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https://github.com/LCPQ/quantum_package
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164 lines
4.0 KiB
Fortran
164 lines
4.0 KiB
Fortran
c************************************************************************
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subroutine maxovl(n,m,s,t,w)
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C
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C This subprogram contains an iterative procedure to find the
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C unitary transformation of a set of n vectors which maximizes
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C the sum of their square overlaps with a set of m reference
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C vectors (m.le.n)
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C
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C S: overlap matrix <ref|vec>
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C T: rotation matrix
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C W: new overlap matrix
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C
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C
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implicit real*8(a-h,o-y),logical*1(z)
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parameter (id1=300)
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dimension s(id1,id1),t(id1,id1),w(id1,id1)
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data small/1.d-6/
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zprt=.true.
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niter=100
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conv=1.d-8
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write (6,5) n,m,conv
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5 format (//5x,'Unitary transformation of',i3,' vectors'/
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* 5x,'following the principle of maximum overlap with a set of',
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* i3,' reference vectors'/5x,'required convergence on rotation ',
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* 'angle =',f13.10///5x,'Starting overlap matrix'/)
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do 6 i=1,m
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write (6,145) i
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6 write (6,150) (s(i,j),j=1,n)
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8 mm=m-1
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if (m.lt.n) mm=m
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iter=0
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do 20 j=1,n
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do 16 i=1,n
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t(i,j)=0.d0
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16 continue
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do 18 i=1,m
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18 w(i,j)=s(i,j)
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20 t(j,j)=1.d0
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sum=0.d0
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do 10 i=1,m
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sum=sum+s(i,i)*s(i,i)
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10 continue
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sum=sum/m
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if (zprt) write (6,12) sum
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12 format (//5x,'Average square overlap =',f10.6)
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if (n.eq.1) goto 100
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last=n
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j=1
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21 if (j.ge.last) goto 30
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sum=0.d0
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do 22 i=1,n
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22 sum=sum+s(i,j)*s(i,j)
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if (sum.gt.small) goto 28
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do 24 i=1,n
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sij=s(i,j)
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s(i,j)=-s(i,last)
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s(i,last)=sij
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tij=t(i,j)
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t(i,j)=-t(i,last)
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t(i,last)=tij
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24 continue
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last=last-1
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goto 21
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28 j=j+1
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goto 21
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30 iter=iter+1
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imax=0
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jmax=0
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dmax=0.d0
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amax=0.d0
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do 60 i=1,mm
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ip=i+1
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do 50 j=ip,n
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a=s(i,j)*s(i,j)-s(i,i)*s(i,i)
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b=-s(i,i)*s(i,j)
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if (j.gt.m) goto 31
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a=a+s(j,i)*s(j,i)-s(j,j)*s(j,j)
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b=b+s(j,i)*s(j,j)
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31 b=b+b
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if (a.eq.0.d0) goto 32
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ba=b/a
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if (dabs(ba).gt.small) goto 32
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if (a.gt.0.d0) goto 33
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tang=-0.5d0*ba
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cosine=1.d0/dsqrt(1.d0+tang*tang)
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sine=tang*cosine
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goto 34
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32 tang=0.d0
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if (b.ne.0.d0) tang=(a+dsqrt(a*a+b*b))/b
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cosine=1.d0/dsqrt(1.d0+tang*tang)
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sine=tang*cosine
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goto 34
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33 cosine=0.d0
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sine=1.d0
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34 delta=sine*(a*sine+b*cosine)
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if (zprt.and.delta.lt.0.d0) write (6,71) i,j,a,b,sine,cosine,delta
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do 35 k=1,m
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p=s(k,i)*cosine-s(k,j)*sine
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q=s(k,i)*sine+s(k,j)*cosine
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s(k,i)=p
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35 s(k,j)=q
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do 40 k=1,n
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p=t(k,i)*cosine-t(k,j)*sine
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q=t(k,i)*sine+t(k,j)*cosine
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t(k,i)=p
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t(k,j)=q
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40 continue
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45 d=dabs(sine)
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if (d.le.amax) goto 50
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imax=i
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jmax=j
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amax=d
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dmax=delta
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50 continue
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60 continue
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if (zprt) write (6,70) iter,amax,imax,jmax,dmax
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70 format (' iter=',i4,' largest rotation=',f12.8,
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* ', vectors',i3,' and',i3,', incr. of diag. squares=',g12.5)
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71 format (' i,j,a,b,sin,cos,delta =',2i3,5f10.5)
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if (amax.lt.conv) goto 100
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if (iter.lt.niter) goto 30
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write (6,80)
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write (6,*) 'niter=',niter
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80 format (//5x,'*** maximum number of cycles exceeded ',
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* 'in subroutine maxovl ***'//)
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stop
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100 continue
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do 120 j=1,n
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if (s(j,j).gt.0.d0) goto 120
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do 105 i=1,m
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105 s(i,j)=-s(i,j)
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do 110 i=1,n
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110 t(i,j)=-t(i,j)
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120 continue
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sum=0.d0
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do 125 i=1,m
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125 sum=sum+s(i,i)*s(i,i)
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sum=sum/m
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do 122 i=1,m
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do 122 j=1,n
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sw=s(i,j)
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s(i,j)=w(i,j)
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122 w(i,j)=sw
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if (.not.zprt) return
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write (6,12) sum
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write (6,130)
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130 format (//5x,'transformation matrix')
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do 140 i=1,n
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write (6,145) i
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140 write (6,150) (t(i,j),j=1,n)
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145 format (i8)
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150 format (2x,10f12.8)
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write (6,160)
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160 format (//5x,'new overlap matrix'/)
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do 170 i=1,m
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write (6,145) i
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170 write (6,150) (w(i,j),j=1,n)
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return
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end
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