!############################################################## MODULE math !############################################################## use prec, only: pReal,pInt implicit none real(pReal), parameter :: pi = (2.0_pReal)*dasin(1.0_pReal) real(pReal), parameter :: inDeg = 180.0_pReal/pi real(pReal), parameter :: inRad = pi/180.0_pReal CONTAINS ! *** Initialize random number generator *** ! *** for later use in mpie_fiber and mpie_disturbOri *** SUBROUTINE math_init () use prec, only: pReal,pInt implicit none integer (pInt) seed call random_seed() call get_seed(seed) call halton_seed_set(seed) call halton_ndim_set(3) END SUBROUTINE !******************************************************************** ! calculate the determinant of a (3x3) !******************************************************************** real(pReal) FUNCTION math_det3x3(m) use prec, only: pReal,pInt implicit none real(pReal) m(3,3) math_det3x3 = m(1,1)*(m(2,2)*m(3,3)-m(2,3)*m(3,2)) & -m(1,2)*(m(2,1)*m(3,3)-m(2,3)*m(3,1)) & +m(1,3)*(m(2,1)*m(3,2)-m(2,2)*m(3,1)) return END FUNCTION !******************************************************************** ! covert a symmetric 3,3 matrix into an array of 6 !******************************************************************** FUNCTION math_33to6(m33) use prec, only: pReal,pInt implicit none real(pReal), dimension(3,3) :: m33 real(pReal), dimension(6) :: math_33to6 math_33to6(1)=m33(1,1) math_33to6(2)=m33(2,2) math_33to6(3)=m33(3,3) math_33to6(4)=m33(1,2) math_33to6(5)=m33(2,3) math_33to6(6)=m33(1,3) return END FUNCTION !******************************************************************** ! This routine coverts an array of 6 into a symmetric 3,3 matrix !******************************************************************** FUNCTION math_6to33(v6) use prec, only: pReal,pInt implicit none real(pReal) math_6to33(3,3), v6(6) math_6to33(1,1)=v6(1) math_6to33(2,2)=v6(2) math_6to33(3,3)=v6(3) math_6to33(1,2)=v6(4) math_6to33(2,1)=v6(4) math_6to33(2,3)=v6(5) math_6to33(3,2)=v6(5) math_6to33(1,3)=v6(6) math_6to33(3,1)=v6(6) return END FUNCTION !******************************************************************************** !** This routine transforms the stiffness matrix ** !******************************************************************************** FUNCTION math_66to3333(C66) use prec, only: pReal, pInt implicit none real(pReal) C66(6,6), math_66to3333(3,3,3,3) math_66to3333(1,1,1,1)=C66(1,1) math_66to3333(1,1,2,2)=C66(1,2) math_66to3333(1,1,3,3)=C66(1,3) math_66to3333(1,1,2,3)=C66(1,4) math_66to3333(1,1,3,2)=C66(1,4) math_66to3333(1,1,1,3)=C66(1,5) math_66to3333(1,1,3,1)=C66(1,5) math_66to3333(1,1,1,2)=C66(1,6) math_66to3333(1,1,2,1)=C66(1,6) math_66to3333(2,2,1,1)=C66(2,1) math_66to3333(2,2,2,2)=C66(2,2) math_66to3333(2,2,3,3)=C66(2,3) math_66to3333(2,2,2,3)=C66(2,4) math_66to3333(2,2,3,2)=C66(2,4) math_66to3333(2,2,1,3)=C66(2,5) math_66to3333(2,2,3,1)=C66(2,5) math_66to3333(2,2,1,2)=C66(2,6) math_66to3333(2,2,2,1)=C66(2,6) math_66to3333(3,3,1,1)=C66(3,1) math_66to3333(3,3,2,2)=C66(3,2) math_66to3333(3,3,3,3)=C66(3,3) math_66to3333(3,3,2,3)=C66(3,4) math_66to3333(3,3,3,2)=C66(3,4) math_66to3333(3,3,1,3)=C66(3,5) math_66to3333(3,3,3,1)=C66(3,5) math_66to3333(3,3,1,2)=C66(3,6) math_66to3333(3,3,2,1)=C66(3,6) math_66to3333(2,3,1,1)=C66(4,1) math_66to3333(3,2,1,1)=C66(4,1) math_66to3333(2,3,2,2)=C66(4,2) math_66to3333(3,2,2,2)=C66(4,2) math_66to3333(2,3,3,3)=C66(4,3) math_66to3333(3,2,3,3)=C66(4,3) math_66to3333(2,3,2,3)=C66(4,4) math_66to3333(2,3,3,2)=C66(4,4) math_66to3333(3,2,2,3)=C66(4,4) math_66to3333(3,2,3,2)=C66(4,4) math_66to3333(2,3,3,1)=C66(4,5) math_66to3333(2,3,1,3)=C66(4,5) math_66to3333(2,3,3,1)=C66(4,5) math_66to3333(3,2,1,3)=C66(4,5) math_66to3333(2,3,1,2)=C66(4,6) math_66to3333(2,3,2,1)=C66(4,6) math_66to3333(3,2,1,2)=C66(4,6) math_66to3333(3,2,2,1)=C66(4,6) math_66to3333(3,1,1,1)=C66(5,1) math_66to3333(1,3,1,1)=C66(5,1) math_66to3333(3,1,2,2)=C66(5,2) math_66to3333(1,3,2,2)=C66(5,2) math_66to3333(3,1,3,3)=C66(5,3) math_66to3333(1,3,3,3)=C66(5,3) math_66to3333(3,1,2,3)=C66(5,4) math_66to3333(3,1,3,2)=C66(5,4) math_66to3333(1,3,2,3)=C66(5,4) math_66to3333(1,3,3,2)=C66(5,4) math_66to3333(3,1,3,1)=C66(5,5) math_66to3333(3,1,1,3)=C66(5,5) math_66to3333(1,3,3,1)=C66(5,5) math_66to3333(1,3,1,3)=C66(5,5) math_66to3333(3,1,1,2)=C66(5,6) math_66to3333(3,1,2,1)=C66(5,6) math_66to3333(1,3,1,2)=C66(5,6) math_66to3333(1,3,2,1)=C66(5,6) math_66to3333(1,2,1,1)=C66(6,1) math_66to3333(2,1,1,1)=C66(6,1) math_66to3333(1,2,2,2)=C66(6,2) math_66to3333(2,1,2,2)=C66(6,2) math_66to3333(1,2,3,3)=C66(6,3) math_66to3333(2,1,3,3)=C66(6,3) math_66to3333(1,2,2,3)=C66(6,4) math_66to3333(1,2,3,2)=C66(6,4) math_66to3333(2,1,2,3)=C66(6,4) math_66to3333(2,1,3,2)=C66(6,4) math_66to3333(1,2,3,1)=C66(6,5) math_66to3333(1,2,1,3)=C66(6,5) math_66to3333(2,1,3,1)=C66(6,5) math_66to3333(2,1,1,3)=C66(6,5) math_66to3333(1,2,1,2)=C66(6,6) math_66to3333(1,2,2,1)=C66(6,6) math_66to3333(2,1,1,2)=C66(6,6) math_66to3333(2,1,2,1)=C66(6,6) return END FUNCTION FUNCTION math_3333to66(C3333) !