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求存在缺省值的左场Y(ny,nt)和右场Z(nz,nt)的左同类相关分布lhomo(ny,np)，右同类相关分布rhomo(nz,np)，左异类相关分布lhete(ny,np)和右异类相关分布rhete(nz,np)，左场和右场的时间系数A(nt,np)和B(nt,np)，奇异值cekma(nmin)，解释协方差平方和百分比scfk(np)，累计解释协方差平方和百分比cscfk(np)，展开系数之间的相关系数rab(np)，解释左场的方差百分比lcovf(np)，解释右场的方差百分比rcovf(np)
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c This program is an example of svd analysis c
c (Coded by Jincheng Wang and Jianping Li) c
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c ---------NOTE------- c
c Stack Overflow c
c Compaq visual fortran 6.5: c
c Project -> settings | link | output | stack allocations c
c Modify 'reserve' and 'commit' value: default value 0x400000 means 4M c
c Intel fortran + vs.net 2003: c
c Properties | link | system c
c Modify the 'stack reserve size' and 'stack commit size' c
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
program svd_test
implicit none
cccccccc---Parameters that you can modify---cccccccc
integer,parameter::NY=161*71
integer,parameter::NZ=153*63
integer,parameter::NT=107
integer,parameter::NMIN=NZ
integer,parameter::NP=10
real,parameter::YMV=-1.0e30
real,parameter::ZMV=-99999.0
cccccccc---The main variables for input and output---cccccccc
real ::Y(NY,NT),Z(NZ,NT)
real ::A(NT,NP),B(NT,NP)
real ::cekma(NMIN)
real ::scfk(NP)
real ::cscfk(NP)
real ::rab(NP)
real ::lcovf(NP)
real ::rcovf(NP)
real ::vara(NP)
real ::varb(NP)
real ::lhomo(NY,NP),lhete(NY,NP)
real ::rhomo(NZ,NP),rhete(NZ,NP)
integer::i,j,k,l,m,n
ccccccccc---Main program---cccccccc
!----Read the left field----!
open(unit=1,file=
$"djf_sst_tropical_lon_-3075_12925_lat_-4075_2925.dat"
$,form="unformatted",
$access="direct",recl=4)
n=0
do j=1,NT
do i=1,NY
n=n+1
read(1,rec=n)Y(i,j)
enddo
enddo
close(1)
!----Read the right field----!
open(unit=1,file=
$"djf_gpcc_africa_lon-3025_4575_lat_-1525_1575.dat"
$,form="unformatted",
$access="direct",recl=4)
n=0
do j=1,NT
do i=1,NZ
n=n+1
read(1,rec=n)Z(i,j)
enddo
enddo
close(1)
!----Call the subroutine meteo_miss_svd----!
call svd(NY,NZ,NMIN,NT,Y,Z,YMV,ZMV,np,A,B,cekma,
$ scfk,cscfk,rab,lcovf,rcovf,vara,varb,lhomo,lhete,rhomo,rhete)
!----Output the left and right time coeffecient series matrices-------!
open(unit=2,file="ltime.dat",form="unformatted",access="direct",
$ recl=4)
open(unit=3,file="rtime.dat",form="unformatted",access="direct",
$ recl=4)
n=0
do j=1,NT
do i=1,NP
n=n+1
write(2,rec=n)a(j,i)
write(3,rec=n)b(j,i)
enddo
enddo
close(2);close(3)
!----Output the left homogeneous and heterogeneous correlation maps----!
open(unit=2,file="lhomo.dat",form="unformatted"
$ ,access="direct",recl=4)
open(unit=3,file="lhete.dat",form="unformatted"
$ ,access="direct",recl=4)
n=0
do j=1,NP
do i=1,NY
n=n+1
write(2,rec=n)lhomo(i,j)
write(3,rec=n)lhete(i,j)
enddo
enddo
close(2)
close(3)
!----Output the right homogeneous and heterogeneous correlation maps----!
