different utils that are useful to manipulate splines on the regular grid of a pw More...

Data Types
type	pw_spline_precond_type
	stores information for the preconditioner used to calculate the coeffs of splines More...

Functions/Subroutines
subroutine, public	pw_spline2_interpolate_values_g (spline_g)
	calculates the FFT of the coefficients of the quadratic spline that interpolates the given values

subroutine, public	pw_spline3_interpolate_values_g (spline_g)
	calculates the FFT of the coefficients of the2 cubic spline that interpolates the given values

subroutine, public	pw_spline_scale_deriv (deriv_vals_r, transpose, scale)
	rescales the derivatives from gridspacing=1 to the real derivatives

subroutine, public	pw_spline3_deriv_g (spline_g, idir)
	calculates the FFT of the values of the x,y,z (idir=1,2,3) derivative of the cubic spline

subroutine, public	pw_spline2_deriv_g (spline_g, idir)
	calculates the FFT of the values of the x,y,z (idir=1,2,3) derivative of the quadratic spline

subroutine, public	pw_nn_smear_r (pw_in, pw_out, coeffs)
	calculates the values of a nearest neighbor smearing

subroutine, public	pw_nn_deriv_r (pw_in, pw_out, coeffs, idir)
	calculates a nearest neighbor central derivative. for the x dir: pw_outarray(i,j,k)=( pw_in(i+1,j,k)-pw_in(i-1,j,k) )coeff(1)+ ( pw_in(i+1,j(+-)1,k)-pw_in(i-1,j(+-)1,k)+ pw_in(i+1,j,k(+-)1)-pw_in(i-1,j,k(+-)1) )coeff(2)+ ( pw_in(i+1,j(+-)1,k(+-)1)-pw_in(i-1,j(+-)1,k(+-)1)+ pw_in(i+1,j(+-)1,k(-+)1)-pw_in(i-1,j(+-)1,k(-+)1) )*coeff(3) periodic boundary conditions are applied

subroutine, public	add_coarse2fine (coarse_coeffs_pw, fine_values_pw, weights_1d, w_border0, w_border1, pbc, safe_computation)
	low level function that adds a coarse grid to a fine grid. If pbc is true periodic boundary conditions are applied

subroutine, public	add_fine2coarse (fine_values_pw, coarse_coeffs_pw, weights_1d, w_border0, w_border1, pbc, safe_computation)
	low level function that adds a coarse grid (without boundary) to a fine grid.

subroutine, public	pw_spline_precond_create (preconditioner, precond_kind, pool, pbc, transpose)
	...

subroutine, public	pw_spline_precond_set_kind (preconditioner, precond_kind, pbc, transpose)
	switches the types of precoditioner to use

subroutine, public	pw_spline_precond_release (preconditioner)
	releases the preconditioner

subroutine, public	pw_spline_do_precond (preconditioner, in_v, out_v)
	applies the preconditioner to the system of equations to find the coefficients of the spline

logical function, public	find_coeffs (values, coeffs, linop, preconditioner, pool, eps_r, eps_x, max_iter, sumtype)
	solves iteratively (CG) a systmes of linear equations linOp(coeffs)=values (for example those needed to find the coefficients of a spline) Returns true if the it succeeded to achieve the requested accuracy

subroutine, public	spl3_nopbc (pw_in, pw_out)
	...

subroutine, public	spl3_nopbct (pw_in, pw_out)
	...

subroutine, public	spl3_pbc (pw_in, pw_out)
	...

real(kind=dp) function, public	eval_interp_spl3_pbc (vec, pw)
	Evaluates the PBC interpolated Spline (pw) function on the generic input vector (vec)

real(kind=dp) function, dimension(3), public	eval_d_interp_spl3_pbc (vec, pw)
	Evaluates the derivatives of the PBC interpolated Spline (pw) function on the generic input vector (vec)