******************************************************************************** !** This routine transforms the stiffness matrix ** !******************************************************************************** use prec, only: pReal, pInt implicit none real(pReal) math_3333to66(6,6), C3333(3,3,3,3) math_3333to66(1,1)=C3333(1,1,1,1) math_3333to66(1,2)=C3333(1,1,2,2) math_3333to66(1,3)=C3333(1,1,3,3) math_3333to66(1,4)=C3333(1,1,2,3) math_3333to66(1,5)=C3333(1,1,3,1) math_3333to66(1,6)=C3333(1,1,1,2) math_3333to66(2,1)=C3333(2,2,1,1) math_3333to66(2,2)=C3333(2,2,2,2) math_3333to66(2,3)=C3333(2,2,3,3) math_3333to66(2,4)=C3333(2,2,2,3) math_3333to66(2,5)=C3333(2,2,3,1) math_3333to66(2,6)=C3333(2,2,1,2) math_3333to66(3,1)=C3333(3,3,1,1) math_3333to66(3,2)=C3333(3,3,2,2) math_3333to66(3,3)=C3333(3,3,3,3) math_3333to66(3,4)=C3333(3,3,2,3) math_3333to66(3,5)=C3333(3,3,3,1) math_3333to66(3,6)=C3333(3,3,1,2) math_3333to66(4,1)=C3333(2,3,1,1) math_3333to66(4,2)=C3333(2,3,2,2) math_3333to66(4,3)=C3333(2,3,3,3) math_3333to66(4,4)=C3333(2,3,2,3) math_3333to66(4,5)=C3333(2,3,3,1) math_3333to66(4,6)=C3333(2,3,1,2) math_3333to66(5,1)=C3333(3,1,1,1) math_3333to66(5,2)=C3333(3,1,2,2) math_3333to66(5,3)=C3333(3,1,3,3) math_3333to66(5,4)=C3333(3,1,2,3) math_3333to66(5,5)=C3333(3,1,3,1) math_3333to66(5,6)=C3333(3,1,1,2) math_3333to66(6,1)=C3333(1,2,1,1) math_3333to66(6,2)=C3333(1,2,2,2) math_3333to66(6,3)=C3333(1,2,3,3) math_3333to66(6,4)=C3333(1,2,2,3) math_3333to66(6,5)=C3333(1,2,3,1) math_3333to66(6,6)=C3333(1,2,1,2) return END FUNCTION !******************************************************************** ! This routine calculates Euler angles from orientation matrix !******************************************************************** SUBROUTINE math_RtoEuler(orimat, phi1, PHI, phi2) use prec, only: pReal, pInt implicit none real(pReal) orimat(3,3), phi1, PHI, phi2 real(pReal) sqhkl, squvw, sqhk, val sqhkl=sqrt(orimat(1,3)*orimat(1,3)+orimat(2,3)*orimat(2,3)+orimat(3,3)*orimat(3,3)) squvw=sqrt(orimat(1,1)*orimat(1,1)+orimat(2,1)*orimat(2,1)+orimat(3,1)*orimat(3,1)) sqhk=sqrt(orimat(1,3)*orimat(1,3)+orimat(2,3)*orimat(2,3)) ! calculate PHI val=orimat(3,3)/sqhkl if(val.GT.1.0_pReal) val=1.0_pReal if(val.LT.-1.0_pReal) val=-1.0_pReal PHI=acos(val) if(PHI.LT.1.0e-30_pReal) then ! calculate phi2 phi2=0.0 ! calculate phi1 val=orimat(1,1)/squvw if(val.GT.1.0_pReal) val=1.0_pReal if(val.LT.-1.0_pReal) val=-1.0_pReal if(orimat(2,1).LE.0.0) then phi1=acos(val) else phi1=2.0_pReal*pi-acos(val) end if else ! calculate phi2 val=orimat(2,3)/sqhk if(val.GT.1.0_pReal) val=1.0_pReal if(val.LT.-1.0_pReal) val=-1.0_pReal if(orimat(1,3).GE.0.0) then phi2=acos(val) else phi2=2.0_pReal*pi-acos(val) end if ! calculate phi1 val=-orimat(3,2)/sin(PHI) if(val.GT.1.0_pReal) val=1.0_pReal if(val.LT.-1.0_pReal) val=-1.0_pReal if(orimat(3,1).GE.0.0) then phi1=acos(val) else phi1=2.0_pReal*pi-acos(val) end if end if ! convert angles to degrees phi1=phi1*inDeg PHI=PHI*inDeg phi2=phi2*inDeg return END SUBROUTINE !##################################################### ! bestimmt Drehmatrix DREH3 fuer Drehung um Omega um Achse (u,v,w) FUNCTION math_RodrigtoR(Omega,U,V,W) use prec, only: pReal, pInt implicit none real(pReal) omega, u, v, w, math_RodrigtoR(3,3) real(pReal) betrag, s, c, u2, v2, w2 BETRAG=SQRT(U**2+V**2+W**2) S=SIN(OMEGA) C=COS(OMEGA) U2=U/BETRAG V2=V/BETRAG W2=W/BETRAG math_RodrigtoR(1,1)=(1-U2**2)*C+U2**2 math_RodrigtoR(1,2)=U2*V2*(1-C)+W2*S math_RodrigtoR(1,3)=U2*W2*(1-C)-V2*S math_RodrigtoR(2,1)=U2*V2*(1-C)-W2*S math_RodrigtoR(2,2)=(1-V2**2)*C+V2**2 math_RodrigtoR(2,3)=V2*W2*(1-C)+U2*S math_RodrigtoR(3,1)=U2*W2*(1-C)+V2*S math_RodrigtoR(3,2)=V2*W2*(1-C)-U2*S math_RodrigtoR(3,3)=(1-W2**2)*C+W2**2 return END FUNCTION ! Best. Drehmatrix ROTA fuer Euler-Winkel FUNCTION math_EulertoR (P1,P,P2) use prec, only: pReal, pInt implicit none real(pReal) p1, p, p2, math_EulertoR(3,3) real(pReal) xp1, xp, xp2, c1, c, c2, s1, s, s2 XP1=P1*inRad XP=P*inRad XP2=P2*inRad C1=COS(XP1) C=COS(XP) C2=COS(XP2) S1=SIN(XP1) S=SIN(XP) S2=SIN(XP2) math_EulertoR(1,1)=C1*C2-S1*S2*C math_EulertoR(1,2)=S1*C2+C1*S2*C math_EulertoR(1,3)=S2*S math_EulertoR(2,1)=-C1*S2-S1*C2*C math_EulertoR(2,2)=-S1*S2+C1*C2*C math_EulertoR(2,3)=C2*S math_EulertoR(3,1)=S1*S math_EulertoR(3,2)=-C1*S math_EulertoR(3,3)=C return END FUNCTION !************************************************************************** ! BERECHNUNG VON ORIENTIERUNGSBEZIEHUNGEN ZWISCHEN ! ZWEI VORGEGEBENEN ORIENTIERUNGEN function math_disorient(P1,P,P2) use prec, only: pReal, pInt implicit none real(pReal) D1(3,3),D2(3,3),P1(2),P(2),P2(2),D1T(3,3),DR(3,3) real(pReal) math_disorient, spur, sp, omega, alpha integer(pInt) i ! ERSTELLEN DER BEIDEN DMATRIZEN d1 = math_EulertoR(p1(1),P(1),p2(1)) d2 = math_EulertoR(p1(2),P(2),p2(2)) !