Repository: spark Updated Branches: refs/heads/master ed730c950 -> 9c65fa76f
http://git-wip-us.apache.org/repos/asf/spark/blob/9c65fa76/mllib/src/main/scala/org/apache/spark/mllib/util/MLUtils.scala ---------------------------------------------------------------------- diff --git a/mllib/src/main/scala/org/apache/spark/mllib/util/MLUtils.scala b/mllib/src/main/scala/org/apache/spark/mllib/util/MLUtils.scala index 08cd9ab..cb85e43 100644 --- a/mllib/src/main/scala/org/apache/spark/mllib/util/MLUtils.scala +++ b/mllib/src/main/scala/org/apache/spark/mllib/util/MLUtils.scala @@ -17,15 +17,13 @@ package org.apache.spark.mllib.util +import breeze.linalg.{Vector => BV, DenseVector => BDV, SparseVector => BSV, + squaredDistance => breezeSquaredDistance} + import org.apache.spark.SparkContext import org.apache.spark.rdd.RDD -import org.apache.spark.SparkContext._ - -import org.jblas.DoubleMatrix - import org.apache.spark.mllib.regression.LabeledPoint - -import breeze.linalg.{Vector => BV, SparseVector => BSV, squaredDistance => breezeSquaredDistance} +import org.apache.spark.mllib.linalg.{Vector, Vectors} /** * Helper methods to load, save and pre-process data used in ML Lib. @@ -41,6 +39,107 @@ object MLUtils { } /** + * Multiclass label parser, which parses a string into double. + */ + val multiclassLabelParser: String => Double = _.toDouble + + /** + * Binary label parser, which outputs 1.0 (positive) if the value is greater than 0.5, + * or 0.0 (negative) otherwise. + */ + val binaryLabelParser: String => Double = label => if (label.toDouble > 0.5) 1.0 else 0.0 + + /** + * Loads labeled data in the LIBSVM format into an RDD[LabeledPoint]. + * The LIBSVM format is a text-based format used by LIBSVM and LIBLINEAR. + * Each line represents a labeled sparse feature vector using the following format: + * {{{label index1:value1 index2:value2 ...}}} + * where the indices are one-based and in ascending order. + * This method parses each line into a [[org.apache.spark.mllib.regression.LabeledPoint]], + * where the feature indices are converted to zero-based. + * + * @param sc Spark context + * @param path file or directory path in any Hadoop-supported file system URI + * @param labelParser parser for labels, default: 1.0 if label > 0.5 or 0.0 otherwise + * @param numFeatures number of features, which will be determined from the input data if a + * negative value is given. The default value is -1. + * @param minSplits min number of partitions, default: sc.defaultMinSplits + * @return labeled data stored as an RDD[LabeledPoint] + */ + def loadLibSVMData( + sc: SparkContext, + path: String, + labelParser: String => Double, + numFeatures: Int, + minSplits: Int): RDD[LabeledPoint] = { + val parsed = sc.textFile(path, minSplits) + .map(_.trim) + .filter(!_.isEmpty) + .map(_.split(' ')) + // Determine number of features. + val d = if (numFeatures >= 0) { + numFeatures + } else { + parsed.map { items => + if (items.length > 1) { + items.last.split(':')(0).toInt + } else { + 0 + } + }.reduce(math.max) + } + parsed.map { items => + val label = labelParser(items.head) + val (indices, values) = items.tail.map { item => + val indexAndValue = item.split(':') + val index = indexAndValue(0).toInt - 1 + val value = indexAndValue(1).toDouble + (index, value) + }.unzip + LabeledPoint(label, Vectors.sparse(d, indices.toArray, values.toArray)) + } + } + + // Convenient methods for calling from Java. + + /** + * Loads binary labeled data in the LIBSVM format into an RDD[LabeledPoint], + * with number of features determined automatically and the default number of partitions. + */ + def loadLibSVMData(sc: SparkContext, path: String): RDD[LabeledPoint] = + loadLibSVMData(sc, path, binaryLabelParser, -1, sc.defaultMinSplits) + + /** + * Loads binary labeled data in the LIBSVM format into an RDD[LabeledPoint], + * with number of features specified explicitly and the default number of partitions. + */ + def loadLibSVMData(sc: SparkContext, path: String, numFeatures: Int): RDD[LabeledPoint] = + loadLibSVMData(sc, path, binaryLabelParser, numFeatures, sc.defaultMinSplits) + + /** + * Loads labeled data in the LIBSVM format into an RDD[LabeledPoint], + * with the given label parser, number of features determined automatically, + * and the default number of partitions. + */ + def loadLibSVMData( + sc: SparkContext, + path: String, + labelParser: String => Double): RDD[LabeledPoint] = + loadLibSVMData(sc, path, labelParser, -1, sc.defaultMinSplits) + + /** + * Loads labeled data in the LIBSVM format into an RDD[LabeledPoint], + * with the given label parser, number of features specified explicitly, + * and the default number of partitions. + */ + def loadLibSVMData( + sc: SparkContext, + path: String, + labelParser: String => Double, + numFeatures: Int): RDD[LabeledPoint] = + loadLibSVMData(sc, path, labelParser, numFeatures, sc.defaultMinSplits) + + /** * Load labeled data from a file. The data format used here is * <L>, <f1> <f2> ... * where <f1>, <f2> are feature values in Double and <L> is the corresponding label as Double. @@ -54,7 +153,7 @@ object MLUtils { sc.textFile(dir).map { line => val parts = line.split(',') val label = parts(0).toDouble - val features = parts(1).trim().split(' ').map(_.toDouble) + val features = Vectors.dense(parts(1).trim().split(' ').map(_.toDouble)) LabeledPoint(label, features) } } @@ -68,7 +167,7 @@ object MLUtils { * @param dir Directory to save the data. */ def saveLabeledData(data: RDD[LabeledPoint], dir: String) { - val dataStr = data.map(x => x.label + "," + x.features.mkString(" ")) + val dataStr = data.map(x => x.label + "," + x.features.toArray.mkString(" ")) dataStr.saveAsTextFile(dir) } @@ -76,44 +175,52 @@ object MLUtils { * Utility function to compute mean and standard deviation on a given dataset. * * @param data - input data set whose statistics are computed - * @param nfeatures - number of features - * @param nexamples - number of examples in input dataset + * @param numFeatures - number of features + * @param numExamples - number of examples in input dataset * * @return (yMean, xColMean, xColSd) - Tuple consisting of * yMean - mean of the labels * xColMean - Row vector with mean for every column (or feature) of the input data * xColSd - Row vector standard deviation for every column (or feature) of the input data. */ - def computeStats(data: RDD[LabeledPoint], nfeatures: Int, nexamples: Long): - (Double, DoubleMatrix, DoubleMatrix) = { - val yMean: Double = data.map { labeledPoint => labeledPoint.label }.reduce(_ + _) / nexamples - - // NOTE: We shuffle X by column here to compute column sum and sum of squares. - val xColSumSq: RDD[(Int, (Double, Double))] = data.flatMap { labeledPoint => - val nCols = labeledPoint.features.length - // Traverse over every column and emit (col, value, value^2) - Iterator.tabulate(nCols) { i => - (i, (labeledPoint.features(i), labeledPoint.features(i)*labeledPoint.features(i))) - } - }.reduceByKey { case(x1, x2) => - (x1._1 + x2._1, x1._2 + x2._2) + def computeStats( + data: RDD[LabeledPoint], + numFeatures: Int, + numExamples: Long): (Double, Vector, Vector) = { + val brzData = data.map { case LabeledPoint(label, features) => + (label, features.toBreeze) } - val xColSumsMap = xColSumSq.collectAsMap() - - val xColMean = DoubleMatrix.zeros(nfeatures, 1) - val xColSd = DoubleMatrix.zeros(nfeatures, 1) - - // Compute mean and unbiased variance using column sums - var col = 0 - while (col < nfeatures) { - xColMean.put(col, xColSumsMap(col)._1 / nexamples) - val variance = - (xColSumsMap(col)._2 - (math.pow(xColSumsMap(col)._1, 2) / nexamples)) / nexamples - xColSd.put(col, math.sqrt(variance)) - col += 1 + val aggStats = brzData.aggregate( + (0L, 0.0, BDV.zeros[Double](numFeatures), BDV.zeros[Double](numFeatures)) + )( + seqOp = (c, v) => (c, v) match { + case ((n, sumLabel, sum, sumSq), (label, features)) => + features.activeIterator.foreach { case (i, x) => + sumSq(i) += x * x + } + (n + 1L, sumLabel + label, sum += features, sumSq) + }, + combOp = (c1, c2) => (c1, c2) match { + case ((n1, sumLabel1, sum1, sumSq1), (n2, sumLabel2, sum2, sumSq2)) => + (n1 + n2, sumLabel1 + sumLabel2, sum1 += sum2, sumSq1 += sumSq2) + } + ) + val (nl, sumLabel, sum, sumSq) = aggStats + + require(nl > 0, "Input data is empty.") + require(nl == numExamples) + + val n = nl.toDouble + val yMean = sumLabel / n + val mean = sum / n + val std = new Array[Double](sum.length) + var i = 0 + while (i < numFeatures) { + std(i) = sumSq(i) / n - mean(i) * mean(i) + i += 1 } - (yMean, xColMean, xColSd) + (yMean, Vectors.fromBreeze(mean), Vectors.dense(std)) } /** @@ -144,6 +251,18 @@ object MLUtils { val sumSquaredNorm = norm1 * norm1 + norm2 * norm2 val normDiff = norm1 - norm2 var sqDist = 0.0 + /* + * The relative error is + * <pre> + * EPSILON * ( \|a\|_2^2 + \|b\\_2^2 + 2 |a^T b|) / ( \|a - b\|_2^2 ), + * </pre> + * which is bounded by + * <pre> + * 2.0 * EPSILON * ( \|a\|_2^2 + \|b\|_2^2 ) / ( (\|a\|_2 - \|b\|_2)^2 ). + * </pre> + * The bound doesn't need the inner product, so we can use it as a sufficient condition to + * check quickly whether the inner product approach is accurate. + */ val precisionBound1 = 2.0 * EPSILON * sumSquaredNorm / (normDiff * normDiff + EPSILON) if (precisionBound1 < precision) { sqDist = sumSquaredNorm - 2.0 * v1.dot(v2) http://git-wip-us.apache.org/repos/asf/spark/blob/9c65fa76/mllib/src/main/scala/org/apache/spark/mllib/util/SVMDataGenerator.scala ---------------------------------------------------------------------- diff --git a/mllib/src/main/scala/org/apache/spark/mllib/util/SVMDataGenerator.scala b/mllib/src/main/scala/org/apache/spark/mllib/util/SVMDataGenerator.scala index c96c94f..e300c3d 100644 --- a/mllib/src/main/scala/org/apache/spark/mllib/util/SVMDataGenerator.scala +++ b/mllib/src/main/scala/org/apache/spark/mllib/util/SVMDataGenerator.scala @@ -23,6 +23,7 @@ import org.jblas.DoubleMatrix import org.apache.spark.SparkContext import org.apache.spark.rdd.RDD +import org.apache.spark.mllib.linalg.Vectors import org.apache.spark.mllib.regression.LabeledPoint /** @@ -58,7 +59,7 @@ object SVMDataGenerator { } val yD = new DoubleMatrix(1, x.length, x: _*).dot(trueWeights) + rnd.nextGaussian() * 0.1 val y = if (yD < 0) 0.0 else 1.0 - LabeledPoint(y, x) + LabeledPoint(y, Vectors.dense(x)) } MLUtils.saveLabeledData(data, outputPath) http://git-wip-us.apache.org/repos/asf/spark/blob/9c65fa76/mllib/src/test/java/org/apache/spark/mllib/classification/JavaNaiveBayesSuite.java ---------------------------------------------------------------------- diff --git a/mllib/src/test/java/org/apache/spark/mllib/classification/JavaNaiveBayesSuite.java b/mllib/src/test/java/org/apache/spark/mllib/classification/JavaNaiveBayesSuite.java index 073ded6..c80b113 100644 --- a/mllib/src/test/java/org/apache/spark/mllib/classification/JavaNaiveBayesSuite.java +++ b/mllib/src/test/java/org/apache/spark/mllib/classification/JavaNaiveBayesSuite.java @@ -19,6 +19,7 @@ package org.apache.spark.mllib.classification; import org.apache.spark.api.java.JavaRDD; import org.apache.spark.api.java.JavaSparkContext; +import org.apache.spark.mllib.linalg.Vectors; import org.apache.spark.mllib.regression.LabeledPoint; import org.junit.After; import org.junit.Assert; @@ -45,12 +46,12 @@ public class JavaNaiveBayesSuite implements Serializable { } private static final List<LabeledPoint> POINTS = Arrays.asList( - new LabeledPoint(0, new double[] {1.0, 0.0, 0.0}), - new LabeledPoint(0, new double[] {2.0, 0.0, 0.0}), - new LabeledPoint(1, new double[] {0.0, 1.0, 0.0}), - new LabeledPoint(1, new double[] {0.0, 2.0, 0.0}), - new LabeledPoint(2, new double[] {0.0, 0.0, 1.0}), - new LabeledPoint(2, new double[] {0.0, 0.0, 2.0}) + new LabeledPoint(0, Vectors.dense(1.0, 0.0, 0.0)), + new LabeledPoint(0, Vectors.dense(2.0, 0.0, 0.0)), + new LabeledPoint(1, Vectors.dense(0.0, 1.0, 0.0)), + new LabeledPoint(1, Vectors.dense(0.0, 2.0, 0.0)), + new LabeledPoint(2, Vectors.dense(0.0, 0.0, 1.0)), + new LabeledPoint(2, Vectors.dense(0.0, 0.0, 2.0)) ); private int validatePrediction(List<LabeledPoint> points, NaiveBayesModel model) { http://git-wip-us.apache.org/repos/asf/spark/blob/9c65fa76/mllib/src/test/java/org/apache/spark/mllib/classification/JavaSVMSuite.java ---------------------------------------------------------------------- diff --git a/mllib/src/test/java/org/apache/spark/mllib/classification/JavaSVMSuite.java b/mllib/src/test/java/org/apache/spark/mllib/classification/JavaSVMSuite.java index 117e5ea..4701a5e 100644 --- a/mllib/src/test/java/org/apache/spark/mllib/classification/JavaSVMSuite.java +++ b/mllib/src/test/java/org/apache/spark/mllib/classification/JavaSVMSuite.java @@ -17,7 +17,6 @@ package org.apache.spark.mllib.classification; - import java.io.Serializable; import java.util.List; @@ -28,7 +27,6 @@ import org.junit.Test; import org.apache.spark.api.java.JavaRDD; import org.apache.spark.api.java.JavaSparkContext; - import org.apache.spark.mllib.regression.LabeledPoint; public class JavaSVMSuite implements Serializable { @@ -94,5 +92,4 @@ public class JavaSVMSuite implements Serializable { int numAccurate = validatePrediction(validationData, model); Assert.assertTrue(numAccurate > nPoints * 4.0 / 5.0); } - } http://git-wip-us.apache.org/repos/asf/spark/blob/9c65fa76/mllib/src/test/java/org/apache/spark/mllib/linalg/JavaVectorsSuite.java ---------------------------------------------------------------------- diff --git a/mllib/src/test/java/org/apache/spark/mllib/linalg/JavaVectorsSuite.java b/mllib/src/test/java/org/apache/spark/mllib/linalg/JavaVectorsSuite.java index 2c4d795..c6d8425 100644 --- a/mllib/src/test/java/org/apache/spark/mllib/linalg/JavaVectorsSuite.java +++ b/mllib/src/test/java/org/apache/spark/mllib/linalg/JavaVectorsSuite.java @@ -19,10 +19,10 @@ package org.apache.spark.mllib.linalg; import java.io.Serializable; -import com.google.common.collect.Lists; - import scala.Tuple2; +import com.google.common.collect.Lists; + import org.junit.Test; import static org.junit.Assert.*; @@ -36,7 +36,7 @@ public class JavaVectorsSuite implements Serializable { @Test public void sparseArrayConstruction() { - Vector v = Vectors.sparse(3, Lists.newArrayList( + Vector v = Vectors.sparse(3, Lists.<Tuple2<Integer, Double>>newArrayList( new Tuple2<Integer, Double>(0, 2.0), new Tuple2<Integer, Double>(2, 3.0))); assertArrayEquals(new double[]{2.0, 0.0, 3.0}, v.toArray(), 0.0); http://git-wip-us.apache.org/repos/asf/spark/blob/9c65fa76/mllib/src/test/java/org/apache/spark/mllib/regression/JavaLassoSuite.java ---------------------------------------------------------------------- diff --git a/mllib/src/test/java/org/apache/spark/mllib/regression/JavaLassoSuite.java b/mllib/src/test/java/org/apache/spark/mllib/regression/JavaLassoSuite.java index f44b25c..f725924 100644 --- a/mllib/src/test/java/org/apache/spark/mllib/regression/JavaLassoSuite.java +++ b/mllib/src/test/java/org/apache/spark/mllib/regression/JavaLassoSuite.java @@ -59,7 +59,7 @@ public class JavaLassoSuite implements Serializable { @Test public void runLassoUsingConstructor() { int nPoints = 10000; - double A = 2.0; + double A = 0.0; double[] weights = {-1.5, 1.0e-2}; JavaRDD<LabeledPoint> testRDD = sc.parallelize(LinearDataGenerator.generateLinearInputAsList(A, @@ -80,7 +80,7 @@ public class JavaLassoSuite implements Serializable { @Test public void runLassoUsingStaticMethods() { int nPoints = 10000; - double A = 2.0; + double A = 0.0; double[] weights = {-1.5, 1.0e-2}; JavaRDD<LabeledPoint> testRDD = sc.parallelize(LinearDataGenerator.generateLinearInputAsList(A, http://git-wip-us.apache.org/repos/asf/spark/blob/9c65fa76/mllib/src/test/java/org/apache/spark/mllib/regression/JavaRidgeRegressionSuite.java ---------------------------------------------------------------------- diff --git a/mllib/src/test/java/org/apache/spark/mllib/regression/JavaRidgeRegressionSuite.java b/mllib/src/test/java/org/apache/spark/mllib/regression/JavaRidgeRegressionSuite.java index 2fdd5fc..03714ae 100644 --- a/mllib/src/test/java/org/apache/spark/mllib/regression/JavaRidgeRegressionSuite.java +++ b/mllib/src/test/java/org/apache/spark/mllib/regression/JavaRidgeRegressionSuite.java @@ -55,30 +55,27 @@ public class JavaRidgeRegressionSuite implements Serializable { return errorSum / validationData.size(); } - List<LabeledPoint> generateRidgeData(int numPoints, int nfeatures, double eps) { + List<LabeledPoint> generateRidgeData(int numPoints, int numFeatures, double std) { org.jblas.util.Random.seed(42); // Pick weights as random values distributed uniformly in [-0.5, 0.5] - DoubleMatrix w = DoubleMatrix.rand(nfeatures, 1).subi(0.5); - // Set first two weights to eps - w.put(0, 0, eps); - w.put(1, 0, eps); - return LinearDataGenerator.generateLinearInputAsList(0.0, w.data, numPoints, 42, eps); + DoubleMatrix w = DoubleMatrix.rand(numFeatures, 1).subi(0.5); + return LinearDataGenerator.generateLinearInputAsList(0.0, w.data, numPoints, 42, std); } @Test public void runRidgeRegressionUsingConstructor() { - int nexamples = 200; - int nfeatures = 20; - double eps = 10.0; - List<LabeledPoint> data = generateRidgeData(2*nexamples, nfeatures, eps); + int numExamples = 50; + int numFeatures = 20; + List<LabeledPoint> data = generateRidgeData(2*numExamples, numFeatures, 10.0); - JavaRDD<LabeledPoint> testRDD = sc.parallelize(data.subList(0, nexamples)); - List<LabeledPoint> validationData = data.subList(nexamples, 2*nexamples); + JavaRDD<LabeledPoint> testRDD = sc.parallelize(data.subList(0, numExamples)); + List<LabeledPoint> validationData = data.subList(numExamples, 2 * numExamples); RidgeRegressionWithSGD ridgeSGDImpl = new RidgeRegressionWithSGD(); - ridgeSGDImpl.optimizer().setStepSize(1.0) - .setRegParam(0.0) - .setNumIterations(200); + ridgeSGDImpl.optimizer() + .setStepSize(1.0) + .setRegParam(0.0) + .setNumIterations(200); RidgeRegressionModel model = ridgeSGDImpl.run(testRDD.rdd()); double unRegularizedErr = predictionError(validationData, model); @@ -91,13 +88,12 @@ public class JavaRidgeRegressionSuite implements Serializable { @Test public void runRidgeRegressionUsingStaticMethods() { - int nexamples = 200; - int nfeatures = 20; - double eps = 10.0; - List<LabeledPoint> data = generateRidgeData(2*nexamples, nfeatures, eps); + int numExamples = 50; + int numFeatures = 20; + List<LabeledPoint> data = generateRidgeData(2 * numExamples, numFeatures, 10.0); - JavaRDD<LabeledPoint> testRDD = sc.parallelize(data.subList(0, nexamples)); - List<LabeledPoint> validationData = data.subList(nexamples, 2*nexamples); + JavaRDD<LabeledPoint> testRDD = sc.parallelize(data.subList(0, numExamples)); + List<LabeledPoint> validationData = data.subList(numExamples, 2 * numExamples); RidgeRegressionModel model = RidgeRegressionWithSGD.train(testRDD.rdd(), 200, 1.0, 0.0); double unRegularizedErr = predictionError(validationData, model); http://git-wip-us.apache.org/repos/asf/spark/blob/9c65fa76/mllib/src/test/scala/org/apache/spark/mllib/classification/LogisticRegressionSuite.scala ---------------------------------------------------------------------- diff --git a/mllib/src/test/scala/org/apache/spark/mllib/classification/LogisticRegressionSuite.scala b/mllib/src/test/scala/org/apache/spark/mllib/classification/LogisticRegressionSuite.scala index 05322b0..1e03c9d 100644 --- a/mllib/src/test/scala/org/apache/spark/mllib/classification/LogisticRegressionSuite.scala +++ b/mllib/src/test/scala/org/apache/spark/mllib/classification/LogisticRegressionSuite.scala @@ -20,11 +20,10 @@ package org.apache.spark.mllib.classification import scala.util.Random import scala.collection.JavaConversions._ -import org.scalatest.BeforeAndAfterAll import org.scalatest.FunSuite import org.scalatest.matchers.ShouldMatchers -import org.apache.spark.SparkContext +import org.apache.spark.mllib.linalg.Vectors import org.apache.spark.mllib.regression._ import org.apache.spark.mllib.util.LocalSparkContext @@ -61,7 +60,7 @@ object LogisticRegressionSuite { if (yVal > 0) 1 else 0 } - val testData = (0 until nPoints).map(i => LabeledPoint(y(i), Array(x1(i)))) + val testData = (0 until nPoints).map(i => LabeledPoint(y(i), Vectors.dense(Array(x1(i))))) testData } @@ -113,7 +112,7 @@ class LogisticRegressionSuite extends FunSuite with LocalSparkContext with Shoul val testData = LogisticRegressionSuite.generateLogisticInput(A, B, nPoints, 42) val initialB = -1.0 - val initialWeights = Array(initialB) + val initialWeights = Vectors.dense(initialB) val testRDD = sc.parallelize(testData, 2) testRDD.cache() http://git-wip-us.apache.org/repos/asf/spark/blob/9c65fa76/mllib/src/test/scala/org/apache/spark/mllib/classification/NaiveBayesSuite.scala ---------------------------------------------------------------------- diff --git a/mllib/src/test/scala/org/apache/spark/mllib/classification/NaiveBayesSuite.scala b/mllib/src/test/scala/org/apache/spark/mllib/classification/NaiveBayesSuite.scala index 9dd6c79..516895d 100644 --- a/mllib/src/test/scala/org/apache/spark/mllib/classification/NaiveBayesSuite.scala +++ b/mllib/src/test/scala/org/apache/spark/mllib/classification/NaiveBayesSuite.scala @@ -19,9 +19,9 @@ package org.apache.spark.mllib.classification import scala.util.Random -import org.scalatest.BeforeAndAfterAll import org.scalatest.FunSuite +import org.apache.spark.mllib.linalg.Vectors import org.apache.spark.mllib.regression.LabeledPoint import org.apache.spark.mllib.util.LocalSparkContext @@ -54,7 +54,7 @@ object NaiveBayesSuite { if (rnd.nextDouble() < _theta(y)(j)) 1 else 0 } - LabeledPoint(y, xi) + LabeledPoint(y, Vectors.dense(xi)) } } } http://git-wip-us.apache.org/repos/asf/spark/blob/9c65fa76/mllib/src/test/scala/org/apache/spark/mllib/classification/SVMSuite.scala ---------------------------------------------------------------------- diff --git a/mllib/src/test/scala/org/apache/spark/mllib/classification/SVMSuite.scala b/mllib/src/test/scala/org/apache/spark/mllib/classification/SVMSuite.scala index bc7abb5..dfacbfe 100644 --- a/mllib/src/test/scala/org/apache/spark/mllib/classification/SVMSuite.scala +++ b/mllib/src/test/scala/org/apache/spark/mllib/classification/SVMSuite.scala @@ -20,7 +20,6 @@ package org.apache.spark.mllib.classification import scala.util.Random import scala.collection.JavaConversions._ -import org.scalatest.BeforeAndAfterAll import org.scalatest.FunSuite import org.jblas.DoubleMatrix @@ -28,6 +27,7 @@ import org.jblas.DoubleMatrix import org.apache.spark.SparkException import org.apache.spark.mllib.regression._ import org.apache.spark.mllib.util.LocalSparkContext +import org.apache.spark.mllib.linalg.Vectors object SVMSuite { @@ -54,7 +54,7 @@ object SVMSuite { intercept + 0.01 * rnd.nextGaussian() if (yD < 0) 0.0 else 1.0 } - y.zip(x).map(p => LabeledPoint(p._1, p._2)) + y.zip(x).map(p => LabeledPoint(p._1, Vectors.dense(p._2))) } } @@ -110,7 +110,7 @@ class SVMSuite extends FunSuite with LocalSparkContext { val initialB = -1.0 val initialC = -1.0 - val initialWeights = Array(initialB,initialC) + val initialWeights = Vectors.dense(initialB, initialC) val testRDD = sc.parallelize(testData, 2) testRDD.cache() @@ -150,10 +150,10 @@ class SVMSuite extends FunSuite with LocalSparkContext { } intercept[SparkException] { - val model = SVMWithSGD.train(testRDDInvalid, 100) + SVMWithSGD.train(testRDDInvalid, 100) } // Turning off data validation should not throw an exception - val noValidationModel = new SVMWithSGD().setValidateData(false).run(testRDDInvalid) + new SVMWithSGD().setValidateData(false).run(testRDDInvalid) } } http://git-wip-us.apache.org/repos/asf/spark/blob/9c65fa76/mllib/src/test/scala/org/apache/spark/mllib/optimization/GradientDescentSuite.scala ---------------------------------------------------------------------- diff --git a/mllib/src/test/scala/org/apache/spark/mllib/optimization/GradientDescentSuite.scala b/mllib/src/test/scala/org/apache/spark/mllib/optimization/GradientDescentSuite.scala index 631d0e2..c4b4334 100644 --- a/mllib/src/test/scala/org/apache/spark/mllib/optimization/GradientDescentSuite.scala +++ b/mllib/src/test/scala/org/apache/spark/mllib/optimization/GradientDescentSuite.scala @@ -20,13 +20,12 @@ package org.apache.spark.mllib.optimization import scala.util.Random import scala.collection.JavaConversions._ -import org.scalatest.BeforeAndAfterAll import org.scalatest.FunSuite import org.scalatest.matchers.ShouldMatchers -import org.apache.spark.SparkContext import org.apache.spark.mllib.regression._ import org.apache.spark.mllib.util.LocalSparkContext +import org.apache.spark.mllib.linalg.Vectors object GradientDescentSuite { @@ -58,8 +57,7 @@ object GradientDescentSuite { if (yVal > 0) 1 else 0 } - val testData = (0 until nPoints).map(i => LabeledPoint(y(i), Array(x1(i)))) - testData + (0 until nPoints).map(i => LabeledPoint(y(i), Vectors.dense(x1(i)))) } } @@ -83,11 +81,11 @@ class GradientDescentSuite extends FunSuite with LocalSparkContext with ShouldMa // Add a extra variable consisting of all 1.0's for the intercept. val testData = GradientDescentSuite.generateGDInput(A, B, nPoints, 42) val data = testData.map { case LabeledPoint(label, features) => - label -> Array(1.0, features: _*) + label -> Vectors.dense(1.0, features.toArray: _*) } val dataRDD = sc.parallelize(data, 2).cache() - val initialWeightsWithIntercept = Array(1.0, initialWeights: _*) + val initialWeightsWithIntercept = Vectors.dense(1.0, initialWeights: _*) val (_, loss) = GradientDescent.runMiniBatchSGD( dataRDD, @@ -113,13 +111,13 @@ class GradientDescentSuite extends FunSuite with LocalSparkContext with ShouldMa // Add a extra variable consisting of all 1.0's for the intercept. val testData = GradientDescentSuite.generateGDInput(2.0, -1.5, 10000, 42) val data = testData.map { case LabeledPoint(label, features) => - label -> Array(1.0, features: _*) + label -> Vectors.dense(1.0, features.toArray: _*) } val dataRDD = sc.parallelize(data, 2).cache() // Prepare non-zero weights - val initialWeightsWithIntercept = Array(1.0, 0.5) + val initialWeightsWithIntercept = Vectors.dense(1.0, 0.5) val regParam0 = 0 val (newWeights0, loss0) = GradientDescent.runMiniBatchSGD( http://git-wip-us.apache.org/repos/asf/spark/blob/9c65fa76/mllib/src/test/scala/org/apache/spark/mllib/regression/LassoSuite.scala ---------------------------------------------------------------------- diff --git a/mllib/src/test/scala/org/apache/spark/mllib/regression/LassoSuite.scala b/mllib/src/test/scala/org/apache/spark/mllib/regression/LassoSuite.scala index 2cebac9..6aad9eb 100644 --- a/mllib/src/test/scala/org/apache/spark/mllib/regression/LassoSuite.scala +++ b/mllib/src/test/scala/org/apache/spark/mllib/regression/LassoSuite.scala @@ -19,6 +19,7 @@ package org.apache.spark.mllib.regression import org.scalatest.FunSuite +import org.apache.spark.mllib.linalg.Vectors import org.apache.spark.mllib.util.