Changeset 5ed76f8 in sasview for src/sas/sasgui/perspectives/fitting/media
- Timestamp:
- Apr 7, 2017 3:11:41 AM (7 years ago)
- Branches:
- master, ESS_GUI, ESS_GUI_Docs, ESS_GUI_batch_fitting, ESS_GUI_bumps_abstraction, ESS_GUI_iss1116, ESS_GUI_iss879, ESS_GUI_iss959, ESS_GUI_opencl, ESS_GUI_ordering, ESS_GUI_sync_sascalc, magnetic_scatt, release-4.2.2, ticket-1009, ticket-1094-headless, ticket-1242-2d-resolution, ticket-1243, ticket-1249, ticket885, unittest-saveload
- Children:
- fca1f50
- Parents:
- 727c05f
- Location:
- src/sas/sasgui/perspectives/fitting/media
- Files:
-
- 5 edited
-
fitting_help.rst (modified) (2 diffs)
-
mag_help.rst (modified) (7 diffs)
-
pd_help.rst (modified) (10 diffs)
-
residuals_help.rst (modified) (3 diffs)
-
sm_help.rst (modified) (12 diffs)
Legend:
- Unmodified
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src/sas/sasgui/perspectives/fitting/media/fitting_help.rst
r6aad2e8 r5ed76f8 381 381 382 382 In the bottom left corner of the *Fit Page* is a box displaying the normalised value 383 of the statistical |chi|\ :sup:`2`parameter returned by the optimiser.383 of the statistical $\chi^2$ parameter returned by the optimiser. 384 384 385 385 Now check the box for another model parameter and click *Fit* again. Repeat this … … 387 387 fit of the theory to the experimental data improves the value of 'chi2/Npts' will 388 388 decrease. A good model fit should easily produce values of 'chi2/Npts' that are 389 close to zero, and certainly <100. See :ref:`Assessing_Fit_Quality`.389 close to one, and certainly <100. See :ref:`Assessing_Fit_Quality`. 390 390 391 391 SasView has a number of different optimisers (see the section :ref:`Fitting_Options`). -
src/sas/sasgui/perspectives/fitting/media/mag_help.rst
r6aad2e8 r5ed76f8 20 20 -------------------------------- 21 21 22 Magnetic scattering is implemented in five (2D) models 22 Magnetic scattering is implemented in five (2D) models 23 23 24 24 * *sphere* … … 28 28 * *parallelepiped* 29 29 30 In general, the scattering length density (SLD, = |beta|) in each region where the30 In general, the scattering length density (SLD, = $\beta$) in each region where the 31 31 SLD is uniform, is a combination of the nuclear and magnetic SLDs and, for polarised 32 32 neutrons, also depends on the spin states of the neutrons. 33 33 34 For magnetic scattering, only the magnetization component, *M*\ :sub:`perp`,35 perpendicular to the scattering vector *Q*contributes to the the magnetic34 For magnetic scattering, only the magnetization component, $M_\perp$, 35 perpendicular to the scattering vector $Q$ contributes to the the magnetic 36 36 scattering length. 37 37 … … 42 42 .. image:: dm_eq.png 43 43 44 where |gamma| = -1.913 is the gyromagnetic ratio, |mu|\ :sub:`B`is the45 Bohr magneton, *r*\ :sub:`0` is the classical radius of electron, and |sigma|44 where $\gamma = -1.913$ is the gyromagnetic ratio, $\mu_B$ is the 45 Bohr magneton, $r_0$ is the classical radius of electron, and $\sigma$ 46 46 is the Pauli spin. 47 47 … … 55 55 .. image:: M_angles_pic.png 56 56 57 If the angles of the *Q* vector and the spin-axis (*x'*) to the *x*-axis are |phi|58 and |theta|\ :sub:`up`, respectively, then, depending on the spin state of the57 If the angles of the $Q$ vector and the spin-axis (*x'*) to the *x*-axis are $\phi$ 58 and $\theta_\text{up}$, respectively, then, depending on the spin state of the 59 59 neutrons, the scattering length densities, including the nuclear scattering 60 length density ( |beta|\ :sub:`N`) are60 length density ($\beta_N$) are 61 61 62 62 .. image:: sld1.png … … 78 78 .. image:: mqy.png 79 79 80 Here, *M*\ :sub:`0x`, *M*\ :sub:`0y` and *M*\ :sub:`0z` are the x, y and zcomponents81 of the magnetization vector given in the laboratory xyzframe given by80 Here, $M_{0x}$, $M_{0y}$ and $M_{0z}$ are the $x$, $y$ and $z$ components 81 of the magnetization vector given in the laboratory $xyz$ frame given by 82 82 83 83 .. image:: m0x_eq.png … … 87 87 .. image:: m0z_eq.png 88 88 89 and the magnetization angles |theta|\ :sub:`M` and |phi|\ :sub:`M`are defined in89 and the magnetization angles $\theta_M$ and $\phi_M$ are defined in 90 90 the figure above. 