rewrote _sampleXXXori functions
set of angles is now always an array
This commit is contained in:
Philip Eisenlohr
parent
656a6808bc
commit
836a22270a
813
trunk/math.f90
813
trunk/math.f90
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@ -1,5 +1,3 @@
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! MISSING agree on Rad as standard in/out
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! MISSING inverse 3x3 and 6x6
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!##############################################################
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MODULE math
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@ -32,7 +30,7 @@
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real(pReal), dimension(6), parameter :: invnrmMandel = &
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(/1.0_pReal,1.0_pReal,1.0_pReal,0.7071067811865476_pReal,0.7071067811865476_pReal,0.7071067811865476_pReal/)
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! *** Voigt notation ***
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integer(pInt), dimension (2,6), parameter :: mapMandel = &
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integer(pInt), dimension (2,6), parameter :: mapVoigt = &
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reshape((/&
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1,1, &
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2,2, &
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@ -58,15 +56,57 @@
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implicit none
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integer (pInt) seed
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real(pReal) poop(3)
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call random_seed()
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call get_seed(seed)
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call halton_seed_set(seed)
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call halton_ndim_set(3)
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poop = dabs((/1.0_8,2.34_8,534.2_8/))
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END SUBROUTINE
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!**************************************************************************
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! second rank identity tensor of specified dimension
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!**************************************************************************
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FUNCTION math_identity2nd(dimen)
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use prec, only: pReal, pInt
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implicit none
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integer(pInt) i,dimen
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real(pReal) math_identity2nd(dimen,dimen)
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math_identity2nd = 0.0_pReal
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forall (i=1:dimen) math_identity2nd(i,i) = 1.0_pReal
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return
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END FUNCTION
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!**************************************************************************
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! fourth rank identity tensor of specified dimension
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!**************************************************************************
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FUNCTION math_identity4th(dimen)
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use prec, only: pReal, pInt
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implicit none
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integer(pInt) i,j,k,l,dimen
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real(pReal) math_identity4th(dimen,dimen,dimen,dimen)
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forall (i=1:dimen,j=1:dimen,k=1:dimen,l=1:dimen) math_identity4th(i,j,k,l) = &
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0.5_pReal*(math_I3(i,k)*math_I3(j,k)+math_I3(i,l)*math_I3(j,k))
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return
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END FUNCTION
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!**************************************************************************
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! Cramer inversion of 3x3 matrix
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!**************************************************************************
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SUBROUTINE math_invert3x3(A, InvA, DetA, err)
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! Bestimmung der Determinanten und Inversen einer 3x3-Matrix
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@ -111,11 +151,12 @@
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InvA(3,3) = ( A(1,1) * A(2,2) - A(1,2) * A(2,1) ) / DetA
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RETURN
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END SUBROUTINE
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END SUBROUTINE math_invert3x3
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! ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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! ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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!**************************************************************************
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! Gauss elimination to invert 6x6 matrix
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!**************************************************************************
