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*/