Mercurial > repos > immport-devteam > cross_sample

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/cross_sample/src/README	Mon Feb 27 13:29:54 2017 -0500
@@ -0,0 +1,139 @@
+This package contains R code for converting and transforming a binary
+FCS file, using the FCSTrans software, and the C code for running the
+flock1 and flock2 population identification software.
+
+src - contains the C code for flock1, flock2 and cent_adjust
+bin - contains the compiled C code for flock1, flock2 and cent_adjust,
+      plus the R code for using the FCSTrans algorithm for file
+      conversion and data transformation.
+doc - documentation for FCSTrans and FLOCK algorithms
+example - sample data and output from FCSTrans and FLOCK
+
+To run this software sucessfully the code assumes the software was installed
+in the /usr/local/flock directory and that R, plus the Bioconductor flowCore
+module has been installed. If you use the ipconvert.sh shell script, you
+may need to adjust the location of the RScript executable and the location
+of the FCSTrans.R code by editing the shell script.
+
+#############################################################################
+# Overview
+#############################################################################
+ImmPort-FLOCK
+
+FLOCK (FLOw Clustering without K), an automated population discovery tool for
+multidimensional FCM data was designed to specifically take into account the
+unique feature of FCM data and produce objective segregation of cell
+populations.
+
+FLOCK parameter settings can be customized by defining Bins and Density
+Threshold.  The number of bins is an integer specifying the number of
+equal-sized regions the data will be partitioned into on each axis. Increasing
+the number of bins increases the sensitivity to detect rare populations but
+may also result in single populations being divided.  Density Threshold is the
+cut-off value to separate the dense regions from background. It is a floating
+point number that helps define population centers; increasing the threshold
+may help separate major populations but could cause the algorithm to overlook
+rare populations.
+
+#############################################################################
+# Compiling C code
+#############################################################################
+cd bin
+cc -o flock1 ../src/flock1.c ../src/find_connected.c -lm
+cc -o flock2 ../src/flock2.c -lm
+cc -o cent_adjust ../src/cent_adjust.c -lm
+
+#############################################################################
+# FCSTrans
+#############################################################################
+A shell script named ipconvert.sh is included that runs the FCSTrans R
+code for converting and transforming a binary FCS file. The output consists
+of one text file containing the transformed channel intensity values and
+another file containing a list of the FCS parameters.
+
+cd bin
+/usr/local/flock/bin/ipconvert.sh ../example/data/FCS2.fcs
+/usr/local/flock/bin/ipconvert.sh ../example/data/FCS3.fcs
+
+#############################################################################
+# Running flock1 or flock2
+#############################################################################
+Running the FLOCK1 and FLOCK2 algorithms generate 8 output files that have
+generic file names. For this reason, it is recommended that one output
+directory be created for one input file to the program.
+
+cd example/output/FCS2
+/usr/local/flock/bin/flock1 ../../data/FCS2.txt
+
+cd example/output/FCS3
+/usr/local/flock/bin/flock2 ../../data/FCS3.txt
+
+Files created: MFI.txt, percentage.txt, population_id.txt, profile.txt,
+               flock_results.txt, coordinates.txt, population_center.txt
+               and percentage.txt
+
+Usage Information for FLOCK1
+----------------------------------------------------------------------------
+basic mode: flock1 fcs.txt
+advanced_ mode: flock1 fcs.txt num_bin density_index max_num_pop
+
+Usage Information for FLOCK2
+----------------------------------------------------------------------------
+basic mode: flock data_file
+advanced mode 0 (specify maximum # of pops): flock data_file max_num_pop
+advanced mode 1 (without # of pops): flock data_file num_bin density_index
+advanced mode 2 (specify # of pops): flock data_file num_bin density_index
+                                           number_of_pop
+advanced mode 3 (specify both # of pops): flock data_file num_bin density_index
+                                           number_of_pop max_num_pop
+
+FLOCK Output Files
+----------------------------------------------------------------------------
+coordinates.txt:
+    Output is the intensity values for each marker and event
+
+flock_results.txt:
+    A combination of the input file, event identifiers and population
+    identifiers.
+
+MFI.txt:
+    Provides the mean fluorescence intensity for each population for each
+    marker/parameter
+
+population_id.txt:
+    Contains population identifiers (i.e, values from [1 to n] where n is
+    the population assigned to the  corresponding events in the input data
+    file, one identifier per row.)
+
+population_center.txt:
+    Contains the centroid coordinates for each identified population
+
+percentage.txt:
+    Includes the population identifiers and percentage of events within that
+    population (relative to the whole data file)
+
+profile.txt:
+    Displays an expression profile, where the approximate expression level
+    for each marker is assigned a numeric value from 1-4, for each identified
+    population
+
+fcs_properties.txt:
+    Contains the number of events, number of populations, and number of
+    markers, as well as the algorithm parameters used in the  analysis
+
+#############################################################################
+# Running cent_adjust
+#############################################################################
+Running the cent_adjust algorithm generates 4 output files that have
+generic file names. For this reason, it is recommened that one output
+directory be created for one input file to the program.
+
+mkdir example/output/FCS2/cent_adjust
+cd example/output/FCS2/cent_adjust
+/usr/local/flock/bin/cent_adjust ../population_center.txt ../coordinates.txt
+
+Files created: MFI.txt, percentage.txt, population_id.txt and profile.txt
+
+Usage Information for cent_adjust
+----------------------------------------------------------------------------
+basic mode: cent_adjust input_center input_data_file
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/cross_sample/src/cent_adjust.c	Mon Feb 27 13:29:54 2017 -0500
@@ -0,0 +1,1009 @@
+/////////////////////////////////////////////////////////
+//  Cent_adjust version number and modification history
+//  ImmPort BISC project
+//  Author: Yu "Max" Qian
+//  v1.01: Oct 16, 2009
+//         Line 899 of the main function:
+//         Changed kmean_term=1 to kmean_term=2
+//////////////////////////////////////////////////////////
+
+
+#include <time.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <string.h>
+
+#define DEBUG 0
+#define LINE_LEN 1024
+#define FILE_NAME_LEN 128
+#define PARA_NAME_LEN 64
+#define MAX_VALUE 1000000000
+#define CUBE 0
+
+
+void getctrfileinfo(FILE *f_src_ctr, long *num_clust)
+{
+	int ch='\n';
+	int prev='\n';
+	long num_rows=0;
+
+	while ((ch = fgetc(f_src_ctr))!= EOF )
+    {
+		if (ch == '\n')
+        {
+			++num_rows;
+        }
+		prev = ch;
+    }
+	if (prev!='\n')
+		++num_rows;
+
+	*num_clust=num_rows;
+	//printf("center file has %ld rows\n", *num_clust);
+}
+
+/************************************* Read basic info of the source file **************************************/
+void getfileinfo(FILE *f_src, long *file_Len, long *num_dm, char *name_string, int *time_ID)
+{
+	char src[LINE_LEN];
+	char current_name[64];
+	char prv;
+
+	long num_rows=0;
+	long num_columns=0;
+	int ch='\n';
+	int prev='\n';
+	long time_pos=0;
+	long i=0;
+	long j=0;
+
+
+
+	src[0]='\0';
+	fgets(src, LINE_LEN, f_src);
+
+	name_string[0]='\0';
+	current_name[0]='\0';
+	prv='\n';
+
+	while ((src[i]==' ') || (src[i]=='\t')) //skip space and tab characters
+		i++;
+
+	while ((src[i]!='\r') && (src[i]!='\n')) //repeat until the end of the line
+	{
+		current_name[j]=src[i];
+
+		if ((src[i]=='\t') && (prv!='\t')) //a complete word
+		{
+			current_name[j]='\0';
+
+          /*
+           * Commented out John Campbell, June 10 2010
+           * We no longer want to automatically remove Time column.
+           * This column should have been removed by column selection
+          if (0!=strcmp(current_name,"Time"))
+            {
+              num_columns++; //num_columns does not inlcude the column of Time
+              time_pos++;
+              strcat(name_string,current_name);
+              strcat(name_string,"\t");
+            }
+          else
+            {
+              *time_ID=time_pos;
+            }
+          */
+
+           num_columns++;
+           strcat(name_string,current_name);
+           strcat(name_string,"\t");
+
+		   current_name[0]='\0';
+		   j=0;
+		}
+
+		if ((src[i]=='\t') && (prv=='\t')) //a duplicate tab or space
+		{
+			current_name[0]='\0';
+			j=0;
+		}
+
+        if (src[i]!='\t')
+	        j++;
+
+
+		prv=src[i];
+		i++;
+	}
+
+	if (prv!='\t') //the last one hasn't been retrieved
+	{
+		current_name[j]='\0';
+      /*
+       * Commented out John Campbell, June 10 2010
+       * We no longer want to automatically remove Time column.
