This module defines various routines, operating on mesh functions. More...

Detailed Description

This module defines various routines, operating on mesh functions.

Data Types
interface	dmf_dotp

interface	dmf_integrate

interface	dmf_nrm2

interface	mf_line_integral

interface	mf_surface_integral

interface	zmf_dotp

interface	zmf_integrate

interface	zmf_nrm2

Functions/Subroutines
subroutine, public	mesh_init_mesh_aux (mesh)
	Initialise a pointer to the grid/mesh, that is globally exposed, such that low level mesh operations implicitly access the mesh without it being part of the routine signature. More...

subroutine, public	zmf_fix_phase (mesh, ff)
	Fix the phase of complex function. More...

real(real64) function	dmf_integrate_1 (mesh, ff, mask, reduce)
	Integrate a function on the mesh. More...

real(real64) function, dimension(1:dim)	dmf_integrate_2 (mesh, dim, ff, mask, reduce)
	Integrate of a vector of functins. More...

subroutine, public	dmf_normalize (mesh, dim, psi, norm)
	Normalize a mesh function psi. More...

real(real64) function	dmf_dotp_1 (mesh, f1, f2, reduce, dotu, np)
	this function returns the dot product between two mesh functions More...

real(real64) function	dmf_dotp_2 (mesh, dim, f1, f2, reduce, dotu, np)
	dot product for vector valued mesh functions More...

real(real64) function	dmf_nrm2_1 (mesh, ff, reduce)
	this function returns the norm of a mesh function More...

real(real64) function	dmf_nrm2_2 (mesh, dim, ff, reduce)
	this function returns the norm of a vector of mesh functions More...

real(real64) function, public	dmf_moment (mesh, ff, idir, order)
	This function calculates the "order" moment of the function ff. More...

subroutine, public	dmf_random (mesh, ff, pre_shift, post_shift, seed, normalized)
	This subroutine fills a function with random values. More...

subroutine, public	dmf_interpolate_points (ndim, npoints_in, x_in, f_in, npoints_out, x_out, f_out)
	This function receives a function f_in defined in a mesh, and returns the interpolated values of the function over the npoints_in defined by x_in. More...

subroutine	dmf_interpolate_on_plane (mesh, plane, ff, f_in_plane)
	Given a function ff defined on mesh, and a plane, it gives back the values of ff on the plane, by doing the appropriate interpolation. More...

subroutine	dmf_interpolate_on_line (mesh, line, ff, f_in_line)
	Given a function ff defined on mesh, and a line, it gives back the values of ff on the line, by doing the appropriate interpolation. More...

real(real64) function	dmf_surface_integral_scalar (mesh, ff, plane)
	This subroutine calculates the surface integral of a scalar function on a given plane. More...

real(real64) function	dmf_surface_integral_vector (mesh, ff, plane)
	This subroutine calculates the surface integral of a vector function on a given plane. More...

real(real64) function	dmf_line_integral_scalar (mesh, ff, line)
	This subroutine calculates the line integral of a scalar function on a given line. More...

real(real64) function	dmf_line_integral_vector (mesh, ff, line)
	This subroutine calculates the line integral of a vector function on a given line. More...

subroutine, public	dmf_multipoles (mesh, ff, lmax, multipole, mask)
	This routine calculates the multipoles of a function ff. More...

subroutine, public	dmf_dipole (mesh, ff, dipole, mask)
	This routine calculates the dipole of a function ff, for arbitrary dimensions. More...

real(real64) function, public	dmf_dotp_aux (f1, f2)
	dot product between two vectors (mesh functions) More...

real(real64) function, public	dmf_dotu_aux (f1, f2)
	dot product between two vectors (mesh functions) without conjugation More...

real(real64) function, public	dmf_nrm2_aux (ff)
	calculate norm2 of a vector (mesh function) More...

complex(real64) function	zmf_integrate_1 (mesh, ff, mask, reduce)
	Integrate a function on the mesh. More...

complex(real64) function, dimension(1:dim)	zmf_integrate_2 (mesh, dim, ff, mask, reduce)
	Integrate of a vector of functins. More...

subroutine, public	zmf_normalize (mesh, dim, psi, norm)
	Normalize a mesh function psi. More...

complex(real64) function	zmf_dotp_1 (mesh, f1, f2, reduce, dotu, np)
	this function returns the dot product between two mesh functions More...

complex(real64) function	zmf_dotp_2 (mesh, dim, f1, f2, reduce, dotu, np)
	dot product for vector valued mesh functions More...

real(real64) function	zmf_nrm2_1 (mesh, ff, reduce)
	this function returns the norm of a mesh function More...

real(real64) function	zmf_nrm2_2 (mesh, dim, ff, reduce)
	this function returns the norm of a vector of mesh functions More...

complex(real64) function, public	zmf_moment (mesh, ff, idir, order)
	This function calculates the "order" moment of the function ff. More...

