sll_splines

Splines computation and interpolation.

Authors

Edwin Chacon-Golcher

Yaman Güçlü

Katharina Kormann

Laura S. Mendoza

Pierre Navaro

Benedikt Perse

Eric Sonnendrücker

Edoardo Zoni

How to use it

• Link with -lsll_splines
• Add use sll_m_<module_name>

List of Components

1. General object-oriented library for 1D and 2D tensor-product splines
2. Box splines on 2D hexagonal mesh with quasi-interpolation property
3. Optimized cubic splines (1D and 2D tensor-product) on uniform grid
4. 1D cubic splines on non-uniform grid
5. 1D quintic splines on uniform grid
6. Low-level evaluation of 1D B-splines on uniform and non-uniform grids
7. De Boor's implementation of 1D and 2D tensor-product splines

1. General object-oriented library for 1D and 2D tensor-product splines

• sll_m_bsplines
• sll_m_bsplines_base
• sll_m_bsplines_uniform
• sll_m_bsplines_non_uniform
• sll_m_spline_1d
• sll_m_spline_2d
• sll_m_spline_interpolator_1d
• sll_m_spline_interpolator_2d
• sll_m_spline_matrix
• sll_m_spline_matrix_base
• sll_m_spline_matrix_dense
• sll_m_spline_matrix_banded
• sll_m_spline_matrix_periodic_banded

Usage example

use sll_m_bsplines, only: &
  sll_c_bsplines        , &
  sll_s_bsplines_new
 
use sll_m_spline_2d             , only: sll_t_spline_2d
use sll_m_spline_interpolator_2d, only: sll_t_spline_interpolator_2d
 
...
 
class(sll_c_bsplines), allocatable :: basis_x1
class(sll_c_bsplines), allocatable :: basis_x2
type(sll_t_spline_2d)              :: spline_2d
type(sll_t_spline_interpolator_2d) :: interp_2d
 
real(wp), allocatable :: breaks_x2(:)
real(wp), allocatable :: tau_x1(:)
real(wp), allocatable :: tau_x2(:)
real(wp), allocatable :: gtau(:,:)
 
...
 
! Create spline bases along x1 and x2 (x1 grid is uniform, x2 grid is non-uniform)
call sll_s_bsplines_new( basis_x1, degree=7, periodic=.false., xmin=0.0_wp, xmax=1.0_wp, ncells=100 )
call sll_s_bsplines_new( basis_x2, degree=4, periodic=.true. , xmin=0.0_wp, xmax=1.0_wp, ncells= 40, breaks_x2 )
 
! Initialize 2D spline as object of 2D tensor-product space
call spline_2d % init( basis_x1, basis_x2 )
 
! Initialize 2D spline interpolator with bases and boundary conditions
call interp_2d % init( &
  basis_x1, &
  basis_x2, &
  bc_xmin = [sll_p_greville, sll_p_periodic], &
  bc_xmax = [sll_p_greville, sll_p_periodic] )
 
! Get x1 and x2 coordinates of interpolation points from interpolator (Greville averaging)
call interp_2d % get_interp_points( tau_x1, tau_x2 )
allocate( gtau( size(tau_x1), size(tau_x2) ) )
 
...
 
! Compute 2D spline that interpolates solution gtau(:,:) at interpolation points
call interp_2d % compute_interpolant( spline_2d, gtau )
 
! Test: evaluate spline at some location (x1,x2)
write(*,*) spline_2d % eval( x1=0.5_wp, x2=0.5_wp )
 
! Test: print spline coefficient c_{1,1}
write(*,*) spline_2d % bcoef(1,1)

2. Box splines on 2D hexagonal mesh with quasi-interpolation property

• sll_m_box_splines
• sll_m_hex_pre_filters

3. Optimized cubic splines (1D and 2D tensor-product) on uniform grid

• sll_m_cubic_splines

4. 1D cubic splines on non-uniform grid

• sll_m_cubic_non_uniform_splines

5. 1D quintic splines on uniform grid

• sll_m_quintic_splines

6. Low-level evaluation of 1D B-splines on uniform and non-uniform grids

• sll_m_low_level_bsplines