+       * This column should have been removed by column selection
+      if (0!=strcmp(current_name,"Time"))
+        {
+          num_columns++;
+          strcat(name_string,current_name);
+          time_pos++;
+        }
+      else
+        {
+          *time_ID=time_pos;
+        }
+      */
+
+      num_columns++;
+      strcat(name_string,current_name);
+	}
+
+	if (DEBUG==1)
+	{
+		printf("time_ID is %d\n",*time_ID);
+		printf("name_string is %s\n",name_string);
+	}
+
+	// # of rows
+
+	while ((ch = fgetc(f_src))!= EOF )
+    {
+		if (ch == '\n')
+        {
+			++num_rows;
+        }
+		prev = ch;
+    }
+	if (prev!='\n')
+		++num_rows;
+
+	*file_Len=num_rows;
+	*num_dm=num_columns;
+
+	//printf("original file size is %ld; number of dimensions is %ld\n", *file_Len, *num_dm);
+}
+
+
+
+///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+/************************************* Read the source file into uncomp_data **************************************/
+void readsource(FILE *f_src, long file_Len, long num_dm, double **uncomp_data, int time_ID)
+{
+	long time_pass=0; //to mark whether the time_ID has been passed
+	long index=0;
+
+	long i=0;
+	long j=0;
+	long t=0;
+
+	char src[LINE_LEN];
+	char xc[LINE_LEN/10];
+
+	src[0]='\0';
+	fgets(src,LINE_LEN, f_src); //skip the first line about parameter names
+
+	while (!feof(f_src) && (index<file_Len)) //index = 0, 1, ..., file_Len-1
+	{
+		src[0]='\0';
+	  	fgets(src,LINE_LEN,f_src);
+		i=0;
+		time_pass=0;
+
+		if (time_ID==-1)
+		{
+			for (t=0;t<num_dm;t++) //there is no time_ID
+			{
+				xc[0]='\0';
+				j=0;
+				while ((src[i]!='\r') && (src[i]!='\n') && (src[i]!=' ') && (src[i]!='\t'))
+				{
+					xc[j]=src[i];
+					i++;
+					j++;
+				}
+
+				xc[j]='\0';
+				i++;
+
+				uncomp_data[index][t]=atof(xc);
+			}
+		}
+		else
+		{
+			for (t=0;t<=num_dm;t++) //the time column needs to be skipped, so there are num_dm+1 columns
+			{
+				xc[0]='\0';
+				j=0;
+				while ((src[i]!='\r') && (src[i]!='\n') && (src[i]!=' ') && (src[i]!='\t'))
+				{
+					xc[j]=src[i];
+					i++;
+					j++;
+				}
+
+				xc[j]='\0';
+				i++;
+
+				if (t==time_ID)
+				{
+					time_pass=1;
+					continue;
+				}
+
+				if (time_pass)
+					uncomp_data[index][t-1]=atof(xc);
+				else
+					uncomp_data[index][t]=atof(xc);
+			}
+		}
+		index++;
+	    //fprintf(fout_ID,"%s",src);
+    } //end of while
+
+	if (DEBUG == 1)
+	{
+		printf("the last line of the source data is:\n");
+		for (j=0;j<num_dm;j++)
+			printf("%f ",uncomp_data[index-1][j]);
+		printf("\n");
+	}
+}
+
+/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+void readcenter(FILE *f_src_ctr, long num_clust, long num_dm, double **cluster_center, long *IDmapping)
+{
+	char src[LINE_LEN];
+	char xc[LINE_LEN/10];
+
+	long i=0;
+	long j=0;
+	int m=0;
+	int t=0;
+
+	for (i=0;i<num_clust;i++)
+	{
+		src[0]='\0';
+		fgets(src,LINE_LEN, f_src_ctr);
+		m=0;
+		for (j=0;j<num_dm+1;j++)
+		{
+			xc[0]='\0';
+			t=0;
+			while ((src[m]!='\r') && (src[m]!='\n') && (src[m]!=' ') && (src[m]!='\t'))
+			{
+				xc[t]=src[m];
+				m++;
+				t++;
+			}
+			xc[t]='\0';
+			m++;
+			if (j==0)
+				IDmapping[i]=atoi(xc);
+			else
+				cluster_center[i][j-1]=atof(xc);
+			//printf("cluster_center[%d][%d]=%f\n",i,j,cluster_center[i][j]);
+		}
+	}
+}
+
+
+/**************************************** Normalization ******************************************/
+void tran(double **orig_data, long clean_Len, long num_dm, long norm_used, double **matrix_to_cluster)
+{
+	long i=0;
+	long j=0;
+
+	double biggest=0;
+	double smallest=MAX_VALUE;
+
+	double *aver; //average of each column
+	double *std; //standard deviation of each column
+
+	aver=(double*)malloc(sizeof(double)*clean_Len);
+	memset(aver,0,sizeof(double)*clean_Len);
+
+	std=(double*)malloc(sizeof(double)*clean_Len);
+	memset(std,0,sizeof(double)*clean_Len);
+
+	if (norm_used==2) //z-score normalization
+	{
+		for (j=0;j<num_dm;j++)
+		{
+			aver[j]=0;
+			for (i=0;i<clean_Len;i++)
+				aver[j]=aver[j]+orig_data[i][j];
+			aver[j]=aver[j]/(double)clean_Len;
+
+			std[j]=0;
+			for (i=0;i<clean_Len;i++)
+				std[j]=std[j]+(orig_data[i][j]-aver[j])*(orig_data[i][j]-aver[j]);
+			std[j]=sqrt(std[j]/(double)clean_Len);
+
+			for (i=0;i<clean_Len;i++)
+				matrix_to_cluster[i][j]=(orig_data[i][j]-aver[j])/std[j];  //z-score normalization
+		}
+	}
+
+	if (norm_used==1) //0-1 min-max normalization
+	{
+		for (j=0;j<num_dm;j++)
+		{
+			biggest=0;
+			smallest=MAX_VALUE;
+			for (i=0;i<clean_Len;i++)
+			{
+				if (orig_data[i][j]>biggest)
+					biggest=orig_data[i][j];
+				if (orig_data[i][j]<smallest)
+					smallest=orig_data[i][j];
+			}
+
+			for (i=0;i<clean_Len;i++)
+			{
+				if (biggest==smallest)
+					matrix_to_cluster[i][j]=biggest;
+				else
+					matrix_to_cluster[i][j]=(orig_data[i][j]-smallest)/(biggest-smallest);
+			}
+		}
+	}
+
+	if (norm_used==0) //no normalization
+	{
+		for (i=0;i<clean_Len;i++)
+			for (j=0;j<num_dm;j++)
+				matrix_to_cluster[i][j]=orig_data[i][j];
+	}
+
+
+}
+
+/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+void assign_event(double **Matrix, long k, long dist_used, double kmean_term, long file_Len, long num_dm, long *shortest_id, double **center, int random_init)
+{
+
+	long i=0;
+
+	long j=0;
+	long t=0;
+	long random=0;
+	long random1=0;
+	long random2=0;
+	long times=0;
+	long times_allowed=0;
+
+ 	long *num;  //num[i]=t means the ith cluster has t points
+
+	double vvv=1.0; // the biggest variation;
+	double distance=0.0;
+	double xv=0.0;
+	double variation=0.0;
+	double EPS=0.0;
+	double diff=0.0;
+	double mean_dx=0;
+	double mean_dy=0;
+	double sum_var=0;
+	double dx=0;
+	double dy=0;
+	double sd_x=0;
+	double sd_y=0;
+
+	double *temp_center;
+	double *shortest_distance;
+
+	double **sum;
+
+	temp_center = (double *)malloc(sizeof(double)*num_dm);
+	memset(temp_center,0,sizeof(double)*num_dm);
+
+	/* Choosing Centers */
+	if (random_init)
+	{
+		for (i=0;i<k;i++)
+		{
+			random1=rand()*rand();
+			//srand( (unsigned)time( NULL ) );
+			random2=abs((random1%5)+1);
+			for (t=0;t<random2;t++)
+				random2=random2*rand()+rand();
+
+			random=abs(random2%file_Len);
+			//printf("random=%d\n",random);
+			for (j=0;j<num_dm;j++)
+				center[i][j]=Matrix[random][j];
+
+		}
+	}
+
+	//printf("finish random selection\n");
+	/* To compute the nearest center for every point */
+
+	shortest_distance = (double *)malloc(sizeof(double)*file_Len);
+	memset(shortest_distance,0,sizeof(double)*file_Len);
+
+	num = (long *)malloc(sizeof(long)*k);
+	memset(num,0,sizeof(long)*k);
+
+	sum = (double **)malloc(sizeof(double*)*k);
+	memset(sum,0,sizeof(double*)*k);
+	for (i=0;i<k;i++)
+	{
+		sum[i] = (double *)malloc(sizeof(double)*num_dm);
+		memset(sum[i],0,sizeof(double)*num_dm);
+	}
+
+	for (i=0;i<k;i++)
+		for (j=0;j<num_dm;j++)
+			sum[i][j]=0.0;        //sum[i][j] = k means the sum of the jth dimension of all points in the ith group is k
+
+	//printf("before recursion\n");
+	if (kmean_term>=1)
+		times_allowed = (long)kmean_term;
+	else
+		EPS = kmean_term;
+
+	times=0;
+
+	while (((vvv>EPS) && (kmean_term<1)) || ((times<times_allowed) && (kmean_term>=1)))
