2015-07-02 00:45:36 +02:00
|
|
|
c************************************************************************
|
|
|
|
|
subroutine maxovl(n,m,s,t,w)
|
|
|
|
|
C
|
|
|
|
|
C This subprogram contains an iterative procedure to find the
|
|
|
|
|
C unitary transformation of a set of n vectors which maximizes
|
|
|
|
|
C the sum of their square overlaps with a set of m reference
|
|
|
|
|
C vectors (m.le.n)
|
|
|
|
|
C
|
|
|
|
|
C S: overlap matrix <ref|vec>
|
|
|
|
|
C T: rotation matrix
|
|
|
|
|
C W: new overlap matrix
|
|
|
|
|
C
|
|
|
|
|
C
|
|
|
|
|
implicit real*8(a-h,o-y),logical*1(z)
|
|
|
|
|
parameter (id1=300)
|
|
|
|
|
dimension s(id1,id1),t(id1,id1),w(id1,id1)
|
|
|
|
|
data small/1.d-6/
|
|
|
|
|
|
|
|
|
|
zprt=.true.
|
2016-02-17 17:15:54 +01:00
|
|
|
niter=500
|
2015-07-02 00:45:36 +02:00
|
|
|
conv=1.d-8
|
|
|
|
|
|
|
|
|
|
write (6,5) n,m,conv
|
|
|
|
|
5 format (//5x,'Unitary transformation of',i3,' vectors'/
|
|
|
|
|
* 5x,'following the principle of maximum overlap with a set of',
|
|
|
|
|
* i3,' reference vectors'/5x,'required convergence on rotation ',
|
|
|
|
|
* 'angle =',f13.10///5x,'Starting overlap matrix'/)
|
|
|
|
|
do 6 i=1,m
|
|
|
|
|
write (6,145) i
|
|
|
|
|
6 write (6,150) (s(i,j),j=1,n)
|
|
|
|
|
8 mm=m-1
|
|
|
|
|
if (m.lt.n) mm=m
|
|
|
|
|
iter=0
|
|
|
|
|
do 20 j=1,n
|
|
|
|
|
do 16 i=1,n
|
|
|
|
|
t(i,j)=0.d0
|
|
|
|
|
16 continue
|
|
|
|
|
do 18 i=1,m
|
|
|
|
|
18 w(i,j)=s(i,j)
|
|
|
|
|
20 t(j,j)=1.d0
|
|
|
|
|
sum=0.d0
|
|
|
|
|
do 10 i=1,m
|
|
|
|
|
sum=sum+s(i,i)*s(i,i)
|
|
|
|
|
10 continue
|
|
|
|
|
sum=sum/m
|
|
|
|
|
if (zprt) write (6,12) sum
|
|
|
|
|
12 format (//5x,'Average square overlap =',f10.6)
|
|
|
|
|
if (n.eq.1) goto 100
|
|
|
|
|
last=n
|
|
|
|
|
j=1
|
|
|
|
|
21 if (j.ge.last) goto 30
|
|
|
|
|
sum=0.d0
|
|
|
|
|
|
|
|
|
|
do 22 i=1,n
|
|
|
|
|
22 sum=sum+s(i,j)*s(i,j)
|
|
|
|
|
if (sum.gt.small) goto 28
|
|
|
|
|
do 24 i=1,n
|
|
|
|
|
sij=s(i,j)
|
|
|
|
|
s(i,j)=-s(i,last)
|
|
|
|
|
s(i,last)=sij
|
|
|
|
|
tij=t(i,j)
|
|
|
|
|
t(i,j)=-t(i,last)
|
|
|
|
|
t(i,last)=tij
|
|
|
|
|
24 continue
|
|
|
|
|
last=last-1
|
|
|
|
|
goto 21
|
|
|
|
|
28 j=j+1
|
|
|
|
|
goto 21
|
|
|
|
|
30 iter=iter+1
|
|
|
|
|
imax=0
|
|
|
|
|
jmax=0
|
|
|
|
|
dmax=0.d0
|
|
|
|
|
amax=0.d0
|
|
|
|
|
do 60 i=1,mm
|
|
|
|
|
ip=i+1
|
|
|
|
|
do 50 j=ip,n
|
|
|
|
|
a=s(i,j)*s(i,j)-s(i,i)*s(i,i)
|
|
|
|
|
b=-s(i,i)*s(i,j)
|
|
|
|
|
if (j.gt.m) goto 31
|
|
|
|
|
a=a+s(j,i)*s(j,i)-s(j,j)*s(j,j)
|
|
|
|
|
b=b+s(j,i)*s(j,j)