subroutine, public	zmf_random (mesh, ff, pre_shift, post_shift, seed, normalized)
	This subroutine fills a function with random values. More...

subroutine, public	zmf_interpolate_points (ndim, npoints_in, x_in, f_in, npoints_out, x_out, f_out)
	This function receives a function f_in defined in a mesh, and returns the interpolated values of the function over the npoints_in defined by x_in. More...

subroutine	zmf_interpolate_on_plane (mesh, plane, ff, f_in_plane)
	Given a function ff defined on mesh, and a plane, it gives back the values of ff on the plane, by doing the appropriate interpolation. More...

subroutine	zmf_interpolate_on_line (mesh, line, ff, f_in_line)
	Given a function ff defined on mesh, and a line, it gives back the values of ff on the line, by doing the appropriate interpolation. More...

complex(real64) function	zmf_surface_integral_scalar (mesh, ff, plane)
	This subroutine calculates the surface integral of a scalar function on a given plane. More...

complex(real64) function	zmf_surface_integral_vector (mesh, ff, plane)
	This subroutine calculates the surface integral of a vector function on a given plane. More...

complex(real64) function	zmf_line_integral_scalar (mesh, ff, line)
	This subroutine calculates the line integral of a scalar function on a given line. More...

complex(real64) function	zmf_line_integral_vector (mesh, ff, line)
	This subroutine calculates the line integral of a vector function on a given line. More...

subroutine, public	zmf_multipoles (mesh, ff, lmax, multipole, mask)
	This routine calculates the multipoles of a function ff. More...

subroutine, public	zmf_dipole (mesh, ff, dipole, mask)
	This routine calculates the dipole of a function ff, for arbitrary dimensions. More...

complex(real64) function, public	zmf_dotp_aux (f1, f2)
	dot product between two vectors (mesh functions) More...

complex(real64) function, public	zmf_dotu_aux (f1, f2)
	dot product between two vectors (mesh functions) without conjugation More...

real(real64) function, public	zmf_nrm2_aux (ff)
	calculate norm2 of a vector (mesh function) More...

Variables
logical, public	sp_parallel

integer, public	sp_np

integer, public	sp_dim

integer, public	sp_st1

integer, public	sp_st2

integer, public	sp_kp1

integer, public	sp_kp2

integer, public	sp_distdot_mode

type(mpi_grp_t), public	sp_grp

class(mesh_t), pointer, public	mesh_aux => null()
	Globally-scoped pointer to the mesh instance. More...

Function/Subroutine Documentation

◆ mesh_init_mesh_aux()

subroutine, public mesh_function_oct_m::mesh_init_mesh_aux ( class(mesh_t), intent(in), target mesh )

Initialise a pointer to the grid/mesh, that is globally exposed, such that low level mesh operations implicitly access the mesh without it being part of the routine signature.

Definition at line 218 of file mesh_function.F90.

◆ zmf_fix_phase()

subroutine, public mesh_function_oct_m::zmf_fix_phase	(	class(mesh_t), intent(in)	mesh,
		complex(real64), dimension(:), intent(inout)	ff
	)

Fix the phase of complex function.

Given a complex function on the grid, we want to minimize its imaginary part For this, we determine the angle that will minimize the imaginary part after rotation in the complex plane. We then choose the solution that maximizes the real part

Definition at line 234 of file mesh_function.F90.

◆ dmf_integrate_1()

real(real64) function mesh_function_oct_m::dmf_integrate_1	(	class(mesh_t), intent(in)	mesh,
		real(real64), dimension(:), intent(in)	ff,
		logical, dimension(:), intent(in), optional	mask,
		logical, intent(in), optional	reduce
	)

private

Integrate a function on the mesh.

\[ d = \sum_i^N f_i dV_i \]

where \( f_i \) is the discrete function, \(dV_i\) is the volume element, and \( N \) is the number of mesh points.

Parameters

[in]	ff	Function to integrate with dimensions (1:mesh%np)
[in]	mask	Define which grid points to integrate over
[in]	reduce	Perform reduction over all grid domains

Definition at line 383 of file mesh_function.F90.

◆ dmf_integrate_2()

real(real64) function, dimension(1:dim) mesh_function_oct_m::dmf_integrate_2	(	class(mesh_t), intent(in)	mesh,
		integer, intent(in)	dim,
		real(real64), dimension(:,:), intent(in)	ff,
		logical, dimension(:), intent(in), optional	mask,
		logical, intent(in), optional	reduce
	)

private

Integrate of a vector of functins.

Parameters

[in]	ff	Function to integrate with dimensions (1:mesh%np)
[in]	mask	Define which grid points to integrate over
[in]	reduce	Perform reduction over all grid domains

Definition at line 429 of file mesh_function.F90.

◆ dmf_normalize()

subroutine, public mesh_function_oct_m::dmf_normalize	(	class(mesh_t), intent(in)	mesh,
		integer, intent(in)	dim,
		real(real64), dimension(:,:), intent(inout), contiguous	psi,
		real(real64), intent(out), optional	norm
	)

Normalize a mesh function psi.

