Classes <code>BunchKaufman</code> and <code>pBunchKaufman</code> represent
 Bunch-Kaufman factorizations of $n \times n$ real,
 symmetric matrices $A$, having 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 $b_{U}$ row-permuted 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 $b_{L}$ row-permuted unit lower triangular
 matrices, each having nonzero entries below the diagonal in 1 or 2 columns. 
These classes store the nonzero entries of the
 $2 b_{U} + 1$ or $2 b_{L} + 1$ factors,
 which are individually sparse,
 in a dense format as a vector of length
 $nn$ (<code>BunchKaufman</code>) or
 $n(n+1)/2$ (<code>pBunchKaufman</code>),
 the latter giving the &#8220;packed&#8221; representation.

BunchKaufman-class

A rich hierarchy of sparse and dense matrix classes,
including general, symmetric, triangular, and diagonal matrices
with numeric, logical, or pattern entries.  Efficient methods for
operating on such matrices, often wrapping the 'BLAS', 'LAPACK',
and 'SuiteSparse' libraries.

Martin Maechler

Matrix

Sparse and Dense Matrix Classes and Methods

Douglas Bates

Mikael Jagan

Timothy A. Davis

George Karypis

Jason Riedy

Jens Oehlschlägel

R Core Team 

BunchKaufman-class function

Dense Bunch-Kaufman Factorizations — BunchKaufman-class

<dl>
 <dt><code>Dim</code>, <code>Dimnames</code></dt>
<dd>inherited from virtual class
 <code>MatrixFactorization</code>.</dd>

 <dt><code>uplo</code></dt>
<dd>a string, either <code>"U"</code> or <code>"L"</code>,
 indicating which triangle (upper or lower) of the factorized
 symmetric matrix was used to compute the factorization and
 in turn how the <code>x</code> slot is partitioned.</dd>

 <dt><code>x</code></dt>
<dd>a numeric vector of length <code>n*n</code>
 (<code>BunchKaufman</code>) or <code>n*(n+1)/2</code> (<code>pBunchKaufman</code>),
 where <code>n=Dim[1]</code>.
 The details of the representation are specified by the manual
 for LAPACK routines <code>dsytrf</code> and <code>dsptrf</code>.</dd>

 <dt><code>perm</code></dt>
<dd>an integer vector of length <code>n=Dim[1]</code>
 specifying row and column interchanges as described in the manual
 for LAPACK routines <code>dsytrf</code> and <code>dsptrf</code>.</dd>

 
</dl>

Slots

Class <code>BunchKaufmanFactorization</code>, directly.
 Class <code>MatrixFactorization</code>, by class
 <code>BunchKaufmanFactorization</code>, distance 2.

Extends

Objects can be generated directly by calls of the form
 <code>new("BunchKaufman", ...)</code> or <code>new("pBunchKaufman", ...)</code>,
 but they are more typically obtained as the value of
 <code>BunchKaufman(x)</code> for <code>x</code> inheriting from
 <code>dsyMatrix</code> or <code>dspMatrix</code>.

Instantiation

<dl>
 <dt><code>coerce</code></dt>
<dd><code>signature(from = "BunchKaufman", to = "dtrMatrix")</code>:
 returns a <code>dtrMatrix</code>, useful for inspecting
 the internal representation of the factorization; see &#8216;Note&#8217;.</dd>

 <dt><code>coerce</code></dt>
<dd><code>signature(from = "pBunchKaufman", to = "dtpMatrix")</code>:
 returns a <code>dtpMatrix</code>, useful for inspecting
 the internal representation of the factorization; see &#8216;Note&#8217;.</dd>

 <dt><code>determinant</code></dt>
<dd><code>signature(from = "p?BunchKaufman", logarithm = "logical")</code>:
 computes the determinant of the factorized matrix $A$
 or its logarithm.</dd>

 <dt><code>expand1</code></dt>
<dd><code>signature(x = "p?BunchKaufman")</code>:
 see <code>expand1-methods</code>.</dd>

 <dt><code>expand2</code></dt>
<dd><code>signature(x = "p?BunchKaufman")</code>:
 see <code>expand2-methods</code>.</dd>

 <dt><code>solve</code></dt>
<dd><code>signature(a = "p?BunchKaufman", b = .)</code>:
 see <code>solve-methods</code>.</dd>

 
</dl>

BunchKaufman-class: Dense Bunch-Kaufman Factorizations

Description

Arguments

References

See Also

Examples