Data Types
type	interp_cs_type

Functions/Subroutines
subroutine, public	regridding_set_ppolys (CS, densities, n0, h0, ppoly0_E, ppoly0_S, ppoly0_coefficients, degree)
	Given the set of target values and cell densities, this routine builds an interpolated profile for the densities within each grid cell. It may happen that, given a high-order interpolator, the number of available layers is insufficient (e.g., there are two available layers for a third-order PPM ih4 scheme). In these cases, we resort to the simplest continuous linear scheme (P1M h2). More...

subroutine, public	interpolate_grid (n0, h0, x0, ppoly0_E, ppoly0_coefficients, target_values, degree, n1, h1, x1)
	Given target values (e.g., density), build new grid based on polynomial. More...

subroutine, public	build_and_interpolate_grid (CS, densities, n0, h0, x0, target_values, n1, h1, x1)

real function	get_polynomial_coordinate (N, h, x_g, ppoly_E, ppoly_coefficients, target_value, degree)
	Given a target value, find corresponding coordinate for given polynomial. More...

integer function	interpolation_scheme (interp_scheme)
	Numeric value of interpolation_scheme corresponding to scheme name. More...

subroutine, public	set_interp_scheme (CS, interp_scheme)

subroutine, public	set_interp_extrap (CS, extrapolation)

Variables
integer, parameter	interpolation_p1m_h2 = 0
	O(h^2) More...

integer, parameter	interpolation_p1m_h4 = 1
	O(h^2) More...

integer, parameter	interpolation_p1m_ih4 = 2
	O(h^2) More...

integer, parameter	interpolation_plm = 3
	O(h^2) More...

integer, parameter	interpolation_ppm_h4 = 4
	O(h^3) More...

integer, parameter	interpolation_ppm_ih4 = 5
	O(h^3) More...

integer, parameter	interpolation_p3m_ih4ih3 = 6
	O(h^4) More...

integer, parameter	interpolation_p3m_ih6ih5 = 7
	O(h^4) More...

integer, parameter	interpolation_pqm_ih4ih3 = 8
	O(h^4) More...

integer, parameter	interpolation_pqm_ih6ih5 = 9
	O(h^5) More...

integer, parameter	degree_1 = 1
	List of interpolant degrees. More...

integer, parameter	degree_2 = 2

integer, parameter	degree_3 = 3

integer, parameter	degree_4 = 4

integer, parameter, public	degree_max = 5

real, parameter, public	nr_offset = 1e-6
	When the N-R algorithm produces an estimate that lies outside [0,1], the estimate is set to be equal to the boundary location, 0 or 1, plus or minus an offset, respectively, when the derivative is zero at the boundary. More...

integer, parameter, public	nr_iterations = 8
	Maximum number of Newton-Raphson iterations. Newton-Raphson iterations are used to build the new grid by finding the coordinates associated with target densities and interpolations of degree larger than 1. More...

real, parameter, public	nr_tolerance = 1e-12
	Tolerance for Newton-Raphson iterations (stop when increment falls below this) More...

Function/Subroutine Documentation

◆ build_and_interpolate_grid()

subroutine, public regrid_interp::build_and_interpolate_grid	(	type(interp_cs_type), intent(in)	CS,
		real, dimension(:), intent(in)	densities,
		integer, intent(in)	n0,
		real, dimension(:), intent(in)	h0,
		real, dimension(:), intent(in)	x0,
		real, dimension(:), intent(in)	target_values,
		integer, intent(in)	n1,
		real, dimension(:), intent(inout)	h1,
		real, dimension(:), intent(inout)	x1
	)

Definition at line 279 of file regrid_interp.F90.

References interpolate_grid(), and regridding_set_ppolys().

Referenced by coord_hycom::build_hycom1_column(), and coord_rho::build_rho_column().

   type(interp_cs_type), intent(in) :: cs
   real, dimension(:), intent(in) :: densities, target_values
   integer, intent(in) :: n0, n1
   real, dimension(:), intent(in) :: h0, x0
   real, dimension(:), intent(inout) :: h1, x1
 
   real, dimension(n0,2) :: ppoly0_e, ppoly0_s
   real, dimension(n0,DEGREE_MAX+1) :: ppoly0_c
   integer :: degree
 
   call regridding_set_ppolys(cs, densities, n0, h0, ppoly0_e, ppoly0_s, ppoly0_c, &
        degree)
   call interpolate_grid(n0, h0, x0, ppoly0_e, ppoly0_c, target_values, degree, &
        n1, h1, x1)

Here is the call graph for this function:

Here is the caller graph for this function:

◆ get_polynomial_coordinate()

real function regrid_interp::get_polynomial_coordinate	(	integer, intent(in)	N,
		real, dimension(:), intent(in)	h,
		real, dimension(:), intent(in)	x_g,
		real, dimension(:,:), intent(in)	ppoly_E,
		real, dimension(:,:), intent(in)	ppoly_coefficients,
		real, intent(in)	target_value,
		integer, intent(in)	degree
	)

private

Given a target value, find corresponding coordinate for given polynomial.

