tem_matrix_module

Contains data_types and function for matrix operations

Uses

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Used by

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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.

Variables

Type	Visibility	Attributes		Name		Initial
integer,	private,	parameter	::	maxIntp_order	=	2
integer,	private,	parameter, dimension(maxIntp_order)	::	nCoeffs_1D	=	(/2, 3/)	For 1D stencil, 2 unknown coeffs: p(x)=a0+a1 x for linear 1st order interpolation 3 unknown coeffs: p(x)=a0+a1 x+a2 x^2 for quadratic 2nd order interpolation
integer,	private,	parameter, dimension(maxIntp_order)	::	nCoeffs_2D	=	(/3, 6/)	For 2D stencil, 3 unknown coeffs for linear 1st order interpolation: p(x,y)=a0+a1 x+a2 y 6 unknown coeffs for quadratic 2nd order interpolation: p(x,y)=a0+a1 x+a2 y+a3 x^2+a4 y^2+ a5 xy
integer,	private,	parameter, dimension(maxIntp_order)	::	nCoeffs_3D	=	(/4, 10/)	For 3D stencil, 4 unknown coeffs for linear 1st order interpolation: p(x,y,z)=a0+a1 x+a2 y+a3 z 10 unknown coeffs for quadratic 2nd order interpolation: p(x,y,z)=a0+a1 x+a2 y+a3 z+a4 x^2+a5 y^2+ a6 z^2+ a7 xy + a8 yz + a9 zx

Interfaces

public interface init

initialize the dynamic array

private subroutine init_ga_matrix(me, length)

Arguments

Type	Intent	Optional	Attributes		Name
type(grw_matrixarray_type),	intent(out)			::	me
integer,	intent(in),	optional		::	length

public interface truncate

truncate the array, meaning cut off the trailing empty entries

private subroutine truncate_ga_matrix(me)

Arguments

Type	Intent	Optional	Attributes		Name
type(grw_matrixarray_type)				::	me

public interface empty

empty the entries without changing arrays

private subroutine empty_ga_matrix(me)

Arguments

Type	Intent	Optional	Attributes		Name
type(grw_matrixarray_type)				::	me

public interface destroy

destroy the dynamic array

private subroutine destroy_ga_matrix(me)

Arguments

Type	Intent	Optional	Attributes		Name
type(grw_matrixarray_type),	intent(inout)			::	me

public interface placeat

insert an element at a given position

private subroutine placeat_ga_matrix(me, val, pos, length)

adds the value to a given position inside the growing array.

if the requested position is outside the current array bounds, the array will be resized accordingly. if it is inside the current array bounds, the element at the requested position will be replaced.

Arguments

Type	Intent	Optional		Name
type(grw_matrixarray_type)			::	me
type(tem_matrix_type),	intent(in)		::	val
integer,	intent(in)		::	pos
integer,	intent(in),	optional	::	length	optional length to expand the array

private subroutine placeat_ga_matrix_vec(me, val, pos, length)

adds the values starting from a given position inside the growing array.

if the requested position is outside the current array bounds, the array will be resized accordingly. if it is inside the current array bounds, the elements starting from the requested position will be replaced up to the element at position pos + size(val) - 1.

Arguments

Type	Intent	Optional		Name
type(grw_matrixarray_type)			::	me
type(tem_matrix_type),	intent(in)		::	val(:)
integer,	intent(in)		::	pos
integer,	intent(in),	optional	::	length	optional length to expand the array

public interface append

append a value to the dynamic array and return its position.

private subroutine append_ga_matrix(me, val, length)

Arguments

Type	Intent	Optional		Name
type(grw_matrixarray_type)			::	me
type(tem_matrix_type),	intent(in)		::	val
integer,	intent(in),	optional	::	length	optional length to expand the array

private subroutine append_ga_matrix_vec(me, val, length)

Arguments

Type	Intent	Optional		Name
type(grw_matrixarray_type)			::	me
type(tem_matrix_type),	intent(in)		::	val(:)
integer,	intent(in),	optional	::	length	optional length to expand the array

private interface expand

increase the size of the container for the array.

private subroutine expand_ga_matrix(me, pos, length)

Arguments

Type	Intent	Optional		Name
type(grw_matrixarray_type)			::	me
integer,	intent(in),	optional	::	pos
integer,	intent(in),	optional	::	length	optional length to expand the array

private interface init

private subroutine init_intpMatrixLSF(me, length, nDims, order)

This routine initialize interpolation matrix for least square fit

Arguments

Type	Intent		Name
type(tem_intpMatrixLSF_type),	intent(out)	::	me
integer,	intent(in)	::	length
integer,	intent(in)	::	nDims
integer,	intent(in)	::	order

private interface append

private subroutine append_intpMatrixLSF(me, order, QQ, nDims, nSources, cxDirRK, neighDir, pos, success)

This routine builds up the matrix for least square fit used in linear and quadratic interpolation.

