add sheet 9
Michi commited on 2012-07-01 21:25:27
Zeige 1 geänderte Dateien mit 177 Einfügungen und 0 Löschungen.
- 9/solution9.R 0000000..c1326d2
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+#Sheet 9 Michael Klauser |
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+library(gplots) |
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+library(fields) |
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+Filepath="ProjectedDensity.dat" |
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+data=scan(Filepath, what=list(x=0., D=0., sigma=0.)) |
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+data=data.frame(x=data$x, D=data$D, sigma=data$sigma) |
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+ |
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+plotCI(data$x, data$D, uiw=data$sigma, xlab="Angular Position", ylab="Projected Density") |
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+ |
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+M=10 |
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+N=length(data$x) |
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+theta=rep(0,M) |
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+delta.x=(max(data$x)-min(data$x))/M |
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+for (j in 1:M){
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+ theta[j]=min(data$x)+delta.x*(j-0.5) |
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+} |
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+ |
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+kron = function(a,b) {
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+ if (a==b) {return(1.)} else {return(0.)}
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+} |
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+ |
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+T=array(0.,c(N,M)) |
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+a=array(0.,c(10,11)) |
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+F=array(0.,c(11,11,N)) |
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+breaks=seq(min(data$x)-1e-9,max(data$x)+1e-9,length.out=11) |
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+bin = findInterval(data$x,breaks) |
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+data = cbind(data,bin) |
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+ |
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+for (k in 1:N) {
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+ for (j in 1:M) {
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+ T[k,j]=max(0,1-abs(data$x[k]-theta[j])/delta.x)+(2*kron(k,1)-kron(k,2))*max(0,1-abs(data$x[k]-theta[j]+delta.x)/delta.x)+(2*kron(k,M)-kron(k,M-1))*max(0,1-abs(data$x[k]-theta[j]-delta.x)/delta.x) |
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+ } |
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+} |
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+ |
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+dum=stats.bin(data$x,data$D,breaks=breaks) |
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+for (j in 1:M) {
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+ if (j!=9) {
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+ for (i in -5:5) {
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+ a[j,i+6]=dum$stats["Q1",j]+i*max(data$sigma[which(data$bin==j)])/10 |
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+ a[9,i+6]=0 |
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+ } |
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+ } |
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+} |
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+ |
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+for (l in 1:M) {
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+ for (i in -5:5) {
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+ for (k in 1:N) {
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+ for (j in 1:M) {
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+ if (j==l) {F[l,i+6,k]=F[l,i+6,k]+T[k,j]*a[j,i+6]} else {F[l,i+6,k]=F[l,i+6,k]+T[k,j]*a[j,0+6]}
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+ } |
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+ } |
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+ } |
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+} |
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+ |
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+Chisq=array(0.,c(M,11)) |
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+for (j in 1:M) {
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+ for (i in -5:5) {
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+ for (k in 1:N) {
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+ Chisq[j,i+6] = Chisq[j,i+6] + (F[j,i+6,k]-data$D[k])^2/(data$sigma[k])^2 |
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+ } |
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+ } |
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+} |
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+ |
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+af = rep(NA,M) |
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+for (i in (1:M)){af[i] = a[which(Chisq==min(Chisq[,i]),arr.ind=TRUE)]}
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+ |
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+#2 |
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+T = t(T)%*%T |
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+dirty = function(i,j){
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+ tmp = 0 |
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+ for(k in (1:M)){
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+ tmp = tmp + (T[k,i] * T[k,j])/(data$sigma[k]**2) |
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+ } |
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+ return(tmp) |
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+ } |
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+H=array(0.,c(M,M)) |
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+for (i in 1:M){
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+ for (j in 1:M){
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+ H[i,j] = 2 * dirty(i,j)}} |
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+ |
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+ |
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+lambda=eigen(H)$val |
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+e=eigen(H)$vec |
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+l=seq(1,10,1) |
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+ |
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+x11() |
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+plot(l,lambda, main="Eigenvalues", xlab="l", ylab="lambda") |
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+x11() |