|
|
|
|
|
31 b=b+b
|
|
|
|
|
if (a.eq.0.d0) goto 32
|
|
|
|
|
ba=b/a
|
|
|
|
|
if (dabs(ba).gt.small) goto 32
|
|
|
|
|
if (a.gt.0.d0) goto 33
|
|
|
|
|
tang=-0.5d0*ba
|
|
|
|
|
cosine=1.d0/dsqrt(1.d0+tang*tang)
|
|
|
|
|
sine=tang*cosine
|
|
|
|
|
goto 34
|
|
|
|
|
32 tang=0.d0
|
|
|
|
|
if (b.ne.0.d0) tang=(a+dsqrt(a*a+b*b))/b
|
|
|
|
|
cosine=1.d0/dsqrt(1.d0+tang*tang)
|
|
|
|
|
sine=tang*cosine
|
|
|
|
|
goto 34
|
|
|
|
|
33 cosine=0.d0
|
|
|
|
|
sine=1.d0
|
|
|
|
|
34 delta=sine*(a*sine+b*cosine)
|
|
|
|
|
if (zprt.and.delta.lt.0.d0) write (6,71) i,j,a,b,sine,cosine,delta
|
|
|
|
|
do 35 k=1,m
|
|
|
|
|
p=s(k,i)*cosine-s(k,j)*sine
|
|
|
|
|
q=s(k,i)*sine+s(k,j)*cosine
|
|
|
|
|
s(k,i)=p
|
|
|
|
|
35 s(k,j)=q
|
|
|
|
|
do 40 k=1,n
|
|
|
|
|
p=t(k,i)*cosine-t(k,j)*sine
|
|
|
|
|
q=t(k,i)*sine+t(k,j)*cosine
|
|
|
|
|
t(k,i)=p
|
|
|
|
|
t(k,j)=q
|
|
|
|
|
40 continue
|
|
|
|
|
45 d=dabs(sine)
|
|
|
|
|
if (d.le.amax) goto 50
|
|
|
|
|
imax=i
|
|
|
|
|
jmax=j
|
|
|
|
|
amax=d
|
|
|
|
|
dmax=delta
|
|
|
|
|
50 continue
|
|
|
|
|
60 continue
|
|
|
|
|
if (zprt) write (6,70) iter,amax,imax,jmax,dmax
|
|
|
|
|
70 format (' iter=',i4,' largest rotation=',f12.8,
|
|
|
|
|
* ', vectors',i3,' and',i3,', incr. of diag. squares=',g12.5)
|
|
|
|
|
71 format (' i,j,a,b,sin,cos,delta =',2i3,5f10.5)
|
|
|
|
|
if (amax.lt.conv) goto 100
|
|
|
|
|
if (iter.lt.niter) goto 30
|
|
|
|
|
write (6,80)
|
|
|
|
|
write (6,*) 'niter=',niter
|
|
|
|
|
80 format (//5x,'*** maximum number of cycles exceeded ',
|
|
|
|
|
* 'in subroutine maxovl ***'//)
|
|
|
|
|
stop
|
|
|
|
|
100 continue
|
|
|
|
|
do 120 j=1,n
|
|
|
|
|
if (s(j,j).gt.0.d0) goto 120
|
|
|
|
|
do 105 i=1,m
|
|
|
|
|
105 s(i,j)=-s(i,j)
|
|
|
|
|
do 110 i=1,n
|
|
|
|
|
110 t(i,j)=-t(i,j)
|
|
|
|
|
120 continue
|
|
|
|
|
sum=0.d0
|
|
|
|
|
do 125 i=1,m
|
|
|
|
|
125 sum=sum+s(i,i)*s(i,i)
|
|
|
|
|
sum=sum/m
|
|
|
|
|
do 122 i=1,m
|
|
|
|
|
do 122 j=1,n
|
|
|
|
|
sw=s(i,j)
|
|
|
|
|
s(i,j)=w(i,j)
|
|
|
|
|
122 w(i,j)=sw
|
|
|
|
|
if (.not.zprt) return
|
|
|
|
|
write (6,12) sum
|
|
|
|
|
write (6,130)
|
|
|
|
|
130 format (//5x,'transformation matrix')
|
|
|
|
|
do 140 i=1,n
|
|
|
|
|
write (6,145) i
|
|
|
|
|
140 write (6,150) (t(i,j),j=1,n)
|
|
|
|
|
145 format (i8)
|
|
|
|
|
150 format (2x,10f12.8)
|
|
|
|
|
write (6,160)
|
|
|
|
|
160 format (//5x,'new overlap matrix'/)
|
|
|
|
|
do 170 i=1,m
|
|
|
|
|
write (6,145) i
|
|
|
|
|
170 write (6,150) (w(i,j),j=1,n)
|
|
|
|
|
return
|
|
|
|
|
end
|
|
|
|
|
|
