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re-introduced special eigenvalues routine for 3x3 matrices

This commit is contained in:
Martin Diehl 2016-01-31 12:25:26 +01:00
parent 7474f4b25c
commit 9bc05acba2
2 changed files with 65 additions and 10 deletions
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64
code/math.f90
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@ -152,6 +152,7 @@ module math
math_sampleGaussVar, &
math_symmetricEulers, &
math_spectralDecompositionSym33, &
math_spectralDecompositionSym, &
math_rotationalPart33, &
math_invariants33, &
math_eigenvaluesSym33, &
@ -1910,9 +1911,9 @@ end function math_symmetricEulers
!--------------------------------------------------------------------------------------------------
!> @brief eigenvalues and eigenvectors of symmetric 3x3 matrix
!> @brief eigenvalues and eigenvectors of symmetric matrix m
!--------------------------------------------------------------------------------------------------
subroutine math_spectralDecompositionSym33(M,values,vectors,error)
subroutine math_spectralDecompositionSym(m,values,vectors,error)
implicit none
real(pReal), dimension(:,:), intent(in) :: m
@ -1931,6 +1932,63 @@ subroutine math_spectralDecompositionSym33(M,values,vectors,error)
#endif
error = (info == 0_pInt)
end subroutine math_spectralDecompositionSym
!--------------------------------------------------------------------------------------------------
!> @brief eigenvalues and eigenvectors of symmetric 3x3 matrix m using an analytical expression
!> and the general LAPACK powered version as fallback
!> @author Joachim Kopp, Max–Planck–Institut für Kernphysik, Heidelberg (Copyright (C) 2006)
!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
!> @details See http://arxiv.org/abs/physics/0610206 (DSYEVH3)
!--------------------------------------------------------------------------------------------------
subroutine math_spectralDecompositionSym33(m,values,vectors)
implicit none
real(pReal), dimension(3,3),intent(in) :: m
real(pReal), dimension(3), intent(out) :: values
real(pReal), dimension(3,3),intent(out) :: vectors
real(pReal) :: T, U, norm, threshold
logical :: error
values = math_eigenvaluesSym33(m)
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, 2)**2_pInt]
T = maxval(abs(values))
U = MAX(T, T**2_pInt)
threshold = sqrt(5.0e-14_pReal * U**2_pInt)
! 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(2,2) + m(2, 3) * values(1), &
(m(1,1) - values(1)) * (m(2,2) - values(1)) - vectors(3,2)]
norm = norm2(vectors(1:3, 1))
fallback1: if(norm < threshold) then
call math_spectralDecompositionSym(m,values,vectors,error)
return
endif fallback1
vectors(1:3,1) = vectors(1:3, 1) / norm
! Calculate second eigenvector by the formula v[1] = (m - lambda[1]).e1 x (m - lambda[1]).e2
vectors(1:3,2) = [ vectors(1,2) + m(1, 3) * values(2), &
vectors(2,2) + m(2, 3) * values(2), &
(m(1,1) - values(2)) * (m(2,2) - values(2)) - vectors(3,2)]
norm = norm2(vectors(1:3, 2))
fallback2: if(norm < threshold) then
call math_spectralDecompositionSym(m,values,vectors,error)
return
endif fallback2
vectors(1:3,2) = vectors(1:3, 2) / norm
! Calculate third eigenvector according to v[2] = v[0] x v[1]
vectors(1:3,3) = math_crossproduct(vectors(1:3,1),vectors(1:3,2))
end subroutine math_spectralDecompositionSym33
@ -1950,7 +2008,7 @@ function math_rotationalPart33(m)
mSquared = math_mul33x33(math_transpose33(m),m)
call math_spectralDecompositionSym33(mSquared,EV,EB,error)
call math_spectralDecompositionSym33(mSquared,EV,EB)
U = sqrt(EV(1)) * math_tensorproduct33(EB(1:3,1),EB(1:3,1)) &
+ sqrt(EV(2)) * math_tensorproduct33(EB(1:3,2),EB(1:3,2)) &

11
code/plastic_dislotwin.f90
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@ -1702,7 +1702,6 @@ subroutine plastic_dislotwin_LpAndItsTangent(Lp,dLp_dTstar99,Tstar_v,Temperature
0, 1,-1, &
0, 1, 1 &
],pReal),[ 3,6])
logical error
!* Shortened notation
of = phasememberAt(ipc,ip,el)
ph = phaseAt(ipc,ip,el)
@ -1783,7 +1782,7 @@ subroutine plastic_dislotwin_LpAndItsTangent(Lp,dLp_dTstar99,Tstar_v,Temperature
abs(plastic_dislotwin_sbResistance(instance)) > tiny(0.0_pReal)) then
gdot_sb = 0.0_pReal
dgdot_dtausb = 0.0_pReal
call math_spectralDecompositionSym33(math_Mandel6to33(Tstar_v),eigValues,eigVectors, error)
call math_spectralDecompositionSym33(math_Mandel6to33(Tstar_v),eigValues,eigVectors)
do j = 1_pInt,6_pInt
sb_s = 0.5_pReal*sqrt(2.0_pReal)*math_mul33x3(eigVectors,sb_sComposition(1:3,j))
sb_m = 0.5_pReal*sqrt(2.0_pReal)*math_mul33x3(eigVectors,sb_mComposition(1:3,j))
@ -2197,6 +2196,7 @@ function plastic_dislotwin_postResults(Tstar_v,Temperature,ipc,ip,el)
use math, only: &
pi, &
math_Mandel6to33, &
math_eigenvaluesSym33, &
math_spectralDecompositionSym33
use material, only: &
material_phase, &
@ -2240,8 +2240,6 @@ function plastic_dislotwin_postResults(Tstar_v,Temperature,ipc,ip,el)
gdot_slip
real(pReal), dimension(3,3) :: eigVectors
real(pReal), dimension (3) :: eigValues
logical :: error
!* Shortened notation
of = phasememberAt(ipc,ip,el)
@ -2517,11 +2515,10 @@ function plastic_dislotwin_postResults(Tstar_v,Temperature,ipc,ip,el)
enddo ; enddo
c = c + ns
case (sb_eigenvalues_ID)
call math_spectralDecompositionSym33(math_Mandel6to33(Tstar_v),eigValues,eigVectors, error)
plastic_dislotwin_postResults(c+1_pInt:c+3_pInt) = eigValues
plastic_dislotwin_postResults(c+1_pInt:c+3_pInt) = math_eigenvaluesSym33(math_Mandel6to33(Tstar_v))
c = c + 3_pInt
case (sb_eigenvectors_ID)
call math_spectralDecompositionSym33(math_Mandel6to33(Tstar_v),eigValues,eigVectors, error)
call math_spectralDecompositionSym33(math_Mandel6to33(Tstar_v),eigValues,eigVectors)
plastic_dislotwin_postResults(c+1_pInt:c+9_pInt) = reshape(eigVectors,[9])
c = c + 9_pInt
case (stress_trans_fraction_ID)