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DAMASK_EICMD
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no pInt

This commit is contained in:
Martin Diehl 2019-03-13 06:46:59 +01:00
parent 81cfa31b31
commit c7f33f4696
1 changed files with 183 additions and 185 deletions
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src/math.f90
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@ -7,8 +7,7 @@
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
module math module math
use prec, only: & use prec, only: &
pReal, & pReal
pInt
implicit none implicit none
private private
@ -34,37 +33,37 @@ module math
1.0_pReal, 1.0_pReal, 1.0_pReal, & 1.0_pReal, 1.0_pReal, 1.0_pReal, &
1.0_pReal/sqrt(2.0_pReal), 1.0_pReal/sqrt(2.0_pReal), 1.0_pReal/sqrt(2.0_pReal) ] !< weighting for Mandel notation (backward) 1.0_pReal/sqrt(2.0_pReal), 1.0_pReal/sqrt(2.0_pReal), 1.0_pReal/sqrt(2.0_pReal) ] !< weighting for Mandel notation (backward)
integer(pInt), dimension (2,6), parameter, private :: & integer, dimension (2,6), parameter, private :: &
mapNye = reshape([& mapNye = reshape([&
1_pInt,1_pInt, & 1,1, &
2_pInt,2_pInt, & 2,2, &
3_pInt,3_pInt, & 3,3, &
1_pInt,2_pInt, & 1,2, &
2_pInt,3_pInt, & 2,3, &
1_pInt,3_pInt & 1,3 &
],[2,6]) !< arrangement in Nye notation. ],[2,6]) !< arrangement in Nye notation.
integer(pInt), dimension (2,6), parameter, private :: & integer, dimension (2,6), parameter, private :: &
mapVoigt = reshape([& mapVoigt = reshape([&
1_pInt,1_pInt, & 1,1, &
2_pInt,2_pInt, & 2,2, &
3_pInt,3_pInt, & 3,3, &
2_pInt,3_pInt, & 2,3, &
1_pInt,3_pInt, & 1,3, &
1_pInt,2_pInt & 1,2 &
],[2,6]) !< arrangement in Voigt notation ],[2,6]) !< arrangement in Voigt notation
integer(pInt), dimension (2,9), parameter, private :: & integer, dimension (2,9), parameter, private :: &
mapPlain = reshape([& mapPlain = reshape([&
1_pInt,1_pInt, & 1,1, &
1_pInt,2_pInt, & 1,2, &
1_pInt,3_pInt, & 1,3, &
2_pInt,1_pInt, & 2,1, &
2_pInt,2_pInt, & 2,2, &
2_pInt,3_pInt, & 2,3, &
3_pInt,1_pInt, & 3,1, &
3_pInt,2_pInt, & 3,2, &
3_pInt,3_pInt & 3,3 &
],[2,9]) !< arrangement in Plain notation ],[2,9]) !< arrangement in Plain notation
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
@ -184,7 +183,7 @@ subroutine math_init
randomSeed randomSeed
implicit none implicit none
integer(pInt) :: i integer :: i
real(pReal), dimension(4) :: randTest real(pReal), dimension(4) :: randTest
integer :: randSize integer :: randSize
integer, dimension(:), allocatable :: randInit integer, dimension(:), allocatable :: randInit
@ -192,10 +191,9 @@ subroutine math_init
write(6,'(/,a)') ' <<<+- math init -+>>>' write(6,'(/,a)') ' <<<+- math init -+>>>'
call random_seed(size=randSize) call random_seed(size=randSize)
if (allocated(randInit)) deallocate(randInit)
allocate(randInit(randSize)) allocate(randInit(randSize))
if (randomSeed > 0_pInt) then if (randomSeed > 0) then
randInit(1:randSize) = int(randomSeed) ! randomSeed is of type pInt, randInit not randInit = randomSeed
call random_seed(put=randInit) call random_seed(put=randInit)
else else
call random_seed() call random_seed()
@ -204,12 +202,12 @@ subroutine math_init
call random_seed(put = randInit) call random_seed(put = randInit)
endif endif
do i = 1_pInt, 4_pInt do i = 1, 4
call random_number(randTest(i)) call random_number(randTest(i))
enddo enddo
write(6,'(a,I2)') ' size of random seed: ', randSize write(6,'(a,I2)') ' size of random seed: ', randSize
do i = 1_pInt,randSize do i = 1,randSize
write(6,'(a,I2,I14)') ' value of random seed: ', i, randInit(i) write(6,'(a,I2,I14)') ' value of random seed: ', i, randInit(i)
enddo enddo
write(6,'(a,4(/,26x,f17.14),/)') ' start of random sequence: ', randTest write(6,'(a,4(/,26x,f17.14),/)') ' start of random sequence: ', randTest
@ -244,7 +242,7 @@ subroutine math_check
any(abs(-q-q2) > tol_math_check) ) then any(abs(-q-q2) > tol_math_check) ) then
write (error_msg, '(a,e14.6)' ) & write (error_msg, '(a,e14.6)' ) &
'quat -> axisAngle -> quat maximum deviation ',min(maxval(abs( q-q2)),maxval(abs(-q-q2))) 'quat -> axisAngle -> quat maximum deviation ',min(maxval(abs( q-q2)),maxval(abs(-q-q2)))
call IO_error(401_pInt,ext_msg=error_msg) call IO_error(401,ext_msg=error_msg)
endif endif
! +++ q -> R -> q +++ ! +++ q -> R -> q +++
@ -254,7 +252,7 @@ subroutine math_check
any(abs(-q-q2) > tol_math_check) ) then any(abs(-q-q2) > tol_math_check) ) then
write (error_msg, '(a,e14.6)' ) & write (error_msg, '(a,e14.6)' ) &
'quat -> R -> quat maximum deviation ',min(maxval(abs( q-q2)),maxval(abs(-q-q2))) 'quat -> R -> quat maximum deviation ',min(maxval(abs( q-q2)),maxval(abs(-q-q2)))
call IO_error(401_pInt,ext_msg=error_msg) call IO_error(401,ext_msg=error_msg)
endif endif
! +++ q -> euler -> q +++ ! +++ q -> euler -> q +++
@ -264,7 +262,7 @@ subroutine math_check
any(abs(-q-q2) > tol_math_check) ) then any(abs(-q-q2) > tol_math_check) ) then
write (error_msg, '(a,e14.6)' ) & write (error_msg, '(a,e14.6)' ) &
'quat -> euler -> quat maximum deviation ',min(maxval(abs( q-q2)),maxval(abs(-q-q2))) 'quat -> euler -> quat maximum deviation ',min(maxval(abs( q-q2)),maxval(abs(-q-q2)))
call IO_error(401_pInt,ext_msg=error_msg) call IO_error(401,ext_msg=error_msg)
endif endif
! +++ R -> euler -> R +++ ! +++ R -> euler -> R +++
@ -273,32 +271,32 @@ subroutine math_check
if ( any(abs( R-R2) > tol_math_check) ) then if ( any(abs( R-R2) > tol_math_check) ) then
