223031012
/
DAMASK_EICMD
mirror of https://github.com/achalhp/DAMASK_EICMD.git
1
0
Fork 0
Code Issues Projects Releases Wiki Activity

fixed random Gaussian sampling 

sampling needs to be performed from unfiform misorientation, NOT uniformly distributed rotations
for Fiber, compute uniform tilt of Fiber axis
This commit is contained in:
Martin Diehl 2018-03-09 16:46:16 +01:00
parent 8fa8427c99
commit 44e5644e78
1 changed files with 52 additions and 59 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

111
src/math.f90
View File

@ -1765,14 +1765,8 @@ end function math_sampleRandomOri
!--------------------------------------------------------------------------------------------------
!> @brief draw a sample from an Gaussian distribution around given orientation and Full Width
! at Half Maximum (FWHM)
!> @details: for very small FWHM values the given orientation is returned.
!> @details: for intermediate FWHM values, an orientation is picked from uniformly distributed
!> @details: oreintations around the nominal orientation with maximum misorientation of 2*FWHM
!> @deatils: according to https://math.stackexchange.com/questions/13133 followed by
!> @details: the application of a Gaussian filter.
!> @details: for large FWHM values, a random orientation from a uniform distribution is picked
!> @details: followed by tge aookucatuib if a Gaussian filter. Additionally, the misorientation is
!> @details: limited to 2*FWHM,
!> @details: A uniform misorientation (limited to 2*FWHM) is sampled followed by convolution with
! a Gausian distribution
!--------------------------------------------------------------------------------------------------
function math_sampleGaussOri(center,FWHM)
@ -1781,35 +1775,25 @@ function math_sampleGaussOri(center,FWHM)
real(pReal), dimension(3), intent(in) :: center
real(pReal) :: angle
real(pReal), dimension(3) :: math_sampleGaussOri, axis
real(pReal), dimension(2) :: rnd
real(pReal), dimension(4) :: rnd
real(pReal), dimension(3,3) :: R
noScatter: if (FWHM < 0.1_pReal*INRAD) then
math_sampleGaussOri = center
else noScatter
if (FWHM < 0.1_pReal*INRAD) then
R = math_I3
else
GaussConvolution: do
selectiveSampling: if (FWHM*INRAD < 90.0_pReal) then
rnd = halton([3_pInt,6_pInt])
axis(1) = rnd(1)*2.0_pReal-1.0_pReal ! uniform on [-1,1]
axis(2:3) = [sqrt(1.0-axis(1)**2.0_pReal)*cos(rnd(2)*2.0*PI),&
sqrt(1.0-axis(1)**2.0_pReal)*sin(rnd(2)*2.0*PI)] ! random axis
do
rnd = halton([14_pInt,10_pInt])
angle = (rnd(1)*(2.0_pReal*FWHM)**3.0_pReal)**(1.0_pReal/3.0_pReal) ! maximum misorientation of 2*FWHM
if (rnd(2) < sin(angle)**2.0_pReal/angle**2.0_pReal) exit ! rejection sampling
enddo
R = math_axisAngleToR(axis,angle)
else selectiveSampling
R = math_EulerToR(math_sampleRandomOri())
endif selectiveSampling
rnd = halton([8_pInt,11_pInt])
angle = math_EulerMisorientation([0.0_pReal,0.0_pReal,0.0_pReal],math_RtoEuler(R))
if (rnd(1) <= exp(-4.0_pReal*log(2.0_pReal)*(angle/FWHM)**2_pReal) .and. & ! rejection sampling (Gaussian)
angle < 2.0_pReal * FWHM) exit ! limit (in case of non-selective orientation selection
rnd = halton([8_pInt,3_pInt,6_pInt,11_pInt])
axis(1) = rnd(1)*2.0_pReal-1.0_pReal ! uniform on [-1,1]
axis(2:3) = [sqrt(1.0-axis(1)**2.0_pReal)*cos(rnd(2)*2.0*PI),&
sqrt(1.0-axis(1)**2.0_pReal)*sin(rnd(2)*2.0*PI)] ! random axis
angle = (rnd(3)-0.5_pReal)*4.0_pReal*FWHM ! rotation by [0, +-2 FWHM]
R = math_axisAngleToR(axis,angle)
angle = math_EulerMisorientation([0.0_pReal,0.0_pReal,0.0_pReal],math_RtoEuler(R))
if (rnd(4) <= exp(-4.0_pReal*log(2.0_pReal)*(angle/FWHM)**2_pReal)) exit ! rejection sampling (Gaussian)
enddo GaussConvolution
endif
math_sampleGaussOri = math_RtoEuler(math_mul33x33(R,math_EulerToR(center)))
endif noScatter