Compute interpolation matrix for least square fit using stencil direction of available sources The parent of target childs coord is 0,0,0 so we could just use of stencil%cxDir to build up this matrix entries Every row in matrix is evaluated with coord of source element

Arguments

Type	Intent		Name
type(tem_intpMatrixLSF_type),	intent(inout)	::	me	intpMatrix for LSF fill
integer,	intent(inout)	::	order	interpolation order calculated for current element depending on nSources if quadratic LSF matrix is singular fall back to linear
integer,	intent(in)	::	QQ	Number of stencil directions
integer,	intent(in)	::	nDims	Number of dimensions
integer,	intent(in)	::	nSources	Number of sources from coarser found
real(kind=rk),	intent(in)	::	cxDirRK(3,QQ)	Stencil directions
integer,	intent(in)	::	neighDir(nSources)	direction in which sources are found
integer,	intent(out)	::	pos	Pointer to position of interpolation matrix in growing array of matrix
logical,	intent(out)	::	success	success if false if matrix is singular reduce interpolation order

private interface truncate

private subroutine truncate_intpMatrixLSF(me)

Arguments

Type	Intent	Optional	Attributes		Name
type(tem_intpMatrixLSF_type),	intent(inout)			::	me

private interface destroy

private subroutine destroy_intpMatrixLSF(me)

Arguments

Type	Intent	Optional	Attributes		Name
type(tem_intpMatrixLSF_type),	intent(inout)			::	me

private interface assignment(=)

private subroutine copy_matrix(left, right)

This routine provides assignment operator of tem_matrix_type

Arguments

Type	Intent	Optional	Attributes		Name
type(tem_matrix_type),	intent(out)			::	left
type(tem_matrix_type),	intent(in)			::	right

Derived Types

type, public :: tem_matrix_type

This derived type encapsulates the definition of the matrix

Components

Type	Visibility	Attributes		Name		Initial
real(kind=rk),	public,	allocatable	::	A(:,:)			inverted matrix to solve linear system of equation
integer,	public		::	nEntries(2)			how many entries are in the 2d matrix?

type, public :: tem_intpMatrixLSF_type

This derived type encapsulates the definition of least square fit matrix for interpolation method which is required for every combination of available nSourceFromCoarser

Components

Type	Visibility		Name
type(grw_matrixarray_type),	public	::	matArray
type(dyn_intarray_type),	public	::	ID	Unique hash ID to identify different combination of available nSourceFromCoarser
integer,	public	::	nCoeffs	nCoeffs required for least square fit. Depends on nDims and order of interpolation
type(grw_logicalarray_type),	public	::	isInvertible	For every matrix in matArray, store if its invertible or not to avoid rebuilding singular matrix

type, private :: grw_matrixarray_type

growing array type for type(tem_matrix_type)

Components

Type	Visibility	Attributes		Name		Initial
integer,	public		::	nvals	=	0
integer,	public		::	containersize	=	0
type(tem_matrix_type),	public,	allocatable	::	val(:)

Functions

public function invert_matrix(A, errCode) result(Ainv)

Returns the inverse of a matrix calculated by finding the LU decomposition. Depends on LAPACK.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=rk),	intent(in),		dimension(:,:)	::	A	Matrix to invert
integer,	intent(out),	optional		::	errCode	If error code is present return error code and do not abort

Return Value real(kind=rk), dimension(size(A,1),size(A,2))

inverse of A

private pure function polyQuadratic_1D(cxDir) result(phi)

This function returns matrix entries for quadratic polynomial for 1D stencil

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=rk),	intent(in)			::	cxDir(3)

Return Value real(kind=rk), (3)

private pure function polyQuadratic_2D(cxDir) result(phi)

This function returns matrix entries for quadratic polynomial for 2D stencil

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=rk),	intent(in)			::	cxDir(3)

Return Value real(kind=rk), (6)

private pure function polyQuadratic_3D(cxDir) result(phi)

This function returns matrix entries for quadratic polynomial for 3D stencil

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=rk),	intent(in)			::	cxDir(3)

Return Value real(kind=rk), (10)

private pure function polyLinear_1D(cxDir) result(phi)

This function returns matrix entries for Linear polynomial for 1D stencil

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=rk),	intent(in)			::	cxDir(3)

Return Value real(kind=rk), (2)

private pure function polyLinear_2D(cxDir) result(phi)

This function returns matrix entries for Linear polynomial for 2D stencil

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=rk),	intent(in)			::	cxDir(3)

