trapz_errors: A Python repository from M-R-Schaefer

This is a fork of the trapz_errors package created by Martin Stroet with the goal to update it to Python 3.X. My main interest is not in using the package itself, but as a dependency of the umbrella_integration package. As such, I do not intend to add features to it, just to make it usable in a modern python environment.

This fork is not an official Kästner group endeavor.

Error Analysis for Trapezoidal Rule Applied to Uncertain Data

A tool to analyse errors associated with applying the Trapezoidal rule to uncertain data.

Author: Martin Stroet (University of Queensland)

Installation

You can install trapz_errors by running one of the commands below

pip install git+https://github.com/M-R-Schaefer/trapz_errors

# to add it as a dependency to your project
poetry add git+https://github.com/M-R-Schaefer/trapz_errors

Usage: Calculate integration error considering y-value uncertainty and truncation error.

python calculate_error.py [-h] -d DATA [-p [PLOT]] [-s SIGFIGS] [-v] [-c]

arguments:
  -h, --help            show this help message and exit
  -d DATA, --data DATA  File containing data to integrate. Lines are read as
                        whitespace separated values of the form: <x> <y>
                        [<y_error>].
  -p [PLOT], --plot [PLOT]
                        Show plot of integration errors, requires matplotlib.
                        Optional argument will determine where and in what
                        format the figure will be saved in.
  -s SIGFIGS, --sigfigs SIGFIGS
                        Number of significant figures in output. Default=3
  -v, --verbose         Output error breakdown.
  -c, --conservative    Make a conservative estimate of the total truncation
                        error; add the maximum interval error to the sum of
                        all interval errors.

Usage: Identify largest sources of uncertainty.

python reduce_error.py [-h] -d DATA [-p [PLOT]] [-s SIGFIGS] [-v] [-c] -t
                       TARGET_ERROR [-r CONVERGENCE_RATE_SCALING]

arguments:
  -h, --help            show this help message and exit
  -d DATA, --data DATA  File containing data to integrate. Lines are read as
                        whitespace separated values of the form: <x> <y>
                        [<y_error>].
  -p [PLOT], --plot [PLOT]
                        Show plot of integration errors, requires matplotlib.
                        Optional argument will determine where and in what
                        format the figure will be saved in.
  -s SIGFIGS, --sigfigs SIGFIGS
                        Number of significant figures in output. Default=3
  -v, --verbose         Output error breakdown.
  -c, --conservative    Make a conservative estimate of the total truncation
                        error; add the maximum interval error to the sum of
                        all interval errors.
  -t TARGET_ERROR, --target_error TARGET_ERROR
                        Target error of integration, used to determine how to
                        reduce integration uncertainty.
  -r CONVERGENCE_RATE_SCALING, --convergence_rate_scaling CONVERGENCE_RATE_SCALING
                        Determines the rate of convergence to the target error
                        i.e. how many iterations will be required to reach
                        target error. A value < 1 will result in more
                        iterations but fewer overall points as the points will
                        be concentrated in regions of high uncertainty;
                        conversely values > 1 will result it more points but
                        fewer iterations required to reach a given target
                        error. Default=1.

Example

For an example of how to use this tool see example/example.sh