general quaternion math, not limited to unit quaternions More...

Data Types
interface	abs

interface	aimag

interface	assignment(=)

interface	conjg

interface	dot_product

interface	exp

interface	log

interface	quaternion

interface	real

Functions/Subroutines
subroutine, public	quaternions_init
	do self test More...

type(quaternion) pure function	init__ (array)
	construct a quaternion from a 4-vector More...

elemental pure subroutine	assign_quat__ (self, other)
	assign a quaternion More...

pure subroutine	assign_vec__ (self, other)
	assign a 4-vector More...

type(quaternion) elemental pure function	add__ (self, other)
	add a quaternion More...

type(quaternion) elemental pure function	pos__ (self)
	return (unary positive operator) More...

type(quaternion) elemental pure function	sub__ (self, other)
	subtract a quaternion More...

type(quaternion) elemental pure function	neg__ (self)
	negate (unary negative operator) More...

type(quaternion) elemental pure function	mul_quat__ (self, other)
	multiply with a quaternion More...

type(quaternion) elemental pure function	mul_scal__ (self, scal)
	multiply with a scalar More...

type(quaternion) elemental pure function	div_quat__ (self, other)
	divide by a quaternion More...

type(quaternion) elemental pure function	div_scal__ (self, scal)
	divide by a scalar More...

logical elemental pure function	eq__ (self, other)
	test equality More...

logical elemental pure function	neq__ (self, other)
	test inequality More...

type(quaternion) elemental pure function	pow_quat__ (self, expon)
	raise to the power of a quaternion More...

type(quaternion) elemental pure function	pow_scal__ (self, expon)
	raise to the power of a scalar More...

type(quaternion) elemental pure function	exp__ (a)
	take exponential More...

type(quaternion) elemental pure function	log__ (a)
	take logarithm More...

real(preal) elemental pure function	abs__ (self)
	return norm More...

real(preal) elemental pure function	dot_product__ (a, b)
	calculate dot product More...

type(quaternion) elemental pure function	conjg__ (self)
	take conjugate complex More...

type(quaternion) elemental pure function	homomorphed (self)
	homomorph More...

pure real(preal) function, dimension(4)	asarray (self)
	return as plain array More...

pure real(preal) function	real__ (self)
	real part (scalar) More...

pure real(preal) function, dimension(3)	aimag__ (self)
	imaginary part (3-vector) More...

type(quaternion) elemental pure function	inverse (self)
	inverse More...

subroutine	unittest
	check correctness of some quaternions functions More...

Variables
real(preal), parameter, public	p = -1.0_pReal
	parameter for orientation conversion. More...

Detailed Description

general quaternion math, not limited to unit quaternions

Author: Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH; Philip Eisenlohr, Michigan State University

w is the real part, (x, y, z) are the imaginary parts.

https://en.wikipedia.org/wiki/Quaternion

Function/Subroutine Documentation

◆ abs__()

real(preal) elemental pure function quaternions::abs__ ( class(quaternion), intent(in) self )

private

return norm

Definition at line 4180 of file DAMASK_marc.f90.

◆ add__()

type(quaternion) elemental pure function quaternions::add__	(	class(quaternion), intent(in)	self,
		class(quaternion), intent(in)	other
	)

private

add a quaternion

Definition at line 3986 of file DAMASK_marc.f90.

Referenced by quaternions::quaternion::operator().

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◆ aimag__()

pure real(preal) function, dimension(3) quaternions::aimag__ ( class(quaternion), intent(in) self )

private

imaginary part (3-vector)

Definition at line 4254 of file DAMASK_marc.f90.

◆ asarray()

pure real(preal) function, dimension(4) quaternions::asarray ( class(quaternion), intent(in) self )

private

return as plain array

Definition at line 4228 of file DAMASK_marc.f90.

◆ assign_quat__()

elemental pure subroutine quaternions::assign_quat__	(	type(quaternion), intent(out)	self,
		type(quaternion), intent(in)	other
	)

private

assign a quaternion

Definition at line 3957 of file DAMASK_marc.f90.

◆ assign_vec__()

pure subroutine quaternions::assign_vec__	(	type(quaternion), intent(out)	self,
		real(preal), dimension(4), intent(in)	other
	)

private

assign a 4-vector

Definition at line 3970 of file DAMASK_marc.f90.

◆ conjg__()

type(quaternion) elemental pure function quaternions::conjg__ ( class(quaternion), intent(in) self )

private

take conjugate complex

Definition at line 4204 of file DAMASK_marc.f90.

◆ div_quat__()

type(quaternion) elemental pure function quaternions::div_quat__	(	class(quaternion), intent(in)	self,
		class(quaternion), intent(in)	other
	)

private

divide by a quaternion

Definition at line 4064 of file DAMASK_marc.f90.

Referenced by quaternions::quaternion::operator().

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◆ div_scal__()

type(quaternion) elemental pure function quaternions::div_scal__	(	class(quaternion), intent(in)	self,
		real(preal), intent(in)	scal
	)

private

divide by a scalar

Definition at line 4076 of file DAMASK_marc.f90.

Referenced by quaternions::quaternion::operator().

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◆ dot_product__()

real(preal) elemental pure function quaternions::dot_product__	(	class(quaternion), intent(in)	a,
		class(quaternion), intent(in)	b
	)

private

calculate dot product

Definition at line 4192 of file DAMASK_marc.f90.

