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moved quaternion disorientation to lattice because it requires the knowledge of the lattice structure.

This commit is contained in:
Martin Diehl 2014-02-28 13:28:27 +00:00
parent 92bf1565fc
commit a0d75ee05e
4 changed files with 219 additions and 174 deletions
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8
code/constitutive_nonlocal.f90
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@ -2887,8 +2887,7 @@ end function constitutive_nonlocal_dotState
subroutine constitutive_nonlocal_updateCompatibility(orientation,i,e) subroutine constitutive_nonlocal_updateCompatibility(orientation,i,e)
use math, only: math_mul3x3, & use math, only: math_mul3x3, &
math_qRot, & math_qRot
math_qDisorientation
use material, only: material_phase, & use material, only: material_phase, &
material_texture, & material_texture, &
phase_localPlasticity, & phase_localPlasticity, &
@ -2902,7 +2901,8 @@ use mesh, only: mesh_element, &
FE_geomtype, & FE_geomtype, &
FE_celltype FE_celltype
use lattice, only: lattice_sn, & use lattice, only: lattice_sn, &
lattice_sd lattice_sd, &
lattice_qDisorientation
implicit none implicit none
@ -3017,7 +3017,7 @@ do n = 1_pInt,Nneighbors
!* Finally the smallest my_compatibility value is decreased until the sum is exactly equal to one. !* Finally the smallest my_compatibility value is decreased until the sum is exactly equal to one.
!* All values below the threshold are set to zero. !* All values below the threshold are set to zero.
else else
absoluteMisorientation = math_qDisorientation(orientation(1:4,1,i,e), & absoluteMisorientation = lattice_qDisorientation(orientation(1:4,1,i,e), &
orientation(1:4,1,neighbor_i,neighbor_e), & orientation(1:4,1,neighbor_i,neighbor_e), &
0_pInt) ! no symmetry 0_pInt) ! no symmetry
do s1 = 1_pInt,ns ! my slip systems do s1 = 1_pInt,ns ! my slip systems

8
code/crystallite.f90
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@ -3324,7 +3324,6 @@ subroutine crystallite_orientations
use math, only: & use math, only: &
math_pDecomposition, & math_pDecomposition, &
math_RtoQ, & math_RtoQ, &
math_qDisorientation, &
math_qConj math_qConj
use FEsolving, only: & use FEsolving, only: &
FEsolving_execElem, & FEsolving_execElem, &
@ -3342,10 +3341,13 @@ subroutine crystallite_orientations
FE_NipNeighbors, & FE_NipNeighbors, &
FE_geomtype, & FE_geomtype, &
FE_celltype FE_celltype
use lattice, only: &
lattice_qDisorientation
use constitutive_nonlocal, only: & use constitutive_nonlocal, only: &
constitutive_nonlocal_structure, & constitutive_nonlocal_structure, &
constitutive_nonlocal_updateCompatibility constitutive_nonlocal_updateCompatibility
implicit none implicit none
integer(pInt) & integer(pInt) &
e, & ! element index e, & ! element index
@ -3384,7 +3386,7 @@ subroutine crystallite_orientations
else else
orientation = math_RtoQ(transpose(R)) orientation = math_RtoQ(transpose(R))
endif endif
crystallite_rotation(1:4,g,i,e) = math_qDisorientation(crystallite_orientation0(1:4,g,i,e), & ! active rotation from ori0 crystallite_rotation(1:4,g,i,e) = lattice_qDisorientation(crystallite_orientation0(1:4,g,i,e), & ! active rotation from ori0
orientation, & ! to current orientation orientation, & ! to current orientation
0_pInt ) ! we don't want symmetry here 0_pInt ) ! we don't want symmetry here
crystallite_orientation(1:4,g,i,e) = orientation crystallite_orientation(1:4,g,i,e) = orientation
@ -3419,7 +3421,7 @@ subroutine crystallite_orientations
neighboringStructure = constitutive_nonlocal_structure(neighboringInstance) ! get my neighbor's crystal structure neighboringStructure = constitutive_nonlocal_structure(neighboringInstance) ! get my neighbor's crystal structure
