Add Range function for Steady State detection

Added a range_value function in utilities/math.py able to compute the range
of a series of y values : [y1, y2, ..., yn].
Implemented a test harness for this range_value function in the tests/utilities
section.
Renamed the math_slope.py and math_range.py test files to add _test.py for
Jenkins.
Cleaned up the code so it is compliant to the pep8 rules.

Renamed the previous 'math' modules (storperf/utilities/math.py
and storperf/test/utilities/math.py) as 'math_slope' to be
coherent with the new notation.

Change-Id: I02ccd2b87f0b72e7a28c416b593aae4d8ad97961
JIRA: STORPERF-57
JIRA: STORPERF-58
Signed-off-by: Tim Rault <tim.rault@cengn.ca>

3 files changed, 200 insertions, 43 deletions

diff --git a/storperf/tests/utilities/math_range_test.py b/storperf/tests/utilities/math_range_test.py
new file mode 100644
index 0000000..6484752
--- /dev/null
+++ b/storperf/tests/utilities/math_range_test.py
@@ -0,0 +1,120 @@
+##############################################################################
+# Copyright (c) 2016 CENGN and others.
+#
+# All rights reserved. This program and the accompanying materials
+# are made available under the terms of the Apache License, Version 2.0
+# which accompanies this distribution, and is available at
+# http://www.apache.org/licenses/LICENSE-2.0
+##############################################################################
+from random import uniform, randrange
+import unittest
+
+from storperf.utilities import math as math
+
+
+class MathRangeTest(unittest.TestCase):
+
+    def setUp(self):
+        unittest.TestCase.setUp(self)
+
+    def test_empty_series(self):
+        expected = 0
+        data_series = []
+        actual = math.range_value(data_series)
+        self.assertEqual(expected, actual)
+
+    def test_integer_series(self):
+        expected = 11946
+        data_series = [5, 351, 847, 2, 1985, 18,
+                       96, 389, 687, 1, 11947, 758, 155]
+        actual = math.range_value(data_series)
+        self.assertEqual(expected, actual)
+
+    def test_float_series_1_decimal(self):
+        expected = 778595.5
+        data_series = [736.4, 9856.4, 684.2, 0.3, 0.9, 778595.8]
+        actual = math.range_value(data_series)
+        self.assertEqual(expected, actual)
+
+    def test_float_series_2_decimals(self):
+        expected = 5693.47
+        data_series = [51.36, 78.40, 1158.24, 5.50, 0.98, 5694.45]
+        actual = math.range_value(data_series)
+        self.assertEqual(expected, actual)
+
+    def test_float_series_3_decimals(self):
+        expected = 992.181
+        data_series = [4.562, 12.582, 689.452,
+                       135.162, 996.743, 65.549, 36.785]
+        actual = math.range_value(data_series)
+        self.assertEqual(expected, actual)
+
+    def test_float_series_4_decimals(self):
+        expected = 122985.3241
+        data_series = [39.4785, 896.7845, 11956.3654,
+                       44.2398, 6589.7134, 0.3671, 122985.6912]
+        actual = math.range_value(data_series)
+        self.assertEqual(expected, actual)
+
+    def test_float_series_5_decimals(self):
+        expected = 8956208.84494
+        data_series = [12.78496, 55.91275, 668.94378,
+                       550396.5671, 512374.9999, 8956221.6299]
+        actual = math.range_value(data_series)
+        self.assertEqual(expected, actual)
+
+    def test_float_series_10_decimals(self):
+        expected = 5984.507397972699
+        data_series = [1.1253914785, 5985.6327894512,
+                       256.1875693287, 995.8497623415]
+        actual = math.range_value(data_series)
+        self.assertEqual(expected, actual)
+
+    def test_float_mix(self):
+        expected = 60781.6245372199
+        data_series = [60785.9962, 899.4, 78.66, 69.58, 4.93795,
+                       587.195486, 96.7694536, 5.13755964,
+                       33.333333334, 60786.5624872199]
+        actual = math.range_value(data_series)
+        self.assertEqual(expected, actual)
+
+    def test_float_integer_mix(self):
+        expected = 460781.05825
+        data_series = [460785.9962, 845.634, 24.1, 69.58, 89, 4.93795]
+        actual = math.range_value(data_series)
+        self.assertEqual(expected, actual)
+
+    def test_negative_values(self):
+        expected = 596.78163
+        data_series = [-4.655, -33.3334, -596.78422, -0.00259, -66.785]
+        actual = math.range_value(data_series)
+        self.assertEqual(expected, actual)
+
+    def test_negative_positive_mix(self):
+        expected = 58.859500000000004
+        data_series = [6.85698, -2.8945, 0, -0.15, 55.965]
+        actual = math.range_value(data_series)
+        self.assertEqual(expected, actual)
+
+    def test_single_element(self):
+        expected = 0
+        data_series = [2.265]
+        actual = math.range_value(data_series)
+        self.assertEqual(expected, actual)
+
+    def test_10000_values_processing(self):
+        expected = 28001.068
+        data_series = [uniform(-10000, 10000) for i in xrange(10000)]
+        data_series.insert(randrange(len(data_series) + 1), 15000.569)
+        data_series.insert(randrange(len(data_series) + 1), -13000.499)
+        actual = math.range_value(data_series)
+        self.assertEqual(expected, actual)
+
+    def test_processing_100_values_100_times(self):
+        expected = 35911.3134
+        for index in range(1, 100):
+            data_series = [uniform(-10000, 10000) for i in xrange(100)]
+            data_series.insert(randrange(len(data_series) + 1), 16956.3334)
+            data_series.insert(randrange(len(data_series) + 1), -18954.98)
+            actual = math.range_value(data_series)
+            self.assertEqual(expected, actual)
diff --git a/storperf/tests/utilities/math.py b/storperf/tests/utilities/math_slope_test.py
index c78538d..a34845b 100644
--- a/storperf/tests/utilities/math.py
+++ b/storperf/tests/utilities/math_slope_test.py
@@ -7,9 +7,10 @@
 # http://www.apache.org/licenses/LICENSE-2.0
 ##############################################################################
 import unittest
-from storperf.utilities.math import math
+from storperf.utilities import math as math
 
