[R] optim and singularity

Thu Dec 30 21:16:48 CET 2010

Hello,

I was unable to find clues to my problem in ?optim.  Using the data and code
below, I get an error ("system is exactly singular") when a particular line
of code is left in, but have found that 'optim' works when I comment it out. 
The line of code in question is after the closeAllConnections() line of code
and contains a call to "na.approx" from the zoo package.  What's confusing
to me is why optim works without it versus with it?  Any clues would be very
helpful in moving forward.  The overall goal of the code below is to
minimize the residuals between the blue circles and green squares by
adjusting the limits of the secondary y-axis.

Thanks, Eric

library(zoo)
temp.dat<-read.table(textConnection("Well Meas_Date WTD ECgw GW_Project_Area
Region Avg.EM.Survey.Value Avg.Soil.Paste.EC SD_EM_Survey
1 4/12/1999 1.75 2.27 LOWER-UPSTREAM US NA NA NA
1 5/11/1999 1.24 5.04 LOWER-UPSTREAM US NA NA NA
1 5/27/1999 1.27 4.45 LOWER-UPSTREAM US NA NA NA
1 6/3/1999 1.27 4.09 LOWER-UPSTREAM US 3.347069 3.126667 0.6347013
1 6/11/1999 1.52 2.84 LOWER-UPSTREAM US NA NA NA
1 6/18/1999 1.19 2.34 LOWER-UPSTREAM US NA NA NA
1 6/24/1999 1.21 2.48 LOWER-UPSTREAM US NA NA NA
1 6/30/1999 1.19 2.45 LOWER-UPSTREAM US NA NA NA
1 7/7/1999 1.59 2.47 LOWER-UPSTREAM US NA NA NA
1 7/14/1999 1.75 2.73 LOWER-UPSTREAM US NA NA NA
1 7/21/1999 1.75 2.33 LOWER-UPSTREAM US NA NA NA
1 7/28/1999 1.78 2.63 LOWER-UPSTREAM US NA NA NA
1 8/4/1999 1.37 2.25 LOWER-UPSTREAM US NA NA NA
1 8/12/1999 0.08 2.37 LOWER-UPSTREAM US 2.858553 NA 0.3560363
1 8/18/1999 2.29 2.48 LOWER-UPSTREAM US NA NA NA
1 9/4/1999 0.02 2.48 LOWER-UPSTREAM US NA NA NA
1 9/16/1999 1.93 2.45 LOWER-UPSTREAM US NA NA NA
1 10/1/1999 2.01 2.49 LOWER-UPSTREAM US NA NA NA
1 11/13/1999 1.91 2.32 LOWER-UPSTREAM US NA NA NA
1 1/4/2000 1.83 2.59 LOWER-UPSTREAM US NA NA NA
1 2/24/2000 1.93 2.83 LOWER-UPSTREAM US NA NA NA
1 3/25/2000 1.73 2.71 LOWER-UPSTREAM US NA NA NA
1 4/15/2000 1.47 3.12 LOWER-UPSTREAM US NA NA NA
1 4/28/2000 1.98 2.76 LOWER-UPSTREAM US NA NA NA
1 5/17/2000 1.80 2.92 LOWER-UPSTREAM US NA NA NA
1 5/30/2000 NA NA <NA> US 3.064330 NA 0.3970829
1 6/1/2000 1.58 2.83 LOWER-UPSTREAM US NA NA NA
1 6/6/2000 1.65 2.97 LOWER-UPSTREAM US NA NA NA
1 6/15/2000 1.85 2.65 LOWER-UPSTREAM US NA NA NA
1 6/23/2000 1.90 2.78 LOWER-UPSTREAM US NA NA NA
