445 lines
14 KiB
Fortran
445 lines
14 KiB
Fortran
! ###################################################################
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! Copyright (c) 2013-2015, Marc De Graef/Carnegie Mellon University
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! Modified 2017-2019, Martin Diehl/Max-Planck-Institut für Eisenforschung GmbH
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! All rights reserved.
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!
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! Redistribution and use in source and binary forms, with or without modification, are
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! permitted provided that the following conditions are met:
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!
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! - Redistributions of source code must retain the above copyright notice, this list
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! of conditions and the following disclaimer.
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! - Redistributions in binary form must reproduce the above copyright notice, this
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! list of conditions and the following disclaimer in the documentation and/or
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! other materials provided with the distribution.
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! - Neither the names of Marc De Graef, Carnegie Mellon University nor the names
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! of its contributors may be used to endorse or promote products derived from
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! this software without specific prior written permission.
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!
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! THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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! AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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! IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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! ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
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! LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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! DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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! SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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! CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
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! OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
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! USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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! ###################################################################
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!---------------------------------------------------------------------------------------------------
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!> @author Marc De Graef, Carnegie Mellon University
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!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
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!> @brief general quaternion math, not limited to unit quaternions
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!> @details w is the real part, (x, y, z) are the imaginary parts.
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!---------------------------------------------------------------------------------------------------
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module quaternions
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use prec, only: &
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pReal
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use future
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implicit none
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public
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real(pReal), parameter, public :: P = -1.0_pReal !< parameter for orientation conversion.
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type, public :: quaternion
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real(pReal) :: w = 0.0_pReal
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real(pReal) :: x = 0.0_pReal
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real(pReal) :: y = 0.0_pReal
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real(pReal) :: z = 0.0_pReal
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contains
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procedure, private :: add__
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procedure, private :: pos__
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generic, public :: operator(+) => add__,pos__
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procedure, private :: sub__
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procedure, private :: neg__
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generic, public :: operator(-) => sub__,neg__
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procedure, private :: mul_quat__
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procedure, private :: mul_scal__
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generic, public :: operator(*) => mul_quat__, mul_scal__
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procedure, private :: div_quat__
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procedure, private :: div_scal__
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generic, public :: operator(/) => div_quat__, div_scal__
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procedure, private :: eq__
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generic, public :: operator(==) => eq__
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procedure, private :: neq__
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generic, public :: operator(/=) => neq__
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procedure, private :: pow_quat__
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procedure, private :: pow_scal__
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generic, public :: operator(**) => pow_quat__, pow_scal__
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procedure, private :: abs__
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procedure, private :: dot_product__
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procedure, private :: conjg__
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procedure, private :: exp__
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procedure, private :: log__
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procedure, public :: homomorphed => quat_homomorphed
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end type
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interface assignment (=)
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module procedure assign_quat__
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module procedure assign_vec__
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end interface assignment (=)
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interface quaternion
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module procedure init__
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end interface quaternion
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interface abs
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procedure abs__
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end interface abs
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interface dot_product
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procedure dot_product__
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end interface dot_product
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interface conjg
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module procedure conjg__
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end interface conjg
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interface exp
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module procedure exp__
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end interface exp
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interface log
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module procedure log__
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end interface log
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contains
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!---------------------------------------------------------------------------------------------------
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!> constructor for a quaternion from a 4-vector
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!---------------------------------------------------------------------------------------------------
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type(quaternion) pure function init__(array)
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implicit none
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real(pReal), intent(in), dimension(4) :: array
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init__%w=array(1)
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init__%x=array(2)
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init__%y=array(3)
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init__%z=array(4)
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end function init__
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!---------------------------------------------------------------------------------------------------
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!> assing a quaternion
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!---------------------------------------------------------------------------------------------------
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elemental subroutine assign_quat__(self,other)
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implicit none
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type(quaternion), intent(out) :: self
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type(quaternion), intent(in) :: other
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self%w = other%w
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self%x = other%x
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self%y = other%y
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self%z = other%z
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end subroutine assign_quat__
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!---------------------------------------------------------------------------------------------------
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!> assing a 4-vector
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!---------------------------------------------------------------------------------------------------
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pure subroutine assign_vec__(self,other)
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implicit none
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type(quaternion), intent(out) :: self
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real(pReal), intent(in), dimension(4) :: other
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self%w = other(1)
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self%x = other(2)
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self%y = other(3)
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self%z = other(4)
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end subroutine assign_vec__
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!---------------------------------------------------------------------------------------------------
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!> addition of two quaternions
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental function add__(self,other)
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implicit none
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class(quaternion), intent(in) :: self,other
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add__%w = self%w + other%w
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add__%x = self%x + other%x
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add__%y = self%y + other%y
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add__%z = self%z + other%z
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end function add__
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!---------------------------------------------------------------------------------------------------
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!> unary positive operator
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental function pos__(self)
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implicit none
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class(quaternion), intent(in) :: self
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pos__%w = self%w
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pos__%x = self%x
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pos__%y = self%y
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pos__%z = self%z
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end function pos__
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!---------------------------------------------------------------------------------------------------
