<code>expand1</code> and <code>expand2</code> construct matrix factors from
 objects specifying matrix factorizations. Such objects typically
 do not store the factors explicitly, employing instead a compact
 representation to save memory.

expand-methods

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 

expand-methods function

Expand Matrix Factorizations — expand-methods

<dl>

 <dt>x</dt>
<dd>a matrix factorization, typically inheriting from
 virtual class <code>MatrixFactorization</code>.</dd>

 <dt>which</dt>
<dd>a character string indicating a matrix factor.</dd>

 <dt>...</dt>
<dd>further arguments passed to or from methods.</dd>

</dl>

Arguments

The following table lists methods for <code>expand1</code> together with
 allowed values of argument <code>which</code>.
<table class='table'>
<tr><td><code>class(x)</code></td><td><code>which</code></td></tr>
<tr><td><code>Schur</code></td><td><code>c("Q", "T", "Q.")</code></td></tr>
<tr><td><code>denseLU</code></td><td><code>c("P1", "P1.", "L", "U")</code></td></tr>
<tr><td><code>sparseLU</code></td><td><code>c("P1", "P1.", "P2", "P2.", "L", "U")</code></td></tr>
<tr><td><code>sparseQR</code></td><td><code>c("P1", "P1.", "P2", "P2.", "Q", "Q1", "R", "R1")</code></td></tr>
<tr><td><code>BunchKaufman</code>, <code>pBunchKaufman</code></td><td><code>c("U", "DU", "U.", "L", "DL", "L.")</code></td></tr>
<tr><td><code>Cholesky</code>, <code>pCholesky</code></td><td><code>c("P1", "P1.", "L1", "D", "L1.", "L", "L.")</code></td></tr>
<tr><td><code>CHMsimpl</code>, <code>CHMsimpl</code></td><td><code>c("P1", "P1.", "L1", "D", "L1.", "L", "L.")</code></td></tr>
</table>


Methods for <code>expand2</code> and <code>expand</code> are described
 below. Factor names and classes apply also to <code>expand1</code>. 
<dl>
 <dt><code>expand2</code></dt>
<dd><code>signature(x = "CHMsimpl")</code>:
 expands the factorization
 \(A = P_{1}' L_{1} D L_{1}' P_{1} = P_{1}' L L' P_{1}\)
 as <code>list(P1., L1, D, L1., P1)</code> (the default)
 or as <code>list(P1., L, L., P1)</code>,
 depending on optional logical argument <code>LDL</code>.
 <code>P1</code> and <code>P1.</code> are <code>pMatrix</code>,
 <code>L1</code>, <code>L1.</code>, <code>L</code>, and <code>L.</code> are
 <code>dtCMatrix</code>,
 and <code>D</code> is a <code>ddiMatrix</code>.</dd>

 <dt><code>expand2</code></dt>
<dd><code>signature(x = "CHMsuper")</code>:
 as <code>CHMsimpl</code>, but the triangular factors are
 stored as <code>dgCMatrix</code>.</dd>

 <dt><code>expand2</code></dt>
<dd><code>signature(x = "p?Cholesky")</code>:
 expands the factorization
 \(A = L_{1} D L_{1}' = L L'\)
 as <code>list(L1, D, L1.)</code> (the default) or as <code>list(L, L.)</code>,
 depending on optional logical argument <code>LDL</code>.
 <code>L1</code>, <code>L1.</code>, <code>L</code>, and <code>L.</code> are
 <code>dtrMatrix</code> or <code>dtpMatrix</code>,
 and <code>D</code> is a <code>ddiMatrix</code>.</dd>

 <dt><code>expand2</code></dt>
<dd><code>signature(x = "p?BunchKaufman")</code>:
 expands the factorization
 \(A = U D_{U} U' = L D_{L} L'\)
 where
 \(U = \prod_{k = 1}^{b_{U}} P_{k} U_{k}\)
 and
 \(L = \prod_{k = 1}^{b_{L}} P_{k} L_{k}\)
 as <code>list(U, DU, U.)</code> or <code>list(L, DL, L.)</code>,
 depending on <code>x@uplo</code>. If optional argument <code>complete</code>
 is <code>TRUE</code>, then an unnamed list giving the full expansion
 with \(2 b_{U} + 1\) or \(2 b_{L} + 1\) matrix
 factors is returned instead.
 \(P_{k}\) are represented as <code>pMatrix</code>,
 \(U_{k}\) and \(L_{k}\) are represented as
 <code>dtCMatrix</code>, and
 \(D_{U}\) and \(D_{L}\) are represented as
 <code>dsCMatrix</code>.</dd>

