diff --git a/python/tests/conftest.py b/python/tests/conftest.py index 97c8ee44e..87aa9a363 100644 --- a/python/tests/conftest.py +++ b/python/tests/conftest.py @@ -104,7 +104,7 @@ def set_of_quaternions(): [1.0,-1.0,-1.0,-1.0], ]) specials /= np.linalg.norm(specials,axis=1).reshape(-1,1) - specials_scatter = specials + np.broadcast_to(np.random.rand(4)*scatter,specials.shape) + specials_scatter = specials + np.broadcast_to((np.random.rand(4)*2.-1.)*scatter,specials.shape) specials_scatter /= np.linalg.norm(specials_scatter,axis=1).reshape(-1,1) specials_scatter[specials_scatter[:,0]<0]*=-1 diff --git a/python/tests/test_Rotation.py b/python/tests/test_Rotation.py index 46c10d8c2..49f57f67f 100644 --- a/python/tests/test_Rotation.py +++ b/python/tests/test_Rotation.py @@ -130,21 +130,21 @@ def qu2ho(qu): #---------- Rotation matrix ---------- -def om2qu(a): - trace = a[0,0] + a[1,1] + a[2,2] +def om2qu(om): + trace = om.trace() if trace > 0: s = 0.5 / np.sqrt(trace+ 1.0) - qu = np.array([0.25 / s,( a[2,1] - a[1,2] ) * s,( a[0,2] - a[2,0] ) * s,( a[1,0] - a[0,1] ) * s]) + qu = np.array([0.25 / s,( om[2,1] - om[1,2] ) * s,( om[0,2] - om[2,0] ) * s,( om[1,0] - om[0,1] ) * s]) else: - if ( a[0,0] > a[1,1] and a[0,0] > a[2,2] ): - s = 2.0 * np.sqrt( 1.0 + a[0,0] - a[1,1] - a[2,2]) - qu = np.array([ (a[2,1] - a[1,2]) / s,0.25 * s,(a[0,1] + a[1,0]) / s,(a[0,2] + a[2,0]) / s]) - elif (a[1,1] > a[2,2]): - s = 2.0 * np.sqrt( 1.0 + a[1,1] - a[0,0] - a[2,2]) - qu = np.array([ (a[0,2] - a[2,0]) / s,(a[0,1] + a[1,0]) / s,0.25 * s,(a[1,2] + a[2,1]) / s]) + if ( om[0,0] > om[1,1] and om[0,0] > om[2,2] ): + s = 2.0 * np.sqrt( 1.0 + om[0,0] - om[1,1] - om[2,2]) + qu = np.array([ (om[2,1] - om[1,2]) / s,0.25 * s,(om[0,1] + om[1,0]) / s,(om[0,2] + om[2,0]) / s]) + elif (om[1,1] > om[2,2]): + s = 2.0 * np.sqrt( 1.0 + om[1,1] - om[0,0] - om[2,2]) + qu = np.array([ (om[0,2] - om[2,0]) / s,(om[0,1] + om[1,0]) / s,0.25 * s,(om[1,2] + om[2,1]) / s]) else: - s = 2.0 * np.sqrt( 1.0 + a[2,2] - a[0,0] - a[1,1] ) - qu = np.array([ (a[1,0] - a[0,1]) / s,(a[0,2] + a[2,0]) / s,(a[1,2] + a[2,1]) / s,0.25 * s]) + s = 2.0 * np.sqrt( 1.0 + om[2,2] - om[0,0] - om[1,1] ) + qu = np.array([ (om[1,0] - om[0,1]) / s,(om[0,2] + om[2,0]) / s,(om[1,2] + om[2,1]) / s,0.25 * s]) if qu[0]<0: qu*=-1 return qu*np.array([1.,_P,_P,_P]) @@ -163,7 +163,6 @@ def om2eu(om): def om2ax(om): """Rotation matrix to axis angle pair.""" - #return qu2ax(om2qu(om)) # HOTFIX ax=np.empty(4) # first get the rotation angle @@ -446,11 +445,6 @@ def mul(me, other): other : numpy.ndarray or Rotation Vector, second or fourth order tensor, or rotation object that