write (error_msg, '(a,e14.6)' ) & write (error_msg, '(a,e14.6)' ) &
'R -> euler -> R maximum deviation ',maxval(abs( R-R2)) 'R -> euler -> R maximum deviation ',maxval(abs( R-R2))
call IO_error(401_pInt,ext_msg=error_msg) call IO_error(401,ext_msg=error_msg)
endif endif
! +++ check rotation sense of q and R +++ ! +++ check rotation sense of q and R +++
v = halton([2_pInt,8_pInt,5_pInt]) ! random vector v = halton([2,8,5]) ! random vector
R = math_qToR(q) R = math_qToR(q)
if (any(abs(math_mul33x3(R,v) - math_qRot(q,v)) > tol_math_check)) then if (any(abs(math_mul33x3(R,v) - math_qRot(q,v)) > tol_math_check)) then
write (error_msg, '(a)' ) 'R(q)*v has different sense than q*v' write (error_msg, '(a)' ) 'R(q)*v has different sense than q*v'
call IO_error(401_pInt,ext_msg=error_msg) call IO_error(401,ext_msg=error_msg)
endif endif
! +++ check vector expansion +++ ! +++ check vector expansion +++
if (any(abs([1.0_pReal,2.0_pReal,2.0_pReal,3.0_pReal,3.0_pReal,3.0_pReal] - & if (any(abs([1.0_pReal,2.0_pReal,2.0_pReal,3.0_pReal,3.0_pReal,3.0_pReal] - &
math_expand([1.0_pReal,2.0_pReal,3.0_pReal],[1_pInt,2_pInt,3_pInt,0_pInt])) > tol_math_check)) then math_expand([1.0_pReal,2.0_pReal,3.0_pReal],[1,2,3,0])) > tol_math_check)) then
write (error_msg, '(a)' ) 'math_expand [1,2,3] by [1,2,3,0] => [1,2,2,3,3,3]' write (error_msg, '(a)' ) 'math_expand [1,2,3] by [1,2,3,0] => [1,2,2,3,3,3]'
call IO_error(401_pInt,ext_msg=error_msg) call IO_error(401,ext_msg=error_msg)
endif endif
if (any(abs([1.0_pReal,2.0_pReal,2.0_pReal] - & if (any(abs([1.0_pReal,2.0_pReal,2.0_pReal] - &
math_expand([1.0_pReal,2.0_pReal,3.0_pReal],[1_pInt,2_pInt])) > tol_math_check)) then math_expand([1.0_pReal,2.0_pReal,3.0_pReal],[1,2])) > tol_math_check)) then
write (error_msg, '(a)' ) 'math_expand [1,2,3] by [1,2] => [1,2,2]' write (error_msg, '(a)' ) 'math_expand [1,2,3] by [1,2] => [1,2,2]'
call IO_error(401_pInt,ext_msg=error_msg) call IO_error(401,ext_msg=error_msg)
endif endif
if (any(abs([1.0_pReal,2.0_pReal,2.0_pReal,1.0_pReal,1.0_pReal,1.0_pReal] - & if (any(abs([1.0_pReal,2.0_pReal,2.0_pReal,1.0_pReal,1.0_pReal,1.0_pReal] - &
math_expand([1.0_pReal,2.0_pReal],[1_pInt,2_pInt,3_pInt])) > tol_math_check)) then math_expand([1.0_pReal,2.0_pReal],[1,2,3])) > tol_math_check)) then
write (error_msg, '(a)' ) 'math_expand [1,2] by [1,2,3] => [1,2,2,1,1,1]' write (error_msg, '(a)' ) 'math_expand [1,2] by [1,2,3] => [1,2,2,1,1,1]'
call IO_error(401_pInt,ext_msg=error_msg) call IO_error(401,ext_msg=error_msg)
endif endif
end subroutine math_check end subroutine math_check
@ -312,9 +310,9 @@ end subroutine math_check
recursive subroutine math_qsort(a, istart, iend, sortDim) recursive subroutine math_qsort(a, istart, iend, sortDim)
implicit none implicit none
integer(pInt), dimension(:,:), intent(inout) :: a integer, dimension(:,:), intent(inout) :: a
integer(pInt), intent(in),optional :: istart,iend, sortDim integer, intent(in),optional :: istart,iend, sortDim
integer(pInt) :: ipivot,s,e,d integer :: ipivot,s,e,d
if(present(istart)) then if(present(istart)) then
s = istart s = istart
@ -336,8 +334,8 @@ recursive subroutine math_qsort(a, istart, iend, sortDim)
if (s < e) then if (s < e) then
ipivot = qsort_partition(a,s, e, d) ipivot = qsort_partition(a,s, e, d)
call math_qsort(a, s, ipivot-1_pInt, d) call math_qsort(a, s, ipivot-1, d)
call math_qsort(a, ipivot+1_pInt, e, d) call math_qsort(a, ipivot+1, e, d)
endif endif
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
@ -346,17 +344,17 @@ recursive subroutine math_qsort(a, istart, iend, sortDim)
!------------------------------------------------------------------------------------------------- !-------------------------------------------------------------------------------------------------
!> @brief Partitioning required for quicksort !> @brief Partitioning required for quicksort
!------------------------------------------------------------------------------------------------- !-------------------------------------------------------------------------------------------------
integer(pInt) function qsort_partition(a, istart, iend, sort) integer function qsort_partition(a, istart, iend, sort)
implicit none implicit none
integer(pInt), dimension(:,:), intent(inout) :: a integer, dimension(:,:), intent(inout) :: a
integer(pInt), intent(in) :: istart,iend,sort integer, intent(in) :: istart,iend,sort
integer(pInt), dimension(size(a,1)) :: tmp integer, dimension(size(a,1)) :: tmp
integer(pInt) :: i,j integer :: i,j
do do
! find the first element on the right side less than or equal to the pivot point ! find the first element on the right side less than or equal to the pivot point
do j = iend, istart, -1_pInt do j = iend, istart, -1
if (a(sort,j) <= a(sort,istart)) exit if (a(sort,j) <= a(sort,istart)) exit
enddo enddo
! find the first element on the left side greater than the pivot point ! find the first element on the left side greater than the pivot point
@ -390,15 +388,15 @@ pure function math_expand(what,how)
implicit none implicit none
real(pReal), dimension(:), intent(in) :: what real(pReal), dimension(:), intent(in) :: what
integer(pInt), dimension(:), intent(in) :: how integer, dimension(:), intent(in) :: how
real(pReal), dimension(sum(how)) :: math_expand real(pReal), dimension(sum(how)) :: math_expand
integer(pInt) :: i integer :: i
