再来做点贡献，关于eof的

568679112 · 发表于 2014-2-7 14:21:46

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前几天一直在琢磨着怎么把eof程序的特征向量场画成特征值的开平方与特征向量乘积形式，因为这样可以使图上的数值显示为主成分与原始场的相关系数，一个偶然的机会让我画了出来，用的是论坛里下的李建平的eof程序，稍微修改了下。不多废话，上程序上图：

cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c c
c EMPIRICAL ORTHOGONAL FUNCTIONS (EOF's) c
c c
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c
c Last updated by YONGJIE HUANG, Mar 2, 2012.
c
c-----*----------------------------------------------------6---------7--
c The parameters you need to change:
c datefname - Name of input data file;
c n - Length of time series, viz. sample size;
c mx - Grids in row;
c my - Grids in column;
c mnl - Min(m,n)
c undef - Missing value;
c mg1 & mg2 - The efficient grids (output on screen) and cancel the
c "stop" in line 96, try again.
c ks - Contral parameter:
c ks=-1: self, i.e., for the raw time series;
c ks=0: departure, i.e., for the anomaly time series from climatological mean;
c ks=1: normalized departure, i.e., for the normalized time series;
c km - Contral parameter:
c km=1: monthly or daily data.
c km=0: data without annual cycle.
c nd - The number of the months or days in a year.
c ------------------------------------------------------------------
c Output:
c er.txt - Ascii file with EOF eigenvalues, accumulated eigenvalues,
c explained variances and accumulated explained variances.
c egvt.dat - Binary file with eigenvactors matrix of EOF.
c ecof.dat - Binary file with time coefficients matrix of EOF.
c egvt.ctl - Control file for 'egvt.dat'.
c ecof.ctl - Control file for 'ecof.dat'.
c
c-----*----------------------------------------------------6---------7--
program main
character*80,parameter ::
& datafname='e:\lunwen\jiala7\gy\svd\qd10.grd'
parameter(n=30,m=81*101,mnl=n)
parameter(undef=-9.99e+8,mg1=m,mg2=m)
parameter(ks=1,km=1,nd=1,std=1e-6)
!-----input array
dimension f0(n,m)
!-----work arrays
dimension f1(n,mg1),f2(n,mg1),g(mg1),h1(mg1,n),h2(mg1,n)
dimension f(mg2,n),gvt(mg2,mnl),cof(mnl,n)
!-----output arrays
dimension er(mnl,4),egvt(m,mnl),ecof(mnl,n)
c-----Read data.
open(20,file=datafname,status='unknown'
&,form='unformatted',access='direct',recl=m)
do j=1,n
read(20,rec=j)(f0(j,i),i=1,m)
end do
close(20)
write(*,*)'Read data OK!'
c-----Remove the terrain or missing value.
l1=0
do j=1,m
if(f0(1,j).ne.undef)then
l1=l1+1
do k=1,n
f1(k,l1)=f0(k,j)
enddo
endif
enddo
write(*,*)'Grids without terrain:'
write(*,*)'mg1=',l1
c-----Remove annual cycle.
if(km.eq.1)then
ny=n/nd
do i=1,l1
call initial(nd,ny,n,f1(1,i),f2(1,i))
end do
do i=1,l1
do k=1,n
f1(k,i)=f2(k,i)
end do
end do
end if
c-----Remove the grids whose variance equal to zero.
l2=0
do i=1,l1
call meanvar(n,f1(1,i),ax,g(i),vx)
if(g(i).gt.std)then
l2=l2+1
do k=1,n
f(l2,k)=f1(k,i)
enddo
endif
end do
write(*,*)'Grids without terrain and constant value:'
write(*,*)'mg2=',l2
c stop
c-----Call the subroutine.
write(*,*)'!!!!'
call eof(l2,n,mnl,f(1:l2,:),ks,er,gvt(1:l2,:),ecof)
write(*,*)'EOF ok and transform to the original form in the next!'
c-----Add the grids whose variance equal to zero.
l3=0
do i=1,mg2
if(g(i).gt.std)then
l3=l3+1
do k=1,mnl
h1(i,k)=gvt(l3,k)
end do
else
do k=1,mnl
h1(i,k)=undef
end do
endif
enddo
c-----Add the terrain or missing value.
l4=0
do i=1,m
if(f0(1,i).ne.undef)then
l4=l4+1
do k=1,mnl
egvt(i,k)=h1(l4,k)
end do
else
do k=1,mnl
egvt(i,k)=undef
end do
endif
enddo
c-----output the result.
c-----output the error.
write(*,*)'Output the results:'
open(10,file='e:\lunwen\jiala7\gy\eofsst\qd10er.txt',
&form='formatted')
c
write(10,*)'EOF lamda (eigenvalues) from big to small'
write(10,*)(er(i,1),i=1,mnl)
write(*,*)' OK: EOF lamda (eigenvalues) from big to small!'
c
write(10,*)'EOF accumulated eigenvalues from big to small'
write(10,*)(er(i,2),i=1,mnl)
write(*,*)' OK: accumulated eigenvalues from big to small!'
c
write(10,*)'EOF explained variances'
write(10,*)(er(i,3),i=1,mnl)
write(*,*)' OK: EOF explained variances!'
c
write(10,*)'EOF accumulated explained variances'
write(10,*)(er(i,4),i=1,mnl)
write(*,*)' OK: EOF accumulated explained variances!'
c
close(10)
c-----output eigenvactors matrix of EOF.
do i=1,m
if(egvt(i,1).ne.undef)then
do k=1,mnl
egvt(i,k)=egvt(i,k)*sqrt(abs(er(k,1)/mnl))
end do
endif
enddo
open(11,file='e:\lunwen\jiala7\gy\eofsst\qd10egvt.dat',
&status='unknown'
&,form='unformatted',access='direct',recl=m)
do j=1,mnl
write(11,rec=j)(egvt(i,j),i=1,m)
end do
write(*,*)' OK: output eigenvactors matrix of EOF!'
close(11)
c-----output time coefficients matrix of EOF.
open(12,file='e:\lunwen\jiala7\gy\eofsst\qd10ecof.dat',
&status='unknown'
&,form='unformatted',access='direct',recl=mnl)
do i=1,n
write(12,rec=i)(ecof(j,i)/sqrt(abs(er(j,1)/mnl)),j=1,mnl)
end do
write(*,*)' OK: output time coefficients matrix of EOF!'
close(12)
write(*,*)'EOF all OK!'
c-----create control files(.ctl) for 'egvt.dat' and 'ecof.dat'
write(*,*) 'Create ''.ctl'' files for ''.dat'' files: '
! open(13,file='e:\lunwen\756mon\egvt.ctl',form='formatted')
write(13,*) 'dset ^egvt.dat'
write(13,*) 'undef ',undef
write(13,*) 'xdef ',mx,' linear 88.75 2.5'
write(13,*) 'ydef ',my,' linear 3.75 2.5'
write(13,*) 'zdef 1 linear 0 1'
write(13,*) 'tdef ',mnl,' linear DEC1979 1yr'
write(13,*) 'vars 1'
write(13,*) 'egvt 0 99 eigenvactors matrix of EOF'
write(13,*) 'endvars'
close(13)
write(*,*) ' OK: ''egvt.ctl'' is created!'
c
! open(14,file='e:\lunwen\756mon\ecof.ctl',form='formatted')
write(14,*) 'dset ^ecof.dat'
write(14,*) 'undef ',undef
write(14,*) 'xdef ',mnl,' linear 0 1'
write(14,*) 'ydef 1 linear 0 1'
write(14,*) 'zdef 1 linear 0 1'
write(14,*) 'tdef ',n,' linear DEC1979 1yr'
write(14,*) 'vars 1'
write(14,*) 'ecof 0 99 eigenvactors matrix of EOF'
write(14,*) 'endvars'
close(14)
write(*,*) ' OK: ''ecof.ctl'' is created!'
c
write(*,*) 'All are finished successfully!'
stop
c-----
end
c=======================================================================
c
c=======================================================================
c-----------------------------------------------------------------------
c eof(m,n,mnl,f,ks,er,egvt,ecof)
c --------------------------------------
c 经验正交函数(EOF)-特征向量场及时间系数
c-----*----------------------------------------------------6---------7--
C EMPIRICAL ORTHOGONAL FUNCTIONS (EOF's)
c This subroutine applies the EOF approach to analysis time series
c of meteorological field f(m,n).
c input: m,n,mnl,f(m,n),ks
c m: number of grid-points
c n: lenth of time series
c mnl=min(m,n)
c f(m,n): the raw spatial-temporal seires
c ks: contral parameter
c ks=-1: self, i.e., for the raw time series;
c ks=0: departure, i.e., for the anomaly time series from climatological mean;
c ks=1: normalized departure, i.e., for the normalized time series;
c output: egvt,ecof,er
c egvt(m,mnl): array of eigenvactors
c ecof(mnl,n): array of time coefficients for the respective eigenvectors
c er(mnl,1): lamda (eigenvalues), its sequence is from big to small.
c er(mnl,2): accumulated eigenvalues from big to small
c er(mnl,3): explained variances (lamda/total explain) from big to small
c er(mnl,4): accumulated explaned variances from big to small
c work variables:
c Last updated by Yongjie HUANG on January 4, 2012
c Dr. Jianping Li on October 20, 2005.
c Citation: Li, J., 2005: EOF subroutine, http://web.lasg.ac.cn/staff/ljp/subroutine/EOF.f.
c-----
subroutine eof(m,n,mnl,f,ks,er,egvt,ecof)
dimension f(m,n),er(mnl,4),egvt(m,mnl),ecof(mnl,n)
dimension cov(mnl,mnl),s(mnl,mnl),d(mnl),v(mnl) !work array
c---- Preprocessing data
call transf(m,n,f,ks)
c---- Crossed product matrix of the data f(m,n)
call crossproduct(m,n,mnl,f,cov)
c---- Eigenvalues and eigenvectors by the Jacobi method
call jacobi(mnl,cov,s,d,0.00001)
c---- Specified eigenvalues
call arrang(mnl,d,s,er)
c---- Normalized eignvectors and their time coefficients
call tcoeff(m,n,mnl,f,s,er,egvt,ecof)
return
end
c-----------------------------------------------------------------------
c
c-----------------------------------------------------------------------
c-----------------------------------------------------------------------
c transf(m,n,f,ks)
c ------------------------------
c 处理资料为距平、标准方差或不变
c-----*----------------------------------------------------6---------7--
c Preprocessing data to provide a field by ks.
c input: m,n,f
c m: number of grid-points
c n: lenth of time series
c f(m,n): the raw spatial-temporal seires
c ks: contral parameter
c ks=-1: self, i.e., for the raw time series;
c ks=0: departure, i.e., for the anomaly time series from climatological mean;
c ks=1: normalized departure, i.e., for the normalized time series;
c output: f
c f(m,n): output field based on the control parameter ks.
c work variables: fw(n)
subroutine transf(m,n,f,ks)
dimension f(m,n)
dimension fw(n),wn(m) !work array
c
i0=0
do i=1,m
do j=1,n
fw(j)=f(i,j)
enddo
call meanvar(n,fw,af,sf,vf)
if(sf.eq.0.)then
i0=i0+1
wn(i0)=i
endif
enddo
c
if(i0.ne.0)then
write(*,*)'**** FAULT ****'
write(*,*)' The program cannot go on because
