FLASHX
Doxygen Generated Documentation From Interface Source Code

Go to the source code of this file.
Functions/Subroutines  
real function, dimension(1:3)  Interpolate_cubic1DFd1d2 (a, x) 
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 4dimensional vector is:
location index of a (i) = 1 + i
The rescaled derivatives are given by the general formula:
r r 3 ir d / dx = sum (i) * a (i) * x i=r r
where the Pochhammer symbols are defined as:
(i) = i * (i1) * (i2) * ... * (ir+1) r
From the derivative formula we see, that the highest nonzero derivative is of 3rd order.
a (i) : the ith 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().