BunchKaufman-methods | R Documentation |
The Bunch-Kaufman Decomposition of a square symmetric matrix A is A = P LDL' P' where P is a permutation matrix, L is unit-lower triangular and D is block-diagonal with blocks of dimension 1 x 1 or 2 x 2.
This is generalization of a pivoting LDL' Cholesky decomposition.
## S4 method for signature 'dsyMatrix' BunchKaufman(x, ...) ## S4 method for signature 'dspMatrix' BunchKaufman(x, ...) ## S4 method for signature 'matrix' BunchKaufman(x, uplo = NULL, ...)
x |
a symmetric square matrix. |
uplo |
optional string, |
... |
potentially further arguments passed to methods. |
FIXME: We really need an expand()
method in order to work with the result!
an object of class BunchKaufman
, which can also
be used as a (triangular) matrix directly. Somewhat amazingly,
it inherits its uplo
slot from x
.
Currently, only methods for dense numeric symmetric matrices are implemented. To compute the Bunch-Kaufman decomposition, the methods use either one of two Lapack routines:
x = "dspMatrix"
routine dsptrf()
; whereas
x = "dsyMatrix"
, and
x = "matrix"
use dsytrf()
.
The original LAPACK source code, including documentation; https://netlib.org/lapack/double/dsytrf.f and https://netlib.org/lapack/double/dsptrf.f
The resulting class, BunchKaufman
.
Related decompositions are the LU, lu
, and the Cholesky,
chol
(and for sparse matrices,
Cholesky
).
data(CAex) dim(CAex) isSymmetric(CAex)# TRUE CAs <- as(CAex, "symmetricMatrix") if(FALSE) # no method defined yet for *sparse* : bk. <- BunchKaufman(CAs) ## does apply to *dense* symmetric matrices: bkCA <- BunchKaufman(as(CAs, "denseMatrix")) bkCA pkCA <- pack(bkCA) stopifnot(is(bkCA, "triangularMatrix"), is(pkCA, "triangularMatrix"), is(pkCA, "packedMatrix")) image(bkCA)# shows how sparse it is, too str(R.CA <- as(bkCA, "sparseMatrix")) ## an upper triangular 72x72 matrix with only 144 non-zero entries stopifnot(is(R.CA, "triangularMatrix"), is(R.CA, "CsparseMatrix"))
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