{LinearDataGenerator, LocalSparkContext} class LassoSuite extends FunSuite with LocalSparkContext { @@ -33,29 +34,33 @@ class LassoSuite extends FunSuite with LocalSparkContext { } test("Lasso local random SGD") { - val nPoints = 10000 + val nPoints = 1000 val A = 2.0 val B = -1.5 val C = 1.0e-2 - val testData = LinearDataGenerator.generateLinearInput(A, Array[Double](B,C), nPoints, 42) - - val testRDD = sc.parallelize(testData, 2) - testRDD.cache() + val testData = LinearDataGenerator.generateLinearInput(A, Array[Double](B, C), nPoints, 42) + .map { case LabeledPoint(label, features) => + LabeledPoint(label, Vectors.dense(1.0 +: features.toArray)) + } + val testRDD = sc.parallelize(testData, 2).cache() val ls = new LassoWithSGD() - ls.optimizer.setStepSize(1.0).setRegParam(0.01).setNumIterations(20) + ls.optimizer.setStepSize(1.0).setRegParam(0.01).setNumIterations(40) val model = ls.run(testRDD) - val weight0 = model.weights(0) val weight1 = model.weights(1) - assert(model.intercept >= 1.9 && model.intercept <= 2.1, model.intercept + " not in [1.9, 2.1]") - assert(weight0 >= -1.60 && weight0 <= -1.40, weight0 + " not in [-1.6, -1.4]") - assert(weight1 >= -1.0e-3 && weight1 <= 1.0e-3, weight1 + " not in [-0.001, 0.001]") + val weight2 = model.weights(2) + assert(weight0 >= 1.9 && weight0 <= 2.1, weight0 + " not in [1.9, 2.1]") + assert(weight1 >= -1.60 && weight1 <= -1.40, weight1 + " not in [-1.6, -1.4]") + assert(weight2 >= -1.0e-3 && weight2 <= 1.0e-3, weight2 + " not in [-0.001, 0.001]") val validationData = LinearDataGenerator.generateLinearInput(A, Array[Double](B,C), nPoints, 17) + .map { case LabeledPoint(label, features) => + LabeledPoint(label, Vectors.dense(1.0 +: features.toArray)) + } val validationRDD = sc.parallelize(validationData, 2) // Test prediction on RDD. @@ -66,33 +71,39 @@ class LassoSuite extends FunSuite with LocalSparkContext { } test("Lasso local random SGD with initial weights") { - val nPoints = 10000 + val nPoints = 1000 val A = 2.0 val B = -1.5 val C = 1.0e-2 - val testData = LinearDataGenerator.generateLinearInput(A, Array[Double](B,C), nPoints, 42) + val testData = LinearDataGenerator.generateLinearInput(A, Array[Double](B, C), nPoints, 42) + .map { case LabeledPoint(label, features) => + LabeledPoint(label, Vectors.dense(1.0 +: features.toArray)) + } + val initialA = -1.0 val initialB = -1.0 val initialC = -1.0 - val initialWeights = Array(initialB,initialC) + val initialWeights = Vectors.dense(initialA, initialB, initialC) - val testRDD = sc.parallelize(testData, 2) - testRDD.cache() + val testRDD = sc.parallelize(testData, 2).cache() val ls = new LassoWithSGD() - ls.optimizer.setStepSize(1.0).setRegParam(0.01).setNumIterations(20) + ls.optimizer.setStepSize(1.0).setRegParam(0.01).setNumIterations(40) val model = ls.run(testRDD, initialWeights) - val weight0 = model.weights(0) val weight1 = model.weights(1) - assert(model.intercept >= 1.9 && model.intercept <= 2.1, model.intercept + " not in [1.9, 2.1]") - assert(weight0 >= -1.60 && weight0 <= -1.40, weight0 + " not in [-1.6, -1.4]") - assert(weight1 >= -1.0e-3 && weight1 <= 1.0e-3, weight1 + " not in [-0.001, 0.001]") + val weight2 = model.weights(2) + assert(weight0 >= 1.9 && weight0 <= 2.1, weight0 + " not in [1.9, 2.1]") + assert(weight1 >= -1.60 && weight1 <= -1.40, weight1 + " not in [-1.6, -1.4]") + assert(weight2 >= -1.0e-3 && weight2 <= 1.0e-3, weight2 + " not in [-0.001, 0.001]") val validationData = LinearDataGenerator.generateLinearInput(A, Array[Double](B,C), nPoints, 17) + .map { case LabeledPoint(label, features) => + LabeledPoint(label, Vectors.dense(1.0 +: features.toArray)) + } val validationRDD = sc.parallelize(validationData,2) // Test prediction on RDD. http://git-wip-us.apache.org/repos/asf/spark/blob/9c65fa76/mllib/src/test/scala/org/apache/spark/mllib/regression/LinearRegressionSuite.scala ---------------------------------------------------------------------- diff --git a/mllib/src/test/scala/org/apache/spark/mllib/regression/LinearRegressionSuite.scala b/mllib/src/test/scala/org/apache/spark/mllib/regression/LinearRegressionSuite.scala index 5d251bc..2f7d307 100644 --- a/mllib/src/test/scala/org/apache/spark/mllib/regression/LinearRegressionSuite.scala +++ b/mllib/src/test/scala/org/apache/spark/mllib/regression/LinearRegressionSuite.scala @@ -19,6 +19,7 @@ package org.apache.spark.mllib.regression import org.scalatest.FunSuite +import org.apache.spark.mllib.linalg.Vectors import org.apache.spark.mllib.util.{LinearDataGenerator, LocalSparkContext} class LinearRegressionSuite extends FunSuite with LocalSparkContext { @@ -40,11 +41,12 @@ class LinearRegressionSuite extends FunSuite with LocalSparkContext { linReg.optimizer.setNumIterations(1000).setStepSize(1.0) val model = linReg.run(testRDD) - assert(model.intercept >= 2.5 && model.intercept <= 3.5) - assert(model.weights.length === 2) - assert(model.weights(0) >= 9.0 && model.weights(0) <= 11.0) - assert(model.weights(1) >= 9.0 && model.weights(1) <= 11.0) + + val weights = model.weights + assert(weights.size === 2) + assert(weights(0) >= 9.0 && weights(0) <= 11.0) + assert(weights(1) >= 9.0 && weights(1) <= 11.0) val validationData = LinearDataGenerator.generateLinearInput( 3.0, Array(10.0, 10.0), 100, 17) @@ -67,9 +69,11 @@ class LinearRegressionSuite extends FunSuite with LocalSparkContext { val model = linReg.run(testRDD) assert(model.intercept === 0.0) - assert(model.weights.length === 2) - assert(model.weights(0) >= 9.0 && model.weights(0) <= 