spatial_rotation – SPHINCS

type, public, extends(lorentz_transformation) :: spatial_rotation

TYPE representing a spatial rotation

Inherits

Help

Variables

euler_angles inv_r inv_r_x inv_r_y inv_r_z r r_x r_y r_z tr_r

Constructor

spatial_rotation

Type-Bound Procedures

apply_as_congruence apply_as_congruence_to_symrank2_tensor apply_as_congruence_to_tensor apply_as_similarity apply_as_similarity_to_symrank2_tensor apply_as_similarity_to_tensor apply_to_vector compute_rotation_matrices

Source Code

spatial_rotation

Components

Type	Visibility	Attributes		Name
double precision,	private,	DIMENSION(3)	::	euler_angles	Euler angles that define the rotation around the $x,y,z$ axes, in this order
double precision,	private,	DIMENSION(3,3)	::	inv_r	Full inverse rotation operator
double precision,	private,	DIMENSION(3,3)	::	inv_r_x	Inverse rotation operator around the $x$ axis
double precision,	private,	DIMENSION(3,3)	::	inv_r_y	Inverse rotation operator around the $y$ axis
double precision,	private,	DIMENSION(3,3)	::	inv_r_z	Inverse rotation operator around the $z$ axis
double precision,	private,	DIMENSION(3,3)	::	r	Full rotation operator
double precision,	private,	DIMENSION(3,3)	::	r_x	Rotation operator around the $x$ axis
double precision,	private,	DIMENSION(3,3)	::	r_y	Rotation operator around the $y$ axis
double precision,	private,	DIMENSION(3,3)	::	r_z	Rotation operator around the $z$ axis
double precision,	private,	DIMENSION(3,3)	::	tr_r	Transpose of the full inverse rotation operator

Constructor

public interface spatial_rotation

public module function construct_rotation(euler_angles) result(rotation)

Arguments

Type	Intent	Optional	Attributes		Name
double precision,	intent(in),		DIMENSION(3)	::	euler_angles	Euler angles that define the rotation around the $x,y,z$ axes, in this order

Return Value type(spatial_rotation)

spatial_rotation object to be constructed

public module function construct_rotation_angles(alpha, beta, gamma) result(rotation)

Arguments

Type	Intent		Name
double precision,	intent(in)	::	alpha	Euler angle that defines the rotation around the $x$ axis
double precision,	intent(in)	::	beta	Euler angle that defines the rotation around the $y$ axis
double precision,	intent(in)	::	gamma	Euler angle that defines the rotation around the $z$ axis

Return Value type(spatial_rotation)

spatial_rotation object to be constructed

Type-Bound Procedures

generic, public :: apply_as_congruence => apply_as_congruence_to_tensor, apply_as_congruence_to_symrank2_tensor

Generic procedure to apply the lorentz_transformation as a congruence

public interface apply_as_congruence_to_tensor()

Arguments
None
public interface apply_as_congruence_to_symrank2_tensor()

Arguments
None

procedure, public, NON_OVERRIDABLE :: apply_as_congruence_to_symrank2_tensor

Action of the lorentz_transformation as a congruence on a $10$ -vector storing the components of a symmetric, purely covariant, $4\times 4$ tensor

interface

public module function apply_as_congruence_to_symrank2_tensor(this, t) result(transformed_t)

Action of the lorentz_transformation on a $4$ -vector

Arguments

Type	Intent	Optional	Attributes		Name
class(lorentz_transformation),	intent(in)			::	this	lorentz_transformation object to apply
double precision,	intent(in),		DIMENSION(n_sym4x4)	::	t	$10$ -vector storing the components of the symmetric $4\times 4$ tensor to be boosted

Return Value double precision, DIMENSION(n_sym4x4)

$10$ -vector storing the components of the boosted symmetric $4\times 4$ tensor

procedure, public, NON_OVERRIDABLE :: apply_as_congruence_to_tensor

Action of the lorentz_transformation as a congruence on a generic purely covariant tensor

interface

public module function apply_as_congruence_to_tensor(this, t) result(transformed_t)

Action of the lorentz_transformation on a $4$ -vector

Arguments

Type	Intent	Optional	Attributes		Name
class(lorentz_transformation),	intent(in)			::	this	lorentz_transformation object to apply
double precision,	intent(in),		DIMENSION(4,4)	::	t(0:3,0:3)	$4\times 4$ tensor to be boosted

Return Value double precision, DIMENSION(4,4), (0:3,0:3)

Boosted $4\times 4$ tensor

generic, public :: apply_as_similarity => apply_as_similarity_to_tensor, apply_as_similarity_to_symrank2_tensor

