polynomial_functions Module Reference

Functions/Subroutines
real function, public	evaluation_polynomial (coefficients, nb_coefficients, x)
real function, public	integration_polynomial (xi0, xi1, C, n)

Function/Subroutine Documentation

evaluation_polynomial()

real function, public polynomial_functions::evaluation_polynomial	(	real, dimension(:), intent(in)	coefficients,
		integer, intent(in)	nb_coefficients,
		real, intent(in)	x
	)

Definition at line 26 of file polynomial_functions.F90.

Referenced by regrid_edge_slopes::edge_slopes_implicit_h3(), regrid_edge_slopes::edge_slopes_implicit_h5(), regrid_edge_values::edge_values_explicit_h4(), regrid_edge_values::edge_values_implicit_h4(), and regrid_edge_values::edge_values_implicit_h6().

! -----------------------------------------------------------------------------
! The polynomial is defined by the coefficients contained in the
! array of the same name, as follows: C(1) + C(2)x + C(3)x^2 + C(4)x^3 + ...
! where C refers to the array 'coefficients'.
! The number of coefficients is given by nb_coefficients and x
! is the coordinate where the polynomial is to be evaluated.
!
! The function returns the value of the polynomial at x.
! -----------------------------------------------------------------------------

  ! Arguments
  real, dimension(:), intent(in)        :: coefficients
  integer, intent(in)                   :: nb_coefficients
  real, intent(in)                      :: x

  ! Local variables
  integer                               :: k
  real                                  :: f    ! value of polynomial at x

  f = 0.0
  do k = 1,nb_coefficients
    f = f + coefficients(k) * ( x**(k-1) )
  end do

  evaluation_polynomial = f

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integration_polynomial()

real function, public polynomial_functions::integration_polynomial	(	real, intent(in)	xi0,
		real, intent(in)	xi1,
		real, dimension(:), intent(in)	C,
		integer, intent(in)	n
	)

Definition at line 58 of file polynomial_functions.F90.

! -----------------------------------------------------------------------------
! Exact integration of a polynomial of degree n over the interval [xi0,xi1].
! The array of coefficients (C) must be of size n+1, where n is the degree of
! the polynomial to integrate.
! -----------------------------------------------------------------------------

  ! Arguments
  real, intent(in)                  :: xi0, xi1
  real, dimension(:), intent(in)    :: c
  integer, intent(in)               :: n

  ! Local variables
  integer                           :: k
  real                              :: integral

  integral = 0.0

  do k = 1,(n+1)
    integral = integral + c(k) * (xi1**k - xi0**k) / real(k)
  end do
!
!One non-answer-changing way of unrolling the above is:
!  k=1
!  integral = integral + C(k) * (xi1**k - xi0**k) / real(k)
!  if (n>=1) then
!    k=2
!    integral = integral + C(k) * (xi1**k - xi0**k) / real(k)
!  endif
!  if (n>=2) then
!    k=3
!    integral = integral + C(k) * (xi1**k - xi0**k) / real(k)
!  endif
!  if (n>=3) then
!    k=4
!    integral = integral + C(k) * (xi1**k - xi0**k) / real(k)
!  endif
!  if (n>=4) then
!    k=5
!    integral = integral + C(k) * (xi1**k - xi0**k) / real(k)
!  endif
!
  integration_polynomial = integral