---

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 : 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

SEE ALSO

o	acos(3) - Arccosine (inverse cosine) function
o	acosh(3) - Inverse hyperbolic cosine function
o	asin(3) - Arcsine function
o	asinh(3) - Inverse hyperbolic sine function
o	atan(3) - Arctangent AKA inverse tangent function
o	atan2(3) - Arctangent (inverse tangent) function
o	atanh(3) - Inverse hyperbolic tangent function
o	cos(3) - Cosine function
o	cosh(3) - Hyperbolic cosine function
o	sin(3) - Sine function
o	sinh(3) - Hyperbolic sine function
o	tan(3) - Tangent function
o	tanh(3) - Hyperbolic tangent function
o	bessel_j0(3) - Bessel function of the first kind of order 0
o	bessel_j1(3) - Bessel function of the first kind of order 1
o	bessel_jn(3) - Bessel function of the first kind
o	bessel_y0(3) - Bessel function of the second kind of order 0
o	bessel_y1(3) - Bessel function of the second kind of order 1
o	bessel_yn(3) - Bessel function of the second kind
o	erf(3) - Error function
o	erfc(3) - Complementary error function
o	erfc_scaled(3) - Scaled complementary error function
o	exp(3) - Base-e exponential function
o	gamma(3) - Gamma function, which yields factorials for positive whole numbers
o	hypot(3) - Returns the Euclidean distance - the distance between a point and the origin.
o	log(3) - Natural logarithm
o	log10(3) - Base 10 or common logarithm
o	log_gamma(3) - Logarithm of the absolute value of the Gamma function
o	norm2(3) - Euclidean vector norm
o	sqrt(3) - Square-root function
o	random_init(3) - Initializes the state of the pseudorandom number generator
o	random_number(3) - Pseudo-random number
o	random_seed(3) - Initialize a pseudo-random number sequence

Fortran intrinsic descriptions (license: MIT) @urbanjost

---

Nemo Release 3.1

hypot (3fortran)

November 02, 2024

Generated by manServer 1.08 from f2c98770-da98-43f6-bef0-a85443e87a98 using man macros.