*the original field has invalid data.'
write(*,*)' There are totally ',i0,
* ' gridpionts with invalid data.'
write(*,*)' These invalid data are those whose standard variance
*equal zero.'
write(*,*)' The array WN stores the positions of those invalid
*grid-points. You must pick off those invalid data from the orignal
*field and then reinput a new field to calculate its EOFs.'
write(*,*)'**** FAULT ****'
stop
endif
c
c
if(ks.eq.-1)return
c
if(ks.eq.0)then !anomaly of f
do i=1,m
do j=1,n
fw(j)=f(i,j)
enddo
call meanvar(n,fw,af,sf,vf)
do j=1,n
f(i,j)=f(i,j)-af
enddo
enddo
return
endif
c
if(ks.eq.1)then !normalizing f
do i=1,m
do j=1,n
fw(j)=f(i,j)
enddo
call meanvar(n,fw,af,sf,vf)
do j=1,n
f(i,j)=(f(i,j)-af)/sf
enddo
enddo
endif
return
end
c-----------------------------------------------------------------------
c
c-----------------------------------------------------------------------
c-----------------------------------------------------------------------
c crossproduct(m,n,mnl,f,cov)
c ---------------------------
c 计算交叉矩阵
c-----*----------------------------------------------------6---------7--
c Crossed product martix of the data. It is n times of
c covariance matrix of the data if ks=0 (i.e. for anomaly).
c input: m,n,mnl,f
c m: number of grid-points
c n: lenth of time series
c mnl=min(m,n)
c f(m,n): the raw spatial-temporal seires
c output: cov(mnl,mnl)
c cov(m,n)=f*f' or f'f dependes on m and n.
c It is a mnl*mnl real symmetric matrix.
subroutine crossproduct(m,n,mnl,f,cov)
dimension f(m,n),cov(mnl,mnl)
if(n-m<0) then
do i=1,mnl
do j=i,mnl
cov(i,j)=0.0
do is=1,m
cov(i,j)=cov(i,j)+f(is,i)*f(is,j)
enddo
cov(j,i)=cov(i,j)
end do
end do
return
else
do i=1,mnl
do j=i,mnl
cov(i,j)=0.0
do js=1,n
cov(i,j)=cov(i,j)+f(i,js)*f(j,js)
enddo
cov(j,i)=cov(i,j)
end do
end do
return
end if
end
c-----------------------------------------------------------------------
c
c-----------------------------------------------------------------------
c-----------------------------------------------------------------------
c jacobi(m,a,s,d,eps)
c ------------------------------------------
c 使用雅克比过关法计算矩阵的特征向量和特征值
c-----*----------------------------------------------------6---------7--
c Computing eigenvalues and eigenvectors of a real symmetric matrix
c a(m,m) by the Jacobi method.
c input: m,a,s,d,eps
c m: order of matrix
c a(m,m): the covariance matrix
c eps: given precision
c output: s,d
c s(m,m): eigenvectors
c d(m): eigenvalues
subroutine jacobi(m,a,s,d,eps)
dimension a(m,m),s(m,m),d(m)
c-----使s(m,m)为单位矩阵E
do i=1,m
do j=1,i
if(i-j==0) then
s(i,j)=1.
else
s(i,j)=0.
s(j,i)=0.
end if
end do
end do
c-----计算m阶实对称矩阵a(m,m)的所有非对角线元素平方之和的平方根
g=0.
do i=2,m
i1=i-1
do j=1,i1
g=g+2.*a(i,j)*a(i,j)
end do
end do
s1=sqrt(g)
c-----设置关口s3
s2=eps/float(m)*s1
s3=s1
l=0
50 s3=s3/float(m)
c-----在非对角线元素中逐行扫描选取第一个绝对值大于或等于s3的元素a(ip,iq),
c-----进行平面旋转变换，直到所有非对角线元素的绝对值都小于s3为止.
60 do 130 iq=2,m
do 130 ip=1,iq-1
if(abs(a(ip,iq)).lt.s3) goto 130
l=1
v1=a(ip,ip)
v2=a(ip,iq)
v3=a(iq,iq)
u=0.5*(v1-v3)
if(u.eq.0.0) g=1.
if(abs(u).ge.1e-10) g=-sign(1.,u)*v2/sqrt(v2*v2+u*u)
st=g/sqrt(2.*(1.+sqrt(1.-g*g)))
ct=sqrt(1.-st*st)
do i=1,m
g=a(i,ip)*ct-a(i,iq)*st
a(i,iq)=a(i,ip)*st+a(i,iq)*ct
a(i,ip)=g
g=s(i,ip)*ct-s(i,iq)*st
s(i,iq)=s(i,ip)*st+s(i,iq)*ct
s(i,ip)=g
end do
do i=1,m
a(ip,i)=a(i,ip)
a(iq,i)=a(i,iq)
end do
g=2.*v2*st*ct
a(ip,ip)=v1*ct*ct+v3*st*st-g
a(iq,iq)=v1*st*st+v3*ct*ct+g
a(ip,iq)=(v1-v3)*st*ct+v2*(ct*ct-st*st)
a(iq,ip)=a(ip,iq)
130 continue
c-----平面旋转变换，直到所有非对角线元素的绝对值都小于s3为止.
if(l-1==0) then
l=0
go to 60
else
if(s3.gt.s2) goto 50 !再设置下一关口
end if
c
do i=1,m
d(i)=a(i,i)
end do
return
end
c-----------------------------------------------------------------------
c
c-----------------------------------------------------------------------
c-----------------------------------------------------------------------
c arrang(mnl,d,s,er)
c ----------------------------------------------------------------
c 重新由大到小排列及计算特征值、累积特征值、解释方差及累积解释方差
c-----*----------------------------------------------------6---------7--
c Provides a series of eigenvalues from maximuim to minimuim.
c input: mnl,d,s
c d(mnl): eigenvalues
c s(mnl,mnl): eigenvectors
c output: er
c er(mnl,1): lamda (eigenvalues), its equence is from big to small.
c er(mnl,2): accumulated eigenvalues from big to small
c er(mnl,3): explained variances (lamda/total explain) from big to small
c er(mnl,4): accumulated explaned variances from big to small
subroutine arrang(mnl,d,s,er)
dimension d(mnl),s(mnl,mnl),er(mnl,4)
c
tr=0.0
do i=1,mnl
tr=tr+d(i)
er(i,1)=d(i)
end do
c-----由大到小排列特征值及将对应的特征向量做相应的移动
mnl1=mnl-1
do k1=mnl1,1,-1
do k2=k1,mnl1
if(er(k2,1).lt.er(k2+1,1)) then
c=er(k2+1,1)
er(k2+1,1)=er(k2,1)
er(k2,1)=c
do i=1,mnl
c=s(i,k2+1)
s(i,k2+1)=s(i,k2)
s(i,k2)=c
end do
endif
end do
end do
c-----计算累积特征值
er(1,2)=er(1,1)
do i=2,mnl
er(i,2)=er(i-1,2)+er(i,1)
end do
c-----计算解释方差及累积解释方差
do i=1,mnl
er(i,3)=er(i,1)/tr
er(i,4)=er(i,2)/tr
end do
c
return
end
c-----------------------------------------------------------------------
c
c-----------------------------------------------------------------------
c-----------------------------------------------------------------------
c tcoeff(m,n,mnl,f,s,er,egvt,ecof)
c --------------------------------
c 归一化特征向量和时间系数
c-----*----------------------------------------------------6---------7--
c Provides standard eigenvectors and their time coefficients
c input: m,n,mnl,f,s,er
c m: number of grid-points
c n: lenth of time series
c mnl=min(m,n)
c f(m,n): the raw spatial-temporal seires
c s(mnl,mnl): eigenvectors
c er(mnl,1): lamda (eigenvalues), its equence is from big to small.
c er(mnl,2): accumulated eigenvalues from big to small
c er(mnl,3): explained variances (lamda/total explain) from big to small
c er(mnl,4): accumulated explaned variances from big to small
c output: egvt,ecof
c egvt(m,mnl): normalized eigenvectors
c ecof(mnl,n): time coefficients of egvt
subroutine tcoeff(m,n,mnl,f,s,er,egvt,ecof)
dimension f(m,n),s(mnl,mnl),er(mnl,4),egvt(m,mnl),ecof(mnl,n)
dimension v(mnl) !work array
c
do j=1,mnl
do i=1,m
egvt(i,j)=0.
enddo
do i=1,n
ecof(j,i)=0.
enddo
enddo
c-----Normalizing the input eignvectors s
do j=1,mnl
c=0.
do i=1,mnl
c=c+s(i,j)*s(i,j)
enddo
c=sqrt(c)
do i=1,mnl
s(i,j)=s(i,j)/c
enddo
enddo
c-----
if(m.le.n) then
do js=1,mnl
do i=1,m
egvt(i,js)=s(i,js)
enddo
enddo
do j=1,n
do i=1,m
v(i)=f(i,j)
enddo
do is=1,mnl
do i=1,m
ecof(is,j)=ecof(is,j)+v(i)*s(i,is)
enddo
enddo
enddo
else
c-----这里使用了时空转换，时间系数得乘以sqrt(abs(er(js,1))，特征向量除以sqrt(abs(er(js,1))
do i=1,m
do j=1,n
v(j)=f(i,j)
enddo
do js=1,mnl
do j=1,n
egvt(i,js)=egvt(i,js)+v(j)*s(j,js)
enddo
enddo
enddo
do js=1,mnl
do j=1,n
ecof(js,j)=s(j,js)*sqrt(abs(er(js,1)))
enddo
do i=1,m
egvt(i,js)=egvt(i,js)/sqrt(abs(er(js,1)))
enddo
enddo
endif
return
end
c-----------------------------------------------------------------------
c
c-----------------------------------------------------------------------
c-----------------------------------------------------------------------
c meanvar(n,x,ax,sx,vx)
c -------------------------------
c 计算矩阵的平均值、标准差和方差
c-----*----------------------------------------------------6---------7--
c Computing the mean ax, standard deviation sx
c and variance vx of a series x(i) (i=1,...,n).
c input: n and x(n)
c n: number of raw series
c x(n): raw series
c output: ax, sx and vx
c ax: the mean value of x(n)
c sx: the standard deviation of x(n)
c vx: the variance of x(n)
c By Dr. LI Jianping, May 6, 1998.
subroutine meanvar(n,x,ax,sx,vx)
dimension x(n)
ax=0.
vx=0.
sx=0.
c calculate the mean value of x(n): ax
do i=1,n
ax=ax+x(i)
end do
ax=ax/float(n)
c calculate the standard deviation of x(n): sx
do i=1,n
vx=vx+(x(i)-ax)**2
end do
vx=vx/float(n)
c calculate the variance of x(n): vx
sx=sqrt(vx)
return
end
c-------------------------------------------------------------------------
c
c-------------------------------------------------------------------------
c-----*----------------------------------------------------6---------7--
c This subroutine is for removing annual cycle (Monthly of daily data)
c
c input:
c nd: number of days or monthes in a year.
c ny: number of year
c ndy=nd*ny
c f(ndy): the daily of monthly data.
c
c output:
c af(ndy): the daily of monthly data without annual cycle
c
c by Dr Jianping Li,
c recomplied by Dong Xiao on May 7, 2007
c-----
subroutine initial(nd,ny,ndy,f,af)
!-----input array
real f(ndy)
!-----work arrays
real fave(nd),fstd(nd)
!-----output array
real af(ndy)
c-----
do i=1,nd
fave(i)=0.
do j=1,ny
fave(i)=fave(i)+f(i+(j-1)*nd)
enddo
fave(i)=fave(i)/ny
fstd(i)=0.0
do j=1,ny
fstd(i)=fstd(i)+(f(i+(j-1)*nd)-fave(i))**2
enddo
fstd(i)=sqrt(fstd(i)/float(ny))
do j=1,ny
ij=i+(j-1)*nd
c-----standard departure
c af(ij)=(f(ij)-fave(i))/fstd(i)
c-----departure
af(ij)=(f(ij)-fave(i))
enddo
enddo
c-----
return
end
c-----*----------------------------------------------------6---------7--
c
c-----------------------------------------------------------------------

cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc 
c                                                                      c 
c            EMPIRICAL ORTHOGONAL FUNCTIONS (EOF's)                    c 
c                                                                      c 
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc 
c 
c     Last updated by YONGJIE HUANG, Mar 2, 2012. 
c 
c-----*----------------------------------------------------6---------7-- 
c     The parameters you need to change:   
c       datefname - Name of input data file;   
c   n         - Length of time series, viz. sample size; 
c       mx        - Grids in row; 
c       my        - Grids in column; 
c       mnl       - Min(m,n) 
c       undef     - Missing value; 
c       mg1 & mg2 - The efficient grids (output on screen) and cancel the 
c                    "stop" in line 96, try again. 
c       ks        - Contral parameter: 
c                     ks=-1: self, i.e., for the raw time series; 
c                     ks=0: departure, i.e., for the anomaly time series from climatological mean; 
c                     ks=1: normalized departure, i.e., for the normalized time series; 
c       km        - Contral parameter: 
c                     km=1: monthly or daily data. 
c                     km=0: data without annual cycle. 
c       nd        - The number of the months or days in a year. 
c     ------------------------------------------------------------------ 
c     Output: 
c       er.txt    - Ascii file with EOF eigenvalues, accumulated eigenvalues, 
c                   explained variances and accumulated explained variances. 
c       egvt.dat  - Binary file with eigenvactors matrix of EOF. 
c       ecof.dat  - Binary file with time coefficients matrix of EOF. 
c       egvt.ctl  - Control file for 'egvt.dat'. 
c       ecof.ctl  - Control file for 'ecof.dat'. 
c    
c-----*----------------------------------------------------6---------7-- 
      program main 
 character*80,parameter :: 
     & datafname='e:\lunwen\jiala7\gy\svd\qd10.grd' 
 parameter(n=30,m=81*101,mnl=n) 
 parameter(undef=-9.99e+8,mg1=m,mg2=m) 
      parameter(ks=1,km=1,nd=1,std=1e-6) 
!-----input array 
      dimension f0(n,m) 
!-----work arrays 
      dimension f1(n,mg1),f2(n,mg1),g(mg1),h1(mg1,n),h2(mg1,n)   
 dimension f(mg2,n),gvt(mg2,mnl),cof(mnl,n) 
!-----output arrays 
      dimension er(mnl,4),egvt(m,mnl),ecof(mnl,n) 
c-----Read data. 
      open(20,file=datafname,status='unknown' 
     &,form='unformatted',access='direct',recl=m) 
  do j=1,n 
   read(20,rec=j)(f0(j,i),i=1,m) 
  end do 
 close(20) 
 write(*,*)'Read data OK!' 
c-----Remove the terrain or missing value. 
      l1=0 
 do j=1,m 
   if(f0(1,j).ne.undef)then 
          l1=l1+1 
     do k=1,n 
            f1(k,l1)=f0(k,j) 
     enddo 
   endif 
 enddo 
      write(*,*)'Grids without terrain:' 
 write(*,*)'mg1=',l1 
c-----Remove annual cycle. 
      if(km.eq.1)then 
   ny=n/nd    
   do i=1,l1 
     call initial(nd,ny,n,f1(1,i),f2(1,i)) 
   end do   
   do i=1,l1 
     do k=1,n 
       f1(k,i)=f2(k,i) 
     end do 
   end do 
 end if 
c-----Remove the grids whose variance equal to zero. 
 l2=0 
 do i=1,l1 
   call meanvar(n,f1(1,i),ax,g(i),vx) 
   if(g(i).gt.std)then 
          l2=l2+1 
     do k=1,n 
            f(l2,k)=f1(k,i) 
     enddo 
   endif 
 end do 
 write(*,*)'Grids without terrain and constant value:' 
 write(*,*)'mg2=',l2 
      
