mothurmetastats.cpp

   1 /*
   2  *  mothurmetastats.cpp
   3  *  Mothur
   4  *
   5  *  Created by westcott on 7/6/11.
   6  *  Copyright 2011 Schloss Lab. All rights reserved.
   7  *
   8  */
   9
  10 #include "mothurmetastats.h"
  11 #include "mothurfisher.h"
  12 #include "spline.h"
  13
  14 /***********************************************************/
  15 MothurMetastats::MothurMetastats(double t, int n) {
  16         try {
  17                 m = MothurOut::getInstance();
  18                 threshold = t;
  19                 numPermutations = n;
  20
  21         }catch(exception& e) {
  22                 m->errorOut(e, "MothurMetastats", "MothurMetastats");
  23                 exit(1);
  24         }
  25 }
  26 /***********************************************************/
  27 MothurMetastats::~MothurMetastats() {}
  28 /***********************************************************/
  29  //main metastats function
  30 int MothurMetastats::runMetastats(string outputFileName, vector< vector<double> >& data, int secGroupingStart) {
  31     try {
  32         row = data.size();               //numBins
  33                 column = data[0].size(); //numGroups in subset
  34         secondGroupingStart = secGroupingStart; //g
  35
  36         vector< vector<double> > Pmatrix; Pmatrix.resize(row);
  37         for (int i = 0; i < row; i++) { Pmatrix[i].resize(column, 0.0);  } // the relative proportion matrix
  38         vector< vector<double> > C1; C1.resize(row);
  39         for (int i = 0; i < row; i++) { C1[i].resize(3, 0.0);  } // statistic profiles for class1 and class 2
  40         vector< vector<double> > C2; C2.resize(row);            // mean[1], variance[2], standard error[3]
  41         for (int i = 0; i < row; i++) { C2[i].resize(3, 0.0);  }
  42         vector<double> T_statistics; T_statistics.resize(row, 1); // a place to store the true t-statistics
  43         vector<double> pvalues; pvalues.resize(row, 1); // place to store pvalues
  44         vector<double> qvalues; qvalues.resize(row, 1); // stores qvalues
  45
  46         //*************************************
  47         //      convert to proportions
  48         //      generate Pmatrix
  49         //*************************************
  50         vector<double> totals; totals.resize(column, 0); // sum of columns
  51         //total[i] = total abundance for group[i]
  52                 for (int i = 0; i < column; i++) {
  53                         for (int j = 0; j < row; j++) {
  54                                 totals[i] += data[j][i];
  55                         }
  56         }
  57
  58         for (int i = 0; i < column; i++) {
  59                         for (int j = 0; j < row; j++) {
  60                                 Pmatrix[j][i] = data[j][i]/totals[i];
  61
  62                         }
  63         }
  64
  65         //#********************************************************************************
  66         //# ************************** STATISTICAL TESTING ********************************
  67         //#********************************************************************************
  68
  69         if (column == 2){  //# then we have a two sample comparison
  70             //#************************************************************
  71             //#  generate p values fisher's exact test
  72             //#************************************************************
  73             double total1, total2;
  74                         //total for first grouping
  75             for (int i = 0; i < secondGroupingStart; i++) { total1 += totals[i]; }
  76
  77             //total for second grouping
  78             for (int i = secondGroupingStart; i < column; i++) { total2 += totals[i]; }
  79
  80             vector<double> fish;        fish.resize(row, 0.0);
  81                         vector<double> fish2;   fish2.resize(row, 0.0);
  82
  83                         for(int i = 0; i < row; i++){
  84
  85                                 for(int j = 0; j < secondGroupingStart; j++)            { fish[i] += data[i][j];        }
  86                                 for(int j = secondGroupingStart; j < column; j++)       { fish2[i] += data[i][j];       }
  87
  88                                 double f11, f12, f21, f22;
