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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
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src/math.f90
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@ -1765,14 +1765,8 @@ end function math_sampleRandomOri
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief draw a sample from an Gaussian distribution around given orientation and Full Width !> @brief draw a sample from an Gaussian distribution around given orientation and Full Width
! at Half Maximum (FWHM) ! at Half Maximum (FWHM)
!> @details: for very small FWHM values the given orientation is returned. !> @details: A uniform misorientation (limited to 2*FWHM) is sampled followed by convolution with
!> @details: for intermediate FWHM values, an orientation is picked from uniformly distributed ! a Gausian distribution
!> @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,
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
function math_sampleGaussOri(center,FWHM) function math_sampleGaussOri(center,FWHM)
@ -1781,35 +1775,25 @@ function math_sampleGaussOri(center,FWHM)
real(pReal), dimension(3), intent(in) :: center real(pReal), dimension(3), intent(in) :: center
real(pReal) :: angle real(pReal) :: angle
real(pReal), dimension(3) :: math_sampleGaussOri, axis real(pReal), dimension(3) :: math_sampleGaussOri, axis
real(pReal), dimension(2) :: rnd real(pReal), dimension(4) :: rnd
real(pReal), dimension(3,3) :: R real(pReal), dimension(3,3) :: R
noScatter: if (FWHM < 0.1_pReal*INRAD) then if (FWHM < 0.1_pReal*INRAD) then
math_sampleGaussOri = center R = math_I3
else noScatter else
GaussConvolution: do GaussConvolution: do
selectiveSampling: if (FWHM*INRAD < 90.0_pReal) then rnd = halton([8_pInt,3_pInt,6_pInt,11_pInt])
rnd = halton([3_pInt,6_pInt])
axis(1) = rnd(1)*2.0_pReal-1.0_pReal ! uniform on [-1,1] 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),& 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 sqrt(1.0-axis(1)**2.0_pReal)*sin(rnd(2)*2.0*PI)] ! random axis
do angle = (rnd(3)-0.5_pReal)*4.0_pReal*FWHM ! rotation by [0, +-2 FWHM]
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) 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)) 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) if (rnd(4) <= exp(-4.0_pReal*log(2.0_pReal)*(angle/FWHM)**2_pReal)) exit ! rejection sampling (Gaussian)
angle < 2.0_pReal * FWHM) exit ! limit (in case of non-selective orientation selection
enddo GaussConvolution enddo GaussConvolution
endif
math_sampleGaussOri = math_RtoEuler(math_mul33x33(R,math_EulerToR(center))) math_sampleGaussOri = math_RtoEuler(math_mul33x33(R,math_EulerToR(center)))
endif noScatter
end function math_sampleGaussOri 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 !> @brief draw a sample from an Gaussian distribution around given fiber texture and Full Width
! at Half Maximum (FWHM) ! 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) function math_sampleFiberOri(alpha,beta,FWHM)
@ -1828,38 +1810,49 @@ function math_sampleFiberOri(alpha,beta,FWHM)
real(pReal), dimension(3) :: math_sampleFiberOri, & real(pReal), dimension(3) :: math_sampleFiberOri, &
fInC,& !< fiber axis in crystal coordinate system fInC,& !< fiber axis in crystal coordinate system
fInS,& !< fiber axis in sample coordinate system fInS,& !< fiber axis in sample coordinate system
axis u
real(pReal), dimension(5) :: rnd real(pReal), dimension(3) :: rnd
real(pReal), dimension(3,3) :: & real(pReal), dimension(:),allocatable :: a !< 2D vector to tilt
R_o, & !< rotation to aling fiber axis in crystal and sample system integer(pInt), dimension(:),allocatable :: idx !< components of 2D vector
R_f, & !< random rotation along fiber axis [0, 2*Pi[ real(pReal), dimension(3,3) :: R !< Rotation matrix (composed of three components)
R_p !< deviation of axis alingment, bound by 2*FWHM real(pReal):: angle,c
real(pReal) :: angle integer(pInt):: j,& !< index of smallest component
i
fInC = [sin(alpha(1))*cos(alpha(2)), sin(alpha(1))*sin(alpha(2)), cos(alpha(1))] 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))] 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])
GaussConvolution: do R = math_mul33x33(R,math_EulerAxisAngleToR(fInS,rnd(1)*2.0_pReal*PI)) !< additional rotation (0..360deg) perpendicular to fiber axis
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] if (FWHM > 0.1_pReal*INRAD) then
axis = [sqrt(1.0_pReal - rnd(2)**2.0_pReal)*sin(rnd(1)),& reducedTo2D: do i=1_pInt,3_pInt
sqrt(1.0_pReal - rnd(2)**2.0_pReal)*cos(rnd(1)),rnd(2)] if (i /= minloc(abs(fInS),1)) then
angle = acos(dot_product([0.0_pReal,0.0_pReal,1.0_pReal],axis)) a=[a,fInS(i)]
if (rnd(3) <= exp(-4.0_pReal*log(2.0_pReal)*(angle/FWHM)**2.0_pReal)) exit idx=[b,i]
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 else
R_p = math_I3 j = i
rnd = halton(int([5,10,3,9,17],pInt))
endif endif
enddo reducedTo2D
GaussConvolution: do
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)
R_f = math_EulerAxisAngleToR(fInS,rnd(5)*2.0_pReal*PI) 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
math_sampleFiberOri = math_RtoEuler(math_mul33x33(R_p,math_mul33x33(R_f,R_o))) exit
endif rejectionSampling
rnd = halton([7_pInt,10_pInt,3_pInt])
enddo GaussConvolution
endif
math_sampleFiberOri = math_RtoEuler(R)
end function math_sampleFiberOri end function math_sampleFiberOri