Manual Reference Pages - hypot (3fortran)

NAME

HYPOT(3) - [MATHEMATICS] Returns the Euclidean distance - the distance between a point and the origin.

SYNOPSIS

result = hypot(x, y)

         elemental real(kind=KIND) function hypot(x,y)

          real(kind=KIND),intent(in) :: x
          real(kind=KIND),intent(in) :: y

CHARACTERISTICS

o X,Y and the result shall all be real and of the same KIND.

DESCRIPTION

HYPOT(3) is referred to as the Euclidean distance function. It is equal to
    sqrt(x**2+y**2)
without undue underflow or overflow.
In mathematics, the Euclidean distance between two points in Euclidean space is the length of a line segment between two points.
HYPOT(X,Y) returns the distance between the point <X,Y> and the origin.

OPTIONS

o X : The type shall be real.

o Y : The type and kind type parameter shall be the same as X.

RESULT

The return value has the same type and kind type parameter as X.
The result is the positive magnitude of the distance of the point <X,Y> from the origin <0.0,0.0> .

EXAMPLES

Sample program:

    program demo_hypot
    use, intrinsic :: iso_fortran_env, only : &
     & real_kinds, real32, real64, real128
    implicit none
    real(kind=real32) :: x, y
    real(kind=real32),allocatable :: xs(:), ys(:)
    integer :: i
    character(len=*),parameter :: f=’(a,/,SP,*(3x,g0,1x,g0:,/))’

       x = 1.e0_real32
       y = 0.5e0_real32

       write(*,*)
       write(*,’(*(g0))’)’point <’,x,’,’,y,’> is ’,hypot(x,y)
       write(*,’(*(g0))’)’units away from the origin’
       write(*,*)

       ! elemental
       xs=[  x,  x**2,  x*10.0,  x*15.0, -x**2  ]
       ys=[  y,  y**2, -y*20.0,  y**2,   -y**2  ]

       write(*,f)"the points",(xs(i),ys(i),i=1,size(xs))
       write(*,f)"have distances from the origin of ",hypot(xs,ys)
       write(*,f)"the closest is",minval(hypot(xs,ys))

    end program demo_hypot

Results:

point <1.00000000,0.500000000> is 1.11803401 units away from the origin

the points +1.00000000 +0.500000000 +1.00000000 +0.250000000 +10.0000000 -10.0000000 +15.0000000 +0.250000000 -1.00000000 -0.250000000 have distances from the origin of +1.11803401 +1.03077638 +14.1421356 +15.0020828 +1.03077638 the closest is +1.03077638

STANDARD

Fortran 2008

o	X : The type shall be real.
o	Y : The type and kind type parameter shall be the same as X.