sll_m_sparse_grid_3d Module Reference

Description

Implementation of a 3D sparse grid with interpolation routines.

Author

Katharina Kormann, IPP

Todo:

Implement the optimized interpolation routines for option boundary=1

<DETAILED_DESCRIPTION>

Derived types and interfaces
type	sll_t_sparse_grid_3d
	Sparse grid object for 3d with interpolation routines. More...

Functions/Subroutines
real(kind=f64) function	interpolate_from_interpolant_value (interpolator, data, eta)
	Compute the value of the sparse grid interpolant at position eta (using standard sparse grid interpolation) More...
subroutine	interpolate_const_disp (interpolator, dorder, displacement, data_in, data_out, hiera)
	Interpolation function for interpolation at (constantly) displaced grid points; displacement only in dimension dim. It is another implementation of the base-class function "interpolate_disp". The advantage is that we can not revisit nodes as we do in the recursive dimension-independently-programmed version. More...
real(kind=f64) function	interpolate_from_hierarchical_surplus (interpolator, data, eta)
	Implements interpolate_from_interpolant_value for periodic sparse grid. More...
real(kind=f64) function	interpolate_from_hierarchical_surplus_boundary (interpolator, data, eta)
	implements interpolation from hierarchical surplus (interpolate_from_interpolant_value) non-periodic More...
subroutine	interpolate_array_disp_sgfft (interpolator, dim, displacment_in, data_in, data_out)
	Compute value at displaced grid points using trigonometric interpolation (based on SG FFT) More...
subroutine	initialize_sg3d (interpolator, levels, order, interpolation, interpolation_type, eta_min, eta_max, boundary, modified)
	Initialization function. Set up the hierarchy of the sparse grid. More...
subroutine	set_hierarchy_info (interpolator, counter, cdim, lvecin, kvecin, novecin)
	Helfer function for initialization. Setting all the information needed for node counter of the sparse grid along dimension cdim For a given sparse grid point fill the hierarchy information (3D specific) More...
subroutine	set_hierarchy_info_boundary (interpolator, counter, cdim, lvecin, kvecin, novecin)
	Helfer function for initialization. Setting all the information needed for node counter of the sparse grid along dimension cdim for points at the boundary along dimension dim. More...
subroutine	fg_to_sg (interpolator, fg_values, sg_values)
	Functions to evaluate fg on sg and sg on fg. More...
integer(kind=i32) function, dimension(3)	fg_index (interpolator, sg_index)
	Compute the index of a sparse grid node on level "level" with index "index_on_level" on full grid with of max_level. More...
subroutine	tohierarchical (interpolator, data_in, data_out)
subroutine	todehi (interpolator, data_array)
subroutine	tohira (interpolator, data_array)
subroutine	tonodal (interpolator, data_in, data_out)
subroutine	displace (interpolator, dim, displacement, data)
subroutine	spfft (interpolator, data_in, data_out)
	Sparse grid FFT. More...
subroutine	ispfft (interpolator, data_in, data_out)
	Sparse grid inverse FFT. More...

Function/Subroutine Documentation

displace()

subroutine sll_m_sparse_grid_3d::displace ( class(sll_t_sparse_grid_3d), intent(inout)  interpolator, integer(kind=i32), intent(in)  dim, real(kind=f64), intent(in)  displacement, complex(kind=f64), dimension(:), intent(inout)  data  )

private

Definition at line 942 of file sll_m_sparse_grid_3d.F90.

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fg_index()

integer(kind=i32) function, dimension(3) sll_m_sparse_grid_3d::fg_index ( class(sll_t_sparse_grid_3d), intent(in)  interpolator, integer(kind=i32), intent(in)  sg_index  )

private

Compute the index of a sparse grid node on level "level" with index "index_on_level" on full grid with of max_level.

Definition at line 751 of file sll_m_sparse_grid_3d.F90.

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fg_to_sg()

subroutine sll_m_sparse_grid_3d::fg_to_sg ( class(sll_t_sparse_grid_3d), intent(in)  interpolator, real(kind=f64), dimension(:, :, :), intent(in)  fg_values, real(kind=f64), dimension(:), intent(out)  sg_values  )

private

Functions to evaluate fg on sg and sg on fg.

Definition at line 736 of file sll_m_sparse_grid_3d.F90.

