Discrete derivative polynomial function evaluation. More...
Functions/Subroutines | |
pure double precision function | evaluate_dd_polynomial (x, derivatives) |
Evaluate a polynomial at x, defined by its derivatives (starting from the \(0^th\) derivative) More... | |
pure double precision function | evaluate_dd_polynomial_derivative (x, derivatives, N) |
Evaluate the polynomial's \(N^{th}\) derivative (. More... | |
pure double precision function, dimension(size(derivatives)) | get_dd_polynomial (derivatives) |
Get the polynomial associated to a DD. More... | |
pure double precision function, dimension(n) | get_dd_lagrange_vector (x, N) |
Get the vector made of the Xvector * ifactorials. More... | |
This DD polynomial module furnishes very useful function to evaluate the DD and its derivatives at a particular place x
. Once one has computed the numerical value of the derivative at a particular point the evaluation is a simple computation of the Taylor expansion at that point.
For that purpose, we use the common evaluate_polynomial function by considering the \(i^th\) polynomial coefficient as \(p_i = \frac{D_i}{i!} \).
pure double precision function mod_dd_polynomial::evaluate_dd_polynomial | ( | double precision, intent(in) | x, |
double precision, dimension(:), intent(in) | derivatives | ||
) |
[in] | x | the position where to evaluate |
[in] | derivatives | an array such that \(derivatives(i)=\frac{d^{i-1}P}{dx^{i-1}}\) |
pure double precision function mod_dd_polynomial::evaluate_dd_polynomial_derivative | ( | double precision, intent(in) | x, |
double precision, dimension(:), intent(in) | derivatives, | ||
integer, intent(in) | N | ||
) |
pure double precision function, dimension(n) mod_dd_polynomial::get_dd_lagrange_vector | ( | double precision, intent(in) | x, |
integer, intent(in) | N | ||
) |
The Lagrange vector can be used when evaluating a discrete derivative or a simple Taylor expansion formulae. It is defined as:
\[ Lv_i = \frac{ x^{i-1} }{i!} \]
[in] | x | the position |
[in] | N | the size of the array @ |
pure double precision function, dimension(size(derivatives)) mod_dd_polynomial::get_dd_polynomial | ( | double precision, dimension(:), intent(in) | derivatives | ) |