Cholesky troubles again.

[Dmitriy Lyubimov]

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  => {}
}