**************************************************** ! BESTIMMUNG DER INVERSEN MATRIX ZUR ORIENTIERUNG 1:DM !**************************************************** d1T=transpose(d1) !*********************************************************** ! MATRIZENMULTIPLIKATION DER MATRIZEN D2 UND DM=DR(I,J) !*********************************************************** dr=matmul(d2,d1T) !******************************* ! BESTIMMUNG DES ROTATIONSWINKELS !******************************* SPUR=DR(1,1)+DR(2,2)+DR(3,3) SP=(SPUR-1._pReal)*0.4999999_pReal OMEGA=PI*0.5_pReal-ASIN(SP) ! Winkel in Grad umrechnen ALPHA=OMEGA*inDeg math_disorient=abs(alpha) return END FUNCTION !**************************************************************** subroutine math_pDecomposition(FE,U,R,ISING) !-----FE=RU !-----INVERT is the subroutine applied by Marc !**************************************************************** use prec, only: pReal, pInt implicit none integer(pInt) ISING real(pReal) FE(3,3),R(3,3),U(3,3),CE(3,3),EW1,EW2,EW3,EB1(3,3),EB2(3,3),EB3(3,3),UI(3,3),det ising=0 ce=matmul(transpose(fe),fe) CALL math_spectral1(CE,EW1,EW2,EW3,EB1,EB2,EB3) U=DSQRT(EW1)*EB1+DSQRT(EW2)*EB2+DSQRT(EW3)*EB3 UI=U call invert(UI,3,0,0,det,3) if (det.EQ.0) then ising=1 return endif R=matmul(fe,ui) return END SUBROUTINE !********************************************************************** subroutine math_spectral1(M,EW1,EW2,EW3,EB1,EB2,EB3) !**** EIGENWERTE UND EIGENWERTBASIS DER SYMMETRISCHEN 3X3 MATRIX M use prec, only: pReal, pInt implicit none real(pReal) M(3,3),EB1(3,3),EB2(3,3),EB3(3,3),EW1,EW2,EW3 real(pReal) HI1M,HI2M,HI3M,TOL,R,S,T,P,Q,RHO,PHI,Y1,Y2,Y3,D1,D2,D3 real(pReal) C1,C2,C3,M1(3,3),M2(3,3),M3(3,3),I3(3,3),arg TOL=1.e-14_pReal I3 = math_identity(3) CALL math_hi(M,HI1M,HI2M,HI3M) R=-HI1M S= HI2M T=-HI3M P=S-R**2.0_pReal/3.0_pReal Q=2.0_pReal/27.0_pReal*R**3.0_pReal-R*S/3.0_pReal+T EB1=0.0_pReal EB2=0.0_pReal EB3=0.0_pReal IF((ABS(P).LT.TOL).AND.(ABS(Q).LT.TOL))THEN ! DREI GLEICHE EIGENWERTE EW1=HI1M/3.0_pReal EW2=EW1 EW3=EW1 ! this is not really correct, but this way U is calculated ! correctly in PDECOMPOSITION (correct is EB?=I) EB1(1,1)=1.0_pReal EB2(2,2)=1.0_pReal EB3(3,3)=1.0_pReal ELSE RHO=SQRT(-3.0_pReal*P**3.0_pReal)/9.0_pReal arg=-Q/RHO/2.0_pReal if(arg.GT.1) arg=1 if(arg.LT.-1) arg=-1 PHI=ACOS(arg) Y1=2*RHO**(1.0_pReal/3.0_pReal)*COS(PHI/3.0_pReal) Y2=2*RHO**(1.0_pReal/3.0_pReal)*COS(PHI/3.0_pReal+2.0_pReal/3.0_pReal*PI) Y3=2*RHO**(1.0_pReal/3.0_pReal)*COS(PHI/3.0_pReal+4.0_pReal/3.0_pReal*PI) EW1=Y1-R/3.0_pReal EW2=Y2-R/3.0_pReal EW3=Y3-R/3.0_pReal C1=ABS(EW1-EW2) C2=ABS(EW2-EW3) C3=ABS(EW3-EW1) IF(C1.LT.TOL) THEN ! EW1 is equal to EW2 D3=1.0_pReal/(EW3-EW1)/(EW3-EW2) M1=M-EW1*I3 M2=M-EW2*I3 EB3=MATMUL(M1,M2)*D3 EB1=I3-EB3 ! both EB2 and EW2 are set to zero so that they do not ! contribute to U in PDECOMPOSITION EW2=0.0_pReal ELSE IF(C2.LT.TOL) THEN ! EW2 is equal to EW3 D1=1.0_pReal/(EW1-EW2)/(EW1-EW3) M2=M-I3*EW2 M3=M-I3*EW3 EB1=MATMUL(M2,M3)*D1 EB2=I3-EB1 ! both EB3 and EW3 are set to zero so that they do not ! contribute to U in PDECOMPOSITION EW3=0.0_pReal ELSE IF(C3.LT.TOL) THEN ! EW1 is equal to EW3 D2=1.0_pReal/(EW2-EW1)/(EW2-EW3) M1=M-I3*EW1 M3=M-I3*EW3 EB2=MATMUL(M1,M3)*D2 EB1=I3-EB2 ! both EB3 and EW3 are set to zero so that they do not ! contribute to U in PDECOMPOSITION EW3=0.0_pReal ELSE ! all three eigenvectors are different D1=1.0_pReal/(EW1-EW2)/(EW1-EW3) D2=1.0_pReal/(EW2-EW1)/(EW2-EW3) D3=1.0_pReal/(EW3-EW1)/(EW3-EW2) M1=M-EW1*I3 M2=M-EW2*I3 M3=M-EW3*I3 EB1=MATMUL(M2,M3)*D1 EB2=MATMUL(M1,M3)*D2 EB3=MATMUL(M1,M2)*D3 END IF END IF RETURN END SUBROUTINE !********************************************************************** !**** EINHEITSMATRIX MIT dim DIAGONALELEMENTEN FUNCTION math_identity(dimen) use prec, only: pReal, pInt implicit none integer(pInt) i,dimen real(pReal) math_identity(dimen,dimen) math_identity = 0.0_pReal forall (i=1:dimen) math_identity(i,i) = 1.0_pReal return END FUNCTION !********************************************************************** !**** HAUPTINVARIANTEN HI1M, HI2M, HI3M DER 3X3 MATRIX M SUBROUTINE math_hi(M,HI1M,HI2M,HI3M) use prec, only: pReal, pInt implicit none real(pReal) M(3,3),HI1M,HI2M,HI3M HI1M=M(1,1)+M(2,2)+M(3,3) HI2M=(M(1,1)+M(2,2)+M(3,3))**2/2.0_pReal-(M(1,1)**2+M(2,2)**2+M(3,3)**2)/2.0_pReal-M(1,2)*M(2,1)-M(1,3)*M(3,1)-M(2,3)*M(3,2) HI3M=M(1,1)*M(2,2)*M(3,3)-M(1,1)*M(2,3)*M(3,2)-M(2,1)*M(1,2)*M(3,3)+M(2,1)*M(1,3)*M(3,2)+M(3,1)*M(1,2)*M(2,3)-M(3,1)*M(1,3)*M(2,2) ! QUESTION: is 3rd equiv det(M) ?? if yes, use function math_det return END SUBROUTINE SUBROUTINE get_seed(seed) ! !