  89                                 f11 = fish[i];
  90                                 f12 = fish2[i];
  91                                 f21 = total1 - fish[i];
  92                                 f22 = total2 - fish2[i];
  93
  94                                 MothurFisher fisher;
  95                                 double pre = fisher.fexact(f11, f12, f21, f22);
  96                                 if (pre > 0.999999999)  { pre = 1.0; }
  97
  98                                 if (m->control_pressed) { return 1; }
  99
 100                                 pvalues[i] = pre;
 101                         }
 102
 103             //#*************************************
 104             //#  calculate q values from p values
 105             //#*************************************
 106             qvalues = calc_qvalues(pvalues);
 107
 108         }else { //we have multiple subjects per population
 109
 110             //#*************************************
 111             //#  generate statistics mean, var, stderr
 112             //#*************************************
 113             for(int i = 0; i < row; i++){ // for each taxa
 114                 //# find the mean of each group
 115                 double g1Total = 0.0; double g2Total = 0.0;
 116                 for (int j = 0; j < secondGroupingStart; j++)       {     g1Total += Pmatrix[i][j]; }
 117                 C1[i][0] = g1Total/(double)(secondGroupingStart);
 118                 for (int j = secondGroupingStart; j < column; j++)  {     g2Total += Pmatrix[i][j]; }
 119                 C2[i][0] = g2Total/(double)(column-secondGroupingStart);
 120
 121                  //# find the variance of each group
 122                 double g1Var = 0.0; double g2Var = 0.0;
 123                 for (int j = 0; j < secondGroupingStart; j++)       {     g1Var += pow((Pmatrix[i][j]-C1[i][0]), 2);  }
 124                 C1[i][1] = g1Var/(double)(secondGroupingStart-1);
 125                 for (int j = secondGroupingStart; j < column; j++)  {     g2Var += pow((Pmatrix[i][j]-C2[i][0]), 2);  }
 126                 C2[i][1] = g2Var/(double)(column-secondGroupingStart-1);
 127
 128                 //# find the std error of each group -std err^2 (will change to std err at end)
 129                 C1[i][2] = C1[i][1]/(double)(secondGroupingStart);
 130                 C2[i][2] = C2[i][1]/(double)(column-secondGroupingStart);
 131             }
 132
 133             //#*************************************
 134             //#  two sample t-statistics
 135             //#*************************************
 136             for(int i = 0; i < row; i++){                  // # for each taxa
 137                 double xbar_diff = C1[i][0] - C2[i][0];
 138                 double denom = sqrt(C1[i][2] + C2[i][2]);
 139                 T_statistics[i] = xbar_diff/denom;  // calculate two sample t-statistic
 140             }
 141
 142             /*for (int i = 0; i < row; i++) {
 143                 for (int j = 0; j < 3; j++) {
 144                     cout << "C1[" << i+1 << "," << j+1 << "]=" << C1[i][j] << ";" << endl;
 145                     cout << "C2[" << i+1 << "," << j+1 << "]=" << C2[i][j] << ";" << endl;
 146                 }
 147                 cout << "T_statistics[" << i+1 << "]=" << T_statistics[i] << ";" << endl;
 148             }*/
 149             //#*************************************
 150             //# generate initial permuted p-values
 151             //#*************************************
 152             pvalues = permuted_pvalues(Pmatrix, T_statistics, data);
 153
 154             //#*************************************
 155             //#  generate p values for sparse data
 156             //#  using fisher's exact test
 157             //#*************************************
 158             double total1, total2;
 159                         //total for first grouping
 160             for (int i = 0; i < secondGroupingStart; i++) { total1 += totals[i]; }
 161
 162             //total for second grouping
 163             for (int i = secondGroupingStart; i < column; i++) { total2 += totals[i]; }
 164
 165             vector<double> fish;        fish.resize(row, 0.0);
 166                         vector<double> fish2;   fish2.resize(row, 0.0);
 167
