pyextal.larbed.peaks¶

Least-squares peak fitting used to locate the direct beam on the detector.

Each model function is a factory: it takes the model parameters and returns a callable evaluated on pixel index arrays, which is what scipy.optimize.leastsq() is driven with here.

Functions¶

`gaussian2D`(height, center_y, center_x, width_x)	Builds a circular 2D Gaussian.
`gaussian1D`(height, center, width)	Builds a 1D Gaussian.
`lorentzian1D`(height, center, width, y0, slope)	Builds a 1D Lorentzian on a linear background.
`lorentzian2D`(height, center_x, center_y, width_x, a, b, c)	Builds a circular 2D Lorentzian on a planar background.
`moments`(data)	Estimates Gaussian parameters of a 2D distribution from its moments.
`fitPeak2D`(data, func)	Fits a 7-parameter 2D peak model with a planar background.
`fitPeak`(data, func)	Fits 1D models to the two projections of a 2D peak.
`fitPeak2DGauss`(data, func)	Fits a 4-parameter circular 2D Gaussian.

Module Contents¶

pyextal.larbed.peaks.gaussian2D(height, center_y, center_x, width_x)¶

Builds a circular 2D Gaussian.

Parameters:

height (float) – Peak amplitude.
center_y (float) – Centre along the first axis.
center_x (float) – Centre along the second axis.
width_x (float) – Standard deviation, shared by both axes.

Returns:

f(x, y) evaluating the Gaussian.

Return type:

callable

pyextal.larbed.peaks.gaussian1D(height, center, width)¶

Builds a 1D Gaussian.

Parameters:

height (float) – Peak amplitude.
center (float) – Peak centre.
width (float) – Standard deviation.

Returns:

f(x) evaluating the Gaussian.

Return type:

callable

pyextal.larbed.peaks.lorentzian1D(height, center, width, y0, slope)¶

Builds a 1D Lorentzian on a linear background.

Parameters:

height (float) – Peak amplitude.
center (float) – Peak centre.
width (float) – Half-width at half-maximum.
y0 (float) – Background offset.
slope (float) – Background slope.

Returns:

f(x) evaluating the Lorentzian plus background.

Return type:

callable

pyextal.larbed.peaks.lorentzian2D(height, center_x, center_y, width_x, a, b, c)¶

Builds a circular 2D Lorentzian on a planar background.

Parameters:

height (float) – Peak amplitude.
center_x (float) – Centre along the second axis.
center_y (float) – Centre along the first axis.
width_x (float) – Half-width at half-maximum.
a (float) – Background gradient along x.
b (float) – Background gradient along y.
c (float) – Background offset.

Returns:

f(y, x) evaluating the Lorentzian plus background.

Return type:

callable

pyextal.larbed.peaks.moments(data)¶

Estimates Gaussian parameters of a 2D distribution from its moments.

Parameters:: data (np.ndarray) – 2D image containing a single peak.
Returns:: Two (height, centre, width) triples, for the second and first axes respectively, suitable as a least-squares starting guess.
Return type:: tuple

pyextal.larbed.peaks.fitPeak2D(data, func)¶

Fits a 7-parameter 2D peak model with a planar background.

Parameters:

data (np.ndarray) – 2D image containing a single peak.
func (callable) – Model factory taking 7 parameters, such as lorentzian2D().

Returns:

The fitted parameters.

Return type:

np.ndarray

pyextal.larbed.peaks.fitPeak(data, func)¶

Fits 1D models to the two projections of a 2D peak.

Parameters:

data (np.ndarray) – 2D image containing a single peak.
func (callable) – 1D model factory taking 5 parameters, such as lorentzian1D().

Returns:

[xh, xc, xw, yh, yc, yw] — amplitude, centre, and width for each projection.

Return type:

np.ndarray

pyextal.larbed.peaks.fitPeak2DGauss(data, func)¶

Fits a 4-parameter circular 2D Gaussian.

Parameters:

data (np.ndarray) – 2D image containing a single peak.
func (callable) – Model factory taking 4 parameters, normally gaussian2D().

Returns:

[height, center_y, center_x, width_x].

Return type:

np.ndarray