# Polyinterp

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### Purpose

Polynomial interpolation, smoothing, and differentiation.

### Synopsis

- yi = polyinterp(x,y,
*xi,width,order,deriv*);

### Description

Estimates `yi` which is the smoothed values of `y` at the points in the vector `x`. (If the points are evenly spaced use the SAVGOL function instead.)

#### Inputs

**y**= (M by N) matrix. Note that (y) is a matrix of ROW

**x**= (1 by N) corresponding axis vector at the points at

#### Optional Inputs

**xi**= a vector of points to interpolate to.

**width**= specifies the number of points in the filter {default = 15}.

**order**= the order of the polynomial {default = 2}.

**deriv**= the derivative {default = 0}.

### Examples

If y is a 5 by 100 matrix, x is a 1 by 100 vector, and xi is a 1 by 91 vector then:

polyinterp(x,y,xi,11,3,1)

gives the 5 by 91 matrix of first-derivative row vectors resulting from an 11-point cubic interpolation to the 91 points in xi.