solve-methods
From distr v2.3.1
by Peter Ruckdeschel
Methods for Function solve in Package `distr'
solve-methods using generalized inverses for various types of matrices
Usage
solve(a,b, ...)
## S3 method for class 'ANY,ANY':
solve(a, b, generalized =
getdistrOption("use.generalized.inverse.by.default"), tol = 1e-10)
## S3 method for class 'PosSemDefSymmMatrix,ANY':
solve(a, b, generalized =
getdistrOption("use.generalized.inverse.by.default"), tol = 1e-10)
## S3 method for class '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,
b
is taken to be an identity matrix andsolve
will return the inverse ofa
. - ...
- further arguments to be passed to specific methods (see
solve
). - generalized
- logical: should generalized / Moore-Penrose inverses be used? By default uses
the corresponding global option to be set by
distroptions
. - tol
- the tolerance for detecting linear dependencies in the
columns of
a
. Default is.Machine$double.eps
.
Details
The method for the Moore-Penrose inverse for
signature(a = "PosSemDefSymmMatrix", b = "ANY")
uses eigen
to find the eigenvalue
decomposition of a
and then simply "pseudo-inverts" the corresponding diagonal matrix built from
eigen(a)$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
.
concept
- pseudo inverse
- inverse
- svd
- eigenvalue decomposition
See Also
solve
for the default method, eigen
and svd
for the pseudo inversion
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