ply_fxt_header_module

The FXT method offers a transformation from Legendre modes to nodes by a fast multipole approach implemented in the FXTPACK library by Reiji Suda: R. Suda, "Fast Spherical Harmonic Transform Algorithm based on Generalized Fast Multiple Method", RIMS Kokyuroku vol 1606, pp. 18-29, Jun. 2008, RIMS, Kyoto University.

Besides the oversampling factor that can be used to increase the number points in the nodal representation to achieve an de-aliasing, there is only one other option to this method: The prec parameter configures the precision up to which the FXTPACK should compute the transformation. It defaults to the square root of the epsilon for the real kind. With double precision this would something around 1.4e-8.

This transformation utilizes the Gauss Legendre integration points in the nodal representation.

Thus, the configuration for a FXT projection takes the following form:

  projection = {
    kind = 'fxt',
    prec = 1.e-10
  }

Uses

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Solid arrows point from a submodule to the (sub)module which it is descended from. Dashed arrows point from a module or program unit to modules which it uses.

Used by

Help

Graph Key

Nodes of different colours represent the following:

Solid arrows point from a submodule to the (sub)module which it is descended from. Dashed arrows point from a module or program unit to modules which it uses.

Interfaces

public interface assignment(=)

private pure subroutine Copy_fxt_header(left, right)

Arguments

Type	Intent	Optional	Attributes		Name
type(ply_fxt_header_type),	intent(out)			::	left	fpt to copy to
type(ply_fxt_header_type),	intent(in)			::	right	fpt to copy from

public interface operator(==)

private pure function isEqual(left, right) result(equality)

This function provides the test for equality of two projections.

Two fxt header are considered to be equal, if their node_header, and the factor are equal.

Arguments

Type	Intent	Optional	Attributes		Name
type(ply_fxt_header_type),	intent(in)			::	left	projection to compare
type(ply_fxt_header_type),	intent(in)			::	right	projection to compare against

Return Value logical

is equal??

public interface operator(/=)

private pure function isUnequal(left, right) result(unequality)

This function provides the test for unequality of two projections.

Two fxt header are considered to be unequal, if their node_header, or the factor are not equal.

Arguments

Type	Intent	Optional	Attributes		Name
type(ply_fxt_header_type),	intent(in)			::	left	projection to compare
type(ply_fxt_header_type),	intent(in)			::	right	projection to compare against

Return Value logical

is unequal??

public interface operator(<)

private pure function isSmaller(left, right) result(small)

This function provides a < comparison of two projections.

Sorting of fxt header is given by node_header and by the factor.

Arguments

Type	Intent	Optional	Attributes		Name
type(ply_fxt_header_type),	intent(in)			::	left	projection to compare
type(ply_fxt_header_type),	intent(in)			::	right	projection to compare against

Return Value logical

is smaller??

public interface operator(<=)

private pure function isSmallerOrEqual(left, right) result(small)

This function provides a <= comparison of two projections.

Sorting of fxt header is given by node_header, fxt_blocksize and last by factor.

Arguments

Type	Intent	Optional	Attributes		Name
type(ply_fxt_header_type),	intent(in)			::	left	projection to compare
type(ply_fxt_header_type),	intent(in)			::	right	projection to compare against

Return Value logical

is smaller??

public interface operator(>)

private pure function isGreater(left, right) result(great)

This function provides a > comparison of two projections.

Sorting of fxt header is given by node_header, fxt_blocksize and last by factor.

Arguments

Type	Intent	Optional	Attributes		Name
type(ply_fxt_header_type),	intent(in)			::	left	projection to compare
type(ply_fxt_header_type),	intent(in)			::	right	projection to compare against

Return Value logical

is greater??

public interface operator(>=)

private pure function isGreaterOrEqual(left, right) result(great)

This function provides a >= comparison of two projections.

Sorting of fxt header is given by node_header, fxt_blocksize and last by factor.

Arguments

Type	Intent	Optional	Attributes		Name
type(ply_fxt_header_type),	intent(in)			::	left	projection to compare
type(ply_fxt_header_type),	intent(in)			::	right	projection to compare against

Return Value logical

is greater??

Derived Types

type, public :: ply_fxt_header_type

Fxt projection header type, consisting of the node header which give information about the type and number of points for the projection

Components

Type	Visibility		Name		Initial
type(ply_nodes_header_type),	public	::	nodes_header
real(kind=rk),	public	::	factor	=	1.0
real(kind=rk),	public	::	prec	=	epsilon(1.0)

Functions

private pure function isEqual(left, right) result(equality)

This function provides the test for equality of two projections.