-class MathTest(unittest.TestCase):
+
+class MathSlopeTest(unittest.TestCase):
 
     def setUp(self):
         unittest.TestCase.setUp(self)
@@ -22,45 +23,45 @@ class MathTest(unittest.TestCase):
 
     def test_slope_integer_series(self):
         expected = 1.4
-        actual = math.slope([[1,6], [2,5], [3,7], [4,10]])
+        actual = math.slope([[1, 6], [2, 5], [3, 7], [4, 10]])
         self.assertEqual(expected, actual)
 
     def test_slope_decimal_series(self):
         expected = 1.4
-        actual = math.slope([[1.0,6.0], [2.0,5.0], [3.0,7.0], [4.0,10.0]])
+        actual = math.slope([[1.0, 6.0], [2.0, 5.0], [3.0, 7.0], [4.0, 10.0]])
         self.assertEqual(expected, actual)
 
     def test_slope_decimal_integer_mix(self):
         expected = 1.4
-        actual = math.slope([[1.0,6], [2,5.0], [3,7], [4.0,10]])
+        actual = math.slope([[1.0, 6], [2, 5.0], [3, 7], [4.0, 10]])
         self.assertEqual(expected, actual)
 
     def test_slope_negative_y_series(self):
         expected = 2
-        actual = math.slope([[1.0,-2], [2,2], [3,2]])
+        actual = math.slope([[1.0, -2], [2, 2], [3, 2]])
         self.assertEqual(expected, actual)
 
     def test_slope_negative_x_series(self):
         expected = 1.4
-        actual = math.slope([[-24,6.0], [-23,5], [-22,7.0], [-21,10]])
+        actual = math.slope([[-24, 6.0], [-23, 5], [-22, 7.0], [-21, 10]])
         self.assertEqual(expected, actual)
 
     def test_slope_out_of_order_series(self):
         expected = 1.4
-        actual = math.slope([[2,5.0], [4,10], [3.0,7], [1,6]])
+        actual = math.slope([[2, 5.0], [4, 10], [3.0, 7], [1, 6]])
         self.assertEqual(expected, actual)
 
     def test_slope_0_in_y(self):
         expected = -0.5
-        actual = math.slope([[15.5,1], [16.5,0], [17.5,0]])
+        actual = math.slope([[15.5, 1], [16.5, 0], [17.5, 0]])
         self.assertEqual(expected, actual)
 
     def test_slope_0_in_x(self):
         expected = 1.4
-        actual = math.slope([[0,6.0], [1,5], [2,7], [3,10]])
+        actual = math.slope([[0, 6.0], [1, 5], [2, 7], [3, 10]])
         self.assertEqual(expected, actual)
 
     def test_slope_0_in_x_and_y(self):
         expected = 1.5
-        actual = math.slope([[0.0,0], [1,1], [2,3]])
+        actual = math.slope([[0.0, 0], [1, 1], [2, 3]])
         self.assertEqual(expected, actual)
diff --git a/storperf/utilities/math.py b/storperf/utilities/math.py
index 3b124cd..031fc3e 100644
--- a/storperf/utilities/math.py
+++ b/storperf/utilities/math.py
@@ -7,46 +7,82 @@
 # http://www.apache.org/licenses/LICENSE-2.0
 ##############################################################################
 
-class math(object):
 
-    @staticmethod
-    def slope(data_series):
+def slope(data_series):
+    """
+    This function implements the linear least squares algorithm described in
+    the following wikipedia article :
+    https://en.wikipedia.org/wiki/Linear_least_squares_(mathematics)
+    in the case of m equations (provided by m data points) and 2 unknown
+    variables (x and y, which represent the time and the Volume performance
+    variable being tested e.g. IOPS, latency...).
+    The data_series is currently assumed to follow the pattern :
+    [[x1,y1], [x2,y2], ..., [xm,ym]].
+    If this data pattern were to change, the data_treatement function
+    should be adjusted to ensure compatibility with the rest of the
+    Steady State Dectection module.
+    """
+
+    # In the particular case of an empty data series
+    if len(data_series) == 0:
+        beta2 = 0
+
+    else:  # The general case
+        m = len(data_series)
+        # To make sure at least one element is a float number so the result
+        # of the algorithm be a float number
+        data_series[0][0] = float(data_series[0][0])
+
         """
-        This function implements the linear least squares algorithm described in the following wikipedia article
-        https://en.wikipedia.org/wiki/Linear_least_squares_(mathematics)
-        in the case of m equations (provided by m data points) and 2 unknown variables (x and
-        y, which represent the time and the Volume performance variable being
-        tested e.g. IOPS, latency...)
+        It consists in solving the normal equations system (2 equations,
+        2 unknowns) by calculating the value of beta2 (slope).
+        The formula of beta1 (the y-intercept) is given as a comment in
+        case it is needed later.
         """
+        sum_xi = 0
+        sum_xi_sq = 0
+        sum_yi_xi = 0
+        sum_yi = 0
+        for i in range(0, m):
+            xi = data_series[i][0]
+            yi = data_series[i][1]
 
-        if len(data_series)==0: #In the particular case of an empty data series
-            beta2 = 0
+            sum_xi += xi
+            sum_xi_sq += xi**2
+            sum_yi_xi += xi * yi
+            sum_yi += yi
 
-        else: #The general case
-            m = len(data_series) #given a [[x1,y1], [x2,y2], ..., [xm,ym]] data series
-            data_series[0][0] = float(data_series[0][0]) #To make sure at least one element is a float number so the result of the algorithm be a float number
+        beta2 = (sum_yi * sum_xi - m * sum_yi_xi) / \
+            (sum_xi**2 - m * sum_xi_sq)  # The slope
+        # beta1 = (sum_yi_xi - beta2*sum_xi_sq)/sum_xi #The y-intercept if
+        # needed
 
-            """
-            It consists in solving the normal equations system (2 equations, 2 unknowns)
-            by calculating the value of beta2 (slope). The formula of beta1 (the y-intercept)
-            is given as a comment in case it is needed later.
-            """
-            sum_xi = 0
-            sum_xi_sq = 0
-            sum_yi_xi = 0
-            sum_yi = 0
-            for i in range(0, m):
-                xi = data_series[i][0]
-                yi = data_series[i][1]
+    return beta2
 
-                sum_xi += xi
-                sum_xi_sq += xi**2
-                sum_yi_xi += xi*yi
-                sum_yi += yi
 
-            beta2 = (sum_yi*sum_xi - m*sum_yi_xi)/(sum_xi**2 - m*sum_xi_sq) #The slope
-            #beta1 = (sum_yi_xi - beta2*sum_xi_sq)/sum_xi #The y-intercept if needed
+def range_value(data_series):
+    """
+    This function implements a range algorithm that returns a float number
+    representing the range of the data_series that is passed to it.
+    The data_series being passed is assumed to follow the following data
+    pattern : [y1, y2, y3, ..., ym] where yi represents the ith
+    measuring point of the y variable. The y variable represents the
+    Volume performance being tested (e.g. IOPS, latency...).
+    If this data pattern were to change, the data_treatment function
+    should be adjusted to ensure compatibility with the rest of the
+    Steady State Dectection module.
+    The conversion of the data series from the original pattern to the
+    [y1, y2, y3, ..., ym] pattern is done outside this function
+    so the original pattern can be changed without breaking this function.
+    """
 
-        return beta2
+    # In the particular case of an empty data series
+    if len(data_series) == 0:
+        range_value = 0
 
+    else:  # The general case
+        max_value = max(data_series)
+        min_value = min(data_series)
+        range_value = max_value - min_value
 
+    return range_value