Parameters

[in]	mesh	underlying mesh
[in]	dim	spinor dimension of the function
[in,out]	psi	mesh function psi(mesh%np, dim)
[out]	norm	optional output of the norm

Definition at line 456 of file mesh_function.F90.

◆ dmf_dotp_1()

real(real64) function mesh_function_oct_m::dmf_dotp_1	(	class(mesh_t), intent(in)	mesh,
		real(real64), dimension(:), intent(in)	f1,
		real(real64), dimension(:), intent(in)	f2,
		logical, intent(in), optional	reduce,
		logical, intent(in), optional	dotu,
		integer, intent(in), optional	np
	)

private

this function returns the dot product between two mesh functions

Parameters

[in]	mesh	underlying mesh
[in]	f2	mesh functions
[in]	reduce	if true, perform mpi reduction
[in]	dotu	if true, use blas_dotu instead of blas_dot; no complex conjugation. Default is false. This has no effect if working with real version

Definition at line 486 of file mesh_function.F90.

◆ dmf_dotp_2()

real(real64) function mesh_function_oct_m::dmf_dotp_2	(	class(mesh_t), intent(in)	mesh,
		integer, intent(in)	dim,
		real(real64), dimension(:,:), intent(in), contiguous	f1,
		real(real64), dimension(:,:), intent(in), contiguous	f2,
		logical, intent(in), optional	reduce,
		logical, intent(in), optional	dotu,
		integer, intent(in), optional	np
	)

private

dot product for vector valued mesh functions

Parameters

[in]	mesh	underlying mesh
[in]	dim	dimensions
[in]	f2	mesh functions of dimension (1:mesh%np, 1:dim)
[in]	reduce	if true, perform mpi reduction
[in]	dotu	if true, use lalg_dotu instead of lalg_dot; no complex conjugation. Default is false.
[in]	np	optional number of points over which the integral is performed

Definition at line 561 of file mesh_function.F90.

◆ dmf_nrm2_1()

real(real64) function mesh_function_oct_m::dmf_nrm2_1	(	class(mesh_t), intent(in)	mesh,
		real(real64), dimension(:), intent(in)	ff,
		logical, intent(in), optional	reduce
	)

private

this function returns the norm of a mesh function

Parameters

[in]	mesh	underlying mesh
[in]	ff	mesh function
[in]	reduce	if true, perform mpi reduction

Definition at line 593 of file mesh_function.F90.

◆ dmf_nrm2_2()

real(real64) function mesh_function_oct_m::dmf_nrm2_2	(	class(mesh_t), intent(in)	mesh,
		integer, intent(in)	dim,
		real(real64), dimension(:,:), intent(in)	ff,
		logical, intent(in), optional	reduce
	)

private

this function returns the norm of a vector of mesh functions

Parameters

[in]	mesh	underlying mesh
[in]	dim	dimensions
[in]	ff	mesh function of dimension (1:mesh%np, 1:dim)
[in]	reduce	if true, perform mpi reduction

Definition at line 630 of file mesh_function.F90.

◆ dmf_moment()

real(real64) function, public mesh_function_oct_m::dmf_moment	(	class(mesh_t), intent(in)	mesh,
		real(real64), dimension(:), intent(in)	ff,
		integer, intent(in)	idir,
		integer, intent(in)	order
	)

This function calculates the "order" moment of the function ff.

moment = \( \int ff({\bf x}) {\bf x}_{\rm idir}^{\rm order} \)

Parameters

[in]	mesh	underlying mesh
[in]	ff	mesh function
[in]	idir	Cartesian direction
[in]	order	order of the moment

Definition at line 656 of file mesh_function.F90.

◆ dmf_random()

subroutine, public mesh_function_oct_m::dmf_random	(	class(mesh_t), intent(in)	mesh,
		real(real64), dimension(:), intent(out), contiguous	ff,
		integer(int64), intent(in), optional	pre_shift,
		integer(int64), intent(in), optional	post_shift,
		integer(int64), intent(in), optional	seed,
		logical, intent(in), optional	normalized
	)

This subroutine fills a function with random values.

Parameters

[in] normalized whether generate states should have norm 1, true by default

Definition at line 685 of file mesh_function.F90.

◆ dmf_interpolate_points()

subroutine, public mesh_function_oct_m::dmf_interpolate_points	(	integer, intent(in)	ndim,
		integer, intent(in)	npoints_in,
		real(real64), dimension(:, :), intent(in)	x_in,
		real(real64), dimension(:), intent(in)	f_in,
		integer, intent(in)	npoints_out,
		real(real64), dimension(:,:), intent(in)	x_out,
		real(real64), dimension(:), intent(out)	f_out
	)

This function receives a function f_in defined in a mesh, and returns the interpolated values of the function over the npoints_in defined by x_in.