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initialize_sg3d()

subroutine sll_m_sparse_grid_3d::initialize_sg3d ( class(sll_t_sparse_grid_3d), intent(inout)  interpolator, integer(kind=i32), dimension(:), intent(in)  levels, integer(kind=i32), intent(in)  order, integer(kind=i32), intent(in)  interpolation, integer(kind=i32), intent(in)  interpolation_type, real(kind=f64), dimension(:), intent(in)  eta_min, real(kind=f64), dimension(:), intent(in)  eta_max, integer(kind=i32), intent(in)  boundary, integer(kind=i32), intent(in)  modified  )

private

Initialization function. Set up the hierarchy of the sparse grid.

Parameters

[in,out]	interpolator	sparse grid object
[in]	eta_min	eta_min defines the lower bound of the domain
[in]	eta_max	eta_max defines the upper bound of the domain
[in]	levels	levels defines the maximum level in the sparse grid for each direction
[in]	order	order of the sparse grid functions
[in]	interpolation	order of the interpolator
[in]	interpolation_type	Choose spline (interpolation_type = 0) or Lagrange (interpolation_type = 1) interpolation for the 1D interpolators if not traditional sparse grid interpolation is used.
[in]	modified	modified defines if we have a traditional sparse grid for modified = 0 (then the l_1 norm of the levels is bounded by max(levels) ) or if the boundary is sparsified for modified = 1 (then the l_1 norm of the levels is bounded by max(levels)+1 )
[in]	boundary	boundary defines the boundary conditions: define 0 for periodic boundary conditions and 1 for zero inflow boundaries

Definition at line 393 of file sll_m_sparse_grid_3d.F90.

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interpolate_array_disp_sgfft()

subroutine sll_m_sparse_grid_3d::interpolate_array_disp_sgfft ( class(sll_t_sparse_grid_3d), intent(inout)  interpolator, integer(kind=i32), intent(in)  dim, real(kind=f64), intent(in)  displacment_in, complex(kind=f64), dimension(:), intent(inout)  data_in, real(kind=f64), dimension(:), intent(out)  data_out  )

private

Compute value at displaced grid points using trigonometric interpolation (based on SG FFT)

Parameters

[in,out]	interpolator	Sparse grid object
[in]	dim	dimension along which the points should be displaced with displacement_in
[in]	displacment_in	displacement of the data points along dimension dim
[in,out]	data_in	Fourier transformed values on the sparse grid
[out]	data_out	Function values on the sparse grid after displacement

Definition at line 373 of file sll_m_sparse_grid_3d.F90.

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interpolate_const_disp()

subroutine sll_m_sparse_grid_3d::interpolate_const_disp ( class(sll_t_sparse_grid_3d), intent(inout)  interpolator, integer(kind=i32), dimension(:), intent(in)  dorder, real(kind=f64), intent(in)  displacement, real(kind=f64), dimension(:), intent(inout)  data_in, real(kind=f64), dimension(:), intent(out)  data_out, logical, intent(in)  hiera  )

private

Interpolation function for interpolation at (constantly) displaced grid points; displacement only in dimension dim. It is another implementation of the base-class function "interpolate_disp". The advantage is that we can not revisit nodes as we do in the recursive dimension-independently-programmed version.

Parameters

[in,out]	interpolator	sparse grid object
[in,out]	data_in	hierarchical surplus
[out]	data_out	Value of the function or the hierarchical surplus (depending on value of hiera) for the displaced data points.
[in]	dorder	dorder(1) gives the dimension along which we have the displacement; dorder(2:3) give the remaining dimensions
[in]	displacement	Constant displacement along dimension dorder(1)
[in]	hiera	If the result should be the hierarchical surplus, define hiera = .TRUE.; if the result should be the function values at the data points give hiera = .FALSE.

Definition at line 65 of file sll_m_sparse_grid_3d.F90.

interpolate_from_hierarchical_surplus()

real(kind=f64) function sll_m_sparse_grid_3d::interpolate_from_hierarchical_surplus ( class(sll_t_sparse_grid_3d), intent(inout)  interpolator, real(kind=f64), dimension(:), intent(in)  data, real(kind=f64), dimension(:), intent(in)  eta  )

private

Implements interpolate_from_interpolant_value for periodic sparse grid.

Definition at line 124 of file sll_m_sparse_grid_3d.F90.

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interpolate_from_hierarchical_surplus_boundary()

real(kind=f64) function sll_m_sparse_grid_3d::interpolate_from_hierarchical_surplus_boundary ( class(sll_t_sparse_grid_3d), intent(inout)  interpolator, real(kind=f64), dimension(:), intent(in)  data, real(kind=f64), dimension(:), intent(in)  eta  )

private

implements interpolation from hierarchical surplus (interpolate_from_interpolant_value) non-periodic

Definition at line 181 of file sll_m_sparse_grid_3d.F90.