if (sum(how) == 0_pInt) & if (sum(how) == 0) &
return return
do i = 1_pInt, size(how) do i = 1, size(how)
math_expand(sum(how(1:i-1))+1:sum(how(1:i))) = what(mod(i-1_pInt,size(what))+1_pInt) math_expand(sum(how(1:i-1))+1:sum(how(1:i))) = what(mod(i-1,size(what))+1)
enddo enddo
end function math_expand end function math_expand
@ -410,11 +408,11 @@ end function math_expand
pure function math_range(N) pure function math_range(N)
implicit none implicit none
integer(pInt), intent(in) :: N !< length of range integer, intent(in) :: N !< length of range
integer(pInt) :: i integer :: i
integer(pInt), dimension(N) :: math_range integer, dimension(N) :: math_range
math_range = [(i,i=1_pInt,N)] math_range = [(i,i=1,N)]
end function math_range end function math_range
@ -425,12 +423,12 @@ end function math_range
pure function math_identity2nd(dimen) pure function math_identity2nd(dimen)
implicit none implicit none
integer(pInt), intent(in) :: dimen !< tensor dimension integer, intent(in) :: dimen !< tensor dimension
integer(pInt) :: i integer :: i
real(pReal), dimension(dimen,dimen) :: math_identity2nd real(pReal), dimension(dimen,dimen) :: math_identity2nd
math_identity2nd = 0.0_pReal math_identity2nd = 0.0_pReal
forall(i=1_pInt:dimen) math_identity2nd(i,i) = 1.0_pReal forall(i=1:dimen) math_identity2nd(i,i) = 1.0_pReal
end function math_identity2nd end function math_identity2nd
@ -441,13 +439,13 @@ end function math_identity2nd
pure function math_identity4th(dimen) pure function math_identity4th(dimen)
implicit none implicit none
integer(pInt), intent(in) :: dimen !< tensor dimension integer, intent(in) :: dimen !< tensor dimension
integer(pInt) :: i,j,k,l integer :: i,j,k,l
real(pReal), dimension(dimen,dimen,dimen,dimen) :: math_identity4th real(pReal), dimension(dimen,dimen,dimen,dimen) :: math_identity4th
real(pReal), dimension(dimen,dimen) :: identity2nd real(pReal), dimension(dimen,dimen) :: identity2nd
identity2nd = math_identity2nd(dimen) identity2nd = math_identity2nd(dimen)
forall(i=1_pInt:dimen,j=1_pInt:dimen,k=1_pInt:dimen,l=1_pInt:dimen) & forall(i=1:dimen,j=1:dimen,k=1:dimen,l=1:dimen) &
math_identity4th(i,j,k,l) = 0.5_pReal*(identity2nd(i,k)*identity2nd(j,l)+identity2nd(i,l)*identity2nd(j,k)) math_identity4th(i,j,k,l) = 0.5_pReal*(identity2nd(i,k)*identity2nd(j,l)+identity2nd(i,l)*identity2nd(j,k))
end function math_identity4th end function math_identity4th
@ -462,15 +460,15 @@ end function math_identity4th
real(pReal) pure function math_civita(i,j,k) real(pReal) pure function math_civita(i,j,k)
implicit none implicit none
integer(pInt), intent(in) :: i,j,k integer, intent(in) :: i,j,k
math_civita = 0.0_pReal math_civita = 0.0_pReal
if (((i == 1_pInt).and.(j == 2_pInt).and.(k == 3_pInt)) .or. & if (((i == 1).and.(j == 2).and.(k == 3)) .or. &
((i == 2_pInt).and.(j == 3_pInt).and.(k == 1_pInt)) .or. & ((i == 2).and.(j == 3).and.(k == 1)) .or. &
((i == 3_pInt).and.(j == 1_pInt).and.(k == 2_pInt))) math_civita = 1.0_pReal ((i == 3).and.(j == 1).and.(k == 2))) math_civita = 1.0_pReal
if (((i == 1_pInt).and.(j == 3_pInt).and.(k == 2_pInt)) .or. & if (((i == 1).and.(j == 3).and.(k == 2)) .or. &
((i == 2_pInt).and.(j == 1_pInt).and.(k == 3_pInt)) .or. & ((i == 2).and.(j == 1).and.(k == 3)) .or. &
((i == 3_pInt).and.(j == 2_pInt).and.(k == 1_pInt))) math_civita = -1.0_pReal ((i == 3).and.(j == 2).and.(k == 1))) math_civita = -1.0_pReal
end function math_civita end function math_civita
@ -484,7 +482,7 @@ end function math_civita
real(pReal) pure function math_delta(i,j) real(pReal) pure function math_delta(i,j)
implicit none implicit none
integer(pInt), intent (in) :: i,j integer, intent (in) :: i,j
math_delta = merge(0.0_pReal, 1.0_pReal, i /= j) math_delta = merge(0.0_pReal, 1.0_pReal, i /= j)
@ -515,9 +513,9 @@ pure function math_outer(A,B)
implicit none implicit none
real(pReal), dimension(:), intent(in) :: A,B real(pReal), dimension(:), intent(in) :: A,B
real(pReal), dimension(size(A,1),size(B,1)) :: math_outer real(pReal), dimension(size(A,1),size(B,1)) :: math_outer
integer(pInt) :: i,j integer :: i,j
forall(i=1_pInt:size(A,1),j=1_pInt:size(B,1)) math_outer(i,j) = A(i)*B(j) forall(i=1:size(A,1),j=1:size(B,1)) math_outer(i,j) = A(i)*B(j)
end function math_outer end function math_outer
@ -543,10 +541,10 @@ real(pReal) pure function math_mul33xx33(A,B)
implicit none implicit none
real(pReal), dimension(3,3), intent(in) :: A,B real(pReal), dimension(3,3), intent(in) :: A,B
integer(pInt) :: i,j integer :: i,j
real(pReal), dimension(3,3) :: C real(pReal), dimension(3,3) :: C
forall(i=1_pInt:3_pInt,j=1_pInt:3_pInt) C(i,j) = A(i,j) * B(i,j) forall(i=1:3,j=1:3) C(i,j) = A(i,j) * B(i,j)
math_mul33xx33 = sum(C) math_mul33xx33 = sum(C)
end function math_mul33xx33 end function math_mul33xx33
@ -561,9 +559,9 @@ pure function math_mul3333xx33(A,B)
real(pReal), dimension(3,3) :: math_mul3333xx33 real(pReal), dimension(3,3) :: math_mul3333xx33
real(pReal), dimension(3,3,3,3), intent(in) :: A real(pReal), dimension(3,3,3,3), intent(in) :: A
real(pReal), dimension(3,3), intent(in) :: B real(pReal), dimension(3,3), intent(in) :: B
integer(pInt) :: i,j integer :: i,j
forall(i = 1_pInt:3_pInt,j = 1_pInt:3_pInt) math_mul3333xx33(i,j) = sum(A(i,j,1:3,1:3)*B(1:3,1:3)) forall(i = 1:3,j = 1:3) math_mul3333xx33(i,j) = sum(A(i,j,1:3,1:3)*B(1:3,1:3))
end function math_mul3333xx33 end function math_mul3333xx33