+	{
+		for (i=0;i<k;i++)
+		{
+			num[i]=0;
+			for (j=0;j<num_dm;j++)
+				sum[i][j]=0.0;
+		}
+
+		for (i=0;i<file_Len;i++)  //for each data point i, we compute the distance between Matrix[i] and center[j]
+		{
+			shortest_distance[i]=MAX_VALUE;
+			for (j=0;j<k;j++)  //for each center j
+			{
+
+				distance=0.0;
+
+				if (dist_used==0)  //Euclidean distance
+				{
+					for (t=0;t<num_dm;t++) //for each dimension
+					{
+						diff=center[j][t]-Matrix[i][t];
+						if (diff<0)
+							diff=-diff;
+
+						if (CUBE)
+							distance = distance+(diff*diff*diff);
+						else
+							distance = distance+(diff*diff);
+					}
+				}
+				else  //pearson correlation
+				{
+					mean_dx=0.0;
+					mean_dy=0.0;
+					sum_var=0.0;
+					dx=0.0;
+					dy=0.0;
+					sd_x=0.0;
+					sd_y=0.0;
+					for (t=0;t<num_dm;t++)
+					{
+						mean_dx+=center[j][t];
+						mean_dy+=Matrix[i][t];
+					}
+					mean_dx=mean_dx/(double)num_dm;
+					mean_dy=mean_dy/(double)num_dm;
+				//printf("mean_dx=%f\n",mean_dx);
+
+					for (t=0;t<num_dm;t++)
+					{
+						dx=center[j][t]-mean_dx;
+						dy=Matrix[i][t]-mean_dy;
+						sum_var+=dx*dy;
+						sd_x+=dx*dx;
+						sd_y+=dy*dy;
+					}
+					if (sqrt(sd_x*sd_y)==0)
+						distance = 1.0;
+					else
+						distance = 1.0 - (sum_var/(sqrt(sd_x*sd_y))); // distance ranges from 0 to 2;
+					//printf("distance=%f\n",distance);
+				}	//pearson correlation ends
+
+
+				if (distance<shortest_distance[i])
+				{
+					shortest_distance[i]=distance;
+					shortest_id[i]=j;
+				}
+			}//end for j
+			num[shortest_id[i]]=num[shortest_id[i]]+1;
+			for (t=0;t<num_dm;t++)
+				sum[shortest_id[i]][t]=sum[shortest_id[i]][t]+Matrix[i][t];
+		}//end for i
+	/* recompute the centers */
+	//compute_mean(group);
+		vvv=0.0;
+		for (j=0;j<k;j++)
+		{
+			memcpy(temp_center,center[j],sizeof(double)*num_dm);
+			variation=0.0;
+			if (num[j]!=0)
+			{
+				for (t=0;t<num_dm;t++)
+				{
+					center[j][t]=sum[j][t]/(double)num[j];
+					xv=(temp_center[t]-center[j][t]);
+					variation=variation+xv*xv;
+				}
+			}
+
+			if (variation>vvv)
+				vvv=variation;  //vvv is the biggest variation among the k clusters;
+		}
+	//compute_variation;
+		times++;
+	} //end for while
+
+
+
+	free(num);
+	for (i=0;i<k;i++)
+		free(sum[i]);
+	free(sum);
+	free(temp_center);
+	free(shortest_distance);
+
+}
+
+//////////////////////////////////////////////////////
+/*************************** Show *****************************/
+void show(double **Matrix, long *cluster_id, long file_Len, long k, long num_dm, char *name_string, long *IDmapping)
+{
+	int situ1=0;
+	int situ2=0;
+
+	long i=0;
+	long id=0;
+	long j=0;
+	long info_id=0;
+	long nearest_id=0;
+	long insert=0;
+	long temp=0;
+	long m=0;
+	long n=0;
+	long t=0;
+
+	long *size_c;
+
+
+
+	long **size_mybound_1;
+	long **size_mybound_2;
+	long **size_mybound_3;
+	long **size_mybound_0;
+
+	double interval=0.0;
+
+	double *big;
+	double *small;
+
+
+	double **center;
+	double **mybound;
+
+	long **prof; //prof[i][j]=1 means population i is + at parameter j
+
+	FILE *fpcnt_id; //proportion id
+	//FILE *fcent_id; //center_id, i.e., centers of clusters within the original data
+	FILE *fprof_id; //profile_id
+
+	big=(double *)malloc(sizeof(double)*num_dm);
+	memset(big,0,sizeof(double)*num_dm);
+
+	small=(double *)malloc(sizeof(double)*num_dm);
+	memset(small,0,sizeof(double)*num_dm);
+
+	for (i=0;i<num_dm;i++)
+	{
+		big[i]=0.0;
+		small[i]=(double)MAX_VALUE;
+	}
+
+
+	size_c=(long *)malloc(sizeof(long)*k);
+	memset(size_c,0,sizeof(long)*k);
+
+	center=(double**)malloc(sizeof(double*)*k);
+	memset(center,0,sizeof(double*)*k);
+	for (i=0;i<k;i++)
+	{
+		center[i]=(double*)malloc(sizeof(double)*num_dm);
+		memset(center[i],0,sizeof(double)*num_dm);
+	}
+
+	mybound=(double**)malloc(sizeof(double*)*num_dm);
+	memset(mybound,0,sizeof(double*)*num_dm);
+	for (i=0;i<num_dm;i++) //there are 3 mybounds for 4 categories
+	{
+		mybound[i]=(double*)malloc(sizeof(double)*3);
+		memset(mybound[i],0,sizeof(double)*3);
+	}
+
+	prof=(long **)malloc(sizeof(long*)*k);
+	memset(prof,0,sizeof(long*)*k);
+	for (i=0;i<k;i++)
+	{
+		prof[i]=(long *)malloc(sizeof(long)*num_dm);
+		memset(prof[i],0,sizeof(long)*num_dm);
+	}
+
+
+	for (i=0;i<file_Len;i++)
+	{
+		id=cluster_id[i];
+		for (j=0;j<num_dm;j++)
+		{
+			center[id][j]=center[id][j]+Matrix[i][j];
+			if (big[j]<Matrix[i][j])
+				big[j]=Matrix[i][j];
+			if (small[j]>Matrix[i][j])
+				small[j]=Matrix[i][j];
+		}
+
+		size_c[id]++;
+	}
+
+	for (i=0;i<k;i++)
+		for (j=0;j<num_dm;j++)
+		{
+			if (size_c[i]!=0)
+				center[i][j]=(center[i][j]/(double)(size_c[i]));
+			else
+				center[i][j]=0;
+		}
+
+	for (j=0;j<num_dm;j++)
+	{
+		interval=((big[j]-small[j])/4.0);
+		//printf("interval[%d] is %f\n",j,interval);
+		for (i=0;i<3;i++)
+			mybound[j][i]=small[j]+((double)(i+1)*interval);
+	}
+
+
+	size_mybound_0=(long **)malloc(sizeof(long*)*k);
+	memset(size_mybound_0,0,sizeof(long*)*k);
+
+	for (i=0;i<k;i++)
+	{
+		size_mybound_0[i]=(long*)malloc(sizeof(long)*num_dm);
+		memset(size_mybound_0[i],0,sizeof(long)*num_dm);
+	}
+
+	size_mybound_1=(long **)malloc(sizeof(long*)*k);
+	memset(size_mybound_1,0,sizeof(long*)*k);
+
+	for (i=0;i<k;i++)
+	{
+		size_mybound_1[i]=(long*)malloc(sizeof(long)*num_dm);
+		memset(size_mybound_1[i],0,sizeof(long)*num_dm);
+	}
+
+	size_mybound_2=(long **)malloc(sizeof(long*)*k);
+	memset(size_mybound_2,0,sizeof(long*)*k);
+
+	for (i=0;i<k;i++)
+	{
+		size_mybound_2[i]=(long*)malloc(sizeof(long)*num_dm);
+		memset(size_mybound_2[i],0,sizeof(long)*num_dm);
+	}
+
+	size_mybound_3=(long **)malloc(sizeof(long*)*k);
+	memset(size_mybound_3,0,sizeof(long*)*k);
+
+	for (i=0;i<k;i++)
+	{
+		size_mybound_3[i]=(long*)malloc(sizeof(long)*num_dm);
+		memset(size_mybound_3[i],0,sizeof(long)*num_dm);
+	}
+
+	for (i=0;i<file_Len;i++)
+		for (j=0;j<num_dm;j++)
+			{
+				if (Matrix[i][j]<mybound[j][0])// && ((Matrix[i][j]-small[j])>0)) //the smallest values excluded
+					size_mybound_0[cluster_id[i]][j]++;
+				else
+				{
+					if (Matrix[i][j]<mybound[j][1])
+						size_mybound_1[cluster_id[i]][j]++;
+					else
+					{
+						if (Matrix[i][j]<mybound[j][2])
+							size_mybound_2[cluster_id[i]][j]++;
+						else
+							//if (Matrix[i][j]!=big[j]) //the biggest values excluded
+								size_mybound_3[cluster_id[i]][j]++;
+					}
+
+				}
+			}
+
+	fprof_id=fopen("profile.txt","w");
+	fprintf(fprof_id,"Population_ID\t");
+	fprintf(fprof_id,"%s\n",name_string);
+
+	for (i=0;i<k;i++)
+	{
+		fprintf(fprof_id,"%ld\t",IDmapping[i]);
+		for (j=0;j<num_dm;j++)
+		{
+
+			if (size_mybound_0[i][j]>size_mybound_1[i][j])
+				situ1=0;
+			else
+				situ1=1;
+			if (size_mybound_2[i][j]>size_mybound_3[i][j])
+				situ2=2;
+			else
+				situ2=3;
+
+			if ((situ1==0) && (situ2==2))
+			{
+				if (size_mybound_0[i][j]>size_mybound_2[i][j])
+					prof[i][j]=0;
+				else
+					prof[i][j]=2;
+			}
+			if ((situ1==0) && (situ2==3))
+			{
+				if (size_mybound_0[i][j]>size_mybound_3[i][j])
+					prof[i][j]=0;
+				else
+					prof[i][j]=3;
+			}
+			if ((situ1==1) && (situ2==2))
+			{