Parameters

[in]	f_in	function (1:npoints_in))
[in]	x_in	coordinates of in points (1:npoints_in, 1:ndim)
[in]	x_out	coordinates of out points (1:npoints_out, 1:ndim)
[out]	f_out	(1:npoints_out)

Definition at line 740 of file mesh_function.F90.

◆ dmf_interpolate_on_plane()

subroutine mesh_function_oct_m::dmf_interpolate_on_plane	(	class(mesh_t), intent(in)	mesh,
		type(mesh_plane_t), intent(in)	plane,
		real(real64), dimension(:), intent(in), target	ff,
		real(real64), dimension(plane%nu:plane%mu, plane%nv:plane%mv), intent(out)	f_in_plane
	)

private

Given a function ff defined on mesh, and a plane, it gives back the values of ff on the plane, by doing the appropriate interpolation.

Parameters

[in]	mesh	underlying mesh
[in]	plane	plane to interpolate onto
[in]	ff	function defined on mesh

Definition at line 795 of file mesh_function.F90.

◆ dmf_interpolate_on_line()

subroutine mesh_function_oct_m::dmf_interpolate_on_line	(	class(mesh_t), intent(in)	mesh,
		type(mesh_line_t), intent(in)	line,
		real(real64), dimension(:), intent(in), target	ff,
		real(real64), dimension(line%nu:line%mu), intent(out)	f_in_line
	)

private

Given a function ff defined on mesh, and a line, it gives back the values of ff on the line, by doing the appropriate interpolation.

Parameters

[in]	mesh	underlying mesh
[in]	line	line to interpolate onto
[in]	ff	function defined on mesh

Definition at line 851 of file mesh_function.F90.

◆ dmf_surface_integral_scalar()

real(real64) function mesh_function_oct_m::dmf_surface_integral_scalar	(	class(mesh_t), intent(in)	mesh,
		real(real64), dimension(:), intent(in)	ff,
		type(mesh_plane_t), intent(in)	plane
	)

private

This subroutine calculates the surface integral of a scalar function on a given plane.

Parameters

[in]	mesh	underlying mesh
[in]	ff	function to integrate; dimensions (1:mesh%np)
[in]	plane	plane for surface integration

Definition at line 899 of file mesh_function.F90.

◆ dmf_surface_integral_vector()

real(real64) function mesh_function_oct_m::dmf_surface_integral_vector	(	class(mesh_t), intent(in)	mesh,
		real(real64), dimension(:, :), intent(in)	ff,
		type(mesh_plane_t), intent(in)	plane
	)

private

This subroutine calculates the surface integral of a vector function on a given plane.

Parameters

[in]	mesh	underlying mesh
[in]	ff	function to integrate; dimensions (mesh%np, mesh%box%dim)
[in]	plane	plane for surface integration

Definition at line 928 of file mesh_function.F90.

◆ dmf_line_integral_scalar()

real(real64) function mesh_function_oct_m::dmf_line_integral_scalar	(	class(mesh_t), intent(in)	mesh,
		real(real64), dimension(:), intent(in)	ff,
		type(mesh_line_t), intent(in)	line
	)

private

This subroutine calculates the line integral of a scalar function on a given line.

Parameters

[in]	mesh	underlying mesh
[in]	ff	function defined on mesh; dimensions (1:mesh%np)
[in]	line	line to integrate along

Definition at line 958 of file mesh_function.F90.

◆ dmf_line_integral_vector()

real(real64) function mesh_function_oct_m::dmf_line_integral_vector	(	class(mesh_t), intent(in)	mesh,
		real(real64), dimension(:, :), intent(in)	ff,
		type(mesh_line_t), intent(in)	line
	)

private

This subroutine calculates the line integral of a vector function on a given line.

Parameters

[in]	mesh	underlying mesh
[in]	ff	function defined on mesh; dimensions (mesh%np, mesh%box%dim)
[in]	line	line to integrate along

Definition at line 987 of file mesh_function.F90.

◆ dmf_multipoles()

subroutine, public mesh_function_oct_m::dmf_multipoles	(	class(mesh_t), intent(in)	mesh,
		real(real64), dimension(:), intent(in)	ff,
		integer, intent(in)	lmax,
		real(real64), dimension(:), intent(out)	multipole,
		logical, dimension(:), intent(in), optional	mask
	)

This routine calculates the multipoles of a function ff.

defined in the following way:

multipole(1) is the trace of ff (defined to be positive; integral of ff).
multipole(2:4) contains the dipole: integral of ff times x, y or z.
multipole(5:9, is) contains the quadrupole, defined in the usual way using the spherical harmonics: multipole(5) = \( \int [ {\rm ff} * Y_{2,-2} ] \),
multipole(6, is) = \( \int [ {\rm ff} * Y_{2, -1} ] \).

And so on.

Parameters

[in]	mesh	underlying mesh
[in]	ff	function to integrate
[in]	lmax	maximum angular momentum
[out]	multipole	((lmax + 1)**2)
[in]	mask	(1:mesh%np)

Definition at line 1024 of file mesh_function.F90.

