Statistics.cpp 13.8 KB
 Gigg, Martyn Anthony committed Jul 20, 2012 1 2 3 ``````// Includes #include "MantidKernel/Statistics.h" `````` 4 ``````#include `````` Campbell, Stuart committed Apr 17, 2015 5 6 ``````#include #include `````` Zhou, Wenduo committed Oct 07, 2013 7 ``````#include `````` Campbell, Stuart committed Apr 17, 2015 8 9 ``````#include #include `````` Zhou, Wenduo committed Mar 20, 2013 10 ``````#include `````` Campbell, Stuart committed Apr 17, 2015 11 ``````#include `````` Alex Buts committed Apr 21, 2015 12 ``````#include `````` Campbell, Stuart committed Apr 17, 2015 13 `````` `````` Whitfield, Ross committed Dec 16, 2014 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 ``````namespace Mantid { namespace Kernel { using std::string; using std::vector; /** * Generate a Statistics object where all of the values are NaN. This is a good * initial default. */ Statistics getNanStatistics() { double nan = std::numeric_limits::quiet_NaN(); Statistics stats; stats.minimum = nan; stats.maximum = nan; stats.mean = nan; stats.median = nan; stats.standard_deviation = nan; return stats; } /** * There are enough special cases in determining the median where it useful to * put it in a single function. */ template double getMedian(const vector &data, const size_t num_data, const bool sorted) { if (num_data == 1) return static_cast(*(data.begin())); bool is_even = ((num_data % 2) == 0); if (is_even) { double left = 0.0; double right = 0.0; if (sorted) { // Just get the centre two elements. left = static_cast(*(data.begin() + num_data / 2 - 1)); right = static_cast(*(data.begin() + num_data / 2)); } else { // If the data is not sorted, make a copy we can mess with vector temp(data.begin(), data.end()); // Get what the centre two elements should be... std::nth_element(temp.begin(), temp.begin() + num_data / 2 - 1, temp.end()); left = static_cast(*(temp.begin() + num_data / 2 - 1)); std::nth_element(temp.begin(), temp.begin() + num_data / 2, temp.end()); right = static_cast(*(temp.begin() + num_data / 2)); `````` Campbell, Stuart committed Mar 30, 2011 65 `````` } `````` Whitfield, Ross committed Dec 16, 2014 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 `````` // return the average return (left + right) / 2.; } else // Odd number { if (sorted) { // If sorted and odd, just return the centre value return static_cast(*(data.begin() + num_data / 2)); } else { // If the data is not sorted, make a copy we can mess with vector temp(data.begin(), data.end()); // Make sure the centre value is in the correct position std::nth_element(temp.begin(), temp.begin() + num_data / 2, temp.end()); // Now return the centre value return static_cast(*(temp.begin() + num_data / 2)); `````` Lynch, Vickie committed May 14, 2012 81 `````` } `````` Whitfield, Ross committed Dec 16, 2014 82 83 84 85 86 87 88 `````` } } /** * There are enough special cases in determining the Z score where it useful to * put it in a single function. */ template `````` Martyn Gigg committed Sep 02, 2015 89 ``````std::vector getZscore(const vector &data) { `````` Whitfield, Ross committed Dec 16, 2014 90 91 92 93 94 `````` if (data.size() < 3) { std::vector Zscore(data.size(), 0.); return Zscore; } std::vector Zscore; `````` Martyn Gigg committed Sep 02, 2015 95 `````` Statistics stats = getStatistics(data); `````` Whitfield, Ross committed Dec 16, 2014 96 97 98 99 `````` if (stats.standard_deviation == 0.) { std::vector Zscore(data.size(), 0.); return Zscore; } `````` Hahn, Steven committed Jan 06, 2016 100 `````` for (auto it = data.cbegin(); it != data.cend(); ++it) { `````` Whitfield, Ross committed Dec 16, 2014 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 `````` double tmp = static_cast(*it); Zscore.push_back(fabs((tmp - stats.mean) / stats.standard_deviation)); } return Zscore; } /** * There are enough special cases in determining the modified Z score where it * useful