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Spark MLContext Programming Guide |
Spark MLContext Programming Guide |
- This will become a table of contents (this text will be scraped). {:toc}
The Spark MLContext API offers a programmatic interface for interacting with SystemML from Spark using languages
such as Scala, Java, and Python. As a result, it offers a convenient way to interact with SystemML from the Spark
Shell and from Notebooks such as Jupyter and Zeppelin.
NOTE: The MLContext API has been redesigned. Currently both the old API and the new API can be used. The old API will be deprecated and removed, so please migrate to the new API.
To use SystemML with Spark Shell, the SystemML jar can be referenced using Spark Shell's --jars option.
{% highlight bash %} spark-shell --executor-memory 4G --driver-memory 4G --jars SystemML.jar {% endhighlight %}
All primary classes that a user interacts with are located in the org.apache.sysml.api.mlcontext package.
For convenience, we can additionally add a static import of ScriptFactory to shorten the syntax for creating Script objects.
An MLContext object can be created by passing its constructor a reference to the SparkContext. If successful, you
should see a "Welcome to Apache SystemML!" message.
scala> import org.apache.sysml.api.mlcontext.ScriptFactory._ import org.apache.sysml.api.mlcontext.ScriptFactory._
scala> val ml = new MLContext(sc)
Welcome to Apache SystemML!
ml: org.apache.sysml.api.mlcontext.MLContext = org.apache.sysml.api.mlcontext.MLContext@12139db0
{% endhighlight %}
The ScriptFactory class allows DML and PYDML scripts to be created from Strings, Files, URLs, and InputStreams.
Here, we'll use the dml method to create a DML "hello world" script based on a String. Notice that the script
reports that it has no inputs or outputs.
We execute the script using MLContext's execute method, which displays "hello world" to the console.
The execute method returns an MLResults object, which contains no results since the script has
no outputs.
Outputs: None
scala> ml.execute(helloScript) hello world res0: org.apache.sysml.api.mlcontext.MLResults = None
{% endhighlight %}
For demonstration purposes, we'll use Spark to create a DataFrame called df of random doubles from 0 to 1 consisting of 10,000 rows and 1,000 columns.
scala> import org.apache.spark.sql.types.{StructType,StructField,DoubleType} import org.apache.spark.sql.types.{StructType, StructField, DoubleType}
scala> import scala.util.Random import scala.util.Random
scala> val numRows = 10000 numRows: Int = 10000
scala> val numCols = 1000 numCols: Int = 1000
scala> val data = sc.parallelize(0 to numRows-1).map { _ => Row.fromSeq(Seq.fill(numCols)(Random.nextDouble)) } data: org.apache.spark.rdd.RDD[org.apache.spark.sql.Row] = MapPartitionsRDD[1] at map at :42
scala> val schema = StructType((0 to numCols-1).map { i => StructField("C" + i, DoubleType, true) } ) schema: org.apache.spark.sql.types.StructType = StructType(StructField(C0,DoubleType,true), StructField(C1,DoubleType,true), StructField(C2,DoubleType,true), StructField(C3,DoubleType,true), StructField(C4,DoubleType,true), StructField(C5,DoubleType,true), StructField(C6,DoubleType,true), StructField(C7,DoubleType,true), StructField(C8,DoubleType,true), StructField(C9,DoubleType,true), StructField(C10,DoubleType,true), StructField(C11,DoubleType,true), StructField(C12,DoubleType,true), StructField(C13,DoubleType,true), StructField(C14,DoubleType,true), StructField(C15,DoubleType,true), StructField(C16,DoubleType,true), StructField(C17,DoubleType,true), StructField(C18,DoubleType,true), StructField(C19,DoubleType,true), StructField(C20,DoubleType,true), StructField(C21,DoubleType,true), ... scala> val df = sqlContext.createDataFrame(data, schema) df: org.apache.spark.sql.DataFrame = [C0: double, C1: double, C2: double, C3: double, C4: double, C5: double, C6: double, C7: double, C8: double, C9: double, C10: double, C11: double, C12: double, C13: double, C14: double, C15: double, C16: double, C17: double, C18: double, C19: double, C20: double, C21: double, C22: double, C23: double, C24: double, C25: double, C26: double, C27: double, C28: double, C29: double, C30: double, C31: double, C32: double, C33: double, C34: double, C35: double, C36: double, C37: double, C38: double, C39: double, C40: double, C41: double, C42: double, C43: double, C44: double, C45: double, C46: double, C47: double, C48: double, C49: double, C50: double, C51: double, C52: double, C53: double, C54: double, C55: double, C56: double, C57: double, C58: double, C5...
{% endhighlight %}
We'll create a DML script to find the minimum, maximum, and mean values in a matrix. This
script has one input variable, matrix Xin, and three output variables, minOut, maxOut, and meanOut.
For performance, we'll specify metadata indicating that the matrix has 10,000 rows and 1,000 columns.
We'll create a DML script using the ScriptFactory dml method with the minMaxMean script String. The
input variable is specified to be our DataFrame df with MatrixMetadata mm. The output
variables are specified to be minOut, maxOut, and meanOut. Notice that inputs are supplied by the
in method, and outputs are supplied by the out method.
We execute the script and obtain the results as a Tuple by calling getTuple on the results, specifying
the types and names of the output variables.
{% endhighlight %}
scala> val mm = new MatrixMetadata(numRows, numCols) mm: org.apache.sysml.api.mlcontext.MatrixMetadata = rows: 10000, columns: 1000, non-zeros: None, rows per block: None, columns per block: None
scala> val minMaxMeanScript = dml(minMaxMean).in("Xin", df, mm).out("minOut", "maxOut", "meanOut") minMaxMeanScript: org.apache.sysml.api.mlcontext.Script = Inputs: [1] (DataFrame) Xin: [C0: double, C1: double, C2: double, C3: double, C4: double, C5: double, C6: double, C7: double, ...
Outputs: [1] minOut [2] maxOut [3] meanOut
scala> val (min, max, mean) = ml.execute(minMaxMeanScript).getTuple[Double, Double, Double]("minOut", "maxOut", "meanOut") min: Double = 2.6257349849956313E-8 max: Double = 0.9999999686609718 mean: Double = 0.49996223966662934
{% endhighlight %}
Many different types of input and output variables are automatically allowed. These types include
Boolean, Long, Double, String, Array[Array[Double]], RDD<String> and JavaRDD<String>
in CSV (dense) and IJV (sparse) formats, DataFrame, BinaryBlockMatrix, Matrix, and
Frame. RDDs and JavaRDDs are assumed to be CSV format unless MatrixMetadata is supplied indicating
IJV format.
Let's take a look at an example of input matrices as RDDs in CSV format. We'll create two 2x2 matrices and input these into a DML script. This script will sum each matrix and create a message based on which sum is greater. We will output the sums and the message.
