Maybe pivoted QR is best solution here.
2014-04-02 11:39 GMT-04:00 Tomas Lycken <[email protected]>: > This is what I get from Matlab R2013a > > >> A > > A = > > 1 1 0 0 0 > 1 1 0 0 0 > 1 1 0 0 0 > 1 1 0 0 0 > 1 1 0 0 0 > 1 0 1 0 0 > 1 0 1 0 0 > 1 0 1 0 0 > 1 0 1 0 0 > 1 0 1 0 0 > 1 0 0 1 0 > 1 0 0 1 0 > 1 0 0 1 0 > 1 0 0 1 0 > 1 0 0 1 0 > 1 0 0 0 1 > 1 0 0 0 1 > 1 0 0 0 1 > 1 0 0 0 1 > 1 0 0 0 1 > > >> orth(A) > > ans = > > -0.2236 0.1060 0.3725 -0.0000 > -0.2236 0.1060 0.3725 -0.0000 > -0.2236 0.1060 0.3725 -0.0000 > -0.2236 0.1060 0.3725 -0.0000 > -0.2236 0.1060 0.3725 -0.0000 > -0.2236 -0.3495 -0.0348 -0.1633 > -0.2236 -0.3495 -0.0348 -0.1633 > -0.2236 -0.3495 -0.0348 -0.1633 > -0.2236 -0.3495 -0.0348 -0.1633 > -0.2236 -0.3495 -0.0348 -0.1633 > -0.2236 -0.0143 -0.1302 0.3645 > -0.2236 -0.0143 -0.1302 0.3645 > -0.2236 -0.0143 -0.1302 0.3645 > -0.2236 -0.0143 -0.1302 0.3645 > -0.2236 -0.0143 -0.1302 0.3645 > -0.2236 0.2577 -0.2076 -0.2012 > -0.2236 0.2577 -0.2076 -0.2012 > -0.2236 0.2577 -0.2076 -0.2012 > -0.2236 0.2577 -0.2076 -0.2012 > -0.2236 0.2577 -0.2076 -0.2012 > > On Wednesday, April 2, 2014 5:22:34 PM UTC+2, Douglas Bates wrote: >> >> On Tuesday, April 1, 2014 10:44:03 PM UTC-5, Gustavo Lacerda wrote: >>> >>> yes, I think that would be useful. >>> >> >> Do you know what Matlab's orth function returns for a rank deficient >> matrix? Suppose you ask for an orthogonal basis of the column space of a >> matrix like >> >> julia> hcat(fill(1.,(20,)), eye(4)[iceil([1:20] ./ 5),:]) >> 20x5 Array{Float64,2}: >> 1.0 1.0 0.0 0.0 0.0 >> 1.0 1.0 0.0 0.0 0.0 >> 1.0 1.0 0.0 0.0 0.0 >> 1.0 1.0 0.0 0.0 0.0 >> 1.0 1.0 0.0 0.0 0.0 >> 1.0 0.0 1.0 0.0 0.0 >> 1.0 0.0 1.0 0.0 0.0 >> 1.0 0.0 1.0 0.0 0.0 >> 1.0 0.0 1.0 0.0 0.0 >> 1.0 0.0 1.0 0.0 0.0 >> 1.0 0.0 0.0 1.0 0.0 >> 1.0 0.0 0.0 1.0 0.0 >> 1.0 0.0 0.0 1.0 0.0 >> 1.0 0.0 0.0 1.0 0.0 >> 1.0 0.0 0.0 1.0 0.0 >> 1.0 0.0 0.0 0.0 1.0 >> 1.0 0.0 0.0 0.0 1.0 >> 1.0 0.0 0.0 0.0 1.0 >> 1.0 0.0 0.0 0.0 1.0 >> 1.0 0.0 0.0 0.0 1.0 >> >> >> Do you get 4 or 5 columns? >> >> The simple calculation gives you 5 columns but there should only be 4 >> columns. >> > -- Med venlig hilsen Andreas Noack Jensen