Here, 'ppoly' is assumed to be a piecewise discontinuous polynomial of degree 'degree' throughout the domain defined by 'grid'. A target value is given and we need to determine the corresponding grid coordinate to define the new grid.

If the target value is out of range, the grid coordinate is simply set to be equal to one of the boundary coordinates, which results in vanished layers near the boundaries.

IT IS ASSUMED THAT THE PIECEWISE POLYNOMIAL IS MONOTONICALLY INCREASING. IF THIS IS NOT THE CASE, THE NEW GRID MAY BE ILL-DEFINED.

It is assumed that the number of cells defining 'grid' and 'ppoly' are the same.

Parameters

[in]	n	Number of grid cells
[in]	h	Grid cell thicknesses
[in]	x_g	Grid interface locations
[in]	ppoly_e	Edge values of interpolating polynomials
[in]	ppoly_coefficients	Coefficients of interpolating polynomials
[in]	target_value	Target value to find position for
[in]	degree	Degree of the interpolating polynomials

Returns: The position of x_g at which target_value is found.

Definition at line 313 of file regrid_interp.F90.

References mom_error_handler::mom_error(), nr_iterations, nr_offset, and nr_tolerance.

Referenced by interpolate_grid().

   ! Arguments
   integer,              intent(in) :: n                  !< Number of grid cells
   real, dimension(:),   intent(in) :: h                  !< Grid cell thicknesses
   real, dimension(:),   intent(in) :: x_g                !< Grid interface locations
   real, dimension(:,:), intent(in) :: ppoly_e            !< Edge values of interpolating polynomials
   real, dimension(:,:), intent(in) :: ppoly_coefficients !< Coefficients of interpolating polynomials
   real,                 intent(in) :: target_value       !< Target value to find position for
   integer,              intent(in) :: degree             !< Degree of the interpolating polynomials
 
   real :: x_tgt !< The position of x_g at which target_value is found.
 
   ! Local variables
   integer                     :: i, k        ! loop indices
   integer                     :: k_found     ! index of target cell
   integer                     :: iter
   real                        :: xi0         ! normalized target coordinate
   real, dimension(DEGREE_MAX) :: a           ! polynomial coefficients
   real                        :: numerator
   real                        :: denominator
   real                        :: delta       ! Newton-Raphson increment
   real                        :: x           ! global target coordinate
   real                        :: eps         ! offset used to get away from
                                              ! boundaries
   real                        :: grad        ! gradient during N-R iterations
 
   eps = nr_offset
   k_found = -1
 
   ! If the target value is outside the range of all values, we
   ! force the target coordinate to be equal to the lowest or
   ! largest value, depending on which bound is overtaken
   if ( target_value <= ppoly_e(1,1) ) then
     x_tgt = x_g(1)
     return  ! return because there is no need to look further
   end if
 
   ! Since discontinuous edge values are allowed, we check whether the target
   ! value lies between two discontinuous edge values at interior interfaces
   do k = 2,n
     if ( ( target_value >= ppoly_e(k-1,2) ) .AND. &
       ( target_value <= ppoly_e(k,1) ) ) then
       x_tgt = x_g(k)
       return   ! return because there is no need to look further
       exit
     end if
   end do
 
   ! If the target value is outside the range of all values, we
   ! force the target coordinate to be equal to the lowest or
   ! largest value, depending on which bound is overtaken
   if ( target_value >= ppoly_e(n,2) ) then
     x_tgt = x_g(n+1)
     return  ! return because there is no need to look further
   end if
 
   ! At this point, we know that the target value is bounded and does not
   ! lie between discontinuous, monotonic edge values. Therefore,
   ! there is a unique solution. We loop on all cells and find which one
   ! contains the target value. The variable k_found holds the index value
   ! of the cell where the taregt value lies.
   do k = 1,n
     if ( ( target_value > ppoly_e(k,1) ) .AND. &
          ( target_value < ppoly_e(k,2) ) ) then
       k_found = k
       exit
     end if
   end do
 