c     stop 
c-----Call the subroutine. 
      write(*,*)'!!!!' 
      call eof(l2,n,mnl,f(1:l2,:),ks,er,gvt(1:l2,:),ecof) 
 write(*,*)'EOF ok and transform to the original form in the next!' 
c-----Add the grids whose variance equal to zero.       
 l3=0 
 do i=1,mg2 
   if(g(i).gt.std)then 
     l3=l3+1 
     do k=1,mnl 
       h1(i,k)=gvt(l3,k) 
     end do 
   else 
     do k=1,mnl 
       h1(i,k)=undef 
     end do 
   endif 
 enddo 
c-----Add the terrain or missing value. 
 l4=0 
 do i=1,m 
   if(f0(1,i).ne.undef)then 
     l4=l4+1 
     do k=1,mnl 
       egvt(i,k)=h1(l4,k) 
     end do 
   else 
     do k=1,mnl 
       egvt(i,k)=undef 
     end do 
   endif 
 enddo 
c-----output the result.         
c-----output the error. 
      write(*,*)'Output the results:' 
 open(10,file='e:\lunwen\jiala7\gy\eofsst\qd10er.txt', 
     &form='formatted') 
c 
      write(10,*)'EOF lamda (eigenvalues) from big to small' 
 write(10,*)(er(i,1),i=1,mnl) 
 write(*,*)' OK: EOF lamda (eigenvalues) from big to small!' 
c 
 write(10,*)'EOF accumulated eigenvalues from big to small' 
 write(10,*)(er(i,2),i=1,mnl) 
 write(*,*)' OK: accumulated eigenvalues from big to small!' 
c 
 write(10,*)'EOF explained variances' 
 write(10,*)(er(i,3),i=1,mnl) 
 write(*,*)' OK: EOF explained variances!' 
c 
 write(10,*)'EOF accumulated explained variances' 
 write(10,*)(er(i,4),i=1,mnl) 
 write(*,*)' OK: EOF accumulated explained variances!' 
c 
 close(10) 
c-----output eigenvactors matrix of EOF. 
 