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SUBROUTINE math_invert6x6(A, InvA, AnzNegEW, err)
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! Invertieren einer 6x6-Matrix
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@ -340,10 +381,8 @@
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END SUBROUTINE Gauss
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!********************************************************************
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! calculate the determinant of a (3x3)
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! determinant of a 3x3 matrix
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!********************************************************************
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real(pReal) FUNCTION math_det3x3(m)
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@ -361,7 +400,7 @@
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!********************************************************************
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! convert a symmetric 3x3 matrix into Mandel vector 6x1
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! convert symmetric 3x3 matrix into Mandel vector 6x1
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!********************************************************************
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FUNCTION math_Mandel33to6(m33)
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@ -464,365 +503,263 @@
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END FUNCTION
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!********************************************************************
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! convert a symmetric 3,3 matrix into an array of 6
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! Euler angles from orientation matrix
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!********************************************************************
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FUNCTION math_33to6(m33)
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FUNCTION math_RtoEuler(R)
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use prec, only: pReal, pInt
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implicit none
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real(pReal), dimension(3,3) :: m33
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real(pReal), dimension(6) :: math_33to6
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real(pReal) R(3,3), sqhkl, squvw, sqhk, val
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real(pReal), dimension(3) :: math_RtoEuler
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math_33to6(1)=m33(1,1)
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math_33to6(2)=m33(2,2)
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math_33to6(3)=m33(3,3)
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math_33to6(4)=m33(1,2)
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math_33to6(5)=m33(2,3)
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math_33to6(6)=m33(1,3)
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return
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END FUNCTION
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!********************************************************************
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! This routine coverts an array of 6 into a symmetric 3,3 matrix
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!********************************************************************
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FUNCTION math_6to33(v6)
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use prec, only: pReal,pInt
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implicit none
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real(pReal) math_6to33(3,3), v6(6)
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math_6to33(1,1)=v6(1)
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math_6to33(2,2)=v6(2)
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math_6to33(3,3)=v6(3)
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math_6to33(1,2)=v6(4)
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math_6to33(2,1)=v6(4)
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math_6to33(2,3)=v6(5)
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math_6to33(3,2)=v6(5)
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math_6to33(1,3)=v6(6)
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math_6to33(3,1)=v6(6)
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return
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END FUNCTION
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!********************************************************************************
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!** This routine transforms the stiffness matrix **
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!********************************************************************************
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FUNCTION math_66to3333(C66)
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use prec, only: pReal, pInt
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implicit none
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real(pReal) C66(6,6), math_66to3333(3,3,3,3)
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math_66to3333(1,1,1,1)=C66(1,1)
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math_66to3333(1,1,2,2)=C66(1,2)
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math_66to3333(1,1,3,3)=C66(1,3)
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math_66to3333(1,1,2,3)=C66(1,4)
