fourier::fourier_class Interface Reference

Base class containing fourier memory. More...

Public Member Functions
procedure, pass	toijsp_2d (this, xmn, xuv, dflag, parity)
	Fourier transform a 2D quantity to real space.
procedure, pass	toijsp_3d (this, xmn, xuv, dflag, parity)
	Convert a quantity from fourier to real space in parallel.
GENERIC	toijsp toijsp_2d, toijsp_3d
procedure, pass	tomnsp_3d (this, xuv, xmn, parity)
	Convert a quantity from real to fourier space in parallel.
procedure, pass	tomnsp_2d (this, xuv, xmn, parity)
	Fourier transform a 2D quantity to fourier space.
procedure, pass	tomnsp_2d_u (this, xuv)
	Sum over the poloidal part.
procedure, pass	tomnsp_2d_v (this, xmn, parity)
	Sum over toroidal angle.
procedure, pass	tomnsp_3d_pest (this, xuv, xmn, lmns, lmnc,
	Convert a quantity from real to fourier space in pest coordinates.
procedure, pass	tomnsp_2d_pest (this, xuv, xmn, lambda, dup
	Fourier transform a 2D quantity to fourier space.
procedure, pass	tomnsp_2d_u_pest (this, xuv, lambda, dupdu,
	Sum over the poloidal part.
GENERIC	tomnsp tomnsp_2d, tomnsp_3d, tomnsp_2d_u,
pass	tomnsp_2d_v tomnsp_2d_v
pass	tomnsp_3d_pest tomnsp_3d_pest
pass	tomnsp_2d_pest tomnsp_2d_pest
pass	tomnsp_2d_u_pest tomnsp_2d_u_pest
procedure	get_origin (this, xuv, mode, asym)
	Computes the origin value of a half-mesh quantity.
procedure	get_index (this, n)
	The the index position of the toroidal mode if it exists.
FINAL	fourier_destruct (this)
	Deconstruct a fourier_class object.
class(fourier_class) function, pointer	fourier_construct (mpol, ntor, ntheta, nzeta, nfp, sym, tor_modes)
	Construct a fourier_class object.

Public Attributes
real(dp), dimension(:,:), pointer	orthonorm => null()
	Orthonorm factors for normalization.
real(dp), dimension(:,:), pointer	cosmu => null()
	Cosine poloidal m and u values.
real(dp), dimension(:,:), pointer	cosmum => null()
	Cosine derivative with respect to u for poloidal m and u values.
real(dp), dimension(:,:), pointer	cosmui => null()
	Normalized Cosine poloidal m and u values.
real(dp), dimension(:,:), pointer	cosnv => null()
	Cosine of nv.
real(dp), dimension(:,:), pointer	cosnvn => null()
	Cosine derivative with respect to v.
real(dp), dimension(:,:), pointer	sinmu => null()
	Sine poloidal m and u values.
real(dp), dimension(:,:), pointer	sinmum => null()
	Sine derivative with respect to u for poloidal m and u values.
real(dp), dimension(:,:), pointer	sinmui => null()
	Normalized Sine poloidal m and u values.
real(dp), dimension(:,:), pointer	sinnv => null()
	Sine of nv.
real(dp), dimension(:,:), pointer	sinnvn => null()
	Sine derivative with respect to v.
real(dp), dimension(:,:), pointer	workmj1 => null()
	Working buffer for first mj terms.
real(dp), dimension(:,:), pointer	workmj2 => null()
	Working buffer for second mj terms.
real(dp), dimension(:,:), pointer	workin1 => null()
	Working buffer for first in terms.
real(dp), dimension(:,:), pointer	workin2 => null()
	Working buffer for second in terms.
integer, dimension(:), pointer	tor_modes => null()
	Toroidal mode numbers.

Detailed Description

Base class containing fourier memory.

Interface for the fourier constructor.

Member Function/Subroutine Documentation

fourier_construct()

class (fourier_class) function, pointer fourier::fourier_class::fourier_construct	(	integer, intent(in)	mpol,
		integer, intent(in)	ntor,
		integer, intent(in)	ntheta,
		integer, intent(in)	nzeta,
		integer, intent(in)	nfp,
		logical, intent(in)	sym,
		integer, dimension(-ntor:ntor), intent(in)	tor_modes
	)

Construct a fourier_class object.

Allocates memory and initializes a fourier_class object. Computes the othronorm and cosine and sine buffers.

