Merge branch 'quaternion-code-unification' into 'development'
always using intrinsic init when assigning quaternions as output variables See merge request damask/DAMASK!116
This commit is contained in:
Martin Diehl
commit
612e8e3431
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@ -170,9 +170,18 @@ class Rotation:
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################################################################################################
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# convert to different orientation representations (numpy arrays)
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def asQuaternion(self):
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"""Unit quaternion: (q, p_1, p_2, p_3)."""
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return self.quaternion.asArray()
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def asQuaternion(self,
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quaternion = False):
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"""
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Unit quaternion [q, p_1, p_2, p_3] unless quaternion == True: damask.quaternion object.
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Parameters
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----------
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quaternion : bool, optional
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return quaternion as DAMASK object.
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"""
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return self.quaternion if quaternion else self.quaternion.asArray()
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def asEulers(self,
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degrees = False):
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@ -190,33 +199,36 @@ class Rotation:
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return eu
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def asAxisAngle(self,
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degrees = False):
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degrees = False,
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pair = False):
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"""
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Axis angle pair: ([n_1, n_2, n_3], ω).
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Axis angle representation [n_1, n_2, n_3, ω] unless pair == True: ([n_1, n_2, n_3], ω).
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Parameters
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----------
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degrees : bool, optional
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return rotation angle in degrees.
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pair : bool, optional
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return tuple of axis and angle.
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"""
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ax = qu2ax(self.quaternion.asArray())
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if degrees: ax[3] = np.degrees(ax[3])
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return ax
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return (ax[:3],np.degrees(ax[3])) if pair else ax
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def asMatrix(self):
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"""Rotation matrix."""
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return qu2om(self.quaternion.asArray())
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def asRodrigues(self,
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vector=False):
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vector = False):
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"""
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Rodrigues-Frank vector: ([n_1, n_2, n_3], tan(ω/2)).
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Rodrigues-Frank vector representation [n_1, n_2, n_3, tan(ω/2)] unless vector == True: [n_1, n_2, n_3] * tan(ω/2).
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Parameters
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----------
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vector : bool, optional
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return as array of length 3, i.e. scale the unit vector giving the rotation axis.
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return as actual Rodrigues--Frank vector, i.e. rotation axis scaled by tan(ω/2).
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"""
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ro = qu2ro(self.quaternion.asArray())
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@ -252,8 +264,8 @@ class Rotation:
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acceptHomomorph = False,
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P = -1):
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qu = quaternion if isinstance(quaternion, np.ndarray) and quaternion.dtype == np.dtype(float) \
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else np.array(quaternion,dtype=float)
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qu = quaternion if isinstance(quaternion, np.ndarray) and quaternion.dtype == np.dtype(float) \
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else np.array(quaternion,dtype=float)
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if P > 0: qu[1:4] *= -1 # convert from P=1 to P=-1
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if qu[0] < 0.0:
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if acceptHomomorph:
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@ -1193,9 +1205,9 @@ class Orientation:
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ref = orientations[0]
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for o in orientations:
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closest.append(o.equivalentOrientations(
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ref.disorientation(o,
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SST = False, # select (o[ther]'s) sym orientation
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symmetries = True)[2]).rotation) # with lowest misorientation
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ref.disorientation(o,
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SST = False, # select (o[ther]'s) sym orientation
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symmetries = True)[2]).rotation) # with lowest misorientation
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return Orientation(Rotation.fromAverage(closest,weights),ref.lattice)
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@ -1,37 +1,9 @@
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! ###################################################################
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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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!> @author Philip Eisenlohr, Michigan State University
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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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!> @details w is the real part, (x, y, z) are the imaginary parts.