 168                         for(int i = 0; i < row; i++){
 169
 170                                 for(int j = 0; j < secondGroupingStart; j++)            { fish[i] += data[i][j];        }
 171                                 for(int j = secondGroupingStart; j < column; j++)       { fish2[i] += data[i][j];       }
 172
 173                 if ((fish[1] < secondGroupingStart) && (fish2[i] < (column-secondGroupingStart))) {
 174                     double f11, f12, f21, f22;
 175                     f11 = fish[i];
 176                     f12 = fish2[i];
 177                     f21 = total1 - fish[i];
 178                     f22 = total2 - fish2[i];
 179
 180                     MothurFisher fisher;
 181                     double pre = fisher.fexact(f11, f12, f21, f22);
 182                     if (pre > 0.999999999)      { pre = 1.0; }
 183
 184                     if (m->control_pressed) { return 1; }
 185
 186                     pvalues[i] = pre;
 187                 }
 188                         }
 189
 190             //#*************************************
 191             //#  calculate q values from p values
 192             //#*************************************
 193             qvalues = calc_qvalues(pvalues);
 194
 195             //#*************************************
 196             //#  convert stderr^2 to std error
 197             //#*************************************
 198             for(int i = 0; i < row; i++){
 199                 C1[i][2] = sqrt(C1[i][2]);
 200                 C2[i][2] = sqrt(C2[i][2]);
 201             }
 202         }
 203
 204         // And now we write the files to a text file.
 205                 struct tm *local;
 206                 time_t t; t = time(NULL);
 207                 local = localtime(&t);
 208
 209                 ofstream out;
 210                 m->openOutputFile(outputFileName, out);
 211                 out.setf(ios::fixed, ios::floatfield); out.setf(ios::showpoint);
 212
 213                 out << "Local time and date of test: " << asctime(local) << endl;
 214                 out << "# rows = " << row << ", # col = " << column << ", g = " << secondGroupingStart << endl << endl;
 215                 out << numPermutations << " permutations" << endl << endl;
 216
 217                 //output column headings - not really sure... documentation labels 9 columns, there are 10 in the output file
 218                 //storage 0 = meanGroup1 - line 529, 1 = varGroup1 - line 532, 2 = err rate1 - line 534, 3 = mean of counts group1?? - line 291, 4 = meanGroup2 - line 536, 5 = varGroup2 - line 539, 6 = err rate2 - line 541, 7 = mean of counts group2?? - line 292, 8 = pvalues - line 293
 219                 out << "OTU\tmean(group1)\tvariance(group1)\tstderr(group1)\tmean(group2)\tvariance(group2)\tstderr(group2)\tp-value\tq-value\n";
 220
 221                 for(int i = 0; i < row; i++){
 222                         if (m->control_pressed) { out.close(); return 0; }
 223
 224             //if there are binlabels use them otherwise count.
 225                         if (m->binLabelsInFile.size() == row) { out << m->binLabelsInFile[i] << '\t'; }
 226             else { out << (i+1) << '\t'; }
 227
 228             out << C1[i][0] << '\t' << C1[i][1] << '\t' << C1[i][2] << '\t' << C2[i][0] << '\t' << C2[i][1] << '\t' << C2[i][2] << '\t' << pvalues[i] << '\t' << qvalues[i] << endl;
 229                 }
 230
 231                 out << endl << endl;
 232                 out.close();
 233
 234
 235
 236         return 0;
 237
 238     }catch(exception& e) {
 239         m->errorOut(e, "MothurMetastats", "runMetastats");
 240         exit(1);
 241     }
 242 }
 243 /***********************************************************/
 244 vector<double> MothurMetastats::permuted_pvalues(vector< vector<double> >& Imatrix, vector<double>& tstats, vector< vector<double> >& Fmatrix) {
 245         try {
 246         //# matrix stores tstats for each taxa(row) for each permuted trial(column)
 247         vector<double> ps;  ps.resize(row, 0.0); //# to store the pvalues
 248         vector< vector<double> > permuted_ttests; permuted_ttests.resize(numPermutations);
 249         for (int i = 0; i < numPermutations; i++) { permuted_ttests[i].resize(row, 0.0);  }
 250
 251         //# calculate null version of tstats using B permutations.