◆ dmf_dipole()

subroutine, public mesh_function_oct_m::dmf_dipole	(	class(mesh_t), intent(in)	mesh,
		real(real64), dimension(:), intent(in)	ff,
		real(real64), dimension(:), intent(out)	dipole,
		logical, dimension(:), intent(in), optional	mask
	)

This routine calculates the dipole of a function ff, for arbitrary dimensions.

Parameters

[in]	mesh	underlying mesh
[in]	ff	(1:mesh%np)
[out]	dipole	(1:mesh%box%dim)
[in]	mask	(1:mesh%np)

Definition at line 1082 of file mesh_function.F90.

◆ dmf_dotp_aux()

real(real64) function, public mesh_function_oct_m::dmf_dotp_aux	(	real(real64), dimension(:), intent(in)	f1,
		real(real64), dimension(:), intent(in)	f2
	)

dot product between two vectors (mesh functions)

This function returns the dot product between two vectors, but using the mesh_aux defined as a global object in this module. This way it can be called by external libraries, passing only the two vectors. First, one has to make sure that mesh_aux is pointing to some defined mesh data structure, by calling mesh_init_mesh_aux.

Definition at line 1124 of file mesh_function.F90.

◆ dmf_dotu_aux()

real(real64) function, public mesh_function_oct_m::dmf_dotu_aux	(	real(real64), dimension(:), intent(in)	f1,
		real(real64), dimension(:), intent(in)	f2
	)

dot product between two vectors (mesh functions) without conjugation

This function returns the dot product between two vectors, but using the mesh_aux defined as a global object in this module. This way it can be called by external libraries, passing only the two vectors. First, one has to make sure that mesh_aux is pointing to some defined mesh data structure, by calling mesh_init_mesh_aux.

Definition at line 1144 of file mesh_function.F90.

◆ dmf_nrm2_aux()

real(real64) function, public mesh_function_oct_m::dmf_nrm2_aux ( real(real64), dimension(:), intent(in) ff )

calculate norm2 of a vector (mesh function)

This uses the mesh_aux defined as a global object in this module. This way it can be called by external libraries, passing only the two vectors. First, one has to make sure that mesh_aux is pointing to some defined mesh data structure, by calling mesh_init_mesh_aux.

Definition at line 1164 of file mesh_function.F90.

◆ zmf_integrate_1()

complex(real64) function mesh_function_oct_m::zmf_integrate_1	(	class(mesh_t), intent(in)	mesh,
		complex(real64), dimension(:), intent(in)	ff,
		logical, dimension(:), intent(in), optional	mask,
		logical, intent(in), optional	reduce
	)

private

Integrate a function on the mesh.

\[ d = \sum_i^N f_i dV_i \]

where \( f_i \) is the discrete function, \(dV_i\) is the volume element, and \( N \) is the number of mesh points.

Parameters

[in]	ff	Function to integrate with dimensions (1:mesh%np)
[in]	mask	Define which grid points to integrate over
[in]	reduce	Perform reduction over all grid domains

Definition at line 1257 of file mesh_function.F90.

◆ zmf_integrate_2()

complex(real64) function, dimension(1:dim) mesh_function_oct_m::zmf_integrate_2	(	class(mesh_t), intent(in)	mesh,
		integer, intent(in)	dim,
		complex(real64), dimension(:,:), intent(in)	ff,
		logical, dimension(:), intent(in), optional	mask,
		logical, intent(in), optional	reduce
	)

private

Integrate of a vector of functins.

Parameters

[in]	ff	Function to integrate with dimensions (1:mesh%np)
[in]	mask	Define which grid points to integrate over
[in]	reduce	Perform reduction over all grid domains

Definition at line 1303 of file mesh_function.F90.

◆ zmf_normalize()

subroutine, public mesh_function_oct_m::zmf_normalize	(	class(mesh_t), intent(in)	mesh,
		integer, intent(in)	dim,
		complex(real64), dimension(:,:), intent(inout), contiguous	psi,
		real(real64), intent(out), optional	norm
	)

Normalize a mesh function psi.

Parameters

[in]	mesh	underlying mesh
[in]	dim	spinor dimension of the function
[in,out]	psi	mesh function psi(mesh%np, dim)
[out]	norm	optional output of the norm

Definition at line 1330 of file mesh_function.F90.

◆ zmf_dotp_1()

complex(real64) function mesh_function_oct_m::zmf_dotp_1	(	class(mesh_t), intent(in)	mesh,
		complex(real64), dimension(:), intent(in)	f1,
		complex(real64), dimension(:), intent(in)	f2,
		logical, intent(in), optional	reduce,
		logical, intent(in), optional	dotu,
		integer, intent(in), optional	np
	)

private

this function returns the dot product between two mesh functions

Parameters

[in]	mesh	underlying mesh
[in]	f2	mesh functions
[in]	reduce	if true, perform mpi reduction
[in]	dotu	if true, use blas_dotu instead of blas_dot; no complex conjugation. Default is false. This has no effect if working with real version

Definition at line 1360 of file mesh_function.F90.