For fun, we'll write the script String to a file and then use ScriptFactory's dmlFromFile method
to create the script object based on the file. We'll also specify the inputs using a Map, although
we could have also chained together two in methods to specify the same inputs.
scala> val rdd2 = sc.parallelize(Array("5.0,6.0", "7.0,8.0")) rdd2: org.apache.spark.rdd.RDD[String] = ParallelCollectionRDD[43] at parallelize at :38
scala> val sums = """ | s1 = sum(m1); | s2 = sum(m2); | if (s1 > s2) { | message = "s1 is greater" | } else if (s2 > s1) { | message = "s2 is greater" | } else { | message = "s1 and s2 are equal" | } | """ sums: String = " s1 = sum(m1); s2 = sum(m2); if (s1 > s2) { message = "s1 is greater" } else if (s2 > s1) { message = "s2 is greater" } else { message = "s1 and s2 are equal" } "
scala> scala.tools.nsc.io.File("sums.dml").writeAll(sums)
scala> val sumScript = dmlFromFile("sums.dml").in(Map("m1"-> rdd1, "m2"-> rdd2)).out("s1", "s2", "message") sumScript: org.apache.sysml.api.mlcontext.Script = Inputs: [1] (RDD) m1: ParallelCollectionRDD[42] at parallelize at :38 [2] (RDD) m2: ParallelCollectionRDD[43] at parallelize at :38
Outputs: [1] s1 [2] s2 [3] message
scala> val sumResults = ml.execute(sumScript) sumResults: org.apache.sysml.api.mlcontext.MLResults = [1] (Double) s1: 10.0 [2] (Double) s2: 26.0 [3] (String) message: s2 is greater
scala> val s1 = sumResults.getDouble("s1") s1: Double = 10.0
scala> val s2 = sumResults.getDouble("s2") s2: Double = 26.0
scala> val message = sumResults.getString("message") message: String = s2 is greater
{% endhighlight %}
If you have metadata that you would like to supply along with the input matrices, this can be accomplished using a Scala Seq, List, or Array.
{% endhighlight %}
scala> val rdd2Metadata = new MatrixMetadata(2, 2) rdd2Metadata: org.apache.sysml.api.mlcontext.MatrixMetadata = rows: 2, columns: 2, non-zeros: None, rows per block: None, columns per block: None
scala> val sumScript = dmlFromFile("sums.dml").in(Seq(("m1", rdd1, rdd1Metadata), ("m2", rdd2, rdd2Metadata))).out("s1", "s2", "message") sumScript: org.apache.sysml.api.mlcontext.Script = Inputs: [1] (RDD) m1: ParallelCollectionRDD[42] at parallelize at :38 [2] (RDD) m2: ParallelCollectionRDD[43] at parallelize at :38
Outputs: [1] s1 [2] s2 [3] message
scala> val (firstSum, secondSum, sumMessage) = ml.execute(sumScript).getTuple[Double, Double, String]("s1", "s2", "message") firstSum: Double = 10.0 secondSum: Double = 26.0 sumMessage: String = s2 is greater
{% endhighlight %}
The same inputs with metadata can be supplied by chaining in methods, as in the example below, which shows that out methods can also be
chained.
{% endhighlight %}
Outputs: [1] s1 [2] s2 [3] message
scala> val (firstSum, secondSum, sumMessage) = ml.execute(sumScript).getTuple[Double, Double, String]("s1", "s2", "message") firstSum: Double = 10.0 secondSum: Double = 26.0 sumMessage: String = s2 is greater
{% endhighlight %}
Let's look at an example of reading a matrix out of SystemML. We'll create a DML script
in which we create a 2x2 matrix m. We'll set the variable n to be the sum of the cells in the matrix.
We create a script object using String s, and we set m and n as the outputs. We execute the script, and in
the results we see we have Matrix m and Double n. The n output variable has a value of 110.0.
We get Matrix m and Double n as a Tuple of values x and y. We then convert Matrix m to an
RDD of IJV values, an RDD of CSV values, a DataFrame, and a two-dimensional Double Array, and we display
the values in each of these data structures.
{% endhighlight %}
scala> val scr = dml(s).out("m", "n"); scr: org.apache.sysml.api.mlcontext.Script = Inputs: None
Outputs: [1] m [2] n
scala> val res = ml.execute(scr) res: org.apache.sysml.api.mlcontext.MLResults = [1] (Matrix) m: Matrix: scratch_space//_p12059_9.31.117.12//_t0/temp26_14, [2 x 2, nnz=4, blocks (1000 x 1000)], binaryblock, dirty [2] (Double) n: 110.0
scala> val (x, y) = res.getTupleMatrix, Double x: org.apache.sysml.api.mlcontext.Matrix = Matrix: scratch_space//_p12059_9.31.117.12//_t0/temp26_14, [2 x 2, nnz=4, blocks (1000 x 1000)], binaryblock, dirty y: Double = 110.0
scala> x.asRDDStringIJV.collect.foreach(println) 1 1 11.0 1 2 22.0 2 1 33.0 2 2 44.0
scala> x.asRDDStringCSV.collect.foreach(println) 11.0,22.0 33.0,44.0
scala> x.asDataFrame.collect.foreach(println) [0.0,11.0,22.0] [1.0,33.0,44.0]
scala> x.asDoubleMatrix res10: Array[Array[Double]] = Array(Array(11.0, 22.0), Array(33.0, 44.0))
{% endhighlight %}
Our next example will involve Haberman's Survival Data Set in CSV format from the Center for Machine Learning and Intelligent Systems. We will run the SystemML Univariate Statistics ("Univar-Stats.dml") script on this data.
We'll pull the data from a URL and convert it to an RDD, habermanRDD. Next, we'll create metadata, habermanMetadata,
stating that the matrix consists of 306 rows and 4 columns.
As we can see from the comments in the script
here, the
script requires a 'TYPES' input matrix that lists the types of the features (1 for scale, 2 for nominal, 3 for
ordinal), so we create a typesRDD matrix consisting of 1 row and 4 columns, with corresponding metadata, typesMetadata.
Next, we create the DML script object called uni using ScriptFactory's dmlFromUrl method, specifying the GitHub URL where the
DML script is located. We bind the habermanRDD matrix to the A variable in Univar-Stats.dml, and we bind
the typesRDD matrix to the K variable. In addition, we supply a $CONSOLE_OUTPUT parameter with a Boolean value
of true, which indicates that we'd like to output labeled results to the console. We'll explain why we bind to the A and K
variables in the Input Variables vs Input Parameters
section below.
