[2f6f4c3] | 1 | r""" |
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| 2 | This model describes a Lorentzian shaped peak on a flat background. |
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| 3 | |
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| 4 | Definition |
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| 5 | ---------- |
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| 6 | |
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| 7 | The scattering intensity $I(q)$ is calculated as |
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| 8 | |
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| 9 | .. math:: |
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| 10 | |
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| 11 | I(q) = \frac{scale}{\bigl(1+\bigl(\frac{q-q_0}{B}\bigr)^2\bigr)} + background |
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| 12 | |
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| 13 | with the peak having height of $I_0$ centered at $q_0$ and having a HWHM (half-width half-maximum) of B. |
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| 14 | |
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| 15 | For 2D data the scattering intensity is calculated in the same way as 1D, |
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| 16 | where the $q$ vector is defined as |
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| 17 | |
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| 18 | .. math:: |
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| 19 | |
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| 20 | q = \sqrt{q_x^2 + q_y^2} |
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| 21 | |
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| 22 | |
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| 23 | .. figure:: img/peak_lorentz_1d.jpg |
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| 24 | |
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| 25 | 1D plot using the default values (w/200 data point). |
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| 26 | |
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| 27 | References |
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| 28 | ---------- |
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| 29 | |
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| 30 | None. |
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| 31 | |
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| 32 | """ |
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| 33 | |
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| 34 | from numpy import inf, sqrt |
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| 35 | |
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| 36 | name = "peak_lorentz" |
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| 37 | title = "A Lorentzian peak on a flat background" |
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| 38 | description = """\ |
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| 39 | Class that evaluates a lorentzian shaped peak. |
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| 40 | |
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| 41 | F(q) = scale/(1+[(q-q0)/B]^2 ) + background |
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| 42 | |
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| 43 | The model has three parameters: |
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| 44 | scale = scale |
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| 45 | peak_pos = peak position |
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| 46 | peak_hwhm = half-width-half-maximum of peak |
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| 47 | background= incoherent background""" |
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| 48 | |
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| 49 | category = "shape-independent" |
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| 50 | |
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| 51 | # ["name", "units", default, [lower, upper], "type", "description"], |
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| 52 | parameters = [["peak_pos", "1/Ang", 0.05, [-inf, inf], "", "Peak postion in q"], |
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| 53 | ["peak_hwhm", "1/Ang", 0.005, [-inf, inf], "", "HWHM of peak"], |
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| 54 | ] |
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| 55 | |
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| 56 | def Iq(q, peak_pos, peak_hwhm): |
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| 57 | inten = (1/(1+((q-peak_pos)/peak_hwhm)**2)) |
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| 58 | return inten |
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| 59 | Iq.vectorized = True # Iq accepts an array of q values |
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| 60 | |
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| 61 | def Iqxy(qx, qy, *args): |
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| 62 | return Iq(sqrt(qx ** 2 + qy ** 2), *args) |
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| 63 | Iqxy.vectorized = True # Iqxy accepts an array of qx, qy values |
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| 64 | |
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| 65 | |
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| 66 | demo = dict(scale=100, background=1.0, |
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| 67 | peak_pos=0.05, peak_hwhm=0.005) |
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| 68 | |
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| 69 | oldname = "PeakLorentzModel" |
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| 70 | oldpars = dict(peak_pos='q0', peak_hwhm='B') |
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| 71 | |
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[14ba6f6] | 72 | tests = [[{'scale':100.0, 'background':1.0}, 0.001, 2.0305]] |
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