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math_66to3333(1,1,3,2)=C66(1,4)
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math_66to3333(1,1,1,3)=C66(1,5)
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math_66to3333(1,1,3,1)=C66(1,5)
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math_66to3333(1,1,1,2)=C66(1,6)
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math_66to3333(1,1,2,1)=C66(1,6)
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math_66to3333(2,2,1,1)=C66(2,1)
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math_66to3333(2,2,2,2)=C66(2,2)
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math_66to3333(2,2,3,3)=C66(2,3)
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math_66to3333(2,2,2,3)=C66(2,4)
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math_66to3333(2,2,3,2)=C66(2,4)
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math_66to3333(2,2,1,3)=C66(2,5)
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math_66to3333(2,2,3,1)=C66(2,5)
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math_66to3333(2,2,1,2)=C66(2,6)
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math_66to3333(2,2,2,1)=C66(2,6)
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math_66to3333(3,3,1,1)=C66(3,1)
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math_66to3333(3,3,2,2)=C66(3,2)
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math_66to3333(3,3,3,3)=C66(3,3)
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math_66to3333(3,3,2,3)=C66(3,4)
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math_66to3333(3,3,3,2)=C66(3,4)
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math_66to3333(3,3,1,3)=C66(3,5)
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math_66to3333(3,3,3,1)=C66(3,5)
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math_66to3333(3,3,1,2)=C66(3,6)
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math_66to3333(3,3,2,1)=C66(3,6)
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math_66to3333(2,3,1,1)=C66(4,1)
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math_66to3333(3,2,1,1)=C66(4,1)
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math_66to3333(2,3,2,2)=C66(4,2)
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math_66to3333(3,2,2,2)=C66(4,2)
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math_66to3333(2,3,3,3)=C66(4,3)
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math_66to3333(3,2,3,3)=C66(4,3)
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math_66to3333(2,3,2,3)=C66(4,4)
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math_66to3333(2,3,3,2)=C66(4,4)
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math_66to3333(3,2,2,3)=C66(4,4)
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math_66to3333(3,2,3,2)=C66(4,4)
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math_66to3333(2,3,3,1)=C66(4,5)
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math_66to3333(2,3,1,3)=C66(4,5)
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math_66to3333(2,3,3,1)=C66(4,5)
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math_66to3333(3,2,1,3)=C66(4,5)
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math_66to3333(2,3,1,2)=C66(4,6)
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math_66to3333(2,3,2,1)=C66(4,6)
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math_66to3333(3,2,1,2)=C66(4,6)
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math_66to3333(3,2,2,1)=C66(4,6)
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math_66to3333(3,1,1,1)=C66(5,1)
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math_66to3333(1,3,1,1)=C66(5,1)
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math_66to3333(3,1,2,2)=C66(5,2)
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math_66to3333(1,3,2,2)=C66(5,2)
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math_66to3333(3,1,3,3)=C66(5,3)
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math_66to3333(1,3,3,3)=C66(5,3)
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math_66to3333(3,1,2,3)=C66(5,4)
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math_66to3333(3,1,3,2)=C66(5,4)
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math_66to3333(1,3,2,3)=C66(5,4)
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math_66to3333(1,3,3,2)=C66(5,4)
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math_66to3333(3,1,3,1)=C66(5,5)
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math_66to3333(3,1,1,3)=C66(5,5)
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math_66to3333(1,3,3,1)=C66(5,5)
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math_66to3333(1,3,1,3)=C66(5,5)
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math_66to3333(3,1,1,2)=C66(5,6)
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math_66to3333(3,1,2,1)=C66(5,6)
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math_66to3333(1,3,1,2)=C66(5,6)
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math_66to3333(1,3,2,1)=C66(5,6)
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math_66to3333(1,2,1,1)=C66(6,1)
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math_66to3333(2,1,1,1)=C66(6,1)
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math_66to3333(1,2,2,2)=C66(6,2)
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math_66to3333(2,1,2,2)=C66(6,2)
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math_66to3333(1,2,3,3)=C66(6,3)
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math_66to3333(2,1,3,3)=C66(6,3)
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math_66to3333(1,2,2,3)=C66(6,4)
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math_66to3333(1,2,3,2)=C66(6,4)
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math_66to3333(2,1,2,3)=C66(6,4)
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math_66to3333(2,1,3,2)=C66(6,4)
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math_66to3333(1,2,3,1)=C66(6,5)