+				if (size_mybound_1[i][j]>size_mybound_2[i][j])
+					prof[i][j]=1;
+				else
+					prof[i][j]=2;
+			}
+			if ((situ1==1) && (situ2==3))
+			{
+				if (size_mybound_1[i][j]>size_mybound_3[i][j])
+					prof[i][j]=1;
+				else
+					prof[i][j]=3;
+			}
+
+			//begin to output profile
+			if (j==num_dm-1)
+			{
+				if (prof[i][j]==0)
+					fprintf(fprof_id,"1\n");
+				if (prof[i][j]==1)
+					fprintf(fprof_id,"2\n");
+				if (prof[i][j]==2)
+					fprintf(fprof_id,"3\n");
+				if (prof[i][j]==3)
+					fprintf(fprof_id,"4\n");
+			}
+			else
+			{
+				if (prof[i][j]==0)
+					fprintf(fprof_id,"1\t");
+				if (prof[i][j]==1)
+					fprintf(fprof_id,"2\t");
+				if (prof[i][j]==2)
+					fprintf(fprof_id,"3\t");
+				if (prof[i][j]==3)
+					fprintf(fprof_id,"4\t");
+			}
+		}
+	}
+	fclose(fprof_id);
+
+	///////////////////////////////////////////////////////////
+
+
+	fpcnt_id=fopen("percentage.txt","w");
+	fprintf(fpcnt_id,"Population_ID\tPercentage\n");
+
+	for (t=0;t<k;t++)
+	{
+		fprintf(fpcnt_id,"%ld\t%.2f\n",IDmapping[t],(double)size_c[t]*100.0/(double)file_Len);
+	}
+	fclose(fpcnt_id);
+
+	free(big);
+	free(small);
+	free(size_c);
+
+	for (i=0;i<k;i++)
+	{
+		free(center[i]);
+		free(prof[i]);
+		free(size_mybound_0[i]);
+		free(size_mybound_1[i]);
+		free(size_mybound_2[i]);
+		free(size_mybound_3[i]);
+	}
+	free(center);
+	free(prof);
+	free(size_mybound_0);
+	free(size_mybound_1);
+	free(size_mybound_2);
+	free(size_mybound_3);
+
+	for (i=0;i<num_dm;i++)
+		free(mybound[i]);
+	free(mybound);
+
+}
+/******************************************************** Main Function **************************************************/
+int main (int argc, char **argv)
+{
+	//inputs
+	FILE *f_src; //source file pointer
+	FILE *f_src_ctr; //source center file
+	//outputs
+	FILE *f_cid; //cluster-id file pointer
+	FILE *f_mfi; //added April 16, 2009
+
+
+	char name_string[LINE_LEN]; //for name use
+
+	int time_id=-1;
+
+	long file_Len=0;
+	long num_clust=0;
+	long num_dm=0;
+	long norm_used=0;
+	long dist_used=0;
+	long i=0;
+	long j=0;
+
+	long *cluster_id;
+	long *IDmapping; //this is to keep the original populationID of the center.txt
+
+	double kmean_term=0;
+
+	double **cluster_center;
+	double **orig_data;
+	double **normalized_data;
+
+/*
+	_strtime( tmpbuf );
+    printf( "Starting time:\t\t\t\t%s\n", tmpbuf );
+	_strdate( tmpbuf );
+    printf( "Starting date:\t\t\t\t%s\n", tmpbuf );
+*/
+
+	if (argc!=3)
+	{
+		printf("usage: cent_adjust input_center input_data_file\n");
+		exit(0);
+	}
+
+
+	f_src_ctr=fopen(argv[1],"r");
+
+	//read source data
+	f_src=fopen(argv[2],"r");
+
+	getfileinfo(f_src, &file_Len, &num_dm, name_string, &time_id); //get the filelength, number of dimensions, and num/name of parameters
+
+	rewind(f_src); //reset data file pointer
+
+	orig_data = (double **)malloc(sizeof(double*)*file_Len);
+	memset(orig_data,0,sizeof(double*)*file_Len);
+	for (i=0;i<file_Len;i++)
+	{
+		orig_data[i]=(double *)malloc(sizeof(double)*num_dm);
+		memset(orig_data[i],0,sizeof(double)*num_dm);
+	}
+
+	readsource(f_src, file_Len, num_dm, orig_data, time_id); //read the data;
+
+	fclose(f_src);
+	/////////////////////////////////////////////////////////////////////////////
+	getctrfileinfo(f_src_ctr, &num_clust); //get how many populations
+	norm_used=0;
+	dist_used=0;
+	kmean_term=2;  //modified on Oct 16, 2009: changed kmean_term=1 to kmean_term=2
+
+	rewind(f_src_ctr); //reset center file pointer
+
+	//read population center
+	cluster_center=(double **)malloc(sizeof(double*)*num_clust);
+	memset(cluster_center,0,sizeof(double*)*num_clust);
+	for (i=0;i<num_clust;i++)
+	{
+		cluster_center[i]=(double*)malloc(sizeof(double)*num_dm);
+		memset(cluster_center[i],0,sizeof(double)*num_dm);
+	}
+	for (i=0;i<num_clust;i++)
+		for (j=0;j<num_dm;j++)
+			cluster_center[i][j]=0;
+
+	IDmapping=(long *)malloc(sizeof(long)*num_clust);
+	memset(IDmapping,0,sizeof(long)*num_clust);
+
+	readcenter(f_src_ctr,num_clust,num_dm,cluster_center,IDmapping); //read population center
+    fclose(f_src_ctr);
+
+	/////////////////////////////////////////////////////////////////////////////
+	normalized_data=(double **)malloc(sizeof(double*)*file_Len);
+	memset(normalized_data,0,sizeof(double*)*file_Len);
+	for (i=0;i<file_Len;i++)
+	{
+		normalized_data[i]=(double *)malloc(sizeof(double)*num_dm);
+		memset(normalized_data[i],0,sizeof(double)*num_dm);
+	}
+
+	tran(orig_data, file_Len, num_dm, norm_used, normalized_data);
+	/************************************************* Compute number of clusters *************************************************/
+
+	cluster_id=(long*)malloc(sizeof(long)*file_Len);
+	memset(cluster_id,0,sizeof(long)*file_Len);
+
+	assign_event(normalized_data,num_clust,dist_used,kmean_term,file_Len,num_dm,cluster_id,cluster_center,0);
+
+
+	//show(orig_data,cluster_id,file_Len,num_clust,num_dm,show_data,num_disp,name_string);
+	show(orig_data, cluster_id, file_Len, num_clust, num_dm, name_string, IDmapping);
+
+	f_cid=fopen("population_id.txt","w");
+
+	for (i=0;i<file_Len;i++)
+		fprintf(f_cid,"%ld\n",IDmapping[cluster_id[i]]);
+
+
+	fclose(f_cid);
+
+	//added April 16, 2009
+	f_mfi=fopen("MFI.txt","w");
+
+	for (i=0;i<num_clust;i++)
+	{
+		fprintf(f_mfi,"%ld\t",IDmapping[i]);
+
+		for (j=0;j<num_dm;j++)
+		{
+			if (j==num_dm-1)
+				fprintf(f_mfi,"%.0f\n",cluster_center[i][j]);
+			else
+				fprintf(f_mfi,"%.0f\t",cluster_center[i][j]);
+		}
+	}
+	fclose(f_mfi);
+
+	//ended April 16, 2009
+
+	for (i=0;i<num_clust;i++)
+		free(cluster_center[i]);
+	free(cluster_center);
+
+
+	/********************************************** Release memory ******************************************/
+
+	for (i=0;i<file_Len;i++)
+	{
+		free(orig_data[i]);
+		free(normalized_data[i]);
+	}
+
+	free(orig_data);
+	free(normalized_data);
+	free(cluster_id);
+	free(IDmapping);
+
+/*
+	_strtime( tmpbuf );
+    printf( "Ending time:\t\t\t\t%s\n", tmpbuf );
+	_strdate( tmpbuf );
+    printf( "Ending date:\t\t\t\t%s\n", tmpbuf );
+*/
+
+}
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/cross_sample/src/find_connected.c	Mon Feb 27 13:29:54 2017 -0500
@@ -0,0 +1,176 @@
+#include <stdlib.h>
+#include <stdio.h>
+#include <string.h>
+#include <assert.h>
+
+//static const char *rcsid = "$Id: find_connected.c,v 1.1 2008/09/05 21:54:40 rpl Exp $";
+
+int find_connected(int **G, int num_dense_grids, int ndim, int *grid_clusterID);
+void depth_first(int startnode);
+
+void bail(const char *);        /* exits via abort */
+static void check_clusters(int *gcID, int ndense);
+static void merge_cluster(int from, int into);
+
+
+/* Vars that will not change througout the depth-first recursion.  We
+   store them here to avoid endless replication on the stack. */
+static int **Gr=0;
+static int *gcID = 0;          /* grid cluster IDs */
+static int *cluster_count=0;   /* count of nodes per cluster */
+static int ndense=0;
+static int ndim=0;
+/* cid changes between depth-first searches, but is constant within a
+   single search, so it goes here. */
+static int cid=0;
+
+/* Find connected components in the graph of neighboring grids defined in G.