@ -574,12 +572,12 @@ end function math_mul3333xx33
pure function math_mul3333xx3333(A,B) pure function math_mul3333xx3333(A,B)
implicit none implicit none
integer(pInt) :: i,j,k,l integer :: i,j,k,l
real(pReal), dimension(3,3,3,3), intent(in) :: A real(pReal), dimension(3,3,3,3), intent(in) :: A
real(pReal), dimension(3,3,3,3), intent(in) :: B real(pReal), dimension(3,3,3,3), intent(in) :: B
real(pReal), dimension(3,3,3,3) :: math_mul3333xx3333 real(pReal), dimension(3,3,3,3) :: math_mul3333xx3333
forall(i = 1_pInt:3_pInt,j = 1_pInt:3_pInt, k = 1_pInt:3_pInt, l= 1_pInt:3_pInt) & forall(i = 1:3,j = 1:3, k = 1:3, l= 1:3) &
math_mul3333xx3333(i,j,k,l) = sum(A(i,j,1:3,1:3)*B(1:3,1:3,k,l)) math_mul3333xx3333(i,j,k,l) = sum(A(i,j,1:3,1:3)*B(1:3,1:3,k,l))
end function math_mul3333xx3333 end function math_mul3333xx3333
@ -593,9 +591,9 @@ pure function math_mul33x33(A,B)
implicit none implicit none
real(pReal), dimension(3,3) :: math_mul33x33 real(pReal), dimension(3,3) :: math_mul33x33
real(pReal), dimension(3,3), intent(in) :: A,B real(pReal), dimension(3,3), intent(in) :: A,B
integer(pInt) :: i,j integer :: i,j
forall(i=1_pInt:3_pInt,j=1_pInt:3_pInt) math_mul33x33(i,j) = A(i,1)*B(1,j) + A(i,2)*B(2,j) + A(i,3)*B(3,j) forall(i=1:3,j=1:3) math_mul33x33(i,j) = A(i,1)*B(1,j) + A(i,2)*B(2,j) + A(i,3)*B(3,j)
end function math_mul33x33 end function math_mul33x33
@ -608,9 +606,9 @@ pure function math_mul66x66(A,B)
implicit none implicit none
real(pReal), dimension(6,6) :: math_mul66x66 real(pReal), dimension(6,6) :: math_mul66x66
real(pReal), dimension(6,6), intent(in) :: A,B real(pReal), dimension(6,6), intent(in) :: A,B
integer(pInt) :: i,j integer :: i,j
forall(i=1_pInt:6_pInt,j=1_pInt:6_pInt) & forall(i=1:6,j=1:6) &
math_mul66x66(i,j) = A(i,1)*B(1,j) + A(i,2)*B(2,j) + A(i,3)*B(3,j) & math_mul66x66(i,j) = A(i,1)*B(1,j) + A(i,2)*B(2,j) + A(i,3)*B(3,j) &
+ A(i,4)*B(4,j) + A(i,5)*B(5,j) + A(i,6)*B(6,j) + A(i,4)*B(4,j) + A(i,5)*B(5,j) + A(i,6)*B(6,j)
@ -625,9 +623,9 @@ pure function math_mul99x99(A,B)
implicit none implicit none
real(pReal), dimension(9,9) :: math_mul99x99 real(pReal), dimension(9,9) :: math_mul99x99
real(pReal), dimension(9,9), intent(in) :: A,B real(pReal), dimension(9,9), intent(in) :: A,B
integer(pInt) i,j integer i,j
forall(i=1_pInt:9_pInt,j=1_pInt:9_pInt) & forall(i=1:9,j=1:9) &
math_mul99x99(i,j) = A(i,1)*B(1,j) + A(i,2)*B(2,j) + A(i,3)*B(3,j) & math_mul99x99(i,j) = A(i,1)*B(1,j) + A(i,2)*B(2,j) + A(i,3)*B(3,j) &
+ A(i,4)*B(4,j) + A(i,5)*B(5,j) + A(i,6)*B(6,j) & + A(i,4)*B(4,j) + A(i,5)*B(5,j) + A(i,6)*B(6,j) &
+ A(i,7)*B(7,j) + A(i,8)*B(8,j) + A(i,9)*B(9,j) + A(i,7)*B(7,j) + A(i,8)*B(8,j) + A(i,9)*B(9,j)
@ -644,9 +642,9 @@ pure function math_mul33x3(A,B)
real(pReal), dimension(3) :: math_mul33x3 real(pReal), dimension(3) :: math_mul33x3
real(pReal), dimension(3,3), intent(in) :: A real(pReal), dimension(3,3), intent(in) :: A
real(pReal), dimension(3), intent(in) :: B real(pReal), dimension(3), intent(in) :: B
integer(pInt) :: i integer :: i
forall (i=1_pInt:3_pInt) math_mul33x3(i) = sum(A(i,1:3)*B) forall (i=1:3) math_mul33x3(i) = sum(A(i,1:3)*B)
end function math_mul33x3 end function math_mul33x3
@ -660,9 +658,9 @@ pure function math_mul33x3_complex(A,B)
complex(pReal), dimension(3) :: math_mul33x3_complex complex(pReal), dimension(3) :: math_mul33x3_complex
complex(pReal), dimension(3,3), intent(in) :: A complex(pReal), dimension(3,3), intent(in) :: A
real(pReal), dimension(3), intent(in) :: B real(pReal), dimension(3), intent(in) :: B
integer(pInt) :: i integer :: i
forall (i=1_pInt:3_pInt) math_mul33x3_complex(i) = sum(A(i,1:3)*cmplx(B,0.0_pReal,pReal)) forall (i=1:3) math_mul33x3_complex(i) = sum(A(i,1:3)*cmplx(B,0.0_pReal,pReal))
end function math_mul33x3_complex end function math_mul33x3_complex
@ -676,9 +674,9 @@ pure function math_mul66x6(A,B)
real(pReal), dimension(6) :: math_mul66x6 real(pReal), dimension(6) :: math_mul66x6
real(pReal), dimension(6,6), intent(in) :: A real(pReal), dimension(6,6), intent(in) :: A
real(pReal), dimension(6), intent(in) :: B real(pReal), dimension(6), intent(in) :: B
integer(pInt) :: i integer :: i
forall (i=1_pInt:6_pInt) math_mul66x6(i) = A(i,1)*B(1) + A(i,2)*B(2) + A(i,3)*B(3) & forall (i=1:6) math_mul66x6(i) = A(i,1)*B(1) + A(i,2)*B(2) + A(i,3)*B(3) &
+ A(i,4)*B(4) + A(i,5)*B(5) + A(i,6)*B(6) + A(i,4)*B(4) + A(i,5)*B(5) + A(i,6)*B(6)
end function math_mul66x6 end function math_mul66x6
@ -690,8 +688,8 @@ end function math_mul66x6
pure function math_exp33(A,n) pure function math_exp33(A,n)
implicit none implicit none
integer(pInt) :: i integer :: i
integer(pInt), intent(in), optional :: n integer, intent(in), optional :: n
real(pReal), dimension(3,3), intent(in) :: A real(pReal), dimension(3,3), intent(in) :: A
real(pReal), dimension(3,3) :: B, math_exp33 real(pReal), dimension(3,3) :: B, math_exp33
real(pReal) :: invFac real(pReal) :: invFac
@ -700,7 +698,7 @@ pure function math_exp33(A,n)
invFac = 1.0_pReal ! 0! invFac = 1.0_pReal ! 0!
math_exp33 = B ! A^0 = eye2 math_exp33 = B ! A^0 = eye2
do i = 1_pInt, merge(n,5_pInt,present(n)) do i = 1, merge(n,5,present(n))
invFac = invFac/real(i,pReal) ! invfac = 1/i! invFac = invFac/real(i,pReal) ! invfac = 1/i!
B = math_mul33x33(B,A) B = math_mul33x33(B,A)
math_exp33 = math_exp33 + invFac*B ! exp = SUM (A^i)/i! math_exp33 = math_exp33 + invFac*B ! exp = SUM (A^i)/i!