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math_66to3333(1,2,1,3)=C66(6,5)
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math_66to3333(2,1,3,1)=C66(6,5)
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math_66to3333(2,1,1,3)=C66(6,5)
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math_66to3333(1,2,1,2)=C66(6,6)
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math_66to3333(1,2,2,1)=C66(6,6)
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math_66to3333(2,1,1,2)=C66(6,6)
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math_66to3333(2,1,2,1)=C66(6,6)
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return
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END FUNCTION
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FUNCTION math_3333to66(C3333)
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!********************************************************************************
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!** This routine transforms the stiffness matrix **
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!********************************************************************************
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use prec, only: pReal, pInt
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implicit none
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real(pReal) math_3333to66(6,6), C3333(3,3,3,3)
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math_3333to66(1,1)=C3333(1,1,1,1)
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math_3333to66(1,2)=C3333(1,1,2,2)
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math_3333to66(1,3)=C3333(1,1,3,3)
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math_3333to66(1,4)=C3333(1,1,2,3)
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math_3333to66(1,5)=C3333(1,1,3,1)
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math_3333to66(1,6)=C3333(1,1,1,2)
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math_3333to66(2,1)=C3333(2,2,1,1)
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math_3333to66(2,2)=C3333(2,2,2,2)
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math_3333to66(2,3)=C3333(2,2,3,3)
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math_3333to66(2,4)=C3333(2,2,2,3)
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math_3333to66(2,5)=C3333(2,2,3,1)
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math_3333to66(2,6)=C3333(2,2,1,2)
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math_3333to66(3,1)=C3333(3,3,1,1)
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math_3333to66(3,2)=C3333(3,3,2,2)
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math_3333to66(3,3)=C3333(3,3,3,3)
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math_3333to66(3,4)=C3333(3,3,2,3)
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math_3333to66(3,5)=C3333(3,3,3,1)
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math_3333to66(3,6)=C3333(3,3,1,2)
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math_3333to66(4,1)=C3333(2,3,1,1)
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math_3333to66(4,2)=C3333(2,3,2,2)
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math_3333to66(4,3)=C3333(2,3,3,3)
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math_3333to66(4,4)=C3333(2,3,2,3)
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math_3333to66(4,5)=C3333(2,3,3,1)
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math_3333to66(4,6)=C3333(2,3,1,2)
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math_3333to66(5,1)=C3333(3,1,1,1)
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math_3333to66(5,2)=C3333(3,1,2,2)
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math_3333to66(5,3)=C3333(3,1,3,3)
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math_3333to66(5,4)=C3333(3,1,2,3)
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math_3333to66(5,5)=C3333(3,1,3,1)
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math_3333to66(5,6)=C3333(3,1,1,2)
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math_3333to66(6,1)=C3333(1,2,1,1)
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math_3333to66(6,2)=C3333(1,2,2,2)
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math_3333to66(6,3)=C3333(1,2,3,3)
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math_3333to66(6,4)=C3333(1,2,2,3)
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math_3333to66(6,5)=C3333(1,2,3,1)
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math_3333to66(6,6)=C3333(1,2,1,2)
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return
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END FUNCTION
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!********************************************************************
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! This routine calculates Euler angles from orientation matrix
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!********************************************************************
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SUBROUTINE math_RtoEuler(orimat, phi1, PHI, phi2)
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use prec, only: pReal, pInt
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implicit none
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real(pReal) orimat(3,3), phi1, PHI, phi2
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real(pReal) sqhkl, squvw, sqhk, val
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sqhkl=sqrt(orimat(1,3)*orimat(1,3)+orimat(2,3)*orimat(2,3)+orimat(3,3)*orimat(3,3))
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squvw=sqrt(orimat(1,1)*orimat(1,1)+orimat(2,1)*orimat(2,1)+orimat(3,1)*orimat(3,1))
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sqhk=sqrt(orimat(1,3)*orimat(1,3)+orimat(2,3)*orimat(2,3))