open(unit=2,file="rhomo.dat",form="unformatted"
$ ,access="direct",recl=4)
open(unit=3,file="rhete.dat",form="unformatted"
$ ,access="direct",recl=4)
n=0
do j=1,NP
do i=1,NZ
n=n+1
write(2,rec=n)rhomo(i,j)
write(3,rec=n)rhete(i,j)
enddo
enddo
close(2);close(3)
end program svd_test
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c----------------subroutine meteo_miss_svd----------------------------------------c
c This subroutine is for SVD analysing Fields with missing values in Atmospheric c
c and Oceanic Sciences c
c (Coded by Jincheng Wang and Jianping Li, 24 June, 2009) c
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c-----------------------------------INPUT-----------------------------------------c
c Y :Left data field that consists of NT observations with missing values c
c ,each of which has NY grid points. c
c Z :Right data field that contains of the same number of c
c observations, each of which has NZ grid points. c
c NY :Number of grid points in left field including the grids of missing value c
c NZ :Number of grid points in right field including the grids of missing value c
c NT :Number of observation (Time length) c
c NMIN : NMIN=min(NY,NZ) c
c YMV :Missing Value of the Left data Y c
c ZMV :Missing Value of the Right data Z c
c NP :Integer,how many pairs of SVD mode are required ? (In general np<10) c
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c-----------------------------------OUTPUT----------------------------------------c
c A :Time coeffecient series matrix of left field. c
c B :Time coeffecient series matrix of right field. c
c cekma:Singular values c
c scfk :The percentage of the total squared covariance explained c
c by a single pair of patterns c
c cscfk:The percentage of the cumulative squared covariance c
c explained by the leading K modes c
c rab :The correlation coefficient between the corresponding c
c expansion coefficents r(a,b) c
c lcovf:The percentages of the variance of left field c
c explained by a single singular vector c
c rcovf:The percentages of the variance of right field c
c explained by a single singular vector c
c vara :The variances of expansion coefficient of left field c
c varb :The variances of expansion coefficient of right field c
c lhomo:The left homogeneous correlation maps c
c lhete:The left heterogeneous correlation maps c
c rhomo:The right homogeneous correlation maps c
c rhete:The right heterogeneous correlation maps c
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c----------------------------------WORK ARRAY------------------------------------ c
c NYM :Number of grid points in left field without the grids of missing value c
c NZM :Number of grid points in right field without the grids of missing value c
c YM :Left data field that consists of NT observations c
c ,each of which has NY grid points without missing values. c
c ZM :right data field that contains of the same number of c
c observations, each of which has NZ grid points without missing values c
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
subroutine svd(NY,NZ,NMIN,NT,Y,Z,YMV,ZMV,np,A,B,cekma,
$ scfk,cscfk,rab,lcovf,rcovf,vara,varb,lhomo,lhete,rhomo,rhete)
implicit none
!!!---The input and output variables---!!!
integer::NY,NZ,NT,NMIN
real ::Y(NY,NT),Z(NZ,NT)
real ::YMV,ZMV
integer::NP
real ::A(NT,NP),B(NT,NP)
real ::cekma(NMIN)
real ::scfk(NP)
real ::cscfk(NP)
real ::rab(NP)
real ::lcovf(NP)
real ::rcovf(NP)
real ::vara(NP)
real ::varb(NP)
real ::lhomo(NY,NP),lhete(NY,NP)
real ::rhomo(NZ,NP),rhete(NZ,NP)
!------Work Variables--------!