This subroutine computes the cosine-sine factors that will be needed when moving between Fourier and real space. All normalizations are contained in the poloidal quantities used in the Fourier to real space transformation:

• sinmui
• cosmui

Fourier representations are assumed to have stellarator symmetry: *# cosine (iparity=0): C(u, v) = sum_u sum_v (C_mn COS(mu + n*nfp*v)) *# sine (iparity=1): S(u, v) = sum_u sum_v (S_mn SIN(mu + n*nfp*v))

The number of collocation points have been set initalially equal to the number of modes: theta_j = j*pi/M, j = 0,...,M Where M = mpol - 1 zeta_k = k*2*pi/(2N + 1) k = 0,...,2N Where N = ntor.

Parameters

[in]	mpol	Number of poloidal modes.
[in]	ntor	Number of toroidal modes.
[in]	ntheta	Number of poloidal real grid points.
[in]	nzeta	Number of toroidal real grid points.
[in]	nfp	Number of field periods.
[in]	sym	Symmetry flag.
[in]	tor_modes	Toroidal mode numbers.

fourier_destruct()

FINAL fourier::fourier_class::fourier_destruct ( type (fourier_class), intent(inout)  this )

final

Deconstruct a fourier_class object.

Deallocates memory and uninitializes a fourier_class object.

Parameters

[in,out]

this

A fourier_class instance.

get_index()

procedure fourier::fourier_class::get_index	(	class (fourier_class), intent(inout)	this,
		integer, intent(inout)	n
	)

The the index position of the toroidal mode if it exists.

Parameters

[in,out]	this	A fourier_class instance.
[in,out]	n	Toroidal mode number to check the index on exit.

Returns

True if the mode number was found.

get_origin()

procedure fourier::fourier_class::get_origin	(	class (fourier_class), intent(inout)	this,
		real(dp), dimension(:,:,:), intent(inout), allocatable	xuv,
		integer, intent(in)	mode,
		logical, intent(in)	asym
	)

Computes the origin value of a half-mesh quantity.

The origin quantity is found from the m mode of the js = 2 value.

Parameters

[in,out]	this	A fourier_class instance.
[in,out]	xuv	Real space quantity.
[in]	mode	Poloidal mode number to be retained.
[in]	asym	Add stellarator asymmetric terms.

toijsp_2d()

procedure, pass fourier::fourier_class::toijsp_2d	(	class (fourier_class), intent(inout)	this,
		real (dp), dimension(:,:), intent(in)	xmn,
		real (dp), dimension(:,:), intent(inout)	xuv,
		integer, intent(in)	dflag,
		integer, intent(in)	parity
	)

Fourier transform a 2D quantity to real space.

Works by reshaping to a 3D array then passing to the normal 3D version.

Parameters

[in]	this	A fourier_class instance.
[in]	xmn	Fourier space quantity.
[in,out]	xuv	Real space quantity.
[in]	dflag	Derivative and sum control flags.
[in]	parity	Fourier parity flag.

toijsp_3d()

procedure, pass fourier::fourier_class::toijsp_3d	(	class (fourier_class), intent(inout)	this,
		real (dp), dimension(:,:,:), intent(in)	xmn,
		real (dp), dimension(:,:,:), intent(inout)	xuv,
		integer, intent(in)	dflag,
		integer, intent(in)	parity
	)

Convert a quantity from fourier to real space in parallel.

This subroutine moves a quantity to real space by summing over its Fourier harmonics. If the f_du flag is set take the poloidal derivative. If the f_dv flag is set take the toroidal derivative. If the f_sum flag is set add the real quanity to the previous value.

Parameters

[in]	this	A fourier_class instance.
[in]	xmn	Fourier space quantity.
[in,out]	xuv	Real space quantity.
[in]	dflag	Derivative and sum control flags.
[in]	parity	Fourier parity flag.

tomnsp_2d()

procedure, pass fourier::fourier_class::tomnsp_2d	(	class (fourier_class), intent(inout)	this,
		real (dp), dimension(:,:), intent(in)	xuv,
		real (dp), dimension(:,:), intent(out)	xmn,
		integer, intent(in)	parity
	)

Fourier transform a 2D quantity to fourier space.

Works by reshaping to a 3D array then passing to the normal 3D version. Have the 3D function call the 2D function for each slice.