 252         for (int i = 0; i < numPermutations; i++) {
 253             permuted_ttests[i] = permute_and_calc_ts(Imatrix);
 254         }
 255
 256         //# calculate each pvalue using the null ts
 257         if ((secondGroupingStart) < 8 || (column-secondGroupingStart) < 8){
 258             vector< vector<double> > cleanedpermuted_ttests; cleanedpermuted_ttests.resize(numPermutations);  //# the array pooling just the frequently observed ts
 259             //# then pool the t's together!
 260             //# count how many high freq taxa there are
 261             int hfc = 1;
 262             for (int i = 0; i < row; i++) {                 // # for each taxa
 263                 double group1Total = 0.0; double group2Total = 0.0;
 264                 for(int j = 0; j < secondGroupingStart; j++)            { group1Total += Fmatrix[i][j]; }
 265                                 for(int j = secondGroupingStart; j < column; j++)       { group2Total += Fmatrix[i][j]; }
 266
 267                 if (group1Total >= secondGroupingStart || group2Total >= (column-secondGroupingStart)){
 268                     hfc++;
 269                     for (int j = 0; j < numPermutations; j++) {   cleanedpermuted_ttests[j].push_back(permuted_ttests[j][i]); }
 270                 }
 271             }
 272
 273             //#now for each taxa
 274             for (int i = 0; i < row; i++) {
 275                 //number of cleanedpermuted_ttests greater than tstat[i]
 276                 int numGreater = 0;
 277                 for (int j = 0; j < numPermutations; j++) {
 278                     for (int k = 0; k < hfc; k++) {
 279                         if (cleanedpermuted_ttests[j][k] > abs(tstats[i])) { numGreater++; }
 280                     }
 281                 }
 282
 283                 ps[i] = (1/(double)(numPermutations*hfc))*numGreater;
 284             }
 285         }else{
 286             for (int i = 0; i < row; i++) {
 287                 //number of permuted_ttests[i] greater than tstat[i] //(sum(permuted_ttests[i,] > abs(tstats[i]))+1)
 288                 int numGreater = 1;
 289                 for (int j = 0; j < numPermutations; j++) { if (permuted_ttests[j][i] > abs(tstats[i])) { numGreater++; }   }
 290                 ps[i] = (1/(double)(numPermutations+1))*numGreater;
 291             }
 292         }
 293
 294         return ps;
 295
 296     }catch(exception& e) {
 297         m->errorOut(e, "MothurMetastats", "permuted_pvalues");
 298         exit(1);
 299     }
 300 }
 301 /***********************************************************/
 302 vector<double> MothurMetastats::permute_and_calc_ts(vector< vector<double> >& Imatrix) {
 303         try {
 304         vector< vector<double> > permutedMatrix = Imatrix;
 305
 306         //randomize columns, ie group abundances.
