Description Usage Arguments Details Value Author(s) References See Also

The function evaluates the smoothing matrix `H`

, the
matrices *Q* and *S* and their associated
coefficients `c`

and `s`

. This function is not intended to be used directly.

1 | ```
betaS1(n,U,tUy,eigenvaluesS1,ddlmini,k,lambda,Sgu,Qgu,index0)
``` |

`n` |
The number of observations. |

`U` |
The the matrix of eigen vectors of the
symmetric smoothing matrix |

`tUy` |
The transpose of the matrix of eigen vectors of the
symmetric smoothing matrix |

`eigenvaluesS1` |
Vector of the eigenvalues of the
symmetric smoothing matrix |

`ddlmini` |
The number of eigen values of |

`k` |
A numeric vector which give the number of iterations. |

`lambda` |
The smoothness coefficient lambda for thin plate splines of
order |

`Sgu` |
The matrix of the polynomial null space |

`Qgu` |
The matrix of the semi kernel (or radial basis) |

`index0` |
The index of the first eigen values of |

See the reference for detailed explanation of *Q* (the
semi kernel or radial basis) and
*S* (the polynomial null space).

Returns a list containing of coefficients for the null space `dgub`

and the semi-kernel `cgub`

Pierre-Andre Cornillon, Nicolas Hengartner and Eric Matzner-Lober

C. Gu (2002) *Smoothing spline anova models*. New York: Springer-Verlag.

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