Variables
integer, parameter, public	no_precond = 0

integer, parameter, public	precond_spl3_aint = 1

integer, parameter, public	precond_spl3_1 = 2

integer, parameter, public	precond_spl3_aint2 = 3

integer, parameter, public	precond_spl3_2 = 4

integer, parameter, public	precond_spl3_3 = 5

real(kind=dp), dimension(4), parameter, public	nn10_coeffs = (/125._dp/216._dp, 25._dp/432._dp, 5._dp/864._dp, 1._dp/1728._dp/)

real(kind=dp), dimension(4), parameter, public	spline3_coeffs = (/8._dp/(27._dp), 2._dp/(27._dp), 1._dp/(27._dp2._dp), 1._dp/(27._dp8._dp)/)

real(kind=dp), dimension(4), parameter, public	spline2_coeffs = (/27._dp/(64._dp), 9._dp/(64._dp2_dp), 3._dp/(64._dp4._dp), 1._dp/(64._dp*8._dp)/)

real(kind=dp), dimension(4), parameter, public	nn50_coeffs = (/15625._dp/17576._dp, 625._dp/35152._dp, 25._dp/70304._dp, 1._dp/140608._dp/)

real(kind=dp), dimension(4), parameter, public	spl3_aint_coeff = (/46._dp/27._dp, -2._dp/(27._dp), -1._dp/(27._dp2._dp), -1._dp/(27._dp8._dp)/)

real(kind=dp), dimension(4), parameter, public	spl3_precond1_coeff = (/64._dp/3._dp, -8._dp/3._dp, -1._dp/3._dp, -1._dp/24._dp/)

real(kind=dp), dimension(4), parameter, public	spl3_1d_transf_coeffs = (/2._dp/3._dp, 23._dp/48._dp, 1._dp/6._dp, 1._dp/48._dp/)

real(kind=dp), dimension(3), parameter, public	spline3_deriv_coeffs = (/2.0_dp/9.0_dp, 1.0_dp/18.0_dp, 1.0_dp/72.0_dp/)

real(kind=dp), dimension(3), parameter, public	spline2_deriv_coeffs = (/9.0_dp/32.0_dp, 3.0_dp/64.0_dp, 1.0_dp/128.0_dp/)

real(kind=dp), dimension(3), parameter, public	nn10_deriv_coeffs = (/25._dp/72._dp, 5._dp/144, 1._dp/288._dp/)

real(kind=dp), dimension(3), parameter, public	nn50_deriv_coeffs = (/625._dp/1352._dp, 25._dp/2704._dp, 1._dp/5408._dp/)

real(kind=dp), dimension(3), parameter, public	spl3_1d_coeffs0 = (/1._dp/6_dp, 2._dp/3._dp, 1._dp/6._dp/)

real(kind=dp), dimension(3), parameter, public	spl3_1d_transf_border1 = (/0.517977704_dp, 0.464044595_dp, 0.17977701e-1_dp/)

Detailed Description

different utils that are useful to manipulate splines on the regular grid of a pw

History: 05.2003 created [fawzi] 08.2004 removed spline evaluation method using more than 2 read streams (pw_compose_stripe_rs3), added linear solver based spline inversion [fawzi]

Author: Fawzi Mohamed

Function/Subroutine Documentation

◆ pw_spline2_interpolate_values_g()

subroutine, public pw_spline_utils::pw_spline2_interpolate_values_g ( type(pw_c1d_gs_type), intent(in) spline_g )

calculates the FFT of the coefficients of the quadratic spline that interpolates the given values

Parameters

spline_g on entry the FFT of the values to interpolate as cc, will contain the FFT of the coefficients of the spline

History: 06.2003 created [fawzi]

Author: Fawzi Mohamed

Note: does not work with spherical cutoff

Definition at line 128 of file pw_spline_utils.F.

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◆ pw_spline3_interpolate_values_g()

subroutine, public pw_spline_utils::pw_spline3_interpolate_values_g ( type(pw_c1d_gs_type), intent(in) spline_g )

calculates the FFT of the coefficients of the2 cubic spline that interpolates the given values

Parameters

spline_g on entry the FFT of the values to interpolate as cc, will contain the FFT of the coefficients of the spline

History: 06.2003 created [fawzi]

Author: Fawzi Mohamed

Note: does not work with spherical cutoff stupid distribution for cos calculation, it should calculate only the needed cos, and avoid the mpi_allreduce

Definition at line 199 of file pw_spline_utils.F.

