neutronpy.functions.gaussian2d¶
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neutronpy.functions.
gaussian2d
(p, q)[source]¶ Returns an arbitrary number of two-dimensional Gaussian profiles.
Parameters: - p : ndarray
Parameters for the Gaussian, in the following format:
p[0] Constant background p[1] Linear background slope p[2] Volume under the first peak p[3] X position of the first peak p[4] Y position of the first peak p[5] FWHM_x of the first peak p[6] FWHM_y of the first peak p[7] Area under the second peak p[…] etc. - q : tuple
Tuple of two one-dimensional input arrays.
Returns: - out : ndarray
One dimensional Gaussian profile.
Notes
A Gaussian profile is defined as:
\[f(q) = \frac{a}{\sigma \sqrt{2\pi}} e^{-\left(\frac{(q_x-q_x0)^2}{2\sigma_x^2} + \frac{(q_y-q_y0)^2}{2\sigma_y^2}\right)},\]where the integral over the whole function is a, and
\[fwhm = 2 \sqrt{2 \ln{2}} \sigma.\]Examples
Plot a single gaussian with an integrated intensity of 1, centered at (0, 0), and fwhm of 0.3:
>>> import matplotlib.pyplot as plt >>> import numpy as np >>> p = np.array([0., 0., 1., 0., 0., 0.3, 0.3]) >>> x, y = np.meshgrid(np.linspace(-1, 1, 101), np.linspace(-1, 1, 101)) >>> z = gaussian(p, (x, y)) >>> plt.pcolormesh(x, y, z) >>> plt.show()
Plot two gaussians, equidistant from the origin with the same intensity and fwhm as above:
>>> p = np.array([0., 0., 1., -0.3, -0.3, 0.3, 0.3, 1., 0.3, 0.3, 0.3, 0.3]) >>> x, y = np.meshgrid(np.linspace(-1, 1, 101), np.linspace(-1, 1, 101)) >>> z = gaussian(p, x) >>> plt.pcolormesh(x, y, z) >>> plt.show()