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!> @details https://en.wikipedia.org/wiki/Quaternion
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!---------------------------------------------------------------------------------------------------
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module quaternions
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use prec
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@ -78,15 +50,16 @@ module quaternions
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procedure, public :: abs__
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procedure, public :: dot_product__
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procedure, public :: conjg__
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procedure, public :: exp__
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procedure, public :: log__
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procedure, public :: homomorphed => quat_homomorphed
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procedure, public :: asArray
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procedure, public :: conjg => conjg__
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procedure, public :: real => real__
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procedure, public :: aimag => aimag__
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procedure, public :: homomorphed
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procedure, public :: asArray
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procedure, public :: inverse
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end type
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interface assignment (=)
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@ -118,6 +91,14 @@ module quaternions
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module procedure log__
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end interface log
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interface real
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module procedure real__
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end interface real
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interface aimag
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module procedure aimag__
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end interface aimag
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private :: &
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unitTest
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@ -125,49 +106,46 @@ contains
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!--------------------------------------------------------------------------------------------------
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!> @brief doing self test
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!> @brief do self test
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!--------------------------------------------------------------------------------------------------
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subroutine quaternions_init
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write(6,'(/,a)') ' <<<+- quaternions init -+>>>'
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write(6,'(/,a)') ' <<<+- quaternions init -+>>>'; flush(6)
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call unitTest
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end subroutine quaternions_init
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!---------------------------------------------------------------------------------------------------
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!> constructor for a quaternion from a 4-vector
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!> construct a quaternion from a 4-vector
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!---------------------------------------------------------------------------------------------------
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type(quaternion) pure function init__(array)
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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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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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!> assign a quaternion
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!---------------------------------------------------------------------------------------------------
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elemental pure subroutine assign_quat__(self,other)
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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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self = [other%w,other%x,other%y,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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!> assign a 4-vector
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!---------------------------------------------------------------------------------------------------
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pure subroutine assign_vec__(self,other)
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@ -183,67 +161,57 @@ end subroutine assign_vec__
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!---------------------------------------------------------------------------------------------------
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!> addition of two quaternions
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!> add a quaternion
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental pure function add__(self,other)
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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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add__ = [ 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 add__
