I guess A'A is always semi-positive-definite since x'(A'A)x = (x'A')(Ax) = y'y >=0.
I also intuitively think that y'y = 0 when x != 0 in this case if and only if A'A is rank-deficient, i.e. it is sufficient to test for rank deficiency of A'A product to figure if QR is going less non-zero column than one desires. (Yes i have a knowledge gap here :) On Wed, Mar 5, 2014 at 7:17 PM, Dmitriy Lyubimov <[email protected]> wrote: > Still though, it seems this code is too sensitive to the error margin. > > Even when i change the input so that the case is not degenerate, i still > get second norm of difference on Q of ~1e-5 between Cholesky and QR even > on 3 x 4 input which is large-ish imo, > > > On Wed, Mar 5, 2014 at 7:05 PM, Dmitriy Lyubimov <[email protected]>wrote: > >> oh, ok. So input is indeed still deficient. ok . >> >> >> On Wed, Mar 5, 2014 at 7:04 PM, Dmitriy Lyubimov <[email protected]>wrote: >> >>> well the positive definite test is failing starting with row 2. I >>> stepped thru it. But i am at loss why. >>> >>> >>> On Wed, Mar 5, 2014 at 6:55 PM, Andrew Musselman < >>> [email protected]> wrote: >>> >>>> Just noticed it looks like some kind of rounding error since rows "2" >>>> and >>>> "3" in rControl have very small values in their elements. >>>> >>>> >>>> On Wed, Mar 5, 2014 at 6:48 PM, Dmitriy Lyubimov <[email protected]> >>>> wrote: >>>> >>>> > Hi, >>>> > >>>> > I am trying to put in Cholesky-based distributed thin QR and having >>>> > troubles again (even with in-core). What am i doing wrong? I am >>>> inclined to >>>> > think there's definitely a bug in our Cholesky implementation, at this >>>> > point. >>>> > >>>> > Here is the test code -- obviously results are different via >>>> Householder QR >>>> > and via Cholesky. Note that two rows of L' (R) matrix match the result >>>> > exactly, and it looks like L is just loosing two of its columns >>>> somehow. >>>> > >>>> > Could somebody perhaps review the CholeskyDecomposition in Mahout? >>>> Because >>>> > of this, tests in spark - QR and spark -SSVD are failing. >>>> > >>>> > here's the code for in-core only and output: >>>> > >>>> > ----------------- >>>> > >>>> > val inCoreA = dense( >>>> > (1, 2, 3, 40), >>>> > (2, 3, 4, 50), >>>> > (3, 4, 5, 60), >>>> > (4, 5, 6, 70), >>>> > (5, 6, 7, 80) >>>> > ) >>>> > >>>> > val (qControl, rControl) = qr(inCoreA) >>>> > >>>> > printf("qControl=\n%s\n", qControl) >>>> > printf("rControl=\n%s\n", rControl) >>>> > >>>> > // Validate with Cholesky >>>> > val ch = chol(inCoreA.t %*% inCoreA) >>>> > val rControl2 = (ch.getL cloned).t >>>> > val qControl2 = ch.solveRight(inCoreA) >>>> > >>>> > printf("qControl2=\n%s\n", qControl2) >>>> > printf("rControl2=\n%s\n", rControl2) >>>> > >>>> > >>>> > >>>> > qControl= >>>> > { >>>> > 0 => >>>> > >>>> > >>>> {0:0.13483997249264842,1:0.7627700713964736,2:0.09950371902099892,3:-0.30053573339989126} >>>> > 1 => >>>> > >>>> > >>>> {0:0.26967994498529685,1:0.4767312946227957,2:0.19900743804199783,3:0.34749444174362476} >>>> > 2 => >>>> > >>>> > >>>> {0:0.40451991747794525,1:0.1906925178491178,2:0.39801487608399566,3:0.22070592921554588} >>>> > 3 => >>>> > >>>> > >>>> {0:0.5393598899705937,1:-0.09534625892456007,2:0.39801487608399566,3:0.6949888834872495} >>>> > 4 => >>>> > >>>> > >>>> {0:0.6741998624632421,1:-0.3813850356982384,2:0.7960297521679913,3:-0.5071540501123155} >>>> > } >>>> > rControl= >>>> > { >>>> > 0 => >>>> > >>>> > >>>> {0:7.416198487095663,1:9.43879807448539,2:11.461397661875116,3:134.83997249264843} >>>> > 1 => >>>> {1:0.9534625892455925,2:1.906925178491185,3:28.603877677367773} >>>> > 2 => {2:2.2315206618374916E-15,3:4.1360462167918654E-14} >>>> > 3 => {3:1.8726762404185252E-15} >>>> > } >>>> > L: >>>> > { >>>> > 0 => {0:7.416198487095663} >>>> > 1 => {0:9.43879807448539,1:0.953462589245576} >>>> > 2 => {0:11.461397661875116,1:1.9069251784911967} >>>> > 3 => {0:134.83997249264843,1:28.603877677367997} >>>> > } >>>> > qControl2= >>>> > { >>>> > 0 => {0:0.13483997249264842,1:0.7627700713964867} >>>> > 1 => {0:0.26967994498529685,1:0.4767312946228039} >>>> > 2 => {0:0.40451991747794525,1:0.19069251784912108} >>>> > 3 => {0:0.5393598899705937,1:-0.09534625892456171} >>>> > 4 => {0:0.674199862463242,1:-0.38138503569824406} >>>> > } >>>> > rControl2= >>>> > { >>>> > 0 => >>>> > >>>> > >>>> {0:7.416198487095663,1:9.43879807448539,2:11.461397661875116,3:134.83997249264843} >>>> > 1 => >>>> {1:0.953462589245576,2:1.9069251784911967,3:28.603877677367997} >>>> > 2 => {} >>>> > 3 => {} >>>> > } >>>> > >>>> >>> >>> >> >