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+plot(theta,e[1,], main = "Eigenvectors") |
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+for (l in 2:M) {
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+ lines(theta+0.0001*l,e[l,],type="p",pch=l) |
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+} |
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+x11() |
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+plot(theta,e[1,]/lambda[1], main = "Eigenvectors --- weighted") |
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+for (l in 2:M) {
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+ lines(theta+0.0001*l,e[l,]/lambda[l],type="p",pch=l) |
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+} |
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+ |
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+T_e = solve(e) %*% T %*%e |
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+ |
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+ |
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+######### |
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+ |
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+Ff = function(T,a){
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+ tmp = 0 |
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+ for (j in (1:length(T))){
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+ tmp = tmp + T[j]*a[j] |
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+ return(tmp) |
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+ }} |
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+afm = array(NA,c(M,M)) |
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+for (Mn in (1:M)){
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+ print('we are at')
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+ print(Mn) |
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+ N=length(data$x) |
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+ theta=rep(0,Mn) |
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+ delta.x=(max(data$x)-min(data$x))/Mn |
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+ for (j in 1:Mn){
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+ theta[j]=min(data$x)+delta.x*(j-0.5) |
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+ } |
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+ |
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+ kron = function(a,b) {
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+ if (a==b) {return(1.)} else {return(0.)}
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+ } |
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+ |
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+ T=array(0.,c(N,Mn)) |
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+ a=array(0.,c(10,11)) |
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+ F=array(0.,c(11,11,N)) |
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+ breaks=seq(min(data$x)-1e-9,max(data$x)+1e-9,length.out=11) |
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+ bin = findInterval(data$x,breaks) |
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+ data = cbind(data,bin) |
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+ |
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+ |
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+ |
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+ dum=stats.bin(data$x,data$D,breaks=breaks) |
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+ for (j in 1:Mn) {
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+ if (j!=9) {
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+ for (i in -5:5) {
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+ a[j,i+6]=dum$stats["Q1",j]+i*max(data$sigma[which(data$bin==j)])/Mn |
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+ a[9,i+6]=0 |
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+ } |
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+ } |
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+ } |
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+ |
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+ for (k in 1:N) {
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+ for (j in 1:Mn) {
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+ T[k,j]=max(0,1-abs(data$x[k]-theta[j])/delta.x)+(2*kron(k,1)-kron(k,2))*max(0,1-abs(data$x[k]-theta[j]+delta.x)/delta.x)+(2*kron(k,M)-kron(k,M-1))*max(0,1-abs(data$x[k]-theta[j]-delta.x)/delta.x) |
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+ } |
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+ } |
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+ T = t(T)%*%T |
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+ dirty = function(i,j){
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+ tmp = 0 |
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+ for(k in (1:Mn)){
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+ tmp = tmp + (T[k,i] * T[k,j])/(data$sigma[k]**2) |
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+ } |
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+ return(tmp) |
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+ } |
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+ H=array(0.,c(Mn,Mn)) |
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+ for (i in 1:Mn){
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+ for (j in 1:Mn){
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+ H[i,j] = 2 * dirty(i,j)}} |
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+ lambda=eigen(H)$val |
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+ e=eigen(H)$vec |
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+ l=seq(1,10,1) |
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+ |
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+ Chisq=array(0.,c(Mn,11)) |
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+ for (j in 1:Mn) {
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+ for (i in -5:5) {
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+ for (k in 1:Mn) {
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+ Chisq[j,i+6] = Chisq[j,i+6] + (Ff(T[k,],a)-data$D[k])^2/(data$sigma[k])^2 |
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+ } |
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+ |
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+ } |
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+ } |
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+ for (i in (1:Mn)){afm[Mn,i] = a[which(Chisq==min(Chisq[,i]),arr.ind=TRUE)[Mn]]}
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+} |
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+print('The best fit c')
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+print(afm) |
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