******************************************************************************* ! !! GET_SEED returns a seed for the random number generator. ! ! ! Discussion: ! ! The seed depends on the current time, and ought to be (slightly) ! different every millisecond. Once the seed is obtained, a random ! number generator should be called a few times to further process ! the seed. ! ! Modified: ! ! 27 June 2000 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Output, integer SEED, a pseudorandom seed value. ! ! Modified: ! ! 29 April 2005 ! ! Author: ! ! Franz Roters ! use prec, only: pReal, pInt implicit none integer(pInt) seed real(pReal) temp character ( len = 10 ) time character ( len = 8 ) today integer(pInt) values(8) character ( len = 5 ) zone call date_and_time ( today, time, zone, values ) temp = 0.0D+00 temp = temp + dble ( values(2) - 1 ) / 11.0D+00 temp = temp + dble ( values(3) - 1 ) / 30.0D+00 temp = temp + dble ( values(5) ) / 23.0D+00 temp = temp + dble ( values(6) ) / 59.0D+00 temp = temp + dble ( values(7) ) / 59.0D+00 temp = temp + dble ( values(8) ) / 999.0D+00 temp = temp / 6.0D+00 if ( temp <= 0.0D+00 ) then temp = 1.0D+00 / 3.0D+00 else if ( 1.0D+00 <= temp ) then temp = 2.0D+00 / 3.0D+00 end if seed = int ( dble ( huge ( 1 ) ) * temp , pInt) ! ! Never use a seed of 0 or maximum integer. ! if ( seed == 0 ) then seed = 1 end if if ( seed == huge ( 1 ) ) then seed = seed - 1 end if return END SUBROUTINE subroutine halton ( ndim, r ) ! !******************************************************************************* ! !! HALTON computes the next element in the Halton sequence. ! ! ! Modified: ! ! 09 March 2003 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer NDIM, the dimension of the element. ! ! Output, real R(NDIM), the next element of the current Halton ! sequence. ! ! Modified: ! ! 29 April 2005 ! ! Author: ! ! Franz Roters ! use prec, ONLY: pReal, pInt implicit none integer(pInt) ndim integer(pInt) base(ndim) real(pReal) r(ndim) integer(pInt) seed integer(pInt) value(1) call halton_memory ( 'GET', 'SEED', 1, value ) seed = value(1) call halton_memory ( 'GET', 'BASE', ndim, base ) call i_to_halton ( seed, base, ndim, r ) value(1) = 1 call halton_memory ( 'INC', 'SEED', 1, value ) return END SUBROUTINE subroutine halton_memory ( action, name, ndim, value ) ! !******************************************************************************* ! !! HALTON_MEMORY sets or returns quantities associated with the Halton sequence. ! ! ! Modified: ! ! 09 March 2003 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, character ( len = * ) ACTION, the desired action. ! 'GET' means get the value of a particular quantity. ! 'SET' means set the value of a particular quantity. ! 'INC' means increment the value of a particular quantity. ! (Only the SEED can be incremented.) ! ! Input, character ( len = * ) NAME, the name of the quantity. ! 'BASE' means the Halton base or bases. ! 'NDIM' means the spatial dimension. ! 'SEED' means the current Halton seed. ! ! Input/output, integer NDIM, the dimension of the quantity. ! If ACTION is 'SET' and NAME is 'BASE', then NDIM is input, and ! is the number of entries in VALUE to be put into BASE. ! ! Input/output, integer VALUE(NDIM), contains a value. ! If ACTION is 'SET', then on input, VALUE contains values to be assigned ! to the internal variable. ! If ACTION is 'GET', then on output, VALUE contains the values of ! the specified internal variable. ! If ACTION is 'INC', then on input, VALUE contains the increment to ! be added to the specified internal variable. ! ! Modified: ! ! 29 April 2005 ! ! Author: ! ! Franz Roters ! use prec, only: pReal, pInt implicit none character ( len = * ) action integer(pInt), allocatable, save :: base(:) logical, save :: first_call = .true. integer(pInt) i character ( len = * ) name integer(pInt) ndim integer(pInt), save :: ndim_save = 0 integer(pInt) prime integer(pInt), save :: seed = 1 integer(pInt) value(*) if ( first_call ) then ndim_save = 1 allocate ( base(ndim_save) ) base(1) = 2 first_call = .false. end if ! ! Set ! if ( action(1:1) == 'S' .or. action(1:1) == 's' ) then if ( name(1:1) == 'B' .or. name(1:1) == 'b' ) then if ( ndim_save /= ndim ) then deallocate ( base ) ndim_save = ndim allocate ( base(ndim_save) ) end if base(1:ndim) = value(1:ndim) else if ( name(1:1) == 'N' .or. name(1:1) == 'n' ) then if ( ndim_save /= value(1) ) then deallocate ( base ) ndim_save = value(1) allocate ( base(ndim_save) ) do i = 1, ndim_save base(i) = prime ( i ) end do else ndim_save = value(1) end if else if ( name(1:1) == 'S' .or. name(1:1) == 's' ) then seed = value(1) end if ! ! Get ! else if ( action(1:1) == 'G' .or. action(1:1) == 'g' ) then if ( name(1:1) == 'B' .or. name(1:1) == 'b' ) then if ( ndim /= ndim_save ) then deallocate ( base ) ndim_save = ndim allocate ( base(ndim_save) ) do i = 1, ndim_save base(i) = prime(i) end do end if value(1:ndim_save) = base(1:ndim_save) else if ( name(1:1) == 'N' .or. name(1:1) == 'n' ) then value(1) = ndim_save else if ( name(1:1) == 'S' .or. name(1:1) == 's' ) then value(1) = seed end if ! ! Increment ! else if ( action(1:1) == 'I' .or. action(1:1) == 'i' ) then if ( name(1:1) == 'S' .or. name(1:1) == 's' ) then seed = seed + value(1) end if end if return END SUBROUTINE subroutine halton_ndim_set ( ndim ) ! !