metas-b-least 0.6.0

METAS B LEAST is a Python implementation of the B LEAST program of the ISO 6143:2001 norm

METAS B LEAST

METAS B LEAST is a Python implementation of the B LEAST program of the ISO 6143:2001 norm. The derivations of the different fit functions have been explicitly programmed, see metas_b_lest.py. The program has been verified against METAS UncLib which is using automatic differentiation.

The following link will launch an interactive Python environment where you can you use METAS B LEAST:

Examples

Take a look at the following code example for the usage of the METAS B LEAST Python package:

from metas_b_least import *

# Calibration and measurement data
cal_data = b_read_cal_data(os.path.join(data_dir, 'b_least_1_data_cal.txt'))
meas_data = b_read_meas_data(os.path.join(data_dir, 'b_least_1_data_meas.txt'))
b_disp_cal_data(cal_data)

# Fit coefficients of the fit function using the calibration data
b, b_cov, b_res = b_least(cal_data, b_linear_func)
b_disp_cal_results(b, b_cov, b_res)

# Evaluate the fit function with the coefficients at the measurement data
x, x_cov = b_eval(meas_data, b, b_cov, b_linear_func)
b_disp_meas_results(x, x_cov, meas_data)

# Plot calibration data, measurement data and fit function
b_plot(cal_data, meas_data, b, b_cov, b_linear_func)

See as well the following Jupyter Notebooks:

• Example 1
• Example 2
• Example 3

Functions

Input Functions

b_read_cal_data reads calibration data from tabular separated text file where the first column are the x values, the second column are the standard uncertainties of x, the third column are the y values and the forth column are the standard uncertainties of y.

b_read_meas_data reads measurement data from tabular separated text file where the first column are the y values and the second column are the standard uncertainties of y.

Processing Functions

b_least fits the coefficients b of the fit function func using the calibration data cal_data.

b_eval evaluates the fit function func with the coefficients b at the measurement data meas_data.

The following fit functions are available:

Name	Function
b_linear_func	$$x = b_0 + b_1y$$
b_second_order_poly	$$x = b_0 + b_1y + b_2y^2$$
b_third_order_poly	$$x = b_0 + b_1y + b_2y^2 + b_3y^3$$
b_power_func	$$x = b_0 + b_1y^{(1 + b_2)}$$
b_exp_func	$$x = b_0 + b_1e^{b_2y}$$

Output Functions

b_disp_cal_data displays the calibration data cal_data.

b_disp_cal_results displays the coefficients b, the uncertainties of b, the covariance matrix of b, the residual and the maximum absolute value of weighted deviations.

b_disp_meas_results displays the measurement data x and meas_data.

b_plot plots the calibration data cal_data, the measurement data meas_data and the fit function using the coefficients b.

Source Code

https://github.com/wollmich/metas-b-least/

Releases

https://pypi.org/project/metas-b-least/

Requirements

• NumPy
• SciPy
• Matplotlib

---

Michael Wollensack METAS - 08.07.2025