is rotated. - Todo - ---- - Document details active/passive) - consider rotation of (3,3,3,3)-matrix - """ if me.quaternion.shape != (4,): raise NotImplementedError('Support for multiple rotations missing') diff --git a/src/C_routines.c b/src/C_routines.c index f8187bb56..723c2978d 100644 --- a/src/C_routines.c +++ b/src/C_routines.c @@ -2,11 +2,10 @@ #include #include #include -#include -#include -#include #include #include +#include +#include /* http://stackoverflow.com/questions/30279228/is-there-an-alternative-to-getcwd-in-fortran-2003-2008 */ diff --git a/src/constitutive_plastic_dislotwin.f90 b/src/constitutive_plastic_dislotwin.f90 index 004238817..c9550ecd6 100644 --- a/src/constitutive_plastic_dislotwin.f90 +++ b/src/constitutive_plastic_dislotwin.f90 @@ -588,7 +588,7 @@ module subroutine plastic_dislotwin_LpAndItsTangent(Lp,dLp_dMp,Mp,T,instance,of) shearBandingContribution: if(dNeq0(prm%sbVelocity)) then BoltzmannRatio = prm%E_sb/(kB*T) - call math_eigh33(Mp,eigValues,eigVectors) ! is Mp symmetric by design? + call math_eigh33(eigValues,eigVectors,Mp) ! is Mp symmetric by design? do i = 1,6 P_sb = 0.5_pReal * math_outer(matmul(eigVectors,sb_sComposition(1:3,i)),& diff --git a/src/math.f90 b/src/math.f90 index 0ef13cc3f..c6e609c63 100644 --- a/src/math.f90 +++ b/src/math.f90 @@ -877,15 +877,14 @@ end function math_sampleGaussVar !-------------------------------------------------------------------------------------------------- !> @brief eigenvalues and eigenvectors of symmetric matrix -! ToDo: has wrong oder of arguments !-------------------------------------------------------------------------------------------------- -subroutine math_eigh(m,w,v,error) +subroutine math_eigh(w,v,error,m) real(pReal), dimension(:,:), intent(in) :: m !< quadratic matrix to compute eigenvectors and values of real(pReal), dimension(size(m,1)), intent(out) :: w !< eigenvalues real(pReal), dimension(size(m,1),size(m,1)), intent(out) :: v !< eigenvectors - - logical, intent(out) :: error + logical, intent(out) :: error + integer :: ierr real(pReal), dimension(size(m,1)**2) :: work @@ -902,9 +901,8 @@ end subroutine math_eigh !> @author Joachim Kopp, Max-Planck-Institut für Kernphysik, Heidelberg (Copyright (C) 2006) !> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH !> @details See http://arxiv.org/abs/physics/0610206 (DSYEVH3) -! ToDo: has wrong oder of arguments !-------------------------------------------------------------------------------------------------- -subroutine math_eigh33(m,w,v) +subroutine math_eigh33(w,v,m) real(pReal), dimension(3,3),intent(in) :: m !