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PySumReg#

Statistics of sequence of \((x, y)\) pairs from calculator-style summation registers.

Why use this package?#

Use this package to obtain summary statistics of a list of \((x, y)\) pairs when the pairs are presented in sequence, such as from a control system. It is not necessary to retain the entire list in memory, this package will retain the cumulative values necessary to compute all analytical results.

There are no external dependencies on add-on packages such as numpy or scipy. Only the math (https://docs.python.org/3/library/math.html) package from the Python Standard Library is used.

Statistics may be calculated at any time from the summation registers.

The \((x, y)\) values may be entered in any order. It is not necessary to sort them.

Examples#

We start these examples by first creating a set of registers:

import pysumreg
reg = pysumreg.SummationRegisters()

Mean and Standard Deviation#

Find the mean and standard deviation of a set of ordered pairs:

reg.clear()
reg.add(1, -1)
reg.add(2, -2)
reg.add(3, -3)
print(f"{reg.mean_x=}")
print(f"{reg.stddev_x=}")
print(f"{reg.mean_y=}")
print(f"{reg.stddev_y=}")
print(f"{reg.min_x=}")
print(f"{reg.max_x=}")
print(f"{reg.min_y=}")
print(f"{reg.max_y=}")
print(f"{reg.x_at_max_y=}")
print(f"{reg.x_at_min_y=}")

which prints these results:

reg.mean_x=2.0
reg.stddev_x=1.0
reg.mean_y=-2.0
reg.stddev_y=1.0
reg.min_x=1
reg.max_x=3
reg.min_y=-3
reg.max_y=-1
reg.x_at_max_y=1
reg.x_at_min_y=3

Linear Analysis#

Using the same data as above, assess if this is a good linear fit. The correlation coefficient provides a measure of the correlation between the \(x\) and \(y\) values. Value of 1.0 indicates an exact fit to a straight line with positive slope (-1 means anti-correlated: a negative straight line). Zero means that the \(x\) and \(y\) values are not correlated, no linear fit.

reg.clear()
reg.add(1, -1)
reg.add(2, -2)
reg.add(3, -3)
print(f"{reg.correlation=}")
print(f"{reg.intercept=}")
print(f"{reg.slope=}")

which prints these results:

reg.correlation=-1.0
reg.intercept=0.0
reg.slope=-1.0

Peak Analysis#

Assuming that the data might represent a peak, compute parameters describing its center and width. We obtain the width (\(~2\sigma_c\)) from the variance (\(\sigma_c^2\)) of the \(x\) values weighted by the \(y\) values.

reg.clear()
reg.add(1, 0)
reg.add(2, 1)
reg.add(3, 0)
print(f"{reg.max_y=}")
print(f"{reg.centroid=}")
print(f"{reg.sigma=}")

which prints these results:

reg.max_y=1
reg.centroid=2.0
reg.sigma=0.0

With only three values, it’s an exact fit to the underlying statistical model of the variance. We need more data (with \(y\) values that are not zero) to obtain a non-zero \(\sigma_c\):

reg.add(1.5, 0.5)
reg.add(2.5, 0.5)
print(f"{reg.max_y=}")
print(f"{reg.centroid=}")
print(f"{reg.sigma=}")

which prints these results:

reg.max_y=1
reg.centroid=2.0
reg.sigma=0.3535533905932738

Summary#

Print the entire contents of the summation registers object:

reg

which prints these results (re-formatted for display here):

SummationRegisters(
  X=10.0,
  XX=22.5,
  XXY=8.25,
  XY=4.0,
  Y=2.0,
  YY=1.5,
  centroid=2.0,
  correlation=0.0,
  intercept=0.4,
  max_x=3,
  max_y=1,
  mean_x=2.0,
  mean_y=0.4,
  min_x=1,
  min_y=0.5,
  n=5,
  sigma=0.3535533905932738,
  slope=0.0,
  stddev_x=0.7905694150420949,
  stddev_y=0.4183300132670378,
  x_at_max_y=2,
  x_at_min_y=3
)

Installation#

This package may be installed by any of these commands:

  • pip install pysumreg

  • conda install -c conda-forge pysumreg

  • conda install -c conda-forge pysumreg

  • mamba install -c conda-forge pysumreg

  • micromamba install -c conda-forge pysumreg

About#

documentation:

https://prjemian.github.io/pysumreg/latest

source:

prjemian/pysumreg

version:

1.0

release:

1.0.7.dev1+gc4a1bdc

published:

2024-02-15 08:50

Contents:

Indices and tables#

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