91 91 … … 93 93 94 94 =========== ================================================================ 95 M0_sld = *D*\ :sub:`M` *M*\ :sub:`0`96 Up_theta = |theta|\ :sub:`up`97 M_theta = |theta|\ :sub:`M`98 M_phi = |phi|\ :sub:`M`95 M0_sld = $D_M M_0$ 96 Up_theta = $\theta_\text{up}$ 97 M_theta = $\theta_M$ 98 M_phi = $\phi_M$ 99 99 Up_frac_i = (spin up)/(spin up + spin down) neutrons *before* the sample 100 100 Up_frac_f = (spin up)/(spin up + spin down) neutrons *after* the sample -
src/sas/sasgui/perspectives/fitting/media/pd_help.rst
r6aad2e8 r5ed76f8 24 24 form factor is normalized by the average particle volume such that 25 25 26 *P(q) = scale* * \ <F*\F> / *V + bkg* 26 .. math:: 27 27 28 where F is the scattering amplitude and the \<\> denote an average over the size 29 distribution. 28 P(q) = \text{scale} \langle F^*F rangle V + \text{background} 29 30 where $F$ is the scattering amplitude and $\langle\cdot\rangle$ denotes an average 31 over the size distribution. 30 32 31 33 Users should note that this computation is very intensive. Applying polydispersion … … 57 59 .. image:: pd_image001.png 58 60 59 where *xmean* is the mean of the distribution, *w* is the half-width, and *Norm* is a60 normalization factor which is determined during the numerical calculation.61 where $x_{mean}$ is the mean of the distribution, $w$ is the half-width, and $Norm$ 62 is a normalization factor which is determined during the numerical calculation. 61 63 62 Note that the standard deviation and the half width *w*are different!64 Note that the standard deviation and the half width $w$ are different! 63 65 64 66 The standard deviation is … … 81 83 .. image:: pd_image005.png 82 84 83 where *xmean* is the mean of the distribution and *Norm*is a normalization factor85 where $x_{mean}$ is the mean of the distribution and $Norm$ is a normalization factor 84 86 which is determined during the numerical calculation. 85 87 … … 100 102 .. image:: pd_image007.png 101 103 102 where |mu|\ =ln(*xmed*), *xmed*is the median value of the distribution, and103 *Norm*is a normalization factor which will be determined during the numerical104 where $\mu=\ln(x_{med})$, $x_{med}$ is the median value of the distribution, and 105 $Norm$ is a normalization factor which will be determined during the numerical 104 106 calculation. 105 107 … … 107 109 size parameter in the *FitPage*, for example, radius = 60. 108 110 109 The polydispersity is given by |sigma|111 The polydispersity is given by $\sigma$ 110 112 111 113 .. image:: pd_image008.png … … 115 117 .. image:: pd_image009.png 116 118 117 The mean value is given by *xmean*\ =exp(|mu|\ +p\ :sup:`2`\ /2). The peak value118 is given by *xpeak*\ =exp(|mu|-p\ :sup:`2`\ ).119 The mean value is given by $x_{mean} =\exp(\mu + p^2 /2)$. The peak value 120 is given by $x_{peak} =\exp(\mu-p^2)$. 119 121 120 122 .. image:: pd_image010.jpg 121 123 122 This distribution function spreads more, and the peak shifts to the left, as *p*124 This distribution function spreads more, and the peak shifts to the left, as $p$ 123 125 increases, requiring higher values of Nsigmas and Npts. 124 126 … … 132 134 .. image:: pd_image011.png 133 135 134 where *xmean* is the mean of the distribution and *Norm*is a normalization factor135 which is determined during the numerical calculation, and *z*is a measure of the136 where $x_{mean}$ is the mean of the distribution and $Norm$ is a normalization factor 137 which is determined during the numerical calculation, and $z$ is a measure of the 136 138 width of the distribution such that 137 139 138 z = (1-p\ :sup:`2`\ ) / p\ :sup:`2` 140 .. math:: 141 142 z = (1-p^2 ) / p^2 139 143 140 144 The polydispersity is … … 156 160 157 161 This user-definable distribution should be given as as a simple ASCII text file 158 where the array is defined by two columns of numbers: *x* and *f(x)*. The *f(x)*162 where the array is defined by two columns of numbers: $x$ and $f(x)$. The $f(x)$ 159 163 will be normalized by SasView during the computation. 