to * put it in a single function. */ template std::vector getModifiedZscore(const vector &data, const bool sorted) { if (data.size() < 3) { std::vector Zscore(data.size(), 0.); return Zscore; } std::vector MADvec; double tmp; size_t num_data = data.size(); // cache since it is frequently used double median = getMedian(data, num_data, sorted); `````` Hahn, Steven committed Jan 06, 2016 122 `````` for (auto it = data.cbegin(); it != data.cend(); ++it) { `````` Whitfield, Ross committed Dec 16, 2014 123 124 125 126 127 128 129 130 131 132 `````` tmp = static_cast(*it); MADvec.push_back(fabs(tmp - median)); } double MAD = getMedian(MADvec, num_data, sorted); if (MAD == 0.) { std::vector Zscore(data.size(), 0.); return Zscore; } MADvec.clear(); std::vector Zscore; `````` Hahn, Steven committed Jan 06, 2016 133 `````` for (auto it = data.begin(); it != data.end(); ++it) { `````` Whitfield, Ross committed Dec 16, 2014 134 135 136 137 138 139 140 141 142 `````` tmp = static_cast(*it); Zscore.push_back(0.6745 * fabs((tmp - median) / MAD)); } return Zscore; } /** * Determine the statistics for a vector of data. If it is sorted then let the * function know so it won't make a copy of the data for determining the median. `````` Martyn Gigg committed Sep 02, 2015 143 144 `````` * @param data Data points whose statistics are to be evaluated * @param flags A set of flags to control the computation of the stats `````` Whitfield, Ross committed Dec 16, 2014 145 146 `````` */ template `````` Martyn Gigg committed Sep 02, 2015 147 ``````Statistics getStatistics(const vector &data, const unsigned int flags) { `````` Whitfield, Ross committed Dec 16, 2014 148 149 `````` Statistics stats = getNanStatistics(); size_t num_data = data.size(); // cache since it is frequently used `````` Martyn Gigg committed Sep 02, 2015 150 `````` if (num_data == 0) { // don't do anything `````` Whitfield, Ross committed Dec 16, 2014 151 152 153 `````` return stats; } `````` Martyn Gigg committed Sep 02, 2015 154 155 156 157 158 159 160 161 162 163 164 165 `````` // calculate the mean if this or the stddev is requested const bool stddev = ((flags & StatOptions::UncorrectedStdDev) || (flags & StatOptions::CorrectedStdDev)); if ((flags & StatOptions::Mean) || stddev) { const TYPE sum = std::accumulate(data.begin(), data.end(), static_cast(0), std::plus()); stats.mean = static_cast(sum) / (static_cast(num_data)); if (stddev) { // calculate the standard deviation, min, max stats.minimum = stats.mean; stats.maximum = stats.mean; double stddev = 0.; `````` Hahn, Steven committed Jan 06, 2016 166 `````` for (auto it = data.cbegin(); it != data.cend(); ++it) { `````` Martyn Gigg committed Sep 02, 2015 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 `````` double temp = static_cast(*it); stddev += ((temp - stats.mean) * (temp - stats.mean)); if (temp > stats.maximum) stats.maximum = temp; if (temp < stats.minimum) stats.minimum = temp; } size_t ndofs = (flags & StatOptions::CorrectedStdDev) ? num_data - 1 : num_data; stats.standard_deviation = sqrt(stddev / (static_cast(ndofs))); } } // calculate the median if requested if (flags & StatOptions::Median) { stats.median = getMedian(data, num_data, flags & StatOptions::SortedData); `````` Whitfield, Ross committed Dec 16, 2014 182 183 184 185 186 187 188 `````` } return stats; } /// Getting statistics of a string array should just give a bunch of NaNs template <> DLLExport Statistics `````` Martyn Gigg committed Sep 02, 2015 189 190 ``````getStatistics(const vector &data, const unsigned int flags) { UNUSED_ARG(flags); `````` Whitfield, Ross committed Dec 16, 2014 191 192 193 194 195 196 197 `````` UNUSED_ARG(data); return getNanStatistics(); } /// Getting statistics of a boolean array should just give a bunch of NaNs template <> DLLExport Statistics `````` Martyn Gigg committed Sep 02, 2015 198 199 ``````getStatistics(const vector &data, const unsigned