {
144:     VecSet(u,one);
145:   }
146:   MatMult(A,u,b);

148:   /*
149:      View the exact solution vector if desired
150:   */
151:   flg  = PETSC_FALSE;
152:   PetscOptionsGetTruth(PETSC_NULL,"-view_exact_sol",&flg,PETSC_NULL);
153:   if (flg) {VecView(u,PETSC_VIEWER_STDOUT_WORLD);}

155:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
156:                 Create the linear solver and set various options
157:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

159:   /* 
160:      Create linear solver context
161:   */
162:   KSPCreate(PETSC_COMM_WORLD,&ksp);

164:   /* 
165:      Set operators. Here the matrix that defines the linear system
166:      also serves as the preconditioning matrix.
167:   */
168:   KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);

170:   /* 
171:      Set linear solver defaults for this problem (optional).
172:      - By extracting the KSP and PC contexts from the KSP context,
173:        we can then directly call any KSP and PC routines to set
174:        various options.
175:      - The following two statements are optional; all of these
176:        parameters could alternatively be specified at runtime via
177:        KSPSetFromOptions().  All of these defaults can be
178:        overridden at runtime, as indicated below.
179:   */
180:   KSPSetTolerances(ksp,1.e-2/((m+1)*(n+1)),1.e-50,PETSC_DEFAULT,
181:                           PETSC_DEFAULT);

183:   /* 
184:     Set runtime options, e.g.,
185:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
186:     These options will override those specified above as long as
187:     KSPSetFromOptions() is called _after_ any other customization
188:     routines.
189:   */
190:   KSPSetFromOptions(ksp);

192:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
193:                       Solve the linear system
194:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

196:   KSPSolve(ksp,b,x);

198:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
199:                       Check solution and clean up
200:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

202:   /* 
203:      Check the error
204:   */
205:   VecAXPY(x,neg_one,u);
206:   VecNorm(x,NORM_2,&norm);
207:   KSPGetIterationNumber(ksp,&its);
208:   /* Scale the norm */
209:   /*  norm *= sqrt(1.0/((m+1)*(n+1))); */

211:   /*
212:      Print convergence information.  PetscPrintf() produces a single 
213:      print statement from all processes that share a communicator.
214:      An alternative is PetscFPrintf(), which prints to a file.
215:   */
216:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A iterations %D\n",
217:                      norm,its);

219:   /*
220:      Free work space.  All PETSc objects should be destroyed when they
221:      are no longer needed.
222:   */
223:   KSPDestroy(ksp);
224:   VecDestroy(u);  VecDestroy(x);
225:   VecDestroy(b);  MatDestroy(A);

227:   /*
228:      Always call PetscFinalize() before exiting a program.  This routine
229:        - finalizes the PETSc libraries as well as MPI
230:        - provides summary and diagnostic information if certain runtime
231:          options are chosen (e.g., -log_summary). 
232:   */
233:   PetscFinalize();
234:   return 0;
235: }