◆ zmf_dotp_2()

complex(real64) function mesh_function_oct_m::zmf_dotp_2	(	class(mesh_t), intent(in)	mesh,
		integer, intent(in)	dim,
		complex(real64), dimension(:,:), intent(in), contiguous	f1,
		complex(real64), dimension(:,:), intent(in), contiguous	f2,
		logical, intent(in), optional	reduce,
		logical, intent(in), optional	dotu,
		integer, intent(in), optional	np
	)

private

dot product for vector valued mesh functions

Parameters

[in]	mesh	underlying mesh
[in]	dim	dimensions
[in]	f2	mesh functions of dimension (1:mesh%np, 1:dim)
[in]	reduce	if true, perform mpi reduction
[in]	dotu	if true, use lalg_dotu instead of lalg_dot; no complex conjugation. Default is false.
[in]	np	optional number of points over which the integral is performed

Definition at line 1442 of file mesh_function.F90.

◆ zmf_nrm2_1()

real(real64) function mesh_function_oct_m::zmf_nrm2_1	(	class(mesh_t), intent(in)	mesh,
		complex(real64), dimension(:), intent(in)	ff,
		logical, intent(in), optional	reduce
	)

private

this function returns the norm of a mesh function

Parameters

[in]	mesh	underlying mesh
[in]	ff	mesh function
[in]	reduce	if true, perform mpi reduction

Definition at line 1474 of file mesh_function.F90.

◆ zmf_nrm2_2()

real(real64) function mesh_function_oct_m::zmf_nrm2_2	(	class(mesh_t), intent(in)	mesh,
		integer, intent(in)	dim,
		complex(real64), dimension(:,:), intent(in)	ff,
		logical, intent(in), optional	reduce
	)

private

this function returns the norm of a vector of mesh functions

Parameters

[in]	mesh	underlying mesh
[in]	dim	dimensions
[in]	ff	mesh function of dimension (1:mesh%np, 1:dim)
[in]	reduce	if true, perform mpi reduction

Definition at line 1511 of file mesh_function.F90.

◆ zmf_moment()

complex(real64) function, public mesh_function_oct_m::zmf_moment	(	class(mesh_t), intent(in)	mesh,
		complex(real64), dimension(:), intent(in)	ff,
		integer, intent(in)	idir,
		integer, intent(in)	order
	)

This function calculates the "order" moment of the function ff.

moment = \( \int ff({\bf x}) {\bf x}_{\rm idir}^{\rm order} \)

Parameters

[in]	mesh	underlying mesh
[in]	ff	mesh function
[in]	idir	Cartesian direction
[in]	order	order of the moment

Definition at line 1537 of file mesh_function.F90.

◆ zmf_random()

subroutine, public mesh_function_oct_m::zmf_random	(	class(mesh_t), intent(in)	mesh,
		complex(real64), dimension(:), intent(out), contiguous	ff,
		integer(int64), intent(in), optional	pre_shift,
		integer(int64), intent(in), optional	post_shift,
		integer(int64), intent(in), optional	seed,
		logical, intent(in), optional	normalized
	)

This subroutine fills a function with random values.

Parameters

[in] normalized whether generate states should have norm 1, true by default

Definition at line 1566 of file mesh_function.F90.

◆ zmf_interpolate_points()

subroutine, public mesh_function_oct_m::zmf_interpolate_points	(	integer, intent(in)	ndim,
		integer, intent(in)	npoints_in,
		real(real64), dimension(:, :), intent(in)	x_in,
		complex(real64), dimension(:), intent(in)	f_in,
		integer, intent(in)	npoints_out,
		real(real64), dimension(:,:), intent(in)	x_out,
		complex(real64), dimension(:), intent(out)	f_out
	)

This function receives a function f_in defined in a mesh, and returns the interpolated values of the function over the npoints_in defined by x_in.

Parameters

[in]	f_in	function (1:npoints_in))
[in]	x_in	coordinates of in points (1:npoints_in, 1:ndim)
[in]	x_out	coordinates of out points (1:npoints_out, 1:ndim)
[out]	f_out	(1:npoints_out)

Definition at line 1621 of file mesh_function.F90.

◆ zmf_interpolate_on_plane()

subroutine mesh_function_oct_m::zmf_interpolate_on_plane	(	class(mesh_t), intent(in)	mesh,
		type(mesh_plane_t), intent(in)	plane,
		complex(real64), dimension(:), intent(in), target	ff,
		complex(real64), dimension(plane%nu:plane%mu, plane%nv:plane%mv), intent(out)	f_in_plane
	)

private

Given a function ff defined on mesh, and a plane, it gives back the values of ff on the plane, by doing the appropriate interpolation.

Parameters

[in]	mesh	underlying mesh
[in]	plane	plane to interpolate onto
[in]	ff	function defined on mesh

Definition at line 1669 of file mesh_function.F90.