+ *
+ * Output:
+ *
+ * grid_clusterID[]  -- cluster to which each dense grid was assigned
+ * return value      -- number of clusters assigned.
+ */
+int find_connected(int **G, int n_dense_grids, int num_dm, int *grid_clusterID)
+{
+  int nclust=0;                  /* number of clusters found */
+  int i;
+  int *subfac;
+  int subval=0,nempty=0;
+    int clustid=0;
+
+  size_t sz = n_dense_grids*sizeof(int);
+  cluster_count = malloc(sz);
+  if(!cluster_count)
+    bail("find_connected: Unable to allocate %zd bytes.\n");
+  memset(cluster_count,0,sz);
+
+  /* set up the statics that will be used in the DFS */
+  Gr=G;
+  gcID = grid_clusterID;
+  ndense = n_dense_grids;
+  ndim = num_dm;
+
+
+  for(i=0;i<ndense;++i)
+    grid_clusterID[i] = -1;
+
+  for(i=0;i<ndense;++i) {
+    if(grid_clusterID[i] < 0) {  /* grid hasn't been assigned yet */
+      cid = nclust++;
+      depth_first(i);
+    }
+  }
+
+#ifndef NDEBUG
+  check_clusters(gcID,ndense);
+#endif
+
+  /* At this point we probably have some clusters that are empty due to merging.
+     We want to compact the cluster numbering to eliminate the empty clusters. */
+
+  subfac = malloc(sz);
+  if(!subfac)
+    bail("find_connected: Unable to allocate %zd bytes.\n");
+ subval=0;
+ nempty=0;
+
+  /* cluster #i needs to have its ID decremented by 1 for each empty cluster with
+     ID < i.  Precaclulate the decrements in this loop: */
+  for(i=0;i<nclust;++i) {
+    //clustid = grid_clusterID[i];
+    if(cluster_count[i] == 0) {
+      subval++;
+      nempty++;
+    }
+    subfac[i] = subval;
+  }
+
+  /* Now apply the decrements to all of the dense grids */
+  for(i=0;i<ndense;++i) {
+   clustid = grid_clusterID[i];
+    grid_clusterID[i] -= subfac[clustid];
+  }
+
+#ifndef NDEBUG
+  //  check_clusters(gcID,ndense);
+#endif
+
+  /* correct the number of clusters found */
+  nclust -= nempty;
+
+  return nclust;
+}
+
+
+/* Do a depth-first search for a single connected component in graph
+ * G.  Start from node, tag the nodes found with cid, and record
+ * the tags in grid_clusterID.  Also, record the node count in
+ * cluster_count.  If we find a node that has already been assigned to
+ * a cluster, that means we're merging two clusters, so zero out the
+ * old cid's node count.
+ *
+ * Note that our graph is constructed as a DAG, so we can be
+ * guaranteed to terminate without checking for cycles.
+ *
+ * Note2: this function can potentially recurse to depth = ndense.
+ * Plan stack size accordingly.
+ *
+ * Output:
+ *
+ * grid_clusterID[] -- array where we tag the nodes.
+ * cluster_count[]  -- count of the number of nodes per cluster.
+ */
+
+void depth_first(int node)
+{
+  int i;
+
+  if(gcID[node] == cid)         // we're guaranteed no cycles, but it is possible to reach a node
+    return;                     // through two different paths in the same cluster.  This early
+                                // return saves us some unneeded work.
+
+  /* Check to see if we are merging a cluster */
+  if(gcID[node] >= 0) {
+    /* We are, so zero the count for the old cluster. */
+    cluster_count[ gcID[node] ] = 0;
+    merge_cluster(gcID[node], cid);
+    return;
+  }
+
+  /* Update for this node */
+  gcID[node] = cid;
+  cluster_count[cid]++;
+
+  /* Recursively search the child nodes */
+  for(i=0; i<ndim; ++i)
+    if(Gr[node][i] >= 0)      /* This is a child node */
+      depth_first(Gr[node][i]);
+}
+
+void bail(const char *msg)
+{
+  fprintf(stderr,"%s",msg);
+  abort();
+}
+
+
+static void check_clusters(int *gcID, int ndense)
+{
+  int i;
+
+  for(i=0; i<ndense; ++i)
+    if(gcID[i] < 0) {
+      fprintf(stderr,"faulty cluster id at i= %d\n",i);
+      abort();
+    }
+}
+
+static void merge_cluster(int from, int into)
+{
+  int i;
+
+  for(i=0; i<ndense; ++i)
+    if(gcID[i] == from)
+      gcID[i] = into;
+}
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/cross_sample/src/flock1.c	Mon Feb 27 13:29:54 2017 -0500
@@ -0,0 +1,2400 @@
+/*****************************************************************************
+
+	FLOCK: FLOw cytometry Clustering without K (Named by: Jamie A. Lee and Richard H. Scheuermann)
+
+	Author: (Max) Yu Qian, Ph.D.
+
+	Copyright: Scheuermann Lab, Dept. of Pathology, UTSW
+
+	Development: November 2005 ~ Forever
+
+	Algorithm Status: May 2007: Release 1.0
+
+	Usage: flock data_file
+		    Note: the input file format must be channel values and the delimiter between two values must be a tab.
+
+    Changes made July 23, 2010: made errors to STDERR
+	Changes made Nov 4, 2010: added one more error (select_num_bin<min_grid) || (select_num_bin>max_grid) to STDERR;
+	                          MAX_GRID changed to 50 as larger than 50 seems not useful for any file we have got
+
+******************************************************************************/
+#include <time.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <string.h>
+#include <sys/stat.h>
+#include <unistd.h>
+#include <assert.h>
+
+
+#define DEBUG 0
+#define LINE_LEN 1024
+#define FILE_NAME_LEN 128
+#define PARA_NAME_LEN 64
+#define MAX_VALUE 1000000000
+#define MIN_GRID 6
+#define MAX_GRID 50
+
+#define NORM_METHOD 2 //2 if z-score; 0 if no normalization; 1 if min-max
+#define KMEANS_TERM 100
+//#define MAX_NUM_POP 30
+
+
+int find_connected(int **G, int num_dense_grids, int ndim, int *grid_clusterID);
+
+/************* Read basic info of the source file ****************************/
+void getfileinfo(FILE *f_src, int *file_Len, int *num_dm, char *name_string, int *time_ID)
+{
+  char src[LINE_LEN];
+  char current_name[64];
+  char prv;
+
+  int num_rows=0;
+  int num_columns=0;
+  int ch='\n';
+  int prev='\n';
+  int time_pos=0;
+  int i=0;
+  int j=0;
+  int sw=0;
+
+  src[0]='\0';
+  fgets(src, LINE_LEN, f_src);
+
+  if ((src[0]=='F') && (src[1]=='C') && (src[2]=='S'))
+	{
+		fprintf(stderr,"the correct input format is a tab-delimited txt file, instead of FCS file.\n");
+		abort();
+	}
+
+  name_string[0]='\0';
+  current_name[0]='\0';
+  prv='\n';
+
+  // skip space and tab characters
+  while ((src[i]==' ') || (src[i]=='\t'))
+    i++;
+
+  // repeat until the end of line is reached
+  while ((src[i]!='\0') && (src[i]!='\n') && (src[i]!='\r'))
+    {
+      current_name[j]=src[i];
+
+      if ((src[i]=='\t') && (prv!='\t')) //a complete word
+        {
+          current_name[j]='\0';
+
+          if (0!=strcmp(current_name,"Time"))
+            {
+              num_columns++; //num_columns does not inlcude the column of Time
+              time_pos++;
+              if (sw) {
+                  strcat(name_string,"\t");
+              }
+              strcat(name_string,current_name);
+              sw = 1;
+            }
+          else
+            {
+              *time_ID=time_pos;
+            }
+
+
+          current_name[0]='\0';
+          j=0;
+        }
+
+      if ((src[i]=='\t') && (prv=='\t')) //a duplicate tab or space
+        {
+          current_name[0]='\0';
+          j=0;
+        }
+
+      if (src[i]!='\t')
+        j++;
+
+      prv=src[i];
+      i++;
+    }
+
+  if (prv!='\t') //the last one hasn't been retrieved
+    {
+      current_name[j]='\0';
+
+      if (0!=strcmp(current_name,"Time"))
+        {
+          num_columns++;
+          strcat(name_string,"\t");
+          strcat(name_string,current_name);
+          time_pos++;
+        }
+      else
+        {
+          *time_ID=time_pos;
+        }
+
+
+    }
+  if (DEBUG==1)
+    {
+      printf("time_ID is %d\n",*time_ID);
+      printf("name_string is %s\n",name_string);
+    }
+
+  //start computing # of rows
+
+  while ((ch = fgetc(f_src))!= EOF )
+    {
+      if (ch == '\n')
+        {
+          ++num_rows;
+        }
+      prev = ch;
+    }
+  if (prev!='\n')
+    ++num_rows;
+
+  //added on July 23, 2010
+  if (num_rows<50)
+  {
+    fprintf(stderr,"Number of events in the input file is too few and should not be processed!\n"); //modified on July 23, 2010
+	abort();
+  }
+
