[2eaae42] | 1 | r""" |
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[9d76d29] | 2 | |
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| 3 | Definition |
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| 4 | ---------- |
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| 5 | |
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[4c8f9cd] | 6 | This model describes a Gaussian shaped peak on a flat background |
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[2eaae42] | 7 | |
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[9d76d29] | 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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[2eaae42] | 18 | |
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[9d76d29] | 19 | .. math:: |
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[2eaae42] | 20 | |
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[9d76d29] | 21 | q = \sqrt{q_x^2 + q_y^2} |
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[2eaae42] | 22 | |
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| 23 | |
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[9d76d29] | 24 | .. image:: img/gaussian_peak_1d.jpg |
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[2eaae42] | 25 | |
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[9d76d29] | 26 | 1D plot using the default values (w/500 data points). |
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[2eaae42] | 27 | |
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[9d76d29] | 28 | Reference |
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[a5d0d00] | 29 | --------- |
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[2eaae42] | 30 | |
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[4c8f9cd] | 31 | None. |
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[2eaae42] | 32 | """ |
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| 33 | |
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[3c56da87] | 34 | from numpy import inf |
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[2eaae42] | 35 | |
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[4c8f9cd] | 36 | name = "gaussian_peak" |
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| 37 | title = "Gaussian shaped peak" |
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| 38 | description = """ |
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| 39 | Model describes a Gaussian shaped peak including a flat background |
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[9d76d29] | 40 | Provide F(q) = scale*exp( -1/2 *[(q-q0)/sigma]^2 )+ background |
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[2eaae42] | 41 | """ |
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[a5d0d00] | 42 | category = "shape-independent" |
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[2eaae42] | 43 | |
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[3e428ec] | 44 | # ["name", "units", default, [lower, upper], "type","description"], |
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| 45 | parameters = [["q0", "1/Ang", 0.05, [-inf, inf], "", "Peak position"], |
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[9d76d29] | 46 | ["sigma", "1/Ang", 0.005, [0, inf], "", |
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[3e428ec] | 47 | "Peak width (standard deviation)"], |
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| 48 | ] |
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[2eaae42] | 49 | |
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| 50 | # No volume normalization despite having a volume parameter |
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| 51 | # This should perhaps be volume normalized? |
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| 52 | form_volume = """ |
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[6ea6902] | 53 | return 1.0; |
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[2eaae42] | 54 | """ |
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| 55 | |
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| 56 | Iq = """ |
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[6ea6902] | 57 | return exp(-0.5*pow((q - q0)/sigma,2.0)); |
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[2eaae42] | 58 | """ |
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| 59 | |
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| 60 | |
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| 61 | Iqxy = """ |
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| 62 | // never called since no orientation or magnetic parameters. |
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| 63 | //return -1.0; |
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[4c8f9cd] | 64 | return Iq(sqrt(qx*qx + qy*qy), q0, sigma); |
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[2eaae42] | 65 | """ |
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| 66 | |
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| 67 | |
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| 68 | # VR defaults to 1.0 |
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| 69 | |
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[3e428ec] | 70 | demo = dict(scale=1, background=0, q0=0.05, sigma=0.005) |
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[4c8f9cd] | 71 | oldname = "PeakGaussModel" |
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| 72 | oldpars = dict(sigma='B') |
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