int flags) { UNUSED_ARG(flags); `````` Whitfield, Ross committed Dec 16, 2014 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 `````` UNUSED_ARG(data); return getNanStatistics(); } /** Return the Rwp of a diffraction pattern data * @param obsI :: array of observed intensity values * @param calI :: array of calculated intensity values; * @param obsE :: array of error of the observed data; * @return :: RFactor including Rp and Rwp * */ Rfactor getRFactor(const std::vector &obsI, const std::vector &calI, const std::vector &obsE) { // 1. Check if (obsI.size() != calI.size() || obsI.size() != obsE.size()) { std::stringstream errss; errss << "GetRFactor() Input Error! Observed Intensity (" << obsI.size() << "), Calculated Intensity (" << calI.size() << ") and Observed Error (" << obsE.size() << ") have different number of elements."; throw std::runtime_error(errss.str()); } if (obsI.size() == 0) { throw std::runtime_error("getRFactor(): the input arrays are empty."); } double sumnom = 0; double sumdenom = 0; double sumrpnom = 0; double sumrpdenom = 0; size_t numpts = obsI.size(); for (size_t i = 0; i < numpts; ++i) { double cal_i = calI[i]; double obs_i = obsI[i]; double sigma = obsE[i]; double weight = 1.0 / (sigma * sigma); double diff = obs_i - cal_i; if (weight == weight && weight <= DBL_MAX) { // If weight is not NaN. sumrpnom += fabs(diff); sumrpdenom += fabs(obs_i); double tempnom = weight * diff * diff; double tempden = weight * obs_i * obs_i; sumnom += tempnom; sumdenom += tempden; if (tempnom != tempnom || tempden != tempden) { std::cout << "***** Error! ****** Data indexed " << i << " is NaN. " << "i = " << i << ": cal = " << calI[i] << ", obs = " << obs_i << ", weight = " << weight << ". \n"; `````` Campbell, Stuart committed Mar 30, 2011 255 256 `````` } } `````` Whitfield, Ross committed Dec 16, 2014 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 `````` } Rfactor rfactor(0., 0.); rfactor.Rp = (sumrpnom / sumrpdenom); rfactor.Rwp = std::sqrt(sumnom / sumdenom); if (rfactor.Rwp != rfactor.Rwp) std::cout << "Rwp is NaN. Denominator = " << sumnom << "; Nominator = " << sumdenom << ". \n"; return rfactor; } /** * This will calculate the first n-moments (inclusive) about the origin. For *example * if maxMoment=2 then this will return 3 values: 0th (total weight), 1st *(mean), 2nd (deviation). * * @param x The independent values * @param y The dependent values * @param maxMoment The number of moments to calculate * @returns The first n-moments. */ template std::vector getMomentsAboutOrigin(const std::vector &x, const std::vector &y, const int maxMoment) { // densities have the same number of x and y bool isDensity(x.size() == y.size()); // if it isn't a density then check for histogram if ((!isDensity) && (x.size() != y.size() + 1)) { std::stringstream msg; msg << "length of x (" << x.size() << ") and y (" << y.size() << ")do not match"; throw std::out_of_range(msg.str()); } // initialize a result vector with all zeros std::vector result(maxMoment + 1, 0.); // cache the maximum index size_t numPoints = y.size(); if (isDensity) numPoints = x.size() - 1; // densities are calculated using Newton's method for numerical integration `````` Martyn Gigg committed Sep 02, 2015 305 306 `````` // as backwards as it sounds, the outer loop should be the points rather // than `````` Whitfield, Ross committed Dec 16, 2014 307 308 309 310 311 312 313 314 315 `````` // the moments for (size_t j = 0; j < numPoints; ++j) { // reduce item lookup - and central x for histogram const double xVal = .5 * static_cast(x[j] + x[j + 1]); // this variable will be (x^n)*y double temp = static_cast(y[j]); // correct for histogram if (isDensity) { const double xDelta = static_cast(x[j + 1] - x[j]); temp = .5 * (temp + static_cast(y[j + 1])) * xDelta; `````` Campbell, Stuart committed Mar 30, 2011 316 317 `````` } `````` Whitfield, Ross committed Dec 16, 2014 318 319 