@ -717,9 +715,9 @@ pure function math_transpose33(A)
implicit none implicit none
real(pReal),dimension(3,3) :: math_transpose33 real(pReal),dimension(3,3) :: math_transpose33
real(pReal),dimension(3,3),intent(in) :: A real(pReal),dimension(3,3),intent(in) :: A
integer(pInt) :: i,j integer :: i,j
forall(i=1_pInt:3_pInt, j=1_pInt:3_pInt) math_transpose33(i,j) = A(j,i) forall(i=1:3, j=1:3) math_transpose33(i,j) = A(j,i)
end function math_transpose33 end function math_transpose33
@ -814,8 +812,8 @@ function math_invSym3333(A)
real(pReal),dimension(3,3,3,3),intent(in) :: A real(pReal),dimension(3,3,3,3),intent(in) :: A
integer(pInt) :: ierr integer :: ierr
integer(pInt), dimension(6) :: ipiv6 integer, dimension(6) :: ipiv6
real(pReal), dimension(6,6) :: temp66_Real real(pReal), dimension(6,6) :: temp66_Real
real(pReal), dimension(6) :: work6 real(pReal), dimension(6) :: work6
external :: & external :: &
@ -825,10 +823,10 @@ function math_invSym3333(A)
temp66_real = math_sym3333to66(A) temp66_real = math_sym3333to66(A)
call dgetrf(6,6,temp66_real,6,ipiv6,ierr) call dgetrf(6,6,temp66_real,6,ipiv6,ierr)
call dgetri(6,temp66_real,6,ipiv6,work6,6,ierr) call dgetri(6,temp66_real,6,ipiv6,work6,6,ierr)
if (ierr == 0_pInt) then if (ierr == 0) then
math_invSym3333 = math_66toSym3333(temp66_real) math_invSym3333 = math_66toSym3333(temp66_real)
else else
call IO_error(400_pInt, ext_msg = 'math_invSym3333') call IO_error(400, ext_msg = 'math_invSym3333')
endif endif
end function math_invSym3333 end function math_invSym3333
@ -859,12 +857,12 @@ end subroutine math_invert2
subroutine math_invert(myDim,A, InvA, error) subroutine math_invert(myDim,A, InvA, error)
implicit none implicit none
integer(pInt), intent(in) :: myDim integer, intent(in) :: myDim
real(pReal), dimension(myDim,myDim), intent(in) :: A real(pReal), dimension(myDim,myDim), intent(in) :: A
integer(pInt) :: ierr integer :: ierr
integer(pInt), dimension(myDim) :: ipiv integer, dimension(myDim) :: ipiv
real(pReal), dimension(myDim) :: work real(pReal), dimension(myDim) :: work
real(pReal), dimension(myDim,myDim), intent(out) :: invA real(pReal), dimension(myDim,myDim), intent(out) :: invA
@ -876,7 +874,7 @@ subroutine math_invert(myDim,A, InvA, error)
invA = A invA = A
call dgetrf(myDim,myDim,invA,myDim,ipiv,ierr) call dgetrf(myDim,myDim,invA,myDim,ipiv,ierr)
call dgetri(myDim,InvA,myDim,ipiv,work,myDim,ierr) call dgetri(myDim,InvA,myDim,ipiv,work,myDim,ierr)
error = merge(.true.,.false., ierr /= 0_pInt) error = merge(.true.,.false., ierr /= 0)
end subroutine math_invert end subroutine math_invert
@ -1029,7 +1027,7 @@ real(pReal) pure function math_detSym33(m)
implicit none implicit none
real(pReal), dimension(3,3), intent(in) :: m real(pReal), dimension(3,3), intent(in) :: m
math_detSym33 = -(m(1,1)*m(2,3)**2_pInt + m(2,2)*m(1,3)**2_pInt + m(3,3)*m(1,2)**2_pInt) & math_detSym33 = -(m(1,1)*m(2,3)**2 + m(2,2)*m(1,3)**2 + m(3,3)*m(1,2)**2) &
+ m(1,1)*m(2,2)*m(3,3) + 2.0_pReal * m(1,2)*m(1,3)*m(2,3) + m(1,1)*m(2,2)*m(3,3) + 2.0_pReal * m(1,2)*m(1,3)*m(2,3)
end function math_detSym33 end function math_detSym33
@ -1044,9 +1042,9 @@ pure function math_33to9(m33)
real(pReal), dimension(9) :: math_33to9 real(pReal), dimension(9) :: math_33to9
real(pReal), dimension(3,3), intent(in) :: m33 real(pReal), dimension(3,3), intent(in) :: m33
integer(pInt) :: i integer :: i
forall(i=1_pInt:9_pInt) math_33to9(i) = m33(mapPlain(1,i),mapPlain(2,i)) forall(i=1:9) math_33to9(i) = m33(mapPlain(1,i),mapPlain(2,i))
end function math_33to9 end function math_33to9
@ -1060,9 +1058,9 @@ pure function math_9to33(v9)
real(pReal), dimension(3,3) :: math_9to33 real(pReal), dimension(3,3) :: math_9to33
real(pReal), dimension(9), intent(in) :: v9 real(pReal), dimension(9), intent(in) :: v9
integer(pInt) :: i integer :: i
forall(i=1_pInt:9_pInt) math_9to33(mapPlain(1,i),mapPlain(2,i)) = v9(i) forall(i=1:9) math_9to33(mapPlain(1,i),mapPlain(2,i)) = v9(i)
end function math_9to33 end function math_9to33
@ -1081,7 +1079,7 @@ pure function math_sym33to6(m33,weighted)
logical, optional, intent(in) :: weighted logical, optional, intent(in) :: weighted
real(pReal), dimension(6) :: w real(pReal), dimension(6) :: w
integer(pInt) :: i integer :: i
if(present(weighted)) then if(present(weighted)) then
w = merge(nrmMandel,1.0_pReal,weighted) w = merge(nrmMandel,1.0_pReal,weighted)
@ -1089,7 +1087,7 @@ pure function math_sym33to6(m33,weighted)
w = nrmMandel w = nrmMandel
endif endif
forall(i=1_pInt:6_pInt) math_sym33to6(i) = w(i)*m33(mapNye(1,i),mapNye(2,i)) forall(i=1:6) math_sym33to6(i) = w(i)*m33(mapNye(1,i),mapNye(2,i))
end function math_sym33to6 end function math_sym33to6
@ -1108,7 +1106,7 @@ pure function math_6toSym33(v6,weighted)
logical, optional, intent(in) :: weighted logical, optional, intent(in) :: weighted
real(pReal), dimension(6) :: w real(pReal), dimension(6) :: w
integer(pInt) :: i integer :: i
if(present(weighted)) then if(present(weighted)) then
w = merge(invnrmMandel,1.0_pReal,weighted) w = merge(invnrmMandel,1.0_pReal,weighted)
@ -1116,7 +1114,7 @@ pure function math_6toSym33(v6,weighted)
w = invnrmMandel w = invnrmMandel
endif endif
do i=1_pInt,6_pInt do i=1,6
math_6toSym33(mapNye(1,i),mapNye(2,i)) = w(i)*v6(i) math_6toSym33(mapNye(1,i),mapNye(2,i)) = w(i)*v6(i)
math_6toSym33(mapNye(2,i),mapNye(1,i)) = w(i)*v6(i) math_6toSym33(mapNye(2,i),mapNye(1,i)) = w(i)*v6(i)
enddo enddo
@ -1133,9 +1131,9 @@ pure function math_3333to99(m3333)
real(pReal), dimension(9,9) :: math_3333to99 real(pReal), dimension(9,9) :: math_3333to99
real(pReal), dimension(3,3,3,3), intent(in) :: m3333 real(pReal), dimension(3,3,3,3), intent(in) :: m3333
integer(pInt) :: i,j integer :: i,j
forall(i=1_pInt:9_pInt,j=1_pInt:9_pInt) & forall(i=1:9,j=1:9) &
math_3333to99(i,j) = m3333(mapPlain(1,i),mapPlain(2,i),mapPlain(1,j),mapPlain(2,j)) math_3333to99(i,j) = m3333(mapPlain(1,i),mapPlain(2,i),mapPlain(1,j),mapPlain(2,j))
end function math_3333to99 end function math_3333to99
@ -1150,9 +1148,9 @@ pure function math_99to3333(m99)
real(pReal), dimension(3,3,3,3) :: math_99to3333 real(pReal), dimension(3,3,3,3) :: math_99to3333
