Binom

Thi function calculates the binomial coefficients.

$$C_{k}^{n}$$ Usage

ans = Binom( n=10, k=2, kind=1.0_Real32 )

܀ See Interface

INTERFACE
  MODULE PURE FUNCTION Binom(n, k, kind) RESULT(ans)
    INTEGER(Int8 | Int16 | Int32 | Int64), INTENT(IN) :: n
    !! n is integer, should be a positive number and greater or equal to k
    INTEGER(Int8 | Int16 | Int32 | Int64), INTENT(IN) :: k
    !! k should be less than or equal to n
    REAL(Real32 | Real64), INTENT(IN) :: kind
    !! kind of output
    REAL(Real32 | Real64) :: ans
  END FUNCTION Binom
END INTERFACE

• The input arguments n and k can be Int8, Int16, Int32, Int64
• The output is always a real number
• If kind is Real32 then the output is Real32
• If the kind is Real64 then the output is Real64

܀ See example

This example shows the usage of Binom method.

program main
  use easifembase
  implicit none

Here we are calculating ${}^{4}C_{m}$, for $m=0,1,2,3,4$

  call display( Binom(4, 0, kind=1.0_DFP), "(4, 0) = " )
  call display( Binom(4, 1, kind=1.0_DFP), "(4, 1) = " )
  call display( Binom(4, 2, kind=1.0_DFP), "(4, 2) = " )
  call display( Binom(4, 3, kind=1.0_DFP), "(4, 3) = " )
  call display( Binom(4, 4, kind=1.0_DFP), "(4, 4) = " )

Results

(4, 0) = 1.00000
(4, 1) = 4.00000
(4, 2) = 6.00000
(4, 3) = 4.00000
(4, 4) = 1.00000

end program main

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