G.inverse {ASRgenomics} | R Documentation |

## Obtains the inverse of the genomic relationship matrix G

### Description

Generates the inverse of a genomic relationship matrix `\boldsymbol{G}`

that is provided.
This input matrix should be of the full form (`n \times n`

)
with individual names assigned to
`rownames`

and `colnames`

. Several checks for the stability of the matrix are
presented based on the reciprocal conditional number.

In case of an ill-conditioned matrix,
options of blending, bending or aligning before inverting are available.
These options will be deprecated (discontinued)
in future versions of `ASRgenomics`

as they can be better implemented in the function `G.tuneup()`

.

Based on procedures published by Nazarian and Gezan *et al.* (2016).

### Usage

```
G.inverse(
G = NULL,
A = NULL,
rcn.thr = 1e-12,
blend = FALSE,
pblend = 0.02,
bend = FALSE,
eig.tol = NULL,
align = FALSE,
digits = 8,
sparseform = FALSE,
message = TRUE
)
```

### Arguments

`G` |
Input of the symmetric genomic relationship matrix |

`A` |
Input of the pedigree relationship matrix |

`rcn.thr` |
A threshold for identifying the |

`blend` |
If |

`pblend` |
If blending is requested this is the proportion of the identity matrix |

`bend` |
If |

`eig.tol` |
Defines relative positiveness ( |

`align` |
If |

`digits` |
Set up the number of digits in used to round the output matrix (default = |

`sparseform` |
If |

`message` |
If |

### Value

A list with three of the following elements:

`Ginv`

: the inverse of`\boldsymbol{G}`

matrix in full form (only if`sparseform = FALSE`

).`Ginv.sparse`

: the inverse of`\boldsymbol{G}`

matrix in sparse form (only if`sparseform = TRUE`

).`status`

: the status (`ill-conditioned`

or`well-conditioned`

) of the inverse of`\boldsymbol{G}`

matrix.`rcn`

: the reciprocal conditional number of the inverse of`\boldsymbol{G}`

matrix.

### References

Nazarian A., Gezan S.A. 2016. GenoMatrix: A software package for pedigree-based and genomic prediction analyses on complex traits. Journal of Heredity 107:372-379.

### Examples

```
# Example: An ill-conditioned matrix.
# Get G matrix.
G <- G.matrix(M = geno.apple, method = "VanRaden")$G
G[1:5, 1:5]
# Get the inverse of G.
GINV <- G.inverse(G = G, bend = FALSE, blend = FALSE, align = FALSE)
GINV$Ginv[1:5, 1:5]
GINV$status
```

*ASRgenomics*version 1.1.4 Index]