ChemCal 0.0.5

A collection of functions that simplify the process of creating calibration curves.

ChemCal

Install

pip install ChemCal

How to use

First we generate some data to work with.

# generate training data and sample data
test_data = pd.DataFrame({'concentration': [0.2, 0.05, 0.1, 0.8, 0.6, 0.4], "abs": [0.221, 0.057, 0.119, 0.73, 0.599, 0.383]})
sample_data = pd.DataFrame({'unknown': [0.490, 0.471, 0.484, 0.473, 0.479, 0.492]})

Now, create a CalibrationModel object and pass the predictor and response variables from our dataset as the x and y values respectively.

cal = CalibrationModel(x=test_data['concentration'], y=test_data['abs'])

When we call .fit_ols(), an ordinary least squares regression is fit to the data and the slope, intercept and values are stored in the object and can be retrieved by calling .slope, .intercept and .r_squared respectively.

cal.fit_ols()

print(f"Slope: {cal.slope: .3f}" )
print(f"Intercept: {cal.intercept: .3f}" )
print(f"R2: {cal.r_squared: .3f}" )

Slope:  0.904
Intercept:  0.027
R2:  0.998

We can also call the method .linest_stats() to return a series of statistics you might expect when using the linest function in excel or sheets.

cal.linest_stats()

<style scoped> .dataframe tbody tr th:only-of-type { vertical-align: middle; } .dataframe tbody tr th { vertical-align: top; } .dataframe thead th { text-align: right; } </style>

	Slope	Intercept	Uncertainty in slope	Uncertainty in intercept	Standard error of regression	F-statistic	Degrees of freedom	Regression sum of squares	Residual sum of squares
0	0.904411	0.027419	0.0312	0.017178	0.020745	840.261133	4	0.361606	0.001721

Finally, we can calculate an inverse prediction from unknown data and retrieve the uncertainty but calling .inverse_prediction().

pred = cal.inverse_prediction(sample_data['unknown'])
print(pred)

0.5020733029033536 ± 0.031053583676141718

The uncertainty is calculated according to the following expression:

$$ U = {S_{\hat{x}}}_0 * T $$

Where if a single sample is provided:

$$ {S_{\hat{x}}}0 = \frac{S{y/x}}{b} \sqrt{\frac{1}{m} + \frac{1}{n}} $$

Or, if multiple replicate samples are provided:

$$ s_{\hat{x}0}=\frac{1}{b} \sqrt{\frac{s_r^2}{m}+\frac{s{y / x}^2}{n}+\frac{s_{y / x}^2\left(y_0-\bar{y}\right)^2}{b^2 \sum_{i=1}^n\left(x_i-\bar{x}\right)^2}} $$