INTERPLIN1 Linear 1-D Interpolation

Section: Optimization and Curve Fitting

Usage

Given a set of monotonically increasing x coordinates and a corresponding set of y values, performs simple linear interpolation to a new set of x coordinates. The general syntax for its usage is 
   yi = interplin1(x1,y1,xi)

where x1 and y1 are vectors of the same length, and the entries in x1 are monotoniccally increasing. The output vector yi is the same size as the input vector xi. For each element of xi, the values in y1 are linearly interpolated. For values in xi that are outside the range of x1 the default value returned is nan. To change this behavior, you can specify the extrapolation flag: 

   yi = interplin1(x1,y1,xi,extrapflag)

Valid options for extrapflag are:

The x1 and xi vectors must be real, although complex types are allowed for y1.

Example

Here is an example of simple linear interpolation with the different extrapolation modes. We start with a fairly coarse sampling of a cosine. 
--> x = linspace(-pi*7/8,pi*7/8,15);
--> y = cos(x);
--> plot(x,y,'ro');

which is shown here

Next, we generate a finer sampling over a slightly broader range (in this case [-pi,pi]). First, we demonstrate the 'nan' extrapolation method 

--> xi = linspace(-4,4,100);
--> yi_nan = interplin1(x,y,xi,'nan');
--> yi_zero = interplin1(x,y,xi,'zero');
--> yi_endpoint = interplin1(x,y,xi,'endpoint');
--> yi_extrap = interplin1(x,y,xi,'extrap');
--> plot(x,y,'ro',xi,yi_nan,'g-x',xi,yi_zero,'g-x',xi,yi_endpoint,'g-x',xi,yi_extrap,'g-x');

which is shown here