solve-methods {distrMod} | R Documentation |
solve-methods using generalized inverses for various types of matrices
solve(a,b, ...) ## S4 method for signature 'ANY, ANY': solve(a, b, generalized = getdistrModOption("use.generalized.inverse.by.default"), tol = 1e-10) ## S4 method for signature 'PosSemDefSymmMatrix, ANY': solve(a, b, generalized = getdistrModOption("use.generalized.inverse.by.default"), tol = 1e-10) ## S4 method for signature 'PosDefSymmMatrix, ANY': solve(a, b, tol = 1e-10)
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 and solve will return the inverse of
a . |
... |
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 distrModoptions . |
tol |
the tolerance for detecting linear dependencies in the
columns of a . Default is .Machine$double.eps . |
The method for the Moore-Penrose inverse for
signature(a = "PosSemDefSymmMatrix", b = "ANY")
uses eigen
to find the eigenvalue
decomposition of a
and then simply "pseudo-inverts" the corresponding diagonal matrix built from
eigen(a)$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
.
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.signature(a = "PosSemDefSymmMatrix", b = "ANY")
: evaluates a^-b where a^- is the pseudo or Moore-Penrose
inverse of a.signature(a = "PosDefSymmMatrix", b = "ANY")
: evaluates solve method from base in classical way.Peter Ruckdeschel Peter.Ruckdeschel@itwm.fraunhofer.de
solve
for the default method, eigen
and svd
for the pseudo inversion