fourier Module Reference

Module contains subroutines for computing FFT on parallel radial intervals. Converts quantities between real and fourier space. Note fixarray must be called once before call any of the Fourier subroutines to calculate all necessary sine and cosine factors on a fixed mesh of collocation angles. More...

Data Types
interface	fourier_class
	Base class containing fourier memory. More...
interface	check
	Interface for checking results of the unit tests. More...

Functions/Subroutines
class(fourier_class) function, pointer	fourier_construct (mpol, ntor, ntheta, nzeta, nfp, sym, tor_modes)
	Construct a fourier_class object. More...
subroutine	fourier_destruct (this)
	Deconstruct a fourier_class object. More...
subroutine	fourier_tomnsp_3d (this, xuv, xmn, parity)
	Convert a quantity from real to fourier space in parallel. More...
subroutine	fourier_tomnsp_3d_pest (this, xuv, xmn, lmns, lmnc,
	Convert a quantity from real to fourier space in pest coordinates. More...
pure subroutine	fourier_tomnsp_2d (this, xuv, xmn, parity)
	Fourier transform a 2D quantity to fourier space. More...
pure subroutine	fourier_tomnsp_2d_pest (this, xuv, xmn, lambda, dup
	Fourier transform a 2D quantity to fourier space. More...
pure subroutine	fourier_tomnsp_2d_u (this, xuv)
	Sum over the poloidal part. More...
pure subroutine	fourier_tomnsp_2d_u_pest (this, xuv, lambda, dupdu,
	Sum over the poloidal part. More...
pure subroutine	fourier_tomnsp_2d_v (this, xmn, parity)
	Sum over toroidal angle. More...
subroutine	fourier_toijsp_3d (this, xmn, xuv, dflag, parity)
	Convert a quantity from fourier to real space in parallel. More...
pure subroutine	fourier_toijsp_2d (this, xmn, xuv, dflag, parity)
	Fourier transform a 2D quantity to real space. More...
subroutine	fourier_get_origin (this, xuv, mode, asym)
	Computes the origin value of a half-mesh quantity. More...
subroutine	fourier_round_trig (cosi, sini)
	Round trig values to whole number for near numbers. More...
logical function	fourier_get_index (this, n)
	The the index position of the toroidal mode if it exists. More...
logical function	test_fourier ()
	Test fourier routines. More...

Variables
integer, parameter	f_cos = 0
	Cosine parity.
integer, parameter	f_sin = 1
	Sine parity.
integer, parameter	f_none = 0
	Do not sum fouier real space transformed quantity. This is used when a stellarator symmetric parity is being converted to real space.
integer, parameter	f_ds = 1
	Radial derivative flag.
integer, parameter	f_du = 2
	Poloidal derivative flag.
integer, parameter	f_dv = 4
	Toroidal derivative flag.
integer, parameter	f_dudv = IOR(f_du, f_dv)
	Combined toroidal and poloidal derivatives.
integer, parameter	f_sum = 8
	Sum fouier real space transformed quantity. This is used when a non-stellarator symmetric parity is being converted to real space.
integer, parameter	f_jac = 16
	Quantity, contains jacobian.
integer, parameter	f_con = 32
	Covariant basis.
integer, parameter	b_ds = 0
	Bit position of the f_ds flag.
integer, parameter	b_du = 1
	Bit position of the f_du flag.
integer, parameter	b_dv = 2
	Bit position of the f_dv flag.
integer, parameter	b_sum = 3
	Bit position of the f_sum flag.
integer, parameter	b_jac = 4
	Bit position of the f_jac flag.
integer, parameter	b_con = 5
	Bit position of the f_co flag.
integer, parameter	m0 = 0
	m = 0 mode.
integer, parameter	m1 = 1
	m = 1 mode.
integer, parameter	m2 = 2
	m = 2 mode.
integer, parameter	n0 = 0
	n = 0 mode.
integer, parameter	n1 = 1
	n = 1 mode.

Detailed Description

Module contains subroutines for computing FFT on parallel radial intervals. Converts quantities between real and fourier space. Note fixarray must be called once before call any of the Fourier subroutines to calculate all necessary sine and cosine factors on a fixed mesh of collocation angles.

Function/Subroutine Documentation

fourier_construct()

class (fourier_class) function, pointer fourier::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()

subroutine fourier::fourier_destruct

(

type (fourier_class), intent(inout)

this

)

Deconstruct a fourier_class object.

Deallocates memory and uninitializes a fourier_class object.

Parameters

[in,out]

this

A fourier_class instance.

fourier_get_index()

logical function fourier::fourier_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.

fourier_get_origin()

subroutine fourier::fourier_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.

fourier_round_trig()

subroutine fourier::fourier_round_trig	(	real (dp), intent(inout)	cosi,
		real (dp), intent(inout)	sini
	)

Round trig values to whole number for near numbers.

Parameters

[in,out]	cosi	Cosine value to round.
[in,out]	sini	Sine value to round.

fourier_toijsp_2d()

pure subroutine fourier::fourier_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.

fourier_toijsp_3d()

subroutine fourier::fourier_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.

fourier_tomnsp_2d()

pure subroutine fourier::fourier_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.

fourier_tomnsp_2d_pest()

pure subroutine fourier::fourier_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.

fourier_tomnsp_2d_u()

pure subroutine fourier::fourier_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.

fourier_tomnsp_2d_u_pest()

pure subroutine fourier::fourier_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.

fourier_tomnsp_2d_v()

pure subroutine fourier::fourier_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.

fourier_tomnsp_3d()

subroutine fourier::fourier_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.

fourier_tomnsp_3d_pest()

subroutine fourier::fourier_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.

test_fourier()

logical function fourier::test_fourier

Test fourier routines.

This tests the routines by fourier transforming form flux to real space then back again.