       
 do i=1,m 
   if(egvt(i,1).ne.undef)then 
      
     do k=1,mnl 
       egvt(i,k)=egvt(i,k)*sqrt(abs(er(k,1)/mnl)) 
     end do 
 
   endif 
 enddo 
      open(11,file='e:\lunwen\jiala7\gy\eofsst\qd10egvt.dat', 
     &status='unknown' 
     &,form='unformatted',access='direct',recl=m) 
 
 do j=1,mnl 
   write(11,rec=j)(egvt(i,j),i=1,m) 
 end do 
      write(*,*)' OK: output eigenvactors matrix of EOF!' 
 close(11) 
 
c-----output time coefficients matrix of EOF. 
      open(12,file='e:\lunwen\jiala7\gy\eofsst\qd10ecof.dat', 
     &status='unknown' 
     &,form='unformatted',access='direct',recl=mnl) 
      do i=1,n 
   write(12,rec=i)(ecof(j,i)/sqrt(abs(er(j,1)/mnl)),j=1,mnl) 
 end do 
      write(*,*)' OK: output time coefficients matrix of EOF!' 
 close(12) 
      write(*,*)'EOF all OK!'   
c-----create control files(.ctl) for 'egvt.dat' and 'ecof.dat' 
      write(*,*) 'Create ''.ctl'' files for ''.dat'' files: ' 
!      open(13,file='e:\lunwen\756mon\egvt.ctl',form='formatted') 
 write(13,*) 'dset ^egvt.dat' 
 write(13,*) 'undef ',undef 
 write(13,*) 'xdef ',mx,' linear  88.75 2.5' 
 write(13,*) 'ydef ',my,' linear  3.75 2.5' 
 write(13,*) 'zdef 1 linear 0 1' 
 write(13,*) 'tdef ',mnl,' linear DEC1979 1yr' 
 write(13,*) 'vars 1' 
 write(13,*) 'egvt  0  99  eigenvactors matrix of EOF' 
 write(13,*) 'endvars' 
 close(13) 
 write(*,*) ' OK: ''egvt.ctl'' is created!' 
c 
!      open(14,file='e:\lunwen\756mon\ecof.ctl',form='formatted') 
 write(14,*) 'dset ^ecof.dat' 
 write(14,*) 'undef ',undef 
 write(14,*) 'xdef ',mnl,' linear 0 1' 
 write(14,*) 'ydef 1 linear 0 1' 
 write(14,*) 'zdef 1 linear 0 1' 
 write(14,*) 'tdef ',n,' linear DEC1979 1yr' 
 write(14,*) 'vars 1' 
 write(14,*) 'ecof  0  99  eigenvactors matrix of EOF' 
 write(14,*) 'endvars' 
 close(14) 
 write(*,*) ' OK: ''ecof.ctl'' is created!' 
c 
 write(*,*) 'All are finished successfully!' 
       
