Here is a test case that captures what you are talking about.
A fix would be grand.
@Test
public void fullRank() {
Matrix a = new DenseMatrix(new double[][]{
{1, 2, 3, 4},
{2, 3, 4, 5},
{3, -4, 5, 6},
{4, 5, 6, 7},
{8, 6, 7, 8}});
Matrix x = a.transpose().times(a);
CholeskyDecomposition cd = new CholeskyDecomposition(x);
Matrix residual =
cd.getPermutedL().times(cd.getPermutedL().transpose()).minus(x);
double error = residual.aggregate(Functions.PLUS, Functions.ABS);
assertEquals(0, error, 1e-10);
assertTrue(cd.isPositiveDefinite());
}
On Thu, Mar 6, 2014 at 12:53 PM, Dmitriy Lyubimov <[email protected]> wrote:
> Hm I think it is a valid bug in Cholesky decomposition. I don't seem to see
> that isPositiveDefinite is initialized to true, anywhere (default valuel in
> java is false). So if degenerate case is detected, it is assigned to false
> but never otherwise.
>
> Are you ok with me fixing this?
>
>
> On Thu, Mar 6, 2014 at 12:45 PM, Dmitriy Lyubimov <[email protected]>
> wrote:
>
> > Hm. I still seem to have trouble, this time with isPositiveDefinite which
> > returns false although i seem to have a fairly nice traingular L' (which
> > is printed here as R). Clearly algorithm has finished all elements
> without
> > encountering a degenerative condition yet reported failure to assert
> > positive-definite-ness :
> >
> >
> >
> >
> > 2243 [ScalaTest-run-running-MathSuite] DEBUG
> > org.apache.mahout.sparkbindings.drm.decompositions.DQR$ - R=
> > {
> > 0 =>
> >
> {0:4.186193378864822,1:-0.3357736566246455,2:0.8607534898896447,3:-4.33523362179746}
> > 1 => {1:9.134979322863726,2:1.4522423059617362,3:-0.315879931815721}
> > 2 => {2:0.8986806052211012,3:-0.03911349897105256}
> > 3 => {3:0.02316192361205758}
> > }
> >
> > for the input of A
> >
> > val inCoreA = dense(
> > (1, 2, 3, 4),
> > (2, 3, 4, 5),
> > (3, -4, 5, 6),
> > (4, 5, 6, 7),
> > (8, 6, 7, 8)
> > )
> >
> >
> > and A'A as
> > 2242 [ScalaTest-run-running-MathSuite] DEBUG
> > org.apache.mahout.sparkbindings.drm.decompositions.DQR$ - A'A=
> > {
> > 0 =>
> >
> {0:17.524215005251673,1:-1.405613458159321,2:3.603280560210819,3:-18.148126283400686}
> > 1 =>
> >
> {0:-1.405613458159321,1:83.5605911776309,2:12.977185089995727,3:-1.4298994001311764}
> > 2 =>
> >
> {0:3.603280560210819,1:12.977185089995727,2:3.6575311157828283,3:-4.225452212963807}
> > 3 =>
> >
> {0:-18.148126283400686,1:-1.4298994001311764,2:-4.225452212963807,3:18.896097027394198}
> > }
> >
> >
> >
> >
> > On Thu, Mar 6, 2014 at 12:28 PM, Ted Dunning <[email protected]
> >wrote:
> >
> >> It may be a knowledge gap, but it seems to have been well filled by
> >> accurate inference.
> >>
> >> A'A is always semi-positive-definite.
> >>
> >> And I think you are correct that only rank deficiency can cause y'y = 0
> >>
> >>
> >> On Thu, Mar 6, 2014 at 10:45 AM, Dmitriy Lyubimov <[email protected]>
> >> wrote:
> >>
> >> > 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 => {}
> >> > >>>> > }
> >> > >>>> >
> >> > >>>>
> >> > >>>
> >> > >>>
> >> > >>
> >> > >
> >> >
> >>
> >
> >
>