{% endhighlight %}
scala> val habermanList = scala.io.Source.fromURL(habermanUrl).mkString.split("\n") habermanList: Array[String] = Array(30,64,1,1, 30,62,3,1, 30,65,0,1, 31,59,2,1, 31,65,4,1, 33,58,10,1, 33,60,0,1, 34,59,0,2, 34,66,9,2, 34,58,30,1, 34,60,1,1, 34,61,10,1, 34,67,7,1, 34,60,0,1, 35,64,13,1, 35,63,0,1, 36,60,1,1, 36,69,0,1, 37,60,0,1, 37,63,0,1, 37,58,0,1, 37,59,6,1, 37,60,15,1, 37,63,0,1, 38,69,21,2, 38,59,2,1, 38,60,0,1, 38,60,0,1, 38,62,3,1, 38,64,1,1, 38,66,0,1, 38,66,11,1, 38,60,1,1, 38,67,5,1, 39,66,0,2, 39,63,0,1, 39,67,0,1, 39,58,0,1, 39,59,2,1, 39,63,4,1, 40,58,2,1, 40,58,0,1, 40,65,0,1, 41,60,23,2, 41,64,0,2, 41,67,0,2, 41,58,0,1, 41,59,8,1, 41,59,0,1, 41,64,0,1, 41,69,8,1, 41,65,0,1, 41,65,0,1, 42,69,1,2, 42,59,0,2, 42,58,0,1, 42,60,1,1, 42,59,2,1, 42,61,4,1, 42,62,20,1, 42,65,0,1, 42,63,1,1, 43,58,52,2, 43,59,2,2, 43,64,0,2, 43,64,0,2, 43,63,14,1, 43,64,2,1, 43... scala> val habermanRDD = sc.parallelize(habermanList) habermanRDD: org.apache.spark.rdd.RDD[String] = ParallelCollectionRDD[159] at parallelize at :43
scala> val habermanMetadata = new MatrixMetadata(306, 4) habermanMetadata: org.apache.sysml.api.mlcontext.MatrixMetadata = rows: 306, columns: 4, non-zeros: None, rows per block: None, columns per block: None
scala> val typesRDD = sc.parallelize(Array("1.0,1.0,1.0,2.0")) typesRDD: org.apache.spark.rdd.RDD[String] = ParallelCollectionRDD[160] at parallelize at :39
scala> val typesMetadata = new MatrixMetadata(1, 4) typesMetadata: org.apache.sysml.api.mlcontext.MatrixMetadata = rows: 1, columns: 4, non-zeros: None, rows per block: None, columns per block: None
scala> val scriptUrl = "https://raw.githubusercontent.com/apache/incubator-systemml/master/scripts/algorithms/Univar-Stats.dml" scriptUrl: String = https://raw.githubusercontent.com/apache/incubator-systemml/master/scripts/algorithms/Univar-Stats.dml
scala> val uni = dmlFromUrl(scriptUrl).in("A", habermanRDD, habermanMetadata).in("K", typesRDD, typesMetadata).in("$CONSOLE_OUTPUT", true) uni: org.apache.sysml.api.mlcontext.Script = Inputs: [1] (RDD) A: ParallelCollectionRDD[159] at parallelize at :43 [2] (RDD) K: ParallelCollectionRDD[160] at parallelize at :39 [3] (Boolean) $CONSOLE_OUTPUT: true
Outputs: None
Feature [1]: Scale (01) Minimum | 30.0 (02) Maximum | 83.0 (03) Range | 53.0 (04) Mean | 52.45751633986928 (05) Variance | 116.71458266366658 (06) Std deviation | 10.803452349303281 (07) Std err of mean | 0.6175922641866753 (08) Coeff of variation | 0.20594669940735139 (09) Skewness | 0.1450718616532357 (10) Kurtosis | -0.6150152487211726 (11) Std err of skewness | 0.13934809593495995 (12) Std err of kurtosis | 0.277810485320835 (13) Median | 52.0 (14) Interquartile mean | 52.16013071895425
Feature [2]: Scale (01) Minimum | 58.0 (02) Maximum | 69.0 (03) Range | 11.0 (04) Mean | 62.85294117647059 (05) Variance | 10.558630665380907 (06) Std deviation | 3.2494046632238507 (07) Std err of mean | 0.18575610076612029 (08) Coeff of variation | 0.051698529971741194 (09) Skewness | 0.07798443581479181 (10) Kurtosis | -1.1324380182967442 (11) Std err of skewness | 0.13934809593495995 (12) Std err of kurtosis | 0.277810485320835 (13) Median | 63.0 (14) Interquartile mean | 62.80392156862745
Feature [3]: Scale (01) Minimum | 0.0 (02) Maximum | 52.0 (03) Range | 52.0 (04) Mean | 4.026143790849673 (05) Variance | 51.691117539912135 (06) Std deviation | 7.189653506248555 (07) Std err of mean | 0.41100513466216837 (08) Coeff of variation | 1.7857418611299172 (09) Skewness | 2.954633471088322 (10) Kurtosis | 11.425776549251449 (11) Std err of skewness | 0.13934809593495995 (12) Std err of kurtosis | 0.277810485320835 (13) Median | 1.0 (14) Interquartile mean | 1.2483660130718954
Feature [4]: Categorical (Nominal) (15) Num of categories | 2 (16) Mode | 1 (17) Num of modes | 1 res23: org.apache.sysml.api.mlcontext.MLResults = None
{% endhighlight %}
Alternatively, we could supply a java.net.URL to the Script in method. Note that if the URL matrix data is in IJV
format, metadata needs to be supplied for the matrix.
scala> val typesRDD = sc.parallelize(Array("1.0,1.0,1.0,2.0")) typesRDD: org.apache.spark.rdd.RDD[String] = ParallelCollectionRDD[50] at parallelize at :33
scala> val scriptUrl = "https://raw.githubusercontent.com/apache/incubator-systemml/master/scripts/algorithms/Univar-Stats.dml" scriptUrl: String = https://raw.githubusercontent.com/apache/incubator-systemml/master/scripts/algorithms/Univar-Stats.dml
scala> val uni = dmlFromUrl(scriptUrl).in("A", new java.net.URL(habermanUrl)).in("K", typesRDD).in("$CONSOLE_OUTPUT", true) uni: org.apache.sysml.api.mlcontext.Script = Inputs: [1] (URL) A: http://archive.ics.uci.edu/ml/machine-learning-databases/haberman/haberman.data [2] (RDD) K: ParallelCollectionRDD[50] at parallelize at :33 [3] (Boolean) $CONSOLE_OUTPUT: true
Outputs: None
(01) Minimum | 30.0 (02) Maximum | 83.0 (03) Range | 53.0 (04) Mean | 52.45751633986928 (05) Variance | 116.71458266366658 (06) Std deviation | 10.803452349303281 (07) Std err of mean | 0.6175922641866753 (08) Coeff of variation | 0.20594669940735139 (09) Skewness | 0.1450718616532357 (10) Kurtosis | -0.6150152487211726 (11) Std err of skewness | 0.13934809593495995 (12) Std err of kurtosis | 0.277810485320835 (13) Median | 52.0 (14) Interquartile mean | 52.16013071895425 Feature [1]: Scale
(01) Minimum | 58.0 (02) Maximum | 69.0 (03) Range | 11.0 (04) Mean | 62.85294117647059 (05) Variance | 10.558630665380907 (06) Std deviation | 3.2494046632238507 (07) Std err of mean | 0.18575610076612029 (08) Coeff of variation | 0.051698529971741194 (09) Skewness | 0.07798443581479181 (10) Kurtosis | -1.1324380182967442 (11) Std err of skewness | 0.13934809593495995 (12) Std err of kurtosis | 0.277810485320835 (13) Median | 63.0 (14) Interquartile mean | 62.80392156862745 Feature [2]: Scale
(01) Minimum | 0.0 (02) Maximum | 52.0 (03) Range | 52.0 (04) Mean | 4.026143790849673 (05) Variance | 51.691117539912135 (06) Std deviation | 7.189653506248555 (07) Std err of mean | 0.41100513466216837 (08) Coeff of variation | 1.7857418611299172 (09) Skewness | 2.954633471088322 (10) Kurtosis | 11.425776549251449 (11) Std err of skewness | 0.13934809593495995 (12) Std err of kurtosis | 0.277810485320835 (13) Median | 1.0 (14) Interquartile mean | 1.2483660130718954 Feature [3]: Scale
Feature [4]: Categorical (Nominal) (15) Num of categories | 2 (16) Mode | 1 (17) Num of modes | 1 res5: org.apache.sysml.api.mlcontext.MLResults = None
{% endhighlight %}
If we examine the
Univar-Stats.dml
file, we see in the comments that it can take 4 input
parameters, $X, $TYPES, $CONSOLE_OUTPUT, and $STATS. Input parameters are typically useful when
executing SystemML in Standalone mode, Spark batch mode, or Hadoop batch mode. For example, $X specifies
the location in the file system where the input data matrix is located, $TYPES specifies the location in the file system
where the input types matrix is located, $CONSOLE_OUTPUT specifies whether or not labeled statistics should be
output to the console, and $STATS specifies the location in the file system where the output matrix should be written.
{% highlight r %} ...
... consoleOutput = ifdef($CONSOLE_OUTPUT, FALSE); A = read($X); # data file K = read($TYPES); # attribute kind file ... write(baseStats, $STATS); ... {% endhighlight %}
Because MLContext is a programmatic interface, it offers more flexibility. You can still use input parameters and files in the file system, such as this example that specifies file paths to the input matrices and the output matrix:
{% highlight scala %} val script = dmlFromFile("scripts/algorithms/Univar-Stats.dml").in("$X", "data/haberman.data").in("$TYPES", "data/types.csv").in("$STATS", "data/univarOut.mtx").in("$CONSOLE_OUTPUT", true) ml.execute(script) {% endhighlight %}
Using the MLContext API, rather than relying solely on input parameters, we can bind to the variables associated
with the read and write statements. In the fragment of Univar-Stats.dml above, notice that the matrix at
path $X is read to variable A, $TYPES is read to variable
K, and baseStats is written to path $STATS. Therefore, we can bind the Haberman input data matrix to the A variable,
the input types matrix to the K variable, and the output matrix to the baseStats variable.
