Actual source code: ex1.c

petsc-3.11.1 2019-04-17
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  2: static char help[] = "Solves a tridiagonal linear system with KSP.\n\n";

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

  9: /*
 10:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
 11:   automatically includes:
 12:      petscsys.h    - base PETSc routines   petscvec.h - vectors
 13:      petscmat.h    - matrices              petscpc.h  - preconditioners
 14:      petscis.h     - index sets
 15:      petscviewer.h - viewers

 17:   Note:  The corresponding parallel example is ex23.c
 18: */
 19:  #include <petscksp.h>

 21: int main(int argc,char **args)
 22: {
 23:   Vec            x, b, u;      /* approx solution, RHS, exact solution */
 24:   Mat            A;            /* linear system matrix */
 25:   KSP            ksp;          /* linear solver context */
 26:   PC             pc;           /* preconditioner context */
 27:   PetscReal      norm;         /* norm of solution error */
 29:   PetscInt       i,n = 10,col[3],its;
 30:   PetscMPIInt    size;
 31:   PetscScalar    value[3];

 33:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
 34:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
 35:   if (size != 1) SETERRQ(PETSC_COMM_WORLD,1,"This is a uniprocessor example only!");
 36:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);


 39:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 40:          Compute the matrix and right-hand-side vector that define
 41:          the linear system, Ax = b.
 42:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 44:   /*
 45:      Create vectors.  Note that we form 1 vector from scratch and
 46:      then duplicate as needed.
 47:   */
 48:   VecCreate(PETSC_COMM_WORLD,&x);
 49:   PetscObjectSetName((PetscObject) x, "Solution");
 50:   VecSetSizes(x,PETSC_DECIDE,n);
 51:   VecSetFromOptions(x);
 52:   VecDuplicate(x,&b);
 53:   VecDuplicate(x,&u);

 55:   /*
 56:      Create matrix.  When using MatCreate(), the matrix format can
 57:      be specified at runtime.

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

 68:   /*
 69:      Assemble matrix
 70:   */
 71:   value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
 72:   for (i=1; i<n-1; i++) {
 73:     col[0] = i-1; col[1] = i; col[2] = i+1;
 74:     MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
 75:   }
 76:   i    = n - 1; col[0] = n - 2; col[1] = n - 1;
 77:   MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
 78:   i    = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
 79:   MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
 80:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 81:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

 83:   /*
 84:      Set exact solution; then compute right-hand-side vector.
 85:   */
 86:   VecSet(u,1.0);
 87:   MatMult(A,u,b);

 89:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 90:                 Create the linear solver and set various options
 91:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 92:   KSPCreate(PETSC_COMM_WORLD,&ksp);

 94:   /*
 95:      Set operators. Here the matrix that defines the linear system
 96:      also serves as the matrix that defines the preconditioner.
 97:   */
 98:   KSPSetOperators(ksp,A,A);

100:   /*
101:      Set linear solver defaults for this problem (optional).
102:      - By extracting the KSP and PC contexts from the KSP context,
103:        we can then directly call any KSP and PC routines to set
104:        various options.
105:      - The following four statements are optional; all of these
106:        parameters could alternatively be specified at runtime via
107:        KSPSetFromOptions();
108:   */
109:   KSPGetPC(ksp,&pc);
110:   PCSetType(pc,PCJACOBI);
111:   KSPSetTolerances(ksp,1.e-5,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);

113:   /*
114:     Set runtime options, e.g.,
115:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
116:     These options will override those specified above as long as
117:     KSPSetFromOptions() is called _after_ any other customization
118:     routines.
119:   */
120:   KSPSetFromOptions(ksp);

122:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
123:                       Solve the linear system
124:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
125:   KSPSolve(ksp,b,x);

127:   /*
128:      View solver info; we could instead use the option -ksp_view to
129:      print this info to the screen at the conclusion of KSPSolve().
130:   */
131:   KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD);

133:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
134:                       Check the solution and clean up
135:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
136:   VecAXPY(x,-1.0,u);
137:   VecNorm(x,NORM_2,&norm);
138:   KSPGetIterationNumber(ksp,&its);
139:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);

141:   /*
142:      Free work space.  All PETSc objects should be destroyed when they
143:      are no longer needed.
144:   */
145:   VecDestroy(&x); VecDestroy(&u);
146:   VecDestroy(&b); MatDestroy(&A);
147:   KSPDestroy(&ksp);

149:   /*
150:      Always call PetscFinalize() before exiting a program.  This routine
151:        - finalizes the PETSc libraries as well as MPI
152:        - provides summary and diagnostic information if certain runtime
153:          options are chosen (e.g., -log_view).
154:   */
155:   PetscFinalize();
156:   return ierr;
157: }

159: /*TEST

161:    test:
162:       args: -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

164:    test:
165:       suffix: 2
166:       args: -pc_type sor -pc_sor_symmetric -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

168:    test:
169:       suffix: 2_aijcusparse
170:       requires: cuda
171:       args: -pc_type sor -pc_sor_symmetric -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always -mat_type aijcusparse -vec_type cuda

173:    test:
174:       suffix: 3
175:       args: -pc_type eisenstat -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

177:    test:
178:       suffix: 3_aijcusparse
179:       requires: cuda
180:       args: -pc_type eisenstat -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always -mat_type aijcusparse -vec_type cuda

182:    test:
183:       suffix: aijcusparse
184:       requires: cuda
185:       args: -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always -mat_type aijcusparse -vec_type cuda
186:       output_file: output/ex1_1_aijcusparse.out

188: TEST*/