< 3x3 matrix to compute eigenvectors and values of real(pReal), dimension(3), intent(out) :: w !< eigenvalues @@ -928,7 +926,7 @@ subroutine math_eigh33(m,w,v) (m(1,1) - w(1)) * (m(2,2) - w(1)) - v(3,2)] norm = norm2(v(1:3, 1)) fallback1: if(norm < threshold) then - call math_eigh(m,w,v,error) + call math_eigh(w,v,error,m) else fallback1 v(1:3,1) = v(1:3, 1) / norm v(1:3,2) = [ v(1,2) + m(1, 3) * w(2), & @@ -936,7 +934,7 @@ subroutine math_eigh33(m,w,v) (m(1,1) - w(2)) * (m(2,2) - w(2)) - v(3,2)] norm = norm2(v(1:3, 2)) fallback2: if(norm < threshold) then - call math_eigh(m,w,v,error) + call math_eigh(w,v,error,m) else fallback2 v(1:3,2) = v(1:3, 2) / norm v(1:3,3) = math_cross(v(1:3,1),v(1:3,2)) @@ -946,87 +944,49 @@ subroutine math_eigh33(m,w,v) end subroutine math_eigh33 - - !-------------------------------------------------------------------------------------------------- -!> @brief rotational part from polar decomposition of 3x3 tensor +!> @brief Calculate rotational part of a deformation gradient +!> @details https://www.jstor.org/stable/43637254 +!! https://www.jstor.org/stable/43637372 +!! https://doi.org/10.1023/A:1007407802076 !-------------------------------------------------------------------------------------------------- -function math_rotationalPart(m) +pure function math_rotationalPart(F) result(R) - real(pReal), intent(in), dimension(3,3) :: m - real(pReal), dimension(3,3) :: math_rotationalPart - real(pReal), dimension(3,3) :: U , Uinv + real(pReal), dimension(3,3), intent(in) :: & + F ! deformation gradient + real(pReal), dimension(3,3) :: & + C, & ! right Cauchy-Green tensor + R ! rotational part + real(pReal), dimension(3) :: & + lambda, & ! principal stretches + I_C, & ! invariants of C + I_U ! invariants of U + real(pReal), dimension(2) :: & + I_F ! first two invariants of F + real(pReal) :: x,Phi - U = eigenvectorBasis(matmul(transpose(m),m)) - Uinv = math_inv33(U) + C = matmul(transpose(F),F) + I_C = math_invariantsSym33(C) + I_F = [math_trace33(F), 0.5*(math_trace33(F)**2 - math_trace33(matmul(F,F)))] - inversionFailed: if (all(dEq0(Uinv))) then - math_rotationalPart = math_I3 - call IO_warning(650) - else inversionFailed - math_rotationalPart = matmul(m,Uinv) - endif inversionFailed + x = math_clip(I_C(1)**2 -3.0_pReal*I_C(2),0.0_pReal)**(3.0_pReal/2.0_pReal) + if(dNeq0(x)) then + Phi = acos(math_clip((I_C(1)**3 -4.5_pReal*I_C(1)*I_C(2) +13.5_pReal*I_C(3))/x,-1.0_pReal,1.0_pReal)) + lambda = I_C(1) +(2.0_pReal * sqrt(math_clip(I_C(1)**2-3.0_pReal*I_C(2),0.0_pReal))) & + *cos((Phi-2.0_pReal * PI*[1.0_pReal,2.0_pReal,3.0_pReal])/3.0_pReal) + lambda = sqrt(math_clip(lambda,0.0_pReal)/3.0_pReal) + else + lambda = sqrt(I_C(1)/3.0_pReal) + endif -contains - !