Given two ranges:

   



[

a

1


,

a

2


]


{\displaystyle [a_{1},a_{2}]}

   and 
   



[

b

1


,

b

2


]


{\displaystyle [b_{1},b_{2}]}

; 
   then a value   



s


{\displaystyle s}

   in range   



[

a

1


,

a

2


]


{\displaystyle [a_{1},a_{2}]}


   is linearly mapped to a value   



t


{\displaystyle t}

   in range   



[

b

1


,

b

2


]


{\displaystyle [b_{1},b_{2}]}


   where:



   



t
=

b

1


+



(
s
−

a

1


)
(

b

2


−

b

1


)


(

a

2


−

a

1


)





{\displaystyle t=b_{1}+{(s-a_{1})(b_{2}-b_{1}) \over (a_{2}-a_{1})}}




Task

Write a function/subroutine/... that takes two ranges and a real number, and returns the mapping of the real number from the first to the second range.

Use this function to map values from the range    [0, 10]    to the range    [-1, 0]. 



Extra credit

Show additional idiomatic ways of performing the mapping, using tools available to the language.




 
function Group-Range
{
    [CmdletBinding()]
    [OutputType([PSCustomObject])]
    Param
    (
        [Parameter(Mandatory=$true,
                   Position=0)]
        [ValidateCount(2,2)]
        [double[]]
        $Range1,
 
        [Parameter(Mandatory=$true,
                   Position=1)]
        [ValidateCount(2,2)]
        [double[]]
        $Range2,
 
        [Parameter(Mandatory=$true,
                   ValueFromPipeline=$true,
                   Position=2)]
        [double]
        $Map
    )
 
    Process
    {
        foreach ($number in $Map)
        {
            [PSCustomObject]@{
                Index   = $number
                Mapping = $Range2[0] + ($number - $Range1[0]) * ($Range2[0] - $Range2[1]) / ($Range1[0] - $Range1[1])
            }
        }
    }
}
 