real(pReal), dimension(9,9), intent(in) :: m99 real(pReal), dimension(9,9), intent(in) :: m99
integer(pInt) :: i,j integer :: i,j
forall(i=1_pInt:9_pInt,j=1_pInt:9_pInt) & forall(i=1:9,j=1:9) &
math_99to3333(mapPlain(1,i),mapPlain(2,i),mapPlain(1,j),mapPlain(2,j)) = m99(i,j) math_99to3333(mapPlain(1,i),mapPlain(2,i),mapPlain(1,j),mapPlain(2,j)) = m99(i,j)
end function math_99to3333 end function math_99to3333
@ -1172,7 +1170,7 @@ pure function math_sym3333to66(m3333,weighted)
logical, optional, intent(in) :: weighted logical, optional, intent(in) :: weighted
real(pReal), dimension(6) :: w real(pReal), dimension(6) :: w
integer(pInt) :: i,j integer :: i,j
if(present(weighted)) then if(present(weighted)) then
w = merge(nrmMandel,1.0_pReal,weighted) w = merge(nrmMandel,1.0_pReal,weighted)
@ -1180,7 +1178,7 @@ pure function math_sym3333to66(m3333,weighted)
w = nrmMandel w = nrmMandel
endif endif
forall(i=1_pInt:6_pInt,j=1_pInt:6_pInt) & forall(i=1:6,j=1:6) &
math_sym3333to66(i,j) = w(i)*w(j)*m3333(mapNye(1,i),mapNye(2,i),mapNye(1,j),mapNye(2,j)) math_sym3333to66(i,j) = w(i)*w(j)*m3333(mapNye(1,i),mapNye(2,i),mapNye(1,j),mapNye(2,j))
end function math_sym3333to66 end function math_sym3333to66
@ -1200,7 +1198,7 @@ pure function math_66toSym3333(m66,weighted)
logical, optional, intent(in) :: weighted logical, optional, intent(in) :: weighted
real(pReal), dimension(6) :: w real(pReal), dimension(6) :: w
integer(pInt) :: i,j integer :: i,j
if(present(weighted)) then if(present(weighted)) then
w = merge(invnrmMandel,1.0_pReal,weighted) w = merge(invnrmMandel,1.0_pReal,weighted)
@ -1208,7 +1206,7 @@ pure function math_66toSym3333(m66,weighted)
w = invnrmMandel w = invnrmMandel
endif endif
do i=1_pInt,6_pInt; do j=1_pInt, 6_pInt do i=1,6; do j=1, 6
math_66toSym3333(mapNye(1,i),mapNye(2,i),mapNye(1,j),mapNye(2,j)) = w(i)*w(j)*m66(i,j) math_66toSym3333(mapNye(1,i),mapNye(2,i),mapNye(1,j),mapNye(2,j)) = w(i)*w(j)*m66(i,j)
math_66toSym3333(mapNye(2,i),mapNye(1,i),mapNye(1,j),mapNye(2,j)) = w(i)*w(j)*m66(i,j) math_66toSym3333(mapNye(2,i),mapNye(1,i),mapNye(1,j),mapNye(2,j)) = w(i)*w(j)*m66(i,j)
math_66toSym3333(mapNye(1,i),mapNye(2,i),mapNye(2,j),mapNye(1,j)) = w(i)*w(j)*m66(i,j) math_66toSym3333(mapNye(1,i),mapNye(2,i),mapNye(2,j),mapNye(1,j)) = w(i)*w(j)*m66(i,j)
@ -1226,9 +1224,9 @@ pure function math_Voigt66to3333(m66)
implicit none implicit none
real(pReal), dimension(3,3,3,3) :: math_Voigt66to3333 real(pReal), dimension(3,3,3,3) :: math_Voigt66to3333
real(pReal), dimension(6,6), intent(in) :: m66 real(pReal), dimension(6,6), intent(in) :: m66
integer(pInt) :: i,j integer :: i,j
do i=1_pInt,6_pInt; do j=1_pInt, 6_pInt do i=1,6; do j=1, 6
math_Voigt66to3333(mapVoigt(1,i),mapVoigt(2,i),mapVoigt(1,j),mapVoigt(2,j)) = m66(i,j) math_Voigt66to3333(mapVoigt(1,i),mapVoigt(2,i),mapVoigt(1,j),mapVoigt(2,j)) = m66(i,j)
math_Voigt66to3333(mapVoigt(2,i),mapVoigt(1,i),mapVoigt(1,j),mapVoigt(2,j)) = m66(i,j) math_Voigt66to3333(mapVoigt(2,i),mapVoigt(1,i),mapVoigt(1,j),mapVoigt(2,j)) = m66(i,j)
math_Voigt66to3333(mapVoigt(1,i),mapVoigt(2,i),mapVoigt(2,j),mapVoigt(1,j)) = m66(i,j) math_Voigt66to3333(mapVoigt(1,i),mapVoigt(2,i),mapVoigt(2,j),mapVoigt(1,j)) = m66(i,j)
@ -1250,7 +1248,7 @@ function math_qRand()
real(pReal), dimension(4) :: math_qRand real(pReal), dimension(4) :: math_qRand
real(pReal), dimension(3) :: rnd real(pReal), dimension(3) :: rnd
rnd = halton([8_pInt,4_pInt,9_pInt]) rnd = halton([8,4,9])
math_qRand = [cos(2.0_pReal*PI*rnd(1))*sqrt(rnd(3)), & math_qRand = [cos(2.0_pReal*PI*rnd(1))*sqrt(rnd(3)), &
sin(2.0_pReal*PI*rnd(2))*sqrt(1.0_pReal-rnd(3)), & sin(2.0_pReal*PI*rnd(2))*sqrt(1.0_pReal-rnd(3)), &
cos(2.0_pReal*PI*rnd(2))*sqrt(1.0_pReal-rnd(3)), & cos(2.0_pReal*PI*rnd(2))*sqrt(1.0_pReal-rnd(3)), &
@ -1346,10 +1344,10 @@ pure function math_qRot(Q,v)
real(pReal), dimension(3), intent(in) :: v real(pReal), dimension(3), intent(in) :: v
real(pReal), dimension(3) :: math_qRot real(pReal), dimension(3) :: math_qRot
real(pReal), dimension(4,4) :: T real(pReal), dimension(4,4) :: T
integer(pInt) :: i, j integer :: i, j
do i = 1_pInt,4_pInt do i = 1,4
do j = 1_pInt,i do j = 1,i
T(i,j) = Q(i) * Q(j) T(i,j) = Q(i) * Q(j)
enddo enddo
enddo enddo
@ -1408,7 +1406,7 @@ pure function math_RtoQ(R)
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
integer, dimension(1) :: largest !no pInt, maxloc returns integer default integer, dimension(1) :: largest
math_RtoQ = 0.0_pReal math_RtoQ = 0.0_pReal
@ -1639,9 +1637,9 @@ 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 :: i, j
forall(i = 1_pInt:3_pInt, j = 1_pInt:3_pInt) T(i,j) = q(i+1_pInt) * q(j+1_pInt) forall(i = 1:3, j = 1:3) T(i,j) = q(i+1) * q(j+1)
S = reshape( [0.0_pReal, -q(4), q(3), & S = reshape( [0.0_pReal, -q(4), q(3), &
q(4), 0.0_pReal, -q(2), & q(4), 0.0_pReal, -q(2), &
@ -1772,7 +1770,7 @@ function math_sampleRandomOri()
implicit none implicit none
real(pReal), dimension(3) :: math_sampleRandomOri, rnd real(pReal), dimension(3) :: math_sampleRandomOri, rnd
rnd = halton([1_pInt,7_pInt,3_pInt]) rnd = halton([1,7,3])
math_sampleRandomOri = [rnd(1)*2.0_pReal*PI, & math_sampleRandomOri = [rnd(1)*2.0_pReal*PI, &
acos(2.0_pReal*rnd(2)-1.0_pReal), & acos(2.0_pReal*rnd(2)-1.0_pReal), &
rnd(3)*2.0_pReal*PI] rnd(3)*2.0_pReal*PI]
@ -1800,7 +1798,7 @@ function math_sampleGaussOri(center,FWHM)
math_sampleGaussOri = center math_sampleGaussOri = center
else else
GaussConvolution: do GaussConvolution: do
rnd = halton([8_pInt,3_pInt,6_pInt,11_pInt]) rnd = halton([8,3,6,11])
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
@ -1830,10 +1828,10 @@ function math_sampleFiberOri(alpha,beta,FWHM)
u u
real(pReal), dimension(3) :: rnd real(pReal), dimension(3) :: rnd
real(pReal), dimension(:),allocatable :: a !< 2D vector to tilt real(pReal), dimension(:),allocatable :: a !< 2D vector to tilt
integer(pInt), dimension(:),allocatable :: idx !< components of 2D vector integer, dimension(:),allocatable :: idx !< components of 2D vector
real(pReal), dimension(3,3) :: R !< Rotation matrix (composed of three components) real(pReal), dimension(3,3) :: R !< Rotation matrix (composed of three components)