160 164 … … 172 176 173 177 SasView only uses these array values during the computation, therefore any mean 174 value of the parameter represented by *x*present in the *FitPage*178 value of the parameter represented by $x$ present in the *FitPage* 175 179 will be ignored. 176 180 … … 181 185 182 186 Many commercial Dynamic Light Scattering (DLS) instruments produce a size 183 polydispersity parameter, sometimes even given the symbol *p*! This parameter is187 polydispersity parameter, sometimes even given the symbol $p$! This parameter is 184 188 defined as the relative standard deviation coefficient of variation of the size 185 189 distribution and is NOT the same as the polydispersity parameters in the Lognormal -
src/sas/sasgui/perspectives/fitting/media/residuals_help.rst
r7805458 r5ed76f8 18 18 also provides two other measures of the quality of a fit: 19 19 20 * |chi|\ :sup:`2`(or 'Chi2'; pronounced 'chi-squared')20 * $\chi^2$ (or 'Chi2'; pronounced 'chi-squared') 21 21 * *Residuals* 22 22 … … 32 32 *Npts* such that 33 33 34 *Chi2/Npts* = { SUM[(*Y_i* - *Y_theory_i*)^2 / (*Y_error_i*)^2] } / *Npts* 34 .. math:: 35 35 36 This differs slightly from what is sometimes called the 'reduced chi-squared' 36 \chi^2/N_{pts} = \sum[(Y_i - Y_{theory}_i)^2 / (Y_error_i)^2] } / N_{pts} 37 38 This differs slightly from what is sometimes called the 'reduced $\chi^2$' 37 39 because it does not take into account the number of fitting parameters (to 38 calculate the number of 'degrees of freedom'), but the 'normalized chi-squared'39 and the 'reduced chi-squared' are very close to each other when *Npts* >> number of40 parameters.40 calculate the number of 'degrees of freedom'), but the 'normalized $\chi^2$ 41 and the 'reduced $\chi^2$ are very close to each other when $N_{pts} \gg 42 \text{number of parameters}. 41 43 42 For a good fit, *Chi2/Npts* tends to 0.44 For a good fit, $\chi^2/N_{pts}$ tends to 1. 43 45 44 *Chi2/Npts*is sometimes referred to as the 'goodness-of-fit' parameter.46 $\chi^2/N_{pts}$ is sometimes referred to as the 'goodness-of-fit' parameter. 45 47 46 48 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ … … 53 55 value and its *true* value is its error). 54 56 55 *SasView* calculates 'normalized residuals', *R_i*, for each data point in the57 *SasView* calculates 'normalized residuals', $R_i$, for each data point in the 56 58 fit: 57 59 58 *R_i* = (*Y_i* - *Y_theory_i*) / (*Y_err_i*) 60 .. math:: 59 61 60 For a good fit, *R_i* ~ 0. 62 R_i = (Y_i - Y_theory_i) / (Y_err_i) 63 64 For a good fit, $R_i \sim 0$. 61 65 62 66 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ -
src/sas/sasgui/perspectives/fitting/media/sm_help.rst
r6aad2e8 r5ed76f8 20 20 ================== 21 21 22 Sometimes the instrumental geometry used to acquire the experimental data has 23 an impact on the clarity of features in the reduced scattering curve. For 24 example, peaks or fringes might be slightly broadened. This is known as 25 *Q resolution smearing*. To compensate for this effect one can either try and 26 remove the resolution contribution - a process called *desmearing* - or add the 27 resolution contribution into a model calculation/simulation (which by definition 28 will be exact) to make it more representative of what has been measured 22 Sometimes the instrumental geometry used to acquire the experimental data has 23 an impact on the clarity of features in the reduced scattering curve. For 24 example, peaks or fringes might be slightly broadened. This is known as 25 *Q resolution smearing*. To compensate for this effect one can either try and 26 remove the resolution contribution - a process called *desmearing* - or add the 27 resolution contribution into a model calculation/simulation (which by definition 28 will be exact) to make it more representative of what has been measured 29 29 experimentally - a process called *smearing*. SasView will do the latter. 