******************************************************************************* ! !! HALTON_NDIM_SET sets the dimension for a Halton sequence. ! ! ! Modified: ! ! 26 February 2001 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer NDIM, the dimension of the Halton vectors. ! ! Modified: ! ! 29 April 2005 ! ! Author: ! ! Franz Roters ! use prec, only: pReal, pInt implicit none integer(pInt) ndim integer(pInt) value(1) value(1) = ndim call halton_memory ( 'SET', 'NDIM', 1, value ) return END SUBROUTINE subroutine halton_seed_set ( seed ) ! !******************************************************************************* ! !! HALTON_SEED_SET sets the "seed" for the Halton sequence. ! ! ! Discussion: ! ! Calling HALTON repeatedly returns the elements of the ! Halton sequence in order, starting with element number 1. ! An internal counter, called SEED, keeps track of the next element ! to return. Each time the routine is called, the SEED-th element ! is computed, and then SEED is incremented by 1. ! ! To restart the Halton sequence, it is only necessary to reset ! SEED to 1. It might also be desirable to reset SEED to some other value. ! This routine allows the user to specify any value of SEED. ! ! The default value of SEED is 1, which restarts the Halton sequence. ! ! Modified: ! ! 26 February 2001 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer SEED, the seed for the Halton sequence. ! ! Modified: ! ! 29 April 2005 ! ! Author: ! ! Franz Roters ! use prec, only: pReal, pInt implicit none integer(pInt), parameter :: ndim = 1 integer(pInt) seed integer(pInt) value(ndim) value(1) = seed call halton_memory ( 'SET', 'SEED', ndim, value ) return END SUBROUTINE subroutine i_to_halton ( seed, base, ndim, r ) ! !******************************************************************************* ! !! I_TO_HALTON computes an element of a Halton sequence. ! ! ! Reference: ! ! J H Halton, ! On the efficiency of certain quasi-random sequences of points ! in evaluating multi-dimensional integrals, ! Numerische Mathematik, ! Volume 2, pages 84-90, 1960. ! ! Modified: ! ! 26 February 2001 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer SEED, the index of the desired element. ! Only the absolute value of SEED is considered. SEED = 0 is allowed, ! and returns R = 0. ! ! Input, integer BASE(NDIM), the Halton bases, which should be ! distinct prime numbers. This routine only checks that each base ! is greater than 1. ! ! Input, integer NDIM, the dimension of the sequence. ! ! Output, real R(NDIM), the SEED-th element of the Halton sequence ! for the given bases. ! ! Modified: ! ! 29 April 2005 ! ! Author: ! ! Franz Roters ! use prec, ONLY: pReal, pInt implicit none integer(pInt) ndim integer(pInt) base(ndim) real(pReal) base_inv(ndim) integer(pInt) digit(ndim) integer(pInt) i real(pReal) r(ndim) integer(pInt) seed integer(pInt) seed2(ndim) seed2(1:ndim) = abs ( seed ) r(1:ndim) = 0.0_pReal if ( any ( base(1:ndim) <= 1 ) ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'I_TO_HALTON - Fatal error!' write ( *, '(a)' ) ' An input base BASE is <= 1!' do i = 1, ndim write ( *, '(i6,i6)' ) i, base(i) end do call flush(6) stop end if base_inv(1:ndim) = 1.0_pReal / real ( base(1:ndim), pReal ) do while ( any ( seed2(1:ndim) /= 0 ) ) digit(1:ndim) = mod ( seed2(1:ndim), base(1:ndim) ) r(1:ndim) = r(1:ndim) + real ( digit(1:ndim), pReal ) * base_inv(1:ndim) base_inv(1:ndim) = base_inv(1:ndim) / real ( base(1:ndim), pReal ) seed2(1:ndim) = seed2(1:ndim) / base(1:ndim) end do return END SUBROUTINE function prime ( n ) ! !******************************************************************************* ! !! PRIME returns any of the first PRIME_MAX prime numbers. ! ! ! Note: ! ! PRIME_MAX is 1500, and the largest prime stored is 12553. ! ! Modified: ! ! 21 June 2002 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Milton Abramowitz and Irene Stegun, ! Handbook of Mathematical Functions, ! US Department of Commerce, 1964, pages 870-873. ! ! Daniel Zwillinger, ! CRC Standard Mathematical Tables and Formulae, ! 30th Edition, ! CRC Press, 1996, pages 95-98. ! ! Parameters: ! ! Input, integer N, the index of the desired prime number. ! N = -1 returns PRIME_MAX, the index of the largest prime available. ! N = 0 is legal, returning PRIME = 1. ! It should generally be true that 0 <= N <= PRIME_MAX. ! ! Output, integer PRIME, the N-th prime. If N is out of range, PRIME ! is returned as 0. ! ! Modified: ! ! 