Outputs: [1] baseStats
scala> val baseStats = ml.execute(uni).getMatrix("baseStats") ... baseStats: org.apache.sysml.api.mlcontext.Matrix = Matrix: scratch_space/_p12059_9.31.117.12/parfor/4_resultmerge1, [17 x 4, nnz=44, blocks (1000 x 1000)], binaryblock, dirty
scala> baseStats.asRDDStringIJV.collect.slice(0,9).foreach(println) 1 1 30.0 1 2 58.0 1 3 0.0 1 4 0.0 2 1 83.0 2 2 69.0 2 3 52.0 2 4 0.0 3 1 53.0
{% endhighlight %}
The info method on a Script object can provide useful information about a DML or PyDML script, such as
the inputs, output, symbol table, script string, and the script execution string that is passed to the internals of
SystemML.
scala> val minMaxMeanScript = dml(minMaxMean).in("Xin", df, mm).out("minOut", "maxOut", "meanOut") minMaxMeanScript: org.apache.sysml.api.mlcontext.Script = Inputs: [1] (DataFrame) Xin: [C0: double, C1: double, C2: double, C3: double, C4: double, C5: double, C6: double, C7: double, ...
Outputs: [1] minOut [2] maxOut [3] meanOut
scala> val (min, max, mean) = ml.execute(minMaxMeanScript).getTuple[Double, Double, Double]("minOut", "maxOut", "meanOut") min: Double = 1.4149740823476975E-7 max: Double = 0.9999999956646207 mean: Double = 0.5000954668004209
scala> println(minMaxMeanScript.info) Script Type: DML
Inputs: [1] (DataFrame) Xin: [C0: double, C1: double, C2: double, C3: double, C4: double, C5: double, C6: double, C7: double, ...
Outputs: [1] (Double) minOut: 1.4149740823476975E-7 [2] (Double) maxOut: 0.9999999956646207 [3] (Double) meanOut: 0.5000954668004209
Input Parameters: None
Input Variables: [1] Xin
Output Variables: [1] minOut [2] maxOut [3] meanOut
Symbol Table: [1] (Double) meanOut: 0.5000954668004209 [2] (Double) maxOut: 0.9999999956646207 [3] (Double) minOut: 1.4149740823476975E-7 [4] (Matrix) Xin: Matrix: scratch_space/temp_1166464711339222, [10000 x 1000, nnz=10000000, blocks (1000 x 1000)], binaryblock, not-dirty
Script String:
minOut = min(Xin) maxOut = max(Xin) meanOut = mean(Xin)
Script Execution String: Xin = read('');
minOut = min(Xin) maxOut = max(Xin) meanOut = mean(Xin) write(minOut, ''); write(maxOut, ''); write(meanOut, '');
{% endhighlight %}
Dealing with large matrices can require a significant amount of memory. To deal help deal with this, you
can call a Script object's clearAll method to clear the inputs, outputs, symbol table, and script string.
In terms of memory, the symbol table is most important because it holds references to matrices.
In this example, we display the symbol table of the minMaxMeanScript, call clearAll on the script, and
then display the symbol table, which is empty.
{% endhighlight %}
scala> minMaxMeanScript.clearAll
scala> println(minMaxMeanScript.displaySymbolTable) Symbol Table: None
{% endhighlight %}
The MLContext object holds references to the scripts that have been executed. Calling clear on
the MLContext clears all scripts that it has references to and then removes the references to these
scripts.
{% highlight scala %} ml.clear {% endhighlight %}
Statistics about script executions can be output to the console by calling MLContext's setStatistics
method with a value of true.
{% endhighlight %}
scala> val minMaxMean = | """ | minOut = min(Xin) | maxOut = max(Xin) | meanOut = mean(Xin) | """ minMaxMean: String = " minOut = min(Xin) maxOut = max(Xin) meanOut = mean(Xin) "
scala> val minMaxMeanScript = dml(minMaxMean).in("Xin", df, mm).out("minOut", "maxOut", "meanOut") minMaxMeanScript: org.apache.sysml.api.mlcontext.Script = Inputs: [1] (DataFrame) Xin: [C0: double, C1: double, C2: double, C3: double, C4: double, C5: double, C6: double, C7: double, ...
Outputs: [1] minOut [2] maxOut [3] meanOut
scala> val (min, max, mean) = ml.execute(minMaxMeanScript).getTuple[Double, Double, Double]("minOut", "maxOut", "meanOut") SystemML Statistics: Total elapsed time: 0.000 sec. Total compilation time: 0.000 sec. Total execution time: 0.000 sec. Number of compiled Spark inst: 0. Number of executed Spark inst: 0. Cache hits (Mem, WB, FS, HDFS): 2/0/0/1. Cache writes (WB, FS, HDFS): 1/0/0. Cache times (ACQr/m, RLS, EXP): 3.137/0.000/0.001/0.000 sec. HOP DAGs recompiled (PRED, SB): 0/0. HOP DAGs recompile time: 0.000 sec. Spark ctx create time (lazy): 0.000 sec. Spark trans counts (par,bc,col):0/0/2. Spark trans times (par,bc,col): 0.000/0.000/6.434 secs. Total JIT compile time: 112.372 sec. Total JVM GC count: 54. Total JVM GC time: 9.664 sec. Heavy hitter instructions (name, time, count): -- 1) uamin 3.150 sec 1 -- 2) uamean 0.021 sec 1 -- 3) uamax 0.017 sec 1 -- 4) rmvar 0.000 sec 3 -- 5) assignvar 0.000 sec 3
min: Double = 2.4982850344024143E-8 max: Double = 0.9999997007231808 mean: Double = 0.5002109404821844
{% endhighlight %}
A DML or PyDML script is converted into a SystemML program during script execution. Information
about this program can be displayed by calling MLContext's setExplain method with a value
of true.
{% endhighlight %}
scala> val minMaxMean = | """ | minOut = min(Xin) | maxOut = max(Xin) | meanOut = mean(Xin) | """ minMaxMean: String = " minOut = min(Xin) maxOut = max(Xin) meanOut = mean(Xin) "
scala> val mm = new MatrixMetadata(numRows, numCols) mm: org.apache.sysml.api.mlcontext.MatrixMetadata = rows: 10000, columns: 1000, non-zeros: None, rows per block: None, columns per block: None
scala> val minMaxMeanScript = dml(minMaxMean).in("Xin", df, mm).out("minOut", "maxOut", "meanOut") minMaxMeanScript: org.apache.sysml.api.mlcontext.Script = Inputs: [1] (DataFrame) Xin: [C0: double, C1: double, C2: double, C3: double, C4: double, C5: double, C6: double, C7: double, ...