+  *file_Len=num_rows;
+  *num_dm=num_columns;
+
+  printf("original file size is %d; number of dimensions is %d\n", *file_Len, *num_dm);
+}
+
+
+
+/************************************* Read the source file into uncomp_data **************************************/
+void readsource(FILE *f_src, int file_Len, int num_dm, double **uncomp_data, int time_ID)
+{
+  int time_pass=0; //to mark whether the time_ID has been passed
+  int index=0;
+
+  int i=0;
+  int j=0;
+  int t=0;
+
+  char src[LINE_LEN];
+  char xc[LINE_LEN/10];
+
+  src[0]='\0';
+  fgets(src,LINE_LEN, f_src); //skip the first line about parameter names
+
+  while (!feof(f_src) && (index<file_Len)) //index = 0, 1, ..., file_Len-1
+    {
+      src[0]='\0';
+      fgets(src,LINE_LEN,f_src);
+      i=0;
+      time_pass=0;
+
+      if (time_ID==-1)
+        {
+          for (t=0;t<num_dm;t++) //there is no time_ID
+            {
+              xc[0]='\0';
+              j=0;
+              while ((src[i]!='\0') && (src[i]!='\n') && (src[i]!=' ') && (src[i]!='\t'))
+                {
+                  xc[j]=src[i];
+                  i++;
+                  j++;
+                }
+
+              xc[j]='\0';
+              i++;
+
+              uncomp_data[index][t]=atof(xc);
+            }
+        }
+      else
+        {
+          for (t=0;t<=num_dm;t++) //the time column needs to be skipped, so there are num_dm+1 columns
+            {
+              xc[0]='\0';
+              j=0;
+              while ((src[i]!='\0') && (src[i]!='\n') && (src[i]!=' ') && (src[i]!='\t'))
+                {
+                  xc[j]=src[i];
+                  i++;
+                  j++;
+                }
+
+              xc[j]='\0';
+              i++;
+
+              if (t==time_ID)
+                {
+                  time_pass=1;
+                  continue;
+                }
+
+              if (time_pass)
+                uncomp_data[index][t-1]=atof(xc);
+              else
+                uncomp_data[index][t]=atof(xc);
+            }
+        }
+      index++;
+      //fprintf(fout_ID,"%s",src);
+    } //end of while
+
+  if (DEBUG == 1)
+    {
+      printf("the last line of the source data is:\n");
+      for (j=0;j<num_dm;j++)
+        printf("%f ",uncomp_data[index-1][j]);
+      printf("\n");
+    }
+}
+
+
+/**************************************** Normalization ******************************************/
+void tran(double **orig_data, int file_Len, int num_dm, int norm_used, double **matrix_to_cluster)
+{
+  int i=0;
+  int j=0;
+
+  double biggest=0;
+  double smallest=MAX_VALUE;
+
+  double *aver; //average of each column
+  double *std; //standard deviation of each column
+
+  aver=(double*)malloc(sizeof(double)*file_Len);
+  memset(aver,0,sizeof(double)*file_Len);
+
+  std=(double*)malloc(sizeof(double)*file_Len);
+  memset(std,0,sizeof(double)*file_Len);
+
+  if (norm_used==2) //z-score normalization
+    {
+      for (j=0;j<num_dm;j++)
+        {
+          aver[j]=0;
+          for (i=0;i<file_Len;i++)
+            aver[j]=aver[j]+orig_data[i][j];
+          aver[j]=aver[j]/(double)file_Len;
+
+          std[j]=0;
+          for (i=0;i<file_Len;i++)
+            std[j]=std[j]+(orig_data[i][j]-aver[j])*(orig_data[i][j]-aver[j]);
+          std[j]=sqrt(std[j]/(double)file_Len);
+
+          for (i=0;i<file_Len;i++)
+            matrix_to_cluster[i][j]=(orig_data[i][j]-aver[j])/std[j];  //z-score normalization
+        }
+    }
+
+  if (norm_used==1) //0-1 min-max normalization
+    {
+      for (j=0;j<num_dm;j++)
+        {
+          biggest=0;
+          smallest=MAX_VALUE;
+          for (i=0;i<file_Len;i++)
+            {
+              if (orig_data[i][j]>biggest)
+                biggest=orig_data[i][j];
+              if (orig_data[i][j]<smallest)
+                smallest=orig_data[i][j];
+            }
+
+          for (i=0;i<file_Len;i++)
+            {
+              if (biggest==smallest)
+                matrix_to_cluster[i][j]=biggest;
+              else
+                matrix_to_cluster[i][j]=(orig_data[i][j]-smallest)/(biggest-smallest);
+            }
+        }
+    }
+
+  if (norm_used==0) //no normalization
+    {
+      for (i=0;i<file_Len;i++)
+        for (j=0;j<num_dm;j++)
+          matrix_to_cluster[i][j]=orig_data[i][j];
+    }
+
+}
+
+
+
+/********************************************** RadixSort *******************************************/
+/* Perform a radix sort using each dimension from the original data as a radix.
+ * Outputs:
+ * sorted_seq   -- a permutation vector mapping the ordered list onto the original data.
+ *                  (sorted_seq[i] -> index in the original data of the ith element of the ordered list)
+ * grid_ID      -- mapping between the original data and the "grids" (see below) found as a byproduct
+ *                  of the sorting procedure.
+ * num_nonempty -- the number of grids that occur in the data (= the number of distinct values assumed
+ *                  by grid_ID)
+ */
+
+void radixsort_flock(int **position,int file_Len,int num_dm,int num_bin,int *sorted_seq,int *num_nonempty,int *grid_ID)
+{
+  int i=0;
+  int length=0;
+  int start=0;
+  int prev_ID=0;
+  int curr_ID=0;
+
+  int j=0;
+  int t=0;
+  int p=0;
+  int loc=0;
+  int temp=0;
+  int equal=0;
+
+  int *count; //count[i]=j means there are j numbers having value i at the processing digit
+  int *index; //index[i]=j means the starting position of grid i is j
+  int *cp; //current position
+  int *mark; //mark[i]=0 means it is not an ending point of a part, 1 means it is (a "part" is a group of items with identical bins for all dimensions)
+  int *seq; //temporary sequence
+
+  count=(int*)malloc(sizeof(int)*num_bin);
+  memset(count,0,sizeof(int)*num_bin);
+
+  cp=(int*)malloc(sizeof(int)*num_bin);
+  memset(cp,0,sizeof(int)*num_bin);
+
+  index=(int*)malloc(sizeof(int)*num_bin); // initialized below
+
+  seq=(int*)malloc(sizeof(int)*file_Len);
+  memset(seq,0,sizeof(int)*file_Len);
+
+  mark=(int*)malloc(sizeof(int)*file_Len);
+  memset(mark,0,sizeof(int)*file_Len);
+
+  for (i=0;i<file_Len;i++)
+    {
+      sorted_seq[i]=i;
+      mark[i]=0;
+      seq[i]=0;
+    }
+  for (i=0;i<num_bin;i++)
+    {
+      index[i]=0;
+      cp[i]=0;
+      count[i]=0;
+    }
+
+  for (j=0;j<num_dm;j++)
+    {
+      if (j==0) //compute the initial values of mark
+        {
+          for (i=0;i<file_Len;i++)
+            count[position[i][j]]++; // initialize the count to the number of items in each bin of the 0th dimension
+
+          index[0] = 0;
+          for (i=0;i<num_bin-1;i++)
+            {
+              index[i+1]=index[i]+count[i];  //index[k]=x means k segment starts at x (in the ordered list)
+              if ((index[i+1]>0) && (index[i+1]<=file_Len))
+                {
+                  mark[index[i+1]-1]=1; // Mark the end of the segment in the ordered list
+                }
+              else
+                {
+                  printf("out of myboundary for mark at index[i+1]-1.\n");
+                }
+            }
+          mark[file_Len-1]=1;
+
+          for (i=0;i<file_Len;i++)
+            {
+              /* Build a permutation vector for the partially ordered data.  Store the PV in sorted_seq */
+              loc=position[i][j];
+              temp=index[loc]+cp[loc]; //cp[i]=j means the offset from the starting position of grid i is j
+              sorted_seq[temp]=i;  //sorted_seq[i]=temp is also another way to sort
+              cp[loc]++;
+            }
+        }
+      else
+        {
+          //reset count, index, loc, temp, cp, start, and length
+          length=0;
+          loc=0;
+          temp=0;
+          start=0;
+          for (p=0;p<num_bin;p++)
+            {
+              cp[p]=0;
+              count[p]=0;
+              index[p]=0;
+            }
+
+          for (i=0;i<file_Len;i++)
+            {
+              int iperm = sorted_seq[i]; // iperm allows us to traverse the data in sorted order.
