1 | r""" |
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2 | This model calculates intensity using simple linear function |
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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) = \text{scale} (A + B \cdot q) + \text{background} |
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12 | |
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13 | .. note:: |
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14 | For 2D plots intensity has different definition than other shape independent models |
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15 | |
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16 | .. math:: |
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17 | |
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18 | I(q) = \text{scale} (I(qx) \cdot I(qy)) + \text{background} |
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19 | |
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20 | References |
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21 | ---------- |
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22 | |
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23 | None. |
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24 | |
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25 | Source |
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26 | ------ |
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27 | |
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28 | `line.py <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/line.py>`_ |
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29 | |
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30 | Authorship and Verification |
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31 | ---------------------------- |
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32 | |
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33 | * **Author:** |
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34 | * **Last Modified by:** |
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35 | * **Last Reviewed by:** |
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36 | * **Source added by :** Steve King **Date:** March 25, 2019""" |
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37 | |
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38 | import numpy as np |
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39 | from numpy import inf |
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40 | |
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41 | name = "line" |
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42 | title = "Line model" |
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43 | description = """\ |
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44 | I(q) = A + B*q |
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45 | |
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46 | List of default parameters: |
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47 | A = intercept |
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48 | B = slope |
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49 | """ |
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50 | category = "shape-independent" |
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51 | |
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52 | # pylint: disable=bad-whitespace, line-too-long |
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53 | # ["name", "units", default, [lower, upper], "type", "description"], |
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54 | parameters = [["intercept", "1/cm", 1.0, [-inf, inf], "", "intercept in linear model"], |
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55 | ["slope", "Ang/cm", 1.0, [-inf, inf], "", "slope in linear model"], |
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56 | ] |
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57 | # pylint: enable=bad-whitespace, line-too-long |
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58 | |
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59 | def Iq(q, intercept, slope): |
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60 | """ |
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61 | :param q: Input q-value |
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62 | :param intercept: Intrecept in linear model |
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63 | :param slope: Slope in linear model |
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64 | :return: Calculated Intensity |
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65 | """ |
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66 | inten = intercept + slope*q |
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67 | return inten |
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68 | |
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69 | Iq.vectorized = True # Iq accepts an array of q values |
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70 | |
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71 | |
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72 | def Iqxy(qx, qy, intercept, slope): |
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73 | """ |
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74 | :param qx: Input q_x-value |
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75 | :param qy: Input q_y-value |
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76 | :param intercept: Intrecept in linear model |
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77 | :param slope: Slope in linear model |
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78 | :return: 2D-Intensity |
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79 | """ |
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80 | # TODO: SasView documents 2D intensity as Iq(qx)*Iq(qy), but returns Iq(qy) |
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81 | # Note: SasView.run([r, theta]) does return Iq(qx)*Iq(qy) |
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82 | return Iq(qx, intercept, slope)*Iq(qy, intercept, slope) |
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83 | |
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84 | Iqxy.vectorized = True # Iqxy accepts an array of qx qy values |
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85 | |
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86 | # uncomment the following to test Iqxy in C models |
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87 | #del Iq, Iqxy |
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88 | #c_code = """ |
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89 | #static double Iq(double q, double b, double m) { return m*q+b; } |
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90 | #static double Iqxy(double qx, double qy, double b, double m) |
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91 | #{ return (m*qx+b)*(m*qy+b); } |
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92 | #""" |
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93 | |
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94 | def random(): |
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95 | """Return a random parameter set for the model.""" |
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96 | scale = 10**np.random.uniform(0, 3) |
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97 | slope = np.random.uniform(-1, 1)*1e2 |
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98 | offset = 1e-5 + (0 if slope > 0 else -slope) |
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99 | intercept = 10**np.random.uniform(0, 1) + offset |
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100 | pars = dict( |
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101 | #background=0, |
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102 | scale=scale, |
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103 | slope=slope, |
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104 | intercept=intercept, |
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105 | ) |
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106 | return pars |
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107 | |
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108 | tests = [ |
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109 | [{'intercept': 1.0, 'slope': 1.0, }, 1.0, 2.001], |
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110 | [{'intercept': 1.0, 'slope': 1.0, }, 0.0, 1.001], |
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111 | [{'intercept': 1.0, 'slope': 1.0, }, 0.4, 1.401], |
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112 | [{'intercept': 1.0, 'slope': 1.0, }, 1.3, 2.301], |
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113 | [{'intercept': 1.0, 'slope': 1.0, }, 0.5, 1.501], |
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114 | [{'intercept': 1.0, 'slope': 1.0, }, [0.4, 0.5], [1.401, 1.501]], |
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115 | [{'intercept': 1.0, 'slope': 1.0, 'background': 0.0, }, (1.3, 1.57), 5.911], |
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116 | ] |
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