MatrixFactorization-class {Matrix} | R Documentation |
MatrixFactorization
is the virtual class of
factorizations of m \times n
matrices A
,
having the general form
P_{1} A P_{2} = A_{1} \cdots A_{p}
or (equivalently)
A = P_{1}' A_{1} \cdots A_{p} P_{2}'
where P_{1}
and P_{2}
are permutation matrices.
Factorizations requiring symmetric A
have the constraint
P_{2} = P_{1}'
, and factorizations without row
or column pivoting have the constraints
P_{1} = I_{m}
and P_{2} = I_{n}
,
where I_{m}
and I_{n}
are the
m \times m
and n \times n
identity matrices.
CholeskyFactorization
, BunchKaufmanFactorization
,
SchurFactorization
, LU
, and QR
are the virtual
subclasses of MatrixFactorization
containing all Cholesky,
Bunch-Kaufman, Schur, LU, and QR factorizations, respectively.
Dim
an integer vector of length 2 giving the dimensions of the factorized matrix.
Dimnames
a list of length 2 preserving the
dimnames
of the factorized matrix. Each element
must be NULL
or a character vector of length equal
to the corresponding element of Dim
.
determinant
signature(x = "MatrixFactorization", logarithm = "missing")
:
sets logarithm = TRUE
and recalls the generic function.
dim
signature(x = "MatrixFactorization")
:
returns x@Dim
.
dimnames
signature(x = "MatrixFactorization")
:
returns x@Dimnames
.
dimnames<-
signature(x = "MatrixFactorization", value = "NULL")
:
returns x
with x@Dimnames
set to list(NULL, NULL)
.
dimnames<-
signature(x = "MatrixFactorization", value = "list")
:
returns x
with x@Dimnames
set to value
.
length
signature(x = "MatrixFactorization")
:
returns prod(x@Dim)
.
show
signature(object = "MatrixFactorization")
:
prints the internal representation of the factorization using
str
.
solve
signature(a = "MatrixFactorization", b = .)
:
see solve-methods
.
unname
signature(obj = "MatrixFactorization")
:
returns obj
with obj@Dimnames
set to
list(NULL, NULL)
.
The virtual class compMatrix
of factorizable matrices.
Classes extending CholeskyFactorization
, namely
Cholesky
, pCholesky
,
and CHMfactor
.
Classes extending BunchKaufmanFactorization
, namely
BunchKaufman
and pBunchKaufman
.
Classes extending SchurFactorization
, namely
Schur
.
Classes extending LU
, namely
denseLU
and sparseLU
.
Classes extending QR
, namely sparseQR
.
Generic functions Cholesky
, BunchKaufman
,
Schur
, lu
, and qr
for
computing factorizations.
Generic functions expand1
and expand2
for constructing matrix factors from MatrixFactorization
objects.
showClass("MatrixFactorization")