1 | r""" |
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2 | |
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3 | Definition |
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4 | ---------- |
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5 | |
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6 | This model describes a Gaussian shaped peak on a flat background |
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7 | |
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8 | .. math:: |
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9 | |
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10 | I(q) = (\text{scale}) \exp\left[ -\tfrac12 (q-q_0)^2 / \sigma^2 \right] |
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11 | + \text{background} |
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12 | |
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13 | with the peak having height of *scale* centered at $q_0$ and having a standard |
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14 | deviation of $\sigma$. The FWHM (full-width half-maximum) is $2.354 \sigma$. |
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15 | |
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16 | For 2D data, scattering intensity is calculated in the same way as 1D, |
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17 | where the $q$ vector is defined as |
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18 | |
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19 | .. math:: |
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20 | |
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21 | q = \sqrt{q_x^2 + q_y^2} |
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22 | |
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23 | |
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24 | References |
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25 | ---------- |
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26 | |
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27 | None. |
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28 | """ |
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29 | |
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30 | import numpy as np |
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31 | from numpy import inf |
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32 | |
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33 | name = "gaussian_peak" |
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34 | title = "Gaussian shaped peak" |
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35 | description = """ |
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36 | Model describes a Gaussian shaped peak including a flat background |
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37 | Provide F(q) = scale*exp( -1/2 *[(q-peak_pos)/sigma]^2 )+ background |
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38 | """ |
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39 | category = "shape-independent" |
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40 | |
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41 | # ["name", "units", default, [lower, upper], "type","description"], |
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42 | parameters = [["peak_pos", "1/Ang", 0.05, [-inf, inf], "", "Peak position"], |
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43 | ["sigma", "1/Ang", 0.005, [0, inf], "", |
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44 | "Peak width (standard deviation)"], |
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45 | ] |
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46 | |
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47 | Iq = """ |
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48 | double scaled_dq = (q - peak_pos)/sigma; |
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49 | return exp(-0.5*scaled_dq*scaled_dq); //sqrt(2*M_PI*sigma*sigma); |
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50 | """ |
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51 | |
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52 | # VR defaults to 1.0 |
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53 | |
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54 | def random(): |
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55 | peak_pos = 10**np.random.uniform(-3, -1) |
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56 | sigma = 10**np.random.uniform(-1.3, -0.3)*peak_pos |
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57 | scale = 10**np.random.uniform(0, 4) |
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58 | pars = dict( |
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59 | #background=1e-8, |
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60 | scale=scale, |
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61 | peak_pos=peak_pos, |
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62 | sigam=sigma, |
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63 | ) |
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64 | return pars |
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