◆ eq__()

logical elemental pure function quaternions::eq__	(	class(quaternion), intent(in)	self,
		class(quaternion), intent(in)	other
	)

private

test equality

Definition at line 4089 of file DAMASK_marc.f90.

Referenced by quaternions::quaternion::operator().

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◆ exp__()

type(quaternion) elemental pure function quaternions::exp__ ( class(quaternion), intent(in) a )

private

take exponential

Definition at line 4140 of file DAMASK_marc.f90.

◆ homomorphed()

type(quaternion) elemental pure function quaternions::homomorphed ( class(quaternion), intent(in) self )

private

homomorph

Definition at line 4216 of file DAMASK_marc.f90.

◆ init__()

type(quaternion) pure function quaternions::init__ ( real(preal), dimension(4), intent(in) array )

private

construct a quaternion from a 4-vector

Definition at line 3942 of file DAMASK_marc.f90.

◆ inverse()

type(quaternion) elemental pure function quaternions::inverse ( class(quaternion), intent(in) self )

private

inverse

Definition at line 4267 of file DAMASK_marc.f90.

Referenced by unittest().

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◆ log__()

type(quaternion) elemental pure function quaternions::log__ ( class(quaternion), intent(in) a )

private

take logarithm

Definition at line 4160 of file DAMASK_marc.f90.

◆ mul_quat__()

type(quaternion) elemental pure function quaternions::mul_quat__	(	class(quaternion), intent(in)	self,
		class(quaternion), intent(in)	other
	)

private

multiply with a quaternion

Definition at line 4036 of file DAMASK_marc.f90.

References p.

Referenced by quaternions::quaternion::operator().

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◆ mul_scal__()

type(quaternion) elemental pure function quaternions::mul_scal__	(	class(quaternion), intent(in)	self,
		real(preal), intent(in)	scal
	)

private

multiply with a scalar

Definition at line 4051 of file DAMASK_marc.f90.

Referenced by quaternions::quaternion::operator().

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◆ neg__()

type(quaternion) elemental pure function quaternions::neg__ ( class(quaternion), intent(in) self )

private

negate (unary negative operator)

Definition at line 4024 of file DAMASK_marc.f90.

Referenced by quaternions::quaternion::operator().

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◆ neq__()

logical elemental pure function quaternions::neq__	(	class(quaternion), intent(in)	self,
		class(quaternion), intent(in)	other
	)

private

test inequality

Definition at line 4102 of file DAMASK_marc.f90.

Referenced by quaternions::quaternion::operator().

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◆ pos__()

type(quaternion) elemental pure function quaternions::pos__ ( class(quaternion), intent(in) self )

private

return (unary positive operator)

Definition at line 3999 of file DAMASK_marc.f90.

Referenced by quaternions::quaternion::operator().

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◆ pow_quat__()

type(quaternion) elemental pure function quaternions::pow_quat__	(	class(quaternion), intent(in)	self,
		type(quaternion), intent(in)	expon
	)

private

raise to the power of a quaternion

Definition at line 4114 of file DAMASK_marc.f90.

Referenced by quaternions::quaternion::operator().

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◆ pow_scal__()

type(quaternion) elemental pure function quaternions::pow_scal__	(	class(quaternion), intent(in)	self,
		real(preal), intent(in)	expon
	)

private

raise to the power of a scalar

Definition at line 4127 of file DAMASK_marc.f90.

Referenced by quaternions::quaternion::operator().

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◆ quaternions_init()

subroutine, public quaternions::quaternions_init

do self test

Definition at line 3931 of file DAMASK_marc.f90.

References prec::unittest().

Referenced by rotations::rotations_init().

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◆ real__()

pure real(preal) function quaternions::real__ ( class(quaternion), intent(in) self )

private

real part (scalar)

Definition at line 4241 of file DAMASK_marc.f90.

◆ sub__()

type(quaternion) elemental pure function quaternions::sub__	(	class(quaternion), intent(in)	self,
		class(quaternion), intent(in)	other
	)

private

subtract a quaternion

Definition at line 4011 of file DAMASK_marc.f90.

Referenced by quaternions::quaternion::operator().

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◆ unittest()

subroutine quaternions::unittest

private

check correctness of some quaternions functions

Definition at line 4279 of file DAMASK_marc.f90.

References inverse().

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Variable Documentation

◆ p

real(preal), parameter, public quaternions::p = -1.0_pReal

parameter for orientation conversion.

Definition at line 3833 of file DAMASK_marc.f90.

Referenced by rotations::ax2om(), rotations::ax2ro(), rotations::eu2ax(), rotations::eu2qu(), rotations::eu2ro(), mul_quat__(), rotations::om2ax(), rotations::qu2eu(), rotations::qu2om(), rotations::qu2ro(), and rotations::rottensor4().

Data Types

Functions/Subroutines

Variables

Detailed Description

Function/Subroutine Documentation

◆ abs__()

◆ add__()

◆ aimag__()

◆ asarray()

◆ assign_quat__()

◆ assign_vec__()

◆ conjg__()

◆ div_quat__()

◆ div_scal__()

◆ dot_product__()

◆ eq__()

◆ exp__()

◆ homomorphed()

◆ init__()

◆ inverse()

◆ log__()

◆ mul_quat__()

◆ mul_scal__()

◆ neg__()

◆ neq__()

◆ pos__()

◆ pow_quat__()

◆ pow_scal__()

◆ quaternions_init()

◆ real__()

◆ sub__()

◆ unittest()

Variable Documentation

◆ p