1 6/29/2000 1.80 2.67 LOWER-UPSTREAM US NA NA NA
1 7/6/2000 2.00 2.69 LOWER-UPSTREAM US NA NA NA
1 7/14/2000 1.97 3.46 LOWER-UPSTREAM US NA NA NA
1 7/20/2000 1.69 2.57 LOWER-UPSTREAM US NA NA NA
1 7/27/2000 1.95 3.16 LOWER-UPSTREAM US NA NA NA
1 8/2/2000 2.03 3.12 LOWER-UPSTREAM US NA NA NA
1 8/8/2000 NA NA <NA> US 3.185567 2.522467 0.3765025
1 8/11/2000 2.00 2.65 LOWER-UPSTREAM US NA NA NA
1 8/19/2000 1.95 2.50 LOWER-UPSTREAM US NA NA NA
1 9/29/2000 2.11 2.11 LOWER-UPSTREAM US NA NA NA
1 10/20/2000 2.16 2.75 LOWER-UPSTREAM US NA NA NA
1 12/1/2000 1.83 2.81 LOWER-UPSTREAM US NA NA NA
1 1/19/2001 2.01 3.01 LOWER-UPSTREAM US NA NA NA
1 3/5/2001 2.01 2.35 LOWER-UPSTREAM US NA NA NA
1 3/30/2001 2.13 2.10 LOWER-UPSTREAM US NA NA NA
1 4/21/2001 1.87 2.36 LOWER-UPSTREAM US NA NA NA
1 5/15/2001 2.00 2.37 LOWER-UPSTREAM US NA NA NA
1 5/29/2001 1.60 2.59 LOWER-UPSTREAM US NA NA NA
1 6/4/2001 NA NA <NA> US 4.233636 NA 1.3738540
1 6/7/2001 1.71 2.55 LOWER-UPSTREAM US NA NA NA
1 6/14/2001 1.83 2.75 LOWER-UPSTREAM US NA NA NA
1 6/20/2001 1.93 3.02 LOWER-UPSTREAM US NA NA NA
1 6/29/2001 1.80 2.74 LOWER-UPSTREAM US NA NA NA
1 7/6/2001 1.91 2.70 LOWER-UPSTREAM US NA NA NA
1 7/12/2001 2.04 2.46 LOWER-UPSTREAM US NA NA NA
1 7/18/2001 1.87 2.55 LOWER-UPSTREAM US NA NA NA
1 7/25/2001 1.96 2.67 LOWER-UPSTREAM US NA NA NA
1 8/2/2001 2.02 2.42 LOWER-UPSTREAM US NA NA NA
1 8/8/2001 NA NA <NA> US 2.946731 NA 0.3748240
1 8/10/2001 1.94 2.36 LOWER-UPSTREAM US NA NA NA
1 8/17/2001 1.94 0.75 LOWER-UPSTREAM US NA NA NA
1 9/1/2001 2.12 2.22 LOWER-UPSTREAM US NA NA NA
1 9/15/2001 2.15 2.35 LOWER-UPSTREAM US NA NA NA
1 9/29/2001 1.95 2.20 LOWER-UPSTREAM US NA NA NA
1 10/27/2001 1.08 1.72 LOWER-UPSTREAM US NA NA NA
1 11/17/2001 1.99 2.21 LOWER-UPSTREAM US NA NA NA
1 1/10/2002 2.01 2.31 LOWER-UPSTREAM US NA NA NA
1 2/16/2002 1.94 1.74 LOWER-UPSTREAM US NA NA NA
1 3/23/2002 2.03 2.46 LOWER-UPSTREAM US NA NA NA
1 4/13/2002 2.11 2.50 LOWER-UPSTREAM US NA NA NA
1 5/11/2002 2.11 2.54 LOWER-UPSTREAM US NA NA NA
1 5/21/2002 NA NA <NA> US 2.368000 NA 0.3235852
1 5/30/2002 2.07 2.56 LOWER-UPSTREAM US NA NA NA
1 6/6/2002 2.11 2.55 LOWER-UPSTREAM US NA NA NA
1 6/13/2002 2.03 2.66 LOWER-UPSTREAM US NA NA NA
1 6/27/2002 2.19 2.55 LOWER-UPSTREAM US NA NA NA
1 7/3/2002 2.22 2.68 LOWER-UPSTREAM US NA NA NA
1 7/11/2002 2.06 2.61 LOWER-UPSTREAM US NA NA NA
1 7/18/2002 2.23 2.58 LOWER-UPSTREAM US NA NA NA
1 7/25/2002 2.23 2.62 LOWER-UPSTREAM US NA NA NA
1 8/1/2002 2.21 2.60 LOWER-UPSTREAM US NA NA NA
1 8/8/2002 2.29 2.60 LOWER-UPSTREAM US NA NA NA
1 8/14/2002 NA NA <NA> US 1.863548 NA 0.2400621
1 8/15/2002 2.26 2.61 LOWER-UPSTREAM US NA NA NA
1 8/21/2002 2.34 2.51 LOWER-UPSTREAM US NA NA NA
1 9/6/2002 2.31 2.51 LOWER-UPSTREAM US NA NA NA
1 9/21/2002 2.25 2.55 LOWER-UPSTREAM US NA NA NA
1 10/5/2002 2.21 2.57 LOWER-UPSTREAM US NA NA NA
1 11/8/2002 2.09 2.50 LOWER-UPSTREAM US NA NA NA
1 12/23/2002 2.19 2.16 LOWER-UPSTREAM US NA NA NA
1 1/16/2003 2.23 2.15 LOWER-UPSTREAM US NA NA NA
1 3/1/2003 2.12 2.11 LOWER-UPSTREAM US NA NA NA
1 4/5/2003 2.03 1.99 LOWER-UPSTREAM US NA NA NA
1 5/2/2003 2.00 2.42 LOWER-UPSTREAM US NA NA NA
1 5/30/2003 1.66 2.09 LOWER-UPSTREAM US NA NA NA
1 6/3/2003 NA NA <NA> US 3.066333 NA 0.2926846
1 6/6/2003 1.43 2.24 LOWER-UPSTREAM US NA NA NA
1 6/12/2003 1.73 2.81 LOWER-UPSTREAM US NA NA NA
1 6/19/2003 1.51 2.97 LOWER-UPSTREAM US NA NA NA
1 7/3/2003 1.84 3.35 LOWER-UPSTREAM US NA NA NA
1 7/11/2003 2.00 2.52 LOWER-UPSTREAM US NA NA NA
1 7/17/2003 2.04 2.76 LOWER-UPSTREAM US NA NA NA
1 7/24/2003 2.02 2.40 LOWER-UPSTREAM US NA NA NA
1 7/31/2003 1.96 2.14 LOWER-UPSTREAM US NA NA NA
1 8/16/2003 2.29 1.85 LOWER-UPSTREAM US NA NA NA
1 8/20/2003 2.14 2.11 LOWER-UPSTREAM US NA NA NA
1 9/5/2003 2.03 1.45 LOWER-UPSTREAM US NA NA NA
1 10/10/2003 2.10 2.21 LOWER-UPSTREAM US NA NA NA
1 11/15/2003 1.95 1.83 LOWER-UPSTREAM US NA NA NA
1 12/22/2003 2.13 NA LOWER-UPSTREAM US NA NA NA
1 1/16/2004 2.16 2.30 LOWER-UPSTREAM US NA NA NA
1 2/13/2004 2.12 2.13 LOWER-UPSTREAM US NA NA NA
1 3/19/2004 2.02 2.11 LOWER-UPSTREAM US NA NA NA
1 4/23/2004 2.09 2.10 LOWER-UPSTREAM US NA NA NA
1 5/3/2004 1.89 2.42 LOWER-UPSTREAM US NA NA NA
1 5/17/2004 2.02 2.31 LOWER-UPSTREAM US NA NA NA
1 5/24/2004 1.97 2.58 LOWER-UPSTREAM US NA NA NA
1 5/26/2004 NA NA <NA> US 3.532614 NA 0.6329923
1 6/7/2004 1.81 2.70 LOWER-UPSTREAM US NA NA NA
1 6/14/2004 1.66 2.35 LOWER-UPSTREAM US NA NA NA
1 6/28/2004 2.10 2.70 LOWER-UPSTREAM US NA NA NA
1 7/5/2004 1.86 3.25 LOWER-UPSTREAM US NA NA NA
1 7/12/2004 2.00 2.93 LOWER-UPSTREAM US NA NA NA
1 7/19/2004 1.63 2.55 LOWER-UPSTREAM US NA NA NA
1 7/26/2004 2.01 2.65 LOWER-UPSTREAM US NA NA NA
1 8/2/2004 1.91 2.89 LOWER-UPSTREAM US NA NA NA
1 8/9/2004 2.00 2.87 LOWER-UPSTREAM US NA NA NA