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!> subtraction of two quaternions
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental function sub__(self,other)
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implicit none
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class(quaternion), intent(in) :: self,other
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sub__%w = self%w - other%w
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sub__%x = self%x - other%x
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sub__%y = self%y - other%y
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sub__%z = self%z - other%z
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end function sub__
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!---------------------------------------------------------------------------------------------------
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!> unary positive operator
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental function neg__(self)
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implicit none
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class(quaternion), intent(in) :: self
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neg__%w = -self%w
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neg__%x = -self%x
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neg__%y = -self%y
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neg__%z = -self%z
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end function neg__
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!---------------------------------------------------------------------------------------------------
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!> multiplication of two quaternions
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental function mul_quat__(self,other)
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implicit none
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class(quaternion), intent(in) :: self, other
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mul_quat__%w = self%w*other%w - self%x*other%x - self%y*other%y - self%z*other%z
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mul_quat__%x = self%w*other%x + self%x*other%w + P * (self%y*other%z - self%z*other%y)
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mul_quat__%y = self%w*other%y + self%y*other%w + P * (self%z*other%x - self%x*other%z)
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mul_quat__%z = self%w*other%z + self%z*other%w + P * (self%x*other%y - self%y*other%x)
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end function mul_quat__
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!---------------------------------------------------------------------------------------------------
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!> multiplication of quaternions with scalar
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental function mul_scal__(self,scal)
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implicit none
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class(quaternion), intent(in) :: self
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real(pReal), intent(in) :: scal
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mul_scal__%w = self%w*scal
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mul_scal__%x = self%x*scal
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mul_scal__%y = self%y*scal
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mul_scal__%z = self%z*scal
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end function mul_scal__
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!---------------------------------------------------------------------------------------------------
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!> division of two quaternions
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental function div_quat__(self,other)
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implicit none
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class(quaternion), intent(in) :: self, other
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div_quat__ = self * (conjg(other)/(abs(other)**2.0_pReal))
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end function div_quat__
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!---------------------------------------------------------------------------------------------------
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!> divisiont of quaternions by scalar
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental function div_scal__(self,scal)
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implicit none
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class(quaternion), intent(in) :: self
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real(pReal), intent(in) :: scal
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div_scal__ = [self%w,self%x,self%y,self%z]/scal
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end function div_scal__
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!---------------------------------------------------------------------------------------------------
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!> equality of two quaternions
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!---------------------------------------------------------------------------------------------------
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logical elemental function eq__(self,other)
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use prec, only: &
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dEq
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implicit none
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class(quaternion), intent(in) :: self,other
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eq__ = all(dEq([ self%w, self%x, self%y, self%z], &
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[other%w,other%x,other%y,other%z]))
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end function eq__
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!---------------------------------------------------------------------------------------------------
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!> inequality of two quaternions
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!---------------------------------------------------------------------------------------------------
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logical elemental function neq__(self,other)
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implicit none
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class(quaternion), intent(in) :: self,other
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neq__ = .not. self%eq__(other)
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end function neq__
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!---------------------------------------------------------------------------------------------------
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!> quaternion to the power of a scalar
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental function pow_scal__(self,expon)
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implicit none
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class(quaternion), intent(in) :: self
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real(pReal), intent(in) :: expon
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pow_scal__ = exp(log(self)*expon)
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end function pow_scal__
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!---------------------------------------------------------------------------------------------------
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!> quaternion to the power of a quaternion
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental function pow_quat__(self,expon)
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implicit none
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class(quaternion), intent(in) :: self
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type(quaternion), intent(in) :: expon
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pow_quat__ = exp(log(self)*expon)
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end function pow_quat__
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!---------------------------------------------------------------------------------------------------
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!> exponential of a quaternion
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!> ToDo: Lacks any check for invalid operations
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental function exp__(self)
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implicit none
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class(quaternion), intent(in) :: self
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real(pReal) :: absImag
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absImag = norm2([self%x, self%y, self%z])
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exp__ = exp(self%w) * [ cos(absImag), &
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self%x/absImag * sin(absImag), &
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self%y/absImag * sin(absImag), &
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self%z/absImag * sin(absImag)]
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end function exp__
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!---------------------------------------------------------------------------------------------------
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!> logarithm of a quaternion
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!> ToDo: Lacks any check for invalid operations
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental function log__(self)
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implicit none
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class(quaternion), intent(in) :: self
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real(pReal) :: absImag
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absImag = norm2([self%x, self%y, self%z])
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log__ = [log(abs(self)), &
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self%x/absImag * acos(self%w/abs(self)), &
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self%y/absImag * acos(self%w/abs(self)), &
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self%z/absImag * acos(self%w/abs(self))]
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end function log__
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!---------------------------------------------------------------------------------------------------
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!> norm of a quaternion
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!---------------------------------------------------------------------------------------------------
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real(pReal) elemental function abs__(a)
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implicit none
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class(quaternion), intent(in) :: a
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abs__ = norm2([a%w,a%x,a%y,a%z])
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end function abs__
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!---------------------------------------------------------------------------------------------------
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!> dot product of two quaternions
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!---------------------------------------------------------------------------------------------------
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real(pReal) elemental function dot_product__(a,b)
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implicit none
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class(quaternion), intent(in) :: a,b
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dot_product__ = a%w*b%w + a%x*b%x + a%y*b%y + a%z*b%z
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end function dot_product__
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!---------------------------------------------------------------------------------------------------
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!> conjugate complex of a quaternion
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental function conjg__(a)
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implicit none
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class(quaternion), intent(in) :: a
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conjg__ = quaternion([a%w, -a%x, -a%y, -a%z])
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end function conjg__
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!---------------------------------------------------------------------------------------------------
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!> homomorphed quaternion of a quaternion
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental function quat_homomorphed(a)
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implicit none
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class(quaternion), intent(in) :: a
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quat_homomorphed = quaternion(-[a%w,a%x,a%y,a%z])
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end function quat_homomorphed
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end module quaternions
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