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sqhkl=sqrt(R(1,3)*R(1,3)+R(2,3)*R(2,3)+R(3,3)*R(3,3))
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squvw=sqrt(R(1,1)*R(1,1)+R(2,1)*R(2,1)+R(3,1)*R(3,1))
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sqhk=sqrt(R(1,3)*R(1,3)+R(2,3)*R(2,3))
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! calculate PHI
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val=orimat(3,3)/sqhkl
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val=R(3,3)/sqhkl
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if(val.GT.1.0_pReal) val=1.0_pReal
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if(val.LT.-1.0_pReal) val=-1.0_pReal
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if(val > 1.0_pReal) val = 1.0_pReal
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if(val < -1.0_pReal) val = -1.0_pReal
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PHI=acos(val)
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math_RtoEuler(2) = acos(val)
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if(PHI.LT.1.0e-30_pReal) then
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if(math_RtoEuler(2) < 1.0e-30_pReal) then
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! calculate phi2
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phi2=0.0
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math_RtoEuler(3) = 0.0_pReal
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! calculate phi1
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val=orimat(1,1)/squvw
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val=R(1,1)/squvw
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if(val > 1.0_pReal) val = 1.0_pReal
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if(val < -1.0_pReal) val = -1.0_pReal
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if(val.GT.1.0_pReal) val=1.0_pReal
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if(val.LT.-1.0_pReal) val=-1.0_pReal
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if(orimat(2,1).LE.0.0) then
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phi1=acos(val)
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else
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phi1=2.0_pReal*pi-acos(val)
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end if
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math_RtoEuler(1) = acos(val)
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if(R(2,1) > 0.0_pReal) math_RtoEuler(1) = 2.0_pReal*pi-math_RtoEuler(1)
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else
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! calculate phi2
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val=orimat(2,3)/sqhk
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val=R(2,3)/sqhk
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if(val > 1.0_pReal) val = 1.0_pReal
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if(val < -1.0_pReal) val = -1.0_pReal
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if(val.GT.1.0_pReal) val=1.0_pReal
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if(val.LT.-1.0_pReal) val=-1.0_pReal
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if(orimat(1,3).GE.0.0) then
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phi2=acos(val)
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else
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phi2=2.0_pReal*pi-acos(val)
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end if
|
||||
math_RtoEuler(3) = acos(val)
|
||||
if(R(1,3) < 0.0) math_RtoEuler(3) = 2.0_pReal*pi-math_RtoEuler(3)
|
||||
! calculate phi1
|
||||
val=-orimat(3,2)/sin(PHI)
|
||||
val=-R(3,2)/sin(math_RtoEuler(2))
|
||||
if(val > 1.0_pReal) val = 1.0_pReal
|
||||
if(val < -1.0_pReal) val = -1.0_pReal
|
||||
|
||||
if(val.GT.1.0_pReal) val=1.0_pReal
|
||||
if(val.LT.-1.0_pReal) val=-1.0_pReal
|
||||
|
||||
if(orimat(3,1).GE.0.0) then
|
||||
phi1=acos(val)
|
||||
else
|
||||
phi1=2.0_pReal*pi-acos(val)
|
||||
math_RtoEuler(1) = acos(val)
|
||||
if(R(3,1) < 0.0) math_RtoEuler(1) = 2.0_pReal*pi-math_RtoEuler(1)
|
||||
end if
|
||||
end if
|
||||
! convert angles to degrees
|
||||
phi1=phi1*inDeg
|
||||
PHI=PHI*inDeg
|
||||
phi2=phi2*inDeg
|
||||
return
|
||||
|
||||
END SUBROUTINE
|
||||
|
||||
|
||||
!#####################################################
|
||||
! bestimmt Drehmatrix DREH3 fuer Drehung um Omega um Achse (u,v,w)
|
||||
FUNCTION math_RodrigtoR(Omega,U,V,W)
|
||||
|
||||
use prec, only: pReal, pInt
|
||||
implicit none
|
||||
|
||||
real(pReal) omega, u, v, w, math_RodrigtoR(3,3)
|
||||
real(pReal) betrag, s, c, u2, v2, w2
|
||||
|
||||
BETRAG=SQRT(U**2+V**2+W**2)
|
||||
S=SIN(OMEGA)
|
||||
C=COS(OMEGA)
|
||||
U2=U/BETRAG
|
||||
V2=V/BETRAG
|
||||
W2=W/BETRAG
|
||||
math_RodrigtoR(1,1)=(1-U2**2)*C+U2**2
|
||||
math_RodrigtoR(1,2)=U2*V2*(1-C)+W2*S
|
||||
math_RodrigtoR(1,3)=U2*W2*(1-C)-V2*S
|
||||
math_RodrigtoR(2,1)=U2*V2*(1-C)-W2*S
|
||||
math_RodrigtoR(2,2)=(1-V2**2)*C+V2**2
|
||||
math_RodrigtoR(2,3)=V2*W2*(1-C)+U2*S
|
||||
math_RodrigtoR(3,1)=U2*W2*(1-C)+V2*S
|
||||
math_RodrigtoR(3,2)=V2*W2*(1-C)-U2*S
|
||||
math_RodrigtoR(3,3)=(1-W2**2)*C+W2**2
|
||||
return
|
||||
|
||||
END FUNCTION
|
||||
|
||||
! Best. Drehmatrix ROTA fuer Euler-Winkel
|
||||
|
||||
FUNCTION math_EulertoR (P1,P,P2)
|
||||
!****************************************************************
|
||||
! rotation matrix from axis and angle (in radians)
|
||||
!****************************************************************
|
||||
FUNCTION math_RodrigToR(axis,omega)
|
||||
|
||||
use prec, only: pReal, pInt
|
||||
implicit none
|
||||
|
||||
real(pReal) p1, p, p2, math_EulertoR(3,3)
|
||||
real(pReal) xp1, xp, xp2, c1, c, c2, s1, s, s2
|
||||
real(pReal), dimension(3) :: axis, axisNrm
|
||||
real(pReal), dimension(3,3) :: math_RodrigToR
|
||||
real(pReal) omega, s,c
|
||||
integer(pInt) i
|
||||
|
||||
XP1=P1*inRad