if (myStructure == neighboringStructure) then ! if my neighbor has same crystal structure like me if (myStructure == neighboringStructure) then ! if my neighbor has same crystal structure like me
crystallite_disorientation(:,n,1,i,e) = & crystallite_disorientation(:,n,1,i,e) = &
math_qDisorientation( crystallite_orientation(1:4,1,i,e), & lattice_qDisorientation( crystallite_orientation(1:4,1,i,e), &
crystallite_orientation(1:4,1,neighboring_i,neighboring_e), & crystallite_orientation(1:4,1,neighboring_i,neighboring_e), &
crystallite_symmetryID(1,i,e)) ! calculate disorientation crystallite_symmetryID(1,i,e)) ! calculate disorientation
else ! for neighbor with different phase else ! for neighbor with different phase

195
code/lattice.f90
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@ -678,6 +678,117 @@ module lattice
lattice_structureID lattice_structureID
real(pReal), dimension(:,:,:), allocatable, public, protected :: & real(pReal), dimension(:,:,:), allocatable, public, protected :: &
lattice_Cslip_66 lattice_Cslip_66
integer(pInt), dimension(2), parameter, private :: &
lattice_NsymOperations = [24_pInt,12_pInt]
real(pReal), dimension(4,36), parameter, private :: &
lattice_symOperations = reshape([&
1.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal, & ! cubic symmetry operations
0.0_pReal, 0.0_pReal, 0.7071067811865476_pReal, 0.7071067811865476_pReal, & ! 2-fold symmetry
0.0_pReal, 0.7071067811865476_pReal, 0.0_pReal, 0.7071067811865476_pReal, &
0.0_pReal, 0.7071067811865476_pReal, 0.7071067811865476_pReal, 0.0_pReal, &
0.0_pReal, 0.0_pReal, 0.7071067811865476_pReal, -0.7071067811865476_pReal, &
0.0_pReal, -0.7071067811865476_pReal, 0.0_pReal, 0.7071067811865476_pReal, &
0.0_pReal, 0.7071067811865476_pReal, -0.7071067811865476_pReal, 0.0_pReal, &
0.5_pReal, 0.5_pReal, 0.5_pReal, 0.5_pReal, & ! 3-fold symmetry
-0.5_pReal, 0.5_pReal, 0.5_pReal, 0.5_pReal, &
0.5_pReal, -0.5_pReal, 0.5_pReal, 0.5_pReal, &
-0.5_pReal, -0.5_pReal, 0.5_pReal, 0.5_pReal, &
0.5_pReal, 0.5_pReal, -0.5_pReal, 0.5_pReal, &
-0.5_pReal, 0.5_pReal, -0.5_pReal, 0.5_pReal, &
0.5_pReal, 0.5_pReal, 0.5_pReal, -0.5_pReal, &
-0.5_pReal, 0.5_pReal, 0.5_pReal, -0.5_pReal, &
0.7071067811865476_pReal, 0.7071067811865476_pReal, 0.0_pReal, 0.0_pReal, & ! 4-fold symmetry
0.0_pReal, 1.0_pReal, 0.0_pReal, 0.0_pReal, &
-0.7071067811865476_pReal, 0.7071067811865476_pReal, 0.0_pReal, 0.0_pReal, &
0.7071067811865476_pReal, 0.0_pReal, 0.7071067811865476_pReal, 0.0_pReal, &
0.0_pReal, 0.0_pReal, 1.0_pReal, 0.0_pReal, &
-0.7071067811865476_pReal, 0.0_pReal, 0.7071067811865476_pReal, 0.0_pReal, &
0.7071067811865476_pReal, 0.0_pReal, 0.0_pReal, 0.7071067811865476_pReal, &
0.0_pReal, 0.0_pReal, 0.0_pReal, 1.0_pReal, &
-0.7071067811865476_pReal, 0.0_pReal, 0.0_pReal, 0.7071067811865476_pReal, &
1.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal, & ! hexagonal symmetry operations
0.0_pReal, 1.0_pReal, 0.0_pReal, 0.0_pReal, & ! 2-fold symmetry
0.0_pReal, 0.0_pReal, 1.0_pReal, 0.0_pReal, &
0.0_pReal, 0.5_pReal, 0.866025403784439_pReal, 0.0_pReal, &
0.0_pReal, -0.5_pReal, 0.866025403784439_pReal, 0.0_pReal, &
0.0_pReal, 0.866025403784439_pReal, 0.5_pReal, 0.0_pReal, &
0.0_pReal, -0.866025403784439_pReal, 0.5_pReal, 0.0_pReal, &
0.866025403784439_pReal, 0.0_pReal, 0.0_pReal, 0.5_pReal, & ! 6-fold symmetry
-0.866025403784439_pReal, 0.0_pReal, 0.0_pReal, 0.5_pReal, &
0.5_pReal, 0.0_pReal, 0.0_pReal, 0.866025403784439_pReal, &
-0.5_pReal, 0.0_pReal, 0.0_pReal, 0.866025403784439_pReal, &
0.0_pReal, 0.0_pReal, 0.0_pReal, 1.0_pReal &
],[4,36]) !< Symmetry operations as quaternions 24 for cubic, 12 for hexagonal = 36
! use this later on to substitute the matrix above
! if self.lattice == 'cubic':
! symQuats = [
! [ 1.0,0.0,0.0,0.0 ],
! [ 0.0,1.0,0.0,0.0 ],
! [ 0.0,0.0,1.0,0.0 ],
! [ 0.0,0.0,0.0,1.0 ],
! [ 0.0, 0.0, 0.5*math.sqrt(2), 0.5*math.sqrt(2) ],
! [ 0.0, 0.0, 0.5*math.sqrt(2),-0.5*math.sqrt(2) ],
! [ 0.0, 0.5*math.sqrt(2), 0.0, 0.5*math.sqrt(2) ],
! [ 0.0, 0.5*math.sqrt(2), 0.0,-0.5*math.sqrt(2) ],
! [ 0.0, 0.5*math.sqrt(2),-0.5*math.sqrt(2), 0.0 ],
! [ 0.0,-0.5*math.sqrt(2),-0.5*math.sqrt(2), 0.0 ],
! [ 0.5, 0.5, 0.5, 0.5 ],
! [-0.5, 0.5, 0.5, 0.5 ],
! [-0.5, 0.5, 0.5,-0.5 ],
! [-0.5, 0.5,-0.5, 0.5 ],
! [-0.5,-0.5, 0.5, 0.5 ],
! [-0.5,-0.5, 0.5,-0.5 ],
! [-0.5,-0.5,-0.5, 0.5 ],
! [-0.5, 0.5,-0.5,-0.5 ],
! [-0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ],
! [ 0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ],
! [-0.5*math.sqrt(2), 0.0, 0.5*math.sqrt(2), 0.0 ],
! [-0.5*math.sqrt(2), 0.0,-0.5*math.sqrt(2), 0.0 ],
! [-0.5*math.sqrt(2), 0.5*math.sqrt(2), 0.0, 0.0 ],
! [-0.5*math.sqrt(2),-0.5*math.sqrt(2), 0.0, 0.0 ],
! ]
! elif self.lattice == 'hexagonal':
! symQuats = [
! [ 1.0,0.0,0.0,0.0 ],
! [ 0.0,1.0,0.0,0.0 ],
! [ 0.0,0.0,1.0,0.0 ],
! [ 0.0,0.0,0.0,1.0 ],
! [-0.5*math.sqrt(3), 0.0, 0.0, 0.5 ],
! [-0.5*math.sqrt(3), 0.0, 0.0,-0.5 ],
! [ 0.0, 0.5*math.sqrt(3), 0.5, 0.0 ],
! [ 0.0,-0.5*math.sqrt(3), 0.5, 0.0 ],
! [ 0.0, 0.5,-0.5*math.sqrt(3), 0.0 ],
! [ 0.0,-0.5,-0.5*math.sqrt(3), 0.0 ],
! [ 0.5, 0.0, 0.0, 0.5*math.sqrt(3) ],
! [-0.5, 0.0, 0.0, 0.5*math.sqrt(3) ],
! ]
! elif self.lattice == 'tetragonal':
! symQuats = [
! [ 1.0,0.0,0.0,0.0 ],
! [ 0.0,1.0,0.0,0.0 ],
! [ 0.0,0.0,1.0,0.0 ],
! [ 0.0,0.0,0.0,1.0 ],
! [ 0.0, 0.5*math.sqrt(2), 0.5*math.sqrt(2), 0.0 ],
! [ 0.0,-0.5*math.sqrt(2), 0.5*math.sqrt(2), 0.0 ],
! [ 0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ],
! [-0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ],
! ]
! elif self.lattice == 'orthorhombic':
! symQuats = [
! [ 1.0,0.0,0.0,0.0 ],
! [ 0.0,1.0,0.0,0.0 ],
! [ 0.0,0.0,1.0,0.0 ],
! [ 0.0,0.0,0.0,1.0 ],
! ]
! else:
! symQuats = [
! [ 1.0,0.0,0.0,0.0 ],
! ]
character(len=*), parameter, public :: & character(len=*), parameter, public :: &
LATTICE_iso_label = 'iso', & LATTICE_iso_label = 'iso', &
LATTICE_fcc_label = 'fcc', & LATTICE_fcc_label = 'fcc', &
@ -691,6 +802,7 @@ module lattice
lattice_symmetryType, & lattice_symmetryType, &
lattice_symmetrizeC66, & lattice_symmetrizeC66, &
lattice_configNchunks, & lattice_configNchunks, &
lattice_qDisorientation, &
LATTICE_undefined_ID, & LATTICE_undefined_ID, &
LATTICE_iso_ID, & LATTICE_iso_ID, &
LATTICE_fcc_ID, & LATTICE_fcc_ID, &
@ -1184,6 +1296,89 @@ pure function lattice_symmetrizeC66(struct_ID,C66)
end function lattice_symmetrizeC66 end function lattice_symmetrizeC66
!--------------------------------------------------------------------------------------------------
!> @brief figures whether unit quat falls into stereographic standard triangle
!--------------------------------------------------------------------------------------------------
logical pure function lattice_qInSST(Q, symmetryType)
use math, only: &
math_qToRodrig
implicit none
real(pReal), dimension(4), intent(in) :: Q ! orientation
integer(pInt), intent(in) :: symmetryType ! Type of crystal symmetry; 1:cubic, 2:hexagonal
real(pReal), dimension(3) :: Rodrig ! Rodrigues vector of Q
Rodrig = math_qToRodrig(Q)
if (any(Rodrig/=Rodrig)) then
lattice_qInSST = .false.
else
select case (symmetryType)
case (1_pInt)
lattice_qInSST = Rodrig(1) > Rodrig(2) .and. &
Rodrig(2) > Rodrig(3) .and. &
Rodrig(3) > 0.0_pReal
case (2_pInt)
lattice_qInSST = Rodrig(1) > sqrt(3.0_pReal)*Rodrig(2) .and. &
Rodrig(2) > 0.0_pReal .and. &
Rodrig(3) > 0.0_pReal
case default
lattice_qInSST = .true.
end select
endif
end function lattice_qInSST
!--------------------------------------------------------------------------------------------------
!> @brief calculates the disorientation for 2 unit quaternions
!--------------------------------------------------------------------------------------------------
function lattice_qDisorientation(Q1, Q2, symmetryType)
use prec, only: &
tol_math_check
use math, only: &
math_qMul, &
math_qConj
real(pReal), dimension(4) :: lattice_qDisorientation
real(pReal), dimension(4), intent(in) :: Q1, & ! 1st orientation
Q2 ! 2nd orientation
integer(pInt), intent(in) :: symmetryType ! Type of crystal symmetry; 1:cubic, 2:hexagonal
! integer(kind(LATTICE_undefined_ID)), optional, intent(in) :: & ! if given, symmetries between the two orientation will be considered
! struct
real(pReal), dimension(4) :: dQ,dQsymA,mis
integer(pInt) :: i,j,k,s
dQ = math_qMul(math_qConj(Q1),Q2)
lattice_qDisorientation = dQ
select case (symmetryType)
case (0_pInt)
if (lattice_qDisorientation(1) < 0.0_pReal) &
lattice_qDisorientation = -lattice_qDisorientation ! keep omega within 0 to 180 deg
case (1_pInt,2_pInt)
s = sum(lattice_NsymOperations(1:symmetryType-1_pInt))
do i = 1_pInt,2_pInt
dQ = math_qConj(dQ) ! switch order of "from -- to"
do j = 1_pInt,lattice_NsymOperations(symmetryType) ! run through first crystal's symmetries
dQsymA = math_qMul(lattice_symOperations(1:4,s+j),dQ) ! apply sym
do k = 1_pInt,lattice_NsymOperations(symmetryType) ! run through 2nd crystal's symmetries
mis = math_qMul(dQsymA,lattice_symOperations(1:4,s+k)) ! apply sym
if (mis(1) < 0.0_pReal) & ! want positive angle
mis = -mis
if (mis(1)-lattice_qDisorientation(1) > -tol_math_check .and. &
lattice_qInSST(mis,symmetryType)) &
lattice_qDisorientation = mis ! found better one
enddo; enddo; enddo
end select
end function lattice_qDisorientation
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief Number of parameters to expect in material.config section !> @brief Number of parameters to expect in material.config section
! NslipFamilies ! NslipFamilies

178
code/math.f90
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@ -91,49 +91,6 @@ module math
3_pInt,3_pInt & 3_pInt,3_pInt &
],[2,9]) !< arrangement in Plain notation ],[2,9]) !< arrangement in Plain notation
integer(pInt), dimension(2), parameter, private :: &
math_NsymOperations = [24_pInt,12_pInt] !< Symmetry operations as quaternions 24 for cubic, 12 for hexagonal = 36
real(pReal), dimension(4,36), parameter, private :: &
math_symOperations = reshape([&
1.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal, & ! cubic symmetry operations
0.0_pReal, 0.0_pReal, 0.7071067811865476_pReal, 0.7071067811865476_pReal, & ! 2-fold symmetry
0.0_pReal, 0.7071067811865476_pReal, 0.0_pReal, 0.7071067811865476_pReal, &
0.0_pReal, 0.7071067811865476_pReal, 0.7071067811865476_pReal, 0.0_pReal, &
0.0_pReal, 0.0_pReal, 0.7071067811865476_pReal, -0.7071067811865476_pReal, &
0.0_pReal, -0.7071067811865476_pReal, 0.0_pReal, 0.7071067811865476_pReal, &
0.0_pReal, 0.7071067811865476_pReal, -0.7071067811865476_pReal, 0.0_pReal, &
0.5_pReal, 0.5_pReal, 0.5_pReal, 0.5_pReal, & ! 3-fold symmetry
-0.5_pReal, 0.5_pReal, 0.5_pReal, 0.5_pReal, &
0.5_pReal, -0.5_pReal, 0.5_pReal, 0.5_pReal, &
-0.5_pReal, -0.5_pReal, 0.5_pReal, 0.5_pReal, &
0.5_pReal, 0.5_pReal, -0.5_pReal, 0.5_pReal, &
-0.5_pReal, 0.5_pReal, -0.5_pReal, 0.5_pReal, &
0.5_pReal, 0.5_pReal, 0.5_pReal, -0.5_pReal, &
-0.5_pReal, 0.5_pReal, 0.5_pReal, -0.5_pReal, &
0.7071067811865476_pReal, 0.7071067811865476_pReal, 0.0_pReal, 0.0_pReal, & ! 4-fold symmetry
0.0_pReal, 1.0_pReal, 0.0_pReal, 0.0_pReal, &
-0.7071067811865476_pReal, 0.7071067811865476_pReal, 0.0_pReal, 0.0_pReal, &
0.7071067811865476_pReal, 0.0_pReal, 0.7071067811865476_pReal, 0.0_pReal, &
0.0_pReal, 0.0_pReal, 1.0_pReal, 0.0_pReal, &
-0.7071067811865476_pReal, 0.0_pReal, 0.7071067811865476_pReal, 0.0_pReal, &
0.7071067811865476_pReal, 0.0_pReal, 0.0_pReal, 0.7071067811865476_pReal, &
0.0_pReal, 0.0_pReal, 0.0_pReal, 1.0_pReal, &
-0.7071067811865476_pReal, 0.0_pReal, 0.0_pReal, 0.7071067811865476_pReal, &
1.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal, & ! hexagonal symmetry operations
0.0_pReal, 1.0_pReal, 0.0_pReal, 0.0_pReal, & ! 2-fold symmetry
0.0_pReal, 0.0_pReal, 1.0_pReal, 0.0_pReal, &
0.0_pReal, 0.5_pReal, 0.866025403784439_pReal, 0.0_pReal, &
0.0_pReal, -0.5_pReal, 0.866025403784439_pReal, 0.0_pReal, &
0.0_pReal, 0.866025403784439_pReal, 0.5_pReal, 0.0_pReal, &
0.0_pReal, -0.866025403784439_pReal, 0.5_pReal, 0.0_pReal, &
0.866025403784439_pReal, 0.0_pReal, 0.0_pReal, 0.5_pReal, & ! 6-fold symmetry
-0.866025403784439_pReal, 0.0_pReal, 0.0_pReal, 0.5_pReal, &
0.5_pReal, 0.0_pReal, 0.0_pReal, 0.866025403784439_pReal, &
-0.5_pReal, 0.0_pReal, 0.0_pReal, 0.866025403784439_pReal, &
0.0_pReal, 0.0_pReal, 0.0_pReal, 1.0_pReal &
],[4,36])
#ifdef Spectral #ifdef Spectral
include 'fftw3.f03' include 'fftw3.f03'
#endif #endif
@ -206,8 +163,6 @@ real(pReal), dimension(4,36), parameter, private :: &
math_qToAxisAngle, & math_qToAxisAngle, &
math_qToR, & math_qToR, &
math_EulerMisorientation, & math_EulerMisorientation, &
math_qInSST, &
math_qDisorientation, &
math_sampleRandomOri, & math_sampleRandomOri, &
math_sampleGaussOri, & math_sampleGaussOri, &
math_sampleFiberOri, & math_sampleFiberOri, &
@ -742,7 +697,6 @@ end function math_mul66x6
pure function math_exp33(A,n) pure function math_exp33(A,n)
implicit none implicit none
integer(pInt) :: i,order integer(pInt) :: i,order
integer(pInt), intent(in), optional :: n integer(pInt), intent(in), optional :: n
real(pReal), dimension(3,3), intent(in) :: A real(pReal), dimension(3,3), intent(in) :: A
@ -828,7 +782,6 @@ pure subroutine math_invert33(A, InvA, DetA, error)
! error = logical ! error = logical
implicit none implicit none
logical, intent(out) :: error logical, intent(out) :: error
real(pReal),dimension(3,3),intent(in) :: A real(pReal),dimension(3,3),intent(in) :: A
real(pReal),dimension(3,3),intent(out) :: InvA real(pReal),dimension(3,3),intent(out) :: InvA
@ -863,8 +816,8 @@ end subroutine math_invert33
!> @brief Inversion of symmetriced 3x3x3x3 tensor. !> @brief Inversion of symmetriced 3x3x3x3 tensor.
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
function math_invSym3333(A) function math_invSym3333(A)
use IO, only: &
use IO, only: IO_error IO_error
implicit none implicit none
real(pReal),dimension(3,3,3,3) :: math_invSym3333 real(pReal),dimension(3,3,3,3) :: math_invSym3333
@ -899,7 +852,6 @@ end function math_invSym3333
subroutine math_invert(myDim,A, InvA, error) subroutine math_invert(myDim,A, InvA, error)
implicit none implicit none
integer(pInt), intent(in) :: myDim integer(pInt), intent(in) :: myDim
real(pReal), dimension(myDim,myDim), intent(in) :: A real(pReal), dimension(myDim,myDim), intent(in) :: A
@ -934,7 +886,6 @@ end subroutine math_invert
function math_symmetric33(m) function math_symmetric33(m)
implicit none implicit none
real(pReal), dimension(3,3) :: math_symmetric33 real(pReal), dimension(3,3) :: math_symmetric33
real(pReal), dimension(3,3), intent(in) :: m real(pReal), dimension(3,3), intent(in) :: m
integer(pInt) :: i,j integer(pInt) :: i,j
@ -950,7 +901,6 @@ end function math_symmetric33
pure function math_symmetric66(m) pure function math_symmetric66(m)
implicit none implicit none
integer(pInt) :: i,j integer(pInt) :: i,j
real(pReal), dimension(6,6), intent(in) :: m real(pReal), dimension(6,6), intent(in) :: m
real(pReal), dimension(6,6) :: math_symmetric66 real(pReal), dimension(6,6) :: math_symmetric66
@ -966,7 +916,6 @@ end function math_symmetric66
pure function math_skew33(m) pure function math_skew33(m)
implicit none implicit none
real(pReal), dimension(3,3) :: math_skew33 real(pReal), dimension(3,3) :: math_skew33
real(pReal), dimension(3,3), intent(in) :: m real(pReal), dimension(3,3), intent(in) :: m
integer(pInt) :: i,j integer(pInt) :: i,j
@ -982,7 +931,6 @@ end function math_skew33
pure function math_deviatoric33(m) pure function math_deviatoric33(m)
implicit none implicit none
real(pReal), dimension(3,3) :: math_deviatoric33 real(pReal), dimension(3,3) :: math_deviatoric33
real(pReal), dimension(3,3), intent(in) :: m real(pReal), dimension(3,3), intent(in) :: m
integer(pInt) :: i integer(pInt) :: i
@ -1125,7 +1073,6 @@ end function math_Mandel33to6
pure function math_Mandel6to33(v6) pure function math_Mandel6to33(v6)
implicit none implicit none
real(pReal), dimension(6), intent(in) :: v6 real(pReal), dimension(6), intent(in) :: v6
real(pReal), dimension(3,3) :: math_Mandel6to33 real(pReal), dimension(3,3) :: math_Mandel6to33
integer(pInt) :: i integer(pInt) :: i
@ -1144,7 +1091,6 @@ end function math_Mandel6to33
pure function math_Plain3333to99(m3333) pure function math_Plain3333to99(m3333)
implicit none implicit none
real(pReal), dimension(3,3,3,3), intent(in) :: m3333 real(pReal), dimension(3,3,3,3), intent(in) :: m3333
real(pReal), dimension(9,9) :: math_Plain3333to99 real(pReal), dimension(9,9) :: math_Plain3333to99
integer(pInt) :: i,j integer(pInt) :: i,j
@ -1160,7 +1106,6 @@ end function math_Plain3333to99
pure function math_Plain99to3333(m99) pure function math_Plain99to3333(m99)
implicit none implicit none
real(pReal), dimension(9,9), intent(in) :: m99 real(pReal), dimension(9,9), intent(in) :: m99
real(pReal), dimension(3,3,3,3) :: math_Plain99to3333 real(pReal), dimension(3,3,3,3) :: math_Plain99to3333
integer(pInt) :: i,j integer(pInt) :: i,j
@ -1177,7 +1122,6 @@ end function math_Plain99to3333
pure function math_Mandel66toPlain66(m66) pure function math_Mandel66toPlain66(m66)
implicit none implicit none
real(pReal), dimension(6,6), intent(in) :: m66 real(pReal), dimension(6,6), intent(in) :: m66
real(pReal), dimension(6,6) :: math_Mandel66toPlain66 real(pReal), dimension(6,6) :: math_Mandel66toPlain66
integer(pInt) :: i,j integer(pInt) :: i,j
@ -1194,7 +1138,6 @@ end function math_Mandel66toPlain66
pure function math_Plain66toMandel66(m66) pure function math_Plain66toMandel66(m66)
implicit none implicit none
real(pReal), dimension(6,6), intent(in) :: m66 real(pReal), dimension(6,6), intent(in) :: m66
real(pReal), dimension(6,6) :: math_Plain66toMandel66 real(pReal), dimension(6,6) :: math_Plain66toMandel66
integer(pInt) i,j integer(pInt) i,j
@ -1402,7 +1345,6 @@ end function math_qRot
pure function math_RtoEuler(R) pure function math_RtoEuler(R)
implicit none implicit none
real(pReal), dimension (3,3), intent(in) :: R real(pReal), dimension (3,3), intent(in) :: R
real(pReal), dimension(3) :: math_RtoEuler real(pReal), dimension(3) :: math_RtoEuler
real(pReal) :: sqhkl, squvw, sqhk, myVal real(pReal) :: sqhkl, squvw, sqhk, myVal
@ -1455,7 +1397,6 @@ end function math_RtoEuler
pure function math_RtoQ(R) pure function math_RtoQ(R)
implicit none implicit none
real(pReal), dimension(3,3), intent(in) :: R real(pReal), dimension(3,3), intent(in) :: R
real(pReal), dimension(4) :: absQ, math_RtoQ real(pReal), dimension(4) :: absQ, math_RtoQ
real(pReal) :: max_absQ real(pReal) :: max_absQ
@ -1513,7 +1454,6 @@ end function math_RtoQ
pure function math_EulerToR(Euler) pure function math_EulerToR(Euler)
implicit none implicit none
real(pReal), dimension(3), intent(in) :: Euler real(pReal), dimension(3), intent(in) :: Euler
real(pReal), dimension(3,3) :: math_EulerToR real(pReal), dimension(3,3) :: math_EulerToR
real(pReal) c1, c, c2, s1, s, s2 real(pReal) c1, c, c2, s1, s, s2
@ -1550,7 +1490,6 @@ end function math_EulerToR
pure function math_EulerToQ(eulerangles) pure function math_EulerToQ(eulerangles)
implicit none implicit none
real(pReal), dimension(3), intent(in) :: eulerangles real(pReal), dimension(3), intent(in) :: eulerangles
real(pReal), dimension(4) :: math_EulerToQ real(pReal), dimension(4) :: math_EulerToQ
real(pReal), dimension(3) :: halfangles real(pReal), dimension(3) :: halfangles
@ -1685,7 +1624,6 @@ end function math_axisAngleToQ
pure function math_qToR(q) pure function math_qToR(q)
implicit none implicit none
real(pReal), dimension(4), intent(in) :: q real(pReal), dimension(4), intent(in) :: q
real(pReal), dimension(3,3) :: math_qToR, T,S real(pReal), dimension(3,3) :: math_qToR, T,S
integer(pInt) :: i, j integer(pInt) :: i, j
@ -1712,7 +1650,6 @@ end function math_qToR
pure function math_qToEuler(qPassive) pure function math_qToEuler(qPassive)
implicit none implicit none
real(pReal), dimension(4), intent(in) :: qPassive real(pReal), dimension(4), intent(in) :: qPassive
real(pReal), dimension(4) :: q real(pReal), dimension(4) :: q
real(pReal), dimension(3) :: math_qToEuler real(pReal), dimension(3) :: math_qToEuler
@ -1753,7 +1690,6 @@ end function math_qToEuler
pure function math_qToAxisAngle(Q) pure function math_qToAxisAngle(Q)
implicit none implicit none
real(pReal), dimension(4), intent(in) :: Q real(pReal), dimension(4), intent(in) :: Q
real(pReal) :: halfAngle, sinHalfAngle real(pReal) :: halfAngle, sinHalfAngle
real(pReal), dimension(4) :: math_qToAxisAngle real(pReal), dimension(4) :: math_qToAxisAngle
@ -1779,7 +1715,6 @@ end function math_qToAxisAngle
pure function math_qToEulerAxisAngle(qPassive) pure function math_qToEulerAxisAngle(qPassive)
implicit none implicit none
real(pReal), dimension(4), intent(in) :: qPassive real(pReal), dimension(4), intent(in) :: qPassive
real(pReal), dimension(4) :: q real(pReal), dimension(4) :: q
real(pReal), dimension(4) :: math_qToEulerAxisAngle real(pReal), dimension(4) :: math_qToEulerAxisAngle
@ -1794,10 +1729,10 @@ end function math_qToEulerAxisAngle
!> @brief Rodrigues vector (x, y, z) from unit quaternion (w+ix+jy+kz) !> @brief Rodrigues vector (x, y, z) from unit quaternion (w+ix+jy+kz)
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
pure function math_qToRodrig(Q) pure function math_qToRodrig(Q)
use prec, only: &
DAMASK_NaN
use prec, only: DAMASK_NaN
implicit none implicit none
real(pReal), dimension(4), intent(in) :: Q real(pReal), dimension(4), intent(in) :: Q
real(pReal), dimension(3) :: math_qToRodrig real(pReal), dimension(3) :: math_qToRodrig
@ -1828,94 +1763,12 @@ real(pReal) pure function math_EulerMisorientation(EulerA,EulerB)
end function math_EulerMisorientation end function math_EulerMisorientation
!--------------------------------------------------------------------------------------------------
!> @brief figures whether unit quat falls into stereographic standard triangle
!--------------------------------------------------------------------------------------------------
logical pure function math_qInSST(Q, symmetryType)
implicit none
real(pReal), dimension(4), intent(in) :: Q ! orientation
integer(pInt), intent(in) :: symmetryType ! Type of crystal symmetry; 1:cubic, 2:hexagonal
real(pReal), dimension(3) :: Rodrig ! Rodrigues vector of Q
Rodrig = math_qToRodrig(Q)
if (any(Rodrig/=Rodrig)) then
math_qInSST = .false.
else
select case (symmetryType)
case (1_pInt)
math_qInSST = Rodrig(1) > Rodrig(2) .and. &
Rodrig(2) > Rodrig(3) .and. &
Rodrig(3) > 0.0_pReal
case (2_pInt)
math_qInSST = Rodrig(1) > sqrt(3.0_pReal)*Rodrig(2) .and. &
Rodrig(2) > 0.0_pReal .and. &
Rodrig(3) > 0.0_pReal
case default
math_qInSST = .true.
end select
endif
end function math_qInSST
!--------------------------------------------------------------------------------------------------
!> @brief calculates the disorientation for 2 unit quaternions
!--------------------------------------------------------------------------------------------------
function math_qDisorientation(Q1, Q2, symmetryType)
use IO, only: IO_error
implicit none
!*** input variables
real(pReal), dimension(4), intent(in) :: Q1, & ! 1st orientation
Q2 ! 2nd orientation
integer(pInt), intent(in) :: symmetryType ! Type of crystal symmetry; 1:cubic, 2:hexagonal
!*** output variables
real(pReal), dimension(4) :: math_qDisorientation ! disorientation
!*** local variables
real(pReal), dimension(4) :: dQ,dQsymA,mis
integer(pInt) :: i,j,k,s
dQ = math_qMul(math_qConj(Q1),Q2)
math_qDisorientation = dQ
select case (symmetryType)
case (0_pInt)
if (math_qDisorientation(1) < 0.0_pReal) &
math_qDisorientation = -math_qDisorientation ! keep omega within 0 to 180 deg
case (1_pInt,2_pInt)
s = sum(math_NsymOperations(1:symmetryType-1_pInt))
do i = 1_pInt,2_pInt
dQ = math_qConj(dQ) ! switch order of "from -- to"
do j = 1_pInt,math_NsymOperations(symmetryType) ! run through first crystal's symmetries
dQsymA = math_qMul(math_symOperations(1:4,s+j),dQ) ! apply sym
do k = 1_pInt,math_NsymOperations(symmetryType) ! run through 2nd crystal's symmetries
mis = math_qMul(dQsymA,math_symOperations(1:4,s+k)) ! apply sym
if (mis(1) < 0.0_pReal) & ! want positive angle
mis = -mis
if (mis(1)-math_qDisorientation(1) > -1e-8_pReal .and. &
math_qInSST(mis,symmetryType)) &
math_qDisorientation = mis ! found better one
enddo; enddo; enddo
case default
call IO_error(450_pInt,symmetryType) ! complain about unknown symmetry
end select
end function math_qDisorientation
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief draw a random sample from Euler space !> @brief draw a random sample from Euler space
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
function math_sampleRandomOri() function math_sampleRandomOri()
implicit none implicit none
real(pReal), dimension(3) :: math_sampleRandomOri, rnd real(pReal), dimension(3) :: math_sampleRandomOri, rnd
call halton(3_pInt,rnd) call halton(3_pInt,rnd)
@ -1932,17 +1785,16 @@ end function math_sampleRandomOri
function math_sampleGaussOri(center,noise) function math_sampleGaussOri(center,noise)
implicit none implicit none
real(pReal), dimension(3) :: math_sampleGaussOri, center, disturb real(pReal), dimension(3) :: math_sampleGaussOri, center, disturb
real(pReal), dimension(3), parameter :: origin = (/0.0_pReal,0.0_pReal,0.0_pReal/) real(pReal), dimension(3), parameter :: ORIGIN = [0.0_pReal,0.0_pReal,0.0_pReal]
real(pReal), dimension(5) :: rnd real(pReal), dimension(5) :: rnd
real(pReal) :: noise,scatter,cosScatter real(pReal) :: noise,scatter,cosScatter
integer(pInt) i integer(pInt) i
if (noise==0.0_pReal) then if (noise==0.0_pReal) then
math_sampleGaussOri = center math_sampleGaussOri = center
return return
endif endif
! Helming uses different distribution with Bessel functions ! Helming uses different distribution with Bessel functions
! therefore the gauss scatter width has to be scaled differently ! therefore the gauss scatter width has to be scaled differently
@ -1955,7 +1807,7 @@ endif
disturb(1) = scatter * rnd(1) ! phi1 disturb(1) = scatter * rnd(1) ! phi1
disturb(2) = sign(1.0_pReal,rnd(2))*acos(cosScatter+(1.0_pReal-cosScatter)*rnd(4)) ! Phi disturb(2) = sign(1.0_pReal,rnd(2))*acos(cosScatter+(1.0_pReal-cosScatter)*rnd(4)) ! Phi
disturb(3) = scatter * rnd(2) ! phi2 disturb(3) = scatter * rnd(2) ! phi2
if (rnd(5) <= exp(-1.0_pReal*(math_EulerMisorientation(origin,disturb)/scatter)**2_pReal)) exit if (rnd(5) <= exp(-1.0_pReal*(math_EulerMisorientation(ORIGIN,disturb)/scatter)**2_pReal)) exit
enddo enddo
math_sampleGaussOri = math_RtoEuler(math_mul33x33(math_EulerToR(disturb),math_EulerToR(center))) math_sampleGaussOri = math_RtoEuler(math_mul33x33(math_EulerToR(disturb),math_EulerToR(center)))
@ -1969,15 +1821,14 @@ end function math_sampleGaussOri
function math_sampleFiberOri(alpha,beta,noise) function math_sampleFiberOri(alpha,beta,noise)
implicit none implicit none
real(pReal), dimension(3) :: math_sampleFiberOri, fiberInC,fiberInS,axis real(pReal), dimension(3) :: math_sampleFiberOri, fiberInC,fiberInS,axis
real(pReal), dimension(2), intent(in) :: alpha,beta real(pReal), dimension(2), intent(in) :: alpha,beta
real(pReal), dimension(6) :: rnd real(pReal), dimension(6) :: rnd
real(pReal), dimension(3,3) :: oRot,fRot,pRot real(pReal), dimension(3,3) :: oRot,fRot,pRot
real(pReal) :: noise, scatter, cos2Scatter, angle real(pReal) :: noise, scatter, cos2Scatter, angle
integer(pInt), dimension(2,3), parameter :: rotMap = reshape((/2_pInt,3_pInt,& integer(pInt), dimension(2,3), parameter :: rotMap = reshape([2_pInt,3_pInt,&
3_pInt,1_pInt,& 3_pInt,1_pInt,&
1_pInt,2_pInt/),(/2,3/)) 1_pInt,2_pInt],[2,3])
integer(pInt) :: i integer(pInt) :: i
! Helming uses different distribution with Bessel functions ! Helming uses different distribution with Bessel functions
@ -2083,7 +1934,6 @@ end function math_sampleGaussVar
pure function math_symmetricEulers(sym,Euler) pure function math_symmetricEulers(sym,Euler)
implicit none implicit none
integer(pInt), intent(in) :: sym integer(pInt), intent(in) :: sym
real(pReal), dimension(3), intent(in) :: Euler real(pReal), dimension(3), intent(in) :: Euler
real(pReal), dimension(3,3) :: math_symmetricEulers real(pReal), dimension(3,3) :: math_symmetricEulers
@ -2267,7 +2117,6 @@ end subroutine math_pDecomposition
function math_eigenvalues33(M) function math_eigenvalues33(M)
implicit none implicit none
real(pReal), intent(in), dimension(3,3) :: M real(pReal), intent(in), dimension(3,3) :: M
real(pReal), dimension(3,3) :: EB1 = 0.0_pReal, EB2 = 0.0_pReal, EB3 = 0.0_pReal real(pReal), dimension(3,3) :: EB1 = 0.0_pReal, EB2 = 0.0_pReal, EB3 = 0.0_pReal
real(pReal), dimension(3) :: math_eigenvalues33 real(pReal), dimension(3) :: math_eigenvalues33
@ -2363,8 +2212,8 @@ end subroutine halton
!> @author John Burkardt !> @author John Burkardt
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
subroutine halton_memory (action_halton, name_halton, ndim, value_halton) subroutine halton_memory (action_halton, name_halton, ndim, value_halton)
implicit none
implicit none
character(len = *), intent(in) :: & character(len = *), intent(in) :: &
action_halton, & !< desired action: GET the value of a particular quantity, SET the value of a particular quantity, INC the value of a particular quantity (only for SEED) action_halton, & !< desired action: GET the value of a particular quantity, SET the value of a particular quantity, INC the value of a particular quantity (only for SEED)
name_halton !< name of the quantity: BASE: Halton base(s), NDIM: spatial dimension, SEED: current Halton seed name_halton !< name of the quantity: BASE: Halton base(s), NDIM: spatial dimension, SEED: current Halton seed
@ -2447,8 +2296,8 @@ end subroutine halton_memory
!> @author John Burkardt !> @author John Burkardt
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
subroutine halton_ndim_set (ndim) subroutine halton_ndim_set (ndim)
implicit none
implicit none
integer(pInt), intent(in) :: ndim !< dimension of the Halton vectors integer(pInt), intent(in) :: ndim !< dimension of the Halton vectors
integer(pInt) :: value_halton(1) integer(pInt) :: value_halton(1)
@ -2782,7 +2631,6 @@ end function math_rotate_forward33
pure function math_rotate_backward33(tensor,rot_tensor) pure function math_rotate_backward33(tensor,rot_tensor)
implicit none implicit none
real(pReal), dimension(3,3) :: math_rotate_backward33 real(pReal), dimension(3,3) :: math_rotate_backward33
real(pReal), dimension(3,3), intent(in) :: tensor, rot_tensor real(pReal), dimension(3,3), intent(in) :: tensor, rot_tensor
@ -2798,7 +2646,6 @@ end function math_rotate_backward33
pure function math_rotate_forward3333(tensor,rot_tensor) pure function math_rotate_forward3333(tensor,rot_tensor)
implicit none implicit none
real(pReal), dimension(3,3,3,3) :: math_rotate_forward3333 real(pReal), dimension(3,3,3,3) :: math_rotate_forward3333
real(pReal), dimension(3,3), intent(in) :: rot_tensor real(pReal), dimension(3,3), intent(in) :: rot_tensor
real(pReal), dimension(3,3,3,3), intent(in) :: tensor real(pReal), dimension(3,3,3,3), intent(in) :: tensor
@ -3393,6 +3240,7 @@ function math_periodicNearestNeighborDistances(geomdim, Favg, querySet, domainSe
use kdtree2_module use kdtree2_module
use IO, only: & use IO, only: &
IO_error IO_error
implicit none implicit none
real(pReal), dimension(3), intent(in) :: geomdim real(pReal), dimension(3), intent(in) :: geomdim
real(pReal), dimension(3,3), intent(in) :: Favg real(pReal), dimension(3,3), intent(in) :: Favg