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◆ pw_spline_scale_deriv()

subroutine, public pw_spline_utils::pw_spline_scale_deriv	(	type(pw_r3d_rs_type), dimension(3), intent(in)	deriv_vals_r,
		logical, intent(in), optional	transpose,
		real(kind=dp), intent(in), optional	scale
	)

rescales the derivatives from gridspacing=1 to the real derivatives

Parameters

deriv_vals_r	an array of x,y,z derivatives
transpose	if true applies the transpose of the map (defaults to false)
scale	a scaling factor (defaults to 1.0)

History: 06.2003 created [fawzi]

Author: Fawzi Mohamed

Definition at line 274 of file pw_spline_utils.F.

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◆ pw_spline3_deriv_g()

subroutine, public pw_spline_utils::pw_spline3_deriv_g	(	type(pw_c1d_gs_type), intent(in)	spline_g,
		integer, intent(in)	idir
	)

calculates the FFT of the values of the x,y,z (idir=1,2,3) derivative of the cubic spline

Parameters

spline_g	on entry the FFT of the coefficients of the spline will contain the FFT of the derivative
idir	direction of the derivative

History: 06.2003 created [fawzi]

Author: Fawzi Mohamed

Note: the distance between gridpoints is assumed to be 1

Definition at line 365 of file pw_spline_utils.F.

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◆ pw_spline2_deriv_g()

subroutine, public pw_spline_utils::pw_spline2_deriv_g	(	type(pw_c1d_gs_type), intent(in)	spline_g,
		integer, intent(in)	idir
	)

calculates the FFT of the values of the x,y,z (idir=1,2,3) derivative of the quadratic spline

Parameters

spline_g	on entry the FFT of the coefficients of the spline will contain the FFT of the derivative
idir	direction of the derivative

History: 06.2003 created [fawzi]

Author: Fawzi Mohamed

Note: the distance between gridpoints is assumed to be 1

Definition at line 500 of file pw_spline_utils.F.

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◆ pw_nn_smear_r()

subroutine, public pw_spline_utils::pw_nn_smear_r	(	type(pw_r3d_rs_type), intent(in)	pw_in,
		type(pw_r3d_rs_type), intent(in)	pw_out,
		real(kind=dp), dimension(4), intent(in)	coeffs
	)

calculates the values of a nearest neighbor smearing

Parameters

pw_in	the argument for the linear operator
pw_out	place where the smeared values should be added
coeffs	array with the coefficent of the smearing, ordered with the distance from the center: coeffs(1) the coeff of the central element, coeffs(2) the coeff of the 6 element with distance 1, coeff(3) the coeff of the 12 elements at distance sqrt(2), coeff(4) the coeff of the 8 elements at distance sqrt(3).

Author: Fawzi Mohamed

Note: does not normalize the smear to 1. with coeff=(/ 8._dp/27._dp, 2._dp/27._dp, 1._dp/54._dp, 1._dp/216._dp /) is equivalent to pw_spline3_evaluate_values_g, with coeff=(/ 27._dp/64._dp, 9._dp/128._dp, 3._dp/256._dp, 1._dp/512._dp /)

Definition at line 855 of file pw_spline_utils.F.

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◆ pw_nn_deriv_r()

subroutine, public pw_spline_utils::pw_nn_deriv_r	(	type(pw_r3d_rs_type), intent(in)	pw_in,
		type(pw_r3d_rs_type), intent(in)	pw_out,
		real(kind=dp), dimension(3), intent(in)	coeffs,
		integer	idir
	)

calculates a nearest neighbor central derivative. for the x dir: pw_outarray(i,j,k)=( pw_in(i+1,j,k)-pw_in(i-1,j,k) )*coeff(1)+ ( pw_in(i+1,j(+-)1,k)-pw_in(i-1,j(+-)1,k)+ pw_in(i+1,j,k(+-)1)-pw_in(i-1,j,k(+-)1) )*coeff(2)+ ( pw_in(i+1,j(+-)1,k(+-)1)-pw_in(i-1,j(+-)1,k(+-)1)+ pw_in(i+1,j(+-)1,k(-+)1)-pw_in(i-1,j(+-)1,k(-+)1) )*coeff(3) periodic boundary conditions are applied

Parameters

pw_in	the argument for the linear operator
pw_out	place where the smeared values should be added
coeffs	array with the coefficent of the front (positive) plane of the central derivative, ordered with the distance from the center: coeffs(1) the coeff of the central element, coeffs(2) the coeff of the 4 element with distance 1, coeff(3) the coeff of the 4 elements at distance sqrt(2)
idir	...