integer::MNY,MNZ
real,allocatable::ym(:,:)
real,allocatable::zm(:,:)
real,allocatable::lhomom(:,:),lhetem(:,:)
real,allocatable::rhomom(:,:),rhetem(:,:)
integer::yc(NY)
integer::zc(NZ)
integer::NYM
integer::NZM
integer::i,j,k,n,ka
print*,"The number of grids before removing missing values:"
print*,"Left : ",NY
print*,"Right: ",NZ
c-----Calculate the number of the grids without missing values----c
cccccccc----Left Field------cccccc
yc=0
NYM=0
do i=1,NY
if(Y(i,1).ne.YMV)then
NYM=NYM+1
yc(i)=1
endif
enddo
cccccccc----Right Field------ccccc
zc=0
NZM=0
do i=1,NZ
if(Z(i,1).ne.ZMV)then
NZM=NZM+1
zc(i)=1
endif
enddo
print*,"The number of grids after removing missing values:"
print*,"Left : ",NYM
print*,"Right: ",NZM
c-----Allocate the work array----c
KA=max(NYM,NZM)+1
allocate(ym(NYM,NT))
allocate(zm(NZM,NT))
allocate(lhomoM(NYM,NP))
allocate(lheteM(NYM,NP))
allocate(rhomoM(NZM,NP))
allocate(rheteM(NZM,NP))
print*,"Start meteo_miss_svd"
c-----Remove the missing values----c
do j=1,NT
n=0
do i=1,NY
if(yc(i).eq.1)then
n=n+1
ym(n,j)=y(i,j)
endif
enddo
enddo
do j=1,NT
n=0
do i=1,NZ
if(zc(i).eq.1)then
n=n+1
zm(n,j)=z(i,j)
endif
enddo
enddo
c-----Call meteo_svd subroutine------c
print*," Call subroutine meteo_svd"
call meteo_svd(NYM,NZM,NT,NMIN,KA,YM,ZM,NP,A,B,cekma,scfk,
$ cscfk,rab,lcovf,rcovf,vara,varb,lhomom,lhetem,rhomom,rhetem)
print*," Successfully run meteo_svd"
c-----
print*," Reconstruct left and right homogeneous and
$ heteogeneous correlation maps"
do j=1,NP
n=0
do i=1,NY
if(yc(i).eq.1)then
n=n+1
lhomo(i,j)=lhomom(n,j)
lhete(i,j)=lhetem(n,j)
else
lhomo(i,j)=YMV
lhete(i,j)=YMV
endif
enddo
enddo
do j=1,NP
n=0
do i=1,NZ
if(zc(i).eq.1)then
n=n+1
rhomo(i,j)=rhomom(n,j)
rhete(i,j)=rhetem(n,j)
else
rhomo(i,j)=ZMV
rhete(i,j)=ZMV
endif
enddo
enddo
print*,"Successfully run meteo_miss_svd"
return
end
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c----------------subroutine meteo_miss_svd----------------------------------------c
c This subroutine uses for SVD analysing in Atmospheric Sciences c
c (Coded by Hongbao Wu) c
c (Modified by Jincheng Wang and Jianping Li, 24 June, 2009) c
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c-----------------------------------INPUT-----------------------------------------c
c Y :Left data field that consists of NT observations c
c ,each of which has NY grid points. c
c Z :right data field that contains of the same number of c
c observations, each of which has NZ grid points. c
c NY :Number of grid points in left field c
c NZ :Number of grid points in right field c
c NT :Number of observation (Time length) c
c NMIN :NMIN=min(NY,NZ) c
c KA :KA=NY+1
c np :Integer,how many pairs of SVD mode are required ? (In general np<10) c
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c-----------------------------------OUTPUT----------------------------------------c
c A :Time coeffecient series matrix of left field. c
c B :Time coeffecient series matrix of right field. c