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!---------------------------------------------------------------------------------------------------
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!> unary positive operator
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!> return (unary positive operator)
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental pure function pos__(self)
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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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pos__ = self * (+1.0_pReal)
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end function pos__
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!---------------------------------------------------------------------------------------------------
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!> subtraction of two quaternions
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!> subtract a quaternion
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental pure function sub__(self,other)
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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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sub__ = [ 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 sub__
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!---------------------------------------------------------------------------------------------------
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!> unary positive operator
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!> negate (unary negative operator)
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental pure function neg__(self)
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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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neg__ = self * (-1.0_pReal)
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end function neg__
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!---------------------------------------------------------------------------------------------------
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!> multiplication of two quaternions
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!> multiply with a quaternion
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental pure function mul_quat__(self,other)
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@ -258,23 +226,20 @@ end function mul_quat__
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!---------------------------------------------------------------------------------------------------
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!> multiplication of quaternions with scalar
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!> multiply with a scalar
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!---------------------------------------------------------------------------------------------------
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type(quaternion) elemental pure function mul_scal__(self,scal)
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class(quaternion), intent(in) :: self
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real(pReal), intent(in) :: scal
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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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mul_scal__ = [self%w,self%x,self%y,self%z]*scal
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end function mul_scal__
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|
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|
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!---------------------------------------------------------------------------------------------------
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!> division of two quaternions
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!> divide by a quaternion
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!---------------------------------------------------------------------------------------------------
|
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type(quaternion) elemental pure function div_quat__(self,other)
|
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|
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|
|
@ -286,12 +251,12 @@ end function div_quat__
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|
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!---------------------------------------------------------------------------------------------------
|
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!> divisiont of quaternions by scalar
|
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!> divide by a scalar
|
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!---------------------------------------------------------------------------------------------------
|
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type(quaternion) elemental pure function div_scal__(self,scal)
|
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|
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class(quaternion), intent(in) :: self
|
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real(pReal), intent(in) :: scal
|
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real(pReal), intent(in) :: scal
|
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|
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div_scal__ = [self%w,self%x,self%y,self%z]/scal
|
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|
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|
|
@ -299,7 +264,7 @@ end function div_scal__
|
|||
|
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|
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!---------------------------------------------------------------------------------------------------
|
||||
!> equality of two quaternions
|
||||
!> test equality
|
||||
