simplified and got MPI Heidelberg solution for eigenvalues/vectors back
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Martin Diehl
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code/math.f90
157
code/math.f90
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@ -150,8 +150,8 @@ module math
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math_sampleFiberOri, &
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math_sampleGaussVar, &
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math_symmetricEulers, &
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math_spectralDecompositionSym33, &
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math_spectralDecompositionSym, &
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math_eigenvectorBasisSym33, &
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math_eigenvectorBasisSym, &
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math_eigenValuesVectorsSym33, &
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math_eigenValuesVectorsSym, &
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math_rotationalPart33, &
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@ -1955,7 +1955,11 @@ end subroutine math_eigenValuesVectorsSym
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!--------------------------------------------------------------------------------------------------
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!> @brief eigenvalues and eigenvectors of symmetric 33 matrix m
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!> @brief eigenvalues and eigenvectors of symmetric 33 matrix m using an analytical expression
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!> and the general LAPACK powered version for arbritrary sized matrices as fallback
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!> @author Joachim Kopp, Max–Planck–Institut für Kernphysik, Heidelberg (Copyright (C) 2006)
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!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
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!> @details See http://arxiv.org/abs/physics/0610206 (DSYEVH3)
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!--------------------------------------------------------------------------------------------------
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subroutine math_eigenValuesVectorsSym33(m,values,vectors)
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@ -1963,76 +1967,100 @@ subroutine math_eigenValuesVectorsSym33(m,values,vectors)
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real(pReal), dimension(3,3),intent(in) :: m
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real(pReal), dimension(3), intent(out) :: values
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real(pReal), dimension(3,3),intent(out) :: vectors
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real(pReal) :: T, U, norm, threshold
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logical :: error
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integer(pInt) :: info
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real(pReal), dimension((64+2)*3) :: work ! block size of 64 taken from http://www.netlib.org/lapack/double/dsyev.f
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vectors = m ! copy matrix to input (doubles as output) array
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#if(FLOAT==8)
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call dsyev('V','U',3,vectors,3,values,work,(64+2)*3,info)
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#elif(FLOAT==4)
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call ssyev('V','U',3,vectors,3,values,work,(64+2)*3,info)
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#endif
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error = (info == 0_pInt)
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values = math_eigenvaluesSym33(m)
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vectors(1:3,2) = [ m(1, 2) * m(2, 3) - m(1, 3) * m(2, 2), &
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m(1, 3) * m(1, 2) - m(2, 3) * m(1, 1), &
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m(1, 2)**2_pInt]
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T = maxval(abs(values))
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U = max(T, T**2_pInt)
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threshold = sqrt(5.68e-14_pReal * U**2_pInt)
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! Calculate first eigenvector by the formula v[0] = (m - lambda[0]).e1 x (m - lambda[0]).e2
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vectors(1:3,1) = [ vectors(1,2) + m(1, 3) * values(1), &
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vectors(2,2) + m(2, 3) * values(1), &
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(m(1,1) - values(1)) * (m(2,2) - values(1)) - vectors(3,2)]
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norm = norm2(vectors(1:3, 1))
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fallback1: if(norm < threshold) then
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call math_eigenValuesVectorsSym(m,values,vectors,error)
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return
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endif fallback1
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vectors(1:3,1) = vectors(1:3, 1) / norm
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! Calculate second eigenvector by the formula v[1] = (m - lambda[1]).e1 x (m - lambda[1]).e2
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vectors(1:3,2) = [ vectors(1,2) + m(1, 3) * values(2), &
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vectors(2,2) + m(2, 3) * values(2), &
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(m(1,1) - values(2)) * (m(2,2) - values(2)) - vectors(3,2)]
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norm = norm2(vectors(1:3, 2))
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fallback2: if(norm < threshold) then
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call math_eigenValuesVectorsSym(m,values,vectors,error)
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return
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endif fallback2
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vectors(1:3,2) = vectors(1:3, 2) / norm
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! Calculate third eigenvector according to v[2] = v[0] x v[1]
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vectors(1:3,3) = math_crossproduct(vectors(1:3,1),vectors(1:3,2))
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end subroutine math_eigenValuesVectorsSym33
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!--------------------------------------------------------------------------------------------------
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!> @brief eigenvalues and eigenvectors of symmetric matrix m
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!> @brief eigenvector basis of symmetric matrix m
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!--------------------------------------------------------------------------------------------------