Outputs: [1] minOut [2] maxOut [3] meanOut
scala> val (min, max, mean) = ml.execute(minMaxMeanScript).getTuple[Double, Double, Double]("minOut", "maxOut", "meanOut")
PROGRAM --MAIN PROGRAM ----GENERIC (lines 1-8) [recompile=false] ------(12) TRead Xin [10000,1000,1000,1000,10000000] [0,0,76 -> 76MB] [chkpt], CP ------(13) ua(minRC) (12) [0,0,-1,-1,-1] [76,0,0 -> 76MB], CP ------(21) TWrite minOut (13) [0,0,-1,-1,-1] [0,0,0 -> 0MB], CP ------(14) ua(maxRC) (12) [0,0,-1,-1,-1] [76,0,0 -> 76MB], CP ------(27) TWrite maxOut (14) [0,0,-1,-1,-1] [0,0,0 -> 0MB], CP ------(15) ua(meanRC) (12) [0,0,-1,-1,-1] [76,0,0 -> 76MB], CP ------(33) TWrite meanOut (15) [0,0,-1,-1,-1] [0,0,0 -> 0MB], CP
min: Double = 5.16651366133658E-9 max: Double = 0.9999999368927975 mean: Double = 0.5001096515241128
{% endhighlight %}
Different explain levels can be set. The explain levels are NONE, HOPS, RUNTIME, RECOMPILE_HOPS, and RECOMPILE_RUNTIME.
scala> val (min, max, mean) = ml.execute(minMaxMeanScript).getTuple[Double, Double, Double]("minOut", "maxOut", "meanOut")
PROGRAM ( size CP/SP = 9/0 ) --MAIN PROGRAM ----GENERIC (lines 1-8) [recompile=false] ------CP uamin Xin.MATRIX.DOUBLE _Var8.SCALAR.DOUBLE 8 ------CP uamax Xin.MATRIX.DOUBLE _Var9.SCALAR.DOUBLE 8 ------CP uamean Xin.MATRIX.DOUBLE _Var10.SCALAR.DOUBLE 8 ------CP assignvar _Var8.SCALAR.DOUBLE.false minOut.SCALAR.DOUBLE ------CP assignvar _Var9.SCALAR.DOUBLE.false maxOut.SCALAR.DOUBLE ------CP assignvar _Var10.SCALAR.DOUBLE.false meanOut.SCALAR.DOUBLE ------CP rmvar _Var8 ------CP rmvar _Var9 ------CP rmvar _Var10
min: Double = 5.16651366133658E-9 max: Double = 0.9999999368927975 mean: Double = 0.5001096515241128
{% endhighlight %}
Script objects can be created using standard Script constructors. A Script can be of two types: DML (R-based syntax) and PYDML (Python-based syntax). If no ScriptType is specified, the default Script type is DML.
scala> val script = new Script(ScriptType.PYDML); ... scala> println(script.getScriptType) PYDML
{% endhighlight %}
The ScriptFactory class offers convenient methods for creating DML and PYDML scripts from a variety of sources. ScriptFactory can create a script object from a String, File, URL, or InputStream.
Script from URL:
Here we create Script object s1 by reading Univar-Stats.dml from a URL.
{% highlight scala %} val uniUrl = "https://raw.githubusercontent.com/apache/incubator-systemml/master/scripts/algorithms/Univar-Stats.dml" val s1 = ScriptFactory.dmlFromUrl(scriptUrl) {% endhighlight %}
Script from String:
We create Script objects s2 and s3 from Strings using ScriptFactory's dml and dmlFromString methods.
Both methods perform the same action. This example reads an algorithm at a URL to String uniString and then
creates two script objects based on this String.
{% highlight scala %} val uniUrl = "https://raw.githubusercontent.com/apache/incubator-systemml/master/scripts/algorithms/Univar-Stats.dml" val uniString = scala.io.Source.fromURL(uniUrl).mkString val s2 = ScriptFactory.dml(uniString) val s3 = ScriptFactory.dmlFromString(uniString) {% endhighlight %}
Script from File:
We create Script object s4 based on a path to a file using ScriptFactory's dmlFromFile method. This example
reads a URL to a String, writes this String to a file, and then uses the path to the file to create a Script object.
{% highlight scala %} val uniUrl = "https://raw.githubusercontent.com/apache/incubator-systemml/master/scripts/algorithms/Univar-Stats.dml" val uniString = scala.io.Source.fromURL(uniUrl).mkString scala.tools.nsc.io.File("uni.dml").writeAll(uniString) val s4 = ScriptFactory.dmlFromFile("uni.dml") {% endhighlight %}
Script from InputStream:
The SystemML jar file contains all the primary algorithm scripts. We can read one of these scripts as an InputStream and use this to create a Script object.
{% highlight scala %} val inputStream = getClass.getResourceAsStream("/scripts/algorithms/Univar-Stats.dml") val s5 = ScriptFactory.dmlFromInputStream(inputStream) {% endhighlight %}
Script from Resource:
As mentioned, the SystemML jar file contains all the primary algorithm script files. For convenience, we can
read these script files or other script files on the classpath using ScriptFactory's dmlFromResource and pydmlFromResource
methods.
{% highlight scala %} val s6 = ScriptFactory.dmlFromResource("/scripts/algorithms/Univar-Stats.dml"); {% endhighlight %}
A Script is executed by a ScriptExecutor. If no ScriptExecutor is specified, a default ScriptExecutor will be created to execute a Script. Script execution consists of several steps, as detailed in SystemML's Optimizer: Plan Generation for Large-Scale Machine Learning Programs. Additional information can be found in the Javadocs for ScriptExecutor.
Advanced users may find it useful to be able to specify their own execution or to override ScriptExecutor methods by subclassing ScriptExecutor.
In this example, we override the parseScript and validateScript methods to display messages to the console
during these execution steps.
{% endhighlight %}
scala> val helloScript = dml("print('hello world')") helloScript: org.apache.sysml.api.mlcontext.Script = Inputs: None
Outputs: None
scala> ml.execute(helloScript, new MyScriptExecutor) Parsing script Validating script hello world res63: org.apache.sysml.api.mlcontext.MLResults = None
{% endhighlight %}
When supplying matrix data to Apache SystemML using the MLContext API, matrix metadata can be
supplied using a MatrixMetadata object. Supplying characteristics about a matrix can significantly
improve performance. For some types of input matrices, supplying metadata is mandatory.
Metadata at a minimum typically consists of the number of rows and columns in
a matrix. The number of non-zeros can also be supplied.
Additionally, the number of rows and columns per block can be supplied, although in typical usage it's probably fine to use the default values used by SystemML (1,000 rows and 1,000 columns per block). SystemML handles a matrix internally by splitting the matrix into chunks, or blocks. The number of rows and columns per block refers to the size of these matrix blocks.
CSV RDD with No Metadata:
Here we see an example of inputting an RDD of Strings in CSV format with no metadata. Note that in general it is recommended that metadata is supplied. We output the sum and mean of the cells in the matrix.
{% endhighlight %}
scala> val sumAndMean = dml("sum = sum(m); mean = mean(m)").in("m", rddCSV).out("sum", "mean") sumAndMean: org.apache.sysml.api.mlcontext.Script = Inputs: [1] (RDD) m: ParallelCollectionRDD[190] at parallelize at :38
Outputs: [1] sum [2] mean
scala> ml.execute(sumAndMean) res20: org.apache.sysml.api.mlcontext.MLResults = [1] (Double) sum: 10.0 [2] (Double) mean: 2.5
{% endhighlight %}
IJV RDD with Metadata:
Next, we'll supply an RDD in IJV format. IJV is a sparse format where each line has three space-separated values. The first value indicates the row number, the second value indicates the column number, and the third value indicates the cell value. Since the total numbers of rows and columns can't be determined from these IJV rows, we need to supply metadata describing the matrix size.
Here, we specify that our matrix has 3 rows and 3 columns.
{% endhighlight %}
scala> val mm3x3 = new MatrixMetadata(MatrixFormat.IJV, 3, 3) mm3x3: org.apache.sysml.api.mlcontext.MatrixMetadata = rows: 3, columns: 3, non-zeros: None, rows per block: None, columns per block: None
scala> val sumAndMean = dml("sum = sum(m); mean = mean(m)").in("m", rddIJV, mm3x3).out("sum", "mean") sumAndMean: org.apache.sysml.api.mlcontext.Script = Inputs: [1] (RDD) m: ParallelCollectionRDD[202] at parallelize at :38
Outputs: [1] sum [2] mean
scala> ml.execute(sumAndMean) res21: org.apache.sysml.api.mlcontext.MLResults = [1] (Double) sum: 10.0 [2] (Double) mean: 1.1111111111111112
{% endhighlight %}
Next, we'll run the same DML, but this time we'll specify that the input matrix is 4x4 instead of 3x3.