Parameters

[in,out]	this	A fourier_class instance.
[in]	xuv	Fourier space quantity.
[out]	xmn	Real space quantity.
[in]	parity	Fourier parity flag.

tomnsp_2d_pest()

procedure, pass fourier::fourier_class::tomnsp_2d_pest	(	class (fourier_class), intent(inout)	this,
		real (dp), dimension(:,:), intent(in)	xuv,
		real (dp), dimension(:,:), intent(out)	xmn,
		real (dp), dimension(:,:), intent(in)	lambda,
			dup
	)

Fourier transform a 2D quantity to fourier space.

Works by reshaping to a 3D array then passing to the normal 3D version. Have the 3D function call the 2D function for each slice.

Parameters

[in,out]	this	A fourier_class instance.
[in]	xuv	Fourier space quantity.
[out]	xmn	Real space quantity.
[in]	lambda	Stellarator symmetric lambda.
[in]	dupdu	Stellarator asymmetric lambda.
[in]	parity	Fourier parity flag.
[in]	asym	Add stellarator asymmetric terms.

tomnsp_2d_u()

procedure, pass fourier::fourier_class::tomnsp_2d_u	(	class (fourier_class), intent(inout)	this,
		real (dp), dimension(:,:), intent(in)	xuv
	)

Sum over the poloidal part.

Pest transforms use the same sum over v but different sums over u. To encourage code reuse break the u and v sums into separate methods. This version uses the regular poloidal sum.

Parameters

[in,out]	this	A fourier_class instance.
[in]	xuv	Fourier space quantity.

tomnsp_2d_u_pest()

procedure, pass fourier::fourier_class::tomnsp_2d_u_pest	(	class (fourier_class), intent(inout)	this,
		real (dp), dimension(:,:), intent(in)	xuv,
		real (dp), dimension(:,:), intent(in)	lambda,
		real (dp), dimension(:,:), intent(in)	dupdu
	)

Sum over the poloidal part.

Pest transforms use the same sum over v but different sums over u. To encourage code reuse break the u and v sums into separate methods. This version uses the lambda poloidal sum.

Parameters

[in,out]	this	A fourier_class instance.
[in]	xuv	Fourier space quantity.
[in]	lmns	Stellarator symmetric lambda.
[in]	lmnc	Stellarator asymmetric lambda.
[in]	asym	Add stellarator asymmetric terms.

tomnsp_2d_v()

procedure, pass fourier::fourier_class::tomnsp_2d_v	(	class (fourier_class), intent(inout)	this,
		real (dp), dimension(:,:), intent(out)	xmn,
		integer, intent(in)	parity
	)

Sum over toroidal angle.

Pest transforms use the same sum over v but different sums over u. To encourage code reuse break the u and v sums into separate methods. This impliments the common toroidal sum.

Parameters

[in]	this	A fourier_class instance.
[in]	xuv	Fourier space quantity.
[out]	xmn	Real space quantity.
[in]	parity	Fourier parity flag.

tomnsp_3d()

procedure, pass fourier::fourier_class::tomnsp_3d	(	class (fourier_class), intent(inout)	this,
		real (dp), dimension(:,:,:), intent(in)	xuv,
		real (dp), dimension(:,:,:), intent(out)	xmn,
		integer, intent(in)	parity
	)

Convert a quantity from real to fourier space in parallel.

This subroutine moves a 3D quantity to fourier space by summing over its real represenetation for each surface.

See also

fourier_tomnsp_2d

Parameters

[in,out]	this	A fourier_class instance.
[in]	xuv	Real space quantity.
[out]	xmn	Fourier space quantity.
[in]	parity	Fourier parity flag.

tomnsp_3d_pest()

procedure, pass fourier::fourier_class::tomnsp_3d_pest	(	class (fourier_class), intent(inout)	this,
		real (dp), dimension(:,:,:), intent(in)	xuv,
		real (dp), dimension(:,:,:), intent(out)	xmn,
		real (dp), dimension(:,:,:), intent(in)	lmns,
		real (dp), dimension(:,:,:), intent(in)	lmnc
	)

Convert a quantity from real to fourier space in pest coordinates.

This subroutine moves a 3D quantity to fourier space by summing over its real represenetation for each surface.

See also

fourier_tomnsp_2d_pest.

Parameters

[in,out]	this	A fourier_class instance.
[in]	xuv	Real space quantity.
[out]	xmn	Fourier space quantity.
[in]	lmns	Stellarator symmetric lambda.
[in]	lmnc	Stellarator asymmetric lambda.
[in]	parity	Fourier parity flag.
[in]	asym	Add stellarator asymmetric terms.

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The documentation for this interface was generated from the following file:

• SIESTA/Sources/fourier.f90