-------------------------------------------------------------------------------------------------- - !> @brief eigenvector basis of positive-definite 3x3 matrix - !-------------------------------------------------------------------------------------------------- - pure function eigenvectorBasis(m) + I_U = [sum(lambda), lambda(1)*lambda(2)+lambda(2)*lambda(3)+lambda(3)*lambda(1), product(lambda)] - real(pReal), dimension(3,3) :: eigenvectorBasis - real(pReal), dimension(3,3), intent(in) :: m !< positive-definite matrix of which the basis is computed - - real(pReal), dimension(3) :: I, v - real(pReal) :: P, Q, rho, phi - real(pReal), parameter :: TOL=1.e-14_pReal - real(pReal), dimension(3,3,3) :: N, EB - - I = math_invariantsSym33(m) - - P = I(2)-I(1)**2.0_pReal/3.0_pReal - Q = -2.0_pReal/27.0_pReal*I(1)**3.0_pReal+product(I(1:2))/3.0_pReal-I(3) - - threeSimilarEigVals: if(all(abs([P,Q]) < TOL)) then - v = I(1)/3.0_pReal - ! this is not really correct, but at least the basis is correct - EB = 0.0_pReal - EB(1,1,1)=1.0_pReal - EB(2,2,2)=1.0_pReal - EB(3,3,3)=1.0_pReal - else threeSimilarEigVals - rho=sqrt(-3.0_pReal*P**3.0_pReal)/9.0_pReal - phi=acos(math_clip(-Q/rho*0.5_pReal,-1.0_pReal,1.0_pReal)) - v = 2.0_pReal*rho**(1.0_pReal/3.0_pReal)* [cos((phi )/3.0_pReal), & - cos((phi+2.0_pReal*PI)/3.0_pReal), & - cos((phi+4.0_pReal*PI)/3.0_pReal) & - ] + I(1)/3.0_pReal - N(1:3,1:3,1) = m-v(1)*math_I3 - N(1:3,1:3,2) = m-v(2)*math_I3 - N(1:3,1:3,3) = m-v(3)*math_I3 - twoSimilarEigVals: if(abs(v(1)-v(2)) < TOL) then - 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))) - EB(1:3,1:3,1) = math_I3-EB(1:3,1:3,3) - EB(1:3,1:3,2) = 0.0_pReal - elseif (abs(v(2)-v(3)) < TOL) then twoSimilarEigVals - 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))) - EB(1:3,1:3,2) = math_I3-EB(1:3,1:3,1) - EB(1:3,1:3,3) = 0.0_pReal - elseif (abs(v(3)-v(1)) < TOL) then twoSimilarEigVals - 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))) - EB(1:3,1:3,3) = math_I3-EB(1:3,1:3,2) - EB(1:3,1:3,1) = 0.0_pReal - else twoSimilarEigVals - 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))) - 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))) - 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))) - endif twoSimilarEigVals - endif threeSimilarEigVals - - eigenvectorBasis = sqrt(v(1)) * EB(1:3,1:3,1) & - + sqrt(v(2)) * EB(1:3,1:3,2) & - + sqrt(v(3)) * EB(1:3,1:3,3) - - end function eigenvectorBasis + R = I_U(1)*I_F(2) * math_I3 & + +(I_U(1)**2-I_U(2)) * F & + - I_U(1)*I_F(1) * transpose(F) & + + I_U(1) * transpose(matmul(F,F)) & + - matmul(F,C) + R = R /(I_U(1)*I_U(2)-I_U(3)) end function math_rotationalPart @@ -1078,7 +1038,7 @@ function math_eigvalsh33(m) rho=sqrt(-3.0_pReal*P**3.0_pReal)/9.0_pReal phi=acos(math_clip(-Q/rho*0.5_pReal,-1.0_pReal,1.0_pReal)) math_eigvalsh33 = 2.0_pReal*rho**(1.0_pReal/3.0_pReal)* & - [cos(phi/3.0_pReal), & + [cos( phi /3.0_pReal), & cos((phi+2.0_pReal*PI)/3.0_pReal), & cos((phi+4.0_pReal*PI)/3.0_pReal) & ] & diff --git a/src/rotations.f90 b/src/rotations.f90 index 07053545d..85f901f5d 100644 --- a/src/rotations.f90 +++ b/src/rotations.f90 @@ -34,7 +34,7 @@ !> @details: rotation is internally stored as quaternion. It can be inialized from different !> representations and also returns itself in different representations. ! -! All methods and naming conventions based on Rowenhorst_etal2015 +! All methods and naming conventions based on Rowenhorst et al. 2015 ! Convention 1: coordinate frames are right-handed ! Convention 2: a rotation angle ω is taken to be positive for a counterclockwise rotation ! when viewing from the end point of the rotation axis towards the origin @@ -566,7 +566,26 @@ pure function om2qu(om) result(qu) real(pReal), intent(in), dimension(3,3) :: om real(pReal), dimension(4) :: qu - qu = eu2qu(om2eu(om)) + real(pReal) :: trace,s + trace = math_trace33(om) + + if(trace > 0.0_pReal) then + s = 0.5_pReal / sqrt(trace+1.0_pReal) + qu = [0.25_pReal/s, (om(3,2)-om(2,3))*s,(om(1,3)-om(3,1))*s,(om(2,1)-om(1,2))*s] + else + if( om(1,1) > om(2,2) .and. om(1,1) > om(3,3) ) then + s = 2.0_pReal * sqrt( 1.0_pReal + om(1,1) - om(2,2) - om(3,3)) + qu = [ (om(3,2) - om(2,3)) /s,0.25_pReal * s,(om(1,2) + om(2,1)) / s,(om(1,3) + om(3,1)) / s] + elseif (om(2,2) > om(3,3)) then + s = 2.0_pReal * sqrt( 1.0_pReal + om(2,2) - om(1,1) - om(3,3)) + qu = [ (om(1,3) - om(3,1)) /s,(om(1,2) + om(2,1)) / s,0.25_pReal * s,(om(2,3) + om(3,2)) / s] + else + s = 2.0_pReal * sqrt( 1.0_pReal + om(3,3) - om(1,1) - om(2,2) ) + qu = [ (om(2,1) - om(1,2)) /s,(om(1,3) + om(3,1)) / s,(om(2,3) + om(3,2)) / s,0.25_pReal * s] + endif + endif + if(qu(1)<0._pReal) qu =-1.0_pReal * qu + qu = qu*[1.0_pReal,P,P,P] end function om2qu @@ -727,7 +746,7 @@ pure function eu2om(eu) result(om) om(3,2) = -c(1)*s(2) om(3,3) = c(2) - where(dEq0(om)) om = 0.0_pReal + where(abs(om)<1.0e-12_pReal) om = 0.0_pReal end function eu2om @@ -1386,49 +1405,37 @@ subroutine selfTest sin(2.0_pReal*PI*x(1))*A] if(qu(1)<0.0_pReal) qu = qu * (-1.0_pReal) endif -#ifndef __PGI - if(dNeq0(norm2(om2qu(qu2om(qu))-qu),1.0e-12_pReal)) msg = trim(msg)//'om2qu/qu2om,' - if(dNeq0(norm2(eu2qu(qu2eu(qu))-qu),1.0e-12_pReal)) msg = trim(msg)//'eu2qu/qu2eu,' - if(dNeq0(norm2(ax2qu(qu2ax(qu))-qu),1.0e-12_pReal)) msg = trim(msg)//'ax2qu/qu2ax,' - if(dNeq0(norm2(ro2qu(qu2ro(qu))-qu),1.0e-12_pReal)) msg = trim(msg)//'ro2qu/qu2ro,' - if(dNeq0(norm2(ho2qu(qu2ho(qu))-qu),1.0e-7_pReal)) msg = trim(msg)//'ho2qu/qu2ho,' - if(dNeq0(norm2(cu2qu(qu2cu(qu))-qu),1.0e-7_pReal)) msg = trim(msg)//'cu2qu/qu2cu,' -#endif + if(.not. quaternion_equal(om2qu(qu2om(qu)),qu)) msg = trim(msg)//'om2qu/qu2om,' + if(.not. quaternion_equal(eu2qu(qu2eu(qu)),qu)) msg = trim(msg)//'eu2qu/qu2eu,' + if(.not. quaternion_equal(ax2qu(qu2ax(qu)),qu)) msg = trim(msg)//'ax2qu/qu2ax,' + if(.not. quaternion_equal(ro2qu(qu2ro(qu)),qu)) msg = trim(msg)//'ro2qu/qu2ro,' + if(.not. quaternion_equal(ho2qu(qu2ho(qu)),qu)) msg = trim(msg)//'ho2qu/qu2ho,' + if(.not. quaternion_equal(cu2qu(qu2cu(qu)),qu)) msg = trim(msg)//'cu2qu/qu2cu,' om = qu2om(qu) -#ifndef __PGI - if(dNeq0(norm2(om2qu(eu2om(om2eu(om)))-qu),1.0e-7_pReal)) msg = trim(msg)//'eu2om/om2eu,' - if(dNeq0(norm2(om2qu(ax2om(om2ax(om)))-qu),1.0e-7_pReal)) msg = trim(msg)//'ax2om/om2ax,' - if(dNeq0(norm2(om2qu(ro2om(om2ro(om)))-qu),1.0e-12_pReal)) msg = trim(msg)//'ro2om/om2ro,' - if(dNeq0(norm2(om2qu(ho2om(om2ho(om)))-qu),1.0e-7_pReal)) msg = trim(msg)//'ho2om/om2ho,' - if(dNeq0(norm2(om2qu(cu2om(om2cu(om)))-qu),1.0e-7_pReal)) msg = trim(msg)//'cu2om/om2cu,' -#endif + if(.not. quaternion_equal(om2qu(eu2om(om2eu(om))),qu)) msg = trim(msg)//'eu2om/om2eu,' + if(.not. quaternion_equal(om2qu(ax2om(om2ax(om))),qu)) msg = trim(msg)//'ax2om/om2ax,' + if(.not. quaternion_equal(om2qu(ro2om(om2ro(om))),qu)) msg = trim(msg)//'ro2om/om2ro,' + if(.not. quaternion_equal(om2qu(ho2om(om2ho(om))),qu)) msg = trim(msg)//'ho2om/om2ho,' + if(.not. quaternion_equal(om2qu(cu2om(om2cu(om))),qu)) msg = trim(msg)//'cu2om/om2cu,' eu = qu2eu(qu) -#ifndef __PGI - if(dNeq0(norm2(eu2qu(ax2eu(eu2ax(eu)))-qu),1.0e-12_pReal)) msg = trim(msg)//'ax2eu/eu2ax,' - if(dNeq0(norm2(eu2qu(ro2eu(eu2ro(eu)))-qu),1.0e-12_pReal)) msg = trim(msg)//'ro2eu/eu2ro,' - if(dNeq0(norm2(eu2qu(ho2eu(eu2ho(eu)))-qu),1.0e-7_pReal)) msg = trim(msg)//'ho2eu/eu2ho,' - if(dNeq0(norm2(eu2qu(cu2eu(eu2cu(eu)))-qu),1.0e-7_pReal)) msg = trim(msg)//'cu2eu/eu2cu,' -#endif + if(.not. quaternion_equal(eu2qu(ax2eu(eu2ax(eu))),qu)) msg = trim(msg)//'ax2eu/eu2ax,' + if(.not. quaternion_equal(eu2qu(ro2eu(eu2ro(eu))),qu)) msg = trim(msg)//'ro2eu/eu2ro,' + if(.not. quaternion_equal(eu2qu(ho2eu(eu2ho(eu))),qu)) msg = trim(msg)//'ho2eu/eu2ho,' + if(.not. quaternion_equal(eu2qu(cu2eu(eu2cu(eu))),qu)) msg = trim(msg)//'cu2eu/eu2cu,' ax = qu2ax(qu) -#ifndef __PGI - if(dNeq0(norm2(ax2qu(ro2ax(ax2ro(ax)))-qu),1.0e-12_pReal)) msg = trim(msg)//'ro2ax/ax2ro,' - if(dNeq0(norm2(ax2qu(ho2ax(ax2ho(ax)))-qu),1.0e-7_pReal)) msg = trim(msg)//'ho2ax/ax2ho,' - if(dNeq0(norm2(ax2qu(cu2ax(ax2cu(ax)))-qu),1.0e-7_pReal)) msg = trim(msg)//'cu2ax/ax2cu,' -#endif + if(.not. quaternion_equal(ax2qu(ro2ax(ax2ro(ax))),qu)) msg = trim(msg)//'ro2ax/ax2ro,' + if(.not. quaternion_equal(ax2qu(ho2ax(ax2ho(ax))),qu)) msg = trim(msg)//'ho2ax/ax2ho,' + if(.not. quaternion_equal(ax2qu(cu2ax(ax2cu(ax))),qu)) msg = trim(msg)//'cu2ax/ax2cu,' ro = qu2ro(qu) -#ifndef __PGI - if(dNeq0(norm2(ro2qu(ho2ro(ro2ho(ro)))-qu),1.0e-7_pReal)) msg = trim(msg)//'ho2ro/ro2ho,' - if(dNeq0(norm2(ro2qu(cu2ro(ro2cu(ro)))-qu),1.0e-7_pReal)) msg = trim(msg)//'cu2ro/ro2cu,' -#endif + if(.not. quaternion_equal(ro2qu(ho2ro(ro2ho(ro))),qu)) msg = trim(msg)//'ho2ro/ro2ho,' + if(.not. quaternion_equal(ro2qu(cu2ro(ro2cu(ro))),qu)) msg = trim(msg)//'cu2ro/ro2cu,' ho = qu2ho(qu) -#ifndef __PGI - if(dNeq0(norm2(ho2qu(cu2ho(ho2cu(ho)))-qu),1.0e-7_pReal)) msg = trim(msg)//'cu2ho/ho2cu,' -#endif + if(.not. quaternion_equal(ho2qu(cu2ho(ho2cu(ho))),qu)) msg = trim(msg)//'cu2ho/ho2cu,' call R%fromMatrix(om) @@ -1447,6 +1454,18 @@ subroutine selfTest if(len_trim(msg) /= 0) call IO_error(0,ext_msg=msg) enddo + contains + + function quaternion_equal(qu1,qu2) result(ok) + + real(pReal), intent(in), dimension(4) :: qu1,qu2 + logical :: ok + + ok = all(dEq(qu1,qu2,1.0e-7_pReal)) + if(dEq0(qu1(1),1.0e-12_pReal)) & + ok = ok .or. all(dEq(-1.0_pReal*qu1,qu2,1.0e-7_pReal)) + + end function quaternion_equal end subroutine selfTest diff --git a/src/system_routines.f90 b/src/system_routines.f90 index 450dfe5b1..6dc1318e4 100644 --- a/src/system_routines.f90 +++ b/src/system_routines.f90 @@ -29,7 +29,7 @@ module system_routines integer(C_INT) :: isDirectory_C character(kind=C_CHAR), dimension(pPathLen), intent(in) :: path ! C string is an array - end function isDirectory_C + end function isDirectory_C subroutine getCurrentWorkDir_C(path, stat) bind(C) use, intrinsic :: ISO_C_Binding, only: & @@ -40,7 +40,7 @@ module system_routines character(kind=C_CHAR), dimension(pPathLen), intent(out) :: path ! C string is an array integer(C_INT), intent(out) :: stat - end subroutine getCurrentWorkDir_C + end subroutine getCurrentWorkDir_C subroutine getHostName_C(str, stat) bind(C) use, intrinsic :: ISO_C_Binding, only: & @@ -51,7 +51,7 @@ module system_routines character(kind=C_CHAR), dimension(pStringLen), intent(out) :: str ! C string is an array integer(C_INT), intent(out) :: stat - end subroutine getHostName_C + end subroutine getHostName_C function chdir_C(path) bind(C) use, intrinsic :: ISO_C_Binding, only: &