|
||||
XP=P*inRad
|
||||
XP2=P2*inRad
|
||||
C1=COS(XP1)
|
||||
C=COS(XP)
|
||||
C2=COS(XP2)
|
||||
S1=SIN(XP1)
|
||||
S=SIN(XP)
|
||||
S2=SIN(XP2)
|
||||
math_EulertoR(1,1)=C1*C2-S1*S2*C
|
||||
math_EulertoR(1,2)=S1*C2+C1*S2*C
|
||||
math_EulertoR(1,3)=S2*S
|
||||
math_EulertoR(2,1)=-C1*S2-S1*C2*C
|
||||
math_EulertoR(2,2)=-S1*S2+C1*C2*C
|
||||
math_EulertoR(2,3)=C2*S
|
||||
math_EulertoR(3,1)=S1*S
|
||||
math_EulertoR(3,2)=-C1*S
|
||||
math_EulertoR(3,3)=C
|
||||
forall (i=1:3) axisNrm(i) = axis(i)/sqrt(dot_product(axis,axis))
|
||||
s = sin(omega)
|
||||
c = cos(omega)
|
||||
math_RodrigtoR(1,1) = (1.0_pReal - axisNrm(1)**2)*c + axisNrm(1)**2
|
||||
math_RodrigtoR(1,2) = axisNrm(1)*axisNrm(2)*(1.0_pReal - c) + axisNrm(3)*s
|
||||
math_RodrigtoR(1,3) = axisNrm(1)*axisNrm(3)*(1.0_pReal - c) - axisNrm(2)*s
|
||||
math_RodrigtoR(2,1) = axisNrm(1)*axisNrm(2)*(1.0_pReal - c) - axisNrm(3)*s
|
||||
math_RodrigtoR(2,2) = (1.0_pReal - axisNrm(2)**2)*c + axisNrm(2)**2
|
||||
math_RodrigtoR(2,3) = axisNrm(2)*axisNrm(3)*(1.0_pReal - c) + axisNrm(1)*s
|
||||
math_RodrigtoR(3,1) = axisNrm(1)*axisNrm(3)*(1.0_pReal - c) + axisNrm(2)*s
|
||||
math_RodrigtoR(3,2) = axisNrm(2)*axisNrm(3)*(1.0_pReal - c) - axisNrm(1)*s
|
||||
math_RodrigtoR(3,3) = (1.0_pReal - axisNrm(3)**2)*c + axisNrm(3)**2
|
||||
return
|
||||
|
||||
END FUNCTION
|
||||
|
||||
|
||||
!****************************************************************
|
||||
! rotation matrix from Euler angles
|
||||
!****************************************************************
|
||||
FUNCTION math_EulerToR (Euler)
|
||||
|
||||
use prec, only: pReal, pInt
|
||||
implicit none
|
||||
|
||||
real(pReal), dimension(3) :: Euler
|
||||
real(pReal), dimension(3,3) :: math_EulerToR
|
||||
real(pReal) c1, c, c2, s1, s, s2
|
||||
|
||||
C1=COS(Euler(1))
|
||||
C=COS(Euler(2))
|
||||
C2=COS(Euler(3))
|
||||
S1=SIN(Euler(1))
|
||||
S=SIN(Euler(2))
|
||||
S2=SIN(Euler(3))
|
||||
math_EulerToR(1,1)=C1*C2-S1*S2*C
|
||||
math_EulerToR(1,2)=S1*C2+C1*S2*C
|
||||
math_EulerToR(1,3)=S2*S
|
||||
math_EulerToR(2,1)=-C1*S2-S1*C2*C
|
||||
math_EulerToR(2,2)=-S1*S2+C1*C2*C
|
||||
math_EulerToR(2,3)=C2*S
|
||||
math_EulerToR(3,1)=S1*S
|
||||
math_EulerToR(3,2)=-C1*S
|
||||
math_EulerToR(3,3)=C
|
||||
return
|
||||
|
||||
END FUNCTION
|
||||
|
||||
|
||||
!**************************************************************************
|
||||
! BERECHNUNG VON ORIENTIERUNGSBEZIEHUNGEN ZWISCHEN
|
||||
! ZWEI VORGEGEBENEN ORIENTIERUNGEN
|
||||
|
||||
function math_disorient(P1,P,P2)
|
||||
! disorientation angle between two sets of Euler angles
|
||||
!**************************************************************************
|
||||
function math_disorient(EulerA,EulerB)
|
||||
|
||||
use prec, only: pReal, pInt
|
||||
implicit none
|
||||
|
||||
real(pReal) D1(3,3),D2(3,3),P1(2),P(2),P2(2),D1T(3,3),DR(3,3)
|
||||
real(pReal) math_disorient, spur, sp, omega, alpha
|
||||
real(pReal), dimension(3):: EulerA,EulerB
|
||||
real(pReal), dimension(3,3) :: r
|
||||
real(pReal) math_disorient, tr
|
||||
|
||||
r = matmul(math_EulerToR(EulerB),transpose(math_EulerToR(EulerA)))
|
||||
tr = (r(1,1)+r(2,2)+r(3,3)-1.0_pReal)*0.4999999_pReal
|
||||
math_disorient = abs(0.5_pReal*pi-asin(tr))
|
||||
return
|
||||
|
||||
END FUNCTION
|
||||
|
||||
|
||||
!********************************************************************
|
||||
! draw a random sample from Euler space
|
||||
!********************************************************************
|
||||
FUNCTION math_sampleRandomOri()
|
||||
|
||||
use prec, only: pReal, pInt
|
||||
implicit none
|
||||
|
||||
real(pReal), dimension(3) :: math_sampleRandomOri, rnd
|
||||
|
||||
call halton(3,rnd)
|
||||
math_sampleRandomOri(1) = rnd(1)*2.0_pReal*pi
|
||||
math_sampleRandomOri(2) = acos(2.0_pReal*rnd(2)-1.0_pReal)
|
||||
math_sampleRandomOri(3) = rnd(3)*2.0_pReal*pi
|
||||
return
|
||||
|
||||
END FUNCTION
|
||||
|
||||
|
||||
!********************************************************************
|
||||
! draw a random sample from Gauss component
|
||||
! with noise (in radians) half-width
|
||||
!********************************************************************
|
||||
FUNCTION math_sampleGaussOri(center,noise)
|
||||
|
||||
use prec, only: pReal, pInt
|
||||
implicit none
|
||||
|
||||
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(5) :: rnd
|
||||
real(pReal) noise,scatter,cosScatter
|
||||
integer(pInt) i
|
||||
|
||||
! ERSTELLEN DER BEIDEN DMATRIZEN
|
||||
! Helming uses different distribution with Bessel functions
|
||||
! therefore the gauss scatter width has to be scaled differently
|
||||
scatter = 0.95_pReal * noise
|
||||
cosScatter = cos(scatter)
|
||||
|
||||
d1 = math_EulertoR(p1(1),P(1),p2(1))
|
||||
d2 = math_EulertoR(p1(2),P(2),p2(2))
|
||||
!****************************************************
|
||||
! BESTIMMUNG DER INVERSEN MATRIX ZUR ORIENTIERUNG 1:DM
|
||||
!****************************************************
|
||||
d1T=transpose(d1)
|
||||
!***********************************************************
|
||||
! MATRIZENMULTIPLIKATION DER MATRIZEN D2 UND DM=DR(I,J)
|
||||
!***********************************************************
|
||||
dr=matmul(d2,d1T)
|
||||
!*******************************
|
||||
! BESTIMMUNG DES ROTATIONSWINKELS
|
||||
!*******************************
|
||||
SPUR=DR(1,1)+DR(2,2)+DR(3,3)
|
||||
SP=(SPUR-1._pReal)*0.4999999_pReal
|
||||
OMEGA=PI*0.5_pReal-ASIN(SP)
|
||||
! Winkel in Grad umrechnen
|
||||
ALPHA=OMEGA*inDeg
|
||||
math_disorient=abs(alpha)
|
||||
do
|
||||
call halton(5,rnd)
|
||||
forall (i=1:3) rnd(i) = 2.0_pReal*rnd(i)-1.0_pReal ! expand 1:3 to range [-1,+1]
|
||||
disturb(1) = scatter * rnd(1) ! phi1
|
||||
disturb(2) = sign(1.0_pReal,rnd(2))*acos(cosScatter+(1.0_pReal-cosScatter)*rnd(4)) ! Phi
|
||||
disturb(3) = scatter * rnd(2) ! phi2
|
||||
if (rnd(5) <= exp(-1.0_pReal*(math_disorient(origin,disturb)/scatter)**2)) exit
