unified documentation and variable names
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Martin Diehl
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src/math.f90
80
src/math.f90
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@ -435,7 +435,7 @@ end function math_exp33
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!--------------------------------------------------------------------------------------------------
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!> @brief Cramer inversion of 33 matrix (function)
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!> @brief Cramer inversion of 3x3 matrix (function)
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!> @details Direct Cramer inversion of matrix A. Returns all zeroes if not possible, i.e.
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! if determinant is close to zero
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!--------------------------------------------------------------------------------------------------
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@ -454,7 +454,7 @@ end function math_inv33
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!--------------------------------------------------------------------------------------------------
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!> @brief Cramer inversion of 33 matrix (subroutine)
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!> @brief Cramer inversion of 3x3 matrix (subroutine)
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!> @details Direct Cramer inversion of matrix A. Also returns determinant
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! Returns an error if not possible, i.e. if determinant is close to zero
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!--------------------------------------------------------------------------------------------------
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@ -491,7 +491,7 @@ end subroutine math_invert33
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!--------------------------------------------------------------------------------------------------
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!> @brief Inversion of symmetriced 3x3x3x3 tensor.
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!> @brief Inversion of symmetriced 3x3x3x3 matrix
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!--------------------------------------------------------------------------------------------------
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function math_invSym3333(A)
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@ -548,7 +548,7 @@ end subroutine math_invert
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!--------------------------------------------------------------------------------------------------
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!> @brief symmetrize a 33 matrix
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!> @brief symmetrize a 3x3 matrix
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!--------------------------------------------------------------------------------------------------
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pure function math_symmetric33(m)
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@ -561,7 +561,7 @@ end function math_symmetric33
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!--------------------------------------------------------------------------------------------------
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!> @brief symmetrize a 66 matrix
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!> @brief symmetrize a 6x6 matrix
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!--------------------------------------------------------------------------------------------------
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pure function math_symmetric66(m)
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@ -574,7 +574,7 @@ end function math_symmetric66
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!--------------------------------------------------------------------------------------------------
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!> @brief skew part of a 33 matrix
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!> @brief skew part of a 3x3 matrix
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!--------------------------------------------------------------------------------------------------
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pure function math_skew33(m)
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@ -587,7 +587,7 @@ end function math_skew33
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!--------------------------------------------------------------------------------------------------
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!> @brief hydrostatic part of a 33 matrix
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!> @brief hydrostatic part of a 3x3 matrix
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!--------------------------------------------------------------------------------------------------
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pure function math_spherical33(m)
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@ -600,7 +600,7 @@ end function math_spherical33
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!--------------------------------------------------------------------------------------------------
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!> @brief deviatoric part of a 33 matrix
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!> @brief deviatoric part of a 3x3 matrix
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!--------------------------------------------------------------------------------------------------
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pure function math_deviatoric33(m)
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@ -613,7 +613,7 @@ end function math_deviatoric33
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!--------------------------------------------------------------------------------------------------
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!> @brief trace of a 33 matrix
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!> @brief trace of a 3x3 matrix
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!--------------------------------------------------------------------------------------------------
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real(pReal) pure function math_trace33(m)
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@ -625,7 +625,7 @@ end function math_trace33
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!--------------------------------------------------------------------------------------------------
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!> @brief determinant of a 33 matrix
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!> @brief determinant of a 3x3 matrix
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!--------------------------------------------------------------------------------------------------
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real(pReal) pure function math_det33(m)
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@ -639,7 +639,7 @@ end function math_det33
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!--------------------------------------------------------------------------------------------------
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!> @brief determinant of a symmetric 33 matrix
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!> @brief determinant of a symmetric 3x3 matrix
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!--------------------------------------------------------------------------------------------------
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real(pReal) pure function math_detSym33(m)
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@ -652,7 +652,7 @@ end function math_detSym33
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!--------------------------------------------------------------------------------------------------
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!> @brief convert 33 matrix into vector 9
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!> @brief convert 3x3 matrix into vector 9
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!--------------------------------------------------------------------------------------------------
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pure function math_33to9(m33)
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@ -669,7 +669,7 @@ end function math_33to9
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!--------------------------------------------------------------------------------------------------
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!> @brief convert 9 vector into 33 matrix
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!> @brief convert 9 vector into 3x3 matrix
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!--------------------------------------------------------------------------------------------------
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pure function math_9to33(v9)
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@ -686,7 +686,7 @@ end function math_9to33
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!--------------------------------------------------------------------------------------------------
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!> @brief convert symmetric 33 matrix into 6 vector
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!> @brief convert symmetric 3x3 matrix into 6 vector
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!> @details Weighted conversion (default) rearranges according to Nye and weights shear
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! components according to Mandel. Advisable for matrix operations.
