Peak fitting

Rampy will soon offer a dedicated function for peak fitting: rampy.fit_peaks will use curve_fit from scipy.optimize to fit your spectrum with a model that is a sum of peaks.

Users can also use dedicated interfaces such as lmfit. We provide an example of peak-fitting with the lmfit for instance here: Example notebooks .

Peak shapes

Rampy offers functions for various peak shapes, including:

  • gaussian peaks > rampy.gaussian

  • lorentzian peaks > rampy.lorentzian

  • pseudo-voigt peaks > rampy.pseudovoigt

  • pearson7 peaks > rampy.pearson7

rampy.gaussian(x: ndarray, amp, freq, HWHM) → ndarray

Computes a Gaussian peak.

Parameters:

  • x (np.ndarray) – x axis

  • amp (float or np.ndarray) – Peak amplitude

  • freq (float or np.ndarray) – Peak position

  • HWHM (float or np.ndarray) – Peak half-width at half-maximum.

Returns:

calculated peak.

Return type:

np.ndarray

Notes

Formula used: ( ext{amp} cdot exp(-log(2) cdot ((x - ext{freq}) / ext{HWHM})^2) ).

Examples

You can create a single peak like:

>>> x = np.linspace(0, 10, 1000)
>>> y = rampy.gaussian(x, 10., 3., 1.0)

You can also create an array with several peaks in columns using arrays for the peak parameters:

>>> x = np.linspace(0, 10, 1000)
>>> y = rampy.gaussian(x.reshape(-1, 1), np.array([[10, 10.]]), np.array([[3, 7.]]), np.array([[1., 1.]]))

In this case, y will be an array of shape (len(x), 2) with one peak per columns. Your peaks can even share parameters, here the HWHM:

>>> y = rampy.gaussian(x.reshape(-1, 1), np.array([[10, 10.]]), np.array([[3, 7.]]), 2.0)

The composite signal is simply given by

>>> y_sum = np.sum(y, axis=1)
rampy.lorentzian(x: ndarray, amp, freq, HWHM) → ndarray

Computes a Lorentzian peak.

Parameters:

  • x (np.ndarray) – x axis

  • amp (float or np.ndarray) – Peak amplitude

  • freq (float or np.ndarray) – Peak position

  • HWHM (float or np.ndarray) – Peak half-width at half-maximum.

Returns:

calculated peak.

Return type:

np.ndarray

Notes

Formula used: ( ext{amp} / (1 + ((x - ext{freq}) / ext{HWHM})^2) ).

Examples

You can create a single peak like:

>>> x = np.linspace(0, 10, 1000)
>>> y = rampy.lorentzian(x, 10., 3., 1.0)

You can also create an array with several peaks in columns using arrays for the peak parameters:

>>> x = np.linspace(0, 10, 1000)
>>> y = rampy.lorentzian(x.reshape(-1, 1), np.array([[10, 10.]]), np.array([[3, 7.]]), np.array([[1., 1.]]))

In this case, y will be an array of shape (len(x), 2) with one peak per columns. Your peaks can even share parameters, here the HWHM:

>>> y = rampy.lorentzian(x.reshape(-1, 1), np.array([[10, 10.]]), np.array([[3, 7.]]), 2.0)

The composite signal is simply given by

>>> y_sum = np.sum(y, axis=1)
rampy.pseudovoigt(x: ndarray, amp, freq, HWHM, L_ratio) → ndarray

Computes a pseudo-Voigt peak.

Parameters:

  • x (np.ndarray) – x axis

  • amp (float or np.ndarray) – Peak amplitude

  • freq (float or np.ndarray) – Peak position

  • HWHM (float or np.ndarray) – Peak half-width at half-maximum.

  • L_ratio (float) – Ratio of the Lorentzian component, must be between 0 and 1 (inclusive).

Returns:

The computed pseudo-Voigt signal.

Return type:

np.ndarray

Raises:

ValueError – If L_ratio is not between 0 and 1.

Notes

Formula used: ( (1 - L_{ ext{ratio}}) cdot ext{gaussian}(x, ext{amp}, ext{freq}, ext{HWHM}) +

L_{ ext{ratio}} cdot ext{lorentzian}(x, ext{amp}, ext{freq}, ext{HWHM}) ).

Examples

You can create a single peak like:

>>> x = np.linspace(0, 10, 1000)
>>> y = rampy.pseudovoigt(x, 10., 3., 1.0, 0.5)

You can also create an array with several peaks in columns using arrays for the peak parameters:

>>> x = np.linspace(0, 10, 1000)
>>> y = rampy.pseudovoigt(x.reshape(-1, 1), np.array([[10, 10]]), np.array([[3, 7]]), np.array([[1., 1.]]), np.array([[0.5, 0.5]]))

In this case, y will be an array of shape (len(x), 2) with one peak per columns. Your peaks can even share parameters, here the L_ratio:

>>> y = rampy.pseudovoigt(x.reshape(-1, 1), np.array([[10, 10]]), np.array([[3, 7]]), np.array([[1., 1.]]), 0.5)

The composite signal is simply given by

>>> y_sum = np.sum(y, axis=1)
rampy.pearson7(x, a0, a1, a2, a3)

Computes a Pearson VII peak.

Parameters:

  • x (np.ndarray) – Positions at which the signal should be sampled.

  • x – x axis

  • a0 (float or np.ndarray) – Peak amplitude

  • a1 (float or np.ndarray) – Peak position

  • a2 (float or np.ndarray) – Peak width

  • a3 (float or np.ndarray) – Peak shape parameter.

Returns:

The computed Pearson VII signal.

Return type:

np.ndarray

Notes

Formula used: ( a_0 / ((1 + ((x - a_1) / a_2)^2 cdot (2^{(1/a_3)} - 1))^{a_3}) ).

Examples

You can create a single peak like:

>>> x = np.linspace(0, 10, 1000)
>>> y = rampy.pearson7(x, 10., 3., 1.0, 0.5)

You can also create an array with several peaks in columns using arrays for the peak parameters:

>>> x = np.linspace(0, 10, 1000)
>>> y = rampy.pearson7(x.reshape(-1, 1), np.array([[10, 10]]), np.array([[3, 7]]), np.array([[1., 1.]]), np.array([[0.5, 0.5]]))

In this case, y will be an array of shape (len(x), 2) with one peak per columns. Your peaks can even share parameters, here the a3:

>>> y = rampy.pearson7(x.reshape(-1, 1), np.array([[10, 10]]), np.array([[3, 7]]), np.array([[1., 1.]]), 0.5)

The composite signal is simply given by

>>> y_sum = np.sum(y, axis=1)

Peak areas

Peak area can be calculated using the rampy.area_peak function, using analytical functions.

Note that the old function rampy.peakarea is still available but it will be removed in a near future. It uses numerical integration and is thus less precise than the rampy.area_peak function.

rampy.area_peak(peak_type: Literal['gaussian', 'lorentzian', 'pseudovoigt', 'pearson7'], amplitude: float, hwhm: float, *, lorentzian_fraction: float | None = None, exponent: float | None = None) → float

Calculates the analytical area under a peak based on its type and parameters.

Parameters:

  • peak_type – Type of peak (gaussian, lorentzian, pseudovoigt, pearson7)

  • amplitude – Amplitude of the peak (maximum height)

  • hwhm – Half-width at half-maximum of the peak

  • lorentzian_fraction – Lorentzian fraction for Pseudo-Voigt [0, 1]

  • exponent – Shape parameter for Pearson VII

Returns:

Area under the specified peak

Raises:

ValueError – For invalid arguments or missing required parameters

Examples

>>> area_peaks("gaussian", 2.0, 0.5)
2.3548200450309493

>>> area_peaks("pseudovoigt", 2.0, 0.5, lorentzian_fraction=0.5)
3.141592653589793

Propagate uncertainties

A good way to propagate the uncertainties of your model is to directly use the uncertainties package, see the docs here.