|
||||
enddo
|
||||
math_sampleGaussOri = math_RtoEuler(matmul(math_EulerToR(disturb),math_EulerToR(center)))
|
||||
return
|
||||
|
||||
END FUNCTION
|
||||
|
||||
|
||||
!********************************************************************
|
||||
! draw a random sample from Fiber component
|
||||
! with noise (in radians)
|
||||
!********************************************************************
|
||||
FUNCTION math_sampleFiberOri(alpha,beta,noise)
|
||||
|
||||
use prec, only: pReal, pInt
|
||||
implicit none
|
||||
|
||||
real(pReal), dimension(3) :: math_sampleFiberOri, fiberInC,fiberInS,axis
|
||||
real(pReal), dimension(2) :: alpha,beta, rnd
|
||||
real(pReal), dimension(3,3) :: oRot,fRot,pRot
|
||||
real(pReal) noise, scatter, cos2Scatter, angle
|
||||
integer(pInt), dimension(2,3), parameter :: rotMap = reshape((/2,3, 3,1, 1,2/),(/2,3/))
|
||||
integer(pInt) i
|
||||
|
||||
! Helming uses different distribution with Bessel functions
|
||||
! therefore the gauss scatter width has to be scaled differently
|
||||
scatter = 0.95_pReal * noise
|
||||
cos2Scatter = cos(2.0_pReal*scatter)
|
||||
|
||||
! fiber axis in crystal coordinate system
|
||||
fiberInC(1)=sin(alpha(1))*cos(alpha(2))
|
||||
fiberInC(2)=sin(alpha(1))*sin(alpha(2))
|
||||
fiberInC(3)=cos(alpha(1))
|
||||
! fiber axis in sample coordinate system
|
||||
fiberInS(1)=sin(beta(1))*cos(beta(2))
|
||||
fiberInS(2)=sin(beta(1))*sin(beta(2))
|
||||
fiberInS(3)=cos(beta(1))
|
||||
|
||||
! ---# rotation matrix from sample to crystal system #---
|
||||
angle=-acos(dot_product(fiberInC,fiberInS))
|
||||
if(angle /= 0.0_pReal) then
|
||||
! rotation axis between sample and crystal system (cross product)
|
||||
forall(i=1:3) axis(i) = fiberInC(rotMap(1,i))*fiberInS(rotMap(2,i))-fiberInC(rotMap(2,i))*fiberInS(rotMap(1,i))
|
||||
oRot = math_RodrigtoR(axis,angle)
|
||||
else
|
||||
oRot = math_I3
|
||||
end if
|
||||
|
||||
! ---# rotation matrix about fiber axis (random angle) #---
|
||||
call halton(1,rnd)
|
||||
fRot = math_RodrigToR(fiberInS,axis(3)*2.0_pReal*pi)
|
||||
|
||||
! ---# rotation about random axis perpend to fiber #---
|
||||
! random axis pependicular to fiber axis
|
||||
call halton(2,axis)
|
||||
if (fiberInS(3) /= 0.0_pReal) then
|
||||
axis(3)=-(axis(1)*fiberInS(1)+axis(2)*fiberInS(2))/fiberInS(3)
|
||||
else if(fiberInS(2) /= 0.0_pReal) then
|
||||
axis(3)=axis(2)
|
||||
axis(2)=-(axis(1)*fiberInS(1)+axis(3)*fiberInS(3))/fiberInS(2)
|
||||
else if(fiberInS(1) /= 0.0_pReal) then
|
||||
axis(3)=axis(1)
|
||||
axis(1)=-(axis(2)*fiberInS(2)+axis(3)*fiberInS(3))/fiberInS(1)
|
||||
end if
|
||||
|
||||
! scattered rotation angle
|
||||
do
|
||||
call halton(2,rnd)
|
||||
angle = acos(cos2Scatter+(1.0_pReal-cos2Scatter)*rnd(1))
|
||||
if (rnd(2) <= exp(-1.0_pReal*(angle/scatter)**2)) exit
|
||||
enddo
|
||||
call halton(1,rnd)
|
||||
if (rnd(1) <= 0.5) angle = -angle
|
||||
pRot = math_RodrigtoR(axis,angle)
|
||||
|
||||
! ---# apply the three rotations #---
|
||||
math_sampleFiberOri = math_RtoEuler(matmul(pRot,matmul(fRot,oRot)))
|
||||
return
|
||||
|
||||
END FUNCTION
|
||||
|
|
@ -842,13 +779,8 @@
|
|||
ce=matmul(transpose(fe),fe)
|
||||
CALL math_spectral1(CE,EW1,EW2,EW3,EB1,EB2,EB3)
|
||||
U=DSQRT(EW1)*EB1+DSQRT(EW2)*EB2+DSQRT(EW3)*EB3
|
||||
UI=U
|
||||
call invert(UI,3,0,0,det,3)
|
||||
if (det.EQ.0) then
|
||||
ising=1
|
||||
return
|
||||
endif
|
||||
R=matmul(fe,ui)
|
||||
call math_invert3x3(U,UI,det,ising)
|
||||
if (ising==0) R=matmul(fe,ui)
|
||||
return
|
||||
|
||||
END SUBROUTINE
|
||||
|
|
@ -947,41 +879,6 @@
|
|||
END SUBROUTINE
|
||||
|
||||
|
||||
!**********************************************************************
|
||||
!**** EINHEITSMATRIX MIT dim DIAGONALELEMENTEN
|
||||
|
||||
FUNCTION math_identity2nd(dimen)
|
||||
|
||||
use prec, only: pReal, pInt
|
||||
implicit none
|
||||
|
||||
integer(pInt) i,dimen
|
||||
real(pReal) math_identity2nd(dimen,dimen)
|
||||
|
||||
math_identity2nd = 0.0_pReal
|
||||
forall (i=1:dimen) math_identity2nd(i,i) = 1.0_pReal
|
||||
return
|
||||
|
||||
END FUNCTION
|
||||
|
||||
!**********************************************************************
|
||||
!**** EINHEITSTENSOR 4th MIT dim "DIAGONAL"ELEMENTEN
|
||||
|
||||
FUNCTION math_identity4th(dimen)
|
||||
|
||||
use prec, only: pReal, pInt
|
||||
implicit none
|
||||
|
||||
integer(pInt) i,j,k,l,dimen
|
||||
real(pReal) math_identity4th(dimen,dimen,dimen,dimen)
|
||||
|
||||
forall (i=1:dimen,j=1:dimen,k=1:dimen,l=1:dimen) math_identity4th(i,j,k,l) = &
|
||||
0.5_pReal*(math_I3(i,k)*math_I3(j,k)+math_I3(i,l)*math_I3(j,k))
|
||||
return
|
||||
|
||||
END FUNCTION
|
||||
|
||||
|
||||
!**********************************************************************
|
||||
!**** HAUPTINVARIANTEN HI1M, HI2M, HI3M DER 3X3 MATRIX M
|
||||
|
||||
|
|
@ -992,7 +889,7 @@
|
|||
real(pReal) M(3,3),HI1M,HI2M,HI3M
|
||||
|
||||
HI1M=M(1,1)+M(2,2)+M(3,3)
|
||||
HI2M=(M(1,1)+M(2,2)+M(3,3))**2/2.0_pReal-(M(1,1)**2+M(2,2)**2+M(3,3)**2)/2.0_pReal-M(1,2)*M(2,1)-M(1,3)*M(3,1)-M(2,3)*M(3,2)
|
||||
HI2M=HI1M**2/2.0_pReal-(M(1,1)**2+M(2,2)**2+M(3,3)**2)/2.0_pReal-M(1,2)*M(2,1)-M(1,3)*M(3,1)-M(2,3)*M(3,2)
|
||||
HI3M=math_det3x3(M)
|
||||
! QUESTION: is 3rd equiv det(M) ?? if yes, use function math_det !agreed on YES
|
||||
return
|
||||
|
|
@ -1717,10 +1614,10 @@
|
|||
prime = npvec(n)
|
||||
else
|
||||
prime = 0
|
||||
write ( *, '(a)' ) ' '
|
||||
write ( *, '(a)' ) 'PRIME - Fatal error!'
|
||||
write ( *, '(a,i6)' ) ' Illegal prime index N = ', n
|
||||
write ( *, '(a,i6)' ) ' N must be between 0 and PRIME_MAX =',prime_max
|
||||
write ( 6, '(a)' ) ' '
|
||||
write ( 6, '(a)' ) 'PRIME - Fatal error!'
|
||||
write ( 6, '(a,i6)' ) ' Illegal prime index N = ', n
|
||||
write ( 6, '(a,i6)' ) ' N must be between 0 and PRIME_MAX =',prime_max
|
||||
call flush(6)
|
||||
stop
|
||||
end if
|
||||
|
|