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! Unweighted conversion only changes order according to Nye
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@ -714,7 +714,7 @@ end function math_sym33to6
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!--------------------------------------------------------------------------------------------------
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!> @brief convert 6 vector into symmetric 33 matrix
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!> @brief convert 6 vector into symmetric 3x3 matrix
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!> @details Weighted conversion (default) rearranges according to Nye and weights shear
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! components according to Mandel. Advisable for matrix operations.
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! Unweighted conversion only changes order according to Nye
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@ -743,7 +743,7 @@ end function math_6toSym33
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!--------------------------------------------------------------------------------------------------
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!> @brief convert 3333 matrix into 99 matrix
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!> @brief convert 3x3x3x3 matrix into 9x9 matrix
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!--------------------------------------------------------------------------------------------------
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pure function math_3333to99(m3333)
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@ -760,7 +760,7 @@ end function math_3333to99
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!--------------------------------------------------------------------------------------------------
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!> @brief convert 99 matrix into 3333 matrix
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!> @brief convert 9x9 matrix into 3x3x3x3 matrix
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!--------------------------------------------------------------------------------------------------
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pure function math_99to3333(m99)
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@ -777,7 +777,7 @@ end function math_99to3333
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!--------------------------------------------------------------------------------------------------
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!> @brief convert symmetric 3333 matrix into 66 matrix
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!> @brief convert symmetric 3x3x3x3 matrix into 6x6 matrix
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!> @details Weighted conversion (default) rearranges according to Nye and weights shear
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! components according to Mandel. Advisable for matrix operations.
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! Unweighted conversion only rearranges order according to Nye
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@ -805,7 +805,7 @@ end function math_sym3333to66
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!--------------------------------------------------------------------------------------------------
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!> @brief convert 66 matrix into symmetric 3333 matrix
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!> @brief convert 66 matrix into symmetric 3x3x3x3 matrix
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!> @details Weighted conversion (default) rearranges according to Nye and weights shear
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! components according to Mandel. Advisable for matrix operations.
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! Unweighted conversion only rearranges order according to Nye
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@ -836,7 +836,7 @@ end function math_66toSym3333
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!--------------------------------------------------------------------------------------------------
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!> @brief convert 66 Voigt matrix into symmetric 3333 matrix
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!> @brief convert 66 Voigt matrix into symmetric 3x3x3x3 matrix
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!--------------------------------------------------------------------------------------------------
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pure function math_Voigt66to3333(m66)
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@ -889,7 +889,7 @@ end function math_sampleGaussVar
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!--------------------------------------------------------------------------------------------------
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!> @brief eigenvalues and eigenvectors of symmetric matrix m
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!> @brief eigenvalues and eigenvectors of symmetric matrix
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! ToDo: has wrong oder of arguments
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!--------------------------------------------------------------------------------------------------
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subroutine math_eigh(m,w,v,error)
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@ -912,7 +912,7 @@ end subroutine math_eigh
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!--------------------------------------------------------------------------------------------------
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!> @brief eigenvalues and eigenvectors of symmetric 33 matrix m using an analytical expression
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!> @brief eigenvalues and eigenvectors of symmetric 3x3 matrix 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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@ -962,26 +962,26 @@ end subroutine math_eigh33
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!--------------------------------------------------------------------------------------------------
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!> @brief eigenvector basis of symmetric 33 matrix m
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!> @brief eigenvector basis of symmetric 3x3 matrix
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!--------------------------------------------------------------------------------------------------
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pure function math_eigenvectorBasisSym33(m)
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real(pReal), dimension(3,3) :: math_eigenvectorBasisSym33
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real(pReal), dimension(3,3), intent(in) :: m !< quadratic matrix of which the eigenvector basis is computed
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real(pReal), dimension(3) :: invariants, v
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real(pReal), dimension(3) :: I, v
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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(3,3,3) :: N, EB