30 30 31 Both smearing and desmearing rely on functions to describe the resolution 31 Both smearing and desmearing rely on functions to describe the resolution 32 32 effect. SasView provides three smearing algorithms: 33 33 … … 36 36 * *2D Smearing* 37 37 38 SasView also has an option to use Q resolution data (estimated at the time of38 SasView also has an option to use $Q$ resolution data (estimated at the time of 39 39 data reduction) supplied in a reduced data file: the *Use dQ data* radio button. 40 40 … … 43 43 dQ Smearing 44 44 ----------- 45 46 If this option is checked, SasView will assume that the supplied dQ values45 46 If this option is checked, SasView will assume that the supplied $dQ$ values 47 47 represent the standard deviations of Gaussian functions. 48 48 … … 65 65 **[Equation 1]** 66 66 67 The functions |inlineimage004| and |inlineimage005|68 refer to the slit width weighting function and the slit height weighting 69 determined at the given *q*point, respectively. It is assumed that the weighting67 The functions $W_v(v)$ and $W_u(u)$ 68 refer to the slit width weighting function and the slit height weighting 69 determined at the given $q$ point, respectively. It is assumed that the weighting 70 70 function is described by a rectangular function, such that 71 71 … … 80 80 **[Equation 3]** 81 81 82 so that |inlineimage008| |inlineimage009| for |inlineimage010| and *u*\ . 83 84 Here |inlineimage011| and |inlineimage012| stand for 85 the slit height (FWHM/2) and the slit width (FWHM/2) in *q* space. 82 so that $\Delta q_\alpha = \int_0^\infty d\alpha W_\alpha(\alpha)$ 83 for $\alpha = v$ and $u$. 84 85 Here $\Delta q_u$ and $\Delta q_v$ stand for 86 the slit height (FWHM/2) and the slit width (FWHM/2) in $q$ space. 86 87 87 88 This simplifies the integral in Equation 1 to … … 91 92 **[Equation 4]** 92 93 93 which may be solved numerically, depending on the nature of |inlineimage011| and |inlineimage012| . 94 which may be solved numerically, depending on the nature of 95 $\Delta q_u$ and $\Delta q_v$. 94 96 95 97 Solution 1 96 98 ^^^^^^^^^^ 97 99 98 **For ** |inlineimage012| **= 0 and** |inlineimage011| **= constant.**100 **For $\Delta q_v= 0$ and $\Delta q_u = \text{constant}$.** 99 101 100 102 .. image:: sm_image016.png 101 103 102 For discrete *q* values, at the *q* values of the data points and at the *q*103 values extended up to *q*\ :sub:`N`\ = *q*\ :sub:`i` + |inlineimage011|the smeared104 For discrete $q$ values, at the $q$ values of the data points and at the $q$ 105 values extended up to $q_N = q_i + \Delta q_u$ the smeared 104 106 intensity can be approximately calculated as 105 107 … … 108 110 **[Equation 5]** 109 111 110 where |inlineimage018| = 0 for *I*\ :sub:`s` when *j* < *i* or *j* > *N-1*.112 where |inlineimage018| = 0 for $I_s$ when $j < i$ or $j > N-1$. 111 113 112 114 Solution 2 113 115 ^^^^^^^^^^ 114 116 115 **For ** |inlineimage012| **= constant and** |inlineimage011| **= 0.**117 **For $\Delta q_v = \text{constant}$ and $\Delta q_u= 0$.** 116 118 117 119 Similar to Case 1 118 120 119 |inlineimage019| for *q*\ :sub:`p` = *q*\ :sub:`i` - |inlineimage012| and *q*\ :sub:`N` = *q*\ :sub:`i` + |inlineimage012|121 |inlineimage019| for $q_p = q_i - \Delta q_v$ and $q_N = q_i + \Delta q_v$ 120 122 121 123 **[Equation 6]** 122 124 123 where |inlineimage018| = 0 for *I*\ :sub:`s` when *j* < *p* or *j* > *N-1*.125 where |inlineimage018| = 0 for $I_s$ when $j < p$ or $j > N-1$. 