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function math_spectralDecompositionSym(m)
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function math_eigenvectorBasisSym(m)
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implicit none
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real(pReal), dimension(:,:), intent(in) :: m
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real(pReal), dimension(size(m,1)) :: values
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real(pReal), dimension(size(m,1),size(m,1)) :: vectors
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real(pReal), dimension(size(m,1),size(m,1)) :: math_spectralDecompositionSym
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real(pReal), dimension(size(m,1),size(m,1)) :: math_eigenvectorBasisSym
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logical :: error
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integer(pInt) :: i
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math_spectralDecompositionSym = 0.0_pReal
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math_eigenvectorBasisSym = 0.0_pReal
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call math_eigenValuesVectorsSym(m,values,vectors,error)
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if(error) return
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do i=1_pInt, size(m,1)
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math_spectralDecompositionSym = math_spectralDecompositionSym &
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math_eigenvectorBasisSym = math_eigenvectorBasisSym &
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+ sqrt(values(i)) * math_tensorproduct(vectors(:,i),vectors(:,i))
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enddo
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end function math_spectralDecompositionSym
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end function math_eigenvectorBasisSym
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!--------------------------------------------------------------------------------------------------
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!> @brief eigenvalues and eigenvectors of symmetric 33 matrix m
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!> @brief eigenvector basis of symmetric 33 matrix m
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!--------------------------------------------------------------------------------------------------
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function math_spectralDecompositionSym33(m)
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function math_eigenvectorBasisSym33(m)
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implicit none
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real(pReal), dimension(3,3) :: math_spectralDecompositionSym33
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real(pReal), dimension(3) :: invariants, values,C
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real(pReal), dimension(3,3) :: math_eigenvectorBasisSym33
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real(pReal), dimension(3) :: invariants, values
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real(pReal), dimension(3,3), intent(in) :: m
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real(pReal) :: P, Q, rho, phi
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real(pReal), parameter :: TOL=1.e-14_pReal
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real(pReal), dimension(3,3) :: M1, M2, M3,EB1, EB2, EB3
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real(pReal) :: D1, D2, D3
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real(pReal), dimension(3,3,3) :: N, EB
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invariants = math_invariantsSym33(m)
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EB = 0.0_pReal
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P = invariants(2)-invariants(1)**2.0_pReal/3.0_pReal
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Q=-2.0_pReal/27.0_pReal*invariants(1)**3.0_pReal+invariants(1)*invariants(2)/3.0_pReal-invariants(3)
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Q = -2.0_pReal/27.0_pReal*invariants(1)**3.0_pReal+product(invariants(1:2))/3.0_pReal-invariants(3)
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EB1=0.0_pReal
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EB2=0.0_pReal
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EB3=0.0_pReal
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if((ABS(P) < TOL).AND.(ABS(Q) < TOL)) then ! EV_2 = EV_1 = EV_3
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threeSimilarEigenvalues: if(all(abs([P,Q]) < TOL)) then
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values = invariants(1)/3.0_pReal
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! this is not really correct, but this way U is calculated
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! correctly in PDECOMPOSITION (correct is EB?=I)
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EB1(1,1)=1.0_pReal
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EB2(2,2)=1.0_pReal
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EB3(3,3)=1.0_pReal
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else
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! this is not really correct, but at least the basis is correct
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EB(1,1,1)=1.0_pReal
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EB(2,2,2)=1.0_pReal
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EB(3,3,3)=1.0_pReal
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else threeSimilarEigenvalues
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rho=sqrt(-3.0_pReal*P**3.0_pReal)/9.0_pReal
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phi=acos(math_limit(-Q/rho*0.5_pReal,-1.0_pReal,1.0_pReal))
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values = 2.0_pReal*rho**(1.0_pReal/3.0_pReal)* &
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@ -2040,35 +2068,36 @@ function math_spectralDecompositionSym33(m)
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cos((phi+2.0_pReal*PI)/3.0_pReal), &
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cos((phi+4.0_pReal*PI)/3.0_pReal) &
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] + invariants(1)/3.0_pReal
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C = abs([values(1)-values(2),values(2)-values(3),values(3)-values(1)])
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M1=M-values(1)*math_I3
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M2=M-values(2)*math_I3
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M3=M-values(3)*math_I3
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if (C(1) < TOL) then ! EV_2 = EV_1, no contribution from EV_2
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D3=1.0_pReal/(values(3)-values(1))/(values(3)-values(2))
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EB3=math_mul33x33(M1,M2)*D3
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EB1=math_I3-EB3
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elseif (C(2) < TOL) then ! EV_2 = EV_3, no contribution from EV_3
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D1=1.0_pReal/(values(1)-values(2))/(values(1)-values(3))
