Github user debasish83 commented on the pull request:

    https://github.com/apache/spark/pull/3221#issuecomment-85161041
  
    @mengxr I added the optimization for lower triangular matrix and now they 
are very close...Let me know what do you think and if there are any other 
tricks you would like me to try...Note that with these optimization, 
QuadraticMinimizer with POSITIVE constraint will also run much faster
    
    Breeze QuadraticMinimizer (default):
    
    unset solver; ./bin/spark-submit --master 
spark://tusca09lmlvt00c.uswin.ad.vzwcorp.com:7077 --class 
org.apache.spark.examples.mllib.MovieLensALS --jars 
~/.m2/repository/com/github/scopt/scopt_2.10/3.2.0/scopt_2.10-3.2.0.jar 
--total-executor-cores 1 
./examples/target/spark-examples_2.10-1.3.0-SNAPSHOT.jar --rank 50 
--numIterations 2 ~/datasets/ml-1m/ratings.dat
    
    Got 1000209 ratings from 6040 users on 3706 movies.
    Training: 800670, test: 199539.
    Quadratic minimization userConstraint SMOOTH productConstraint SMOOTH
    Running Breeze QuadraticMinimizer for users with constraint SMOOTH
    Running Breeze QuadraticMinimizer for items with constraint SMOOTH
    Test RMSE = 2.4985081126233846.
    
    15/03/23 12:26:55 INFO ALS: solveTime 205.379 ms
    15/03/23 12:26:55 INFO ALS: solveTime 72.116 ms
    15/03/23 12:26:56 INFO ALS: solveTime 74.034 ms
    15/03/23 12:26:56 INFO ALS: solveTime 77.379 ms
    15/03/23 12:26:57 INFO ALS: solveTime 36.532 ms
    15/03/23 12:26:57 INFO ALS: solveTime 29.775 ms
    15/03/23 12:26:58 INFO ALS: solveTime 48.925 ms
    15/03/23 12:26:58 INFO ALS: solveTime 51.904 ms
    15/03/23 12:26:59 INFO ALS: solveTime 30.882 ms
    15/03/23 12:26:59 INFO ALS: solveTime 30.658 ms
    
    ML CholeskySolver:
    
    export solver=mllib; ./bin/spark-submit --master 
spark://tusca09lmlvt00c.uswin.ad.vzwcorp.com:7077 --class 
org.apache.spark.examples.mllib.MovieLensALS --jars 
~/.m2/repository/com/github/scopt/scopt_2.10/3.2.0/scopt_2.10-3.2.0.jar 
--total-executor-cores 1 
./examples/target/spark-examples_2.10-1.3.0-SNAPSHOT.jar --rank 50 
--numIterations 2 ~/datasets/ml-1m/ratings.dat
    
    Got 1000209 ratings from 6040 users on 3706 movies.
    Training: 800670, test: 199539.
    Quadratic minimization userConstraint SMOOTH productConstraint SMOOTH
    Test RMSE = 2.4985081126233846.
    
    TUSCA09LMLVT00C:spark-qp-als v606014$ grep solveTime 
./work/app-20150323122612-0002/0/stderr 
    15/03/23 12:26:20 INFO ALS: solveTime 102.243 ms
    15/03/23 12:26:21 INFO ALS: solveTime 38.195 ms
    15/03/23 12:26:21 INFO ALS: solveTime 60.583 ms
    15/03/23 12:26:22 INFO ALS: solveTime 59.882 ms
    15/03/23 12:26:22 INFO ALS: solveTime 36.59 ms
    15/03/23 12:26:23 INFO ALS: solveTime 36.021 ms
    15/03/23 12:26:23 INFO ALS: solveTime 59.271 ms
    15/03/23 12:26:24 INFO ALS: solveTime 59.217 ms
    15/03/23 12:26:24 INFO ALS: solveTime 36.344 ms
    15/03/23 12:26:25 INFO ALS: solveTime 35.838 ms
    
    I am running only 2 iterations but you can see in the tail the solvers run 
at par...


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