basis_vectors_oct_m::basis_vectors_t Interface Reference

Vectors defining a basis in a vector space. This class provides methods to convert vector coordinates in this basis to and from Cartesian coordinates. Given a vector v, its coordinates in the basis are related to the Cartesian coordinates y_i in the following way: More...

Detailed Description

Vectors defining a basis in a vector space. This class provides methods to convert vector coordinates in this basis to and from Cartesian coordinates. Given a vector v, its coordinates in the basis are related to the Cartesian coordinates y_i in the following way:

\[ x_i = \sum_j a_{ij} y_j \]

where a_{ij} are the elements of the change of basis matrix A. The previous expression can be expressed in matrix form:

\[ X = A Y \]

Obtaining the Cartesian coordinates from the basis coordinates is then straighforward using the inverse of A:

\[ Y = A^{-1} X \]

Note that the columns of \(A^{-1}\) are simply the basis vectors.

Definition at line 149 of file basis_vectors.F90.

Private Member Functions
procedure	copy => basis_vectors_copy
generic	assignment => copy
procedure	scale => basis_vectors_scale
generic	from_cartesian => from_cartesian1, from_cartesian2
generic	to_cartesian => to_cartesian1, to_cartesian2
procedure	from_cartesian1 => basis_vectors_from_cartesian1
procedure	to_cartesian1 => basis_vectors_to_cartesian1
procedure	from_cartesian2 => basis_vectors_from_cartesian2
procedure	to_cartesian2 => basis_vectors_to_cartesian2
final	basis_vectors_finalize
type(basis_vectors_t) function	basis_vectors_constructor (namespace, dim, vectors)

Private Attributes
integer, private	dim
real(real64), dimension(:,:), allocatable	vectors
	the vectors of the basis More...
real(real64), dimension(:,:), allocatable	change_of_basis_matrix
	the change-of-basis matrix to convert from a Cartesian basis to this basis More...
logical	orthogonal

Member Function/Subroutine Documentation

copy()

procedure basis_vectors_oct_m::basis_vectors_t::copy

private

Definition at line 156 of file basis_vectors.F90.

assignment()

generic basis_vectors_oct_m::basis_vectors_t::assignment

private

Definition at line 157 of file basis_vectors.F90.

scale()

procedure basis_vectors_oct_m::basis_vectors_t::scale

private

Definition at line 158 of file basis_vectors.F90.

from_cartesian()

generic basis_vectors_oct_m::basis_vectors_t::from_cartesian

private

Definition at line 159 of file basis_vectors.F90.

to_cartesian()

generic basis_vectors_oct_m::basis_vectors_t::to_cartesian

private

Definition at line 160 of file basis_vectors.F90.

from_cartesian1()

procedure basis_vectors_oct_m::basis_vectors_t::from_cartesian1

private

Definition at line 161 of file basis_vectors.F90.

to_cartesian1()

procedure basis_vectors_oct_m::basis_vectors_t::to_cartesian1

private

Definition at line 162 of file basis_vectors.F90.

from_cartesian2()

procedure basis_vectors_oct_m::basis_vectors_t::from_cartesian2

private

Definition at line 163 of file basis_vectors.F90.

to_cartesian2()

procedure basis_vectors_oct_m::basis_vectors_t::to_cartesian2

private

Definition at line 164 of file basis_vectors.F90.

basis_vectors_finalize()

final basis_vectors_oct_m::basis_vectors_t::basis_vectors_finalize

finalprivate

Definition at line 165 of file basis_vectors.F90.

basis_vectors_constructor()

type(basis_vectors_t) function basis_vectors_oct_m::basis_vectors_t::basis_vectors_constructor ( type(namespace_t), intent(in)  namespace, integer, intent(in)  dim, real(real64), dimension(dim, dim), intent(in)  vectors  )

private

Definition at line 175 of file basis_vectors.F90.

Member Data Documentation

dim

integer, private basis_vectors_oct_m::basis_vectors_t::dim

private

Definition at line 151 of file basis_vectors.F90.

vectors

real(real64), dimension(:,:), allocatable basis_vectors_oct_m::basis_vectors_t::vectors

private

the vectors of the basis

Definition at line 152 of file basis_vectors.F90.

change_of_basis_matrix

real(real64), dimension(:,:), allocatable basis_vectors_oct_m::basis_vectors_t::change_of_basis_matrix

private

the change-of-basis matrix to convert from a Cartesian basis to this basis

Definition at line 153 of file basis_vectors.F90.

orthogonal

logical basis_vectors_oct_m::basis_vectors_t::orthogonal

private

Definition at line 154 of file basis_vectors.F90.

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The documentation for this interface was generated from the following file:

• math/basis_vectors.F90