Arguments

Type	Intent	Optional	Attributes		Name
type(ply_fxt_header_type),	intent(in)			::	left	projection to compare
type(ply_fxt_header_type),	intent(in)			::	right	projection to compare against

Return Value logical

is equal??

private pure function isUnequal(left, right) result(unequality)

This function provides the test for unequality of two projections.

Arguments

Type	Intent	Optional	Attributes		Name
type(ply_fxt_header_type),	intent(in)			::	left	projection to compare
type(ply_fxt_header_type),	intent(in)			::	right	projection to compare against

Return Value logical

is unequal??

private pure function isSmaller(left, right) result(small)

This function provides a < comparison of two projections.

Arguments

Type	Intent	Optional	Attributes		Name
type(ply_fxt_header_type),	intent(in)			::	left	projection to compare
type(ply_fxt_header_type),	intent(in)			::	right	projection to compare against

Return Value logical

is smaller??

private pure function isSmallerOrEqual(left, right) result(small)

This function provides a <= comparison of two projections.

Arguments

Type	Intent	Optional	Attributes		Name
type(ply_fxt_header_type),	intent(in)			::	left	projection to compare
type(ply_fxt_header_type),	intent(in)			::	right	projection to compare against

Return Value logical

is smaller??

private pure function isGreater(left, right) result(great)

This function provides a > comparison of two projections.

Arguments

Type	Intent	Optional	Attributes		Name
type(ply_fxt_header_type),	intent(in)			::	left	projection to compare
type(ply_fxt_header_type),	intent(in)			::	right	projection to compare against

Return Value logical

is greater??

private pure function isGreaterOrEqual(left, right) result(great)

This function provides a >= comparison of two projections.

Arguments

Type	Intent	Optional	Attributes		Name
type(ply_fxt_header_type),	intent(in)			::	left	projection to compare
type(ply_fxt_header_type),	intent(in)			::	right	projection to compare against

Return Value logical

is greater??

Subroutines

public subroutine ply_fxt_header_load(me, conf, thandle)

Load settings to describe a projection method from a Lua table.

Arguments

Type	Intent		Name
type(ply_fxt_header_type),	intent(out)	::	me
type(flu_State)		::	conf
integer,	intent(in)	::	thandle

public subroutine ply_fxt_header_out(me, conf)

Write FXT settings into a Lua table.

Arguments

Type	Intent	Optional	Attributes		Name
type(ply_fxt_header_type),	intent(in)			::	me
type(aot_out_type)				::	conf

public subroutine ply_fxt_header_display(me)

Arguments

Type	Intent	Optional	Attributes		Name
type(ply_fxt_header_type),	intent(in)			::	me

private pure subroutine Copy_fxt_header(left, right)

Arguments

Type	Intent	Optional	Attributes		Name
type(ply_fxt_header_type),	intent(out)			::	left	fpt to copy to
type(ply_fxt_header_type),	intent(in)			::	right	fpt to copy from

ply_fxt_header_module Module

Contents

Interfaces

Derived Types

Functions

Subroutines

Uses

Used by

Interfaces

public interface assignment(=)

private pure subroutine Copy_fxt_header(left, right)

Arguments

public interface operator(==)

private pure function isEqual(left, right) result(equality)

Arguments

Return Value logical

public interface operator(/=)

private pure function isUnequal(left, right) result(unequality)

Arguments

Return Value logical

public interface operator(<)

private pure function isSmaller(left, right) result(small)

Arguments

Return Value logical

public interface operator(<=)

private pure function isSmallerOrEqual(left, right) result(small)

Arguments

Return Value logical

public interface operator(>)

private pure function isGreater(left, right) result(great)

Arguments

Return Value logical

public interface operator(>=)

private pure function isGreaterOrEqual(left, right) result(great)

Arguments

Return Value logical

Derived Types

type, public :: ply_fxt_header_type

Components

Functions

private pure function isEqual(left, right) result(equality)

Arguments

Return Value logical

private pure function isUnequal(left, right) result(unequality)

Arguments

Return Value logical

private pure function isSmaller(left, right) result(small)

Arguments

Return Value logical

private pure function isSmallerOrEqual(left, right) result(small)

Arguments

Return Value logical

private pure function isGreater(left, right) result(great)

Arguments

Return Value logical

private pure function isGreaterOrEqual(left, right) result(great)

Arguments

Return Value logical

Subroutines

public subroutine ply_fxt_header_load(me, conf, thandle)

Arguments

public subroutine ply_fxt_header_out(me, conf)

Arguments

public subroutine ply_fxt_header_display(me)

Arguments

private pure subroutine Copy_fxt_header(left, right)

Arguments