!---------------------------------------------------------------------------------------------------
|
||||
logical elemental pure function eq__(self,other)
|
||||
|
||||
|
|
@ -312,7 +277,7 @@ end function eq__
|
|||
|
||||
|
||||
!---------------------------------------------------------------------------------------------------
|
||||
!> inequality of two quaternions
|
||||
!> test inequality
|
||||
!---------------------------------------------------------------------------------------------------
|
||||
logical elemental pure function neq__(self,other)
|
||||
|
||||
|
|
@ -324,20 +289,7 @@ end function neq__
|
|||
|
||||
|
||||
!---------------------------------------------------------------------------------------------------
|
||||
!> quaternion to the power of a scalar
|
||||
!---------------------------------------------------------------------------------------------------
|
||||
type(quaternion) elemental pure function pow_scal__(self,expon)
|
||||
|
||||
class(quaternion), intent(in) :: self
|
||||
real(pReal), intent(in) :: expon
|
||||
|
||||
pow_scal__ = exp(log(self)*expon)
|
||||
|
||||
end function pow_scal__
|
||||
|
||||
|
||||
!---------------------------------------------------------------------------------------------------
|
||||
!> quaternion to the power of a quaternion
|
||||
!> raise to the power of a quaternion
|
||||
!---------------------------------------------------------------------------------------------------
|
||||
type(quaternion) elemental pure function pow_quat__(self,expon)
|
||||
|
||||
|
|
@ -350,45 +302,60 @@ end function pow_quat__
|
|||
|
||||
|
||||
!---------------------------------------------------------------------------------------------------
|
||||
!> exponential of a quaternion
|
||||
!> ToDo: Lacks any check for invalid operations
|
||||
!> raise to the power of a scalar
|
||||
!---------------------------------------------------------------------------------------------------
|
||||
type(quaternion) elemental pure function pow_scal__(self,expon)
|
||||
|
||||
class(quaternion), intent(in) :: self
|
||||
real(pReal), intent(in) :: expon
|
||||
|
||||
pow_scal__ = exp(log(self)*expon)
|
||||
|
||||
end function pow_scal__
|
||||
|
||||
|
||||
!---------------------------------------------------------------------------------------------------
|
||||
!> take exponential
|
||||
!---------------------------------------------------------------------------------------------------
|
||||
type(quaternion) elemental pure function exp__(self)
|
||||
|
||||
class(quaternion), intent(in) :: self
|
||||
real(pReal) :: absImag
|
||||
|
||||
absImag = norm2([self%x, self%y, self%z])
|
||||
absImag = norm2(aimag(self))
|
||||
|
||||
exp__ = exp(self%w) * [ cos(absImag), &
|
||||
self%x/absImag * sin(absImag), &
|
||||
self%y/absImag * sin(absImag), &
|
||||
self%z/absImag * sin(absImag)]
|
||||
exp__ = merge(exp(self%w) * [ cos(absImag), &
|
||||
self%x/absImag * sin(absImag), &
|
||||
self%y/absImag * sin(absImag), &
|
||||
self%z/absImag * sin(absImag)], &
|
||||
IEEE_value(1.0_pReal,IEEE_SIGNALING_NAN), &
|
||||
dNeq0(absImag))
|
||||
|
||||
end function exp__
|
||||
|
||||
|
||||
!---------------------------------------------------------------------------------------------------
|
||||
!> logarithm of a quaternion
|
||||
!> ToDo: Lacks any check for invalid operations
|
||||
!> take logarithm
|
||||
!---------------------------------------------------------------------------------------------------
|
||||
type(quaternion) elemental pure function log__(self)
|
||||
|
||||
class(quaternion), intent(in) :: self
|
||||
real(pReal) :: absImag
|
||||
|
||||
absImag = norm2([self%x, self%y, self%z])
|
||||
absImag = norm2(aimag(self))
|
||||
|
||||
log__ = [log(abs(self)), &
|
||||
self%x/absImag * acos(self%w/abs(self)), &
|
||||
self%y/absImag * acos(self%w/abs(self)), &
|
||||
self%z/absImag * acos(self%w/abs(self))]
|
||||
log__ = merge([log(abs(self)), &
|
||||
self%x/absImag * acos(self%w/abs(self)), &
|
||||
self%y/absImag * acos(self%w/abs(self)), &
|
||||
self%z/absImag * acos(self%w/abs(self))], &
|
||||
IEEE_value(1.0_pReal,IEEE_SIGNALING_NAN), &
|
||||
dNeq0(absImag))
|
||||
|
||||
end function log__
|
||||
|
||||
|
||||
!---------------------------------------------------------------------------------------------------
|
||||
!> norm of a quaternion
|
||||
!> return norm
|
||||
!---------------------------------------------------------------------------------------------------
|
||||
real(pReal) elemental pure function abs__(a)
|
||||
|
||||
|
|
@ -400,7 +367,7 @@ end function abs__
|
|||
|
||||
|
||||
!---------------------------------------------------------------------------------------------------
|
||||
!> dot product of two quaternions
|
||||
!> calculate dot product
|
||||
!---------------------------------------------------------------------------------------------------
|
||||
real(pReal) elemental pure function dot_product__(a,b)
|
||||
|
||||
|
|
@ -412,31 +379,31 @@ end function dot_product__
|
|||
|
||||
|
||||
!---------------------------------------------------------------------------------------------------
|
||||
!> conjugate complex of a quaternion
|
||||
!> take conjugate complex
|
||||
!---------------------------------------------------------------------------------------------------
|
||||
type(quaternion) elemental pure function conjg__(a)
|
||||
|
||||
class(quaternion), intent(in) :: a
|
||||
|
||||
conjg__ = quaternion([a%w, -a%x, -a%y, -a%z])
|
||||
conjg__ = [a%w, -a%x, -a%y, -a%z]
|
||||
|
||||
end function conjg__
|
||||
|
||||
|
||||
!---------------------------------------------------------------------------------------------------
|
||||
!> homomorphed quaternion of a quaternion
|
||||
!> homomorph
|
||||
!---------------------------------------------------------------------------------------------------
|
||||
type(quaternion) elemental pure function quat_homomorphed(self)
|
||||
type(quaternion) elemental pure function homomorphed(self)
|
||||
|
||||