124 126 125 127 Solution 3 126 128 ^^^^^^^^^^ 127 129 128 **For ** |inlineimage011| **= constant and** |inlineimage011| **= constant.**130 **For $\Delta q_u = \text{constant}$ and $\Delta q_v = \text{constant}$.** 129 131 130 132 In this case, the best way is to perform the integration of Equation 1 … … 142 144 **[Equation 7]** 143 145 144 for *q*\ :sub:`p` = *q*\ :sub:`i` - |inlineimage012| and *q*\ :sub:`N` = *q*\ :sub:`i` + |inlineimage012| 145 146 where |inlineimage018| = 0 for *I*\ :sub:`s` when *j* < *p* or *j* > *N-1*. 146 for *q_p = q_i - \Delta q_v$ and $q_N = q_i + \Delta q_v$ 147 where |inlineimage018| = 0 for *I_s$ when $j < p$ or $j > N-1$. 147 148 148 149 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ … … 175 176 **[Equation 9]** 176 177 177 In Equation 9, *x*\ :sub:`0` = *q* cos(|theta|), *y*\ :sub:`0` = *q* sin(|theta|), and 178 the primed axes, are all in the coordinate rotated by an angle |theta| about 179 the z-axis (see the figure below) so that *x'*\ :sub:`0` = *x*\ :sub:`0` cos(|theta|) + 180 *y*\ :sub:`0` sin(|theta|) and *y'*\ :sub:`0` = -*x*\ :sub:`0` sin(|theta|) + 181 *y*\ :sub:`0` cos(|theta|). Note that the rotation angle is zero for a x-y symmetric 182 elliptical Gaussian distribution. The *A* is a normalization factor. 178 In Equation 9, $x_0 = q \cos(\theta)$, $y_0 = q \sin(\theta)$, and 179 the primed axes, are all in the coordinate rotated by an angle $\theta$ about 180 the z-axis (see the figure below) so that 181 $x'_0 = x_0 \cos(\theta) + y_0 \sin(\theta)$ and 182 $y'_0 = -x_0 \sin(\theta) + y_0 \cos(\theta)$. 183 Note that the rotation angle is zero for a $xy$ symmetric 184 elliptical Gaussian distribution. The $A$ is a normalization factor. 183 185 184 186 .. image:: sm_image023.png 185 187 186 Now we consider a numerical integration where each of the bins in |theta| and *R*are187 *evenly* (this is to simplify the equation below) distributed by |bigdelta|\ |theta|188 and |bigdelta|\ R, respectively, and it is further assumed that *I(x',y')*is constant188 Now we consider a numerical integration where each of the bins in $\theta$ and $R$ are 189 *evenly* (this is to simplify the equation below) distributed by $\Delta \theta$ 190 and $\Delta R$, respectively, and it is further assumed that $I(x',y')$ is constant 189 191 within the bins. Then 190 192 … … 194 196 195 197 Since the weighting factor on each of the bins is known, it is convenient to 196 transform *x'-y'* back to *x-y* coordinates (by rotating it by -|theta|around the197 *z*axis).198 transform $x'y'$ back to $xy$ coordinates (by rotating it by $-\theta$ around the 199 $z$ axis). 198 200 199 201 Then, for a polar symmetric smear … … 207 209 .. image:: sm_image026.png 208 210 209 while for a *x-y*symmetric smear211 while for a $xy$ symmetric smear 210 212 211 213 .. image:: sm_image027.png … … 225 227 ------------------------- 226 228 227 In all the cases above, the weighting matrix *W*is calculated on the first call228 to a smearing function, and includes ~60 *q*values (finely and evenly binned)229 below (>0) and above the *q*range of data in order to smear all data points for230 a given model and slit/pinhole size. The *Norm*factor is found numerically with the231 weighting matrix and applied on the computation of *I*\ :sub:`s`.229 In all the cases above, the weighting matrix $W$ is calculated on the first call 230 to a smearing function, and includes ~60 $q$ values (finely and evenly binned) 231 below (>0) and above the $q$ range of data in order to smear all data points for 232 a given model and slit/pinhole size. The $Norm$ factor is found numerically with the 233 weighting matrix and applied on the computation of $I_s$. 232 234 233 235 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
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