   ! At this point, 'k_found' should be strictly positive. If not, this is
   ! a major failure because it means we could not find any target cell
   ! despite the fact that the target value lies between the extremes. It
   ! means there is a major problem with the interpolant. This needs to be
   ! reported.
   if ( k_found == -1 ) then
       write(*,*) target_value, ppoly_e(1,1), ppoly_e(n,2)
       write(*,*) 'Could not find target coordinate in ' //&
                  '"get_polynomial_coordinate". This is caused by an '//&
                  'inconsistent interpolant (perhaps not monotonically '//&
                  'increasing)'
       call mom_error( fatal, 'Aborting execution' )
   end if
 
   ! Reset all polynomial coefficients to 0 and copy those pertaining to
   ! the found cell
   a(:) = 0.0
   do i = 1,degree+1
     a(i) = ppoly_coefficients(k_found,i)
   end do
 
   ! Guess value to start Newton-Raphson iterations (middle of cell)
   xi0 = 0.5
   iter = 1
   delta = 1e10
 
   ! Newton-Raphson iterations
   do
     ! break if converged or too many iterations taken
     if ( ( iter > nr_iterations ) .OR. &
          ( abs(delta) < nr_tolerance ) ) then
       exit
     end if
 
     numerator = a(1) + a(2)*xi0 + a(3)*xi0*xi0 + a(4)*xi0*xi0*xi0 + &
                 a(5)*xi0*xi0*xi0*xi0 - target_value
 
     denominator = a(2) + 2*a(3)*xi0 + 3*a(4)*xi0*xi0 + 4*a(5)*xi0*xi0*xi0
 
     delta = -numerator / denominator
 
     xi0 = xi0 + delta
 
     ! Check whether new estimate is out of bounds. If the new estimate is
     ! indeed out of bounds, we manually set it to be equal to the overtaken
     ! bound with a small offset towards the interior when the gradient of
     ! the function at the boundary is zero (in which case, the Newton-Raphson
     ! algorithm does not converge).
     if ( xi0 < 0.0 ) then
       xi0 = 0.0
       grad = a(2)
       if ( grad == 0.0 ) xi0 = xi0 + eps
     end if
 
     if ( xi0 > 1.0 ) then
       xi0 = 1.0
       grad = a(2) + 2*a(3) + 3*a(4) + 4*a(5)
       if ( grad == 0.0 ) xi0 = xi0 - eps
     end if
 
     iter = iter + 1
   end do ! end Newton-Raphson iterations
 
   x_tgt = x_g(k_found) + xi0 * h(k_found)

Here is the call graph for this function:

Here is the caller graph for this function:

◆ interpolate_grid()

subroutine, public regrid_interp::interpolate_grid	(	integer, intent(in)	n0,
		real, dimension(:), intent(in)	h0,
		real, dimension(:), intent(in)	x0,
		real, dimension(:,:), intent(in)	ppoly0_E,
		real, dimension(:,:), intent(in)	ppoly0_coefficients,
		real, dimension(:), intent(in)	target_values,
		integer, intent(in)	degree,
		integer, intent(in)	n1,
		real, dimension(:), intent(inout)	h1,
		real, dimension(:), intent(inout)	x1
	)

Given target values (e.g., density), build new grid based on polynomial.

Given the grid 'grid0' and the piecewise polynomial interpolant 'ppoly0' (possibly discontinuous), the coordinates of the new grid 'grid1' are determined by finding the corresponding target interface densities.

Parameters

[in]	n0	Number of points on source grid
[in]	h0	Thicknesses of source grid cells
[in]	x0	Source interface positions
[in]	ppoly0_e	Edge values of interpolating polynomials
[in]	ppoly0_coefficients	Coefficients of interpolating polynomials
[in]	target_values	Target values of interfaces
[in]	degree	Degree of interpolating polynomials
[in]	n1	Number of points on target grid
[in,out]	h1	Thicknesses of target grid cells
[in,out]	x1	Target interface positions

Definition at line 247 of file regrid_interp.F90.

References get_polynomial_coordinate().

Referenced by build_and_interpolate_grid().