+              if (mark[i]!=1)
+                {
+                  /* Count the number of items in each bin of
+                     dimension j, BUT we are going to reset at the end
+                     of each "part".  Thus, the total effect is to do
+                     a sort by bin on the jth dimension for each group
+                     of data that has been identical for the
+                     dimensions processed up to this point.  This is
+                     the standard radix sort procedure, but doing it
+                     this way saves us having to allocate buckets to
+                     hold the data in each group of "identical-so-far"
+                     elements. */
+                  count[position[iperm][j]]++;  //count[position[i][j]]++;
+                  length++;                     // This is the total length of the part, irrespective of the value of the jth component
+                                                // (actually, less one, since we don't increment for the final element below)
+                }
+              if (mark[i]==1)
+                {
+                  //length++;
+                  count[position[iperm][j]]++;//count[position[i][j]]++;  //the current point must be counted in
+                  start=i-length; //this part starts from start to i: [start,i]
+                  /* Now we sort on the jth radix, just like we did for the 0th above, but we restrict it to just the current part.
+                     This would be a lot more clear if we broke this bit of code out into a separate function and processed recursively,
+                     plus we could multi-thread over the parts.  (Hmmm...)
+                  */
+                  index[0] = start; // Let index give the offset within the whole ordered list.
+                  for (t=0;t<num_bin-1;t++)
+                    {
+                      index[t+1]=index[t]+count[t];
+
+                      if ((index[t+1]<=file_Len) && (index[t+1]>0))
+                        {
+                          mark[index[t+1]-1]=1; // update the part boundaries to include the differences in the current radix.
+                        }
+
+                    }
+                  mark[i]=1;
+
+                  /* Update the permutation vector for the current part (i.e., from start to i).  By the time we finish the loop over i
+                     the PV will be completely updated for the partial ordering up to the current radix. */
+                  for (t=start;t<=i;t++)
+                    {
+                      loc=position[sorted_seq[t]][j];//loc=position[t][j];
+                      temp=index[loc]+cp[loc];
+                      if ((temp<file_Len) && (temp>=0))
+                        {
+                          // seq is a temporary because we have to maintain the old PV until we have finished this step.
+                          seq[temp]=sorted_seq[t];  //sorted_seq[i]=temp is also another way to sort
+                          cp[loc]++;
+                        }
+                      else
+                        {
+                          printf("out of myboundary for seq at temp.\n");
+                        }
+                    }
+
+                  for (t=start;t<=i;t++)
+                    {
+                      // copy the temporary back into sorted_seq.  sorted_seq is now updated for radix j up through
+                      // entry i in the ordered list.
+                      if ((t>=0) && (t<file_Len))
+                        sorted_seq[t]=seq[t];
+                      else
+                        printf("out of myboundary for seq and sorted_seq at t.\n");
+                    }
+                  //reset count, index, seq, length, and cp
+                  length=0;
+                  loc=0;
+                  temp=0;
+                  for (p=0;p<num_bin;p++)
+                    {
+                      cp[p]=0;
+                      count[p]=0;
+                      index[p]=0;
+                    }
+                }
+            }//end for i
+        }//end else
+    }//end for j
+
+  /* sorted_seq[] now contains the ordered list for all radices.  mark[] gives the boundaries between groups of elements that are
+     identical over all radices (= dimensions in the original data) (although it appears we aren't going to make use of this fact) */
+
+  for (i=0;i<file_Len;i++)
+    grid_ID[i]=0; //in case the initial value hasn't been assigned
+  *num_nonempty=1; //starting from 1!
+
+  /* assign the "grid" identifiers for all of the data.  A grid will be what we were calling a "part" above.  We will number them
+     serially and tag the *unordered* data with the grid IDs.  We will also count the number of populated grids (in general there will
+     be many possible combinations of bin values that simply never occur) */
+
+  for (i=1;i<file_Len;i++)
+    {
+      equal=1;
+      prev_ID=sorted_seq[i-1];
+      curr_ID=sorted_seq[i];
+      for (j=0;j<num_dm;j++)
+        {
+          if (position[prev_ID][j]!=position[curr_ID][j])
+            {
+              equal=0;  //not equal
+              break;
+            }
+        }
+
+      if (equal)
+        {
+          grid_ID[curr_ID]=grid_ID[prev_ID];
+        }
+      else
+        {
+          *num_nonempty=*num_nonempty+1;
+          grid_ID[curr_ID]=grid_ID[prev_ID]+1;
+        }
+      //all_grid_vol[grid_ID[curr_ID]]++;
+    }
+
+  //free memory
+  free(count);
+  free(index);
+  free(cp);
+  free(seq);
+  free(mark);
+
+}
+
+/********************************************** Compute Position of Events ************************************************/
+void compute_position(double **data_in, int file_Len, int num_dm, int num_bin, int **position, double *interval)
+{
+  /* What we are really doing here is binning the data, with the bins
+     spanning the range of the data and number of bins = num_bin */
+  int i=0;
+  int j=0;
+
+  double *small; //small[j] is the smallest value within dimension j
+  double *big; //big[j] is the biggest value within dimension j
+
+  small=(double*)malloc(sizeof(double)*num_dm);
+  memset(small,0,sizeof(double)*num_dm);
+
+  big=(double*)malloc(sizeof(double)*num_dm);
+  memset(big,0,sizeof(double)*num_dm);
+
+
+  for (j=0;j<num_dm;j++)
+    {
+      big[j]=MAX_VALUE*(-1);
+      small[j]=MAX_VALUE;
+      for (i=0;i<file_Len;i++)
+        {
+          if (data_in[i][j]>big[j])
+            big[j]=data_in[i][j];
+
+          if (data_in[i][j]<small[j])
+            small[j]=data_in[i][j];
+        }
+
+      interval[j]=(big[j]-small[j])/(double)num_bin;	//interval is computed using the biggest value and smallest value instead of the channel limit
+      /* XXX: I'm pretty sure the denominator of the fraction above should be num_bin-1. */
+	  /* I don't think so: num_bin is the number of bins */
+    }
+
+  for (j=0;j<num_dm;j++)
+  {
+     for (i=0;i<file_Len;i++)
+     {
+        if (data_in[i][j]>=big[j])
+           position[i][j]=num_bin-1;
+        else
+        {
+           position[i][j]=(int)((data_in[i][j]-small[j])/interval[j]); //position[i][j]=t means point i is at the t grid of dimensional j
+           if ((position[i][j]>=num_bin) || (position[i][j]<0))
+           {
+               //printf("position mis-computed in density analysis!\n");
+               //exit(0);
+			   fprintf(stderr,"Incorrect input file format or input parameters (number of bins overflows)!\n"); //modified on July 23, 2010
+				abort();
+
+           }
+        }
+     }
+  }
+
+
+  free(small);
+  free(big);
+}
+
+/********************************************** select_bin to select the number of bins **********************************/
+//num_bin=select_bin(normalized_data, file_Len, num_dm, MIN_GRID, MAX_GRID, position, sorted_seq, all_grid_ID, &num_nonempty);
+/* Determine the number of bins to use in each dimension.  Additionally sort the data elements according to the binned
+ * values, and partition the data into "grids" with identical (binned) values.  We try progressively more bins until we
+ * maximize a merit function, then return the results obtained using the optimal number of bins.
+ *
+ * Outputs:
+ * position     -- binned data values
+ * sorted_seq   -- permutation vector mapping the ordered list to the original data
+ * all_grid_ID  -- grid to which each data element was assigned.
+ * num_nonempty -- number of distinct values assumed by all_grid_ID
+ * interval     -- bin width for each data dimension
+ * return value -- the number of bins selected.
+ */
+
+int select_bin(double **normalized_data, int file_Len, int num_dm, int min_grid, int max_grid, int **position, int *sorted_seq,
+                int *all_grid_ID, int *num_nonempty, double *interval, int user_num_bin)
+{
+
+  int num_bin=0;
+  int select_num_bin=0;
+  int m=0;
+  int n=0;
+
+  int i=0;
+  int bin_scope=0;
+  int temp_num_nonempty=0;
+
+  int *temp_grid_ID;
+  int *temp_sorted_seq;
+  int **temp_position;
+
+  //sorted_seq[i]=j means the event j ranks i
+
+  double temp_index=0;
+  double *bin_index;
+  double *temp_interval;
+
+
+
+  temp_grid_ID=(int *)malloc(sizeof(int)*file_Len);
+  memset(temp_grid_ID,0,sizeof(int)*file_Len);
+
+  temp_sorted_seq=(int *)malloc(sizeof(int)*file_Len);
+  memset(temp_sorted_seq,0,sizeof(int)*file_Len);
+
+  temp_position=(int **)malloc(sizeof(int*)*file_Len);
+  memset(temp_position,0,sizeof(int*)*file_Len);
+  for (m=0;m<file_Len;m++)
+    {
+      temp_position[m]=(int*)malloc(sizeof(int)*num_dm);
+      memset(temp_position[m],0,sizeof(int)*num_dm);
+    }
+
+  temp_interval=(double*)malloc(sizeof(double)*num_dm);
+  memset(temp_interval,0,sizeof(double)*num_dm);
+
+  bin_scope=max_grid-min_grid+1;
+  bin_index=(double *)malloc(sizeof(double)*bin_scope);
+  memset(bin_index,0,sizeof(double)*bin_scope);
+
+  i=0;
+
+  for (num_bin=min_grid;num_bin<=max_grid;num_bin++)
+    {
+      /* compute_position bins the data into num_bin bins.  Each
+         dimension is binned independently.