 stop 
c----- 
 end 
c======================================================================= 
c 
c======================================================================= 
c----------------------------------------------------------------------- 
c                      eof(m,n,mnl,f,ks,er,egvt,ecof) 
c                  -------------------------------------- 
c                  经验正交函数(EOF)-特征向量场及时间系数 
c-----*----------------------------------------------------6---------7-- 
C     EMPIRICAL ORTHOGONAL FUNCTIONS (EOF's) 
c     This subroutine applies the EOF approach to analysis time series 
c       of meteorological field f(m,n). 
c     input: m,n,mnl,f(m,n),ks 
c       m: number of grid-points 
c       n: lenth of time series 
c       mnl=min(m,n) 
c       f(m,n): the raw spatial-temporal seires 
c       ks: contral parameter 
c           ks=-1: self, i.e., for the raw time series; 
c           ks=0: departure, i.e., for the anomaly time series from climatological mean; 
c           ks=1: normalized departure, i.e., for the normalized time series; 
c     output: egvt,ecof,er 
c       egvt(m,mnl): array of eigenvactors 
c       ecof(mnl,n): array of time coefficients for the respective eigenvectors 
c       er(mnl,1): lamda (eigenvalues), its sequence is from big to small. 
c       er(mnl,2): accumulated eigenvalues from big to small 
c       er(mnl,3): explained variances (lamda/total explain) from big to small 
c       er(mnl,4): accumulated explaned variances from big to small 
c     work variables: 
c     Last updated by Yongjie HUANG on January 4, 2012 
c     Dr. Jianping Li on October 20, 2005. 
c     Citation: Li, J., 2005: EOF subroutine, <a href=\"http://web.lasg.ac.cn/staff/ljp/subroutine/EOF.f\" target=\"_blank\">http://web.lasg.ac.cn/staff/ljp/subroutine/EOF.f</a>. 
c----- 
      subroutine eof(m,n,mnl,f,ks,er,egvt,ecof) 
      dimension f(m,n),er(mnl,4),egvt(m,mnl),ecof(mnl,n) 
      dimension cov(mnl,mnl),s(mnl,mnl),d(mnl),v(mnl) !work array 
c---- Preprocessing data 
      call transf(m,n,f,ks) 
c---- Crossed product matrix of the data f(m,n) 
      call crossproduct(m,n,mnl,f,cov) 
c---- Eigenvalues and eigenvectors by the Jacobi method 
      call jacobi(mnl,cov,s,d,0.00001) 
c---- Specified eigenvalues 
      call arrang(mnl,d,s,er) 
c---- Normalized eignvectors and their time coefficients 
      call tcoeff(m,n,mnl,f,s,er,egvt,ecof) 
      return 
      end 
c----------------------------------------------------------------------- 
c 
c-----------------------------------------------------------------------    
c----------------------------------------------------------------------- 
c                           transf(m,n,f,ks) 
c                    ------------------------------ 
c                    处理资料为距平、标准方差或不变          
c-----*----------------------------------------------------6---------7-- 
c     Preprocessing data to provide a field by ks. 
c     input: m,n,f 
c       m: number of grid-points 
c       n: lenth of time series 
c       f(m,n): the raw spatial-temporal seires 
c       ks: contral parameter 
c           ks=-1: self, i.e., for the raw time series; 
c           ks=0: departure, i.e., for the anomaly time series from climatological mean; 
c           ks=1: normalized departure, i.e., for the normalized time series; 
c     output: f 
c       f(m,n): output field based on the control parameter ks. 
c     work variables: fw(n) 
      subroutine transf(m,n,f,ks) 
      dimension f(m,n) 
      dimension fw(n),wn(m)           !work array 
c 
 i0=0 
 do i=1,m 
   do j=1,n 
          fw(j)=f(i,j) 
        enddo 
   call meanvar(n,fw,af,sf,vf) 
   if(sf.eq.0.)then 
     i0=i0+1 
     wn(i0)=i 
   endif 
 enddo 
c 
 if(i0.ne.0)then 
   write(*,*)'****  FAULT  ****' 
   write(*,*)' The program cannot go on because 
     *the original field has invalid data.' 
   write(*,*)' There are totally ',i0, 
     *    '  gridpionts with invalid data.' 
        write(*,*)' These invalid data are those whose standard variance 
     *equal zero.' 
        write(*,*)' The array WN stores the positions of those invalid 
     *grid-points. You must pick off those invalid data from the orignal 
     *field and then reinput a new field to calculate its EOFs.'    
   write(*,*)'****  FAULT  ****' 
   stop 
 endif      
c 
c 
      if(ks.eq.-1)return 
c 
      if(ks.eq.0)then                !anomaly of f 
        do i=1,m 
          do j=1,n 
            fw(j)=f(i,j) 
          enddo 
          call meanvar(n,fw,af,sf,vf) 
          do j=1,n 
            f(i,j)=f(i,j)-af 
          enddo 
        enddo 
        return 
      endif 
c 
      if(ks.eq.1)then                 !normalizing f 
        do i=1,m 
          do j=1,n 
            fw(j)=f(i,j) 
          enddo 
          call meanvar(n,fw,af,sf,vf) 
          do j=1,n 
            f(i,j)=(f(i,j)-af)/sf 
          enddo 
        enddo 
      endif 
      return 
      end 
c----------------------------------------------------------------------- 
c 
c----------------------------------------------------------------------- 
 
c----------------------------------------------------------------------- 
c                      crossproduct(m,n,mnl,f,cov) 
c                      --------------------------- 
c                              计算交叉矩阵 
c-----*----------------------------------------------------6---------7-- 
c     Crossed product martix of the data. It is n times of 
c       covariance matrix of the data if ks=0 (i.e. for anomaly). 
c     input: m,n,mnl,f 
c       m: number of grid-points 
c       n: lenth of time series 
c       mnl=min(m,n) 
c       f(m,n): the raw spatial-temporal seires 
c     output: cov(mnl,mnl)   
c       cov(m,n)=f*f' or f'f dependes on m and n. 
c         It is a mnl*mnl real symmetric matrix. 
      subroutine crossproduct(m,n,mnl,f,cov) 
      dimension f(m,n),cov(mnl,mnl) 
 if(n-m<0) then 
        do i=1,mnl 
  do j=i,mnl 
    cov(i,j)=0.0 
            do is=1,m 
    cov(i,j)=cov(i,j)+f(is,i)*f(is,j) 
            enddo 
          cov(j,i)=cov(i,j) 
     end do 
   end do 
        return 
 else 
        do i=1,mnl 
   do j=i,mnl 
             cov(i,j)=0.0 
     do js=1,n 
     cov(i,j)=cov(i,j)+f(i,js)*f(j,js) 
             enddo 
           cov(j,i)=cov(i,j) 
   end do 
   end do 
        return 
 end if 
      end 
c----------------------------------------------------------------------- 
c 
c----------------------------------------------------------------------- 
 
c----------------------------------------------------------------------- 
c                           jacobi(m,a,s,d,eps) 
c                ------------------------------------------          
c                使用雅克比过关法计算矩阵的特征向量和特征值 
c-----*----------------------------------------------------6---------7-- 
c     Computing eigenvalues and eigenvectors of a real symmetric matrix 
c       a(m,m) by the Jacobi method. 
c     input: m,a,s,d,eps 
c       m: order of matrix 
c       a(m,m): the covariance matrix 
c       eps: given precision 
c     output: s,d 
c       s(m,m): eigenvectors 
c       d(m): eigenvalues 
      subroutine jacobi(m,a,s,d,eps) 
      dimension a(m,m),s(m,m),d(m) 
c-----使s(m,m)为单位矩阵E 
      do i=1,m 
       do j=1,i 
        if(i-j==0) then 
      s(i,j)=1. 
   else 
   s(i,j)=0. 
   s(j,i)=0. 
   end if 
  end do 
 end do 
c-----计算m阶实对称矩阵a(m,m)的所有非对角线元素平方之和的平方根 
      g=0. 
      do i=2,m 
        i1=i-1 
        do j=1,i1 
          g=g+2.*a(i,j)*a(i,j) 
   end do 
 end do 
      s1=sqrt(g) 
c-----设置关口s3 
      s2=eps/float(m)*s1 
      s3=s1 
      l=0 
  50  s3=s3/float(m) 
c-----在非对角线元素中逐行扫描选取第一个绝对值大于或等于s3的元素a(ip,iq), 
c-----进行平面旋转变换，直到所有非对角线元素的绝对值都小于s3为止. 
  60  do 130 iq=2,m 
        do 130 ip=1,iq-1 
    if(abs(a(ip,iq)).lt.s3) goto 130 
    l=1 
    v1=a(ip,ip) 
    v2=a(ip,iq) 
    v3=a(iq,iq) 
    u=0.5*(v1-v3) 
    if(u.eq.0.0) g=1. 
    if(abs(u).ge.1e-10) g=-sign(1.,u)*v2/sqrt(v2*v2+u*u) 
    st=g/sqrt(2.*(1.+sqrt(1.-g*g))) 
    ct=sqrt(1.-st*st) 
    do i=1,m 
   g=a(i,ip)*ct-a(i,iq)*st 
      a(i,iq)=a(i,ip)*st+a(i,iq)*ct 
       a(i,ip)=g 
   g=s(i,ip)*ct-s(i,iq)*st 
   s(i,iq)=s(i,ip)*st+s(i,iq)*ct 
   s(i,ip)=g 
    end do 
    do i=1,m 
    a(ip,i)=a(i,ip) 
    a(iq,i)=a(i,iq) 
    end do 
    g=2.*v2*st*ct 
    a(ip,ip)=v1*ct*ct+v3*st*st-g 
    a(iq,iq)=v1*st*st+v3*ct*ct+g 
            a(ip,iq)=(v1-v3)*st*ct+v2*(ct*ct-st*st) 
            a(iq,ip)=a(ip,iq) 
  130 continue 
c-----平面旋转变换，直到所有非对角线元素的绝对值都小于s3为止. 
      if(l-1==0) then 
        l=0 
        go to 60 
 else 
   if(s3.gt.s2) goto 50 !再设置下一关口 
 end if 
c 
      do i=1,m 
        d(i)=a(i,i) 
 end do 
      return 
      end 
c----------------------------------------------------------------------- 
c 
c----------------------------------------------------------------------- 
 
c----------------------------------------------------------------------- 
c                            arrang(mnl,d,s,er) 
c   ---------------------------------------------------------------- 
c   重新由大到小排列及计算特征值、累积特征值、解释方差及累积解释方差 
c-----*----------------------------------------------------6---------7-- 
c     Provides a series of eigenvalues from maximuim to minimuim. 
c     input: mnl,d,s 
c       d(mnl): eigenvalues 
c       s(mnl,mnl): eigenvectors 
c     output: er 
c       er(mnl,1): lamda (eigenvalues), its equence is from big to small. 
c       er(mnl,2): accumulated eigenvalues from big to small 
c       er(mnl,3): explained variances (lamda/total explain) from big to small 
c       er(mnl,4): accumulated explaned variances from big to small 
      subroutine arrang(mnl,d,s,er) 
      dimension d(mnl),s(mnl,mnl),er(mnl,4) 
c 
      tr=0.0 
      do i=1,mnl 
        tr=tr+d(i) 
        er(i,1)=d(i) 
      end do 
c-----由大到小排列特征值及将对应的特征向量做相应的移动 
      mnl1=mnl-1 
      do k1=mnl1,1,-1 
       do k2=k1,mnl1 
        if(er(k2,1).lt.er(k2+1,1)) then 
          c=er(k2+1,1) 
          er(k2+1,1)=er(k2,1) 
          er(k2,1)=c 
          do i=1,mnl 
            c=s(i,k2+1) 
            s(i,k2+1)=s(i,k2) 
            s(i,k2)=c 
  end do 
        endif 
  end do 
 end do 
c-----计算累积特征值 
      er(1,2)=er(1,1) 
      do i=2,mnl 
        er(i,2)=er(i-1,2)+er(i,1) 
      end do 
c-----计算解释方差及累积解释方差 
      do i=1,mnl 
        er(i,3)=er(i,1)/tr 
        er(i,4)=er(i,2)/tr 
 end do 
c 
      return 
      end 
c----------------------------------------------------------------------- 
c 
c----------------------------------------------------------------------- 
c----------------------------------------------------------------------- 
c                   tcoeff(m,n,mnl,f,s,er,egvt,ecof) 
c                   -------------------------------- 
c                       归一化特征向量和时间系数 
c-----*----------------------------------------------------6---------7-- 
c     Provides standard eigenvectors and their time coefficients 
c     input: m,n,mnl,f,s,er 
c       m: number of grid-points 
c       n: lenth of time series 
c       mnl=min(m,n) 
c       f(m,n): the raw spatial-temporal seires 
c       s(mnl,mnl): eigenvectors 
c       er(mnl,1): lamda (eigenvalues), its equence is from big to small. 
c       er(mnl,2): accumulated eigenvalues from big to small 
c       er(mnl,3): explained variances (lamda/total explain) from big to small 
c       er(mnl,4): accumulated explaned variances from big to small 
c     output: egvt,ecof 
c       egvt(m,mnl): normalized eigenvectors 
c       ecof(mnl,n): time coefficients of egvt 
      subroutine tcoeff(m,n,mnl,f,s,er,egvt,ecof) 
      dimension f(m,n),s(mnl,mnl),er(mnl,4),egvt(m,mnl),ecof(mnl,n) 
      dimension v(mnl)  !work array 
c 
      do j=1,mnl 
        do i=1,m 
          egvt(i,j)=0. 
        enddo 
        do i=1,n 
          ecof(j,i)=0. 
        enddo 
      enddo 
c-----Normalizing the input eignvectors s 
      do j=1,mnl 
        c=0. 
        do i=1,mnl 
          c=c+s(i,j)*s(i,j) 
        enddo 
        c=sqrt(c) 
        do i=1,mnl 
          s(i,j)=s(i,j)/c 
        enddo 
      enddo 
c----- 
      if(m.le.n) then 
        do js=1,mnl 
  do i=1,m 
   egvt(i,js)=s(i,js) 
  enddo 
        enddo 
        do j=1,n 
          do i=1,m 
            v(i)=f(i,j) 
          enddo 
          do is=1,mnl 
   do i=1,m 
     ecof(is,j)=ecof(is,j)+v(i)*s(i,is) 
   enddo 
          enddo 
   enddo 
      else 
c-----这里使用了时空转换，时间系数得乘以sqrt(abs(er(js,1))，特征向量除以sqrt(abs(er(js,1)) 
        do i=1,m 
          do j=1,n 
            v(j)=f(i,j) 
          enddo 
          do js=1,mnl 
   do j=1,n 
            egvt(i,js)=egvt(i,js)+v(j)*s(j,js) 
   enddo 
          enddo 
   enddo 
        do js=1,mnl 
          do j=1,n 
            ecof(js,j)=s(j,js)*sqrt(abs(er(js,1))) 
          enddo 
          do i=1,m 
            egvt(i,js)=egvt(i,js)/sqrt(abs(er(js,1))) 
          enddo 
   enddo 
      endif 
      return 
      end 
c----------------------------------------------------------------------- 
c 
c----------------------------------------------------------------------- 
    
c----------------------------------------------------------------------- 
c                      meanvar(n,x,ax,sx,vx) 
c                      ------------------------------- 
c                       计算矩阵的平均值、标准差和方差 
c-----*----------------------------------------------------6---------7-- 
c     Computing the mean ax, standard deviation sx 
c       and variance vx of a series x(i) (i=1,...,n). 
c     input: n and x(n) 
c       n: number of raw series 
c       x(n): raw series 
c     output: ax, sx and vx 
c       ax: the mean value of x(n) 
c       sx: the standard deviation of x(n) 
c       vx: the variance of x(n) 
c     By Dr. LI Jianping, May 6, 1998. 
      subroutine meanvar(n,x,ax,sx,vx) 
      dimension x(n) 
      ax=0. 
      vx=0. 
      sx=0. 
c     calculate the mean value of x(n): ax 
      do i=1,n 
        ax=ax+x(i) 
 end do 
      ax=ax/float(n) 
c     calculate the standard deviation of x(n): sx 
      do i=1,n 
        vx=vx+(x(i)-ax)**2 
 end do 
      vx=vx/float(n) 
c     calculate the variance of x(n): vx   
      sx=sqrt(vx) 
      return 
      end 
c------------------------------------------------------------------------- 
c 
c------------------------------------------------------------------------- 
c-----*----------------------------------------------------6---------7-- 
c     This subroutine is for removing annual cycle (Monthly of daily data) 
c      
c     input: 
c       nd: number of days or monthes in a year. 
c       ny: number of year 
c       ndy=nd*ny 
c       f(ndy): the daily of monthly data. 
c 
c     output: 
c       af(ndy): the daily of monthly data without annual cycle 
c 
c     by Dr Jianping Li,   
c     recomplied by Dong Xiao on May 7, 2007 
c----- 
      subroutine initial(nd,ny,ndy,f,af) 
!-----input array 
 real f(ndy) 
!-----work arrays 
 real fave(nd),fstd(nd) 
!-----output array 
 real af(ndy) 
c----- 
 do i=1,nd 
   fave(i)=0. 
   do j=1,ny 
     fave(i)=fave(i)+f(i+(j-1)*nd) 
   enddo 
   fave(i)=fave(i)/ny 
   fstd(i)=0.0 
   do j=1,ny 
     fstd(i)=fstd(i)+(f(i+(j-1)*nd)-fave(i))**2 
   enddo 
   fstd(i)=sqrt(fstd(i)/float(ny)) 
   do j=1,ny 
     ij=i+(j-1)*nd 
c-----standard departure 
c     af(ij)=(f(ij)-fave(i))/fstd(i) 
c-----departure 
 af(ij)=(f(ij)-fave(i)) 
   enddo 
 enddo 
c----- 
 return 
 end 
c-----*----------------------------------------------------6---------7-- 
c 
c-----------------------------------------------------------------------

river · 发表于 2014-2-7 14:48:17

谢谢分享，不过程序修改的地方好像没有注明啊······

scwjx520 · 发表于 2014-2-7 22:39:09

{:5_213:}{:5_213:}

yuhuofenghuang · 发表于 2014-2-8 01:06:28

{:eb303:}{:eb303:}

kongfeng0824 · 发表于 2014-2-8 09:10:50

谢谢分享

leswell · 发表于 2014-2-9 09:27:34

不明觉厉，感谢分享

哈哈哈哈哈哈哈 · 发表于 2014-2-10 18:38:02

不错啊有空研究研究

geophylika · 发表于 2014-2-10 22:35:54

不明觉厉，学习一下

desert_mt · 发表于 2014-2-12 11:41:17

谢谢分享

snowie · 发表于 2014-2-14 09:03:25

同不明觉厉...学eof的时候就不知道讲的是什么

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