@ -1730,175 +1627,5 @@
|
|||
END FUNCTION
|
||||
|
||||
|
||||
!********************************************************************
|
||||
! This routine generates a random orientation
|
||||
!********************************************************************
|
||||
subroutine math_random_ori (phi1, PHI, phi2, scatter)
|
||||
|
||||
use prec, only: pReal, pInt
|
||||
implicit none
|
||||
|
||||
real(pReal) phi1, PHI, phi2, scatter, x, y, z
|
||||
|
||||
call random_number(x)
|
||||
call random_number(y)
|
||||
call random_number(z)
|
||||
phi1=x*360.0_pReal
|
||||
PHI=acos(y)*inDeg
|
||||
phi2=z*360.0_pReal
|
||||
scatter=0.0_pReal
|
||||
return
|
||||
|
||||
END SUBROUTINE
|
||||
|
||||
|
||||
subroutine math_halton_ori (phi1, PHI, phi2, scatter)
|
||||
!********************************************************************
|
||||
! This routine generates a random orientation using Halton series
|
||||
!********************************************************************
|
||||
use prec, only: pReal, pInt
|
||||
implicit none
|
||||
|
||||
real(pReal) phi1, PHI, phi2, scatter, r(3)
|
||||
|
||||
call halton(3,r)
|
||||
phi1=r(1)*360.0_pReal
|
||||
PHI=acos(r(2))*inDeg
|
||||
phi2=r(3)*360.0_pReal
|
||||
scatter=0.0_pReal
|
||||
return
|
||||
|
||||
END SUBROUTINE
|
||||
|
||||
|
||||
!********************************************************************
|
||||
! This routine applies gaussian scatter to the texture components
|
||||
!********************************************************************
|
||||
subroutine math_disturbOri (phi1, PHI, phi2, scatter)
|
||||
|
||||
use prec, only: pReal, pInt
|
||||
implicit none
|
||||
|
||||
real(pReal) phi1, PHI, phi2, scatter
|
||||
real(pReal) orot(3,3), srot(3,3), p1(2), P(2), p2(2), rot(3,3)
|
||||
real(pReal) gscatter,scale,x,y,s,z,arg,angle,rand,gauss
|
||||
|
||||
p1(1)=0
|
||||
P(1)=0
|
||||
p2(1)=0
|
||||
|
||||
! Helming uses different distribution with Bessel functions
|
||||
! therefore the gauss scatter width has to be scaled differently
|
||||
gscatter=0.95*scatter
|
||||
scale=cos(gscatter*inRad)
|
||||
|
||||
100 call random_number(x)
|
||||
call random_number(y)
|
||||
call random_number(s)
|
||||
call random_number(z)
|
||||
x=x-0.5
|
||||
s=s-0.5
|
||||
z=z-0.5
|
||||
p1(2)=x*gscatter*2.0_pReal
|
||||
p2(2)=z*gscatter*2.0_pReal
|
||||
arg=scale+y*(1.0-scale)
|
||||
P(2)=sign(1.0_pReal,s)*acos(arg)*inDeg
|
||||
angle = math_disorient(p1,P,p2)
|
||||
call random_number(rand)
|
||||
gauss=exp(-1.0*(angle/gscatter)**2)
|
||||
if(gauss.LT.rand) then
|
||||
goto 100
|
||||
end if
|
||||
! calculate rotation matrix for rotation angles
|
||||
srot = math_EulertoR(p1(2),p(2),p2(2))
|
||||
! calculate rotation matrix for original euler angles
|
||||
orot = math_EulertoR(phi1,PHI,phi2)
|
||||
! rotate originial orientation matrix
|
||||
rot=matmul(srot,orot)
|
||||
! calculate Euler angles for new rotation matrix
|
||||
call math_RtoEuler(rot, phi1,PHI,phi2)
|
||||
return
|
||||
|
||||
END SUBROUTINE
|
||||
|
||||
|
||||
!********************************************************************
|
||||
! This routine computes one orientation of a fiber component
|
||||
!********************************************************************
|
||||
subroutine math_fiber(alpha1, alpha2,beta1,beta2,scatter,phi1,PHI,phi2)
|
||||
|
||||
use prec, only: pReal, pInt
|
||||
implicit none
|
||||
|
||||
real(pReal) alpha1, alpha2,beta1,beta2,scatter, phi1, PHI, phi2
|
||||
real(pReal) orot(3,3), srot(3,3), ac(3), as(3),ori(3,3), rrot(3,3)
|
||||
real(pReal) a1r,a2r,b1r,b2r,angle,axis_u,axis_v,axis_w,rand,x,y,z,gscatter,scale,gauss
|
||||
integer(pInt) i
|
||||
|
||||
! convert angles to radians
|
||||
a1r=alpha1*inRad
|
||||
a2r=alpha2*inRad
|
||||
b1r=beta1*inRad
|
||||
b2r=beta2*inRad
|
||||
! calculate fiber axis in crystal coordinate system
|
||||
ac(1)=sin(a1r)*cos(a2r)
|
||||
ac(2)=sin(a1r)*sin(a2r)
|
||||
ac(3)=cos(a1r)
|
||||
! calculate fiber axis in sample coordinate system
|
||||
as(1)=sin(b1r)*cos(b2r)
|
||||
as(2)=sin(b1r)*sin(b2r)
|
||||
as(3)=cos(b1r)
|
||||
! calculate rotation angle between sample and crystal system
|
||||
angle=-acos(dot_product(ac, as))
|
||||
if(angle.NE.0.0) then
|
||||
! calculate rotation axis between sample and crystal system
|
||||
axis_u=ac(2)*as(3)-ac(3)*as(2)
|
||||
axis_v=ac(3)*as(1)-ac(1)*as(3)
|
||||
axis_w=ac(1)*as(2)-ac(2)*as(1)
|
||||
! calculate rotation matrix
|
||||
orot = math_RodrigtoR(angle, axis_u, axis_v, axis_w)
|
||||
else
|
||||
orot = math_I3
|
||||
end if
|
||||
|
||||
! calculate random rotation angle about fiber axis
|
||||
call random_number(rand)
|
||||
angle=rand*2.0_pReal*pi
|
||||
rrot = math_RodrigtoR(angle, as(1), as(2), as(3))
|
||||
! find random axis pependicular to fiber axis
|
||||
call random_number(x)
|
||||
call random_number(y)
|
||||
if (as(3).NE.0) then
|
||||
z=-(x*as(1)+y*as(2))/as(3)
|
||||
else if(as(2).NE.0) then
|
||||
z=y
|
||||
y=-(x*as(1)+z*as(3))/as(2)
|
||||
else if(as(1).NE.0) then
|
||||
z=x
|
||||
x=-(y*as(2)+z*as(3))/as(1)
|
||||
end if
|
||||
! Helming uses different distribution with Bessel functions
|
||||
! therefore the gauss scatter width has to be scalled differently
|
||||
gscatter=0.95*scatter
|
||||
scale=cos(2*gscatter*inRad)
|
||||
! calculate rotation angle
|
||||
100 call random_number(rand)
|
||||
angle=sign(1.0_pReal,rand)*acos(abs(rand)*scale)*inDeg
|
||||
call random_number(rand)
|
||||
gauss=exp(-1.0*(angle/gscatter)**2)
|
||||
if(gauss.LT.rand) then
|
||||
goto 100
|
||||
end if
|
||||
! convert angle to radians
|
||||
angle=angle*inRad
|
||||
srot = math_RodrigtoR(angle, x, y, z)
|
||||
ori=matmul(srot, matmul(rrot, orot))
|
||||
! calculate Euler angles for new rotation matrix
|
||||
call math_RtoEuler(ori, phi1,PHI,phi2)
|
||||
|
||||
return
|
||||
END SUBROUTINE
|
||||
|
||||
|
||||
END MODULE math
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue