Homework Problem 4, STAT 705,   Fall 2017.
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Assigned 9/11/2017,    Due Monday 9/18/2017       worth 12 points


Write a function LinInterp to linearly interpolate values y as a function 
of x, where  x  and  y  are input vectors of the same length, given as 
a matrix  Mxy  with column names  x  and  y , and  xalt  is an input 
vector of values for  x  at which interpolated  y  values are desired. 
The output should be a matrix  cbind(xnew, ynew) , where  xnew  is the 
subvector of entries of  xalt that fall between  min(x) and max(x), inclusive.

Write such a function in two different ways, (a) using a for-loop, and
(b) vectorizing the interpolation operation.  

Do timing runs using "system.time" for both of your functions, and show by 
applying the functions (a), (b) to input matrices  Mxy  with 100,000 rows 
and vectors  xalt  of length at least  1000 ,  that it does indeed make 
a difference which way you do the coding.

Check that your two functions give exactly the same result, and SHOW 
that they do (on moderate sized input matrices) visually, by using the 
commands  "plot"  and "lines".