solve-methods {distr} | R Documentation |

## Methods for Function solve in Package ‘distr’

### Description

solve-methods using generalized inverses for various types of matrices

### Usage

```
solve(a,b, ...)
## S4 method for signature 'ANY,ANY'
solve(a, b, generalized =
getdistrOption("use.generalized.inverse.by.default"), tol = 1e-10)
## S4 method for signature 'PosSemDefSymmMatrix,ANY'
solve(a, b, generalized =
getdistrOption("use.generalized.inverse.by.default"), tol = 1e-10)
## S4 method for signature 'PosDefSymmMatrix,ANY'
solve(a, b, tol = 1e-10)
```

### Arguments

`a` |
matrix to be inverted / to be solved for RHS. |

`b` |
a numeric or complex vector or matrix giving the right-hand
side(s) of the linear system. If missing, |

`...` |
further arguments to be passed to specific methods (see |

`generalized` |
logical: should generalized / Moore-Penrose inverses be used? By default uses
the corresponding global option to be set by |

`tol` |
the tolerance for detecting linear dependencies in the
columns of |

### Details

The method for the Moore-Penrose inverse for
`signature(a = "PosSemDefSymmMatrix", b = "ANY")`

uses `eigen`

to find the eigenvalue
decomposition of `a`

and then simply "pseudo-inverts" the corresponding diagonal matrix built from
`eigen(a)$values`

, while for `signature(a = "ANY", b = "ANY")`

it uses the svd
decomposition of `a`

and then simply "pseudo-inverts" the corresponding diagonal matrix built from
`svd(a)$d`

.

### Methods

- solve
`signature(a = "ANY", b = "ANY")`

: tries to evaluate`solve.default`

method from base in classical way; if this gives an error, this one is returned if`generalized`

is`TRUE`

, else it will then return`a^-b`

where`a^-`

is the pseudo or Moore-Penrose inverse of`a`

.- solve
`signature(a = "PosSemDefSymmMatrix", b = "ANY")`

: evaluates`a^-b`

where`a^-`

is the pseudo or Moore-Penrose inverse of`a`

.- solve
`signature(a = "PosDefSymmMatrix", b = "ANY")`

: evaluates solve method from base in classical way.

### Author(s)

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

### See Also

`solve`

for the default method, `eigen`

and `svd`

for the pseudo inversion

*distr*version 2.9.3 Index]