11.0) - assert(model.weights(1) >= 9.0 && model.weights(1) <= 11.0) + + val weights = model.weights + assert(weights.size === 2) + assert(weights(0) >= 9.0 && weights(0) <= 11.0) + assert(weights(1) >= 9.0 && weights(1) <= 11.0) val validationData = LinearDataGenerator.generateLinearInput( 0.0, Array(10.0, 10.0), 100, 17) @@ -81,4 +85,40 @@ class LinearRegressionSuite extends FunSuite with LocalSparkContext { // Test prediction on Array. validatePrediction(validationData.map(row => model.predict(row.features)), validationData) } + + // Test if we can correctly learn Y = 10*X1 + 10*X10000 + test("sparse linear regression without intercept") { + val denseRDD = sc.parallelize( + LinearDataGenerator.generateLinearInput(0.0, Array(10.0, 10.0), 100, 42), 2) + val sparseRDD = denseRDD.map { case LabeledPoint(label, v) => + val sv = Vectors.sparse(10000, Seq((0, v(0)), (9999, v(1)))) + LabeledPoint(label, sv) + }.cache() + val linReg = new LinearRegressionWithSGD().setIntercept(false) + linReg.optimizer.setNumIterations(1000).setStepSize(1.0) + + val model = linReg.run(sparseRDD) + + assert(model.intercept === 0.0) + + val weights = model.weights + assert(weights.size === 10000) + assert(weights(0) >= 9.0 && weights(0) <= 11.0) + assert(weights(9999) >= 9.0 && weights(9999) <= 11.0) + + val validationData = LinearDataGenerator.generateLinearInput(0.0, Array(10.0, 10.0), 100, 17) + val sparseValidationData = validationData.map { case LabeledPoint(label, v) => + val sv = Vectors.sparse(10000, Seq((0, v(0)), (9999, v(1)))) + LabeledPoint(label, sv) + } + val sparseValidationRDD = sc.parallelize(sparseValidationData, 2) + + // Test prediction on RDD. + validatePrediction( + model.predict(sparseValidationRDD.map(_.features)).collect(), sparseValidationData) + + // Test prediction on Array. + validatePrediction( + sparseValidationData.map(row => model.predict(row.features)), sparseValidationData) + } } http://git-wip-us.apache.org/repos/asf/spark/blob/9c65fa76/mllib/src/test/scala/org/apache/spark/mllib/regression/RidgeRegressionSuite.scala ---------------------------------------------------------------------- diff --git a/mllib/src/test/scala/org/apache/spark/mllib/regression/RidgeRegressionSuite.scala b/mllib/src/test/scala/org/apache/spark/mllib/regression/RidgeRegressionSuite.scala index b2044ed..f66fc6e 100644 --- a/mllib/src/test/scala/org/apache/spark/mllib/regression/RidgeRegressionSuite.scala +++ b/mllib/src/test/scala/org/apache/spark/mllib/regression/RidgeRegressionSuite.scala @@ -17,9 +17,10 @@ package org.apache.spark.mllib.regression -import org.jblas.DoubleMatrix import org.scalatest.FunSuite +import org.jblas.DoubleMatrix + import org.apache.spark.mllib.util.{LinearDataGenerator, LocalSparkContext} class RidgeRegressionSuite extends FunSuite with LocalSparkContext { @@ -30,22 +31,22 @@ class RidgeRegressionSuite extends FunSuite with LocalSparkContext { }.reduceLeft(_ + _) / predictions.size } - test("regularization with skewed weights") { - val nexamples = 200 - val nfeatures = 20 - val eps = 10 + test("ridge regression can help avoid overfitting") { + + // For small number of examples and large variance of error distribution, + // ridge regression should give smaller generalization error that linear regression. + + val numExamples = 50 + val numFeatures = 20 org.jblas.util.Random.seed(42) // Pick weights as random values distributed uniformly in [-0.5, 0.5] - val w = DoubleMatrix.rand(nfeatures, 1).subi(0.5) - // Set first two weights to eps - w.put(0, 0, eps) - w.put(1, 0, eps) + val w = DoubleMatrix.rand(numFeatures, 1).subi(0.5) // Use half of data for training and other half for validation - val data = LinearDataGenerator.generateLinearInput(3.0, w.toArray, 2*nexamples, 42, eps) - val testData = data.take(nexamples) - val validationData = data.takeRight(nexamples) + val data = LinearDataGenerator.generateLinearInput(3.0, w.toArray, 2 * numExamples, 42, 10.0) + val testData = data.take(numExamples) + val validationData = data.takeRight(numExamples) val testRDD = sc.parallelize(testData, 2).cache() val validationRDD = sc.parallelize(validationData, 2).cache() @@ -67,7 +68,7 @@ class RidgeRegressionSuite extends FunSuite with LocalSparkContext { val ridgeErr = predictionError( ridgeModel.predict(validationRDD.map(_.features)).collect(), validationData) - // Ridge CV-error should be lower than linear regression + // Ridge validation error should be lower than linear regression. assert(ridgeErr < linearErr, "ridgeError (" + ridgeErr + ") was not less than linearError(" + linearErr + ")") } http://git-wip-us.apache.org/repos/asf/spark/blob/9c65fa76/mllib/src/test/scala/org/apache/spark/mllib/tree/DecisionTreeSuite.scala ---------------------------------------------------------------------- diff --git a/mllib/src/test/scala/org/apache/spark/mllib/tree/DecisionTreeSuite.scala b/mllib/src/test/scala/org/apache/spark/mllib/tree/DecisionTreeSuite.scala index 4349c70..350130c 100644 --- a/mllib/src/test/scala/org/apache/spark/mllib/tree/DecisionTreeSuite.scala +++ b/mllib/src/test/scala/org/apache/spark/mllib/tree/DecisionTreeSuite.scala @@ -27,6 +27,7 @@ import org.apache.spark.mllib.tree.model.Filter import org.apache.spark.mllib.tree.configuration.Strategy import org.apache.spark.mllib.tree.configuration.Algo._ import org.apache.spark.mllib.tree.configuration.FeatureType._ +import org.apache.spark.mllib.linalg.Vectors