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Diffstat (limited to 'storperf/utilities/math.py')
| -rw-r--r-- | storperf/utilities/math.py | 52 |
1 files changed, 52 insertions, 0 deletions
diff --git a/storperf/utilities/math.py b/storperf/utilities/math.py new file mode 100644 index 0000000..3b124cd --- /dev/null +++ b/storperf/utilities/math.py @@ -0,0 +1,52 @@ +############################################################################## +# 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 +############################################################################## + +class math(object): + + @staticmethod + 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...) + """ + + if len(data_series)==0: #In the particular case of an empty data series + beta2 = 0 + + 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 + + """ + 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] + + 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 + + return beta2 + + |