Author: Fawzi Mohamed

Note: with coeff=(/ 2.0_dp/9.0_dp, 1.0_dp/18.0_dp, 1.0_dp/72.0_dp /) is equivalent to pw_spline3_deriv_r, with coeff=(/ 9.0_dp/32.0_dp, 3.0_dp/64.0_dp, 1.0_dp/128.0_dp /) to pw_spline2_deriv_r coeff=(/ 25._dp/72._dp, 5._dp/144, 1._dp/288._dp /)

Definition at line 898 of file pw_spline_utils.F.

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◆ add_coarse2fine()

subroutine, public pw_spline_utils::add_coarse2fine	(	type(pw_r3d_rs_type), intent(in)	coarse_coeffs_pw,
		type(pw_r3d_rs_type), intent(in)	fine_values_pw,
		real(kind=dp), dimension(4), intent(in)	weights_1d,
		real(kind=dp), intent(in)	w_border0,
		real(kind=dp), dimension(3), intent(in)	w_border1,
		logical, intent(in)	pbc,
		logical, intent(in), optional	safe_computation
	)

low level function that adds a coarse grid to a fine grid. If pbc is true periodic boundary conditions are applied

It will add to

fine_values(2*coarse_bounds(1,1):2*coarse_bounds(2,1), 2*coarse_bounds(1,2):2*coarse_bounds(2,2), 2*coarse_bounds(1,3):2*coarse_bounds(2,3))

using

coarse_coeffs(coarse_bounds(1,1):coarse_bounds(2,1), coarse_bounds(1,2):coarse_bounds(2,2), coarse_bounds(1,3):coarse_bounds(2,3))

composed with the weights obtained by the direct product of the 1d coefficients weights:

for i,j,k in -3..3 w(i,j,k)=weights_1d(abs(i)+1)*weights_1d(abs(j)+1)* weights_1d(abs(k)+1)

Parameters

coarse_coeffs_pw	the values of the coefficients
fine_values_pw	where to add the values due to the coarse coeffs
weights_1d	the weights of the 1d smearing
w_border0	the 1d weight at the border (when pbc is false)
w_border1	the 1d weights for a point one off the border (w_border1(1) is the weight of the coefficent at the border) (used if pbc is false)
pbc	if periodic boundary conditions should be applied
safe_computation	...

Author: fawzi

Note: coarse looping is continuos, I did not check if keeping the fine looping contiguous is better. And I ask myself yet again why, why we use x-slice distribution, z-slice distribution would be much better performancewise (and would semplify this code enormously). fine2coarse has much more understandable parallel part (build up of send/rcv sizes,... but worse if you have really a lot of processors, probabily irrelevant because it is not critical) [fawzi].

Definition at line 975 of file pw_spline_utils.F.

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◆ add_fine2coarse()

subroutine, public pw_spline_utils::add_fine2coarse	(	type(pw_r3d_rs_type), intent(in)	fine_values_pw,
		type(pw_r3d_rs_type), intent(in)	coarse_coeffs_pw,
		real(kind=dp), dimension(4), intent(in)	weights_1d,
		real(kind=dp), intent(in)	w_border0,
		real(kind=dp), dimension(3), intent(in)	w_border1,
		logical, intent(in)	pbc,
		logical, intent(in), optional	safe_computation
	)

low level function that adds a coarse grid (without boundary) to a fine grid.

It will add to

coarse_coeffs(coarse_bounds(1,1):coarse_bounds(2,1), coarse_bounds(1,2):coarse_bounds(2,2), coarse_bounds(1,3):coarse_bounds(2,3))

using

fine_values(2*coarse_bounds(1,1):2*coarse_bounds(2,1), 2*coarse_bounds(1,2):2*coarse_bounds(2,2), 2*coarse_bounds(1,3):2*coarse_bounds(2,3))

composed with the weights obtained by the direct product of the 1d coefficients weights:

for i,j,k in -3..3 w(i,j,k)=weights_1d(abs(i)+1)*weights_1d(abs(j)+1)* weights_1d(abs(k)+1)

Parameters

fine_values_pw	3d array where to add the values due to the coarse coeffs
coarse_coeffs_pw	3d array with boundary of size 1 with the values of the coefficients
weights_1d	the weights of the 1d smearing
w_border0	the 1d weight at the border
w_border1	the 1d weights for a point one off the border (w_border1(1) is the weight of the coefficent at the border)
pbc	...
safe_computation	...