Generic procedure to apply the lorentz_transformation as a similarity

public interface apply_as_similarity_to_tensor()

Arguments
None
public interface apply_as_similarity_to_symrank2_tensor()

Arguments
None

procedure, public, NON_OVERRIDABLE :: apply_as_similarity_to_symrank2_tensor

Action of the lorentz_transformation as a similarity on a $10$ -vector storing the components of a symmetric $4\times 4$ tensor

interface

public module function apply_as_similarity_to_symrank2_tensor(this, t) result(transformed_t)

Action of the lorentz_transformation on a $4$ -vector

Arguments

Type	Intent	Optional	Attributes		Name
class(lorentz_transformation),	intent(in)			::	this	lorentz_transformation object to apply
double precision,	intent(in),		DIMENSION(n_sym4x4)	::	t	$10$ -vector storing the components of the symmetric $4\times 4$ tensor to be boosted

Return Value double precision, DIMENSION(n_sym4x4)

$10$ -vector storing the components of the boosted symmetric $4\times 4$ tensor

procedure, public, NON_OVERRIDABLE :: apply_as_similarity_to_tensor

Action of the lorentz_transformation as a similarity on a generic tensor

interface

public module function apply_as_similarity_to_tensor(this, t) result(transformed_t)

Action of the lorentz_transformation on a $4$ -vector

Arguments

Type	Intent	Optional	Attributes		Name
class(lorentz_transformation),	intent(in)			::	this	lorentz_transformation object to apply
double precision,	intent(in),		DIMENSION(4,4)	::	t(0:3,0:3)	$4\times 4$ tensor to be boosted

Return Value double precision, DIMENSION(4,4), (0:3,0:3)

Boosted $4\times 4$ tensor

procedure, public, NON_OVERRIDABLE :: apply_to_vector

Action of the lorentz_transformation on a $4$ -vector

interface

public module function apply_to_vector(this, u) result(transformed_u)

Action of the lorentz_transformation on a $4$ -vector

Arguments

Type	Intent	Optional	Attributes		Name
class(lorentz_transformation),	intent(in)			::	this	lorentz_transformation object to apply
double precision,	intent(in),		DIMENSION(4)	::	u(0:3)	$4$ -vector to be boosted

Return Value double precision, DIMENSION(4), (0:3)

Boosted $4$ -vector

procedure, public :: compute_rotation_matrices

Computes the spatial part of the matrix of the Lorentz

interface

public module subroutine compute_rotation_matrices(this, euler_angles, r_x, r_y, r_z, r, matrix, inv_r_x, inv_r_y, inv_r_z, inv_r, inv_matrix)

Compute the matrices for the spatial_rotation

Arguments

Type	Intent	Attributes		Name
class(spatial_rotation),	intent(inout)		::	this	spatial_rotation object to compuet the matrices for
double precision,	intent(in),	DIMENSION(3)	::	euler_angles	lambda $\times$ v
double precision,	intent(out),	DIMENSION(3,3)	::	r_x	Rotation operator around the $x$ axis
double precision,	intent(out),	DIMENSION(3,3)	::	r_y	Rotation operator around the $y$ axis
double precision,	intent(out),	DIMENSION(3,3)	::	r_z	Rotation operator around the $z$ axis
double precision,	intent(out),	DIMENSION(3,3)	::	r	Full $3\times 3$ rotation operator
double precision,	intent(out),	DIMENSION(4,4)	::	matrix(0:3,0:3)	$4\times 4$ matrix representing the Lorentz boost
double precision,	intent(out),	DIMENSION(3,3)	::	inv_r_x	Inverse rotation operator around the $x$ axis
double precision,	intent(out),	DIMENSION(3,3)	::	inv_r_y	Inverse rotation operator around the $y$ axis
double precision,	intent(out),	DIMENSION(3,3)	::	inv_r_z	Inverse rotation operator around the $z$ axis
double precision,	intent(out),	DIMENSION(3,3)	::	inv_r	Inverse of the full $3\times 3$ rotation operator
double precision,	intent(out),	DIMENSION(4,4)	::	inv_matrix(0:3,0:3)	Inverse of the $4\times 4$ matrix representing the Lorentz boost

Source Code

  TYPE, EXTENDS(lorentz_transformation):: spatial_rotation
  !! TYPE representing a spatial rotation

    PRIVATE

    DOUBLE PRECISION, DIMENSION(3):: euler_angles
    !# Euler angles that define the rotation around the \(x,y,z\) axes,
    !  in this order