29 April 2005 ! ! Author: ! ! Franz Roters ! use prec, only: pReal, pInt implicit none integer(pInt), parameter :: prime_max = 1500 integer(pInt), save :: icall = 0 integer(pInt) n integer(pInt), save, dimension ( prime_max ) :: npvec integer(pInt) prime if ( icall == 0 ) then icall = 1 npvec(1:100) = (/& 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, & 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, & 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, & 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, & 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, & 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, & 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, & 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, & 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, & 467, 479, 487, 491, 499, 503, 509, 521, 523, 541 /) npvec(101:200) = (/ & 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, & 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, & 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, & 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, & 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, & 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, & 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, & 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, & 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, & 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223 /) npvec(201:300) = (/ & 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, & 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, & 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, & 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, & 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, & 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, & 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, & 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, & 91823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, & 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987 /) npvec(301:400) = (/ & 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, & 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, & 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, & 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, & 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, & 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, & 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, & 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, & 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, & 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741 /) npvec(401:500) = (/ & 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, & 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, & 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, & 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, & 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, & 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, & 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, & 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, & 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, & 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571 /) npvec(501:600) = (/ & 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, & 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, & 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, & 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, & 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, & 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, & 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, & 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, & 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, & 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409 /) npvec(601:700) = (/ & 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, & 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, & 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, & 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, & 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, & 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, & 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, & 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, & 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, & 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279 /) npvec(701:800) = (/ & 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, & 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, & 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, & 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, & 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, & 