Author: fawzi

Note: see coarse2fine for some relevant notes

Definition at line 1770 of file pw_spline_utils.F.

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◆ pw_spline_precond_create()

subroutine, public pw_spline_utils::pw_spline_precond_create	(	type(pw_spline_precond_type), intent(out)	preconditioner,
		integer, intent(in)	precond_kind,
		type(pw_pool_type), intent(in), pointer	pool,
		logical, intent(in)	pbc,
		logical, intent(in)	transpose
	)

...

Parameters

preconditioner	the preconditioner to create
precond_kind	the kind of preconditioner to use
pool	a pool with grids of the same type as the elements to precondition
pbc	if periodic boundary conditions should be applied
transpose	...

Author: fawzi

Definition at line 2473 of file pw_spline_utils.F.

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◆ pw_spline_precond_set_kind()

subroutine, public pw_spline_utils::pw_spline_precond_set_kind	(	type(pw_spline_precond_type), intent(inout)	preconditioner,
		integer, intent(in)	precond_kind,
		logical, intent(in), optional	pbc,
		logical, intent(in), optional	transpose
	)

switches the types of precoditioner to use

Parameters

preconditioner	the preconditioner to be changed
precond_kind	the new kind of preconditioner to use
pbc	...
transpose	...

Author: fawzi

Definition at line 2496 of file pw_spline_utils.F.

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◆ pw_spline_precond_release()

subroutine, public pw_spline_utils::pw_spline_precond_release ( type(pw_spline_precond_type), intent(inout) preconditioner )

releases the preconditioner

Parameters

preconditioner the preconditioner to release

Author: fawzi

Definition at line 2580 of file pw_spline_utils.F.

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◆ pw_spline_do_precond()

subroutine, public pw_spline_utils::pw_spline_do_precond	(	type(pw_spline_precond_type), intent(in)	preconditioner,
		type(pw_r3d_rs_type), intent(in)	in_v,
		type(pw_r3d_rs_type), intent(inout)	out_v
	)

applies the preconditioner to the system of equations to find the coefficients of the spline

Parameters

preconditioner	the preconditioner to apply
in_v	the grid on which the preconditioner should be applied
out_v	place to store the preconditioner applied on v_out

Author: fawzi

Definition at line 2594 of file pw_spline_utils.F.

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◆ find_coeffs()

logical function, public pw_spline_utils::find_coeffs	(	type(pw_r3d_rs_type), intent(in)	values,
		type(pw_r3d_rs_type), intent(inout)	coeffs,
		external subroutine(type(pw_r3d_rs_type), intent(in) pw_in, type(pw_r3d_rs_type), intent(inout) pw_out)	linop,
		type(pw_spline_precond_type), intent(in)	preconditioner,
		type(pw_pool_type), pointer	pool,
		real(kind=dp), intent(in)	eps_r,
		real(kind=dp), intent(in)	eps_x,
		integer, intent(in)	max_iter,
		integer, intent(in), optional	sumtype
	)

solves iteratively (CG) a systmes of linear equations linOp(coeffs)=values (for example those needed to find the coefficients of a spline) Returns true if the it succeeded to achieve the requested accuracy

Parameters

values	the right hand side of the system
coeffs	will contain the solution of the system (and on entry it contains the starting point)
linOp	the linear operator to be inverted
preconditioner	the preconditioner to apply
pool	a pool of grids (for the temporary objects)
eps_r	the requested precision on the residual
eps_x	the requested precision on the solution
max_iter	maximum number of iteration allowed
sumtype	...

Returns: ...

Author: fawzi

Definition at line 2647 of file pw_spline_utils.F.

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◆ spl3_nopbc()

subroutine, public pw_spline_utils::spl3_nopbc	(	type(pw_r3d_rs_type), intent(in)	pw_in,
		type(pw_r3d_rs_type), intent(inout)	pw_out
	)

...

Parameters

pw_in	...
pw_out	...

Definition at line 3096 of file pw_spline_utils.F.

