G2SWEEP | R Documentation |

Generalized inverse is usually not unique. Some programs use this algorithm to get a unique generalized inverse matrix.

```
G2SWEEP(A, Augmented=FALSE, eps=1e-08)
```

`A` |
a matrix to be inverted |

`Augmented` |
If this is |

`eps` |
Less than this value is considered as zero. |

Generalized inverse of g2-type is used by some softwares to do linear regression. See 'SAS Technical Report R106, The Sweep Operator: Its importance in Statistical Computing' by J. H. Goodnight for the detail.

`when Augmented=FALSE` |
ordinary g2 inverse |

`when Augmented=TRUE` |
g2 inverse and beta hats in the last column and the last row, and sum of square error (SSE) in the last cell |

`attribute "rank"` |
the rank of input matrix |

Kyun-Seop Bae k@acr.kr

`lfit`

, `ModelMatrix`

```
f1 = uptake ~ Type + Treatment # formula
x = ModelMatrix(f1, CO2) # Model matrix and relevant information
y = model.frame(f1, CO2)[, 1] # observation vector
nc = ncol(x$X) # number of columns of model matrix
XpY = crossprod(x$X, y)
aXpX = rbind(cbind(crossprod(x$X), XpY), cbind(t(XpY), crossprod(y)))
ag2 = G2SWEEP(aXpX, Augmented=TRUE)
b = ag2[1:nc, (nc + 1)] ; b # Beta hat
iXpX = ag2[1:nc, 1:nc] ; iXpX # g2 inverse of X'X
SSE = ag2[(nc + 1), (nc + 1)] ; SSE # Sum of Square Error
DFr = nrow(x$X) - attr(ag2, "rank") ; DFr # Degree of freedom for the residual
# Compare the below with the above
REG(f1, CO2)
aov1(f1, CO2)
```

sasLM documentation built on Nov. 19, 2023, 5:12 p.m.

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