# polyfit: Fitting by Polynomial In pracma: Practical Numerical Math Functions

## Description

Polynomial curve fitting

## Usage

 ```1 2 3``` ```polyfit(x, y, n) polyfix(x, y, n, xfix, yfix) ```

## Arguments

 `x` x-coordinates of points `y` y-coordinates of points `n` degree of the fitting polynomial `xfix,yfix` x- and y-coordinates of points to be fixed

## Details

`polyfit` finds the coefficients of a polynomial of degree `n` fitting the points given by their `x`, `y` coordinates in a least-squares sense. In `polyfit`, if `x`, `y` are matrices of the same size, the coordinates are taken elementwise. Complex values are not allowed.

`polyfix` finds a polynomial that fits the data in a least-squares sense, but also passes exactly through all the points with coordinates `xfix` and `yfix`. Degree `n` should be greater or equal to the number of fixed points, but not too big to avoid ‘singular matrix’ or similar error messages

## Value

vector representing a polynomial.

## Note

Please not that `polyfit2` is has been removed since 1.9.3; please use `polyfix` instead.

`poly`, `polyval`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35``` ``` # Fitting the sine function by a polynomial x <- seq(0, pi, length.out=25) y <- sin(x) p <- polyfit(x, y, 6) ## Not run: # Plot sin and fitted polynomial plot(x, y, type="b") yf <- polyval(p, x) lines(x, yf, col="red") grid() ## End(Not run) ## Not run: n <- 3 N <- 100 x <- linspace(0, 2*pi, N); y = sin(x) + 0.1*rnorm(N) xfix <- c(0, 2*pi); yfix = c(0, 0) xs <- linspace(0, 2*pi); ys <- sin(xs) plot(xs, ys, type = 'l', col = "gray", main = "Polynom Approximation of Degree 3") grid() points(x, y, pch='o', cex=0.5) points(xfix, yfix, col = "darkred") p0 <- polyfit(x, y, n) lines(xs, polyval(p0, xs), col = "blue") p1 <- polyfix(x, y, n, xfix, yfix) lines(xs, polyval(p1, xs), col = "red") legend(4, 1, c("sin", "polyfit", "polyfix"), col=c("gray", "blue", "red"), lty=c(1,1,1)) ## End(Not run) ```

### Example output

```
```

pracma documentation built on Dec. 11, 2021, 9:57 a.m.