{% endhighlight %}
scala> val mm4x4 = new MatrixMetadata(MatrixFormat.IJV, 4, 4) mm4x4: org.apache.sysml.api.mlcontext.MatrixMetadata = rows: 4, columns: 4, non-zeros: None, rows per block: None, columns per block: None
scala> val sumAndMean = dml("sum = sum(m); mean = mean(m)").in("m", rddIJV, mm4x4).out("sum", "mean") sumAndMean: org.apache.sysml.api.mlcontext.Script = Inputs: [1] (RDD) m: ParallelCollectionRDD[210] at parallelize at :38
Outputs: [1] sum [2] mean
scala> ml.execute(sumAndMean) res22: org.apache.sysml.api.mlcontext.MLResults = [1] (Double) sum: 10.0 [2] (Double) mean: 0.625
{% endhighlight %}
Internally, Apache SystemML uses a binary-block matrix representation, where a matrix is represented as a grouping of blocks. Each block is equal in size to the other blocks in the matrix and consists of a number of rows and columns. The default block size is 1,000 rows by 1,000 columns.
Conversion of a large set of data to a SystemML matrix representation can potentially be time-consuming. Therefore, if you use a set of data multiple times, one way to potentially improve performance is to convert it to a SystemML matrix representation and then use this representation rather than performing the data conversion each time.
There are currently two mechanisms for this in SystemML: (1) BinaryBlockMatrix and (2) Matrix.
BinaryBlockMatrix:
If you have an input DataFrame, it can be converted to a BinaryBlockMatrix, and this BinaryBlockMatrix can be passed as an input rather than passing in the DataFrame as an input.
For example, suppose we had a 10000x1000 matrix represented as a DataFrame, as we saw in an earlier example. Now suppose we create two Script objects with the DataFrame as an input, as shown below. In the Spark Shell, when executing this code, you can see that each of the two Script object creations requires the time-consuming data conversion step.
{% highlight scala %} import org.apache.spark.sql._ import org.apache.spark.sql.types.{StructType,StructField,DoubleType} import scala.util.Random val numRows = 10000 val numCols = 1000 val data = sc.parallelize(0 to numRows-1).map { _ => Row.fromSeq(Seq.fill(numCols)(Random.nextDouble)) } val schema = StructType((0 to numCols-1).map { i => StructField("C" + i, DoubleType, true) } ) val df = sqlContext.createDataFrame(data, schema) val mm = new MatrixMetadata(numRows, numCols) val minMaxMeanScript = dml(minMaxMean).in("Xin", df, mm).out("minOut", "maxOut", "meanOut") val minMaxMeanScript = dml(minMaxMean).in("Xin", df, mm).out("minOut", "maxOut", "meanOut") {% endhighlight %}
Rather than passing in a DataFrame each time to the Script object creation, let's instead create a BinaryBlockMatrix object based on the DataFrame and pass this BinaryBlockMatrix to the Script object creation. If we run the code below in the Spark Shell, we see that the data conversion step occurs when the BinaryBlockMatrix object is created. However, when we create a Script object twice, we see that no conversion penalty occurs, since this conversion occurred when the BinaryBlockMatrix was created.
{% highlight scala %} import org.apache.spark.sql._ import org.apache.spark.sql.types.{StructType,StructField,DoubleType} import scala.util.Random val numRows = 10000 val numCols = 1000 val data = sc.parallelize(0 to numRows-1).map { _ => Row.fromSeq(Seq.fill(numCols)(Random.nextDouble)) } val schema = StructType((0 to numCols-1).map { i => StructField("C" + i, DoubleType, true) } ) val df = sqlContext.createDataFrame(data, schema) val mm = new MatrixMetadata(numRows, numCols) val bbm = new BinaryBlockMatrix(df, mm) val minMaxMeanScript = dml(minMaxMean).in("Xin", bbm).out("minOut", "maxOut", "meanOut") val minMaxMeanScript = dml(minMaxMean).in("Xin", bbm).out("minOut", "maxOut", "meanOut") {% endhighlight %}
Matrix:
When a matrix is returned as an output, it is returned as a Matrix object, which is a wrapper around a SystemML MatrixObject. As a result, an output Matrix is already in a SystemML representation, meaning that it can be passed as an input with no data conversion penalty.
As an example, here we read in matrix x as an RDD in CSV format. We create a Script that adds one to all
values in the matrix. We obtain the resulting matrix y as a Matrix. We execute the
script five times, feeding the output matrix as the input matrix for the next script execution.
{% endhighlight %}
scala> val add = dml("y = x + 1").in("x", rddCSV).out("y") add: org.apache.sysml.api.mlcontext.Script = Inputs: [1] (RDD) x: ParallelCollectionRDD[341] at parallelize at :53
Outputs: [1] y
scala> for (i <- 1 to 5) { | println("#" + i + ":"); | val m = ml.execute(add).getMatrix("y") | m.asRDDStringCSV.collect.foreach(println) | add.in("x", m) | } #1: 2.0,3.0 4.0,5.0 #2: 3.0,4.0 5.0,6.0 #3: 4.0,5.0 6.0,7.0 #4: 5.0,6.0 7.0,8.0 #5: 6.0,7.0 8.0,9.0
{% endhighlight %}
Next, we'll consider an example of a SystemML linear regression algorithm run from Spark through an Apache Zeppelin notebook. Instructions to clone and build Zeppelin can be found at the GitHub Apache Zeppelin site. This example also will look at the Spark ML linear regression algorithm.
This Zeppelin notebook example can be imported by choosing Import note -> Add from URL from the Zeppelin main page, then insert the following URL:
https://raw.githubusercontent.com/apache/incubator-systemml/master/samples/zeppelin-notebooks/2AZ2AQ12B/note.json
Alternatively download note.json, then import it by choosing Import note -> Choose a JSON here from the Zeppelin main page.
A conf/zeppelin-env.sh file is created based on conf/zeppelin-env.sh.template. For
this demonstration, it features SPARK_HOME, SPARK_SUBMIT_OPTIONS, and ZEPPELIN_SPARK_USEHIVECONTEXT
environment variables:
export SPARK_HOME=/Users/example/spark-1.5.1-bin-hadoop2.6
export SPARK_SUBMIT_OPTIONS="--jars /Users/example/systemml/system-ml/target/SystemML.jar"
export ZEPPELIN_SPARK_USEHIVECONTEXT=false
Start Zeppelin using the zeppelin.sh script:
bin/zeppelin.sh
After opening Zeppelin in a brower, we see the "SystemML - Linear Regression" note in the list of available Zeppelin notes.
If we go to the "SystemML - Linear Regression" note, we see that the note consists of several cells of code.
Let's briefly consider these cells.
This cell triggers Spark to initialize by calling the SparkContext sc object. Information regarding these startup operations can be viewed in the
console window in which zeppelin.sh is running.
Cell: {% highlight scala %} // Trigger Spark Startup sc {% endhighlight %}
Output: {% highlight scala %} res8: org.apache.spark.SparkContext = org.apache.spark.SparkContext@6ce70bf3 {% endhighlight %}
The Spark LinearDataGenerator is used to generate test data for the Spark ML and SystemML linear regression algorithms.
