Changeset 318b5bbb in sasview for sansmodels/src/sans/models/media/pd_help.html
- Timestamp:
- Dec 18, 2012 10:55:24 AM (12 years ago)
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- 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, costrafo411, magnetic_scatt, release-4.1.1, release-4.1.2, release-4.2.2, release_4.0.1, ticket-1009, ticket-1094-headless, ticket-1242-2d-resolution, ticket-1243, ticket-1249, ticket885, unittest-saveload
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sansmodels/src/sans/models/media/pd_help.html (modified) (3 diffs)
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sansmodels/src/sans/models/media/pd_help.html
r17574ae r318b5bbb 1 <html>2 3 1 <head> 4 2 <meta http-equiv=Content-Type content="text/html; charset=windows-1252"> … … 29 27 style='font-family:"Times New Roman","serif"'>The following five distribution 30 28 functions are provided;</span></p> 31 <p> </p>32 29 <ul> 33 30 <li><a href="#Rectangular">Rectangular distribution</a></li> … … 38 35 </ul> 39 36 <p> </p> 40 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 41 style='font-family:"Times New Roman","serif"'> </span></p> 37 <p><a name="Rectangular"><h4>Rectangular distribution</a></h4></p> 38 <p><img src="./img/pd_image001.png"></p> 39 <p> </p> 40 <p>The x<sub>mean</sub> is the mean 41 of the distribution, w is the half-width, and Norm is a normalization factor 42 which is determined during the numerical calculation. Note that the Sigma and 43 the half width <i>w</i> are different.</p> 44 <p>The standard deviation is </p> 45 <p><img src="./img/pd_image002.png"></p> 46 <p> </p> 47 <p>The PD (polydispersity) is </p> 48 <p><img src="./img/pd_image003.png"></p> 49 <p> </p> 50 <p><img width=511 height=270 51 id="Picture 1" src="./img/pd_image004.jpg" alt=flat.gif></p> 52 <p> </p> 53 <p> </p> 54 <p><a name="Array"><h4>Array distribution</h4></a></p> 42 55 43 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 44 style='font-family:"Times New Roman","serif"'> </span></p> 56 <p>This distribution is to be given 57 by users as a txt file where the array should be defined by two columns in the 58 order of x and f(x) values. The f(x) will be normalized by SansView during the 59 computation.</p> 45 60 46 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 47 style='font-family:"Times New Roman","serif"'><a name="Rectangular"><h4>Rectangular distribution</a></h4></span></p> 61 <p>Example of an array in the file;</p> 48 62 49 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 50 style='font-family:"Times New Roman","serif";position:relative;top:22.0pt'><img 51 width=248 height=67 src="./img/pd_image001.png"></span></p> 63 <p>30 0.1</p> 64 65 <p>32 0.3</p> 66 67 <p>35 0.4</p> 68 69 <p>36 0.5</p> 70 71 <p>37 0.6</p> 72 73 <p>39 0.7</p> 74 75 <p>41 0.9</p> 76 77 <p'> </p> 78 79 <p>We use only these array values in 80 the computation, therefore the mean value given in the control panel, for 81 example radius = 60, will be ignored.</p> 82 <p> </p> 83 84 85 <p><a name="Gaussian"><h4>Gaussian distribution</h4></a></p> 86 <p> </p> 87 88 <p><img src="./img/pd_image005.png"></p> 52 89 53 90 <p> </p> 54 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span55 style='font-family:"Times New Roman","serif"'>The x<sub>mean</sub> is the mean56 of the distribution, w is the half-width, and Norm is a normalization factor57 which is determined during the numerical calculation. Note that the Sigma and58 the half width <i>w</i> are different.</span></p>59 91 60 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 61 style='font-family:"Times New Roman","serif"'>The standard deviation is </span></p> 92 <p>The x<sub>mean</sub> is the mean 93 of the distribution and Norm is a normalization factor which is determined 94 during the numerical calculation.</p> 62 95 63 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 64 style='font-family:"Times New Roman","serif";position:relative;top:4.0pt'><img 65 width=72 height=24 src="./img/pd_image002.png"></span><span 66 style='font-family:"Times New Roman","serif"'>. </span></p> 96 <p> </p> 67 97 68 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 69 style='font-family:"Times New Roman","serif"'> </span></p> 98 <p>The PD (polydispersity) is </p> 70 99 71 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 72 style='font-family:"Times New Roman","serif"'>The PD (polydispersity) is </span></p> 100 <p><img src="./img/pd_image003.png"></p> 73 101 74 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 75 style='font-family:"Times New Roman","serif";position:relative;top:6.0pt'><img 76 width=93 height=24 src="./img/pd_image003.png"></span><span 77 style='font-family:"Times New Roman","serif"'>.