Bunch-Kaufman Decomposition Methods

Description

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.

Usage

BunchKaufman(x, ...)

Arguments

Value

an object of class BunchKaufman, which can also be used as a (triangular) matrix directly.

Methods

Currently, only methods for dense numeric symmetric matrices are implemented.

x = "dspMatrix"

uses Lapack routine dsptrf,

x = "dsyMatrix"

uses Lapack routine dsytrf, computing the Bunch-Kaufman decomposition.

References

The original LAPACK source code, including documentation; http://www.netlib.org/lapack/double/dsytrf.f and http://www.netlib.org/lapack/double/dsptrf.f

See Also

The resulting class, BunchKaufman. Related decompositions are the LU, lu, and the Cholesky, chol (and for sparse matrices, Cholesky).

Examples

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

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

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
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Platform: x86_64-pc-linux-gnu (64-bit)

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> library(Matrix)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/Matrix/BunchKaufman-methods.Rd_%03d_medium.png", width=480, height=480)
> ### Name: BunchKaufman-methods
> ### Title: Bunch-Kaufman Decomposition Methods
> ### Aliases: BunchKaufman BunchKaufman-methods
> ###   BunchKaufman,dspMatrix-method BunchKaufman,dsyMatrix-method
> ### Keywords: methods
> 
> ### ** Examples
> 
> data(CAex)
> dim(CAex)
[1] 72 72
> isSymmetric(CAex)# TRUE
[1] 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
'Bunch-Kaufman' factorization of Formal class 'BunchKaufman' [package "Matrix"] with 6 slots
  ..@ perm    : int [1:72] 1 2 3 4 5 6 7 8 9 10 ...
  ..@ x       : num [1:5184] 4.16e-16 0.00 0.00 0.00 0.00 ...
  ..@ Dim     : int [1:2] 72 72
  ..@ Dimnames:List of 2
  .. ..$ : NULL
  .. ..$ : NULL
  ..@ uplo    : chr "U"
  ..@ diag    : chr "N"
> 
> image(bkCA)# shows how sparse it is, too
> str(R.CA <- as(bkCA, "sparseMatrix"))
Formal class 'dtCMatrix' [package "Matrix"] with 7 slots
  ..@ i       : int [1:144] 0 1 2 3 4 5 6 7 8 9 ...
  ..@ p       : int [1:73] 0 1 2 3 4 5 6 7 8 9 ...
  ..@ Dim     : int [1:2] 72 72
  ..@ Dimnames:List of 2
  .. ..$ : NULL
  .. ..$ : NULL
  ..@ x       : num [1:144] 4.16e-16 -7.77e-16 -4.16e-16 -2.78e-16 -5.00e-16 ...
  ..@ uplo    : chr "U"
  ..@ diag    : chr "N"
> ## an upper triangular 72x72 matrix with only 144 non-zero entries
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>