NIPALS algorithm for PLS1 regression (y is univariate)

1 | ```
pls1_nipals(X, y, a, it = 50, tol = 1e-08, scale = FALSE)
``` |

`X` |
original X data matrix |

`y` |
original y-data |

`a` |
number of PLS components |

`it` |
number of iterations |

`tol` |
tolerance for convergence |

`scale` |
if TRUE the X and y data will be scaled in addition to centering, if FALSE only mean centering is performed |

The NIPALS algorithm is the originally proposed algorithm for PLS. Here, the y-data are only allowed to be univariate. This simplifies the algorithm.

`P` |
matrix with loadings for X |

`T` |
matrix with scores for X |

`W` |
weights for X |

`C` |
weights for Y |

`b` |
final regression coefficients |

Peter Filzmoser <P.Filzmoser@tuwien.ac.at>

K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.

1 2 | ```
data(PAC)
res <- pls1_nipals(PAC$X,PAC$y,a=5)
``` |

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