</span></p> 102 <p> </p> 78 103 79 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span80 style='font-family:"Times New Roman","serif"'> </span></p>104 <p><img width=518 height=275 105 id="Picture 2" src="./img/pd_image006.jpg" alt=gauss.gif></p> 81 106 82 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 83 style='font-family:"Times New Roman","serif"'><img width=511 height=270 84 id="Picture 1" src="./img/pd_image004.jpg" alt=flat.gif></span></p> 107 <p> </p> 85 108 86 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 87 style='font-family:"Times New Roman","serif"'> </span></p> 109 <p><a name="Lognormal"><h4>Lognormal distribution</h4></a></p> 88 110 89 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 90 style='font-family:"Times New Roman","serif"'> </span></p> 111 <p> </p> 91 112 92 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 93 style='font-family:"Times New Roman","serif"'><a name="Array"><h4>Array distribution</h4></a></span></p> 113 <p><img src="./img/pd_image007.png"></p> 94 114 95 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 96 style='font-family:"Times New Roman","serif"'> </span></p> 115 <p> </p> 97 116 98 99 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 100 style='font-family:"Times New Roman","serif"'>This distribution is to be given 101 by users as a txt file where the array should be defined by two columns in the 102 order of x and f(x) values. The f(x) will be normalized by SansView during the 103 computation.</span></p> 104 105 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 106 style='font-family:"Times New Roman","serif"'> </span></p> 107 108 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 109 style='font-family:"Times New Roman","serif"'>Example of an array in the file;</span></p> 110 111 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 112 style='font-family:"Times New Roman","serif"'> </span></p> 113 114 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 115 style='font-family:"Times New Roman","serif"'>30 0.1</span></p> 116 117 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 118 style='font-family:"Times New Roman","serif"'>32 0.3</span></p> 119 120 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 121 style='font-family:"Times New Roman","serif"'>35 0.4</span></p> 122 123 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 124 style='font-family:"Times New Roman","serif"'>36 0.5</span></p> 125 126 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 127 style='font-family:"Times New Roman","serif"'>37 0.6</span></p> 128 129 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 130 style='font-family:"Times New Roman","serif"'>39 0.7</span></p> 131 132 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 133 style='font-family:"Times New Roman","serif"'>41 0.9</span></p> 134 135 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 136 style='font-family:"Times New Roman","serif"'> </span></p> 137 138 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 139 style='font-family:"Times New Roman","serif"'>We use only these array values in 140 the computation, therefore the mean value given in the control panel, for 141 example radius = 60, will be ignored.</span></p> 142 143 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 144 style='font-family:"Times New Roman","serif"'> </span></p> 145 146 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 147 style='font-family:"Times New Roman","serif"'> </span></p> 148 149 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 150 style='font-family:"Times New Roman","serif"'><a name="Gaussian"><h4>Gaussian distribution</h4></a></span></p> 151 152 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 153 style='font-family:"Times New Roman","serif"'> </span></p> 154 155 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 156 style='font-family:"Times New Roman","serif";position:relative;top:12.0pt'><img 157 width=212 height=44 src="./img/pd_image005.png"></span></p> 158 159 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 160 style='font-family:"Times New Roman","serif"'> </span></p> 161 162 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 163 style='font-family:"Times New Roman","serif"'>The x<sub>mean</sub> is the mean 164 of the distribution and Norm is a normalization factor which is determined 165 during the numerical calculation.