# rcond: Estimate the Reciprocal Condition Number using GPU and... In HiPLARM: High Performance Linear Algebra in R

## Description

Estimate the reciprocal of the condition number of a matrix using the MAGMA library for GPU or PLASMA library for multi-core CPUs.

## Usage

 ```1 2 3 4``` ```## S4 method for signature 'dgeMatrix' rcond(x, norm, ...) ## S4 method for signature 'dpoMatrix' rcond(x, norm, ...) ```

## Arguments

 `x` an R object that inherits from the `Matrix` class. `norm` Character indicating the type of norm to be used in the estimate. The default is `"O"` for the 1-norm (`"O"` is equivalent to `"1"`). The other possible value is `"I"` for the infinity norm, see also `norm`. `...` further arguments passed to or from other methods.

## Details

Uses the LU decomposition using `magma_dgetrf` or `PLASMA_dgetrf` with the respective MAGMA or PLASMA norms if available (see norm documentation for more info).It also calls LAPACK `dgecon` as this is not supported in MAGMA/PLASMA. For further details on classes and methods see the Matrix package documentation.

## Value

An estimate of the reciprocal condition number of `x`.

## References

Martin Maechler, Douglas Bates (Matrix package)

## Examples

 ```1 2 3 4 5 6 7 8 9``` ```x <- Matrix(rnorm(9), 3, 3) rcond(x) ## typically "the same" (with more computational effort): 1 / (norm(x) * norm(solve(x))) rcond(Hilbert(9)) # should be about 9.1e-13 ## For non-square matrices: rcond(x1 <- cbind(1,1:10))# 0.05278 rcond(x2 <- cbind(x1, 2:11))# practically 0, since x2 does not have full rank ```

HiPLARM documentation built on May 29, 2017, 10:42 p.m.