 307         for (int i = 0; i < permutedMatrix.size(); i++) {   random_shuffle(permutedMatrix[i].begin(), permutedMatrix[i].end());     }
 308
 309         //calc ts
 310         vector< vector<double> > C1; C1.resize(row);
 311         for (int i = 0; i < row; i++) { C1[i].resize(3, 0.0);  } // statistic profiles for class1 and class 2
 312         vector< vector<double> > C2; C2.resize(row);            // mean[1], variance[2], standard error[3]
 313         for (int i = 0; i < row; i++) { C2[i].resize(3, 0.0);  }
 314         vector<double> Ts; Ts.resize(row, 0.0); // a place to store the true t-statistics
 315
 316         //#*************************************
 317         //#  generate statistics mean, var, stderr
 318         //#*************************************
 319         for(int i = 0; i < row; i++){ // for each taxa
 320             //# find the mean of each group
 321             double g1Total = 0.0; double g2Total = 0.0;
 322             for (int j = 0; j < secondGroupingStart; j++)       {     g1Total += permutedMatrix[i][j]; }
 323             C1[i][0] = g1Total/(double)(secondGroupingStart);
 324             for (int j = secondGroupingStart; j < column; j++)  {     g2Total += permutedMatrix[i][j]; }
 325             C2[i][0] = g2Total/(double)(column-secondGroupingStart);
 326
 327             //# find the variance of each group
 328             double g1Var = 0.0; double g2Var = 0.0;
 329             for (int j = 0; j < secondGroupingStart; j++)       {     g1Var += pow((permutedMatrix[i][j]-C1[i][0]), 2);  }
 330             C1[i][1] = g1Var/(double)(secondGroupingStart-1);
 331             for (int j = secondGroupingStart; j < column; j++)  {     g2Var += pow((permutedMatrix[i][j]-C2[i][0]), 2);  }
 332             C2[i][1] = g2Var/(double)(column-secondGroupingStart-1);
 333
 334             //# find the std error of each group -std err^2 (will change to std err at end)
 335             C1[i][2] = C1[i][1]/(double)(secondGroupingStart);
 336             C2[i][2] = C2[i][1]/(double)(column-secondGroupingStart);
 337         }
 338
 339         //#*************************************
 340         //#  two sample t-statistics
 341         //#*************************************
 342         for(int i = 0; i < row; i++){                  // # for each taxa
 343             double xbar_diff = C1[i][0] - C2[i][0];
 344             double denom = sqrt(C1[i][2] + C2[i][2]);
 345             Ts[i] = abs(xbar_diff/denom);  // calculate two sample t-statistic
 346         }
 347
 348         return Ts;
 349
 350
 351     }catch(exception& e) {
 352         m->errorOut(e, "MothurMetastats", "permuted_ttests");
 353         exit(1);
 354     }
 355 }
 356 /***********************************************************/
 357 vector<double> MothurMetastats::calc_qvalues(vector<double>& pValues) {
 358         try {
 359
 360        /* cout << "x <- c(" << pValues[0];
 361         for (int l = 1; l < pValues.size(); l++){
 362             cout << ", " << pValues[l];
 363         }
 364         cout << ")\n";*/
 365
 366                 int numRows = pValues.size();
 367                 vector<double> qvalues(numRows, 0.0);
 368
 369                 //fill lambdas with 0.00, 0.01, 0.02... 0.95
 370                 vector<double> lambdas(96, 0);
 371                 for (int i = 1; i < lambdas.size(); i++) { lambdas[i] = lambdas[i-1] + 0.01; }
 372
 373                 vector<double> pi0_hat(lambdas.size(), 0);
 374
 375                 //calculate pi0_hat
 376                 for (int l = 0; l < lambdas.size(); l++){ // for each lambda value
 377                         int count = 0;
 378                         for (int i = 0; i < numRows; i++){ // for each p-value in order
 379                                 if (pValues[i] > lambdas[l]){ count++; }
 380                         }
 381                         pi0_hat[l] = count/(double)(numRows*(1-lambdas[l]));
 382                 }
 383
 384                 double pi0 = smoothSpline(lambdas, pi0_hat, 3);
 385
 386                 //order p-values
 387                 vector<double> ordered_qs = qvalues;
 388                 vector<int> ordered_ps(pValues.size(), 0);
 389                 for (int i = 1; i < ordered_ps.size(); i++) {  ordered_ps[i] = ordered_ps[i-1] + 1; }
 390                 vector<double> tempPvalues = pValues;
