# FLASH4.5 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.