polynomial_functions Module Reference

Detailed Description

Polynomial functions.

Date of creation: 2008.06.12 L. White

This module contains routines that handle polynomials.

Functions/Subroutines
real function, public	evaluation_polynomial (coeff, ncoef, x)
	Pointwise evaluation of a polynomial at x. More...
real function, public	first_derivative_polynomial (coeff, ncoef, x)
	Calculates the first derivative of a polynomial evaluated at a point x. More...
real function, public	integration_polynomial (xi0, xi1, Coeff, npoly)
	Exact integration of polynomial of degree npoly. More...

Function/Subroutine Documentation

evaluation_polynomial()

real function, public polynomial_functions::evaluation_polynomial	(	real, dimension(:), intent(in)	coeff,
		integer, intent(in)	ncoef,
		real, intent(in)	x
	)

Pointwise evaluation of a polynomial at x.

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 'coeff'. The number of coefficients is given by ncoef and x is the coordinate where the polynomial is to be evaluated.

Parameters

[in]	coeff	The coefficients of the polynomial
[in]	ncoef	The number of polynomial coefficients
[in]	x	The position at which to evaluate the polynomial

Definition at line 20 of file polynomial_functions.F90.

  real, dimension(:), intent(in) :: coeff !< The coefficients of the polynomial
  integer,            intent(in) :: ncoef !< The number of polynomial coefficients
  real,               intent(in) :: x     !< The position at which to evaluate the polynomial
  ! Local variables
  integer :: k
  real    :: f    ! value of polynomial at x
 
  f = 0.0
  do k = 1,ncoef
    f = f + coeff(k) * ( x**(k-1) )
  enddo
 
  evaluation_polynomial = f
 

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(), regrid_edge_values::edge_values_implicit_h6(), mom_neutral_diffusion::find_neutral_pos_full(), mom_neutral_diffusion::find_neutral_pos_linear(), mom_neutral_diffusion::neutral_diffusion_calc_coeffs(), and mom_neutral_diffusion::neutral_surface_t_eval().

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first_derivative_polynomial()

real function, public polynomial_functions::first_derivative_polynomial	(	real, dimension(:), intent(in)	coeff,
		integer, intent(in)	ncoef,
		real, intent(in)	x
	)

Calculates the first derivative of a polynomial evaluated at a point x.

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 'coeff'. The number of coefficients is given by ncoef and x is the coordinate where the polynomial's derivative is to be evaluated.

Parameters

[in]	coeff	The coefficients of the polynomial
[in]	ncoef	The number of polynomial coefficients
[in]	x	The position at which to evaluate the derivative

Definition at line 44 of file polynomial_functions.F90.

  real, dimension(:), intent(in) :: coeff !< The coefficients of the polynomial
  integer,            intent(in) :: ncoef !< The number of polynomial coefficients
  real, intent(in)               :: x     !< The position at which to evaluate the derivative
  ! Local variables
  integer                               :: k
  real                                  :: f    ! value of polynomial at x
 
  f = 0.0
  do k = 2,ncoef
    f = f + real(k-1)*coeff(k) * ( x**(k-2) )
  enddo
 
  first_derivative_polynomial = f
 

Referenced by mom_neutral_diffusion::find_neutral_pos_linear().

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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)	Coeff,
		integer, intent(in)	npoly
	)

Exact integration of polynomial of degree npoly.

The array of coefficients (Coeff) must be of size npoly+1.

Parameters

[in]	xi0	The lower bound of the integral
[in]	xi1	The lower bound of the integral
[in]	coeff	The coefficients of the polynomial
[in]	npoly	The degree of the polynomial

Definition at line 64 of file polynomial_functions.F90.

  real,               intent(in) :: xi0   !< The lower bound of the integral
  real,               intent(in) :: xi1   !< The lower bound of the integral
  real, dimension(:), intent(in) :: Coeff !< The coefficients of the polynomial
  integer,            intent(in) :: npoly !< The degree of the polynomial
  ! Local variables
  integer                           :: k
  real                              :: integral
 
  integral = 0.0
 
  do k = 1,npoly+1
    integral = integral + coeff(k) * (xi1**k - xi0**k) / real(k)
  enddo
!
!One non-answer-changing way of unrolling the above is:
!  k=1
!  integral = integral + Coeff(k) * (xi1**k - xi0**k) / real(k)
!  if (npoly>=1) then
!    k=2
!    integral = integral + Coeff(k) * (xi1**k - xi0**k) / real(k)
!  endif
!  if (npoly>=2) then
!    k=3
!    integral = integral + Coeff(k) * (xi1**k - xi0**k) / real(k)
!  endif
!  if (npoly>=3) then
!    k=4
!    integral = integral + Coeff(k) * (xi1**k - xi0**k) / real(k)
!  endif
!  if (npoly>=4) then
!    k=5
!    integral = integral + Coeff(k) * (xi1**k - xi0**k) / real(k)
!  endif
!
  integration_polynomial = integral