 391                 OrderPValues(0, numRows-1, tempPvalues, ordered_ps);
 392
 393                 ordered_qs[numRows-1] = min((pValues[ordered_ps[numRows-1]]*pi0), 1.0);
 394                 for (int i = (numRows-2); i >= 0; i--){
 395                         double p = pValues[ordered_ps[i]];
 396                         double temp = p*numRows*pi0/(double)(i+1);
 397
 398                         ordered_qs[i] = min(temp, ordered_qs[i+1]);
 399                 }
 400
 401                 //re-distribute calculated qvalues to appropriate rows
 402                 for (int i = 0; i < numRows; i++){
 403                         qvalues[ordered_ps[i]] = ordered_qs[i];
 404                 }
 405
 406                 return qvalues;
 407
 408         }catch(exception& e) {
 409                 m->errorOut(e, "MothurMetastats", "calc_qvalues");
 410                 exit(1);
 411         }
 412 }
 413 /***********************************************************/
 414 int MothurMetastats::OrderPValues(int low, int high, vector<double>& p, vector<int>& order) {
 415         try {
 416
 417                 if (low < high) {
 418                         int i = low+1;
 419                         int j = high;
 420                         int pivot = (low+high) / 2;
 421
 422                         swapElements(low, pivot, p, order);  //puts pivot in final spot
 423
 424                         /* compare value */
 425                         double key = p[low];
 426
 427                         /* partition */
 428                         while(i <= j) {
 429                                 /* find member above ... */
 430                                 while((i <= high) && (p[i] <= key))     {  i++;  }
 431
 432                                 /* find element below ... */
 433                                 while((j >= low) && (p[j] > key))       {  j--;  }
 434
 435                                 if(i < j) {
 436                                         swapElements(i, j, p, order);
 437                                 }
 438                         }
 439
 440                         swapElements(low, j, p, order);
 441
 442                         /* recurse */
 443                         OrderPValues(low, j-1, p, order);
 444                         OrderPValues(j+1, high, p, order);
 445                 }
 446
 447                 return 0;
 448
 449         }catch(exception& e) {
 450                 m->errorOut(e, "MothurMetastats", "OrderPValues");
 451                 exit(1);
 452         }
 453 }
 454 /***********************************************************/
 455 int MothurMetastats::swapElements(int i, int j, vector<double>& p, vector<int>& order) {
 456         try {
 457
 458                 double z = p[i];
 459                 p[i] = p[j];
 460                 p[j] = z;
 461
 462                 int temp = order[i];
 463                 order[i] = order[j];
 464                 order[j] = temp;
 465
 466                 return 0;
 467
 468         }catch(exception& e) {
 469                 m->errorOut(e, "MothurMetastats", "swapElements");
 470                 exit(1);
 471         }
 472 }
 473 /***********************************************************/
 474 double MothurMetastats::smoothSpline(vector<double>& x, vector<double>& y, int df) {
 475         try {
 476
 477                 double result = 0.0;
 478                 int n = x.size();
 479                 vector<double> w(n, 1);
 480                 double* xb = new double[n];
 481                 double* yb = new double[n];
 482                 double* wb = new double[n];
 483                 double yssw = 0.0;
 484                 for (int i = 0; i < n; i++) {
 485                         wb[i] = w[i];
 486                         yb[i] = w[i]*y[i];
 487                         yssw += (w[i] * y[i] * y[i]) - wb[i] * (yb[i] * yb[i]);
 488                         xb[i] = (x[i] - x[0]) / (x[n-1] - x[0]);
 489                 }
 490
 491                 vector<double> knot = sknot1(xb, n);
 492                 int nk = knot.size() - 4;
 493
 494                 double low = -1.5; double high = 1.5; double tol = 1e-04; double eps = 2e-08; int maxit = 500;
 495                 int ispar = 0; int icrit = 3; double dofoff = 3.0;
 496                 double penalty = 1.0;
 497                 int ld4 = 4; int isetup = 0; int ldnk = 1; int ier; double spar = 1.0; double crit;