 <dt><code>expand2</code></dt>
<dd><code>signature(x = "Schur")</code>:
 expands the factorization
 \(A = Q T Q'\)
 as <code>list(Q, T, Q.)</code>.
 <code>Q</code> and <code>Q.</code> are <code>x@Q</code> and <code>t(x@Q)</code>
 modulo <code>Dimnames</code>, and <code>T</code> is <code>x@T</code>.</dd>

 <dt><code>expand2</code></dt>
<dd><code>signature(x = "sparseLU")</code>:
 expands the factorization
 \(A = P_{1}' L U P_{2}'\)
 as <code>list(P1., L, U, P2.)</code>.
 <code>P1.</code> and <code>P2.</code> are <code>pMatrix</code>,
 and <code>L</code> and <code>U</code> are <code>dtCMatrix</code>.</dd>

 <dt><code>expand2</code></dt>
<dd><code>signature(x = "denseLU")</code>:
 expands the factorization
 \(A = P_{1}' L U\)
 as <code>list(P1., L, U)</code>.
 <code>P1.</code> is a <code>pMatrix</code>,
 and <code>L</code> and <code>U</code> are <code>dtrMatrix</code>
 if square and <code>dgeMatrix</code> otherwise.</dd>

 <dt><code>expand2</code></dt>
<dd><code>signature(x = "sparseQR")</code>:
 expands the factorization
 \(A = P_{1}' Q R P_{2}' = P_{1}' Q_{1} R_{1} P_{2}'\)
 as <code>list(P1., Q, R, P2.)</code> or <code>list(P1., Q1, R1, P2.)</code>,
 depending on optional logical argument <code>complete</code>.
 <code>P1.</code> and <code>P2.</code> are <code>pMatrix</code>,
 <code>Q</code> and <code>Q1</code> are <code>dgeMatrix</code>,
 <code>R</code> is a <code>dgCMatrix</code>,
 and <code>R1</code> is a <code>dtCMatrix</code>.</dd>

 <dt><code>expand</code></dt>
<dd><code>signature(x = "CHMfactor")</code>:
 as <code>expand2</code>, but returning <code>list(P, L)</code>.
 <code>expand(x)[["P"]]</code> and <code>expand2(x)[["P1"]]</code>
 represent the same permutation matrix \(P_{1}\)
 but have opposite <code>margin</code> slots and inverted
 <code>perm</code> slots. The components of <code>expand(x)</code>
 do not preserve <code>x@Dimnames</code>.</dd>

 <dt><code>expand</code></dt>
<dd><code>signature(x = "sparseLU")</code>:
 as <code>expand2</code>, but returning <code>list(P, L, U, Q)</code>.
 <code>expand(x)[["Q"]]</code> and <code>expand2(x)[["P2."]]</code>
 represent the same permutation matrix \(P_{2}'\)
 but have opposite <code>margin</code> slots and inverted
 <code>perm</code> slots. <code>expand(x)[["P"]]</code> represents
 the permutation matrix \(P_{1}\) rather than its
 transpose \(P_{1}'\); it is <code>expand2(x)[["P1."]]</code>
 with an inverted <code>perm</code> slot. <code>expand(x)[["L"]]</code>
 and <code>expand2(x)[["L"]]</code> represent the same unit lower
 triangular matrix \(L\), but with <code>diag</code> slot equal
 to <code>"N"</code> and <code>"U"</code>, respectively.
 <code>expand(x)[["L"]]</code> and <code>expand(x)[["U"]]</code>
 store the permuted first and second components of
 <code>x@Dimnames</code> in their <code>Dimnames</code> slots.</dd>

 <dt><code>expand</code></dt>
<dd><code>signature(x = "denseLU")</code>:
 as <code>expand2</code>, but returning <code>list(L, U, P)</code>.
 <code>expand(x)[["P"]]</code> and <code>expand2(x)[["P1."]]</code>
 are identical modulo <code>Dimnames</code>. The components
 of <code>expand(x)</code> do not preserve <code>x@Dimnames</code>.</dd>

 
</dl>

Methods

Expand Matrix Factorizations

expand-methods: Expand Matrix Factorizations

Description

Usage

Arguments

Value

Details

See Also

Examples