qr-methods {Matrix} R Documentation

## QR Decomposition – S4 Methods and Generic

### Description

The `"Matrix"` package provides methods for the QR decomposition of special classes of matrices. There is a generic function which uses `qr` as default, but methods defined in this package can take extra arguments. In particular there is an option for determining a fill-reducing permutation of the columns of a sparse, rectangular matrix.

### Usage

```qr(x, ...)
qrR(qr, complete=FALSE, backPermute=TRUE)
```

### Arguments

 `x` a numeric or complex matrix whose QR decomposition is to be computed. Logical matrices are coerced to numeric. `qr` a QR decomposition of the type computed by `qr`. `complete` logical indicating whether the \bold{R} matrix is to be completed by binding zero-value rows beneath the square upper triangle. `backPermute` logical indicating if the rows of the \bold{R} matrix should be back permuted such that `qrR()`'s result can be used directly to reconstruct the original matrix \bold{X}. `...` further arguments passed to or from other methods

### Methods

x = "dgCMatrix"

QR decomposition of a general sparse double-precision matrix with `nrow(x) >= ncol(x)`. Returns an object of class `"sparseQR"`.

x = "sparseMatrix"

works via `"dgCMatrix"`.

`qr`; then, the class documentations, mainly `sparseQR`, and also `dgCMatrix`.

### Examples

```##------------- example of pivoting -- from base'  qraux.Rd -------------
X <- Matrix(cbind(int = 1,
b1=rep(1:0, each=3), b2=rep(0:1, each=3),
c1=rep(c(1,0,0), 2), c2=rep(c(0,1,0), 2), c3=rep(c(0,0,1),2)),
sparse=TRUE)
X # is singular, columns "b2" and "c3" are "extra"
(qx <- qr(X))
# both @p and @q are non-trivial permutations

drop0(R. <- qr.R(qx), tol=1e-15) # columns are int b1 c1 c2 b2 c3
Q. <- qr.Q(qx)
qI <- sort.list(qx@q) # the inverse 'q' permutation
(X. <- drop0(Q. %*% R.[, qI], tol=1e-15))## just = X
stopifnot(all(X - X.) < 8*.Machine\$double.eps,
## qR(.) returns R already "back permuted" (as with qI):
identical(R.[, qI], qrR(qx)) )
```

[Package Matrix version 1.0-11 Index]