MODULE m_ylm IMPLICIT NONE private !---> check whether or not normalizations are needed REAL, ALLOCATABLE, SAVE :: ynorm(:) INTEGER, SAVE :: lmaxd = -1 ! initial value public ylm4,ylmnorm_init CONTAINS SUBROUTINE ylm4( > lmax,v, < ylm) !************************************************************ ! generate the spherical harmonics for the vector v ! using a stable upward recursion in l. (see notes ! by m. weinert.) ! m.weinert january 1982 ! modified by R. Podloucky (added in ynorm); July 1989 ! cleaned up mw 1995 ! ! modified to make use of f90 constructs. note that ! the normalization is an internal subroutine and hence ! can only be called from here. also, no need to dimension ! arrays for ynorm, done dynamically. mw 1999 !************************************************************ USE m_juDFT INTEGER, INTENT (IN) :: lmax REAL, INTENT (IN) :: v(3) COMPLEX, INTENT (OUT):: ylm( (lmax+1)**2 ) REAL, PARAMETER :: small = 1.0e-12 INTEGER l,lm0,m REAL fac,x,y,z,xy,r,rxy,cth,sth,cph,sph,cph2 REAL p(0:lmax,0:lmax),c(0:lmax),s(0:lmax) COMPLEX ylms IF (lmax.GT.lmaxd) THEN CALL juDFT_error("lmaxd too small in ylm4") ENDIF !---> calculate sin and cos of theta and phi x = v(1) y = v(2) z = v(3) xy = x*x + y*y r = sqrt(xy + z*z) rxy = sqrt(xy) IF (r.GT.small) THEN cth = z/r sth = rxy/r ELSE sth = 0.0 cth = 1.0 ENDIF IF(rxy.GT.small) THEN cph = x/rxy sph = y/rxy ELSE cph = 1.0 sph = 0.0 ENDIF !---> generate associated legendre functions for m.ge.0 fac = 1.0 !---> loop over m values DO m = 0, lmax - 1 fac = -(m+m-1)*fac p(m,m) = fac p(m+1,m) = (m+m+1)*cth*fac !---> recurse upward in l DO l = m+2, lmax p(l,m)=((l+l-1)*cth*p(l-1,m)-(l+m-1)*p(l-2,m))/(l-m) ENDDO fac = fac*sth ENDDO p(lmax,lmax) = -(lmax+lmax-1)*fac !---> determine sin and cos of phi s(0) = 0.0 s(1) = sph c(0) = 1.0 c(1) = cph cph2 = cph+cph DO m = 2, lmax s(m) = cph2*s(m-1)-s(m-2) c(m) = cph2*c(m-1)-c(m-2) ENDDO !---> multiply in the normalization factors DO l=0,lmax ylm(l*(l+1)+1) = ynorm(l*(l+1)+1)*cmplx(p(l,0),0.0) ENDDO DO m = 1, lmax DO l = m, lmax lm0 = l*(l+1)+1 ylms = p(l,m)*cmplx(c(m),s(m)) ylm(lm0+m) = ynorm(lm0+m)*ylms ylm(lm0-m) = conjg(ylms)*ynorm(lm0-m) ENDDO ENDDO RETURN END SUBROUTINE ylm4 SUBROUTINE ylmnorm_init(lmax) !******************************************************************** ! normalization constants for ylm (internal subroutine has access ! to lmax and ynorm from above) !******************************************************************** !\$ USE OMP_LIB use m_juDFT USE m_constants, ONLY : pimach INTEGER,INTENT(IN):: lmax INTEGER l,lm0,m REAL a,cd,fpi IF ( allocated(ynorm) ) DEALLOCATE(ynorm) ALLOCATE ( ynorm( (lmax+1)**2 ) ) ! allocate array lmaxd = lmax fpi = 4.0*pimach() !\$ if (omp_in_parallel()) call juDFT_error( !\$ + "ylmnorm should not called in parallel",calledby="ylm4.f") DO l=0,lmax lm0 = l*(l+1) + 1 cd=1.0 a = sqrt( (2*l+1)/fpi ) ynorm(lm0) = a DO m=1,l cd=cd/( (l+1-m)*(l+m) ) ynorm(lm0+m) = a*sqrt(cd) ynorm(lm0-m) = ( (-1.0)**m )*ynorm(lm0+m) ENDDO ENDDO RETURN END SUBROUTINE ylmnorm_init END MODULE m_ylm