BunchKaufmanmethods  R Documentation 
Computes the BunchKaufman factorization of an n \times n
real, symmetric matrix A
, which has the general form
A = U D_{U} U' = L D_{L} L'
where
D_{U}
and D_{L}
are symmetric, block diagonal
matrices composed of b_{U}
and b_{L}
1 \times 1
or 2 \times 2
diagonal blocks;
U = \prod_{k = 1}^{b_{U}} P_{k} U_{k}
is the product of b_{U}
rowpermuted unit upper triangular
matrices, each having nonzero entries above the diagonal in 1 or 2 columns;
and
L = \prod_{k = 1}^{b_{L}} P_{k} L_{k}
is the product of b_{L}
rowpermuted unit lower triangular
matrices, each having nonzero entries below the diagonal in 1 or 2 columns.
Methods are built on LAPACK routines dsytrf
and dsptrf
.
BunchKaufman(x, ...)
## S4 method for signature 'dsyMatrix'
BunchKaufman(x, warnSing = TRUE, ...)
## S4 method for signature 'dspMatrix'
BunchKaufman(x, warnSing = TRUE, ...)
## S4 method for signature 'matrix'
BunchKaufman(x, uplo = "U", ...)
x 
a finite symmetric matrix or

warnSing 
a logical indicating if a warning should
be signaled for singular 
uplo 
a string, either 
... 
further arguments passed to or from methods. 
An object representing the factorization, inheriting from
virtual class BunchKaufmanFactorization
.
The specific class is BunchKaufman
unless
x
inherits from virtual class packedMatrix
,
in which case it is pBunchKaufman
.
The LAPACK source code, including documentation; see https://netlib.org/lapack/double/dsytrf.f and https://netlib.org/lapack/double/dsptrf.f.
Golub, G. H., & Van Loan, C. F. (2013). Matrix computations (4th ed.). Johns Hopkins University Press. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.56021/9781421407944")}
Classes BunchKaufman
and
pBunchKaufman
and their methods.
Classes dsyMatrix
and
dspMatrix
.
Generic functions expand1
and expand2
,
for constructing matrix factors from the result.
Generic functions Cholesky
, Schur
,
lu
, and qr
,
for computing other factorizations.
showMethods("BunchKaufman", inherited = FALSE)
set.seed(0)
data(CAex, package = "Matrix")
class(CAex) # dgCMatrix
isSymmetric(CAex) # symmetric, but not formally
A < as(CAex, "symmetricMatrix")
class(A) # dsCMatrix
## Have methods for denseMatrix (unpacked and packed),
## but not yet sparseMatrix ...
## Not run:
(bk.A < BunchKaufman(A))
## End(Not run)
(bk.A < BunchKaufman(as(A, "unpackedMatrix")))
## A ~ U DU U' in floating point
str(e.bk.A < expand2(bk.A), max.level = 2L)
stopifnot(all.equal(as(A, "matrix"), as(Reduce(`%*%`, e.bk.A), "matrix")))
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.