◆ zmf_interpolate_on_line()

subroutine mesh_function_oct_m::zmf_interpolate_on_line	(	class(mesh_t), intent(in)	mesh,
		type(mesh_line_t), intent(in)	line,
		complex(real64), dimension(:), intent(in), target	ff,
		complex(real64), dimension(line%nu:line%mu), intent(out)	f_in_line
	)

private

Given a function ff defined on mesh, and a line, it gives back the values of ff on the line, by doing the appropriate interpolation.

Parameters

[in]	mesh	underlying mesh
[in]	line	line to interpolate onto
[in]	ff	function defined on mesh

Definition at line 1725 of file mesh_function.F90.

◆ zmf_surface_integral_scalar()

complex(real64) function mesh_function_oct_m::zmf_surface_integral_scalar	(	class(mesh_t), intent(in)	mesh,
		complex(real64), dimension(:), intent(in)	ff,
		type(mesh_plane_t), intent(in)	plane
	)

private

This subroutine calculates the surface integral of a scalar function on a given plane.

Parameters

[in]	mesh	underlying mesh
[in]	ff	function to integrate; dimensions (1:mesh%np)
[in]	plane	plane for surface integration

Definition at line 1773 of file mesh_function.F90.

◆ zmf_surface_integral_vector()

complex(real64) function mesh_function_oct_m::zmf_surface_integral_vector	(	class(mesh_t), intent(in)	mesh,
		complex(real64), dimension(:, :), intent(in)	ff,
		type(mesh_plane_t), intent(in)	plane
	)

private

This subroutine calculates the surface integral of a vector function on a given plane.

Parameters

[in]	mesh	underlying mesh
[in]	ff	function to integrate; dimensions (mesh%np, mesh%box%dim)
[in]	plane	plane for surface integration

Definition at line 1802 of file mesh_function.F90.

◆ zmf_line_integral_scalar()

complex(real64) function mesh_function_oct_m::zmf_line_integral_scalar	(	class(mesh_t), intent(in)	mesh,
		complex(real64), dimension(:), intent(in)	ff,
		type(mesh_line_t), intent(in)	line
	)

private

This subroutine calculates the line integral of a scalar function on a given line.

Parameters

[in]	mesh	underlying mesh
[in]	ff	function defined on mesh; dimensions (1:mesh%np)
[in]	line	line to integrate along

Definition at line 1832 of file mesh_function.F90.

◆ zmf_line_integral_vector()

complex(real64) function mesh_function_oct_m::zmf_line_integral_vector	(	class(mesh_t), intent(in)	mesh,
		complex(real64), dimension(:, :), intent(in)	ff,
		type(mesh_line_t), intent(in)	line
	)

private

This subroutine calculates the line integral of a vector function on a given line.

Parameters

[in]	mesh	underlying mesh
[in]	ff	function defined on mesh; dimensions (mesh%np, mesh%box%dim)
[in]	line	line to integrate along

Definition at line 1861 of file mesh_function.F90.

◆ zmf_multipoles()

subroutine, public mesh_function_oct_m::zmf_multipoles	(	class(mesh_t), intent(in)	mesh,
		complex(real64), dimension(:), intent(in)	ff,
		integer, intent(in)	lmax,
		complex(real64), dimension(:), intent(out)	multipole,
		logical, dimension(:), intent(in), optional	mask
	)

This routine calculates the multipoles of a function ff.

defined in the following way:

multipole(1) is the trace of ff (defined to be positive; integral of ff).
multipole(2:4) contains the dipole: integral of ff times x, y or z.
multipole(5:9, is) contains the quadrupole, defined in the usual way using the spherical harmonics: multipole(5) = \( \int [ {\rm ff} * Y_{2,-2} ] \),
multipole(6, is) = \( \int [ {\rm ff} * Y_{2, -1} ] \).

And so on.

Parameters

[in]	mesh	underlying mesh
[in]	ff	function to integrate
[in]	lmax	maximum angular momentum
[out]	multipole	((lmax + 1)**2)
[in]	mask	(1:mesh%np)

Definition at line 1898 of file mesh_function.F90.

◆ zmf_dipole()

subroutine, public mesh_function_oct_m::zmf_dipole	(	class(mesh_t), intent(in)	mesh,
		complex(real64), dimension(:), intent(in)	ff,
		complex(real64), dimension(:), intent(out)	dipole,
		logical, dimension(:), intent(in), optional	mask
	)

This routine calculates the dipole of a function ff, for arbitrary dimensions.

Parameters

[in]	mesh	underlying mesh
[in]	ff	(1:mesh%np)
[out]	dipole	(1:mesh%box%dim)
[in]	mask	(1:mesh%np)

Definition at line 1956 of file mesh_function.F90.

