better make internal function
- not used - no check whether matrix is positive-definite, i.e. danger of NaN
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src/math.f90
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src/math.f90
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@ -961,12 +961,34 @@ subroutine math_eigh33(m,w,v)
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end subroutine math_eigh33
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!--------------------------------------------------------------------------------------------------
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!> @brief rotational part from polar decomposition of 3x3 tensor
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!--------------------------------------------------------------------------------------------------
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function math_rotationalPart(m)
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real(pReal), intent(in), dimension(3,3) :: m
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real(pReal), dimension(3,3) :: math_rotationalPart
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real(pReal), dimension(3,3) :: U , Uinv
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U = eigenvectorBasis(matmul(transpose(m),m))
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Uinv = math_inv33(U)
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inversionFailed: if (all(dEq0(Uinv))) then
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math_rotationalPart = math_I3
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call IO_warning(650)
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else inversionFailed
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math_rotationalPart = matmul(m,Uinv)
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endif inversionFailed
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contains
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!--------------------------------------------------------------------------------------------------
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!> @brief eigenvector basis of positive-definite 3x3 matrix
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!--------------------------------------------------------------------------------------------------
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pure function math_eigenvectorBasisSym33(m)
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pure function eigenvectorBasis(m)
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real(pReal), dimension(3,3) :: math_eigenvectorBasisSym33
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real(pReal), dimension(3,3) :: eigenvectorBasis
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real(pReal), dimension(3,3), intent(in) :: m !< positive-definite matrix of which the basis is computed
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real(pReal), dimension(3) :: I, v
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@ -1015,31 +1037,11 @@ pure function math_eigenvectorBasisSym33(m)
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endif twoSimilarEigVals
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endif threeSimilarEigVals
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math_eigenvectorBasisSym33 = sqrt(v(1)) * EB(1:3,1:3,1) &
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eigenvectorBasis = sqrt(v(1)) * EB(1:3,1:3,1) &
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+ sqrt(v(2)) * EB(1:3,1:3,2) &
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+ sqrt(v(3)) * EB(1:3,1:3,3)
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end function math_eigenvectorBasisSym33
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!--------------------------------------------------------------------------------------------------
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!> @brief rotational part from polar decomposition of 3x3 tensor
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!--------------------------------------------------------------------------------------------------
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function math_rotationalPart(m)
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real(pReal), intent(in), dimension(3,3) :: m
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real(pReal), dimension(3,3) :: math_rotationalPart
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real(pReal), dimension(3,3) :: U , Uinv
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U = math_eigenvectorBasisSym33(matmul(transpose(m),m))
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Uinv = math_inv33(U)
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inversionFailed: if (all(dEq0(Uinv))) then
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math_rotationalPart = math_I3
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call IO_warning(650)
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else inversionFailed
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math_rotationalPart = matmul(m,Uinv)
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endif inversionFailed
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end function eigenvectorBasis
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end function math_rotationalPart
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