1 8/17/2004 2.07 2.77 LOWER-UPSTREAM US NA NA NA
1 9/18/2004 2.18 2.67 LOWER-UPSTREAM US NA NA NA
1 10/23/2004 2.14 2.43 LOWER-UPSTREAM US NA NA NA
1 11/22/2004 2.17 2.38 LOWER-UPSTREAM US NA NA NA
1 12/20/2004 0.32 2.48 LOWER-UPSTREAM US NA NA NA
1 1/11/2005 2.16 2.44 LOWER-UPSTREAM US NA NA NA
1 2/18/2005 2.22 2.27 LOWER-UPSTREAM US NA NA NA
1 3/16/2005 2.06 2.59 LOWER-UPSTREAM US NA NA NA
1 4/9/2005 2.02 2.50 LOWER-UPSTREAM US NA NA NA
1 5/13/2005 1.96 2.62 LOWER-UPSTREAM US NA NA NA
1 6/7/2005 1.96 2.99 LOWER-UPSTREAM US NA NA NA
1 6/13/2005 1.77 2.22 LOWER-UPSTREAM US NA NA NA
1 6/20/2005 1.87 3.05 LOWER-UPSTREAM US NA NA NA
1 6/28/2005 1.76 3.50 LOWER-UPSTREAM US NA NA NA
1 7/5/2005 1.58 3.56 LOWER-UPSTREAM US NA NA NA
1 7/11/2005 1.72 3.22 LOWER-UPSTREAM US NA NA NA
1 7/19/2005 1.98 3.11 LOWER-UPSTREAM US NA NA NA
1 8/1/2005 2.14 3.02 LOWER-UPSTREAM US NA NA NA
1 8/10/2005 NA NA <NA> US 3.465650 4.032000 0.3743813
1 8/16/2005 1.79 3.00 LOWER-UPSTREAM US NA NA NA
1 10/21/2005 4.34 1.07 LOWER-UPSTREAM US NA NA NA
1 11/23/2005 2.08 1.08 LOWER-UPSTREAM US NA NA NA
1 12/21/2005 1.64 2.54 LOWER-UPSTREAM US NA NA NA
1 1/13/2006 2.05 2.01 LOWER-UPSTREAM US NA NA NA
1 2/9/2006 2.10 1.73 LOWER-UPSTREAM US NA NA NA
1 3/13/2006 2.03 2.22 LOWER-UPSTREAM US NA NA NA
1 5/22/2006 1.62 2.38 LOWER-UPSTREAM US NA NA NA
1 5/29/2006 1.61 2.29 LOWER-UPSTREAM US NA NA NA
1 6/13/2006 1.53 2.39 LOWER-UPSTREAM US NA NA NA
1 6/19/2006 1.77 2.49 LOWER-UPSTREAM US NA NA NA
1 6/20/2006 1.86 NA LOWER-UPSTREAM US NA NA NA
1 6/26/2006 1.89 3.12 LOWER-UPSTREAM US NA NA NA
1 7/3/2006 1.90 2.95 LOWER-UPSTREAM US NA NA NA
1 7/11/2006 1.26 2.49 LOWER-UPSTREAM US NA NA NA
1 7/18/2006 1.83 2.86 LOWER-UPSTREAM US NA NA NA
1 7/31/2006 1.92 2.89 LOWER-UPSTREAM US NA NA NA
1 8/15/2006 2.00 1.87 LOWER-UPSTREAM US NA NA NA
1 9/22/2006 2.07 1.62 LOWER-UPSTREAM US NA NA NA
1 11/5/2006 1.92 1.67 LOWER-UPSTREAM US NA NA NA
1 12/18/2006 2.03 1.66 LOWER-UPSTREAM US NA NA NA
1 5/24/2007 1.49 NA LOWER-UPSTREAM US NA NA NA
1 10/6/2007 2.13 NA LOWER-UPSTREAM US NA NA NA
1 12/16/2007 2.03 1.36 LOWER-UPSTREAM US NA NA NA
1 1/18/2008 2.07 1.73 LOWER-UPSTREAM US NA NA NA
1 4/19/2008 1.92 1.91 LOWER-UPSTREAM US NA NA NA
1 3/18/2010 0.61 3.20 LOWER-UPSTREAM US NA NA NA
1 5/24/2010 2.04 2.22 LOWER-UPSTREAM US NA NA NA"),header=T)
closeAllConnections()