class(quaternion), intent(in) :: self
|
||||
|
||||
quat_homomorphed = quaternion(-[self%w,self%x,self%y,self%z])
|
||||
homomorphed = - self
|
||||
|
||||
end function quat_homomorphed
|
||||
end function homomorphed
|
||||
|
||||
|
||||
!---------------------------------------------------------------------------------------------------
|
||||
!> quaternion as plain array
|
||||
!> return as plain array
|
||||
!---------------------------------------------------------------------------------------------------
|
||||
pure function asArray(self)
|
||||
|
||||
|
|
@ -449,7 +416,7 @@ end function asArray
|
|||
|
||||
|
||||
!---------------------------------------------------------------------------------------------------
|
||||
!> real part of a quaternion
|
||||
!> real part (scalar)
|
||||
!---------------------------------------------------------------------------------------------------
|
||||
pure function real__(self)
|
||||
|
||||
|
|
@ -462,7 +429,7 @@ end function real__
|
|||
|
||||
|
||||
!---------------------------------------------------------------------------------------------------
|
||||
!> imaginary part of a quaternion
|
||||
!> imaginary part (3-vector)
|
||||
!---------------------------------------------------------------------------------------------------
|
||||
pure function aimag__(self)
|
||||
|
||||
|
|
@ -474,45 +441,86 @@ pure function aimag__(self)
|
|||
end function aimag__
|
||||
|
||||
|
||||
!---------------------------------------------------------------------------------------------------
|
||||
!> inverse
|
||||
!---------------------------------------------------------------------------------------------------
|
||||
type(quaternion) elemental pure function inverse(self)
|
||||
|
||||
class(quaternion), intent(in) :: self
|
||||
|
||||
inverse = conjg(self)/abs(self)**2.0_pReal
|
||||
|
||||
end function inverse
|
||||
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief check correctness of (some) quaternions functions
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
subroutine unitTest
|
||||
|
||||
real(pReal), dimension(4) :: qu
|
||||
|
||||
type(quaternion) :: q, q_2
|
||||
|
||||
call random_number(qu)
|
||||
q = qu
|
||||
qu = (qu-0.5_pReal) * 2.0_pReal
|
||||
q = quaternion(qu)
|
||||
|
||||
q_2= qu
|
||||
if(any(dNeq(q%asArray(),q_2%asArray()))) call IO_error(401,ext_msg='assign_vec__')
|
||||
|
||||
q_2 = q + q
|
||||
if(any(dNeq(q_2%asArray(),2.0_pReal*qu))) call IO_error(401,ext_msg='add__')
|
||||
if(any(dNeq(q_2%asArray(),2.0_pReal*qu))) call IO_error(401,ext_msg='add__')
|
||||
|
||||
q_2 = q - q
|
||||
if(any(dNeq0(q_2%asArray()))) call IO_error(401,ext_msg='sub__')
|
||||
if(any(dNeq0(q_2%asArray()))) call IO_error(401,ext_msg='sub__')
|
||||
|
||||
q_2 = q * 5.0_preal
|
||||
if(any(dNeq(q_2%asArray(),5.0_pReal*qu))) call IO_error(401,ext_msg='mul__')
|
||||
q_2 = q * 5.0_pReal
|
||||
if(any(dNeq(q_2%asArray(),5.0_pReal*qu))) call IO_error(401,ext_msg='mul__')
|
||||
|
||||
q_2 = q / 0.5_preal
|
||||
if(any(dNeq(q_2%asArray(),2.0_pReal*qu))) call IO_error(401,ext_msg='div__')
|
||||
q_2 = q / 0.5_pReal
|
||||
if(any(dNeq(q_2%asArray(),2.0_pReal*qu))) call IO_error(401,ext_msg='div__')
|
||||
|
||||
q_2 = q * 0.3_pReal
|
||||
if(dNeq0(abs(q)) .and. q_2 == q) call IO_error(401,ext_msg='eq__')
|
||||
|
||||
q_2 = q
|
||||
if(q_2 /= q) call IO_error(401,ext_msg='eq__')
|
||||
if(q_2 /= q) call IO_error(401,ext_msg='neq__')
|
||||
|
||||
if(any(dNeq(q%asArray(),qu))) call IO_error(401,ext_msg='eq__')
|
||||
if(dNeq(q%real(), qu(1))) call IO_error(401,ext_msg='real()')
|
||||
if(any(dNeq(q%aimag(), qu(2:4)))) call IO_error(401,ext_msg='aimag()')
|
||||
if(dNeq(abs(q),norm2(qu))) call IO_error(401,ext_msg='abs__')
|
||||
if(dNeq(abs(q)**2.0_pReal, real(q*q%conjg()),1.0e-14_pReal)) &
|
||||
call IO_error(401,ext_msg='abs__/*conjg')
|
||||
|
||||
if(any(dNeq(q%asArray(),qu))) call IO_error(401,ext_msg='eq__')
|
||||
if(dNeq(q%real(), qu(1))) call IO_error(401,ext_msg='real()')
|
||||
if(any(dNeq(q%aimag(), qu(2:4)))) call IO_error(401,ext_msg='aimag()')
|
||||
|
||||
q_2 = q%homomorphed()
|
||||
if(q /= q_2* (-1.0_pReal)) call IO_error(401,ext_msg='homomorphed')
|
||||
if(dNeq(q_2%real(), qu(1)* (-1.0_pReal))) call IO_error(401,ext_msg='homomorphed/real')
|
||||
if(any(dNeq(q_2%aimag(),qu(2:4)*(-1.0_pReal)))) call IO_error(401,ext_msg='homomorphed/aimag')
|
||||
if(q /= q_2* (-1.0_pReal)) call IO_error(401,ext_msg='homomorphed')
|
||||
if(dNeq(q_2%real(), qu(1)* (-1.0_pReal))) call IO_error(401,ext_msg='homomorphed/real')
|
||||
if(any(dNeq(q_2%aimag(),qu(2:4)*(-1.0_pReal)))) call IO_error(401,ext_msg='homomorphed/aimag')
|
||||
|
||||
q_2 = conjg(q)
|
||||
if(dNeq(q_2%real(), q%real())) call IO_error(401,ext_msg='conjg/real')
|
||||
if(any(dNeq(q_2%aimag(),q%aimag()*(-1.0_pReal)))) call IO_error(401,ext_msg='conjg/aimag')
|
||||
if(dNeq(abs(q),abs(q_2))) call IO_error(401,ext_msg='conjg/abs')
|
||||
if(q /= conjg(q_2)) call IO_error(401,ext_msg='conjg/involution')
|
||||
if(dNeq(q_2%real(), q%real())) call IO_error(401,ext_msg='conjg/real')
|
||||
if(any(dNeq(q_2%aimag(),q%aimag()*(-1.0_pReal)))) call IO_error(401,ext_msg='conjg/aimag')
|
||||
|
||||
if(abs(q) > 0.0_pReal) then
|
||||
q_2 = q * q%inverse()
|
||||
if( dNeq(real(q_2), 1.0_pReal,1.0e-15_pReal)) call IO_error(401,ext_msg='inverse/real')
|
||||
if(any(dNeq0(aimag(q_2), 1.0e-15_pReal))) call IO_error(401,ext_msg='inverse/aimag')
|
||||
|
||||
q_2 = q/abs(q)
|
||||
q_2 = conjg(q_2) - inverse(q_2)
|
||||
if(any(dNeq0(q_2%asArray(),1.0e-15_pReal))) call IO_error(401,ext_msg='inverse/conjg')
|
||||
endif
|
||||
|
||||
#if !(defined(__GFORTRAN__) && __GNUC__ < 9)
|
||||
if (norm2(aimag(q)) > 0.0_pReal) then
|
||||
if (dNeq0(abs(q-exp(log(q))),1.0e-13_pReal)) call IO_error(401,ext_msg='exp/log')
|
||||
if (dNeq0(abs(q-log(exp(q))),1.0e-13_pReal)) call IO_error(401,ext_msg='log/exp')
|
||||
endif
|
||||
#endif
|
||||
|
||||
end subroutine unitTest
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue