Date: 2021-03-03T22:25:59+00:00

Actual source code: ex18.c
petsc-3.14.5 2021-03-03
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      2: static char help[] = "Computes the integral of 2*x/(1+x^2) from x=0..1 \nThis is equal to the ln(2).\n\n";

      4: /*T
      5:    Concepts: vectors^assembling vectors;
      6:    Processors: n

      8:    Contributed by Mike McCourt <mccomic@iit.edu> and Nathan Johnston <johnnat@iit.edu>
      9: T*/

     11: /*
     12:   Include "petscvec.h" so that we can use vectors.  Note that this file
     13:   automatically includes:
     14:      petscsys.h       - base PETSc routines   petscis.h     - index sets
     15:      petscviewer.h - viewers
     16: */
     17: #include <petscvec.h>

     19: PetscScalar func(PetscScalar a)
     20: {
     21:   return (PetscScalar)2.*a/((PetscScalar)1.+a*a);
     22: }

     24: int main(int argc,char **argv)
     25: {
     27:   PetscMPIInt    rank,size;
     28:   PetscInt       rstart,rend,i,k,N,numPoints=1000000;
     29:   PetscScalar    dummy,result=0,h=1.0/numPoints,*xarray;
     30:   Vec            x,xend;

     32:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
     33:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
     34:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

     36:   /*
     37:      Create a parallel vector.
     38:        Here we set up our x vector which will be given values below.
     39:        The xend vector is a dummy vector to find the value of the
     40:          elements at the endpoints for use in the trapezoid rule.
     41:   */
     42:   VecCreate(PETSC_COMM_WORLD,&x);
     43:   VecSetSizes(x,PETSC_DECIDE,numPoints);
     44:   VecSetFromOptions(x);
     45:   VecGetSize(x,&N);
     46:   VecSet(x,result);
     47:   VecDuplicate(x,&xend);
     48:   result = 0.5;
     49:   if (!rank) {
     50:     i    = 0;
     51:     VecSetValues(xend,1,&i,&result,INSERT_VALUES);
     52:   }
     53:   if (rank == size-1) {
     54:     i    = N-1;
     55:     VecSetValues(xend,1,&i,&result,INSERT_VALUES);
     56:   }
     57:   /*
     58:      Assemble vector, using the 2-step process:
     59:        VecAssemblyBegin(), VecAssemblyEnd()
     60:      Computations can be done while messages are in transition
     61:      by placing code between these two statements.
     62:   */
     63:   VecAssemblyBegin(xend);
     64:   VecAssemblyEnd(xend);

     66:   /*
     67:      Set the x vector elements.
     68:       i*h will return 0 for i=0 and 1 for i=N-1.
     69:       The function evaluated (2x/(1+x^2)) is defined above.
     70:       Each evaluation is put into the local array of the vector without message passing.
     71:   */
     72:   VecGetOwnershipRange(x,&rstart,&rend);
     73:   VecGetArray(x,&xarray);
     74:   k    = 0;
     75:   for (i=rstart; i<rend; i++) {
     76:     xarray[k] = (PetscScalar)i*h;
     77:     xarray[k] = func(xarray[k]);
     78:     k++;
     79:   }
     80:   VecRestoreArray(x,&xarray);

     82:   /*
     83:      Evaluates the integral.  First the sum of all the points is taken.
     84:      That result is multiplied by the step size for the trapezoid rule.
     85:      Then half the value at each endpoint is subtracted,
     86:      this is part of the composite trapezoid rule.
     87:   */
     88:   VecSum(x,&result);
     89:   result = result*h;
     90:   VecDot(x,xend,&dummy);
     91:   result = result-h*dummy;

     93:   /*
     94:       Return the value of the integral.
     95:   */
     96:   PetscPrintf(PETSC_COMM_WORLD,"ln(2) is %g\n",(double)PetscRealPart(result));
     97:   VecDestroy(&x);
     98:   VecDestroy(&xend);

    100:   PetscFinalize();
    101:   return ierr;
    102: }

    104: /*TEST

    106:      test:
    107:        nsize: 1

    109:      test:
    110:        nsize: 2
    111:        suffix: 2
    112:        output_file: output/ex18_1.out

    114: TEST*/