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◆ spl3_nopbct()

subroutine, public pw_spline_utils::spl3_nopbct	(	type(pw_r3d_rs_type), intent(in)	pw_in,
		type(pw_r3d_rs_type), intent(inout)	pw_out
	)

...

Parameters

pw_in	...
pw_out	...

Definition at line 3112 of file pw_spline_utils.F.

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◆ spl3_pbc()

subroutine, public pw_spline_utils::spl3_pbc	(	type(pw_r3d_rs_type), intent(in)	pw_in,
		type(pw_r3d_rs_type), intent(inout)	pw_out
	)

...

Parameters

pw_in	...
pw_out	...

Definition at line 3128 of file pw_spline_utils.F.

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◆ eval_interp_spl3_pbc()

real(kind=dp) function, public pw_spline_utils::eval_interp_spl3_pbc	(	real(kind=dp), dimension(3), intent(in)	vec,
		type(pw_r3d_rs_type), intent(in)	pw
	)

Evaluates the PBC interpolated Spline (pw) function on the generic input vector (vec)

Parameters

vec	...
pw	...

Returns: ...

History: 12.2007 Adapted for use with distributed grids [rdeclerck]

Author: Teodoro Laino 12/2005 [tlaino]

Note: Requires the Spline coefficients to be computed with PBC

Definition at line 3150 of file pw_spline_utils.F.

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◆ eval_d_interp_spl3_pbc()

real(kind=dp) function, dimension(3), public pw_spline_utils::eval_d_interp_spl3_pbc	(	real(kind=dp), dimension(3), intent(in)	vec,
		type(pw_r3d_rs_type), intent(in)	pw
	)

Evaluates the derivatives of the PBC interpolated Spline (pw) function on the generic input vector (vec)

Parameters

vec	...
pw	...

Returns: ...

History: 12.2007 Adapted for use with distributed grids [rdeclerck]

Author: Teodoro Laino 12/2005 [tlaino]

Note: Requires the Spline coefficients to be computed with PBC

Definition at line 3299 of file pw_spline_utils.F.

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Variable Documentation

◆ no_precond

integer, parameter, public pw_spline_utils::no_precond = 0

Definition at line 44 of file pw_spline_utils.F.

◆ precond_spl3_aint

integer, parameter, public pw_spline_utils::precond_spl3_aint = 1

Definition at line 44 of file pw_spline_utils.F.

◆ precond_spl3_1

integer, parameter, public pw_spline_utils::precond_spl3_1 = 2

Definition at line 44 of file pw_spline_utils.F.

◆ precond_spl3_aint2

integer, parameter, public pw_spline_utils::precond_spl3_aint2 = 3

Definition at line 44 of file pw_spline_utils.F.

◆ precond_spl3_2

integer, parameter, public pw_spline_utils::precond_spl3_2 = 4

Definition at line 44 of file pw_spline_utils.F.

◆ precond_spl3_3

integer, parameter, public pw_spline_utils::precond_spl3_3 = 5

Definition at line 44 of file pw_spline_utils.F.

◆ nn10_coeffs

real(kind=dp), dimension(4), parameter, public pw_spline_utils::nn10_coeffs = (/125._dp/216._dp, 25._dp/432._dp, 5._dp/864._dp, 1._dp/1728._dp/)

Definition at line 51 of file pw_spline_utils.F.

◆ spline3_coeffs

real(kind=dp), dimension(4), parameter, public pw_spline_utils::spline3_coeffs = (/8._dp/(27._dp), 2._dp/(27._dp), 1._dp/(27._dp*2._dp), 1._dp/(27._dp*8._dp)/)

Definition at line 51 of file pw_spline_utils.F.

◆ spline2_coeffs

real(kind=dp), dimension(4), parameter, public pw_spline_utils::spline2_coeffs = (/27._dp/(64._dp), 9._dp/(64._dp*2_dp), 3._dp/(64._dp*4._dp), 1._dp/(64._dp*8._dp)/)

Definition at line 51 of file pw_spline_utils.F.

◆ nn50_coeffs

real(kind=dp), dimension(4), parameter, public pw_spline_utils::nn50_coeffs = (/15625._dp/17576._dp, 625._dp/35152._dp, 25._dp/70304._dp, 1._dp/140608._dp/)

Definition at line 51 of file pw_spline_utils.F.