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interpolate_from_interpolant_value()

real(kind=f64) function sll_m_sparse_grid_3d::interpolate_from_interpolant_value ( class(sll_t_sparse_grid_3d), intent(inout)  interpolator, real(kind=f64), dimension(:), intent(in)  data, real(kind=f64), dimension(:), intent(in)  eta  )

private

Compute the value of the sparse grid interpolant at position eta (using standard sparse grid interpolation)

Parameters

[in,out]

interpolator

sparse grid object

Returns

interpolated value

Parameters

[in]	data	Value of hierarchical surplus
[in]	eta	Coordinates of the point where to interpolate

Definition at line 47 of file sll_m_sparse_grid_3d.F90.

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ispfft()

subroutine sll_m_sparse_grid_3d::ispfft ( class(sll_t_sparse_grid_3d), intent(inout)  interpolator, complex(kind=f64), dimension(:), intent(inout)  data_in, real(kind=f64), dimension(:), intent(out)  data_out  )

private

Sparse grid inverse FFT.

Definition at line 995 of file sll_m_sparse_grid_3d.F90.

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set_hierarchy_info()

subroutine sll_m_sparse_grid_3d::set_hierarchy_info ( class(sll_t_sparse_grid_3d), intent(inout)  interpolator, integer(kind=i32), intent(in)  counter, integer(kind=i32), intent(in)  cdim, integer(kind=i32), dimension(:), intent(in)  lvecin, integer(kind=i32), dimension(:), intent(in)  kvecin, integer(kind=i32), dimension(:), intent(in)  novecin  )

private

Helfer function for initialization. Setting all the information needed for node counter of the sparse grid along dimension cdim For a given sparse grid point fill the hierarchy information (3D specific)

Parameters

[in]	cdim	current dimension
[in]	counter	counter for node
[in]	lvecin	vector of current levels
[in]	kvecin	vector of current index within level
[in]	novecin	vector with number of points on the current level along each dimension

Definition at line 542 of file sll_m_sparse_grid_3d.F90.

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set_hierarchy_info_boundary()

subroutine sll_m_sparse_grid_3d::set_hierarchy_info_boundary ( class(sll_t_sparse_grid_3d), intent(inout)  interpolator, integer(kind=i32), intent(in)  counter, integer(kind=i32), intent(in)  cdim, integer(kind=i32), dimension(:), intent(in)  lvecin, integer(kind=i32), dimension(:), intent(in)  kvecin, integer(kind=i32), dimension(:), intent(in)  novecin  )

private

Helfer function for initialization. Setting all the information needed for node counter of the sparse grid along dimension cdim for points at the boundary along dimension dim.

Parameters

[in]	cdim	current dimension
[in]	counter	counter for node
[in]	lvecin	vector of current levels
[in]	kvecin	vector of current index within level
[in]	novecin	vector with number of points on the current level along each dimension

Definition at line 621 of file sll_m_sparse_grid_3d.F90.

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spfft()

subroutine sll_m_sparse_grid_3d::spfft ( class(sll_t_sparse_grid_3d), intent(inout)  interpolator, real(kind=f64), dimension(:), intent(in)  data_in, complex(kind=f64), dimension(:), intent(out)  data_out  )

private

Sparse grid FFT.

Definition at line 984 of file sll_m_sparse_grid_3d.F90.

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todehi()

subroutine sll_m_sparse_grid_3d::todehi ( class(sll_t_sparse_grid_3d), intent(inout)  interpolator, complex(kind=f64), dimension(:), intent(inout)  data_array  )

private

Definition at line 815 of file sll_m_sparse_grid_3d.F90.

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tohierarchical()

subroutine sll_m_sparse_grid_3d::tohierarchical ( class(sll_t_sparse_grid_3d), intent(inout)  interpolator, real(kind=f64), dimension(:), intent(in)  data_in, complex(kind=f64), dimension(:), intent(out)  data_out  )

private

Definition at line 771 of file sll_m_sparse_grid_3d.F90.

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tohira()

subroutine sll_m_sparse_grid_3d::tohira ( class(sll_t_sparse_grid_3d), intent(inout)  interpolator, complex(kind=f64), dimension(:), intent(inout)  data_array  )

private

Definition at line 857 of file sll_m_sparse_grid_3d.F90.

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tonodal()

subroutine sll_m_sparse_grid_3d::tonodal ( class(sll_t_sparse_grid_3d), intent(inout)  interpolator, complex(kind=f64), dimension(:), intent(inout)  data_in, real(kind=f64), dimension(:), intent(out)  data_out  )

private

Definition at line 899 of file sll_m_sparse_grid_3d.F90.

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