◆ zmf_dotp_aux()

complex(real64) function, public mesh_function_oct_m::zmf_dotp_aux	(	complex(real64), dimension(:), intent(in)	f1,
		complex(real64), dimension(:), intent(in)	f2
	)

dot product between two vectors (mesh functions)

This function returns the dot product between two vectors, but using the mesh_aux defined as a global object in this module. This way it can be called by external libraries, passing only the two vectors. First, one has to make sure that mesh_aux is pointing to some defined mesh data structure, by calling mesh_init_mesh_aux.

Definition at line 1998 of file mesh_function.F90.

◆ zmf_dotu_aux()

complex(real64) function, public mesh_function_oct_m::zmf_dotu_aux	(	complex(real64), dimension(:), intent(in)	f1,
		complex(real64), dimension(:), intent(in)	f2
	)

dot product between two vectors (mesh functions) without conjugation

This function returns the dot product between two vectors, but using the mesh_aux defined as a global object in this module. This way it can be called by external libraries, passing only the two vectors. First, one has to make sure that mesh_aux is pointing to some defined mesh data structure, by calling mesh_init_mesh_aux.

Definition at line 2018 of file mesh_function.F90.

◆ zmf_nrm2_aux()

real(real64) function, public mesh_function_oct_m::zmf_nrm2_aux ( complex(real64), dimension(:), intent(in) ff )

calculate norm2 of a vector (mesh function)

This uses the mesh_aux defined as a global object in this module. This way it can be called by external libraries, passing only the two vectors. First, one has to make sure that mesh_aux is pointing to some defined mesh data structure, by calling mesh_init_mesh_aux.

Definition at line 2038 of file mesh_function.F90.

Variable Documentation

◆ sp_parallel

logical, public mesh_function_oct_m::sp_parallel

Definition at line 170 of file mesh_function.F90.

◆ sp_np

integer, public mesh_function_oct_m::sp_np

Definition at line 171 of file mesh_function.F90.

◆ sp_dim

integer, public mesh_function_oct_m::sp_dim

Definition at line 171 of file mesh_function.F90.

◆ sp_st1

integer, public mesh_function_oct_m::sp_st1

Definition at line 171 of file mesh_function.F90.

◆ sp_st2

integer, public mesh_function_oct_m::sp_st2

Definition at line 171 of file mesh_function.F90.

◆ sp_kp1

integer, public mesh_function_oct_m::sp_kp1

Definition at line 171 of file mesh_function.F90.

◆ sp_kp2

integer, public mesh_function_oct_m::sp_kp2

Definition at line 171 of file mesh_function.F90.

◆ sp_distdot_mode

integer, public mesh_function_oct_m::sp_distdot_mode

Definition at line 172 of file mesh_function.F90.

◆ sp_grp

type(mpi_grp_t), public mesh_function_oct_m::sp_grp

Definition at line 173 of file mesh_function.F90.

◆ mesh_aux

class(mesh_t), pointer, public mesh_function_oct_m::mesh_aux => null()

Globally-scoped pointer to the mesh instance.

Definition at line 211 of file mesh_function.F90.

Detailed Description

Data Types

Functions/Subroutines

Variables

Function/Subroutine Documentation

◆ mesh_init_mesh_aux()

◆ zmf_fix_phase()

◆ dmf_integrate_1()

◆ dmf_integrate_2()

◆ dmf_normalize()

◆ dmf_dotp_1()

◆ dmf_dotp_2()

◆ dmf_nrm2_1()

◆ dmf_nrm2_2()

◆ dmf_moment()

◆ dmf_random()

◆ dmf_interpolate_points()

◆ dmf_interpolate_on_plane()

◆ dmf_interpolate_on_line()

◆ dmf_surface_integral_scalar()

◆ dmf_surface_integral_vector()

◆ dmf_line_integral_scalar()

◆ dmf_line_integral_vector()

◆ dmf_multipoles()

◆ dmf_dipole()

◆ dmf_dotp_aux()

◆ dmf_dotu_aux()

◆ dmf_nrm2_aux()

◆ zmf_integrate_1()

◆ zmf_integrate_2()

◆ zmf_normalize()

◆ zmf_dotp_1()

◆ zmf_dotp_2()

◆ zmf_nrm2_1()

◆ zmf_nrm2_2()

◆ zmf_moment()

◆ zmf_random()

◆ zmf_interpolate_points()

◆ zmf_interpolate_on_plane()

◆ zmf_interpolate_on_line()

◆ zmf_surface_integral_scalar()

◆ zmf_surface_integral_vector()

◆ zmf_line_integral_scalar()

◆ zmf_line_integral_vector()

◆ zmf_multipoles()

◆ zmf_dipole()

◆ zmf_dotp_aux()

◆ zmf_dotu_aux()

◆ zmf_nrm2_aux()

Variable Documentation

◆ sp_parallel

◆ sp_np

◆ sp_dim

◆ sp_st1

◆ sp_st2

◆ sp_kp1

◆ sp_kp2

◆ sp_distdot_mode

◆ sp_grp

◆ mesh_aux