FLASH4.6.1 API

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[Functions] source/numericalTools/Interpolate/Interpolate_cubic1DFd1

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NAME

  Interpolate_cubic1DFd1

SYNOPSIS

  Interpolate_cubic1DFd1 (real, intent (in) :: a (1:4),
                          real, intent (in) :: x)

DESCRIPTION

  Calculates the function value and the rescaled 1st derivative value for a single [x]
  rescaled [0,1] coordinate and the 4 monocubic expansion coefficients. The monocubic
  expansion reads, for one line, in terms of the rescaled [0,1] x coordinate:

                                 3          i
                        F (x) = sum  a (i) x
                                i=0

  The location index of the a (i) inside the 4-dimensional vector is:

                location index of a (i)  =  1 + i

  The rescaled derivatives are given by the general formula:

                 r    r    3                  i-r
                d / dx  = sum (i)  * a (i) * x
                          i=r    r

  where the Pochhammer symbols are defined as:

                  (i)  = i * (i-1) * (i-2) * ... * (i-r+1)
                     r

  From the derivative formula we see, that the highest non-zero derivative is of
  3-rd order.

ARGUMENTS

  a (i) : the i-th monocubic expansion coefficient
  x     : rescaled [0,1] x coordinate

NOTES

  1) The function is defined as a real array of size 2:

           Interpolate_cubic1DFd1 (1) = the function value
           Interpolate_cubic1DFd1 (2) = the rescaled d/dx value

  2) The code checks, if the supplied coordinate [x] is rescaled.