◆ spl3_aint_coeff

real(kind=dp), dimension(4), parameter, public pw_spline_utils::spl3_aint_coeff = (/46._dp/27._dp, -2._dp/(27._dp), -1._dp/(27._dp*2._dp), -1._dp/(27._dp*8._dp)/)

Definition at line 51 of file pw_spline_utils.F.

◆ spl3_precond1_coeff

real(kind=dp), dimension(4), parameter, public pw_spline_utils::spl3_precond1_coeff = (/64._dp/3._dp, -8._dp/3._dp, -1._dp/3._dp, -1._dp/24._dp/)

Definition at line 51 of file pw_spline_utils.F.

◆ spl3_1d_transf_coeffs

real(kind=dp), dimension(4), parameter, public pw_spline_utils::spl3_1d_transf_coeffs = (/2._dp/3._dp, 23._dp/48._dp, 1._dp/6._dp, 1._dp/48._dp/)

Definition at line 51 of file pw_spline_utils.F.

◆ spline3_deriv_coeffs

real(kind=dp), dimension(3), parameter, public pw_spline_utils::spline3_deriv_coeffs = (/2.0_dp/9.0_dp, 1.0_dp/18.0_dp, 1.0_dp/72.0_dp/)

Definition at line 70 of file pw_spline_utils.F.

◆ spline2_deriv_coeffs

real(kind=dp), dimension(3), parameter, public pw_spline_utils::spline2_deriv_coeffs = (/9.0_dp/32.0_dp, 3.0_dp/64.0_dp, 1.0_dp/128.0_dp/)

Definition at line 70 of file pw_spline_utils.F.

◆ nn10_deriv_coeffs

real(kind=dp), dimension(3), parameter, public pw_spline_utils::nn10_deriv_coeffs = (/25._dp/72._dp, 5._dp/144, 1._dp/288._dp/)

Definition at line 70 of file pw_spline_utils.F.

◆ nn50_deriv_coeffs

real(kind=dp), dimension(3), parameter, public pw_spline_utils::nn50_deriv_coeffs = (/625._dp/1352._dp, 25._dp/2704._dp, 1._dp/5408._dp/)

Definition at line 70 of file pw_spline_utils.F.

◆ spl3_1d_coeffs0

real(kind=dp), dimension(3), parameter, public pw_spline_utils::spl3_1d_coeffs0 = (/1._dp/6_dp, 2._dp/3._dp, 1._dp/6._dp/)

Definition at line 70 of file pw_spline_utils.F.

◆ spl3_1d_transf_border1

real(kind=dp), dimension(3), parameter, public pw_spline_utils::spl3_1d_transf_border1 = (/0.517977704_dp, 0.464044595_dp, 0.17977701e-1_dp/)

Definition at line 70 of file pw_spline_utils.F.

Data Types

Functions/Subroutines

Variables

Detailed Description

Function/Subroutine Documentation

◆ pw_spline2_interpolate_values_g()

◆ pw_spline3_interpolate_values_g()

◆ pw_spline_scale_deriv()

◆ pw_spline3_deriv_g()

◆ pw_spline2_deriv_g()

◆ pw_nn_smear_r()

◆ pw_nn_deriv_r()

◆ add_coarse2fine()

◆ add_fine2coarse()

◆ pw_spline_precond_create()

◆ pw_spline_precond_set_kind()

◆ pw_spline_precond_release()

◆ pw_spline_do_precond()

◆ find_coeffs()

◆ spl3_nopbc()

◆ spl3_nopbct()

◆ spl3_pbc()

◆ eval_interp_spl3_pbc()

◆ eval_d_interp_spl3_pbc()

Variable Documentation

◆ no_precond

◆ precond_spl3_aint

◆ precond_spl3_1

◆ precond_spl3_aint2

◆ precond_spl3_2

◆ precond_spl3_3

◆ nn10_coeffs

◆ spline3_coeffs

◆ spline2_coeffs

◆ nn50_coeffs

◆ spl3_aint_coeff

◆ spl3_precond1_coeff

◆ spl3_1d_transf_coeffs

◆ spline3_deriv_coeffs

◆ spline2_deriv_coeffs

◆ nn10_deriv_coeffs

◆ nn50_deriv_coeffs

◆ spl3_1d_coeffs0

◆ spl3_1d_transf_border1