#interpolate missing WTD values
temp.dat$WTD<-na.approx(temp.dat$WTD,as.numeric(as.Date(temp.dat$Meas_Date,"%m/%d/%Y")))

#the current limits of the left and right y-axes
ylim_1<-rev(c(0,max(na.omit(temp.dat$WTD))+1))
ylim_2<-c(floor(min(range(na.omit(temp.dat$Avg.EM.Survey.Value))[1],range(na.omit(temp.dat$Avg.Soil.Paste.EC))[1])),ceiling(max(range(na.omit(temp.dat$Avg.EM.Survey.Value))[2],range(na.omit(temp.dat$Avg.Soil.Paste.EC))[2])))

plot(as.Date(temp.dat$Meas_Date,"%m/%d/%Y"),temp.dat$WTD,xlim=c(as.Date("1999-01-01"),as.Date("2005-11-01")),ylim=ylim_1,pch=19,lwd=1.5,col="blue",cex=0.5,xlab="",ylab="",xaxt="n",type="p",las=1)
par(new=T)
plot(as.Date(temp.dat$Meas_Date,"%m/%d/%Y"),temp.dat$Avg.EM.Survey.Value,xlim=c(as.Date("1999-01-01"),as.Date("2005-11-01")),ylim=ylim_2,xlab="",ylab="WTD
(m)",xaxt="n",yaxt="n",pch=15,col="darkgreen",cex=0.75)
axis(side=4,at=seq(floor(min(range(na.omit(temp.dat$Avg.EM.Survey.Value))[1],range(na.omit(temp.dat$Avg.Soil.Paste.EC))[1])),ceiling(max(range(na.omit(temp.dat$Avg.EM.Survey.Value))[2],range(na.omit(temp.dat$Avg.Soil.Paste.EC))[2])),by=1),labels=seq(floor(min(range(na.omit(temp.dat$Avg.EM.Survey.Value))[1],range(na.omit(temp.dat$Avg.Soil.Paste.EC))[1])),ceiling(max(range(na.omit(temp.dat$Avg.EM.Survey.Value))[2],range(na.omit(temp.dat$Avg.Soil.Paste.EC))[2])),by=1),las=1)

f<-function(ylim_2){
  y2_l<-ylim_2[1]
  y2_u<-ylim_2[2]
  #solve for "x", the coeffs to map the right 
  #referenced values to their left-axis equivalent
  A<-matrix(c(y2_l,y2_u,1,1),nrow=2,ncol=2,byrow=F)
  RHS<-matrix(ylim_1,nrow=2,ncol=1,byrow=T)
  x<-solve(A,RHS)

  #map the right-referenced values to their 
  #corresponding left-axis values
  temp.dat.mapped<-x[1,1]*temp.dat$Avg.EM.Survey.Value+x[2,1]

  #calculate the resids between green squares and blue circles

resids<-na.omit(data.frame(Col1=temp.dat$WTD,Col2=temp.dat.mapped,SumSqrDiff=(temp.dat$WTD-temp.dat.mapped)^2))

  #quantity to be minimized
  min_this<-sum(resids$SumSqrDiff)
  min_this
}
edm<-optim(ylim_2,f,lower=c(0,0),upper=c(100,100),method="L-BFGS-B")
ylim_2<-edm$par

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