needed cleaning and copyright
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Martin Diehl
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@ -2004,8 +2004,6 @@ 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, mSquared , Uinv, EB
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real(pReal), dimension(3) :: EV
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logical :: error
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mSquared = math_mul33x33(math_transpose33(m),m)
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call math_spectralDecompositionSym33(mSquared,EV,EB)
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@ -2026,16 +2024,16 @@ end function math_rotationalPart33
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!--------------------------------------------------------------------------------------------------
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!> @brief Eigenvalues of symmetric 3X3 matrix m
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!> @brief Eigenvalues of symmetric matrix m
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! will return NaN on error
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!--------------------------------------------------------------------------------------------------
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function math_eigenvaluesSym33(m)
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function math_eigenvaluesSym(m)
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use prec, only: &
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DAMASK_NaN
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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)) :: math_eigenvaluesSym33
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real(pReal), dimension(size(m,1)) :: math_eigenvaluesSym
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real(pReal), dimension(size(m,1),size(m,1)) :: vectors
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integer(pInt) :: info
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@ -2043,49 +2041,47 @@ function math_eigenvaluesSym33(m)
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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('N','U',size(m,1),vectors,size(m,1),math_eigenvaluesSym33,work,(64+2)*size(m,1),info)
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call dsyev('N','U',size(m,1),vectors,size(m,1),math_eigenvaluesSym,work,(64+2)*size(m,1),info)
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#elif(FLOAT==4)
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call ssyev('N','U',size(m,1),vectors,size(m,1),math_eigenvaluesSym33,work,(64+2)*size(m,1),info)
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call ssyev('N','U',size(m,1),vectors,size(m,1),math_eigenvaluesSym,work,(64+2)*size(m,1),info)
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#endif
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if (info /= 0_pInt) math_eigenvaluesSym33 = DAMASK_NaN
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if (info /= 0_pInt) math_eigenvaluesSym = DAMASK_NaN
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end function math_eigenvaluesSym
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!--------------------------------------------------------------------------------------------------
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!> @brief eigenvalues of symmetric 3x3 matrix m using an analytical expression
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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 (DSYEVC3)
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!--------------------------------------------------------------------------------------------------
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function math_eigenvaluesSym33(m)
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implicit none
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real(pReal), dimension(3,3), intent(in) :: m
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real(pReal), dimension(3) :: math_eigenvaluesSym33
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real(pReal) :: C1, C0
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real(pReal) :: P, Q, C, S, PHI
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C1 = m(1,1)*m(2,2) + m(1,1)*m(3,3) + m(2,2)*m(3,3) &
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-(m(1,2)**2 + m(2,3)**2 +m(1,3)**2)
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C0 = m(3,3)*m(1,2)**2 + m(1,1)*m(2,3)**2 + m(2,2)*m(2,3)**2 &
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-(m(1,1)*m(2,2)*m(3,3) + 2.0_pReal * m(1,3)*m(1,2)*m(2,3))
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P = math_trace33(m)**2 - 3.0_pReal * C1
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Q = math_trace33(m)*(P - (3.0_pReal/2.0_pReal)*C1) - (27.0_pReal/2.0_pReal)*C0
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PHI = atan2(sqrt(abs(27.0_pReal * (0.25_pReal*C1**2 *(P-C1) +C0 *(Q + (27.0_pReal/4.0_pReal)*C0) ))), Q)&
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*(1.0_pReal/3.0_pReal)
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C = sqrt(abs(P)) * cos(PHI)
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S = (1.0_pReal/sqrt(3.0_pReal)) * sqrt(abs(P)) * sin(PHI)
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math_eigenvaluesSym33 = [C,-S,C] + (1.0_pReal/3.0_pReal) * (math_trace33(m) - C)
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end function math_eigenvaluesSym33
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!--------------------------------------------------------------------------------------------------
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!> @brief Eigenvalues of symmetric 3X3 matrix m
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! will return NaN on error
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!--------------------------------------------------------------------------------------------------
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!function math_eigenvaluesSym33(m)
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! use prec, only: &
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! DAMASK_NaN
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!
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! implicit none
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! real(pReal), dimension(3,3), intent(in) :: m
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! real(pReal), dimension(3) :: math_eigenvaluesSym33
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!
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! real(pReal) :: C1, C0
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! real(pReal) :: P, Q, C, S, PHI
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!
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!! Determine coefficients of characteristic poynomial. We write
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!
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! C1 = m(1,1)*m(2,2) + m(1,1)*m(3,3) + m(2,2)*m(3,3) &
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! -(m(1,2)**2 + m(2,3)**2 +m(1,3)**2)
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! C0 = m(3,3)*m(1,2)**2 + m(1,1)*m(2,3)**2 + m(2,2)*m(2,3)**2 &
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! - m(1,1)*m(2,2)*m(3,3) - 2.0_pReal * m(1,3)*m(1,2)*m(2,3)
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!
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! P = math_trace33(m)**2 - 3.0_pReal * C1
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! Q = math_trace33(m)*(P - (3.0_pReal/2.0_pReal)*C1) - (27.0_pReal/2.0_pReal)*C0
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!
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! PHI = 27.0_pReal * ( 0.25_pReal * C1**2 * (P - C1) + C0 * (Q + (27.0_pReal/4.0_pReal)*C0) )
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! PHI = (1.0_pReal/3.0_pReal) * ATAN2(SQRT(ABS(PHI)), Q)
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!
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! C = sqrt(abs(P)) * COS(PHI)
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! S = (1.0_pReal/sqrt(3.0_pReal)) * sqrt(abs(P)) * SIN(PHI)
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!
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! math_eigenvaluesSym33 = [C,-S,C] + (1.0_pReal/3.0_pReal) * (math_trace33(m) - C)
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!
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!end function math_eigenvaluesSym33
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!--------------------------------------------------------------------------------------------------
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!> @brief invariants of matrix m
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!--------------------------------------------------------------------------------------------------
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