!     Last change:  G    25 Feb 2003    1:56 pm
PROGRAM padeex1

USE pade
IMPLICIT NONE
CHARACTER(1)::test
REAL(KIND=8)::endpt, h ,ans, begtime, endtime, total
INTEGER:: n, eqs=1, cauchy=1, steps, i, jj
REAL(KIND=8), DIMENSION(:,:), ALLOCATABLE ::y, p


DO


  WRITE(*,*)"Would you like to continue enter y or n "
  READ(*,*) test

  WRITE(*,*)
IF (test=='n') EXIT

  WRITE(*,*)"please input end point "
  READ(*,*) endpt

  WRITE(*,*)"please input number of steps "
  READ(*,*) steps

  WRITE(*,*)"please input an even degree "
  READ(*,*) n


  ALLOCATE(y(1:eqs,0:n))
  ALLOCATE(p(1:cauchy,0:n))

  h=endpt/REAL(steps)

  !SET BEG INTIAL CONDITIONS
  y=0.0D0
  y(1,0)=0.0D0


  CALL CPU_TIME(begtime)

  ! MARCHING PICARD-PADE
  DO jj=1,steps

  ! PICARD
   p=0.0

   p(1,0)=y(1,0)*y(1,0)
   y(1,1)=1.0D0 + p(1,0)
   DO i=1,n-1
       !Cauchy Products
       p(1,i)=cp(y,1,y,1,i)


       !Setting the next term in the Taylor Series

       y(1,i+1)=p(1,i)/(i+1)
       !WRITE(*,*) y(1,i+1)
   END DO

   DO i=1,1
      y(i,0)=padterm(y,h,i)
   END DO
   !DO i=1,1
   !  y(i,0)=picterm(y,h,i)
   !END DO


 !MARCH ON
 END DO




 DO i=0,0
   WRITE(*,*) "y(1,",i,")=",y(1,i)
 END DO

 ans=(TAN(endpt))
 WRITE(*,*) "answer=",ans
 WRITE(*,*) "error=",ABS(ans-y(1,0))
 WRITE(*,*) "relerror=",ABS((ans-y(1,0))/ans)
 CALL CPU_TIME(endtime)
  total=endtime-begtime
 WRITE(*,*) "total_CPU time=",total

 DEALLOCATE (y,p)
END DO

STOP

END PROGRAM padeex1