periodic {assist} | R Documentation |

## Calculate Reproducing Kernels for Periodic Polynomial Splines with Period 1

### Description

Return a matrix evaluating reproducing kernels for periodic polynomial splines at observed points.

### Usage

```
periodic(s, t=s, order=2)
```

### Arguments

`s` |
a numeric vector. |

`t` |
an optional vector. Default is the same as s. |

`order` |
an optional integer sepcifying the order of the polynomial spline. Default is 2 for the periodic cubic spline. |

### Details

The general formula of the reproducing kernel is sum of an infinite series, which is approximated by taking the first 50 terms. For the case of order=2, the close form is available and used.

### Value

a matrix with the numbers of row and column equal to the lengths of s and t respectively. The [i, j] element is the reproducing kernel evaluated at (s[i], t[j]).

### References

Wahba, G. (1990). Spline Models for Observational Data. SIAM, Vol. 59.

Gu, C. (2001). Smoothing Spline ANOVA Modes. Chapman and Hall.

### See Also

### Examples

```
## Not run:
x<- seq(0, 1, len=100)
periodic(x, order=3)
## End(Not run)
```

*assist*version 3.1.9 Index]