functionality to rotate 4-tensor
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Martin Diehl
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@ -68,7 +68,7 @@ contains
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!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
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!> @brief map from 3D cubic grid to 3D ball
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!--------------------------------------------------------------------------
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function Lambert_CubeToBall(cube) result(ball)
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pure function Lambert_CubeToBall(cube) result(ball)
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real(pReal), intent(in), dimension(3) :: cube
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real(pReal), dimension(3) :: ball, LamXYZ, XYZ
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21
src/math.f90
21
src/math.f90
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@ -1428,12 +1428,12 @@ end function math_areaTriangle
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!--------------------------------------------------------------------------------------------------
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!> @brief rotate 33 tensor forward
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!--------------------------------------------------------------------------------------------------
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pure function math_rotate_forward33(tensor,rot_tensor)
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pure function math_rotate_forward33(tensor,R)
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real(pReal), dimension(3,3) :: math_rotate_forward33
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real(pReal), dimension(3,3), intent(in) :: tensor, rot_tensor
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real(pReal), dimension(3,3), intent(in) :: tensor, R
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math_rotate_forward33 = matmul(rot_tensor,matmul(tensor,transpose(rot_tensor)))
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math_rotate_forward33 = matmul(R,matmul(tensor,transpose(R)))
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end function math_rotate_forward33
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@ -1441,12 +1441,12 @@ end function math_rotate_forward33
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!--------------------------------------------------------------------------------------------------
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!> @brief rotate 33 tensor backward
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!--------------------------------------------------------------------------------------------------
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pure function math_rotate_backward33(tensor,rot_tensor)
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pure function math_rotate_backward33(tensor,R)
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real(pReal), dimension(3,3) :: math_rotate_backward33
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real(pReal), dimension(3,3), intent(in) :: tensor, rot_tensor
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real(pReal), dimension(3,3), intent(in) :: tensor, R
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math_rotate_backward33 = matmul(transpose(rot_tensor),matmul(tensor,rot_tensor))
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math_rotate_backward33 = matmul(transpose(R),matmul(tensor,R))
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end function math_rotate_backward33
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@ -1454,19 +1454,18 @@ end function math_rotate_backward33
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!--------------------------------------------------------------------------------------------------
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!> @brief rotate 3333 tensor C'_ijkl=g_im*g_jn*g_ko*g_lp*C_mnop
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!--------------------------------------------------------------------------------------------------
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pure function math_rotate_forward3333(tensor,rot_tensor)
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pure function math_rotate_forward3333(tensor,R)
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real(pReal), dimension(3,3,3,3) :: math_rotate_forward3333
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real(pReal), dimension(3,3), intent(in) :: rot_tensor
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real(pReal), dimension(3,3), intent(in) :: R
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real(pReal), dimension(3,3,3,3), intent(in) :: tensor
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integer :: i,j,k,l,m,n,o,p
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math_rotate_forward3333 = 0.0_pReal
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do i = 1,3;do j = 1,3;do k = 1,3;do l = 1,3
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do m = 1,3;do n = 1,3;do o = 1,3;do p = 1,3
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math_rotate_forward3333(i,j,k,l) &
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= math_rotate_forward3333(i,j,k,l) &
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+ rot_tensor(i,m) * rot_tensor(j,n) * rot_tensor(k,o) * rot_tensor(l,p) * tensor(m,n,o,p)
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math_rotate_forward3333(i,j,k,l) = math_rotate_forward3333(i,j,k,l) &
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+ R(i,m) * R(j,n) * R(k,o) * R(l,p) * tensor(m,n,o,p)
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enddo; enddo; enddo; enddo; enddo; enddo; enddo; enddo
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end function math_rotate_forward3333
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@ -70,9 +70,10 @@ module rotations
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!------------------------------------------
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procedure, private :: rotRot__
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generic, public :: operator(*) => rotRot__
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generic, public :: rotate => rotVector,rotTensor2,rotTensor4
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procedure, public :: rotVector
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procedure, public :: rotTensor2
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!procedure, public :: rotTensor4
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procedure, public :: rotTensor4
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procedure, public :: misorientation
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end type rotation
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@ -209,12 +210,12 @@ end subroutine fromRotationMatrix
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!> @brief: Rotate a rotation
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!> ToDo: completly untested
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!---------------------------------------------------------------------------------------------------
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function rotRot__(self,r) result(rRot)
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pure elemental function rotRot__(self,R) result(rRot)
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type(rotation) :: rRot
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class(rotation), intent(in) :: self,r
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class(rotation), intent(in) :: self,R
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rRot = rotation(self%q*r%q)
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rRot = rotation(self%q*R%q)
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end function rotRot__
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@ -223,7 +224,7 @@ end function rotRot__
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!> @author Marc De Graef, Carnegie Mellon University
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!> @brief rotate a vector passively (default) or actively
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!---------------------------------------------------------------------------------------------------
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function rotVector(self,v,active) result(vRot)
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pure function rotVector(self,v,active) result(vRot)
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real(pReal), dimension(3) :: vRot
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class(rotation), intent(in) :: self
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@ -257,14 +258,14 @@ end function rotVector
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!---------------------------------------------------------------------------------------------------
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!> @author Marc De Graef, Carnegie Mellon University
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!> @brief rotate a second rank tensor passively (default) or actively
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!> @brief rotate a rank-2 tensor passively (default) or actively
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!> @details: rotation is based on rotation matrix
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!---------------------------------------------------------------------------------------------------
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function rotTensor2(self,m,active) result(mRot)
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pure function rotTensor2(self,T,active) result(tRot)
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real(pReal), dimension(3,3) :: mRot
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real(pReal), dimension(3,3) :: tRot
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class(rotation), intent(in) :: self
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real(pReal), intent(in), dimension(3,3) :: m
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real(pReal), intent(in), dimension(3,3) :: T
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logical, intent(in), optional :: active
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logical :: passive
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@ -276,18 +277,49 @@ function rotTensor2(self,m,active) result(mRot)
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endif
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if (passive) then
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mRot = matmul(matmul(self%asRotationMatrix(),m),transpose(self%asRotationMatrix()))
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tRot = matmul(matmul(self%asRotationMatrix(),T),transpose(self%asRotationMatrix()))
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else
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mRot = matmul(matmul(transpose(self%asRotationMatrix()),m),self%asRotationMatrix())
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tRot = matmul(matmul(transpose(self%asRotationMatrix()),T),self%asRotationMatrix())
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endif
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end function rotTensor2
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!---------------------------------------------------------------------------------------------------
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!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
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!> @brief rotate a rank-4 tensor passively (default) or actively
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!> @details: rotation is based on rotation matrix
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!! ToDo: Need to check active/passive !!!
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!---------------------------------------------------------------------------------------------------
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pure function rotTensor4(self,T,active) result(tRot)
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real(pReal), dimension(3,3,3,3) :: tRot
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class(rotation), intent(in) :: self
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real(pReal), intent(in), dimension(3,3,3,3) :: T
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logical, intent(in), optional :: active
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real(pReal), dimension(3,3) :: R
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integer :: i,j,k,l,m,n,o,p
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if (present(active)) then
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R = merge(transpose(self%asRotationMatrix()),self%asRotationMatrix(),active)
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else
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R = self%asRotationMatrix()
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endif
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tRot = 0.0_pReal
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do i = 1,3;do j = 1,3;do k = 1,3;do l = 1,3
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do m = 1,3;do n = 1,3;do o = 1,3;do p = 1,3
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tRot(i,j,k,l) = tRot(i,j,k,l) &
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+ R(i,m) * R(j,n) * R(k,o) * R(l,p) * T(m,n,o,p)
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enddo; enddo; enddo; enddo; enddo; enddo; enddo; enddo
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end function rotTensor4
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!---------------------------------------------------------------------------------------------------
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!> @brief misorientation
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!---------------------------------------------------------------------------------------------------
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function misorientation(self,other)
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pure elemental function misorientation(self,other)
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type(rotation) :: misorientation
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class(rotation), intent(in) :: self, other
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@ -436,7 +468,7 @@ end function qu2ho
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!> @author Marc De Graef, Carnegie Mellon University
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!> @brief convert unit quaternion to cubochoric
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!---------------------------------------------------------------------------------------------------
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function qu2cu(qu) result(cu)
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pure function qu2cu(qu) result(cu)
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real(pReal), intent(in), dimension(4) :: qu
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real(pReal), dimension(3) :: cu
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@ -922,7 +954,7 @@ end function ro2ho
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!> @author Marc De Graef, Carnegie Mellon University
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!> @brief convert Rodrigues vector to cubochoric
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!---------------------------------------------------------------------------------------------------
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function ro2cu(ro) result(cu)
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pure function ro2cu(ro) result(cu)
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real(pReal), intent(in), dimension(4) :: ro
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real(pReal), dimension(3) :: cu
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@ -1032,7 +1064,7 @@ end function ho2ro
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!> @author Marc De Graef, Carnegie Mellon University
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!> @brief convert homochoric to cubochoric
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!---------------------------------------------------------------------------------------------------
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function ho2cu(ho) result(cu)
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pure function ho2cu(ho) result(cu)
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real(pReal), intent(in), dimension(3) :: ho
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real(pReal), dimension(3) :: cu
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@ -1046,7 +1078,7 @@ end function ho2cu
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!> @author Marc De Graef, Carnegie Mellon University
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!> @brief convert cubochoric to unit quaternion
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!---------------------------------------------------------------------------------------------------
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function cu2qu(cu) result(qu)
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pure function cu2qu(cu) result(qu)
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real(pReal), intent(in), dimension(3) :: cu
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real(pReal), dimension(4) :: qu
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@ -1060,7 +1092,7 @@ end function cu2qu
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!> @author Marc De Graef, Carnegie Mellon University
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!> @brief convert cubochoric to rotation matrix
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!---------------------------------------------------------------------------------------------------
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function cu2om(cu) result(om)
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pure function cu2om(cu) result(om)
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real(pReal), intent(in), dimension(3) :: cu
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real(pReal), dimension(3,3) :: om
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@ -1074,7 +1106,7 @@ end function cu2om
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!> @author Marc De Graef, Carnegie Mellon University
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!> @brief convert cubochoric to Euler angles
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!---------------------------------------------------------------------------------------------------
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function cu2eu(cu) result(eu)
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pure function cu2eu(cu) result(eu)
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real(pReal), intent(in), dimension(3) :: cu
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real(pReal), dimension(3) :: eu
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@ -1102,7 +1134,7 @@ end function cu2ax
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!> @author Marc De Graef, Carnegie Mellon University
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!> @brief convert cubochoric to Rodrigues vector
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!---------------------------------------------------------------------------------------------------
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function cu2ro(cu) result(ro)
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pure function cu2ro(cu) result(ro)
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real(pReal), intent(in), dimension(3) :: cu
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real(pReal), dimension(4) :: ro
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@ -1116,7 +1148,7 @@ end function cu2ro
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!> @author Marc De Graef, Carnegie Mellon University
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!> @brief convert cubochoric to homochoric
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!---------------------------------------------------------------------------------------------------
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function cu2ho(cu) result(ho)
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pure function cu2ho(cu) result(ho)
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real(pReal), intent(in), dimension(3) :: cu
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real(pReal), dimension(3) :: ho
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