math_sampleGaussOri = math_RtoEuler(math_mul33x33(R,math_EulerToR(center)))
end function math_sampleGaussOri
@ -1817,8 +1801,6 @@ end function math_sampleGaussOri
!--------------------------------------------------------------------------------------------------
!> @brief draw a sample from an Gaussian distribution around given fiber texture and Full Width
! at Half Maximum (FWHM)
!>@details: vector in cone around axis is uniformly distributed according to
! https://math.stackexchange.com/questions/56784
!-------------------------------------------------------------------------------------------------
function math_sampleFiberOri(alpha,beta,FWHM)
@ -1828,38 +1810,49 @@ function math_sampleFiberOri(alpha,beta,FWHM)
real(pReal), dimension(3) :: math_sampleFiberOri, &
fInC,& !< fiber axis in crystal coordinate system
fInS,& !< fiber axis in sample coordinate system
axis
real(pReal), dimension(5) :: rnd
real(pReal), dimension(3,3) :: &
R_o, & !< rotation to aling fiber axis in crystal and sample system
R_f, & !< random rotation along fiber axis [0, 2*Pi[
R_p !< deviation of axis alingment, bound by 2*FWHM
real(pReal) :: angle
u
real(pReal), dimension(3) :: rnd
real(pReal), dimension(:),allocatable :: a !< 2D vector to tilt
integer(pInt), dimension(:),allocatable :: idx !< components of 2D vector
real(pReal), dimension(3,3) :: R !< Rotation matrix (composed of three components)
real(pReal):: angle,c
integer(pInt):: j,& !< index of smallest component
i
fInC = [sin(alpha(1))*cos(alpha(2)), sin(alpha(1))*sin(alpha(2)), cos(alpha(1))]
fInS = [sin(beta(1))*cos(beta(2)), sin(beta(1))*sin(beta(2)), cos(beta(1))]
R_o = math_EulerAxisAngleToR(math_crossproduct(fInC,fInS),-acos(dot_product(fInC,fInS)))
R = math_EulerAxisAngleToR(math_crossproduct(fInC,fInS),-acos(dot_product(fInC,fInS))) !< rotation to align fiber axis in crystal and sample system
if (FWHM > 0.0_pReal) then
rnd = halton([7_pInt,10_pInt,3_pInt])
R = math_mul33x33(R,math_EulerAxisAngleToR(fInS,rnd(1)*2.0_pReal*PI)) !< additional rotation (0..360deg) perpendicular to fiber axis
if (FWHM > 0.1_pReal*INRAD) then
reducedTo2D: do i=1_pInt,3_pInt
if (i /= minloc(abs(fInS),1)) then
a=[a,fInS(i)]
idx=[b,i]
else
j = i
endif
enddo reducedTo2D
GaussConvolution: do
rnd = halton(int([5,10,3,9,17],pInt))
rnd(1:2) = [cos(FWHM*2.0_pReal),-1.0_pReal] + rnd(1:2)*[1.0_pReal - cos(FWHM*2.0_pReal),2.0_pReal]
axis = [sqrt(1.0_pReal - rnd(2)**2.0_pReal)*sin(rnd(1)),&
sqrt(1.0_pReal - rnd(2)**2.0_pReal)*cos(rnd(1)),rnd(2)]
angle = acos(dot_product([0.0_pReal,0.0_pReal,1.0_pReal],axis))
if (rnd(3) <= exp(-4.0_pReal*log(2.0_pReal)*(angle/FWHM)**2.0_pReal)) exit
enddo GaussConvolution
if (rnd(4) <= 0.5) angle = -angle
R_p = math_EulerAxisAngleToR(math_crossproduct(axis,[0.0_pReal,0.0_pReal,1.0_pReal]),angle)
else
R_p = math_I3
rnd = halton(int([5,10,3,9,17],pInt))
endif
R_f = math_EulerAxisAngleToR(fInS,rnd(5)*2.0_pReal*PI)
angle = (rnd(2)-0.5_pReal)*4.0_pReal*FWHM ! rotation by [0, +-2 FWHM]
! solve cos(angle) = dot_product(fInS,u) under the assumption that their smallest component is the same
c = cos(angle)-fInS(j)**2
u(idx(2)) = -(2.0_pReal*c*a(2) + sqrt(4*((c*a(2))**2-sum(a**2)*(c**2-a(1)**2*(1-fInS(j)**2)))))/&
(2*sum(a**2))
u(idx(1)) = sqrt(1-u(idx(2))**2-fInS(j)**2)
u(j) = fInS(j)
math_sampleFiberOri = math_RtoEuler(math_mul33x33(R_p,math_mul33x33(R_f,R_o)))
rejectionSampling: if (rnd(3) <= exp(-4.0_pReal*log(2.0_pReal)*(angle/FWHM)**2_pReal)) then
R = math_mul33x33(R,math_EulerAxisAngleToR(math_crossproduct(u,fInS),angle)) ! tilt around direction of smallest component
exit
endif rejectionSampling
rnd = halton([7_pInt,10_pInt,3_pInt])
enddo GaussConvolution
endif
math_sampleFiberOri = math_RtoEuler(R)
end function math_sampleFiberOri