# QRupdate

Update the "Q-less" QR factorization of a matrix. Routines are provided for adding and deleting columns, adding rows, and solving the least-squares systems.

## Installing

```
Pkg.clone("https://github.com/mpf/QRupdate.jl.git")
Pkg.test("QRupdate")
```

## Examples

### Adding columns

Build the "Q-less" QR factorization of A one column at a time.

```
m, n = 100, 50
A = randn(m,0)
R = Array{Float64}(0,0)
for i in 1:n
a = randn(m)
R = qraddcol(A, R, a)
A = [A a]
end
```

Solve a least-squares problem using R.

```
b = randn(m)
x, r = csne(R, A, b)
```

### Deleting columns

Delete a column and compute new R.

```
n = size(A,2)
k = rand(1:n)
A = A[:, 1:n .!= k]
R = qrdelcol(R, k)
```

Solve a least-squares problem using R.

`x, r = csne(R, A, b)`

### Adding rows

Add a row to A.

```
n = size(A,2)
a = randn(n)' # must be row vector
A = [A; a]
R = qraddrow(R, a)
```

Solve a least-squares problem using R.

```
b = [b; randn()]
x, r = csne(R, A, b)
```

## Reference

Björck, A. (1996). Numerical methods for least squares problems. SIAM.