class DecisionTreeSuite extends FunSuite with BeforeAndAfterAll { @@ -396,7 +397,7 @@ object DecisionTreeSuite { def generateOrderedLabeledPointsWithLabel0(): Array[LabeledPoint] = { val arr = new Array[LabeledPoint](1000) for (i <- 0 until 1000){ - val lp = new LabeledPoint(0.0,Array(i.toDouble,1000.0-i)) + val lp = new LabeledPoint(0.0, Vectors.dense(i.toDouble, 1000.0 - i)) arr(i) = lp } arr @@ -405,7 +406,7 @@ object DecisionTreeSuite { def generateOrderedLabeledPointsWithLabel1(): Array[LabeledPoint] = { val arr = new Array[LabeledPoint](1000) for (i <- 0 until 1000){ - val lp = new LabeledPoint(1.0,Array(i.toDouble,999.0-i)) + val lp = new LabeledPoint(1.0, Vectors.dense(i.toDouble, 999.0 - i)) arr(i) = lp } arr @@ -415,9 +416,9 @@ object DecisionTreeSuite { val arr = new Array[LabeledPoint](1000) for (i <- 0 until 1000){ if (i < 600){ - arr(i) = new LabeledPoint(1.0,Array(0.0,1.0)) + arr(i) = new LabeledPoint(1.0, Vectors.dense(0.0, 1.0)) } else { - arr(i) = new LabeledPoint(0.0,Array(1.0,0.0)) + arr(i) = new LabeledPoint(0.0, Vectors.dense(1.0, 0.0)) } } arr http://git-wip-us.apache.org/repos/asf/spark/blob/9c65fa76/mllib/src/test/scala/org/apache/spark/mllib/util/MLUtilsSuite.scala ---------------------------------------------------------------------- diff --git a/mllib/src/test/scala/org/apache/spark/mllib/util/MLUtilsSuite.scala b/mllib/src/test/scala/org/apache/spark/mllib/util/MLUtilsSuite.scala index 60f053b..27d41c7 100644 --- a/mllib/src/test/scala/org/apache/spark/mllib/util/MLUtilsSuite.scala +++ b/mllib/src/test/scala/org/apache/spark/mllib/util/MLUtilsSuite.scala @@ -17,14 +17,20 @@ package org.apache.spark.mllib.util +import java.io.File + import org.scalatest.FunSuite import breeze.linalg.{DenseVector => BDV, SparseVector => BSV, norm => breezeNorm, squaredDistance => breezeSquaredDistance} +import com.google.common.base.Charsets +import com.google.common.io.Files +import org.apache.spark.mllib.linalg.Vectors +import org.apache.spark.mllib.regression.LabeledPoint import org.apache.spark.mllib.util.MLUtils._ -class MLUtilsSuite extends FunSuite { +class MLUtilsSuite extends FunSuite with LocalSparkContext { test("epsilon computation") { assert(1.0 + EPSILON > 1.0, s"EPSILON is too small: $EPSILON.") @@ -49,4 +55,55 @@ class MLUtilsSuite extends FunSuite { assert((fastSquaredDist2 - squaredDist) <= precision * squaredDist, s"failed with m = $m") } } + + test("compute stats") { + val data = Seq.fill(3)(Seq( + LabeledPoint(1.0, Vectors.dense(1.0, 2.0, 3.0)), + LabeledPoint(0.0, Vectors.dense(3.0, 4.0, 5.0)) + )).flatten + val rdd = sc.parallelize(data, 2) + val (meanLabel, mean, std) = MLUtils.computeStats(rdd, 3, 6) + assert(meanLabel === 0.5) + assert(mean === Vectors.dense(2.0, 3.0, 4.0)) + assert(std === Vectors.dense(1.0, 1.0, 1.0)) + } + + test("loadLibSVMData") { + val lines = + """ + |+1 1:1.0 3:2.0 5:3.0 + |-1 + |-1 2:4.0 4:5.0 6:6.0 + """.stripMargin + val tempDir = Files.createTempDir() + val file = new File(tempDir.getPath, "part-00000") + Files.write(lines, file, Charsets.US_ASCII) + val path = tempDir.toURI.toString + + val pointsWithNumFeatures = MLUtils.loadLibSVMData(sc, path, 6).collect() + val pointsWithoutNumFeatures = MLUtils.loadLibSVMData(sc, path).collect() + + for (points <- Seq(pointsWithNumFeatures, pointsWithoutNumFeatures)) { + assert(points.length === 3) + assert(points(0).label === 1.0) + assert(points(0).features === Vectors.sparse(6, Seq((0, 1.0), (2, 2.0), (4, 3.0)))) + assert(points(1).label == 0.0) + assert(points(1).features == Vectors.sparse(6, Seq())) + assert(points(2).label === 0.0) + assert(points(2).features === Vectors.sparse(6, Seq((1, 4.0), (3, 5.0), (5, 6.0)))) + } + + val multiclassPoints = MLUtils.loadLibSVMData(sc, path, MLUtils.multiclassLabelParser).collect() + assert(multiclassPoints.length === 3) + assert(multiclassPoints(0).label === 1.0) + assert(multiclassPoints(1).label === -1.0) + assert(multiclassPoints(2).label === -1.0) + + try { + file.delete() + tempDir.delete() + } catch { + case t: Throwable => + } + } } http://git-wip-us.apache.org/repos/asf/spark/blob/9c65fa76/python/pyspark/mllib/classification.py ---------------------------------------------------------------------- diff --git a/python/pyspark/mllib/classification.py b/python/pyspark/mllib/classification.py index 19b90df..d2f9cdb 100644 --- a/python/pyspark/mllib/classification.py +++ b/python/pyspark/mllib/classification.py @@ -87,18 +87,19 @@ class NaiveBayesModel(object): >>> data = array([0.0, 0.0, 1.0, 0.0, 0.0, 2.0, 1.0, 1.0, 0.0]).reshape(3,3) >>> model = NaiveBayes.train(sc.parallelize(data)) >>> model.predict(array([0.0, 1.0])) - 0 + 0.0 >>> model.predict(array([1.0, 0.0])) - 1 + 1.0 """ - def __init__(self, pi, theta): + def __init__(self, labels, pi, theta): + self.labels = labels self.pi = pi self.theta = theta def predict(self, x): """Return the most likely class for a data vector x""" - return numpy.argmax(self.pi + dot(x, self.theta)) + return self.labels[numpy.argmax(self.pi + dot(x, self.theta))] class NaiveBayes(object): @classmethod @@ -122,7 +123,8 @@ class NaiveBayes(object): ans = sc._jvm.PythonMLLibAPI().trainNaiveBayes(dataBytes._jrdd, lambda_) return NaiveBayesModel( _deserialize_double_vector(ans[0]), - _deserialize_double_matrix(ans[1])) + _deserialize_double_vector(ans[1]), + _deserialize_double_matrix(ans[2])) def _test():