Cell: {% highlight scala %} // Generate data import org.apache.spark.mllib.util.LinearDataGenerator
val numRows = 10000 val numCols = 1000 val rawData = LinearDataGenerator.generateLinearRDD(sc, numRows, numCols, 1).toDF()
// Repartition into a more parallelism-friendly number of partitions val data = rawData.repartition(64).cache() {% endhighlight %}
Output: {% highlight scala %} import org.apache.spark.mllib.util.LinearDataGenerator numRows: Int = 10000 numCols: Int = 1000 rawData: org.apache.spark.sql.DataFrame = [label: double, features: vector] data: org.apache.spark.sql.DataFrame = [label: double, features: vector] {% endhighlight %}
For purpose of comparison, we can train a model using the Spark ML linear regression algorithm.
Cell: {% highlight scala %} // Spark ML import org.apache.spark.ml.regression.LinearRegression
// Model Settings val maxIters = 100 val reg = 0 val elasticNetParam = 0 // L2 reg
// Fit the model val lr = new LinearRegression() .setMaxIter(maxIters) .setRegParam(reg) .setElasticNetParam(elasticNetParam) val start = System.currentTimeMillis() val model = lr.fit(data) val trainingTime = (System.currentTimeMillis() - start).toDouble / 1000.0
// Summarize the model over the training set and gather some metrics val trainingSummary = model.summary val r2 = trainingSummary.r2 val iters = trainingSummary.totalIterations val trainingTimePerIter = trainingTime / iters {% endhighlight %}
Output: {% highlight scala %} import org.apache.spark.ml.regression.LinearRegression maxIters: Int = 100 reg: Int = 0 elasticNetParam: Int = 0 lr: org.apache.spark.ml.regression.LinearRegression = linReg_a7f51d676562 start: Long = 1444672044647 model: org.apache.spark.ml.regression.LinearRegressionModel = linReg_a7f51d676562 trainingTime: Double = 12.985 trainingSummary: org.apache.spark.ml.regression.LinearRegressionTrainingSummary = org.apache.spark.ml.regression.LinearRegressionTrainingSummary@227ba28b r2: Double = 0.9677118209276552 iters: Int = 17 trainingTimePerIter: Double = 0.7638235294117647 {% endhighlight %}
Summary statistics for the Spark ML linear regression algorithm are displayed by this cell.
Cell:
{% highlight scala %}
// Print statistics
println(s"R2:
Output: {% highlight scala %} R2: 0.9677118209276552 Iterations: 17 Training time per iter: 0.7638235294117647 seconds {% endhighlight %}
The linearReg fixed String variable is set to
a linear regression algorithm written in DML, SystemML's Declarative Machine Learning language.
Cell: {% highlight scala %} // SystemML kernels val linearReg = """
fileX = ""; fileY = ""; fileB = "";
intercept_status = ifdef ($icpt, 0); # $icpt=0; tolerance = ifdef ($tol, 0.000001); # $tol=0.000001; max_iteration = ifdef ($maxi, 0); # $maxi=0; regularization = ifdef ($reg, 0.000001); # $reg=0.000001;
X = read (fileX); y = read (fileY);
n = nrow (X); m = ncol (X); ones_n = matrix (1, rows = n, cols = 1); zero_cell = matrix (0, rows = 1, cols = 1);
m_ext = m; if (intercept_status == 1 | intercept_status == 2) # add the intercept column { X = append (X, ones_n); m_ext = ncol (X); }
scale_lambda = matrix (1, rows = m_ext, cols = 1); if (intercept_status == 1 | intercept_status == 2) { scale_lambda [m_ext, 1] = 0; }
if (intercept_status == 2) # scale-&-shift X columns to mean 0, variance 1 { # Important assumption: X [, m_ext] = ones_n avg_X_cols = t(colSums(X)) / n; var_X_cols = (t(colSums (X ^ 2)) - n * (avg_X_cols ^ 2)) / (n - 1); is_unsafe = ppred (var_X_cols, 0.0, "<="); scale_X = 1.0 / sqrt (var_X_cols * (1 - is_unsafe) + is_unsafe); scale_X [m_ext, 1] = 1; shift_X = - avg_X_cols * scale_X; shift_X [m_ext, 1] = 0; } else { scale_X = matrix (1, rows = m_ext, cols = 1); shift_X = matrix (0, rows = m_ext, cols = 1); }
lambda = scale_lambda * regularization; beta_unscaled = matrix (0, rows = m_ext, cols = 1);
if (max_iteration == 0) { max_iteration = m_ext; } i = 0;
r = - t(X) %*% y;
if (intercept_status == 2) { r = scale_X * r + shift_X %*% r [m_ext, ]; }
p = - r; norm_r2 = sum (r ^ 2); norm_r2_initial = norm_r2; norm_r2_target = norm_r2_initial * tolerance ^ 2;
while (i < max_iteration & norm_r2 > norm_r2_target) { if (intercept_status == 2) { ssX_p = scale_X * p; ssX_p [m_ext, ] = ssX_p [m_ext, ] + t(shift_X) %*% p; } else { ssX_p = p; }
q = t(X) %*% (X %*% ssX_p);
if (intercept_status == 2) {
q = scale_X * q + shift_X %*% q [m_ext, ];
}
q = q + lambda * p;
a = norm_r2 / sum (p * q);
beta_unscaled = beta_unscaled + a * p;
r = r + a * q;
old_norm_r2 = norm_r2;
norm_r2 = sum (r ^ 2);
p = -r + (norm_r2 / old_norm_r2) * p;
i = i + 1;
}
if (intercept_status == 2) { beta = scale_X * beta_unscaled; beta [m_ext, ] = beta [m_ext, ] + t(shift_X) %*% beta_unscaled; } else { beta = beta_unscaled; }
avg_tot = sum (y) / n; ss_tot = sum (y ^ 2); ss_avg_tot = ss_tot - n * avg_tot ^ 2; var_tot = ss_avg_tot / (n - 1); y_residual = y - X %*% beta; avg_res = sum (y_residual) / n; ss_res = sum (y_residual ^ 2); ss_avg_res = ss_res - n * avg_res ^ 2;
R2_temp = 1 - ss_res / ss_avg_tot R2 = matrix(R2_temp, rows=1, cols=1) write(R2, "")
totalIters = matrix(i, rows=1, cols=1) write(totalIters, "")
if (intercept_status == 2) { beta_out = append (beta, beta_unscaled); } else { beta_out = beta; }
write (beta_out, fileB); """ {% endhighlight %}
Output:
None
This cell contains helper methods to return Double and Int values from output generated by the MLContext API.
Cell: {% highlight scala %} // Helper functions import org.apache.sysml.api.MLOutput
def getScalar(outputs: MLOutput, symbol: String): Any = outputs.getDF(sqlContext, symbol).first()(1)
def getScalarDouble(outputs: MLOutput, symbol: String): Double = getScalar(outputs, symbol).asInstanceOf[Double]
def getScalarInt(outputs: MLOutput, symbol: String): Int = getScalarDouble(outputs, symbol).toInt {% endhighlight %}
Output: {% highlight scala %} import org.apache.sysml.api.MLOutput getScalar: (outputs: org.apache.sysml.api.MLOutput, symbol: String)Any getScalarDouble: (outputs: org.apache.sysml.api.MLOutput, symbol: String)Double getScalarInt: (outputs: org.apache.sysml.api.MLOutput, symbol: String)Int {% endhighlight %}
SystemML uses a binary-block format for matrix data representation. This cell
explicitly converts the DataFrame data object to a binary-block features matrix
and single-column label matrix, both represented by the
JavaPairRDD[MatrixIndexes, MatrixBlock] datatype.