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, & 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, & 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, & 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, & 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133 /) npvec(801:900) = (/ & 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, & 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, & 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, & 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, & 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, & 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, & 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, & 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, & 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, & 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997 /) npvec(901:1000) = (/ & 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, & 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, & 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, & 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, & 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, & 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, & 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, & 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, & 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, & 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919 /) npvec(1001:1100) = (/ & 7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, & 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, & 8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, & 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, & 8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, & 8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, & 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, & 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, & 8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, & 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831 /) npvec(1101:1200) = (/ & 8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, & 8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, & 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, & 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, & 9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, & 9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, & 9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, & 9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533, & 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, & 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733 /) npvec(1201:1300) = (/ & 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, & 9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, & 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973,10007, & 10009,10037,10039,10061,10067,10069,10079,10091,10093,10099, & 10103,10111,10133,10139,10141,10151,10159,10163,10169,10177, & 10181,10193,10211,10223,10243,10247,10253,10259,10267,10271, & 10273,10289,10301,10303,10313,10321,10331,10333,10337,10343, & 10357,10369,10391,10399,10427,10429,10433,10453,10457,10459, & 10463,10477,10487,10499,10501,10513,10529,10531,10559,10567, & 10589,10597,10601,10607,10613,10627,10631,10639,10651,10657 /) npvec(1301:1400) = (/ & 10663,10667,10687,10691,10709,10711,10723,10729,10733,10739, & 10753,10771,10781,10789,10799,10831,10837,10847,10853,10859, & 10861,10867,10883,10889,10891,10903,10909,19037,10939,10949, & 10957,10973,10979,10987,10993,11003,11027,11047,11057,11059, & 11069,11071,11083,11087,11093,11113,11117,11119,11131,11149, & 11159,11161,11171,11173,11177,11197,11213,11239,11243,11251, & 11257,11261,11273,11279,11287,11299,11311,11317,11321,11329, & 11351,11353,11369,11383,11393,11399,11411,11423,11437,11443, & 11447,11467,11471,11483,11489,11491,11497,11503,11519,11527, & 11549,11551,11579,11587,11593,11597,11617,11621,11633,11657 /) npvec(1401:1500) = (/ & 11677,11681,11689,11699,11701,11717,11719,11731,11743,11777, & 11779,11783,11789,11801,11807,11813,11821,11827,11831,11833, & 11839,11863,11867,11887,11897,11903,11909,11923,11927,11933, & 11939,11941,11953,11959,11969,11971,11981,11987,12007,12011, & 12037,12041,12043,12049,12071,12073,12097,12101,12107,12109, & 12113,12119,12143,12149,12157,12161,12163,12197,12203,12211, & 12227,12239,12241,12251,12253,12263,12269,12277,12281,12289, & 12301,12323,12329,12343,12347,12373,12377,12379,12391,12401, & 12409,12413,12421,12433,12437,12451,12457,12473,12479,12487, & 12491,12497,12503,12511,12517,12527,12539,12541,12547,12553 /) end if if ( n == -1 ) then prime = prime_max else if ( n == 0 ) then prime = 1 else if ( n <= prime_max ) then prime = npvec(n) else prime = 0 write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'PRIME - Fatal error!' write ( *, '(a,i6)' ) ' Illegal prime index N = ', n write ( *, '(a,i6)' ) ' N must be between 0 and PRIME_MAX =',prime_max call flush(6) stop end if return END FUNCTION !******************************************************************** ! This routine generates a random orientation !******************************************************************** subroutine math_random_ori (phi1, PHI, phi2, scatter) use prec, only: pReal, pInt implicit none real(pReal) phi1, PHI, phi2, scatter, x, y, z call random_number(x) call random_number(y) call random_number(z) phi1=x*360.0_pReal PHI=acos(y)*inDeg phi2=z*360.0_pReal scatter=0.0_pReal return END SUBROUTINE subroutine math_halton_ori (phi1, PHI, phi2, scatter) !******************************************************************** ! This routine generates a random orientation using Halton series !******************************************************************** use prec, only: pReal, pInt implicit none real(pReal) phi1, PHI, phi2, scatter, r(3) call halton(3,r) phi1=r(1)*360.0_pReal PHI=acos(r(2))*inDeg phi2=r(3)*360.0_pReal scatter=0.0_pReal return END SUBROUTINE !******************************************************************** ! This routine applies gaussian scatter to the texture components !******************************************************************** subroutine math_disturbOri (phi1, PHI, phi2, scatter) use prec, only: pReal, pInt implicit none real(pReal) phi1, PHI, phi2, scatter real(pReal) orot(3,3), srot(3,3), p1(2), P(2), p2(2), rot(3,3) real(pReal) gscatter,scale,x,y,s,z,arg,angle,rand,gauss p1(1)=0 P(1)=0 p2(1)=0 ! Helming uses different distribution with Bessel functions ! therefore the gauss scatter width has to be scaled differently gscatter=0.95*scatter scale=cos(gscatter*inRad) 100 call random_number(x) call random_number(y) call random_number(s) call random_number(z) x=x-0.5 s=s-0.5 z=z-0.5 p1(2)=x*gscatter*2.0_pReal p2(2)=z*gscatter*2.0_pReal arg=scale+y*(1.0-scale) P(2)=sign(1.0_pReal,s)*acos(arg)*inDeg angle = math_disorient(p1,P,p2) call random_number(rand) gauss=exp(-1.0*(angle/gscatter)**2) if(gauss.LT.rand) then goto 100 end if ! calculate rotation matrix for rotation angles srot = math_EulertoR(p1(2),p(2),p2(2)) ! calculate rotation matrix for original euler angles orot = math_EulertoR(phi1,PHI,phi2) ! rotate originial orientation matrix rot=matmul(srot,orot) ! calculate Euler angles for new rotation matrix call math_RtoEuler(rot, phi1,PHI,phi2) return END SUBROUTINE !******************************************************************** ! This routine computes one orientation of a fiber component !******************************************************************** subroutine math_fiber(alpha1, alpha2,beta1,beta2,scatter,phi1,PHI,phi2) use prec, only: pReal, pInt implicit none real(pReal) alpha1, alpha2,beta1,beta2,scatter, phi1, PHI, phi2 real(pReal) orot(3,3), srot(3,3), ac(3), as(3),ori(3,3), rrot(3,3) real(pReal) a1r,a2r,b1r,b2r,angle,axis_u,axis_v,axis_w,rand,x,y,z,gscatter,scale,gauss integer(pInt) i ! convert angles to radians a1r=alpha1*inRad a2r=alpha2*inRad b1r=beta1*inRad b2r=beta2*inRad ! calculate fiber axis in crystal coordinate system ac(1)=sin(a1r)*cos(a2r) ac(2)=sin(a1r)*sin(a2r) ac(3)=cos(a1r) ! calculate fiber axis in sample coordinate system as(1)=sin(b1r)*cos(b2r) as(2)=sin(b1r)*sin(b2r) as(3)=cos(b1r) ! calculate rotation angle between sample and crystal system angle=-acos(dot_product(ac, as)) if(angle.NE.0.0) then ! calculate rotation axis between sample and crystal system axis_u=ac(2)*as(3)-ac(3)*as(2) axis_v=ac(3)*as(1)-ac(1)*as(3) axis_w=ac(1)*as(2)-ac(2)*as(1) ! calculate rotation matrix orot = math_RodrigtoR(angle, axis_u, axis_v, axis_w) else orot = math_identity(3) end if ! calculate random rotation angle about fiber axis call random_number(rand) angle=rand*2.0_pReal*pi rrot = math_RodrigtoR(angle, as(1), as(2), as(3)) ! find random axis pependicular to fiber axis call random_number(x) call random_number(y) if (as(3).NE.0) then z=-(x*as(1)+y*as(2))/as(3) else if(as(2).NE.0) then z=y y=-(x*as(1)+z*as(3))/as(2) else if(as(1).NE.0) then z=x x=-(y*as(2)+z*as(3))/as(1) end if ! Helming uses different distribution with Bessel functions ! therefore the gauss scatter width has to be scalled differently gscatter=0.95*scatter scale=cos(2*gscatter*inRad) ! calculate rotation angle 100 call random_number(rand) angle=sign(1.0_pReal,rand)*acos(abs(rand)*scale)*inDeg call random_number(rand) gauss=exp(-1.0*(angle/gscatter)**2) if(gauss.LT.rand) then goto 100 end if ! convert angle to radians angle=angle*inRad srot = math_RodrigtoR(angle, x, y, z) ori=matmul(srot, matmul(rrot, orot)) ! calculate Euler angles for new rotation matrix call math_RtoEuler(ori, phi1,PHI,phi2) return END SUBROUTINE END MODULE math