mod_banded_matrix – Legolas v. 2.1.1

Contains types and routines to handle banded matrices. We use the same conventions as explained in the LAPACK guide http://www.netlib.org/lapack/lug/node124.html.

Uses

- mod_logging
- mod_global_variables

Functions

new_banded_matrix get_element get_total_nb_elements get_total_nb_nonzero_elements is_within_band is_compatible_with dimensions_are_valid

Derived Types

type, public :: banded_matrix_t

type to represent a complex banded matrix

Components

Type	Visibility	Attributes		Name
integer,	public		::	m	number of rows
integer,	public		::	n	number of columns
integer,	public		::	kl	number of subdiagonals
integer,	public		::	ku	number of superdiagonals
complex(kind=dp),	public,	allocatable	::	AB(:,:)	array containing the banded storage

Type-Bound Procedures

procedure, public :: get_element
procedure, public :: set_element
procedure, public :: get_total_nb_elements
procedure, public :: get_total_nb_nonzero_elements
procedure, public :: is_compatible_with
procedure, public :: destroy

Functions

public function new_banded_matrix(rows, cols, subdiags, superdiags) result(matrix)

Constructor for a new banded matrix with a given number of rows, columns, subdiagonals and superdiagonals. Allocates and initialises the datatype.

Arguments

Type	Intent		Name
integer,	intent(in)	::	rows	number of rows
integer,	intent(in)	::	cols	number of columns
integer,	intent(in)	::	subdiags	number of subdiagonals
integer,	intent(in)	::	superdiags	number of superdiagonals

Return Value type(banded_matrix_t)

banded matrix datatype

private pure function get_element(this, row, col) result(element)

Retrieves the element at position (row, col) of the original matrix. See the LAPACK documentation, element $a_{ij}$ of the original matrix is stored at position $(ku + 1 + i - j, j)$ (with $ku$ the number of superdiagonals).

Arguments

Type	Intent		Name
class(banded_matrix_t),	intent(in)	::	this	type instance
integer,	intent(in)	::	row	the row index of the original position
integer,	intent(in)	::	col	the column index of the original position

Return Value complex(kind=dp)

the element at original position (row, col)

private pure function get_total_nb_elements(this)

Returns the total number of elements inside the banded matrix.

Arguments

Type	Intent	Optional	Attributes		Name
class(banded_matrix_t),	intent(in)			::	this	type instance

Return Value integer

private pure function get_total_nb_nonzero_elements(this)

Returns the total number of nonzero elements inside the banded matrix.

Arguments

Type	Intent	Optional	Attributes		Name
class(banded_matrix_t),	intent(in)			::	this	type instance

Return Value integer

private pure function is_within_band(matrix, row, col)

Checks if a given position (row, col) is within the banded structure, i.e. $max(1, col - ku) \leq row \leq min(m, col + kl)$ with $ku$ the number of superdiagonals and $kl$ the number of subdiagonals.

Arguments

Type	Intent		Name
type(banded_matrix_t),	intent(in)	::	matrix	the banded matrix structure
integer,	intent(in)	::	row	row index
integer,	intent(in)	::	col	column index

Return Value logical

private pure function is_compatible_with(this, other)

Checks if a banded matrix is compatibe with another banded matrix. This implies that the following attributes should be equal: - dimensions of the original matrices - number of superdiagonals and subdiagonals - dimensions of the banded matrices themselves Returns .true. if these three criteria are satisfied, .false. otherwise.

Arguments

Type	Intent	Optional	Attributes		Name
class(banded_matrix_t),	intent(in)			::	this	type instance
type(banded_matrix_t),	intent(in)			::	other	other banded matrix

Return Value logical

private pure function dimensions_are_valid(rows, cols)

Checks if the given matrix dimensions are valid. For now, we only accept square matrices. Returns .true. if rows equals cols, .false. otherwise.

Arguments

Type	Intent	Optional	Attributes		Name
integer,	intent(in)			::	rows	number of rows in the original matrix
integer,	intent(in)			::	cols	number of columns in the original matrix

Return Value logical

Subroutines

private pure subroutine set_element(this, row, col, element)

Sets the element $a_{ij}$ of the original array into the banded structure. The row and col arguments refer to the row and column indices of the element in the original array. This routine has no effect if the location falls outside of the banded structure.

Arguments

Type	Intent		Name
class(banded_matrix_t),	intent(inout)	::	this	type instance
integer,	intent(in)	::	row	row index of element
integer,	intent(in)	::	col	column index of element
complex(kind=dp),	intent(in)	::	element	value for the element at (row, col)

private pure subroutine destroy(this)

Destructor, deallocates the datastructure.

Arguments

Type	Intent	Optional	Attributes		Name
class(banded_matrix_t),	intent(inout)			::	this	type instance

mod_banded_matrix Module

Contents

Derived Types

Functions

Subroutines

Uses

Contents

Derived Types

Functions

Subroutines

Derived Types

type, public :: banded_matrix_t

Components

Type-Bound Procedures

Functions

public function new_banded_matrix(rows, cols, subdiags, superdiags) result(matrix)

Arguments

Return Value type(banded_matrix_t)

private pure function get_element(this, row, col) result(element)

Arguments

Return Value complex(kind=dp)

private pure function get_total_nb_elements(this)

Arguments

Return Value integer

private pure function get_total_nb_nonzero_elements(this)

Arguments

Return Value integer

private pure function is_within_band(matrix, row, col)

Arguments

Return Value logical

private pure function is_compatible_with(this, other)

Arguments

Return Value logical

private pure function dimensions_are_valid(rows, cols)

Arguments

Return Value logical

Subroutines

private pure subroutine set_element(this, row, col, element)

Arguments

private pure subroutine destroy(this)

Arguments