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Interpolate_cubic1DFd1d2.F90 File Reference

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## Functions/Subroutines

real function, dimension(1:3) Interpolate_cubic1DFd1d2 (a, x)

## ◆ Interpolate_cubic1DFd1d2()

 real function, dimension (1:3) Interpolate_cubic1DFd1d2 ( real, dimension (1:4), intent(in) a, real, intent(in) x )

Calculates the function value and the rescaled 1st and 2nd 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.

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 3:

Interpolate_cubic1DFd1d2 (1) = the function value Interpolate_cubic1DFd1d2 (2) = the rescaled d/dx value Interpolate_cubic1DFd1d2 (3) = the rescaled d2/dx2 value

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

Definition at line 59 of file Interpolate_cubic1DFd1d2.F90.

References Interpolate_cubic1DFd1d2().

Referenced by Interpolate_cubic1DFd1d2().

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