finding the intersection of two vectors

Hi,

Suppose I have two vectors, not necessarily the same length (in  
fact, they usually are different lengths): y.1 that has increasing  
values between 0 and 1; y.2 that has decreasing values between 1.0  
and 0.  You can picture these as being supply (= y.1) and demand (=  
y.2) curves from economics.  I typically plot these vectors on the  
same graph against a common x variable, which happens to be price  
for what I do.  The price variable runs from, say, $0 to $25.  When  
I plot y.1 and y.2, I've been eye-balling a vertical line at a price  
point where y.1 intersects y.2.  I'm now tired of eye-balling a line  
through the intersection -- takes too much time to get it right or  
just close enough.  I can't figure out how to find the price value  
at which the two curves intersect.  Going back to the economics  
interpretation, I want the price where supply equals demand.  Any  
suggestions as to how I can find that price point in R?  Any  
functions that help?

On Jul 6, 2011, at 4:43 PM, Data Analytics Corp. wrote:

Hi,

Suppose I have two vectors, not necessarily the same length (in fact, they usually are different lengths): y.1 that has increasing values between 0 and 1; y.2 that has decreasing values between 1.0 and 0.  You can picture these as being supply (= y.1) and demand (= y.2) curves from economics.  I typically plot these vectors on the same graph against a common x variable, which happens to be price for what I do.  The price variable runs from, say, $0 to $25.  When I plot y.1 and y.2, I've been eye-balling a vertical line at a price point where y.1 intersects y.2.  I'm now tired of eye-balling a line through the intersection -- takes too much time to get it right or just close enough.  I can't figure out how to find the price value at which the two curves intersect.  Going back to the economics interpretation, I want the price where supply equals demand.  Any suggestions as to how I can find that price point in R?  Any functions that help?

?approxfun # or..
?splinefun  #  should allow you to make two functions and then solve for the X taht minimizes the difference.

-- 

David Winsemius, MD
West Hartford, CT

Hi,

Suppose I have two vectors, not necessarily the same length (in fact, 
they usually are different lengths): y.1 that has increasing values 
between 0 and 1; y.2 that has decreasing values between 1.0 and 0.  
You can picture these as being supply (= y.1) and demand (= y.2) 
curves from economics.  I typically plot these vectors on the same 
graph against a common x variable, which happens to be price for what 
I do.  The price variable runs from, say, $0 to $25.  When I plot y.1 
and y.2, I've been eye-balling a vertical line at a price point where 
y.1 intersects y.2.  I'm now tired of eye-balling a line through the 
intersection -- takes too much time to get it right or just close 
enough.  I can't figure out how to find the price value at which the 
two curves intersect.  Going back to the economics interpretation, I 
want the price where supply equals demand.  Any suggestions as to how 
I can find that price point in R?  Any functions that help?

findInt <- function (x1,y1,x2,y2,plot=FALSE) {
#
# x1 and y1 are the coordinates of the points on the INCREASING curve.
# x2 and y2 are the coordinates of the points on the DECREASING curve.
#
y1star <- approx(x2,y2,xout=x1,yleft=Inf,yright=-Inf)$y
k <- sum(y1 <= y1star)
y2star <- approx(x1,y1,xout=x2,yleft=-Inf,yright=Inf)$y
ell <- sum(y2 >= y2star)
b1 <- y1[k]
b2 <- y2[ell]
m1 <- (y1[k+1] - y1[k])/(x1[k+1] - x1[k])
m2 <- (y2[ell+1] - y2[ell])/(x2[ell+1] - x2[ell])
x <- (b1-b2-m1*x1[k]+m2*x2[ell])/(m2-m1)
y <- b1 + m1*(x-x1[k])
if(plot) {
        plot(x1,y1,xlim=range(x1,x2),ylim=range(y1,y2))
        points(x2,y2,col="red")
        segments(x1[k],y1[k],x1[k+1],y1[k+1])
        segments(x2[ell],y2[ell],x2[ell+1],y2[ell+1])
        points(x,y,pch=20)
}
c(x=x,y=y)
}

close enough. ?I can't figure out how to find the price value at which the
two curves intersect. ?Going back to the economics interpretation, I want
the price where supply equals demand. ?Any suggestions as to how I can find
that price point in R? ?Any functions that help?