Hi Ted,
I am getting Cholesky test failures when trying to solve of Ax=B
The L matrix and solveLeft() output do not make much sense to me. For once,
L doesn't even have the expected L-shape:
Do you have an idea where i go wrong? (the test is wrapped into scala DSL
but it is Mahout's cholesky underwraps) .
test code:
test("chol") {
// try to solve Ax=b with cholesky:
// this requires
// (LL')x = B
// L'x= (L^-1)B
// x=(L'^-1)(L^-1)B
val a = dense((1, 2, 3), (2, 3, 4), (3, 4, 5))
// make sure it is symmetric for a valid solution
a := a.t %*% a
printf("A= \n%s\n", a)
val b = dense((9, 8, 7)).t
printf ("b = \n%s\n", b)
val ch = chol(a)
printf ("L = \n%s\n", ch.getL)
printf ( "(L^-1)b =\n%s\n", ch.solveLeft(b))
val x = ch.solveRight(diag(1,3)) %*% ch.solveLeft(b)
printf("x = \n%s\n", x.toString)
val axmb = (a %*% b) - b
printf("AX - B = \n%s\n", axmb.toString)
assert(axmb.norm < 1e-10)
}
Output:
A=
{
0 => {0:14.0,1:20.0,2:26.0}
1 => {0:20.0,1:29.0,2:38.0}
2 => {0:26.0,1:38.0,2:50.0}
}
b =
{
0 => {0:9.0}
1 => {0:8.0}
2 => {0:7.0}
}
L =
{
0 => {0:0.6928203230275511,2:3.676955262170047}
1 => {0:0.3464101615137781,2:5.374011537017761}
2 => {2:7.0710678118654755}
}
(L^-1)b =
{
0 => {0:1.2727922061357855}
1 => {0:11.547005383792511}
2 => {}
}
X =
{
0 => {0:0.18}
1 => {0:5.119661282874144}
2 => {}
}
AX - B =
{
0 => {0:459.0}
1 => {0:670.0}
2 => {0:881.0}
}
org.scalatest.exceptions.TestFailedException was thrown.
