Add Steady State Detection module

Added a Steady State Detection module containing a steady_state(data_series)
function that is able to return a boolean indicating wether or not steady
state is reached with the data_series being passed.
This module requires a data_treatment(data_series) and an average(data_series)
modules that have been added in this commit as well. The data treatment function
aims at formatting the data series that is passed to the high level steady_state
function to reach the requirement of each sub-module (slope, average and range).

Modified the Slope and Range functions so they return None when passed an empty
data series instead of 0 which was wrong. Modified the corresponding test cases.

Modified the math_range_test.py file to fix a bug in the 2 last tests.

Change-Id: I9c3854cb0a21cc37b0787b8afca0821eefaa203d
JIRA: STORPERF-60
JIRA: STORPERF-59
JIRA: STORPERF-61
JIRA: STORPERF-62
Signed-off-by: Tim Rault <tim.rault@cengn.ca>

3 files changed, 109 insertions, 2 deletions

diff --git a/storperf/utilities/data_treatment.py b/storperf/utilities/data_treatment.py
new file mode 100644
index 0000000..2368fd9
--- /dev/null
+++ b/storperf/utilities/data_treatment.py
@@ -0,0 +1,39 @@
+##############################################################################
+# 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
+##############################################################################
+
+
+def data_treatment(data_series):
+    """
+    This function aims at performing any necessary pre treatment on the
+    data_series passed to the steady_state function before being passed
+    under to the different math utilities (slope, range and average)
+    so the data can match the requirements of each algorithm.
+    The function returns a dictionary composed of three values that can be
+    accessed with the following keys : 'slope_data', 'range_data' and
+    'average_data'.
+    The data_series is currently assumed to follow the pattern :
+    [[x1,y1], [x2,y2], ..., [xm,ym]]. If this pattern were to change, or
+    the input data pattern of one of the math module, this data_treatment
+    function should be the only part of the Steady State detection module
+    that would need to be modified too.
+    """
+
+    x_values = []
+    y_values = []
+    for l in data_series:
+        x_values.append(l[0])
+        y_values.append(l[1])
+
+    treated_data = {
+        'slope_data': data_series,  # No treatment necessary so far
+        'range_data': y_values,  # The y_values only
+        'average_data': y_values
+    }
+
+    return treated_data
diff --git a/storperf/utilities/math.py b/storperf/utilities/math.py
index 031fc3e..a11ec19 100644
--- a/storperf/utilities/math.py
+++ b/storperf/utilities/math.py
@@ -25,7 +25,7 @@ def slope(data_series):
 
     # In the particular case of an empty data series
     if len(data_series) == 0:
-        beta2 = 0
+        beta2 = None
 
     else:  # The general case
         m = len(data_series)
@@ -78,7 +78,7 @@ def range_value(data_series):
 
     # In the particular case of an empty data series
     if len(data_series) == 0:
-        range_value = 0
+        range_value = None
 
     else:  # The general case
         max_value = max(data_series)
@@ -86,3 +86,26 @@ def range_value(data_series):
         range_value = max_value - min_value
 
     return range_value
+
+
+def average(data_series):
+    """
+    This function seeks to calculate the average value of the data series
+    given a series following the pattern : [y1, y2, y3, ..., ym].
+    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 function returns a float number corresponding to the average of the yi.
+    """
+    m = len(data_series)
+
+    if m == 0:  # In the particular case of an empty data series
+        average = None
+
+    else:
+        data_sum = 0
+        for value in data_series:
+            data_sum += value
+        average = data_sum / float(m)
+
+    return average
diff --git a/storperf/utilities/steady_state.py b/storperf/utilities/steady_state.py
new file mode 100644
index 0000000..8bfcb93
--- /dev/null
+++ b/storperf/utilities/steady_state.py
@@ -0,0 +1,45 @@
+##############################################################################
+# 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 storperf.utilities import data_treatment as DataTreatment
+from storperf.utilities import math as math
+
+
+def steady_state(data_series):
+    """
+    This function seeks to detect steady state given on a measurement
+    window given the data series of that measurement window following
+    the pattern : [[x1,y1], [x2,y2], ..., [xm,ym]]. m represents the number
+    of points recorded in the measurement window, x which represents the
+    time, and y which represents the Volume performance variable being
+    tested e.g. IOPS, latency...
+    The function returns a boolean describing wether or not steady state
+    has been reached with the data that is passed to it.
+    """
+
+    # Pre conditioning the data to match the algorithms
+    treated_data = DataTreatment.data_treatment(data_series)
+
+    # Calculating useful values invoking dedicated functions
+    slope_value = math.slope(treated_data['slope_data'])
+    range_value = math.range_value(treated_data['range_data'])
+    average_value = math.average(treated_data['average_data'])
+
+    if (slope_value is not None and range_value is not None and
+            average_value is not None):
+        # Verification of the Steady State conditions following the SNIA
+        # definition
+        range_condition = range_value < 0.20 * abs(average_value)
+        slope_condition = slope_value < 0.10 * abs(average_value)
+
+        steady_state = range_condition and slope_condition
+
+    else:
+        steady_state = False
+
+    return steady_state