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EB1=math_mul33x33(M2,M3)*D1
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EB2=math_I3-EB1
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elseif(C(3) < TOL) then ! EV_1 = EV_3, no contribution from EV_3
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D2=1.0_pReal/(values(2)-values(1))/(values(2)-values(3))
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EB2=math_mul33x33(M1,M3)*D2
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EB1=math_I3-EB2
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else ! all three eigenvectors are different
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D1=1.0_pReal/(values(1)-values(2))/(values(1)-values(3))
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D2=1.0_pReal/(values(2)-values(1))/(values(2)-values(3))
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D3=1.0_pReal/(values(3)-values(1))/(values(3)-values(2))
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EB1=math_mul33x33(M2,M3)*D1
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EB2=math_mul33x33(M1,M3)*D2
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EB3=math_mul33x33(M1,M2)*D3
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endif
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endif
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N(1:3,1:3,1) = m-values(1)*math_I3
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N(1:3,1:3,2) = m-values(2)*math_I3
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N(1:3,1:3,3) = m-values(3)*math_I3
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twoSimilarEigenvalues: if(abs(values(1)-values(2)) < TOL) then
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EB(1:3,1:3,3)=math_mul33x33(N(1:3,1:3,1),N(1:3,1:3,2))/ &
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((values(3)-values(1))*(values(3)-values(2)))
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EB(1:3,1:3,1)=math_I3-EB(1:3,1:3,3)
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elseif(abs(values(2)-values(3)) < TOL) then twoSimilarEigenvalues
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EB(1:3,1:3,1)=math_mul33x33(N(1:3,1:3,2),N(1:3,1:3,3))/ &
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((values(1)-values(2))*(values(1)-values(3)))
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EB(1:3,1:3,2)=math_I3-EB(1:3,1:3,1)
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elseif(abs(values(3)-values(1)) < TOL) then twoSimilarEigenvalues
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EB(1:3,1:3,2)=math_mul33x33(N(1:3,1:3,1),N(1:3,1:3,3))/ &
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((values(2)-values(1))*(values(2)-values(3)))
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EB(1:3,1:3,1)=math_I3-EB(1:3,1:3,2)
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else twoSimilarEigenvalues
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EB(1:3,1:3,1)=math_mul33x33(N(1:3,1:3,2),N(1:3,1:3,3))/ &
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((values(1)-values(2))*(values(1)-values(3)))
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EB(1:3,1:3,2)=math_mul33x33(N(1:3,1:3,1),N(1:3,1:3,3))/ &
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((values(2)-values(1))*(values(2)-values(3)))
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EB(1:3,1:3,3)=math_mul33x33(N(1:3,1:3,1),N(1:3,1:3,2))/ &
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((values(3)-values(1))*(values(3)-values(2)))
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endif twoSimilarEigenvalues
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endif threeSimilarEigenvalues
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math_spectralDecompositionSym33 = sqrt(values(1)) * EB1 + sqrt(values(2)) * EB2 + sqrt(values(3)) * EB3
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math_eigenvectorBasisSym33 = sqrt(values(1)) * EB(1:3,1:3,1) &
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+ sqrt(values(2)) * EB(1:3,1:3,2) &
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+ sqrt(values(3)) * EB(1:3,1:3,3)
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end function math_spectralDecompositionSym33
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end function math_eigenvectorBasisSym33
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!--------------------------------------------------------------------------------------------------
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@ -2083,7 +2112,7 @@ function math_rotationalPart33(m)
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real(pReal), dimension(3,3) :: math_rotationalPart33
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real(pReal), dimension(3,3) :: U , Uinv
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U = math_spectralDecompositionSym33(math_mul33x33(transpose(m),m))
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U = math_eigenvectorBasisSym33(math_mul33x33(transpose(m),m))
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Uinv = math_inv33(U)
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if (all(abs(Uinv) <= tiny(Uinv))) then ! math_inv33 returns zero when failed, avoid floating point equality comparison
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@ -2143,7 +2172,7 @@ function math_eigenvaluesSym33(m)
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P = invariants(2)-invariants(1)**2.0_pReal/3.0_pReal
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Q = -2.0_pReal/27.0_pReal*invariants(1)**3.0_pReal+product(invariants(1:2))/3.0_pReal-invariants(3)
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if(any(abs([p,q]) < TOL)) then
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if(all(abs([P,Q]) < TOL)) then
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math_eigenvaluesSym33 = math_eigenvaluesSym(m)
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else
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rho=sqrt(-3.0_pReal*P**3.0_pReal)/9.0_pReal
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@ -1207,13 +1207,11 @@ subroutine plastic_disloUCLA_LpAndItsTangent(Lp,dLp_dTstar99,Tstar_v,Temperature
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math_Plain3333to99, &
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math_Mandel6to33, &
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math_Mandel33to6, &
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math_spectralDecompositionSym33, &
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math_symmetric33, &
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math_mul33x3
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use material, only: &
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material_phase, &
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phase_plasticityInstance, &
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!plasticState, &
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phaseAt, phasememberAt
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use lattice, only: &
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lattice_Sslip, &
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