   ! Arguments
   integer,            intent(in)    :: n0                  !< Number of points on source grid
   real, dimension(:), intent(in)    :: h0                  !< Thicknesses of source grid cells
   real, dimension(:), intent(in)    :: x0                  !< Source interface positions
   real, dimension(:,:), intent(in)  :: ppoly0_e            !< Edge values of interpolating polynomials
   real, dimension(:,:), intent(in)  :: ppoly0_coefficients !< Coefficients of interpolating polynomials
   real, dimension(:), intent(in)    :: target_values       !< Target values of interfaces
   integer,            intent(in)    :: degree              !< Degree of interpolating polynomials
   integer,            intent(in)    :: n1                  !< Number of points on target grid
   real, dimension(:), intent(inout) :: h1                  !< Thicknesses of target grid cells
   real, dimension(:), intent(inout) :: x1                  !< Target interface positions
 
   ! Local variables
   integer        :: k ! loop index
   real           :: t ! current interface target density
 
   ! Make sure boundary coordinates of new grid coincide with boundary
   ! coordinates of previous grid
   x1(1) = x0(1)
   x1(n1+1) = x0(n0+1)
 
   ! Find coordinates for interior target values
   do k = 2,n1
     t = target_values(k)
     x1(k) = get_polynomial_coordinate( n0, h0, x0, ppoly0_e, ppoly0_coefficients, t, degree )
     h1(k-1) = x1(k) - x1(k-1)
   end do
   h1(n1) = x1(n1+1) - x1(n1)
 

Here is the call graph for this function:

Here is the caller graph for this function:

◆ interpolation_scheme()

integer function regrid_interp::interpolation_scheme ( character(len=*), intent(in) interp_scheme )

private

Numeric value of interpolation_scheme corresponding to scheme name.

Parameters

[in] interp_scheme Name of interpolation scheme

Definition at line 449 of file regrid_interp.F90.

References interpolation_p1m_h2, interpolation_p1m_h4, interpolation_p1m_ih4, interpolation_p3m_ih4ih3, interpolation_p3m_ih6ih5, interpolation_plm, interpolation_ppm_h4, interpolation_ppm_ih4, interpolation_pqm_ih4ih3, interpolation_pqm_ih6ih5, mom_error_handler::mom_error(), and mom_string_functions::uppercase().

Referenced by set_interp_scheme().

   character(len=*), intent(in) :: interp_scheme !< Name of interpolation scheme
 
   select case ( uppercase(trim(interp_scheme)) )
     case ("P1M_H2");     interpolation_scheme = interpolation_p1m_h2
     case ("P1M_H4");     interpolation_scheme = interpolation_p1m_h4
     case ("P1M_IH2");    interpolation_scheme = interpolation_p1m_ih4
     case ("PLM");        interpolation_scheme = interpolation_plm
     case ("PPM_H4");     interpolation_scheme = interpolation_ppm_h4
     case ("PPM_IH4");    interpolation_scheme = interpolation_ppm_ih4
     case ("P3M_IH4IH3"); interpolation_scheme = interpolation_p3m_ih4ih3
     case ("P3M_IH6IH5"); interpolation_scheme = interpolation_p3m_ih6ih5
     case ("PQM_IH4IH3"); interpolation_scheme = interpolation_pqm_ih4ih3
     case ("PQM_IH6IH5"); interpolation_scheme = interpolation_pqm_ih6ih5
     case default ; call mom_error(fatal, "regrid_interp: "//&
      "Unrecognized choice for INTERPOLATION_SCHEME ("//trim(interp_scheme)//").")
   end select

Here is the call graph for this function:

Here is the caller graph for this function:

◆ regridding_set_ppolys()

subroutine, public regrid_interp::regridding_set_ppolys	(	type(interp_cs_type), intent(in)	CS,
		real, dimension(:), intent(in)	densities,
		integer, intent(in)	n0,
		real, dimension(:), intent(in)	h0,
		real, dimension(:,:), intent(inout)	ppoly0_E,
		real, dimension(:,:), intent(inout)	ppoly0_S,
		real, dimension(:,:), intent(inout)	ppoly0_coefficients,
		integer, intent(inout)	degree
	)

Given the set of target values and cell densities, this routine builds an interpolated profile for the densities within each grid cell. It may happen that, given a high-order interpolator, the number of available layers is insufficient (e.g., there are two available layers for a third-order PPM ih4 scheme). In these cases, we resort to the simplest continuous linear scheme (P1M h2).

Parameters

[in]	cs	Interpolation control structure
[in]	densities	Actual cell densities
[in]	n0	Number of cells on source grid
[in]	h0	cell widths on source grid
[in,out]	ppoly0_e	Edge value of polynomial
[in,out]	ppoly0_s	Edge slope of polynomial
[in,out]	ppoly0_coefficients	Coefficients of polynomial
[in,out]	degree	The degree of the polynomials

Definition at line 73 of file regrid_interp.F90.

References degree_1, degree_2, degree_3, degree_4, regrid_edge_slopes::edge_slopes_implicit_h3(), regrid_edge_slopes::edge_slopes_implicit_h5(), regrid_edge_values::edge_values_implicit_h4(), regrid_edge_values::edge_values_implicit_h6(), interpolation_p1m_h2, interpolation_p1m_h4, interpolation_p1m_ih4, interpolation_p3m_ih4ih3, interpolation_p3m_ih6ih5, interpolation_plm, interpolation_ppm_h4, interpolation_ppm_ih4, interpolation_pqm_ih4ih3, interpolation_pqm_ih6ih5, p1m_functions::p1m_boundary_extrapolation(), p1m_functions::p1m_interpolation(), p3m_functions::p3m_boundary_extrapolation(), p3m_functions::p3m_interpolation(), plm_functions::plm_boundary_extrapolation(), plm_functions::plm_reconstruction(), ppm_functions::ppm_boundary_extrapolation(), ppm_functions::ppm_reconstruction(), pqm_functions::pqm_boundary_extrapolation_v1(), and pqm_functions::pqm_reconstruction().

Referenced by build_and_interpolate_grid().

   type(interp_cs_type),intent(in)    :: cs !< Interpolation control structure
   real, dimension(:),  intent(in)    :: densities !< Actual cell densities
   integer,             intent(in)    :: n0 !< Number of cells on source grid
   real, dimension(:),  intent(in)    :: h0 !< cell widths on source grid
   real, dimension(:,:),intent(inout) :: ppoly0_e            !< Edge value of polynomial
   real, dimension(:,:),intent(inout) :: ppoly0_s            !< Edge slope of polynomial
   real, dimension(:,:),intent(inout) :: ppoly0_coefficients !< Coefficients of polynomial
   integer,             intent(inout) :: degree  !< The degree of the polynomials
 
   logical :: extrapolate
 
   ! Reset piecewise polynomials
   ppoly0_e(:,:) = 0.0
   ppoly0_s(:,:) = 0.0
   ppoly0_coefficients(:,:) = 0.0
 
   extrapolate = cs%boundary_extrapolation
 
   ! Compute the interpolated profile of the density field and build grid
   select case (cs%interpolation_scheme)
 
     case ( interpolation_p1m_h2 )
       degree = degree_1
       call edge_values_explicit_h2( n0, h0, densities, ppoly0_e )
       call p1m_interpolation( n0, h0, densities, ppoly0_e, ppoly0_coefficients )
       if (extrapolate) then
         call p1m_boundary_extrapolation( n0, h0, densities, ppoly0_e, ppoly0_coefficients )
       end if
 
     case ( interpolation_p1m_h4 )
       degree = degree_1
       if ( n0 >= 4 ) then
         call edge_values_explicit_h4( n0, h0, densities, ppoly0_e )
       else
         call edge_values_explicit_h2( n0, h0, densities, ppoly0_e )
       end if
       call p1m_interpolation( n0, h0, densities, ppoly0_e, ppoly0_coefficients )
       if (extrapolate) then
         call p1m_boundary_extrapolation( n0, h0, densities, ppoly0_e, ppoly0_coefficients )
       end if
 
     case ( interpolation_p1m_ih4 )
       degree = degree_1
       if ( n0 >= 4 ) then
         call edge_values_implicit_h4( n0, h0, densities, ppoly0_e )
       else
         call edge_values_explicit_h2( n0, h0, densities, ppoly0_e )
       end if
       call p1m_interpolation( n0, h0, densities, ppoly0_e, ppoly0_coefficients )
       if (extrapolate) then
         call p1m_boundary_extrapolation( n0, h0, densities, ppoly0_e, ppoly0_coefficients )
       end if
 
     case ( interpolation_plm )
       degree = degree_1
       call plm_reconstruction( n0, h0, densities, ppoly0_e, ppoly0_coefficients )
       if (extrapolate) then
         call plm_boundary_extrapolation( n0, h0, densities, ppoly0_e, ppoly0_coefficients )
       end if
 
     case ( interpolation_ppm_h4 )
       if ( n0 >= 4 ) then
         degree = degree_2
         call edge_values_explicit_h4( n0, h0, densities, ppoly0_e )
         call ppm_reconstruction( n0, h0, densities, ppoly0_e, ppoly0_coefficients )
         if (extrapolate) then
           call ppm_boundary_extrapolation( n0, h0, densities, ppoly0_e, ppoly0_coefficients )
         end if
       else
         degree = degree_1
         call edge_values_explicit_h2( n0, h0, densities, ppoly0_e )
         call p1m_interpolation( n0, h0, densities, ppoly0_e, ppoly0_coefficients )
         if (extrapolate) then
           call p1m_boundary_extrapolation( n0, h0, densities, ppoly0_e, ppoly0_coefficients )
         end if
       end if
 
     case ( interpolation_ppm_ih4 )
       if ( n0 >= 4 ) then
         degree = degree_2
         call edge_values_implicit_h4( n0, h0, densities, ppoly0_e )
         call ppm_reconstruction( n0, h0, densities, ppoly0_e, ppoly0_coefficients )
         if (extrapolate) then
           call ppm_boundary_extrapolation( n0, h0, densities, ppoly0_e, ppoly0_coefficients )
         end if
       else
         degree = degree_1
         call edge_values_explicit_h2( n0, h0, densities, ppoly0_e )
         call p1m_interpolation( n0, h0, densities, ppoly0_e, ppoly0_coefficients )
         if (extrapolate) then
           call p1m_boundary_extrapolation( n0, h0, densities, ppoly0_e, ppoly0_coefficients )
         end if
       end if
 
     case ( interpolation_p3m_ih4ih3 )
       if ( n0 >= 4 ) then
         degree = degree_3
         call edge_values_implicit_h4( n0, h0, densities, ppoly0_e )
         call edge_slopes_implicit_h3( n0, h0, densities, ppoly0_s )
         call p3m_interpolation( n0, h0, densities, ppoly0_e, ppoly0_s, ppoly0_coefficients )
         if (extrapolate) then
           call p3m_boundary_extrapolation( n0, h0, densities, ppoly0_e, ppoly0_s, ppoly0_coefficients )
         end if
       else
         degree = degree_1
         call edge_values_explicit_h2( n0, h0, densities, ppoly0_e )
         call p1m_interpolation( n0, h0, densities, ppoly0_e, ppoly0_coefficients )
         if (extrapolate) then
           call p1m_boundary_extrapolation( n0, h0, densities, ppoly0_e, ppoly0_coefficients )
         end if
       end if
 
     case ( interpolation_p3m_ih6ih5 )
       if ( n0 >= 6 ) then
         degree = degree_3
         call edge_values_implicit_h6( n0, h0, densities, ppoly0_e )
         call edge_slopes_implicit_h5( n0, h0, densities, ppoly0_s )
         call p3m_interpolation( n0, h0, densities, ppoly0_e, ppoly0_s, ppoly0_coefficients )
         if (extrapolate) then
           call p3m_boundary_extrapolation( n0, h0, densities, ppoly0_e, ppoly0_s, ppoly0_coefficients )
         end if
       else
         degree = degree_1
         call edge_values_explicit_h2( n0, h0, densities, ppoly0_e )
         call p1m_interpolation( n0, h0, densities, ppoly0_e, ppoly0_coefficients )
         if (extrapolate) then
           call p1m_boundary_extrapolation( n0, h0, densities, ppoly0_e, ppoly0_coefficients )
         end if
       end if
 
     case ( interpolation_pqm_ih4ih3 )
       if ( n0 >= 4 ) then
         degree = degree_4
         call edge_values_implicit_h4( n0, h0, densities, ppoly0_e )
         call edge_slopes_implicit_h3( n0, h0, densities, ppoly0_s )
         call pqm_reconstruction( n0, h0, densities, ppoly0_e, ppoly0_s, ppoly0_coefficients )
         if (extrapolate) then
           call pqm_boundary_extrapolation_v1( n0, h0, densities, ppoly0_e, ppoly0_s, ppoly0_coefficients )
         end if
       else
         degree = degree_1
         call edge_values_explicit_h2( n0, h0, densities, ppoly0_e )
         call p1m_interpolation( n0, h0, densities, ppoly0_e, ppoly0_coefficients )
         if (extrapolate) then
           call p1m_boundary_extrapolation( n0, h0, densities, ppoly0_e, ppoly0_coefficients )
         end if
       end if
 
     case ( interpolation_pqm_ih6ih5 )
       if ( n0 >= 6 ) then
         degree = degree_4
         call edge_values_implicit_h6( n0, h0, densities, ppoly0_e )
         call edge_slopes_implicit_h5( n0, h0, densities, ppoly0_s )
         call pqm_reconstruction( n0, h0, densities, ppoly0_e, ppoly0_s, ppoly0_coefficients )
         if (extrapolate) then
           call pqm_boundary_extrapolation_v1( n0, h0, densities, ppoly0_e, ppoly0_s, ppoly0_coefficients )
         end if
       else
         degree = degree_1
         call edge_values_explicit_h2( n0, h0, densities, ppoly0_e )
         call p1m_interpolation( n0, h0, densities, ppoly0_e, ppoly0_coefficients )
         if (extrapolate) then
           call p1m_boundary_extrapolation( n0, h0, densities, ppoly0_e, ppoly0_coefficients )
         end if
       end if
   end select

Here is the call graph for this function:

Here is the caller graph for this function:

◆ set_interp_extrap()

subroutine, public regrid_interp::set_interp_extrap	(	type(interp_cs_type), intent(inout)	CS,
		logical, intent(in)	extrapolation
	)

Definition at line 475 of file regrid_interp.F90.

   type(interp_cs_type), intent(inout) :: cs
   logical,         intent(in)    :: extrapolation
 
   cs%boundary_extrapolation = extrapolation

◆ set_interp_scheme()

subroutine, public regrid_interp::set_interp_scheme	(	type(interp_cs_type), intent(inout)	CS,
		character(len=*), intent(in)	interp_scheme
	)

Definition at line 468 of file regrid_interp.F90.

References interpolation_scheme().

   type(interp_cs_type),  intent(inout) :: cs
   character(len=*), intent(in)    :: interp_scheme
 
   cs%interpolation_scheme = interpolation_scheme(interp_scheme)

Here is the call graph for this function:

Variable Documentation

◆ degree_1

integer, parameter regrid_interp::degree_1 = 1

private

List of interpolant degrees.

Definition at line 49 of file regrid_interp.F90.

Referenced by regridding_set_ppolys().

49 integer, parameter :: degree_1 = 1, degree_2 = 2, degree_3 = 3, degree_4 = 4

◆ degree_2

integer, parameter regrid_interp::degree_2 = 2

private

Definition at line 49 of file regrid_interp.F90.

Referenced by regridding_set_ppolys().

◆ degree_3

integer, parameter regrid_interp::degree_3 = 3

private

Definition at line 49 of file regrid_interp.F90.

Referenced by regridding_set_ppolys().

◆ degree_4

integer, parameter regrid_interp::degree_4 = 4

private

Definition at line 49 of file regrid_interp.F90.

Referenced by regridding_set_ppolys().

◆ degree_max

integer, parameter, public regrid_interp::degree_max = 5

Definition at line 50 of file regrid_interp.F90.

50 integer, public, parameter :: degree_max = 5

◆ interpolation_p1m_h2

integer, parameter regrid_interp::interpolation_p1m_h2 = 0

O(h^2)

Definition at line 37 of file regrid_interp.F90.

Referenced by interpolation_scheme(), and regridding_set_ppolys().

37 integer, parameter :: interpolation_p1m_h2 = 0 !< O(h^2)

◆ interpolation_p1m_h4

integer, parameter regrid_interp::interpolation_p1m_h4 = 1

private

O(h^2)

Definition at line 38 of file regrid_interp.F90.

Referenced by interpolation_scheme(), and regridding_set_ppolys().

38 integer, parameter :: interpolation_p1m_h4 = 1 !< O(h^2)

◆ interpolation_p1m_ih4

integer, parameter regrid_interp::interpolation_p1m_ih4 = 2

private

O(h^2)

Definition at line 39 of file regrid_interp.F90.

Referenced by interpolation_scheme(), and regridding_set_ppolys().

39 integer, parameter :: interpolation_p1m_ih4 = 2 !< O(h^2)

◆ interpolation_p3m_ih4ih3

integer, parameter regrid_interp::interpolation_p3m_ih4ih3 = 6

private

O(h^4)

Definition at line 43 of file regrid_interp.F90.

Referenced by interpolation_scheme(), and regridding_set_ppolys().

