guesslow<-function(A1,A2,Y)
{
  invA1<-solve(A1)
  first<-rep(0,ncol(A2))
  trythis<-simula.x1(A1, Y, A2,first)
  if(all(trythis>=0))return(first)
  else
    {
      temp<-invA1%*%A2
      tochange<-which(trythis<0)
      for(i in 1:length(tochange))
	{
	  touse<-which(temp[tochange[i],]==-1)
	  j<-1
	  first[touse[j]]<-abs(trythis[tochange[i]])
	  if(any(simula.x1(A1, Y, A2,first)[tochange]<
		 trythis[tochange])||
	     simula.x1(A1, Y, A2,first)[tochange[i]]<0){
	    first[touse[j]]<-0
	    j<-j+1				      }
	}
    }
  names(first)<-dimnames(A2)[[2]]
  return(first)
}


simula.x1<-function(A1, Y, A2,X2)return(solve(A1)%*%(Y-A2%*%X2))


guessup<-function(A1,A2,Y)
  {
  invA1<-solve(A1)
  first<-numeric(ncol(A2))
  for(i in 1:length(first))
    {
      first[i]<-min(Y[A2[,i]==1])
    }
  trythis <- simula.x1(A1, Y, A2, first)
  if(all(trythis >= 0))
    {
      names(first)<-dimnames(A2)[[2]]
      return(first)
    }
  else
    {
      temp<-invA1%*%A2
      tochange<-which(trythis<0)
      for(i in 1:length(tochange))
	{
	  touse<-which(temp[tochange[i],]==1)
	  j<-1
	  old<-first[touse[j]]
	  first[touse[j]]<-first[touse[j]]-abs(trythis[tochange[i]])
	  if(any(simula.x1(A1, Y, A2,first)[tochange]<
		 trythis[tochange])||
	     simula.x1(A1, Y, A2,first)[tochange[i]]<0)
	    {
	      first[touse[j]]<-old
	      j<-j+1
	    }
	}
      names(first)<-dimnames(A2)[[2]]
      return(first)
    }
}
	       

get12<-function(A){
  if(ncol(A)<=nrow(A))stop("expecting rectangular matrix with less rows than columns") 
  qrA<-qr(A)
  rank<-qrA$rank
  pivot<-qrA$pivot
  A1<-A[,pivot[1:rank]]
  A2<-A[,pivot[(rank+1):ncol(A)]]
  return(list(A=A,A1=A1,A2=A2,pivot=pivot))}