    DOUBLE PRECISION, DIMENSION(3,3):: r_x
    !! Rotation operator around the \(x\) axis
    DOUBLE PRECISION, DIMENSION(3,3):: r_y
    !! Rotation operator around the \(y\) axis
    DOUBLE PRECISION, DIMENSION(3,3):: r_z
    !! Rotation operator around the \(z\) axis
    DOUBLE PRECISION, DIMENSION(3,3):: r
    !! Full rotation operator

    DOUBLE PRECISION, DIMENSION(3,3):: tr_r
    !! Transpose of the full inverse rotation operator

    DOUBLE PRECISION, DIMENSION(3,3):: inv_r_x
    !! Inverse rotation operator around the \(x\) axis
    DOUBLE PRECISION, DIMENSION(3,3):: inv_r_y
    !! Inverse rotation operator around the \(y\) axis
    DOUBLE PRECISION, DIMENSION(3,3):: inv_r_z
    !! Inverse rotation operator around the \(z\) axis
    DOUBLE PRECISION, DIMENSION(3,3):: inv_r
    !! Full inverse rotation operator


    CONTAINS


    PROCEDURE:: compute_rotation_matrices
    !! Computes the spatial part of the matrix of the Lorentz
    !  boost, and its whole matrix, starting from the vector
    !  \(p\)


  END TYPE spatial_rotation

spatial_rotation Derived Type

Contents

Variables

Constructor

Type-Bound Procedures

Source Code

type, public, extends(lorentz_transformation) :: spatial_rotation

Inherits

Contents

Variables

Constructor

Type-Bound Procedures

Source Code

Components

Constructor

public interface spatial_rotation

public module function construct_rotation(euler_angles) result(rotation)

Arguments

Return Value type(spatial_rotation)

public module function construct_rotation_angles(alpha, beta, gamma) result(rotation)

Arguments

Return Value type(spatial_rotation)

Type-Bound Procedures

generic, public :: apply_as_congruence => apply_as_congruence_to_tensor, apply_as_congruence_to_symrank2_tensor

public interface apply_as_congruence_to_tensor()

Arguments

public interface apply_as_congruence_to_symrank2_tensor()

Arguments

procedure, public, NON_OVERRIDABLE :: apply_as_congruence_to_symrank2_tensor

interface

public module function apply_as_congruence_to_symrank2_tensor(this, t) result(transformed_t) Implementation →

Arguments

Return Value double precision, DIMENSION(n_sym4x4)

procedure, public, NON_OVERRIDABLE :: apply_as_congruence_to_tensor

interface

public module function apply_as_congruence_to_tensor(this, t) result(transformed_t) Implementation →

Arguments

Return Value double precision, DIMENSION(4,4), (0:3,0:3)

generic, public :: apply_as_similarity => apply_as_similarity_to_tensor, apply_as_similarity_to_symrank2_tensor

public interface apply_as_similarity_to_tensor()

Arguments

public interface apply_as_similarity_to_symrank2_tensor()

Arguments

procedure, public, NON_OVERRIDABLE :: apply_as_similarity_to_symrank2_tensor

interface

public module function apply_as_similarity_to_symrank2_tensor(this, t) result(transformed_t) Implementation →

Arguments

Return Value double precision, DIMENSION(n_sym4x4)

procedure, public, NON_OVERRIDABLE :: apply_as_similarity_to_tensor

interface

public module function apply_as_similarity_to_tensor(this, t) result(transformed_t) Implementation →

Arguments

Return Value double precision, DIMENSION(4,4), (0:3,0:3)

procedure, public, NON_OVERRIDABLE :: apply_to_vector

interface

public module function apply_to_vector(this, u) result(transformed_u) Implementation →

Arguments

Return Value double precision, DIMENSION(4), (0:3)

procedure, public :: compute_rotation_matrices

interface

public module subroutine compute_rotation_matrices(this, euler_angles, r_x, r_y, r_z, r, matrix, inv_r_x, inv_r_y, inv_r_z, inv_r, inv_matrix) Implementation →

Arguments

Source Code

public module function apply_as_congruence_to_symrank2_tensor(this, t) result(transformed_t)

public module function apply_as_congruence_to_tensor(this, t) result(transformed_t)

public module function apply_as_similarity_to_symrank2_tensor(this, t) result(transformed_t)

public module function apply_as_similarity_to_tensor(this, t) result(transformed_t)

public module function apply_to_vector(this, u) result(transformed_u)

public module subroutine compute_rotation_matrices(this, euler_angles, r_x, r_y, r_z, r, matrix, inv_r_x, inv_r_y, inv_r_z, inv_r, inv_matrix)