Centre of Mass

ibex_bluesky_core.callbacks.CentreOfMass provides functionality for calculating a specific definition of a “centre of mass”: it computes the centre of mass of a 2-dimensional region bounded by:

  • min(x)

  • max(x)

  • min(y)

  • Straight-line segments joining (x, y) data points with their nearest neighbours along the x axis

CentreOfMass stores its result in the result property.

Note

This will return different results from the com property available from bluesky.callbacks.fitting.PeakStats in the following cases:

  • Points irregularly sampled along the x-axis

  • Points with negative y-values

  • x data which does not monotonically increase

For a detailed comparison of the two implementations, see unit tests written to expose tricky cases.

Given non-continuous arrays of collected data x and y, CentreOfMass returns the x value of the centre of mass.

Many of our use cases require that our algorithm follows the following rules:

  • Any background on data should not change the centre of mass.

  • The order in which data is received should not change the centre of mass

  • Should support non-constant point spacing without skewing the centre of mass

Note

Note that this is designed for only positive peaks.

ibex_bluesky_core.callbacks.CentreOfMass is included in our callbacks collection.

Implementation details

  1. Sort x and y arrays in respect of x ascending. This is so that data can be received in any order.

  2. From each y element, subtract min(y). This means that any constant background over data is ignored.

  3. Decompose the curve into a series of trapezoidal regions, and then further decompose those trapezoidal regions into rectangular and triangular regions.

  4. Compute centre of mass of the overall shape by composition of each region:

\[C_x = \frac{\sum_{i}^{} C_{ix} * A_i}{\sum_{i}^{} A_i}\]