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){return 2*a/(1+a*a);}

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

 31:   PetscInitialize(&argc,&argv,(char *)0,help);
 32:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
 33:   MPI_Comm_size(PETSC_COMM_WORLD,&nproc);

 35:   /*
 36:      Create a parallel vector.
 37:        Here we set up our x vector which will be given values below.
 38:        The xend vector is a dummy vector to find the value of the
 39:          elements at the endpoints for use in the trapezoid rule.
 40:   */
 41:   VecCreate(PETSC_COMM_WORLD,&x);
 42:   VecSetSizes(x,PETSC_DECIDE,numPoints);
 43:   VecSetFromOptions(x);
 44:   VecGetSize(x,&N);
 45:   VecSet(x,result);
 46:   VecDuplicate(x,&xend);
 47:   result=0.5;
 48:   if (rank == 0){
 49:     i=0;
 50:     VecSetValues(xend,1,&i,&result,INSERT_VALUES);
 51:   } else if (rank == nproc){
 52:     i=N-1;
 53:     VecSetValues(xend,1,&i,&result,INSERT_VALUES);
 54:   }
 55:   /* 
 56:      Assemble vector, using the 2-step process:
 57:        VecAssemblyBegin(), VecAssemblyEnd()
 58:      Computations can be done while messages are in transition
 59:      by placing code between these two statements.
 60:   */
 61:   VecAssemblyBegin(xend);
 62:   VecAssemblyEnd(xend);

 64:   /*
 65:      Set the x vector elements.
 66:       i*h will return 0 for i=0 and 1 for i=N-1.
 67:       The function evaluated (2x/(1+x^2)) is defined above.
 68:       Each evaluation is put into the local array of the vector without message passing.
 69:   */
 70:   VecGetOwnershipRange(x,&rstart,&rend);
 71:   VecGetArray(x,&xarray);
 72:   k = 0;
 73:   for (i=rstart; i<rend; i++){
 74:     xarray[k] = i*h;
 75:     xarray[k] = func(xarray[k]);
 76:     k++;
 77:   }
 78:   VecRestoreArray(x,&xarray);

 80:   /*
 81:      Evaluates the integral.  First the sum of all the points is taken.
 82:      That result is multiplied by the step size for the trapezoid rule.
 83:      Then half the value at each endpoint is subtracted,
 84:         this is part of the composite trapezoid rule.
 85:   */
 86:   VecSum(x,&result);
 87:   result = result*h;
 88:   VecDot(x,xend,&dummy);
 89:   result = result-h*dummy;

 91:   /*
 92:       Return the value of the integral.
 93:   */
 94:   PetscPrintf(PETSC_COMM_WORLD,"ln(2) is %G\n",result);
 95:   VecDestroy(&x);
 96:   VecDestroy(&xend);

 98:   PetscFinalize();
 99:   return 0;
100: }
101: