www.gusucode.com > EasyKrig_V3.0工具箱matlab源码程序 > EasyKrig_V3.0/krig/krig2d.m
function [Vp,Ep]=krig2d(xp,yp,xn,yn,var,model_para,hmsg)
% function [Vp,Ep]=krig2d(xp,yp,xn,yn,var,model_para,hmsg) perform the 2-D kriging
%% INPUT:
%% xn, yn - coordinates of the input data
%% xp, yp - coordinates of the kriged output
%% var - input data value array
%% model_para - model parameters for computing the semi-variogram/correlogram
%% hmsg - handle of the message window
%%
%% OUTPUT:
%% Vp - kriged values
%% EP - Kriging variance
%%
%% Kriging Software Package version 3.0, May 1, 2004
%% Copyright (c) 1999, 2001, 2004, property of Dezhang Chu and Woods Hole Oceanographic
%% Institution. All Rights Reserved.
global para data
model=para.vario.model;
model_type=2-para.vario.corr;
mod_opt=para.krig.model;
eplim=para.krig.elim;
EPS=para.krig.eps;
Ratio=para.krig.ratio;
blk_opt=para.krig.scheme;
nx=length(xp);
ny=length(yp);
nbx=para.krig.blk_nx;
nby=para.krig.blk_ny;
kmin=para.krig.kmin;
kmax=para.krig.kmax;
R=para.krig.srad;
dx=para.krig.dx;
dy=para.krig.dy;
%% process anisotrophic data
if abs(para.vario.azm_rot) > eps | abs(para.vario.dip_rot) > eps ...
| abs(1-para.vario.ytox_ratio) > 1e-5 | abs(1-para.vario.ztox_ratio)
%% observations
cz_in_obs=[xn(:) yn(:)];
cz_out_obs=coordtransform3d(cz_in_obs);
xn=cz_out_obs(:,1);yn=cz_out_obs(:,2);
%% predictions
cz_in_pred=[xp(:) yp(:)];
cz_out_pred=coordtransform3d(cz_in_pred);
xp=cz_out_pred(:,1);yp=cz_out_pred(:,2);
end
n=length(xn);
xn=reshape(xn,1,n);
yn=reshape(yn,1,n);
if model_type == 1
model=-abs(model);
end
nmax_var=500;
rR=linspace(0,sqrt(2)+0.01,nmax_var);dr=rR(2)-rR(1);
vgram=variogrammodel3d(model,rR,model_para);
if blk_opt == 2
model_para1=[0 1 model_para(3:5)];
% The semi-variogram/covariance between a grid block and itself:
CVV=blk2blk2d(0,0,0,0,nbx,nby,dx,dy,model,model_para1);
end
pad=zeros(1,4); % needed to pad K in the main routine
if 0
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if blk_opt == 2 & model < 0
model_para1=[0 1 model_para(3:5)];
% The covariance between a grid block and itself:
CVV=blk2blk2d(0,0,0,0,nbx,nby,dx,dy,model,model_para1);
end
end
n=length(xn);
val_m=max(var);
Anomaly_cnt1=0;
Anomaly_cnt2=0;
Anomaly_cnt3=0;
nv=nx;
nv_cnt=max(1,round(0.01*nv));
Vp=nan*ones(nv,1);
Ep=nan*ones(nv,1);
if mod_opt == 3 % for universal kriging with linear drift
% delx=-(xp(ones(n,1),:)'-xn(ones(nv,1),:));
% dely=-(yp(ones(n,1),:)'-yn(ones(nv,1),:));
end
pad=zeros(1,3); % needed to pad K in the main routine
if nargin == 7 tic;end
for i=1:nv
Dx=(xp(i)-xn);
Dx2=Dx.*Dx;
Dy=(yp(i)-yn);
Dy2=Dy.*Dy;
if rem(i,nv_cnt) == 0 & nv > 100 & nargin == 7
percent=sprintf(' %g percent done in %g sec.', floor(100*i/nv),round(toc));
if ~isempty(hmsg) message(4,percent,' ',hmsg); end
end
r=sqrt(Dx2+Dy2);
if kmin >= n
indx_sort=1:n;
indx1=1:n;nk=n;
else
[r_sort,indx_sort]=sort(r);
indx=find(r_sort <= R);
if length(indx) > kmax
indx1=indx_sort(1:kmax);
elseif length(indx) < kmin
indx1=indx_sort(1:kmin);
else
indx1=indx_sort(indx);
end
nk=length(indx1);
end
if blk_opt == 2
M20=sta2blk2d(xn(indx1),yn(indx1),xp(i),yp(i),nbx,nby,dx,dy,model,model_para);
else
M20=variogrammodel3d(model,r(indx1),model_para);
end
switch mod_opt
case 1 % Objective mapping, follow Journel and Huijbregts, p. 307
M2=M20';
case 2 % Ordinary Kriging, follow Journel and Huijbregts, p. 307
M2=[M20 1 ]';
case 3 % Universal Kriging w/ Linear drift, follow Journel and Huijbregts, p. 319
M2=[M20 1 0 0 ]'; % x,y
end
if i == 1 | kmin < n % for kmin > n only needs to compute SVD once
% Construct the coefficient matrix and its inverse matrix
% to avoid repeated computation in the loop
x1=xn(indx1);
y1=yn(indx1);
var1=var(indx1);
dx1=(x1(ones(nk,1),:)'-x1(ones(nk,1),:));
dy1=(y1(ones(nk,1),:)'-y1(ones(nk,1),:));
rs=sqrt(dx1.*dx1+dy1.*dy1);
K0=variogrammodel3d(model,rs,model_para); % semi-variagram
if model_type == 1 % correlogram
K0(1:nk+1:nk*nk)=ones(nk,1);
else % variogram
K0(1:nk+1:nk*nk)=zeros(nk,1);
end
switch mod_opt
case 1 % Objective mapping, follow Journel and Huijbregts, p. 307
K=K0;
case 2 % Ordinary Kriging, follow Journel and Huijbregts, p. 307
K=[K0 ones(nk,1);ones(1,nk) 0];
case 3 % Universal kriging w/ linear drift, follow Journel and Huijbregts, p. 319
delx=xp(i)-x1;
dely=yp(i)-y1;
K=[K0 ones(nk,1) xn(indx1)' yn(indx1)' ; ...
ones(1,nk) pad; delx pad; dely pad];
end
[U,S,V]=svd(K);
% kindx=find(diag(S) > EPS);
kindx=find(abs(diag(S)/S(1,1)) > Ratio);
Sinv=diag(1./diag(S(kindx,kindx)));
K_inv=V(:,kindx)*Sinv*U(:,kindx)';
end % end of if loop for computing SVD
lambda=K_inv*M2;
lnan=find(isnan(var1));
if length(lnan) > 0
var1(lnan)=zeros(length(lnan),1);
end
Vp(i)=sum_nan(lambda(1:nk).*var1);
if abs(mean_nan(var(indx1)-Vp(i))) > 2
% disp(sprintf('|Vp-mean(var)|>2 i=%g',i));
% plot(1:length(indx1),var(indx1),'.-',length(indx1)/2,Vp(i),'o')
Anomaly_cnt1=Anomaly_cnt1+1;
end
if blk_opt == 2
if model_type == 1
Ep(i)=CVV-sum_nan(lambda.*M2); % Error estimate for tp(j)
else
Ep(i)=sum_nan(lambda.*M2)-CVV; % CVV = GammaVV
end
else
if model_type == 1
Ep(i)=1-sum_nan(lambda.*M2);
else
Ep(i)=sum_nan(lambda.*M2);
end
end
if abs(Vp(i)) > 3.0*val_m
% disp(sprintf('Var > 3*Var_max i=%g',i));
Anomaly_cnt2=Anomaly_cnt2+1;
% Ep(i)=3.0*val_m;
end
if abs(Ep(i)) > eplim
% disp(sprintf('Err > eplim i=%g',i));
Vp(i)=NaN;
Ep(i)=abs(Ep(i));
Anomaly_cnt3=Anomaly_cnt3+1;
end
end
if Anomaly_cnt1 > 1
% disp(sprintf(' Anomaly_cnt for |<var(indx1)-Vp(i)>| > 2 = %g',Anomaly_cnt1));
end
if Anomaly_cnt2 > 1
% disp(sprintf(' Anomaly_cnt for Vp > 3*Var_max =%g ',Anomaly_cnt2));
end
if Anomaly_cnt3 > 1
disp(sprintf(' Anomaly_cnt for |Ep| > Relative Error =%g ',Anomaly_cnt3));
end