</span></p> 166 167 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 168 style='font-family:"Times New Roman","serif"'> </span></p> 169 170 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 171 style='font-family:"Times New Roman","serif"'>The PD (polydispersity) is </span></p> 172 173 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 174 style='font-family:"Times New Roman","serif";position:relative;top:6.0pt'><img 175 width=93 height=24 src="./img/pd_image003.png"></span><span 176 style='font-family:"Times New Roman","serif"'>.</span></p> 177 178 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 179 style='font-family:"Times New Roman","serif"'> </span></p> 180 181 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 182 style='font-family:"Times New Roman","serif"'><img width=518 height=275 183 id="Picture 2" src="./img/pd_image006.jpg" alt=gauss.gif></span></p> 184 185 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 186 style='font-family:"Times New Roman","serif"'> </span></p> 187 188 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 189 style='font-family:"Times New Roman","serif"'> </span></p> 190 191 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 192 style='font-family:"Times New Roman","serif"'><a name="Lognormal"><h4>Lognormal distribution</h4></a></span></p> 193 194 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 195 style='font-family:"Times New Roman","serif"'> </span></p> 196 197 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 198 style='font-family:"Times New Roman","serif"'> </span></p> 199 200 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 201 style='font-family:"Times New Roman","serif";position:relative;top:14.0pt'><img 202 width=236 height=47 src="./img/pd_image007.png"></span></p> 203 204 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 205 style='font-family:"Times New Roman","serif"'> </span></p> 206 207 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 208 style='font-family:"Times New Roman","serif"'>The mu = ln(x<sub>med</sub>), x<sub>med</sub> 117 <p>The μ = ln(x<sub>med</sub>), x<sub>med</sub> 209 118 is the median value of the distribution, and Norm is a normalization factor 210 119 which will be determined during the numerical calculation. The median value is 211 120 the value given in the size parameter in the control panel, for example, 212 radius = 60.</ span></p>121 radius = 60.</p> 213 122 214 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 215 style='font-family:"Times New Roman","serif"'> </span></p> 123 <p > </p> 216 124 217 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 218 style='font-family:"Times New Roman","serif"'>The PD (polydispersity) is given 219 by sigma,</span></p> 125 <p>The PD (polydispersity) is given 126 by σ,</p> 220 127 221 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 222 style='font-family:"Times New Roman","serif";position:relative;top:5.0pt'><img 223 width=55 height=21 src="./img/pd_image008.png"></span><span 224 style='font-family:"Times New Roman","serif"'>.</span></p> 128 <p><img src="./img/pd_image008.png"></p> 225 129 226 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 227 style='font-family:"Times New Roman","serif"'> </span></p> 130 <p> </p> 228 131 229 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 230 style='font-family:"Times New Roman","serif"'>For the angular distribution,</span></p> 132 <p>For the angular distribution,</p> 231 133 232 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 233 style='font-family:"Times New Roman","serif";position:relative;top:6.0pt'><img 234 width=76 height=24 src="./img/pd_image009.png"></span></p> 134 <p><img src="./img/pd_image009.png"></p> 235 135 236 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 237 style='font-family:"Times New Roman","serif"'> </span></p> 136 <p> </p> 238 137 239 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 240 style='font-family:"Times New Roman","serif"'>The mean value is given by x<sub>mean</sub> 241 =exp(mu+p^2/2).</span></p> 138 <p>The mean value is given by x<sub>mean</sub> 139 =exp(μ+p<sup>2</sup>/2).