Estimate the reciprocal of the condition number of a matrix.
This is a generic function with several methods, as seen by
 <code>showMethods(rcond)</code>.

rcond-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 

rcond-methods function

Estimate the Reciprocal Condition Number — rcond-methods

<dl>

 <dt>x</dt>
<dd>an R object that inherits from the <code>Matrix</code> class.</dd>

 <dt>norm</dt>
<dd>character string indicating the type of norm to be used in
 the estimate. The default is <code>"O"</code> for the 1-norm (<code>"O"</code> is
 equivalent to <code>"1"</code>). For sparse matrices, when <code>useInv=TRUE</code>,
 <code>norm</code> can be any of the <code>kind</code>s allowed for <code><a href='https://rdrr.io/r/base/norm.html'>norm</a></code>;
 otherwise, the other possible value is <code>"I"</code> for the infinity
 norm, see also <code><a href='https://rdrr.io/r/base/norm.html'>norm</a></code>.</dd>

 <dt>useInv</dt>
<dd>logical (or <code>"Matrix"</code> containing
 <code><a href='https://rdrr.io/r/base/solve.html'>solve</a>(x)</code>). If not false, compute the reciprocal
 condition number as $1/(\|x\| \cdot \|x^{-1}\|)$,
 where $x^{-1}$ is the inverse of $x$, <code>solve(x)</code>.
This may be an efficient alternative (only) in situations where
 <code>solve(x)</code> is fast (or known), e.g., for (very) sparse or
 triangular matrices.
Note that the result may differ depending on <code>useInv</code>,
 as per default, when it is false, an approximation is
 computed.</dd>

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

</dl>

Arguments

The condition number of a regular (square) matrix is the product of
 the <code><a href='https://rdrr.io/r/base/norm.html'>norm</a></code> of the matrix and the norm of its inverse (or
 pseudo-inverse).
More generally, the condition number is defined (also for
 non-square matrices $A$) as
 $$\kappa(A) = \frac{\max_{\|v\| = 1} \|A v\|}{\min_{\|v\| = 1} \|A v\|}.$$
 Whenever <code>x</code> is not a square matrix, in our method
 definitions, this is typically computed via <code>rcond(qr.R(qr(X)), ...)</code>
 where <code>X</code> is <code>x</code> or <code>t(x)</code>.
The condition number takes on values between 1 and infinity,
 inclusive, and can be viewed as a factor by which errors in solving
 linear systems with this matrix as coefficient matrix could be
 magnified.
<code><a href='https://rdrr.io/r/base/kappa.html'>rcond()</a></code> computes the reciprocal condition number
 $1/\kappa$ with values in $[0,1]$ and can be viewed as a
 scaled measure of how close a matrix is to being rank deficient (aka
 &#8220;singular&#8221;).
Condition numbers are usually estimated, since exact computation is
 costly in terms of floating-point operations. An (over) estimate of
 reciprocal condition number is given, since by doing so overflow is
 avoided. Matrices are well-conditioned if the reciprocal condition
 number is near 1 and ill-conditioned if it is near zero.

BACKGROUND

Estimate the Reciprocal Condition Number

rcond-methods: Estimate the Reciprocal Condition Number

Description

Usage

Arguments

Value

References

See Also

Examples