Return Value real(kind=rk), (3)

private pure function polyLinear_3D(cxDir) result(phi)

This function returns matrix entries for Linear polynomial for 3D stencil

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=rk),	intent(in)			::	cxDir(3)

Return Value real(kind=rk), (4)

Subroutines

public subroutine tem_matrix_dump(me, outUnit)

Arguments

Type	Intent	Optional	Attributes		Name
type(tem_matrix_type),	intent(in)			::	me
integer,	intent(in)			::	outUnit

private subroutine init_ga_matrix(me, length)

Arguments

Type	Intent	Optional	Attributes		Name
type(grw_matrixarray_type),	intent(out)			::	me
integer,	intent(in),	optional		::	length

private subroutine destroy_ga_matrix(me)

Arguments

Type	Intent	Optional	Attributes		Name
type(grw_matrixarray_type),	intent(inout)			::	me

private subroutine truncate_ga_matrix(me)

Arguments

Type	Intent	Optional	Attributes		Name
type(grw_matrixarray_type)				::	me

private subroutine empty_ga_matrix(me)

Arguments

Type	Intent	Optional	Attributes		Name
type(grw_matrixarray_type)				::	me

private subroutine placeat_ga_matrix(me, val, pos, length)

adds the value to a given position inside the growing array.

Arguments

Type	Intent	Optional		Name
type(grw_matrixarray_type)			::	me
type(tem_matrix_type),	intent(in)		::	val
integer,	intent(in)		::	pos
integer,	intent(in),	optional	::	length	optional length to expand the array

private subroutine placeat_ga_matrix_vec(me, val, pos, length)

adds the values starting from a given position inside the growing array.

Arguments

Type	Intent	Optional		Name
type(grw_matrixarray_type)			::	me
type(tem_matrix_type),	intent(in)		::	val(:)
integer,	intent(in)		::	pos
integer,	intent(in),	optional	::	length	optional length to expand the array

private subroutine append_ga_matrix(me, val, length)

Arguments

Type	Intent	Optional		Name
type(grw_matrixarray_type)			::	me
type(tem_matrix_type),	intent(in)		::	val
integer,	intent(in),	optional	::	length	optional length to expand the array

private subroutine append_ga_matrix_vec(me, val, length)

Arguments

Type	Intent	Optional		Name
type(grw_matrixarray_type)			::	me
type(tem_matrix_type),	intent(in)		::	val(:)
integer,	intent(in),	optional	::	length	optional length to expand the array

private subroutine expand_ga_matrix(me, pos, length)

Arguments

Type	Intent	Optional		Name
type(grw_matrixarray_type)			::	me
integer,	intent(in),	optional	::	pos
integer,	intent(in),	optional	::	length	optional length to expand the array

private subroutine init_intpMatrixLSF(me, length, nDims, order)

This routine initialize interpolation matrix for least square fit

Arguments

Type	Intent		Name
type(tem_intpMatrixLSF_type),	intent(out)	::	me
integer,	intent(in)	::	length
integer,	intent(in)	::	nDims
integer,	intent(in)	::	order

private subroutine append_intpMatrixLSF(me, order, QQ, nDims, nSources, cxDirRK, neighDir, pos, success)

This routine builds up the matrix for least square fit used in linear and quadratic interpolation.

Arguments

Type	Intent		Name
type(tem_intpMatrixLSF_type),	intent(inout)	::	me	intpMatrix for LSF fill
integer,	intent(inout)	::	order	interpolation order calculated for current element depending on nSources if quadratic LSF matrix is singular fall back to linear
integer,	intent(in)	::	QQ	Number of stencil directions
integer,	intent(in)	::	nDims	Number of dimensions
integer,	intent(in)	::	nSources	Number of sources from coarser found
real(kind=rk),	intent(in)	::	cxDirRK(3,QQ)	Stencil directions
integer,	intent(in)	::	neighDir(nSources)	direction in which sources are found
integer,	intent(out)	::	pos	Pointer to position of interpolation matrix in growing array of matrix
logical,	intent(out)	::	success	success if false if matrix is singular reduce interpolation order

private subroutine build_matrixLSF_quadIntp(me, QQ, nDims, nSources, cxDirRK, neighDir, nCoeffs, success)

This routine builds up the matrix for least square fit used in quadratic interpolation. We extract momentum information completely on the view of the source coordinate system Set the right hand side of the equation system Solve the problem, where b = rhs, x = coefficients Ax = b overdetermined, solve the least Square fit problem (A^T)Ax = (A^T)b x = ((A^T)A)^-1(A^T)b Solve linear system of equation with inverted matrix. Size of matrix: (nCoeffs, QQ) matrix_LSF = ((A^T)A)^-1(A^T)

