## 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:

- `'nan'` - extrapolated values are tagged with `nan`s
- `'zero'` - extrapolated values are set to zero
- `'endpoint'` - extrapolated values are set to the endpoint values
- `'extrap'` - linear extrapolation is performed

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