better make internal function
- not used - no check whether matrix is positive-definite, i.e. danger of NaN
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Martin Diehl
parent
8c78347a8b
commit
5b71f1050f
122
src/math.f90
122
src/math.f90
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@ -961,65 +961,6 @@ subroutine math_eigh33(m,w,v)
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end subroutine math_eigh33
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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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real(pReal), dimension(3,3) :: math_eigenvectorBasisSym33
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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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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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I = math_invariantsSym33(m)
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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 = 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 = 0.0_pReal
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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 threeSimilarEigVals
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rho=sqrt(-3.0_pReal*P**3.0_pReal)/9.0_pReal
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phi=acos(math_clip(-Q/rho*0.5_pReal,-1.0_pReal,1.0_pReal))
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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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] + 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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twoSimilarEigVals: if(abs(v(1)-v(2)) < TOL) then
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EB(1:3,1:3,3) = matmul(N(1:3,1:3,1),N(1:3,1:3,2))/((v(3)-v(1))*(v(3)-v(2)))
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EB(1:3,1:3,1) = math_I3-EB(1:3,1:3,3)
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EB(1:3,1:3,2) = 0.0_pReal
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elseif (abs(v(2)-v(3)) < TOL) then twoSimilarEigVals
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EB(1:3,1:3,1) = matmul(N(1:3,1:3,2),N(1:3,1:3,3))/((v(1)-v(2))*(v(1)-v(3)))
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EB(1:3,1:3,2) = math_I3-EB(1:3,1:3,1)
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EB(1:3,1:3,3) = 0.0_pReal
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elseif (abs(v(3)-v(1)) < TOL) then twoSimilarEigVals
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EB(1:3,1:3,2) = matmul(N(1:3,1:3,3),N(1:3,1:3,1))/((v(2)-v(3))*(v(2)-v(1)))
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EB(1:3,1:3,3) = math_I3-EB(1:3,1:3,2)
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EB(1:3,1:3,1) = 0.0_pReal
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else twoSimilarEigVals
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EB(1:3,1:3,1) = matmul(N(1:3,1:3,2),N(1:3,1:3,3))/((v(1)-v(2))*(v(1)-v(3)))
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EB(1:3,1:3,2) = matmul(N(1:3,1:3,3),N(1:3,1:3,1))/((v(2)-v(3))*(v(2)-v(1)))
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EB(1:3,1:3,3) = matmul(N(1:3,1:3,1),N(1:3,1:3,2))/((v(3)-v(1))*(v(3)-v(2)))
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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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+ 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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@ -1031,7 +972,7 @@ function math_rotationalPart(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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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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@ -1041,6 +982,67 @@ function math_rotationalPart(m)
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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 eigenvectorBasis(m)
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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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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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I = math_invariantsSym33(m)
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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 = 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 = 0.0_pReal
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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 threeSimilarEigVals
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rho=sqrt(-3.0_pReal*P**3.0_pReal)/9.0_pReal
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phi=acos(math_clip(-Q/rho*0.5_pReal,-1.0_pReal,1.0_pReal))
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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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] + 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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twoSimilarEigVals: if(abs(v(1)-v(2)) < TOL) then
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EB(1:3,1:3,3) = matmul(N(1:3,1:3,1),N(1:3,1:3,2))/((v(3)-v(1))*(v(3)-v(2)))
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EB(1:3,1:3,1) = math_I3-EB(1:3,1:3,3)
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EB(1:3,1:3,2) = 0.0_pReal
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elseif (abs(v(2)-v(3)) < TOL) then twoSimilarEigVals
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EB(1:3,1:3,1) = matmul(N(1:3,1:3,2),N(1:3,1:3,3))/((v(1)-v(2))*(v(1)-v(3)))
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EB(1:3,1:3,2) = math_I3-EB(1:3,1:3,1)
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EB(1:3,1:3,3) = 0.0_pReal
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elseif (abs(v(3)-v(1)) < TOL) then twoSimilarEigVals
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EB(1:3,1:3,2) = matmul(N(1:3,1:3,3),N(1:3,1:3,1))/((v(2)-v(3))*(v(2)-v(1)))
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EB(1:3,1:3,3) = math_I3-EB(1:3,1:3,2)
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EB(1:3,1:3,1) = 0.0_pReal
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else twoSimilarEigVals
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EB(1:3,1:3,1) = matmul(N(1:3,1:3,2),N(1:3,1:3,3))/((v(1)-v(2))*(v(1)-v(3)))
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EB(1:3,1:3,2) = matmul(N(1:3,1:3,3),N(1:3,1:3,1))/((v(2)-v(3))*(v(2)-v(1)))
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EB(1:3,1:3,3) = matmul(N(1:3,1:3,1),N(1:3,1:3,2))/((v(3)-v(1))*(v(3)-v(2)))
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endif twoSimilarEigVals
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endif threeSimilarEigVals
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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 eigenvectorBasis
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end function math_rotationalPart
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