 498
 499                 double* knotb = new double[knot.size()];
 500                 double* coef1 = new double[nk];
 501                 double* lev1 = new double[n];
 502                 double* sz1 = new double[n];
 503                 for (int i = 0; i < knot.size(); i++) { knotb[i] = knot[i];     }
 504
 505                 Spline spline;
 506                 spline.sbart(&penalty, &dofoff, &xb[0], &yb[0], &wb[0], &yssw, &n, &knotb[0], &nk, &coef1[0], &sz1[0], &lev1[0], &crit,
 507                                 &icrit, &spar, &ispar, &maxit, &low, &high, &tol, &eps, &isetup, &ld4, &ldnk, &ier);
 508
 509                 result = coef1[nk-1];
 510
 511                 //free memory
 512                 delete [] xb;
 513                 delete [] yb;
 514                 delete [] wb;
 515                 delete [] knotb;
 516                 delete [] coef1;
 517                 delete [] lev1;
 518                 delete [] sz1;
 519
 520                 return result;
 521
 522         }catch(exception& e) {
 523                 m->errorOut(e, "MothurMetastats", "smoothSpline");
 524                 exit(1);
 525         }
 526 }
 527 /***********************************************************/
 528 vector<double> MothurMetastats::sknot1(double* x, int n) {
 529         try {
 530                 vector<double> knots;
 531                 int nk = nkn(n);
 532
 533                 //R equivalent - rep(x[1L], 3L)
 534                 knots.push_back(x[0]); knots.push_back(x[0]); knots.push_back(x[0]);
 535
 536                 //generate a sequence of nk equally spaced values from 1 to n. R equivalent = seq.int(1, n, length.out = nk)
 537                 vector<int> indexes = getSequence(0, n-1, nk);
 538                 for (int i = 0; i < indexes.size(); i++) { knots.push_back(x[indexes[i]]);  }
 539
 540                 //R equivalent - rep(x[n], 3L)
 541                 knots.push_back(x[n-1]); knots.push_back(x[n-1]); knots.push_back(x[n-1]);
 542
 543                 return knots;
 544
 545         }catch(exception& e) {
 546                 m->errorOut(e, "MothurMetastats", "sknot1");
 547                 exit(1);
 548         }
 549 }
 550 /***********************************************************/
 551 vector<int> MothurMetastats::getSequence(int start, int end, int length) {
 552         try {
 553                 vector<int> sequence;
 554                 double increment = (end-start) / (double) (length-1);
 555
 556                 sequence.push_back(start);
 557                 for (int i = 1; i < length-1; i++) {
 558                         sequence.push_back(int(i*increment));
 559                 }
 560                 sequence.push_back(end);
 561
 562                 return sequence;
 563
 564         }catch(exception& e) {
 565                 m->errorOut(e, "MothurMetastats", "getSequence");
 566                 exit(1);
 567         }
 568 }
 569 /***********************************************************/
 570 //not right, havent fully figured out the variable types yet...
 571 int MothurMetastats::nkn(int n) {
 572         try {
 573
 574                 if (n < 50) { return n; }
 575                 else {
 576                         double a1 = log2(50);
 577                         double a2 = log2(100);
 578                         double a3 = log2(140);
 579                         double a4 = log2(200);
 580
 581                         if (n < 200) {
 582                                 return (int)pow(2.0, (a1 + (a2 - a1) * (n - 50)/(float)150));
 583                         }else if (n < 800) {
 584                                 return (int)pow(2.0, (a2 + (a3 - a2) * (n - 200)/(float)600));
 585                         }else if (n < 3200) {
 586                                 return (int)pow(2.0, (a3 + (a4 - a3) * (n - 800)/(float)2400));
 587                         }else {
 588                                 return (int)pow((double)(200 + (n - 3200)), 0.2);
 589                         }
 590                 }
 591
 592                 return 0;
 593
 594         }catch(exception& e) {
 595                 m->errorOut(e, "MothurMetastats", "nkn");
 596                 exit(1);
 597         }
 598 }
 599 /***********************************************************/
 600
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