real(pReal):: angle,c real(pReal):: angle,c
integer(pInt):: j,& !< index of smallest component integer:: j,& !< index of smallest component
i i
allocate(a(0)) allocate(a(0))
@ -1843,11 +1841,11 @@ function math_sampleFiberOri(alpha,beta,FWHM)
R = math_EulerAxisAngleToR(math_crossproduct(fInC,fInS),-acos(dot_product(fInC,fInS))) !< rotation to align fiber axis in crystal and sample system R = math_EulerAxisAngleToR(math_crossproduct(fInC,fInS),-acos(dot_product(fInC,fInS))) !< rotation to align fiber axis in crystal and sample system
rnd = halton([7_pInt,10_pInt,3_pInt]) rnd = halton([7,10,3])
R = math_mul33x33(R,math_EulerAxisAngleToR(fInS,rnd(1)*2.0_pReal*PI)) !< additional rotation (0..360deg) perpendicular to fiber axis 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 if (FWHM > 0.1_pReal*INRAD) then
reducedTo2D: do i=1_pInt,3_pInt reducedTo2D: do i=1,3
if (i /= minloc(abs(fInS),1)) then if (i /= minloc(abs(fInS),1)) then
a=[a,fInS(i)] a=[a,fInS(i)]
idx=[idx,i] idx=[idx,i]
@ -1868,7 +1866,7 @@ function math_sampleFiberOri(alpha,beta,FWHM)
R = math_mul33x33(R,math_EulerAxisAngleToR(math_crossproduct(u,fInS),angle)) ! tilt around direction of smallest component R = math_mul33x33(R,math_EulerAxisAngleToR(math_crossproduct(u,fInS),angle)) ! tilt around direction of smallest component
exit exit
endif rejectionSampling endif rejectionSampling
rnd = halton([7_pInt,10_pInt,3_pInt]) rnd = halton([7,10,3])
enddo GaussConvolution enddo GaussConvolution
endif endif
math_sampleFiberOri = math_RtoEuler(R) math_sampleFiberOri = math_RtoEuler(R)
@ -1897,7 +1895,7 @@ real(pReal) function math_sampleGaussVar(meanvalue, stddev, width)
myWidth = merge(width,3.0_pReal,present(width)) ! use +-3*sigma as default value for scatter if not given myWidth = merge(width,3.0_pReal,present(width)) ! use +-3*sigma as default value for scatter if not given
do do
rnd = halton([6_pInt,2_pInt]) rnd = halton([6,2])
scatter = myWidth * (2.0_pReal * rnd(1) - 1.0_pReal) scatter = myWidth * (2.0_pReal * rnd(1) - 1.0_pReal)
if (rnd(2) <= exp(-0.5_pReal * scatter ** 2.0_pReal)) exit ! test if scattered value is drawn if (rnd(2) <= exp(-0.5_pReal * scatter ** 2.0_pReal)) exit ! test if scattered value is drawn
enddo enddo
@ -1915,7 +1913,7 @@ 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 !< symmetry Class integer, intent(in) :: sym !< symmetry Class
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
@ -1926,9 +1924,9 @@ pure function math_symmetricEulers(sym,Euler)
math_symmetricEulers = modulo(math_symmetricEulers,2.0_pReal*pi) math_symmetricEulers = modulo(math_symmetricEulers,2.0_pReal*pi)
select case (sym) select case (sym)
case (4_pInt) ! orthotropic: all done case (4) ! orthotropic: all done
case (2_pInt) ! monoclinic: return only first case (2) ! monoclinic: return only first
math_symmetricEulers(1:3,2:3) = 0.0_pReal math_symmetricEulers(1:3,2:3) = 0.0_pReal
case default ! triclinic: return blank case default ! triclinic: return blank
@ -1949,14 +1947,14 @@ subroutine math_eigenValuesVectorsSym(m,values,vectors,error)
real(pReal), dimension(size(m,1)), intent(out) :: values real(pReal), dimension(size(m,1)), intent(out) :: values
real(pReal), dimension(size(m,1),size(m,1)), intent(out) :: vectors real(pReal), dimension(size(m,1),size(m,1)), intent(out) :: vectors
logical, intent(out) :: error logical, intent(out) :: error
integer(pInt) :: info integer :: info
real(pReal), dimension((64+2)*size(m,1)) :: work ! block size of 64 taken from http://www.netlib.org/lapack/double/dsyev.f real(pReal), dimension((64+2)*size(m,1)) :: work ! block size of 64 taken from http://www.netlib.org/lapack/double/dsyev.f
external :: & external :: &
dsyev dsyev
vectors = m ! copy matrix to input (doubles as output) array vectors = m ! copy matrix to input (doubles as output) array
call dsyev('V','U',size(m,1),vectors,size(m,1),values,work,(64+2)*size(m,1),info) call dsyev('V','U',size(m,1),vectors,size(m,1),values,work,(64+2)*size(m,1),info)
error = (info == 0_pInt) error = (info == 0)
end subroutine math_eigenValuesVectorsSym end subroutine math_eigenValuesVectorsSym
@ -1982,11 +1980,11 @@ subroutine math_eigenValuesVectorsSym33(m,values,vectors)
vectors(1:3,2) = [ m(1, 2) * m(2, 3) - m(1, 3) * m(2, 2), & vectors(1:3,2) = [ m(1, 2) * m(2, 3) - m(1, 3) * m(2, 2), &
m(1, 3) * m(1, 2) - m(2, 3) * m(1, 1), & m(1, 3) * m(1, 2) - m(2, 3) * m(1, 1), &
m(1, 2)**2_pInt] m(1, 2)**2]
T = maxval(abs(values)) T = maxval(abs(values))
U = max(T, T**2_pInt) U = max(T, T**2)
threshold = sqrt(5.68e-14_pReal * U**2_pInt) threshold = sqrt(5.68e-14_pReal * U**2)
! Calculate first eigenvector by the formula v[0] = (m - lambda[0]).e1 x (m - lambda[0]).e2 ! Calculate first eigenvector by the formula v[0] = (m - lambda[0]).e1 x (m - lambda[0]).e2
vectors(1:3,1) = [ vectors(1,2) + m(1, 3) * values(1), & vectors(1:3,1) = [ vectors(1,2) + m(1, 3) * values(1), &
@ -2030,13 +2028,13 @@ function math_eigenvectorBasisSym(m)
real(pReal), dimension(size(m,1),size(m,1)) :: vectors real(pReal), dimension(size(m,1),size(m,1)) :: vectors
real(pReal), dimension(size(m,1),size(m,1)) :: math_eigenvectorBasisSym real(pReal), dimension(size(m,1),size(m,1)) :: math_eigenvectorBasisSym
logical :: error logical :: error
integer(pInt) :: i integer :: i
math_eigenvectorBasisSym = 0.0_pReal math_eigenvectorBasisSym = 0.0_pReal
call math_eigenValuesVectorsSym(m,values,vectors,error) call math_eigenValuesVectorsSym(m,values,vectors,error)
if(error) return if(error) return
do i=1_pInt, size(m,1) do i=1, size(m,1)
math_eigenvectorBasisSym = math_eigenvectorBasisSym & math_eigenvectorBasisSym = math_eigenvectorBasisSym &
+ sqrt(values(i)) * math_outer(vectors(:,i),vectors(:,i)) + sqrt(values(i)) * math_outer(vectors(:,i),vectors(:,i))
enddo enddo
@ -2193,7 +2191,7 @@ function math_rotationalPart33(m)
inversionFailed: if (all(dEq0(Uinv))) then inversionFailed: if (all(dEq0(Uinv))) then
math_rotationalPart33 = math_I3 math_rotationalPart33 = math_I3
call IO_warning(650_pInt) call IO_warning(650)
else inversionFailed else inversionFailed
