Port LR example to PySpark using numpy.

This version of the example crashes after the first iteration with
"OverflowError: math range error" because Python's math.exp()
behaves differently than Scala's; see SPARK-646.

pyspark/examples/lr.py

@@ -0,0 +1,57 @@
+"""
+This example requires numpy (http://www.numpy.org/)
+"""
+from collections import namedtuple
+from math import exp
+from os.path import realpath
+import sys
+
+import numpy as np
+from pyspark.context import SparkContext
+
+
+N = 100000  # Number of data points
+D = 10  # Number of dimensions
+R = 0.7   # Scaling factor
+ITERATIONS = 5
+np.random.seed(42)
+
+
+DataPoint = namedtuple("DataPoint", ['x', 'y'])
+from lr import DataPoint  # So that DataPoint is properly serialized
+
+
+def generateData():
+    def generatePoint(i):
+        y = -1 if i % 2 == 0 else 1
+        x = np.random.normal(size=D) + (y * R)
+        return DataPoint(x, y)
+    return [generatePoint(i) for i in range(N)]
+
+
+if __name__ == "__main__":
+    if len(sys.argv) == 1:
+        print >> sys.stderr, \
+            "Usage: PythonLR <host> [<slices>]"
+        exit(-1)
+    sc = SparkContext(sys.argv[1], "PythonLR", pyFiles=[realpath(__file__)])
+    slices = int(sys.argv[2]) if len(sys.argv) > 2 else 2
+    points = sc.parallelize(generateData(), slices).cache()
+
+    # Initialize w to a random value
+    w = 2 * np.random.ranf(size=D) - 1
+    print "Initial w: " + str(w)
+
+    def add(x, y):
+        x += y
+        return x
+
+    for i in range(1, ITERATIONS + 1):
+        print "On iteration %i" % i
+
+        gradient = points.map(lambda p:
+            (1.0 / (1.0 + exp(-p.y * np.dot(w, p.x)))) * p.y * p.x
+        ).reduce(add)
+        w -= gradient
+
+    print "Final w: " + str(w)