Arguments

Type	Intent		Name
type(tem_matrix_type),	intent(out)	::	me	Matrix to fill
integer,	intent(in)	::	QQ	Number of stencil directions
integer,	intent(in)	::	nDims	Number of dimensions
integer,	intent(in)	::	nSources	Number of sources from coarser found
real(kind=rk),	intent(in)	::	cxDirRK(3,QQ)	Stencil directions
integer,	intent(in)	::	neighDir(nSources)	direction in which sources are found
integer,	intent(in)	::	nCoeffs	nUnknown coeffs
logical,	intent(out)	::	success	success if false if matrix is singular reduce interpolation order

private subroutine build_matrixLSF_linearIntp(me, QQ, nDims, nSources, cxDirRK, neighDir, nCoeffs, success)

This routine builds up the matrix for least square fit used in linear interpolation.

Arguments

Type	Intent		Name
type(tem_matrix_type),	intent(out)	::	me	Matrix to fill
integer,	intent(in)	::	QQ	Number of stencil directions
integer,	intent(in)	::	nDims	Number of dimensions
integer,	intent(in)	::	nSources	Number of sources from coarser found
real(kind=rk),	intent(in)	::	cxDirRK(3,QQ)	Stencil directions
integer,	intent(in)	::	neighDir(nSources)	direction in which sources are found
integer,	intent(in)	::	nCoeffs	nUnknown coeffs
logical,	intent(out)	::	success	success if false if matrix is singular reduce interpolation order

private subroutine truncate_intpMatrixLSF(me)

Arguments

Type	Intent	Optional	Attributes		Name
type(tem_intpMatrixLSF_type),	intent(inout)			::	me

private subroutine destroy_intpMatrixLSF(me)

Arguments

Type	Intent	Optional	Attributes		Name
type(tem_intpMatrixLSF_type),	intent(inout)			::	me

private subroutine copy_matrix(left, right)

This routine provides assignment operator of tem_matrix_type

Arguments

Type	Intent	Optional	Attributes		Name
type(tem_matrix_type),	intent(out)			::	left
type(tem_matrix_type),	intent(in)			::	right

private subroutine alloc_matrix(me, dim1, dim2)

This routine allocates matrix with given dimentions

Arguments

Type	Intent		Name
type(tem_matrix_type)		::	me
integer,	intent(in)	::	dim1
integer,	intent(in)	::	dim2

tem_matrix_module Module

Contents

Variables

Interfaces

Derived Types

Functions

Subroutines

Uses

Used by

Variables

Interfaces

public interface init

private subroutine init_ga_matrix(me, length)

Arguments

public interface truncate

private subroutine truncate_ga_matrix(me)

Arguments

public interface empty

private subroutine empty_ga_matrix(me)

Arguments

public interface destroy

private subroutine destroy_ga_matrix(me)

Arguments

public interface placeat

private subroutine placeat_ga_matrix(me, val, pos, length)

Arguments

private subroutine placeat_ga_matrix_vec(me, val, pos, length)

Arguments

public interface append

private subroutine append_ga_matrix(me, val, length)

Arguments

private subroutine append_ga_matrix_vec(me, val, length)

Arguments

private interface expand

private subroutine expand_ga_matrix(me, pos, length)

Arguments

private interface init

private subroutine init_intpMatrixLSF(me, length, nDims, order)

Arguments

private interface append

private subroutine append_intpMatrixLSF(me, order, QQ, nDims, nSources, cxDirRK, neighDir, pos, success)

Arguments

private interface truncate

private subroutine truncate_intpMatrixLSF(me)

Arguments

private interface destroy

private subroutine destroy_intpMatrixLSF(me)

Arguments

private interface assignment(=)

private subroutine copy_matrix(left, right)

Arguments

Derived Types

type, public :: tem_matrix_type

Components

type, public :: tem_intpMatrixLSF_type

Components

type, private :: grw_matrixarray_type

Components

Functions

public function invert_matrix(A, errCode) result(Ainv)

Arguments

Return Value real(kind=rk), dimension(size(A,1),size(A,2))

private pure function polyQuadratic_1D(cxDir) result(phi)

Arguments

Return Value real(kind=rk), (3)

private pure function polyQuadratic_2D(cxDir) result(phi)

Arguments

Return Value real(kind=rk), (6)

private pure function polyQuadratic_3D(cxDir) result(phi)

Arguments

Return Value real(kind=rk), (10)

private pure function polyLinear_1D(cxDir) result(phi)

Arguments

Return Value real(kind=rk), (2)

private pure function polyLinear_2D(cxDir) result(phi)

Arguments

Return Value real(kind=rk), (3)

private pure function polyLinear_3D(cxDir) result(phi)

Arguments

Return Value real(kind=rk), (4)