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invariants = math_invariantsSym33(m)
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I = 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+product(invariants(1:2))/3.0_pReal-invariants(3)
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P = I(2)-I(1)**2.0_pReal/3.0_pReal
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Q = -2.0_pReal/27.0_pReal*I(1)**3.0_pReal+product(I(1:2))/3.0_pReal-I(3)
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threeSimilarEigVals: if(all(abs([P,Q]) < TOL)) then
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v = invariants(1)/3.0_pReal
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v = I(1)/3.0_pReal
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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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@ -992,7 +992,7 @@ pure function math_eigenvectorBasisSym33(m)
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v = 2.0_pReal*rho**(1.0_pReal/3.0_pReal)* [cos((phi )/3.0_pReal), &
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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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] + I(1)/3.0_pReal
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N(1:3,1:3,1) = m-v(1)*math_I3
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N(1:3,1:3,2) = m-v(2)*math_I3
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N(1:3,1:3,3) = m-v(3)*math_I3
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@ -1020,7 +1020,7 @@ end function math_eigenvectorBasisSym33
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!--------------------------------------------------------------------------------------------------
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!> @brief rotational part from polar decomposition of 33 tensor m
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!> @brief rotational part from polar decomposition of 3x3 tensor
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!--------------------------------------------------------------------------------------------------
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function math_rotationalPart33(m)
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@ -1042,7 +1042,7 @@ end function math_rotationalPart33
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!--------------------------------------------------------------------------------------------------
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!> @brief Eigenvalues of symmetric matrix m
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!> @brief Eigenvalues of symmetric matrix
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! will return NaN on error
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!--------------------------------------------------------------------------------------------------
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function math_eigvalsh(m)
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@ -1064,7 +1064,7 @@ end function math_eigvalsh
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!--------------------------------------------------------------------------------------------------
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!> @brief eigenvalues of symmetric 33 matrix m using an analytical expression
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!> @brief eigenvalues of symmetric 3x3 matrix using an analytical expression
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!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
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!> @details similar to http://arxiv.org/abs/physics/0610206 (DSYEVC3)
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!> but apparently more stable solution and has general LAPACK powered version for arbritrary sized
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@ -1073,16 +1073,16 @@ end function math_eigvalsh
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function math_eigvalsh33(m)
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real(pReal), intent(in), dimension(3,3) :: m !< 3x3 symmetric matrix to compute eigenvalues of
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real(pReal), dimension(3) :: math_eigvalsh33,invariants
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real(pReal), dimension(3) :: math_eigvalsh33,I
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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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invariants = math_invariantsSym33(m) ! invariants are coefficients in characteristic polynomial apart for the sign of c0 and c2 in http://arxiv.org/abs/physics/0610206
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I = math_invariantsSym33(m) ! invariants are coefficients in characteristic polynomial apart for the sign of c0 and c2 in http://arxiv.org/abs/physics/0610206
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P = invariants(2)-invariants(1)**2.0_pReal/3.0_pReal ! different from http://arxiv.org/abs/physics/0610206 (this formulation was in DAMASK)
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Q = product(invariants(1:2))/3.0_pReal &
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- 2.0_pReal/27.0_pReal*invariants(1)**3.0_pReal &
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- invariants(3) ! different from http://arxiv.org/abs/physics/0610206 (this formulation was in DAMASK)
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P = I(2)-I(1)**2.0_pReal/3.0_pReal ! different from http://arxiv.org/abs/physics/0610206 (this formulation was in DAMASK)
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Q = product(I(1:2))/3.0_pReal &
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- 2.0_pReal/27.0_pReal*I(1)**3.0_pReal &
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- I(3) ! different from http://arxiv.org/abs/physics/0610206 (this formulation was in DAMASK)
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if(all(abs([P,Q]) < TOL)) then
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math_eigvalsh33 = math_eigvalsh(m)
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@ -1094,14 +1094,14 @@ function math_eigvalsh33(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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] &
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+ invariants(1)/3.0_pReal
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+ I(1)/3.0_pReal
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endif
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end function math_eigvalsh33
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!--------------------------------------------------------------------------------------------------
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!> @brief invariants of symmetrix 33 matrix m
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!> @brief invariants of symmetrix 3x3 matrix
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!--------------------------------------------------------------------------------------------------
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pure function math_invariantsSym33(m)
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