320 321 322 `````` // accumulate the moments result[0] += temp; for (size_t i = 1; i < result.size(); ++i) { temp *= xVal; result[i] += temp; `````` Gigg, Martyn Anthony committed Jun 20, 2012 323 `````` } `````` Whitfield, Ross committed Dec 16, 2014 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 `````` } return result; } /** * This will calculate the first n-moments (inclusive) about the mean (1st *moment). For example * if maxMoment=2 then this will return 3 values: 0th (total weight), 1st *(mean), 2nd (deviation). * * @param x The independent values * @param y The dependent values * @param maxMoment The number of moments to calculate * @returns The first n-moments. */ template std::vector getMomentsAboutMean(const std::vector &x, const std::vector &y, const int maxMoment) { // get the zeroth (integrated value) and first moment (mean) std::vector momentsAboutOrigin = getMomentsAboutOrigin(x, y, 1); const double mean = momentsAboutOrigin[1]; // initialize a result vector with all zeros std::vector result(maxMoment + 1, 0.); result[0] = momentsAboutOrigin[0]; // escape early if we need to if (maxMoment == 0) return result; // densities have the same number of x and y bool isDensity(x.size() == y.size()); // cache the maximum index size_t numPoints = y.size(); if (isDensity) numPoints = x.size() - 1; // densities are calculated using Newton's method for numerical integration `````` Martyn Gigg committed Sep 02, 2015 365 366 `````` // as backwards as it sounds, the outer loop should be the points rather // than `````` Whitfield, Ross committed Dec 16, 2014 367 368 369 370 371 372 373 374 375 376 377 378 379 380 `````` // the moments for (size_t j = 0; j < numPoints; ++j) { // central x in histogram with a change of variables - and just change for // density const double xVal = .5 * static_cast(x[j] + x[j + 1]) - mean; // change of variables // this variable will be (x^n)*y double temp; if (isDensity) { const double xDelta = static_cast(x[j + 1] - x[j]); temp = xVal * .5 * static_cast(y[j] + y[j + 1]) * xDelta; } else { temp = xVal * static_cast(y[j]); `````` Peterson, Peter committed Sep 09, 2013 381 382 `````` } `````` Whitfield, Ross committed Dec 16, 2014 383 384 385 386 387 `````` // accumulate the moment result[1] += temp; for (size_t i = 2; i < result.size(); ++i) { temp *= xVal; result[i] += temp; `````` Peterson, Peter committed Sep 09, 2013 388 `````` } `````` Whitfield, Ross committed Dec 16, 2014 389 390 391 392 393 394 395 396 397 `````` } return result; } // -------------------------- Macro to instantiation concrete types // -------------------------------- #define INSTANTIATE(TYPE) \ template MANTID_KERNEL_DLL Statistics \ `````` Martyn Gigg committed Sep 02, 2015 398 `````` getStatistics(const vector &, const unsigned int); \ `````` Whitfield, Ross committed Dec 16, 2014 399 `````` template MANTID_KERNEL_DLL std::vector getZscore( \ `````` Whitfield, Ross committed Oct 05, 2015 400 `````` const vector &); \ `````` Whitfield, Ross committed Dec 16, 2014 401 402 403 404 405 406 407 408 409 410 411 `````` template MANTID_KERNEL_DLL std::vector getModifiedZscore( \ const vector &, const bool); \ template MANTID_KERNEL_DLL std::vector getMomentsAboutOrigin( \ const std::vector &x, const std::vector &y, \ const int maxMoment); \ template MANTID_KERNEL_DLL std::vector getMomentsAboutMean( \ const std::vector &x, const std::vector &y, \ const int maxMoment); // --------------------------- Concrete instantiations // --------------------------------------------- `````` Harry Jeffery committed Mar 19, 2015 412 413 414 415 416 417 418 419 ``````INSTANTIATE(float) INSTANTIATE(double) INSTANTIATE(int) INSTANTIATE(long) INSTANTIATE(long long) INSTANTIATE(unsigned int) INSTANTIATE(unsigned long) INSTANTIATE(unsigned long long) `````` Whitfield, Ross committed Dec 16, 2014 420 421 `````` } // namespace Kernel `````` 422 ``} // namespace Mantid``