43 integer, parameter :: interpolation_p3m_ih4ih3 = 6 !< O(h^4)

◆ interpolation_p3m_ih6ih5

integer, parameter regrid_interp::interpolation_p3m_ih6ih5 = 7

private

O(h^4)

Definition at line 44 of file regrid_interp.F90.

Referenced by interpolation_scheme(), and regridding_set_ppolys().

44 integer, parameter :: interpolation_p3m_ih6ih5 = 7 !< O(h^4)

◆ interpolation_plm

integer, parameter regrid_interp::interpolation_plm = 3

private

O(h^2)

Definition at line 40 of file regrid_interp.F90.

Referenced by interpolation_scheme(), and regridding_set_ppolys().

40 integer, parameter :: interpolation_plm = 3 !< O(h^2)

◆ interpolation_ppm_h4

integer, parameter regrid_interp::interpolation_ppm_h4 = 4

private

O(h^3)

Definition at line 41 of file regrid_interp.F90.

Referenced by interpolation_scheme(), and regridding_set_ppolys().

41 integer, parameter :: interpolation_ppm_h4 = 4 !< O(h^3)

◆ interpolation_ppm_ih4

integer, parameter regrid_interp::interpolation_ppm_ih4 = 5

private

O(h^3)

Definition at line 42 of file regrid_interp.F90.

Referenced by interpolation_scheme(), and regridding_set_ppolys().

42 integer, parameter :: interpolation_ppm_ih4 = 5 !< O(h^3)

◆ interpolation_pqm_ih4ih3

integer, parameter regrid_interp::interpolation_pqm_ih4ih3 = 8

private

O(h^4)

Definition at line 45 of file regrid_interp.F90.

Referenced by interpolation_scheme(), and regridding_set_ppolys().

45 integer, parameter :: interpolation_pqm_ih4ih3 = 8 !< O(h^4)

◆ interpolation_pqm_ih6ih5

integer, parameter regrid_interp::interpolation_pqm_ih6ih5 = 9

private

O(h^5)

Definition at line 46 of file regrid_interp.F90.

Referenced by interpolation_scheme(), and regridding_set_ppolys().

46 integer, parameter :: interpolation_pqm_ih6ih5 = 9 !< O(h^5)

◆ nr_iterations

integer, parameter, public regrid_interp::nr_iterations = 8

Maximum number of Newton-Raphson iterations. Newton-Raphson iterations are used to build the new grid by finding the coordinates associated with target densities and interpolations of degree larger than 1.

Definition at line 59 of file regrid_interp.F90.

Referenced by get_polynomial_coordinate(), and coord_slight::rho_interfaces_col().

59 integer, public, parameter :: nr_iterations = 8

◆ nr_offset

real, parameter, public regrid_interp::nr_offset = 1e-6

When the N-R algorithm produces an estimate that lies outside [0,1], the estimate is set to be equal to the boundary location, 0 or 1, plus or minus an offset, respectively, when the derivative is zero at the boundary.

Definition at line 55 of file regrid_interp.F90.

Referenced by get_polynomial_coordinate().

55 real, public, parameter :: nr_offset = 1e-6

◆ nr_tolerance

real, parameter, public regrid_interp::nr_tolerance = 1e-12

Tolerance for Newton-Raphson iterations (stop when increment falls below this)

Definition at line 61 of file regrid_interp.F90.

Referenced by get_polynomial_coordinate(), and coord_slight::rho_interfaces_col().

61 real, public, parameter :: nr_tolerance = 1e-12

Data Types

Functions/Subroutines

Variables

Function/Subroutine Documentation

◆ build_and_interpolate_grid()

◆ get_polynomial_coordinate()

◆ interpolate_grid()

◆ interpolation_scheme()

◆ regridding_set_ppolys()

◆ set_interp_extrap()

◆ set_interp_scheme()

Variable Documentation

◆ degree_1

◆ degree_2

◆ degree_3

◆ degree_4

◆ degree_max

◆ interpolation_p1m_h2

◆ interpolation_p1m_h4

◆ interpolation_p1m_ih4

◆ interpolation_p3m_ih4ih3

◆ interpolation_p3m_ih6ih5

◆ interpolation_plm

◆ interpolation_ppm_h4

◆ interpolation_ppm_ih4

◆ interpolation_pqm_ih4ih3

◆ interpolation_pqm_ih6ih5

◆ nr_iterations

◆ nr_offset

◆ nr_tolerance