</p> 242 140 243 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 244 style='font-family:"Times New Roman","serif"'>The peak value is given by x<sub>peak</sub>=exp(mu-p^2).</span></p> 141 <p>The peak value is given by x<sub>peak</sub>=exp(μ-p<sup>2</sup>).</span></p> 245 142 246 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 247 style='font-family:"Times New Roman","serif"'> </span></p> 143 <p> </p> 248 144 249 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 250 style='font-family:"Times New Roman","serif"'><img width=450 height=239 251 id="Picture 7" src="./img/pd_image010.jpg" alt=lognormal.gif></span></p> 145 <p><img width=450 height=239 146 id="Picture 7" src="./img/pd_image010.jpg" alt=lognormal.gif></p> 252 147 253 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 254 style='font-family:"Times New Roman","serif"'> </span></p> 148 <p> </p> 255 149 256 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 257 style='font-family:"Times New Roman","serif"'>This distribution function 150 <p>This distribution function 258 151 spreads more and the peak shifts to the left as the p increases, requiring 259 higher values of Nsigmas and Npts.</ span></p>152 higher values of Nsigmas and Npts.</p> 260 153 261 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 262 style='font-family:"Times New Roman","serif"'> </span></p> 154 <p> </p> 263 155 264 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 265 style='font-family:"Times New Roman","serif"'> </span></p> 156 <p><a name="Schulz"><h4>Schulz distribution</h4></a></p> 266 157 267 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 268 style='font-family:"Times New Roman","serif"'><a name="Schulz"><h4>Schulz distribution</h4></a></span></p> 158 <p> </p> 269 159 270 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 271 style='font-family:"Times New Roman","serif"'> </span></p> 160 <p><img src="./img/pd_image011.png"></p> 272 161 273 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 274 style='font-family:"Times New Roman","serif";position:relative;top:15.0pt'><img 275 width=347 height=45 src="./img/pd_image011.png"></span></p> 162 <p> </p> 276 163 277 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 278 style='font-family:"Times New Roman","serif"'> </span></p> 164 <p>The x<sub>mean</sub> is the mean 165 of the distribution and Norm is a normalization factor which is determined 166 during the numerical calculation. </p> 279 167 280 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 281 style='font-family:"Times New Roman","serif"'>The x<sub>mean</sub> is the mean 282 of the distribution and Norm is a normalization factor which is determined 283 during the numerical calculation. </span></p> 168 <p>The z = 1/p<sup>2</sup> 1.</p> 169 <p> </p> 284 170 285 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 286 style='font-family:"Times New Roman","serif"'>The z = 1/p^2 1.</span></p> 287 288 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 289 style='font-family:"Times New Roman","serif"'> </span></p> 290 291 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 292 style='font-family:"Times New Roman","serif"'>The PD (polydispersity) is </span></p> 293 294 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 295 style='font-family:"Times New Roman","serif";position:relative;top:6.0pt'><img 296 width=80 height=24 src="./img/pd_image012.png"></span><span 297 style='font-family:"Times New Roman","serif"'>.</span></p> 298 <p/> 299 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 300 style='font-family:"Times New Roman","serif"'>Note that the higher PD (polydispersity) 171 <p>The PD (polydispersity) is </p> 172 <p'><img src="./img/pd_image012.png"></p> 173 <p>Note that the higher PD (polydispersity) 301 174 might need higher values of Npts and Nsigmas. For example, at PD = 0.7 and radisus = 60 A, 302 Npts >= 160, and Nsigmas >= 15 at least.</ span></p>175 Npts >= 160, and Nsigmas >= 15 at least.</p> 303 176 <p/> 304 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt'><span 305 style='font-family:"Times New Roman","serif"'><img width=438 height=232 306 id="Picture 4" src="./img/pd_image013.jpg" alt=schulz.gif></span></p> 177 <p><img width=438 height=232 178 id="Picture 4" src="./img/pd_image013.jpg" alt=schulz.gif></p> 307 179 308 180 </div> 309 181 <br> 310 182 </body> 311 312 </html>
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