GitHub user hl475 opened a pull request:
https://github.com/apache/spark/pull/16556
[SPARK-19184][MLlib] Improve numerical stability for method tallSkinnyQR.
## What changes were proposed in this pull request?
In method tallSkinnyQR, the final Q is calculated by A * inv(R). When the
upper triangular matrix R is ill-conditioned, computing the inverse of R can
result in catastrophic cancellation. Instead, we should consider using a
forward solve for solving Q such that Q * R = A.
## How was this patch tested?
unit tests and the following codes in Spark Shell:
```
import org.apache.spark.mllib.linalg.{Matrices, Vector, Vectors}
import org.apache.spark.mllib.linalg.distributed.RowMatrix
// Create RowMatrix A.
val mat = Seq(Vectors.dense(1,1,1,1), Vectors.dense(0, 1E-5, 1,1),
Vectors.dense(0,0,1E-10,1), Vectors.dense(0,0,0,1E-14))
val denseMat = new RowMatrix(sc.parallelize(mat, 2))
// Apply tallSkinnyQR to A.
val result = denseMat.tallSkinnyQR(true)
// Print the calculated Q and R.
result.Q.rows.collect.foreach(println)
result.R
// Calculate Q*R. Ideally, this should be close to A.
val reconstruct = result.Q.multiply(result.R)
reconstruct.rows.collect.foreach(println)
// Calculate Q'*Q. Ideally, this should be close to the identity matrix.
result.Q.computeGramianMatrix()
System.exit(0)
```
I first create a 4 by 4 RowMatrix A =
(1,1,1,1;0,1E-5,0,0;0,0,1E-10,1;0,0,0,1E-14), and then I apply method
tallSkinnyQR to A to find RowMatrix Q and Matrix R such that A = Q*R. In this
case, A is ill-conditioned and so is R.
You can merge this pull request into a Git repository by running:
$ git pull https://github.com/hl475/spark tallSkinnyQR
Alternatively you can review and apply these changes as the patch at:
https://github.com/apache/spark/pull/16556.patch
To close this pull request, make a commit to your master/trunk branch
with (at least) the following in the commit message:
This closes #16556
----
commit db737275d563b6057a5b4a2f116badc1f362f2f0
Author: Huamin Li <[email protected]>
Date: 2017-01-12T02:13:07Z
modify tallSkinnyQR so it will use forward solve instead of computing the
inverse of upper triangular matrix R.
----
---
If your project is set up for it, you can reply to this email and have your
reply appear on GitHub as well. If your project does not have this feature
enabled and wishes so, or if the feature is enabled but not working, please
contact infrastructure at [email protected] or file a JIRA ticket
with INFRA.
---
---------------------------------------------------------------------
To unsubscribe, e-mail: [email protected]
For additional commands, e-mail: [email protected]