Cell: {% highlight scala %} // Imports import org.apache.sysml.api.MLContext import org.apache.sysml.runtime.instructions.spark.utils.{RDDConverterUtilsExt => RDDConverterUtils} import org.apache.sysml.runtime.matrix.MatrixCharacteristics;
// Create SystemML context val ml = new MLContext(sc)
// Convert data to proper format val mcX = new MatrixCharacteristics(numRows, numCols, 1000, 1000) val mcY = new MatrixCharacteristics(numRows, 1, 1000, 1000) val X = RDDConverterUtils.vectorDataFrameToBinaryBlock(sc, data, mcX, false, "features") val y = RDDConverterUtils.dataFrameToBinaryBlock(sc, data.select("label"), mcY, false) // val y = data.select("label")
// Cache val X2 = X.cache() val y2 = y.cache() val cnt1 = X2.count() val cnt2 = y2.count() {% endhighlight %}
Output: {% highlight scala %} import org.apache.sysml.api.MLContext import org.apache.sysml.runtime.instructions.spark.utils.{RDDConverterUtilsExt=>RDDConverterUtils} import org.apache.sysml.runtime.matrix.MatrixCharacteristics ml: org.apache.sysml.api.MLContext = org.apache.sysml.api.MLContext@38d59245 mcX: org.apache.sysml.runtime.matrix.MatrixCharacteristics = [10000 x 1000, nnz=-1, blocks (1000 x 1000)] mcY: org.apache.sysml.runtime.matrix.MatrixCharacteristics = [10000 x 1, nnz=-1, blocks (1000 x 1000)] X: org.apache.spark.api.java.JavaPairRDD[org.apache.sysml.runtime.matrix.data.MatrixIndexes,org.apache.sysml.runtime.matrix.data.MatrixBlock] = org.apache.spark.api.java.JavaPairRDD@b5a86e3 y: org.apache.spark.api.java.JavaPairRDD[org.apache.sysml.runtime.matrix.data.MatrixIndexes,org.apache.sysml.runtime.matrix.data.MatrixBlock] = org.apache.spark.api.java.JavaPairRDD@56377665 X2: org.apache.spark.api.java.JavaPairRDD[org.apache.sysml.runtime.matrix.data.MatrixIndexes,org.apache.sysml.runtime.matrix.data.MatrixBlock] = org.apache.spark.api.java.JavaPairRDD@650f29d2 y2: org.apache.spark.api.java.JavaPairRDD[org.apache.sysml.runtime.matrix.data.MatrixIndexes,org.apache.sysml.runtime.matrix.data.MatrixBlock] = org.apache.spark.api.java.JavaPairRDD@334857a8 cnt1: Long = 10 cnt2: Long = 10 {% endhighlight %}
Now, we can train our model using the SystemML linear regression algorithm. We register the features matrix X and the label matrix y as inputs. We register the beta_out matrix,
R2, and totalIters as outputs.
Cell:
{% highlight scala %}
// Register inputs & outputs
ml.reset()
ml.registerInput("X", X, numRows, numCols)
ml.registerInput("y", y, numRows, 1)
// ml.registerInput("y", y)
ml.registerOutput("beta_out")
ml.registerOutput("R2")
ml.registerOutput("totalIters")
// Run the script val start = System.currentTimeMillis() val outputs = ml.executeScript(linearReg) val trainingTime = (System.currentTimeMillis() - start).toDouble / 1000.0
// Get outputs val B = outputs.getDF(sqlContext, "beta_out").sort("ID").drop("ID") val r2 = getScalarDouble(outputs, "R2") val iters = getScalarInt(outputs, "totalIters") val trainingTimePerIter = trainingTime / iters {% endhighlight %}
Output: {% highlight scala %} start: Long = 1444672090620 outputs: org.apache.sysml.api.MLOutput = org.apache.sysml.api.MLOutput@5d2c22d0 trainingTime: Double = 1.176 B: org.apache.spark.sql.DataFrame = [C1: double] r2: Double = 0.9677079547216473 iters: Int = 12 trainingTimePerIter: Double = 0.09799999999999999 {% endhighlight %}
SystemML linear regression summary statistics are displayed by this cell.
Cell:
{% highlight scala %}
// Print statistics
println(s"R2:
Output: {% highlight scala %} R2: 0.9677079547216473 Iterations: 12 Training time per iter: 0.2334166666666667 seconds +-------+-------------------+ |summary| C1| +-------+-------------------+ | count| 1000| | mean| 0.0184500840658385| | stddev| 0.2764750319432085| | min|-0.5426068958986378| | max| 0.5225309861616542| +-------+-------------------+ {% endhighlight %}
Here, we'll explore the use of SystemML via PySpark in a Jupyter notebook. This Jupyter notebook example can be nicely viewed in a rendered state on GitHub, and can be downloaded here to a directory of your choice.
From the directory with the downloaded notebook, start Jupyter with PySpark:
PYSPARK_DRIVER_PYTHON=jupyter PYSPARK_DRIVER_PYTHON_OPTS="notebook" $SPARK_HOME/bin/pyspark --master local[*] --driver-class-path $SYSTEMML_HOME/SystemML.jar
This will open Jupyter in a browser:
We can then open up the SystemML-PySpark-Recommendation-Demo notebook:
{% highlight python %} %load_ext autoreload %autoreload 2 %matplotlib inline
import numpy as np import matplotlib.pyplot as plt plt.rcParams['figure.figsize'] = (10, 6) {% endhighlight %}
{% highlight python %} %%sh
curl -O http://snap.stanford.edu/data/amazon0601.txt.gz gunzip amazon0601.txt.gz {% endhighlight %}
{% highlight python %}
import pyspark.sql.functions as F dataPath = "amazon0601.txt"
X_train = (sc.textFile(dataPath) .filter(lambda l: not l.startswith("#")) .map(lambda l: l.split("\t")) .map(lambda prods: (int(prods[0]), int(prods[1]), 1.0)) .toDF(("prod_i", "prod_j", "x_ij")) .filter("prod_i < 500 AND prod_j < 500") # Filter for memory constraints .cache())
max_prod_i = X_train.select(F.max("prod_i")).first()[0] max_prod_j = X_train.select(F.max("prod_j")).first()[0] numProducts = max(max_prod_i, max_prod_j) + 1 # 0-based indexing print("Total number of products: {}".format(numProducts)) {% endhighlight %}
{% highlight python %}
from SystemML import MLContext ml = MLContext(sc) {% endhighlight %}
{% highlight python %}
pnmf = """
X = read($X) X = X+1 # change product IDs to be 1-based, rather than 0-based V = table(X[,1], X[,2]) size = ifdef($size, -1) if(size > -1) { V = V[1:size,1:size] } max_iteration = as.integer($maxiter) rank = as.integer($rank)
n = nrow(V) m = ncol(V) range = 0.01 W = Rand(rows=n, cols=rank, min=0, max=range, pdf="uniform") H = Rand(rows=rank, cols=m, min=0, max=range, pdf="uniform") losses = matrix(0, rows=max_iteration, cols=1)
i=1 while(i <= max_iteration) {
H = (H * (t(W) %% (V/(W%%H))))/t(colSums(W)) W = (W * ((V/(W%%H)) %% t(H)))/t(rowSums(H))
losses[i,] = -1 * (sum(Vlog(W%%H)) - as.scalar(colSums(W)%*%rowSums(H))) i = i + 1; }
write(losses, $lossout) write(W, $Wout) write(H, $Hout) """ {% endhighlight %}
{% highlight python %}
ml.reset() outputs = ml.executeScript(pnmf, {"X": X_train, "maxiter": 100, "rank": 10}, ["W", "H", "losses"]) {% endhighlight %}
{% highlight python %}
losses = outputs.getDF(sqlContext, "losses") xy = losses.sort(losses.ID).map(lambda r: (r[0], r[1])).collect() x, y = zip(*xy) plt.plot(x, y) plt.xlabel('Iteration') plt.ylabel('Loss') plt.title('PNMF Training Loss') {% endhighlight %}
For best performance, we recommend setting the following flags when running SystemML with Spark:
--conf spark.driver.maxResultSize=0 --conf spark.akka.frameSize=128.