program distances
   !Subroutine distances(x1,y1,x2,y2,x3,y3,d1,d2,d3)
   !Subroutine to calculate three distances between three points.
   !Variables used are:
   !A(x1,y1),B(x2,y2),C(x3,y3) are the coordinates of three points.
   !d1: the distance between A and B
   !d2: the distance between A and B
   !d3: the distance between A and B
   !Input:The points A,B,C
   !Output:The distances between A and B, B and C,C and A
   !Variable declerations
   real:: x1,x2,x3,y1,y2,y3,d1,d2,d3,a1,a2,a3
   !Read the coordinates of points
   print*, "Enter the coordinates x1,y1,x2,y2,x3,y3"
   read*, x1,y1,x2,y2,x3,y3
   !Calculate d1,d2,d3
    a1=(x2-x1)**2+(y2-y1)**2
    a2=(x3-x2)**2+(y3-y2)**2
    a3=(x3-x1)**2+(y3-y1)**2
    d1=sqrt(a1)
    d2=sqrt(a2)
    d3=sqrt(a3)
   !Calculate and print distances
   if (( d1==d2) .and. ( d1==d3 )) then
       !If the distances are equal, the shape is a equilateral triangle.
       print*, "The distances d1 , d2 , d3 have the same value",d1
   else if (d1==d2 .and. d3<d1+d2) then
       !If two of the sides are equal lenght, the shape is a isosceles triangle.
       print*, "The values of the two distances d1 and d2 are equal and d3 is", &
                              "smaller than d1 + d2 ",d2
   else
   endif
   if (((d1 /= d2) .and. (d1 /= d3)) .or. (d3 < d1+d2)  &
         .or. (d2 < d1+d3) .or. (d1 < d2+d3)) then
       !None of the distances are equal.
       print*, "The values of three distances are different",d3
   else
   endif
end program distances



! Find averages of ten number pairs.
    implicit none
    integer, parameter :: LIMIT = 10
    integer :: Loop
    real :: Average, X, Y
! start program E01
    open (unit = 1, file = "e01.txt", status = "old", action = "read", position = "rewind")
    do Loop = 1, LIMIT
      read (unit = 1, fmt = *) X, Y
      Average = (X +  Y) / 2.0
      write (unit = *, fmt = *) Loop, X, Y, Average
    end do
    stop
  end program E01

! Print index value at normal termination.
  program E03
    implicit none
    integer :: I
    real :: Total, Datum
    integer, parameter :: LIMIT = 40
! start program E03
    Total = 0
    open (unit = 1, file = "e03.txt", status = "old", action = "read", position = "rewind")
    do I = 1, LIMIT
      read (unit = 1, fmt = *) Datum
      Total = Total + Datum
    end do
    write (unit = *, fmt = *) I, Total
    stop
  end program E03

! Sum alternating harmonic series until term is small.
  program E06
    implicit none
    integer, parameter :: K = selected_real_kind( 12 )
    real(kind = K) :: Total, Term_Sign, Next_Term
    integer :: N
    real(kind = K), parameter :: TOLERANCE = 1.0e-4
! start program E06
    Total = 0.0_K
    Term_Sign = 1.0_K
    N = 1
    do ! forever
      Next_Term = Term_Sign / real( N, kind = K )
      if (abs( Next_Term ) < TOLERANCE) then
        exit
      end if
      Total = Total + Next_Term
      N = N + 1
      Term_Sign = - Term_Sign
    end do
    write (unit = *, fmt = *) " The sum after: ", N - 1, " terms is: ", Total
    stop
  end program E06

! Sum a power series until next term is small enough.
  program E09
    implicit none
    integer, parameter :: K = selected_real_kind( 12 )
    real(kind = K) :: Total, Next_Term
    real(kind = K), parameter :: TOLERANCE = 1.0e-6_K
! start program E09
    Total = 0.0_K
    Next_Term = 1.0_K
    do
      if (Next_Term < TOLERANCE) then
        exit
      end if
      Total = Total + Next_Term
      Next_Term = 0.5_K * Next_Term
    end do
    write (unit = *, fmt = *) " Sum of terms greater than: ", real(TOLERANCE), " is: ", Total
    stop
  end program E09

program E23
    use E23M
    implicit none
    integer :: EoF
! start program E23
    open (unit = 2, file = "numeroso.txt", &
      status = "old", action = "read", position = "rewind")
    do
      read (unit = 2, fmt = *, iostat = EoF) X, Y
      if (EoF < 0) then
        exit
      end if
      call Tally( )
    end do
    call Report( )
      write (unit = *, fmt = *) " Item Count: ", How_Many
      if (How_Many > 0 ) then
      write (unit = *, fmt = *) " Means: ", real( X_Mean ), real( Y_Mean )
      if (How_Many > 1) then
        write (unit = *, fmt = *) real( X_Dev ), real( Y_Dev ), real( Covar ), real( Correlation )
        write (unit = *, fmt = *) " Regression: ", real( A ), real( B )
      end if
    else
      write (unit = *, fmt = *) " Insufficient data in this file. "
    end if
    stop
  end program E23

! Example 5.39. Compute exponential of a matrix.
  program Matress
    implicit none
    integer, parameter :: P = 4, K = Selected_Real_Kind (P)
    integer :: Dim
    real (kind = K), allocatable, dimension(:, :) :: Array, X
! start program Matress
    open (1, file = "f39.dat", position = "rewind")
    read (1, *) Dim
    allocate (Array(Dim, Dim), X(Dim, Dim))
    read (1, *) Array
    X = Mat_Exp (Array)
    print *, X
    stop
  contains
    function Mat_Exp (M) result (E)
      real (kind = K), dimension(:, :), intent (in) :: M
      real (kind = K), dimension(Size(M, Dim = 1), Size(M, Dim = 2)) :: E
      integer :: I, N, M_Shape(2)
      real (kind = K) :: Sign = 1.0
      real (kind = K), allocatable, dimension(:, :) :: Term
    ! start function Mat_Exp
      E = 0.0_K      ! Initialize power series.
      M_Shape = Shape(M)
      if (Sum (M ** 2) > 0.5_K) return  ! M will probably not converge fast enough.
      if (M_Shape(1) /= M_Shape(2)) return ! M must be a square matrix
      allocate (Term(M_Shape(1), M_Shape(2)))
      Term = 0.0_K  ! Initialize Term to identity matrix.
      do I = 1, Dim
        Term(I, I) = 1.0_K
      end do
      do N = 0, 100  ! Exit when Term is small or after Term is 100.
        E = E + Term  ! Exp (M) power series
        if (Sum(Term ** 2) < 2.0_K * Spacing (1.0_K)) return  ! Converged OK.
        Term = Sign * MatMul (Term, M) / Real (N + 1, Kind = K)  ! Calculate next Term.
        Sign = - Sign
      end do
      return
    end function Mat_Exp
  end program Matress