math_rotationalPart33 = math_mul33x33(m,Uinv) math_rotationalPart33 = math_mul33x33(m,Uinv)
endif inversionFailed endif inversionFailed
@ -2213,14 +2211,14 @@ function math_eigenvaluesSym(m)
real(pReal), dimension(:,:), intent(in) :: m real(pReal), dimension(:,:), intent(in) :: m
real(pReal), dimension(size(m,1)) :: math_eigenvaluesSym real(pReal), dimension(size(m,1)) :: math_eigenvaluesSym
real(pReal), dimension(size(m,1),size(m,1)) :: vectors real(pReal), dimension(size(m,1),size(m,1)) :: vectors
integer(pInt) :: info integer :: info
real(pReal), dimension((64+2)*size(m,1)) :: work ! block size of 64 taken from http://www.netlib.org/lapack/double/dsyev.f real(pReal), dimension((64+2)*size(m,1)) :: work ! block size of 64 taken from http://www.netlib.org/lapack/double/dsyev.f
external :: & external :: &
dsyev dsyev
vectors = m ! copy matrix to input (doubles as output) array vectors = m ! copy matrix to input (doubles as output) array
call dsyev('N','U',size(m,1),vectors,size(m,1),math_eigenvaluesSym,work,(64+2)*size(m,1),info) call dsyev('N','U',size(m,1),vectors,size(m,1),math_eigenvaluesSym,work,(64+2)*size(m,1),info)
if (info /= 0_pInt) math_eigenvaluesSym = IEEE_value(1.0_pReal,IEEE_quiet_NaN) if (info /= 0) math_eigenvaluesSym = IEEE_value(1.0_pReal,IEEE_quiet_NaN)
end function math_eigenvaluesSym end function math_eigenvaluesSym
@ -2294,19 +2292,19 @@ end function math_invariantsSym33
function halton(bases) function halton(bases)
implicit none implicit none
integer(pInt), intent(in), dimension(:):: & integer, intent(in), dimension(:):: &
bases !< bases (prime number ID) bases !< bases (prime number ID)
real(pReal), dimension(size(bases)) :: & real(pReal), dimension(size(bases)) :: &
halton halton
integer(pInt), save :: & integer, save :: &
current = 1_pInt current = 1
real(pReal), dimension(size(bases)) :: & real(pReal), dimension(size(bases)) :: &
base_inv base_inv
integer(pInt), dimension(size(bases)) :: & integer, dimension(size(bases)) :: &
base, & base, &
t t
integer(pInt), dimension(0:1600), parameter :: & integer, dimension(0:1600), parameter :: &
prime = int([& prime = [&
1, & 1, &
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, & 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, &
31, 37, 41, 43, 47, 53, 59, 61, 67, 71, & 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, &
@ -2482,9 +2480,9 @@ function halton(bases)
13121, 13127, 13147, 13151, 13159, 13163, 13171, 13177, 13183, 13187, & 13121, 13127, 13147, 13151, 13159, 13163, 13171, 13177, 13183, 13187, &
13217, 13219, 13229, 13241, 13249, 13259, 13267, 13291, 13297, 13309, & 13217, 13219, 13229, 13241, 13249, 13259, 13267, 13291, 13297, 13309, &
13313, 13327, 13331, 13337, 13339, 13367, 13381, 13397, 13399, 13411, & 13313, 13327, 13331, 13337, 13339, 13367, 13381, 13397, 13399, 13411, &
13417, 13421, 13441, 13451, 13457, 13463, 13469, 13477, 13487, 13499],pInt) 13417, 13421, 13441, 13451, 13457, 13463, 13469, 13477, 13487, 13499]
current = current + 1_pInt current = current + 1
base = prime(bases) base = prime(bases)
base_inv = 1.0_pReal/real(base,pReal) base_inv = 1.0_pReal/real(base,pReal)
@ -2492,7 +2490,7 @@ function halton(bases)
halton = 0.0_pReal halton = 0.0_pReal
t = current t = current
do while (any( t /= 0_pInt) ) do while (any( t /= 0) )
halton = halton + real(mod(t,base), pReal) * base_inv halton = halton + real(mod(t,base), pReal) * base_inv
base_inv = base_inv / real(base, pReal) base_inv = base_inv / real(base, pReal)
t = t / base t = t / base
@ -2504,11 +2502,11 @@ end function halton
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief factorial !> @brief factorial
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
integer(pInt) pure function math_factorial(n) integer pure function math_factorial(n)
implicit none implicit none
integer(pInt), intent(in) :: n integer, intent(in) :: n
integer(pInt) :: i integer :: i
math_factorial = product([(i, i=1,n)]) math_factorial = product([(i, i=1,n)])
@ -2518,11 +2516,11 @@ end function math_factorial
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief binomial coefficient !> @brief binomial coefficient
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
integer(pInt) pure function math_binomial(n,k) integer pure function math_binomial(n,k)
implicit none implicit none
integer(pInt), intent(in) :: n, k integer, intent(in) :: n, k
integer(pInt) :: i, j integer :: i, j
j = min(k,n-k) j = min(k,n-k)
math_binomial = product([(i, i=n, n-j+1, -1)])/math_factorial(j) math_binomial = product([(i, i=n, n-j+1, -1)])/math_factorial(j)
@ -2533,13 +2531,13 @@ end function math_binomial
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief multinomial coefficient !> @brief multinomial coefficient
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
integer(pInt) pure function math_multinomial(alpha) integer pure function math_multinomial(alpha)
implicit none implicit none
integer(pInt), intent(in), dimension(:) :: alpha integer, intent(in), dimension(:) :: alpha
integer(pInt) :: i integer :: i
math_multinomial = 1_pInt math_multinomial = 1
do i = 1, size(alpha) do i = 1, size(alpha)
math_multinomial = math_multinomial*math_binomial(sum(alpha(1:i)),alpha(i)) math_multinomial = math_multinomial*math_binomial(sum(alpha(1:i)),alpha(i))
enddo enddo
@ -2616,11 +2614,11 @@ pure function math_rotate_forward3333(tensor,rot_tensor)
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
integer(pInt) :: i,j,k,l,m,n,o,p integer :: i,j,k,l,m,n,o,p
math_rotate_forward3333 = 0.0_pReal math_rotate_forward3333 = 0.0_pReal
do i = 1_pInt,3_pInt;do j = 1_pInt,3_pInt;do k = 1_pInt,3_pInt;do l = 1_pInt,3_pInt do i = 1,3;do j = 1,3;do k = 1,3;do l = 1,3
do m = 1_pInt,3_pInt;do n = 1_pInt,3_pInt;do o = 1_pInt,3_pInt;do p = 1_pInt,3_pInt do m = 1,3;do n = 1,3;do o = 1,3;do p = 1,3
math_rotate_forward3333(i,j,k,l) & math_rotate_forward3333(i,j,k,l) &
= math_rotate_forward3333(i,j,k,l) & = math_rotate_forward3333(i,j,k,l) &
+ rot_tensor(i,m) * rot_tensor(j,n) * rot_tensor(k,o) * rot_tensor(l,p) * tensor(m,n,o,p) + rot_tensor(i,m) * rot_tensor(j,n) * rot_tensor(k,o) * rot_tensor(l,p) * tensor(m,n,o,p)