mod_banded_matrix_hermitian – Legolas v. 2.1.1

Contains types and routines to handle banded Hermitian 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_hermitian_banded_matrix get_element get_total_nb_elements uplo_is_valid is_within_band is_compatible_with

Derived Types

type, public :: hermitian_banded_matrix_t

type to represent a complex Hermitian banded matrix

Components

Type	Visibility	Attributes		Name
integer,	public		::	n	number of rows/columns
character,	public		::	uplo	store upper ("U") or lower ("L") triangular part
integer,	public		::	kd	number of sub/superdiagonals
complex(kind=dp),	public,	allocatable	::	AB(:,:)	the matrix in banded storage

Type-Bound Procedures

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

Functions

public function new_hermitian_banded_matrix(rows, diags, uplo) result(matrix)

Constructor for a new Hermitian banded matrix with a given number of rows and diagonals. Allocates and initialises the datatype. initialise all to zero

Arguments

Type	Intent		Name
integer,	intent(in)	::	rows	number of rows/columns
integer,	intent(in)	::	diags	number of sub/superdiagonals
character,	intent(in)	::	uplo	store upper ("U") or lower ("L") triangular part

Return Value type(hermitian_banded_matrix_t)

the Hermitian matrix in banded storage

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 $(kd + 1 + i - j, j)$ if uplo = "U" and at position $(1 + i - j, j)$ if uplo = "L" in the banded storage.

Arguments

Type	Intent		Name
class(hermitian_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 the 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(hermitian_banded_matrix_t),	intent(in)			::	this	type instance

Return Value integer

private pure function uplo_is_valid(uplo)

Checks whether the given uplo parameter is valid.

Arguments

Type	Intent	Optional	Attributes		Name
character,	intent(in)			::	uplo	uplo character to check

Return Value logical

private pure function is_within_band(matrix, row, col)

Checks if a given position (row, col) is within the banded structure. For uplo = "U" the position is within the band if $max(1, col - kd) \leq row \leq col,$ for uplo = "L" the position is within the band if $col \leq row \leq min(n, col + kd)$ with $kd$ the number of sub/superdiagonals and $n$ the number of rows/columns.

Arguments

Type	Intent		Name
class(hermitian_banded_matrix_t),	intent(in)	::	matrix	Hermitian banded matrix structure
integer,	intent(in)	::	row	the row index
integer,	intent(in)	::	col	the column index

Return Value logical

private pure function is_compatible_with(this, other)

Checks if a Hermitian band matrix is compatible with another Hermitian band matrix. This implies that the following attributes should be equal: - number of rows/columns - number of sub/superdiagonals - storage of upper or lower triangular part - dimensions of the banded matrices themselves Returns .true. if all criteria are satisfied, .false. otherwise.

Arguments

Type	Intent	Optional	Attributes		Name
class(hermitian_banded_matrix_t),	intent(in)			::	this	type instance
class(hermitian_banded_matrix_t),	intent(in)			::	other	other banded 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(hermitian_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(hermitian_banded_matrix_t),	intent(inout)			::	this	type instance

mod_banded_matrix_hermitian Module

Contents

Derived Types

Functions

Subroutines

Uses

Contents

Derived Types

Functions

Subroutines

Derived Types

type, public :: hermitian_banded_matrix_t

Components

Type-Bound Procedures

Functions

public function new_hermitian_banded_matrix(rows, diags, uplo) result(matrix)

Arguments

Return Value type(hermitian_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 uplo_is_valid(uplo)

Arguments

Return Value logical

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

Subroutines

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

Arguments

private pure subroutine destroy(this)

Arguments