c cekma:Singular values c
c scfk :The percentage of the total squared covariance explained c
c by a single pair of patterns c
c cscfk:The percentage of the cumulative squared covariance c
c explained by the leading K modes c
c rab :The correlation coefficient between the corresponding c
c expansion coefficents r(a,b) c
c lcovf:The percentages of the variance of left field c
c explained by a single singular vector c
c rcovf:The percentages of the variance of right field c
c explained by a single singular vector c
c vara :The variances of expansion coefficient of left field c
c varb :The variances of expansion coefficient of right field c
c lhomo:The left homogeneous correlation maps c
c lhete:The left heterogeneous correlation maps c
c rhomo:The right homogeneous correlation maps c
c rhete:The right heterogeneous correlation maps c
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c------------------------------------WORK ARRAY---------------------------------- c
c P :Left singular vector matrix,(u) c
c Q :Right singular vector matrix,(v) c
c Cyz :Work Array, Cross-covarince matrix between the left and right fields c
c C :C is an NY*NZ matrix whose elements equal zero except c
c for the first R( R<=min(NS,NZ)) diagonal elements(cekma) c
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
subroutine meteo_svd(NY,NZ,NT,NMIN,KA,Y,Z,NP,A,B,cekma,scfk,
$ cscfk,rab,lcovf,rcovf,vara,varb,lhomo,lhete,rhomo,rhete)
c--------------------------------------------------------------------
!-----*Input and Output Variables*----------
integer::NY,NZ,NT,NMIN,KA
real ::Y(NY,NT),Z(NZ,NT)
integer::NP
real ::A(NT,NP),B(NT,NP)
real ::cekma(NMIN)
real ::scfk(NP)
real ::cscfk(np)
real ::rab(NP)
real ::lcovf(NP)
real ::rcovf(NP)
real ::vara(NP)
real ::varb(NP)
real ::lhomo(NY,NP),lhete(NY,NP)
real ::rhomo(NZ,NP),rhete(NZ,NP)
!-------------------------------------
!--------Work Variables---------------
real::P(NY,NY),Q(NZ,NZ)
real::s(KA),e(KA),work(KA)
real::y8(ny,nt),rain(nt,nz)
real::ym(ny),zm(nz),yd(ny),zd(nz)
real::cyz(ny,nz)
real::c(ny,nz)
real::xxx(nt),yyy(nt)
!-------------------------------
!-------------Start-------------
cccc******************************************************************
OPEN(6,FILE='svd_info.txt',STATUS='unknown')
c if(job1.eq.1) then
c write(6,111)
c do i=1,ny
c write(6,110) i
c write(6,112) (y(i,k),k=1,nt)
c enddo
c write(6,113)
c do i=1,nz
c write(6,110) i
c write(6,112) (z(i,k),k=1,nt)
c enddo
c end if
110 format(5x,' No. of station ',i3)
112 format(10f8.2)
111 format(/5x,'The original data of left field')
113 format(/5x,'The original data of right field')
fny=real(ny)
fnz=real(nz)
fnt=real(nt)
do i=1,ny
ym(i)=0.0
do k=1,nt
ym(i)=ym(i)+y(i,k)
enddo
ym(i)=ym(i)/fnt
yd(i)=0.0
do k=1,nt
yd(i)=yd(i)+(y(i,k)-ym(I))**2
enddo
yd(i)=sqrt(yd(i)/fnt)
enddo
do i=1,nz
zm(i)=0.0
do k=1,nt
zm(i)=zm(i)+z(i,k)
enddo
zm(i)=zm(i)/fnt
zd(i)=0.0
do k=1,nt
zd(i)=zd(i)+(z(i,k)-zm(I))**2
enddo
zd(i)=sqrt(zd(i)/fnt)
enddo
do i=1,ny
do k=1,nt
y(i,k)=(y(i,k)-ym(I))/yd(I)
enddo
enddo
do i=1,nz
do k=1,nt
z(i,k)=(z(i,k)-zm(I))/zd(I)
enddo
enddo
c if(job1.eq.0) then
c write(6,100)
c write(6,101)
c write(6,102) ym
c write(6,103)
c write(6,102) yd
c write(6,105)
c write(6,102) zm
c write(6,107)
c write(6,102) zd
c end if
100 format(/5x,'The basic statistical quantity')
101 format(/5x,'The mean value at each point of left data field')
102 format(1x,10f12.4)
103 format(/5x,'The standard deviation at each point of left data
$ field')
105 format(/5x,'The mean value at each point of right data field')
107 format(/5x,'The standard deviation at each point of right data
&field')
do i=1,ny
do j=1,nz
cyz(i,j)=0.0
do k=1,nt
cyz(i,j)=cyz(i,j)+y(i,k)*z(j,k)
enddo
cyz(i,j)=cyz(i,j)/fnt
enddo
enddo
c if(job2.eq.1) then
c write(6,78)
c write(6,49)((cyz(i,j),j=1,nz),i=1,ny)
c end if
78 format(1x,'the cross-coverence matrix:')
49 format(1x,10f8.4)
sss=0.0
do i=1,ny
do j=1,nz
sss=sss+cyz(i,j)**2
enddo
enddo
write(6,76) sss
76 format(/2x,' The total squared covariance=',f12.5)
eps=0.000001
c******************************************
call uav(cyz,ny,nz,p,q,l,eps,ka,s,e,work)
write(6,9)l
9 format(/5x,'l=',i1,'(l=0 indicate that call subroutine UAV(SVD)
& normal finished,else unnormal finished)')
ir=nz
if(ny.lt.nz) ir=ny
do k=1,ir
cekma(k)=cyz(k,k)
enddo
ss=0.0
do k=1,ir
ss=ss+cekma(k)**2
enddo
write(6,56) ss
56 format(/2x,' The sum of squared singular value=',f12.5)
write(6,55)
55 format(/4x,'According to properties of SVD, the sum of squared
&singular value must'/2x,'be equal to the total squared covariance
& ! ')
write(6,53) (cekma(k),k=1,np)
53 format(/2x,'The singular values:',(/1x,8f10.3))
do k=1,np
scfk(K)=(cekma(k)**2/ss)*100.0
enddo
write(6,44)
44 format(/4x,'The percentage of the squared covariance explained
* by a single pair of patterns (give first NP pairs) is:')
write(6,382) (scfk(k),k=1,np)
382 format((10f8.2))
cscfk(1)=scfk(1)
do k=2,np
j=k-1
cscfk(k)=cscfk(j)+scfk(k)
enddo
write(6,43)
43 format(/4x,'The percentage of the cumulative squared covariance
$ explained by the leading K modes is:')
write(6,382) (cscfk(k),k=1,np)
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c Note that: c
c Output from subroutine uav: c
c Column of matrix p is left singular vectors c
c rows of matrix q is right singular vectors c
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
29 format(1x,10f8.4)
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
do i=1,nz-1
do j=i+1,nz
ggg=q(i,j)
q(i,j)=q(j,i)
q(j,i)=ggg
enddo
enddo
c write(6,509)
c509 format(/2x,'After transpose Q output singular vectors again')
c write(6,511)
c511 format(/4x,'The left singular vector')
c write(6,512)
c512 format(/4x,'The right singular vector')
do id=1,np
do k=1,nt
a(k,id)=0.0
b(k,id)=0.0
do i=1,ny
a(k,id)=a(k,id)+p(i,id)*y(i,k)
enddo
do j=1,nz
b(k,id)=b(k,id)+q(j,id)*z(j,k)
enddo
enddo
enddo
c write(6,311)
c do id=1,np
c write(6,317) id
c write(6,316) (a(k,id),k=1,nt)
c enddo
c write(6,312)
c do id=1,np
c write(6,317) id
c write(6,316) (b(k,id),k=1,nt)
c enddo
311 format(/4x,'The time coeffecient series of left singular vector')
312 format(/4x,'The time coeffecient series of right singular vector')
317 format(/4x,i2,'-th')
316 format(10f8.3)
cccccccccccccc*********************************************
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
rnt=real(nt)
do id=1,np
vara(id)=0.
varb(id)=0.
do k=1,nt
vara(id)=vara(id)+a(k,id)**2/rnt
varb(id)=varb(id)+b(k,id)**2/rnt
enddo
enddo
do id=1,np
lcovf(id)=100.0*vara(id)/fny
rcovf(id)=100.0*varb(id)/fnz
enddo
do id=1,np
do k=1,nt
xxx(k)=a(k,id)
yyy(k)=b(k,id)
enddo
rab(id)=rxy(xxx,yyy,nt)
enddo
c*******************************************************
write(6,463)
463 format(/2x,'The correlation coefficient between the corresponding
& expansion coefficents r(a,b) (first to NP-th pair) are: ')
write(6,382) (rab(id),id=1,np)
write(6,481)
481 format(/3x,'The percentages of the variance of left field
& explained by a single singular vector are:')
write(6,382) (lcovf(id),id=1,np)
write(6,482)
482 format(/3x,'The percentages of the variance of right field
& explained by a single singular vector are:')
write(6,382) (rcovf(id),id=1,np)
c*****************************************
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
do id=1,np
do is=1,ny
do k=1,nt
xxx(k)=a(k,id)
yyy(k)=y(is,k)
enddo
lhomo(is,id)=rxy(xxx,yyy,nt)
enddo
enddo
c*****************************************
do id=1,np
do is=1,ny
do k=1,nt
xxx(k)=b(k,id)
yyy(k)=y(is,k)
enddo
lhete(is,id)=rxy(xxx,yyy,nt)
enddo
enddo
c*****************************************
do id=1,np
do is=1,nz
do k=1,nt
xxx(k)=b(k,id)
yyy(k)=z(is,k)
enddo
rhomo(is,id)=rxy(xxx,yyy,nt)
enddo
enddo
c*****************************************
do id=1,np
do is=1,nz
do k=1,nt
xxx(k)=a(k,id)
yyy(k)=z(is,k)
enddo
rhete(is,id)=rxy(xxx,yyy,nt)
enddo
enddo
c********************************************************
c open(11,file='left.dat',STATUS='unknown')
c write(11,812)
812 format(/4x,'The left heterogeneous correlation maps')
c do id=1,np
c write(11,317) id
c write(11,382)(lhete(j,id),j=1,ny)
c enddo
c write(11,814)
814 format(/4x,'The left homogeneous correlation maps')
c do id=1,np
c write(11,317) id
c write(11,382)(lhomo(j,id),j=1,ny)
c enddo
c close(11)
c***********************************************************
c open(12,file='g:\svd\right.dat',STATUS='unknown')
c write(12,817)
c 817 format(/4x,'The right heterogeneous correlation maps')
c do id=1,np
c write(12,317) id
c write(12,382) (rhete(j,id),j=1,nz)
c enddo
c write(12,819)
819 format(/4x,'The right homogeneous correlation maps')
c do id=1,np
c write(12,317) id
c write(12,382) (rhomo(j,id),j=1,nz)
c enddo
c close(12)
end
c-----*----------------------------------------------------6---------7--
subroutine uav(a,m,n,u,v,l,eps,ka,s,e,work)
dimension a(m,n),u(m,m),v(n,n),s(ka),e(ka),work(ka)
real a,u,v,s,e,d,work,dd,f,g,cs,sn,
* shh,sk,ek,b,c,sm,sm1,em1
it=60
k=n
if(m-1.lt.n)k=m-1
l=m
if(n-2.lt.m)l=n-2
if(l.lt.0)l=0
ll=k
if(l.gt.k)ll=l
if(ll.ge.1)then
do 150 kk=1,ll
if(kk.le.k)then
d=0.0
do 10 i=kk,m
d=d+a(i,kk)*a(i,kk)
10 continue
s(kk)=sqrt(d)
if(s(kk).ne.0.0)then
if(a(kk,kk).ne.0.0)s(kk)=sign(s(kk),a(kk,kk))
do 20 i=kk,m
20 a(i,kk)=a(i,kk)/s(kk)
a(kk,kk)=1.0+a(kk,kk)
end if
s(kk)=-s(kk)
end if
if(n.ge.kk+1)then
do 50 j=kk+1,n
if((kk.le.k).and.(s(kk).ne.0.0))then
d=0.0
do 30 i=kk,m
d=d+a(i,kk)*a(i,j)
30 continue
d=-d/a(kk,kk)
do 40 i=kk,m
40 a(i,j)=a(i,j)+d*a(i,kk)
end if
e(j)=a(kk,j)
50 continue
end if
if(kk.le.k)then
do 60 i=kk,m
60 u(i,kk)=a(i,kk)
end if
if(kk.le.l)then
d=0.0
do 70 i=kk+1,n
70 d=d+e(i)*e(i)
e(kk)=sqrt(d)
if(e(kk).ne.0.0)then
if(e(kk+1).ne.0.0)e(kk)=sign(e(kk),e(kk+1))
do 80 i=kk+1,n
80 e(i)=e(i)/e(kk)
e(kk+1)=1.0+e(kk+1)
end if
e(kk)=-e(kk)
if((kk+1.le.m).and.(e(kk).ne.0.0))then
do 90 i=kk+1,m
90 work(i)=0.0
do 110 j=kk+1,n
do 100 i=kk+1,m
100 work(i)=work(i)+e(j)*a(i,j)
110 continue
do 130 j=kk+1,n
do 120 i=kk+1,m
120 a(i,j)=a(i,j)-work(i)*e(j)/e(kk+1)
130 continue
end if
do 140 i=kk+1,n
140 v(i,kk)=e(i)
end if
150 continue
end if
mm=n
if(m+1.lt.n)mm=m+1
if(k.lt.n)s(k+1)=a(k+1,k+1)
if(m.lt.mm)s(mm)=0.0
if(l+1.lt.mm)e(l+1)=a(l+1,mm)
e(mm)=0.0
nn=m
if(m.gt.n)nn=n
if(nn.ge.k+1)then
do 190 j=k+1,nn
do 180 i=1,m
180 u(i,j)=0.0
u(j,j)=1.0
190 continue
end if
if(k.ge.1)then
do 250 ll=1,k
kk=k-ll+1
if(s(kk).ne.0.0)then
if(nn.ge.kk+1)then
do 220 j=kk+1,nn
d=0.0
do 200 i=kk,m
200 d=d+u(i,kk)*u(i,j)/u(kk,kk)
d=-d
do 210 i=kk,m
210 u(i,j)=u(i,j)+d*u(i,kk)
220 continue
end if
do 225 i=kk,m
225 u(i,kk)=-u(i,kk)
u(kk,kk)=1.0+u(kk,kk)
if(kk-1.ge.1)then
do 230 i=1,kk-1
230 u(i,kk)=0.0
end if
else
do 240 i=1,m
240 u(i,kk)=0.0
u(kk,kk)=1.0
end if
250 continue
end if
do 300 ll=1,n
kk=n-ll+1
if((kk.le.l).and.(e(kk).ne.0.0))then
do 280 j=kk+1,n
d=0.0
do 260 i=kk+1,n
260 d=d+v(i,kk)*v(i,j)/v(kk+1,kk)
d=-d
do 270 i=kk+1,n
270 v(i,j)=v(i,j)+d*v(i,kk)
280 continue
end if
do 290 i=1,n
290 v(i,kk)=0.0
v(kk,kk)=1.0
300 continue
do 305 i=1,m
do 305 j=1,n
305 a(i,j)=0.0
m1=mm
it=60
310 if(mm.eq.0)then
l=0
if(m.ge.n)then
i=n
else
i=m
end if
do 315 j=1,i-1
a(j,j)=s(j)
a(j,j+1)=e(j)
315 continue
a(i,i)=s(i)
if(m.lt.n)a(i,i+1)=e(i)
do 314 i=1,n-1
do 313 j=i+1,n
d=v(i,j)
v(i,j)=v(j,i)
v(j,i)=d
313 continue
314 continue
return
end if
if(it.eq.0)then
l=mm
if(m.ge.n)then
i=n
else
i=m
end if
do 316 j=1,i-1
a(j,j)=s(j)
a(j,j+1)=e(j)
316 continue
a(i,i)=s(i)
if(m.lt.n)a(i,i+1)=e(i)
do 318 i=1,n-1
do 317 j=i+1,n
d=v(i,j)
v(i,j)=v(j,i)
v(j,i)=d
317 continue
318 continue
return
end if
kk=mm
320 kk=kk-1
if(kk.ne.0)then
d=abs(s(kk))+abs(s(kk+1))
dd=abs(e(kk))
if(dd.gt.eps*d)go to 320
e(kk)=0.0
end if
if(kk.eq.mm-1)then
kk=kk+1
if(s(kk).lt.0.0)then
s(kk)=-s(kk)
do 330 i=1,n
330 v(i,kk)=-v(i,kk)
end if
335 if(kk.ne.m1)then
if(s(kk).lt.s(kk+1))then
d=s(kk)
s(kk)=s(kk+1)
s(kk+1)=d
if(kk.lt.n)then
do 340 i=1,n
d=v(i,kk)
v(i,kk)=v(i,kk+1)
v(i,kk+1)=d
340 continue
end if
if(kk.lt.m)then
do 350 i=1,m
d=u(i,kk)
u(i,kk)=u(i,kk+1)
u(i,kk+1)=d
350 continue
end if
kk=kk+1
go to 335
end if
end if
it=60
mm=mm-1
go to 310
end if
ks=mm+1
360 ks=ks-1
if(ks.gt.kk)then
d=0.0
if(ks.ne.mm)d=d+abs(e(ks))
if(ks.ne.kk+1)d=d+abs(e(ks-1))
dd=abs(s(ks))
if(dd.gt.eps*d)go to 360
s(ks)=0.0
end if
if(ks.eq.kk)then
kk=kk+1
d=abs(s(mm))
if(abs(s(mm-1)).gt.d)d=abs(s(mm-1))
if(abs(e(mm-1)).gt.d)d=abs(e(mm-1))
if(abs(s(kk)).gt.d)d=abs(s(kk))
if(abs(e(kk)).gt.d)d=abs(e(kk))
sm=s(mm)/d
sm1=s(mm-1)/d
em1=e(mm-1)/d
sk=s(kk)/d
ek=e(kk)/d
b=((sm1+sm)*(sm1-sm)+em1*em1)/2.0
c=sm*em1
c=c*c
shh=0.0
if((b.ne.0.0).or.(c.ne.0.0))then
shh=sqrt(b*b+c)
if(b.lt.0.0)shh=-shh
shh=c/(b+shh)
end if
f=(sk+sm)*(sk-sm)-shh
g=sk*ek
do 400 i=kk,mm-1
call sss(f,g,cs,sn)
if(i.ne.kk)e(i-1)=f
f=cs*s(i)+sn*e(i)
e(i)=cs*e(i)-sn*s(i)
g=sn*s(i+1)
s(i+1)=cs*s(i+1)
if((cs.ne.1.0).or.(sn.ne.0.0))then
do 370 j=1,n
d=cs*v(j,i)+sn*v(j,i+1)
v(j,i+1)=-sn*v(j,i)+cs*v(j,i+1)
v(j,i)=d
370 continue
end if
call sss(f,g,cs,sn)
s(i)=f
f=cs*e(i)+sn*s(i+1)
s(i+1)=-sn*e(i)+cs*s(i+1)
g=sn*e(i+1)
e(i+1)=cs*e(i+1)
if(i.lt.m)then
if((cs.ne.1.0).or.(sn.ne.0.0))then
do 380 j=1,m
d=cs*u(j,i)+sn*u(j,i+1)
u(j,i+1)=-sn*u(j,i)+cs*u(j,i+1)
u(j,i)=d
380 continue
end if
end if
400 continue
e(mm-1)=f
it=it-1
go to 310
end if
if(ks.eq.mm)then
kk=kk+1
f=e(mm-1)
e(mm-1)=0.0
do 420 ll=kk,mm-1
i=mm+kk-ll-1
g=s(i)
call sss(g,f,cs,sn)
s(i)=g
if(i.ne.kk)then
f=-sn*e(i-1)
e(i-1)=cs*e(i-1)
end if
if((cs.ne.1.0).or.(sn.ne.0.0))then
do 410 j=1,n
d=cs*v(j,i)+sn*v(j,mm)
v(j,mm)=-sn*v(j,i)+cs*v(j,mm)
v(j,i)=d
410 continue
end if
420 continue
go to 310
end if
kk=ks+1
f=e(kk-1)
e(kk-1)=0.0
do 450 i=kk,mm
g=s(i)
call sss(g,f,cs,sn)
s(i)=g
f=-sn*e(i)
e(i)=cs*e(i)
if((cs.ne.1.0).or.(sn.ne.0.0))then
do 430 j=1,m
d=cs*u(j,i)+sn*u(j,kk-1)
u(j,kk-1)=-sn*u(j,i)+cs*u(j,kk-1)
u(j,i)=d
430 continue
end if
450 continue
go to 310
end
subroutine sss(f,g,cs,sn)
c double precision f,g,cs,sn,d,r
real f,g,cs,sn,d,r
if((abs(f)+abs(g)).eq.0.0)then
cs=1.0
sn=0.0
d=0.0
else
d=sqrt(f*f+g*g)
if(abs(f).gt.abs(g))d=sign(d,f)
if(abs(g).ge.abs(f))d=sign(d,g)
cs=f/d
sn=g/d
end if
r=1.0
if(abs(f).gt.abs(g))then
r=sn
else
if(cs.ne.0.0)r=1.0/cs
end if
f=d
g=r
return
end
subroutine mul(a,b,m,n,k,c)
dimension a(m,n),b(n,k),c(m,k)
c double precision a,b,c
real a,b,c
do 50 i=1,m
do 50 j=1,k
c(i,j)=0.0
do 10 l=1,n
c(i,j)=c(i,j)+a(i,l)*b(l,j)
10 continue
50 continue
return
end
function rxy(x,y,n)
dimension x(n),y(n)
rn=real(n)
xm=0.0
ym=0.0
do 10 i=1,n
xm=xm+x(i)/rn
10 ym=ym+y(i)/rn
do 20 i=1,n
x(i)=x(i)-xm
20 y(i)=y(i)-ym
sxy=0.0
sx=0.0
sy=0.0
do 30 i=1,n
sx=sx+x(i)*x(i)/rn
sy=sy+y(i)*y(i)/rn
30 sxy=sxy+x(i)*y(i)/rn
sx=sqrt(sx)
sy=sqrt(sy)
rxy=sxy/(sx*sy)
return
end
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发表于 2012-12-1 20:51:54
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发表于 2012-12-2 07:57:38
楼主
好吧······