+
+         Outputs:
+         temp_position[i][j] -- bin for the jth component of data element i.
+         temp_interval[j]    -- bin-width for the jth component
+      */
+      compute_position(normalized_data, file_Len, num_dm, num_bin, temp_position, temp_interval);
+      radixsort_flock(temp_position,file_Len,num_dm,num_bin,temp_sorted_seq,&temp_num_nonempty,temp_grid_ID);
+
+      /* our figure of merit is the number of non-empty grids divided by number of bins per dimension.
+         We declare victory when we have found a local maximum */
+      bin_index[i]=((double)temp_num_nonempty)/((double)num_bin);
+	  if ((double)(temp_num_nonempty)>=(double)(file_Len)*0.95)
+		  break;
+      if ((bin_index[i]<temp_index) && (user_num_bin==0))
+         break;
+	  if ((user_num_bin==num_bin-1) && (user_num_bin!=0))
+		 break;
+
+      /* Since we have accepted this trial bin, copy all the temporary results into
+         the output buffers */
+      memcpy(all_grid_ID,temp_grid_ID,sizeof(int)*file_Len);
+      memcpy(sorted_seq,temp_sorted_seq,sizeof(int)*file_Len);
+      memcpy(interval,temp_interval,sizeof(double)*num_dm);
+
+      for (m=0;m<file_Len;m++)
+        for (n=0;n<num_dm;n++)
+          position[m][n]=temp_position[m][n];
+
+      temp_index=bin_index[i];
+      select_num_bin=num_bin;
+      num_nonempty[0]=temp_num_nonempty;
+      i++;
+    }
+
+   if ((select_num_bin<min_grid) || (select_num_bin>max_grid))
+  {
+    fprintf(stderr,"Number of events collected is too few in terms of number of markers used. The file should not be processed!\n"); //modified on Nov 4, 2010
+	exit(0);
+  }
+
+  if (temp_index==0)
+  {
+	 fprintf(stderr,"Too many dimensions with too few events in the input file, or a too large number of bins used.\n"); //modified on July 23, 2010
+	 abort();
+  }
+
+
+  free(temp_grid_ID);
+  free(temp_sorted_seq);
+  free(bin_index);
+  free(temp_interval);
+
+  for (m=0;m<file_Len;m++)
+    free(temp_position[m]);
+  free(temp_position);
+
+  return select_num_bin;
+}
+
+/************************************* Select dense grids **********************************/
+// compute num_dense_grids, num_dense_events, dense_grid_reverse, and all_grid_vol
+// den_cutoff=select_dense(file_Len, all_grid_ID, num_nonempty, &num_dense_grids, &num_dense_events, dense_grid_reverse);
+/*
+ * Prune away grids that are insufficiently "dense" (i.e., contain too few data items)
+ *
+ * Outputs:
+ * num_dense_grids    -- number of dense grids
+ * num_dense_events   -- total number of data items in all dense grids
+ * dense_grid_reverse -- mapping from list of all grids to list of dense grids.
+ * return value       -- density cutoff for separating dense from non-dense grids.
+ */
+
+int select_dense(int file_Len, int *all_grid_ID, int num_nonempty, int *num_dense_grids, int *num_dense_events, int *dense_grid_reverse, int den_t_event)
+{
+
+
+  int i=0;
+  int vol_ID=0;
+  int biggest_size=0; //biggest grid_size, to define grid_size_index
+  int biggest_index=0;
+  //int actual_threshold=0; //the actual threshold on grid_size, e.g., 1 implies 1 event in the grid
+  //int num_remain=0; //number of remaining grids with different density thresholds
+  int temp_num_dense_grids=0;
+  int temp_num_dense_events=0;
+
+  int *grid_size_index;
+  int *all_grid_vol;
+  int *grid_density_index;
+
+  //double den_average=0;
+ // double avr_index=0;
+
+
+  /////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+  // Compute all_grid_vol
+  /////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+  all_grid_vol=(int *)malloc(sizeof(int)*num_nonempty);
+  memset(all_grid_vol,0,sizeof(int)*num_nonempty);
+
+  /* Grid "volume" is just the number of data contained in the grid. */
+  for (i=0;i<file_Len;i++)
+    {
+      vol_ID=all_grid_ID[i]; //vol_ID=all_grid_ID[sorted_seq[i]];
+      all_grid_vol[vol_ID]++;  //all_grid_vol[i]=j means grid i has j points
+    }
+
+
+
+  //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+  // Compute grid_size_index (histogram of grid sizes)
+  //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+
+  for (i=0;i<num_nonempty;i++)
+    {
+      if (biggest_size<all_grid_vol[i])
+        {
+          biggest_size=all_grid_vol[i];
+        }
+    }
+
+  //added on July 23, 2010
+  if (biggest_size<3)
+  {
+	 fprintf(stderr,"Too many dimensions with too few events in the input file, or a too large number of bins used.\n"); //modified on July 23, 2010
+	 abort();
+  }
+
+  grid_size_index=(int*)malloc(sizeof(int)*biggest_size);
+  memset(grid_size_index,0,sizeof(int)*biggest_size);
+
+  for (i=0;i<num_nonempty;i++)
+    {
+      grid_size_index[all_grid_vol[i]-1]++; //grid_size_index[0]=5 means there are 5 grids having size 1
+    }
+
+
+
+  ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+  // Compute den_cutoff
+  ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+
+  grid_density_index=(int *)malloc(sizeof(int)*(biggest_size-2));//from event 2 to biggest_size-1, i.e., from 0 to biggest_size-3
+  memset(grid_density_index,0,sizeof(int)*(biggest_size-2));
+
+  if (den_t_event==0)  //user doesn't define the density threshold
+  {
+	  biggest_index=0;
+
+	  for (i=2;i<biggest_size-1;i++) //the grid with 1 event will be skipped, i.e., grid_density_index[0] won't be defined
+	  {
+		  grid_density_index[i-1]=(grid_size_index[i-1]+grid_size_index[i+1]-2*grid_size_index[i]);
+		  if (biggest_index<grid_density_index[i-1])
+		  {
+			biggest_index=grid_density_index[i-1];
+			den_t_event=i+1;
+		  }
+	  }
+  }
+
+  if (den_t_event==0) //if something is wrong
+	  den_t_event=3;
+
+  for (i=0;i<num_nonempty;i++)
+	  if (all_grid_vol[i]>=den_t_event)
+		temp_num_dense_grids++;
+
+  if (temp_num_dense_grids<=1)
+  {
+	  //modified on July 23, 2010
+	  //printf("a too high density threshold is set! Please decrease your density threshold.\n");
+	  //exit(0);
+	  fprintf(stderr,"a too high density threshold is set! Please decrease your density threshold.\n"); //modified on July 23, 2010
+	  abort();
+  }
+
+  if (temp_num_dense_grids>=100000)
+  {
+	  //modified on July 23, 2010
+	  //printf("a too low density threshold is set! Please increase your density threshold.\n");
+	  //exit(0);
+	  fprintf(stderr,"a too low density threshold is set! Please increase your density threshold.\n"); //modified on July 23, 2010
+	  abort();
+  }
+
+  ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+  // Compute dense_grid_reverse
+  ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+  temp_num_dense_grids=0;
+  temp_num_dense_events=0;
+  for (i=0;i<num_nonempty;i++)
+    {
+      dense_grid_reverse[i]=-1;
+
+      if (all_grid_vol[i]>=den_t_event)
+        {
+          dense_grid_reverse[i]=temp_num_dense_grids;  //dense_grid_reverse provides a mapping from all nonempty grids to dense grids.
+          temp_num_dense_grids++;
+          temp_num_dense_events+=all_grid_vol[i];
+        }
+    }
+
+  num_dense_grids[0]=temp_num_dense_grids;
+  num_dense_events[0]=temp_num_dense_events;
+
+  free(grid_size_index);
+  free(all_grid_vol);
+
+  return den_t_event;
+}
+
+/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+// Compute densegridID_To_gridevent and eventID_To_denseventID
+/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+//	grid_To_event(file_Len, dense_grid_reverse, all_grid_ID, eventID_To_denseventID, densegridID_To_gridevent);
+/*
+ * Filter the data so that only the data belonging to dense grids is left
+ *
+ * Output:
+ * eventID_To_denseeventID   -- mapping from original event ID to ID in list containing only events contained in dense grids.
+ * densegridID_To_gridevent  -- mapping from dense grids to prototype members of the grids.
+ *
+ */
+
+void grid_To_event(int file_Len, int *dense_grid_reverse, int *all_grid_ID, int *eventID_To_denseventID, int *densegridID_To_gridevent)
+{
+  int i=0;
+  int dense_grid_ID=0;
+  int dense_event_ID=0;
+
+  for (i=0;i<file_Len;i++)
+    {
+      dense_grid_ID=dense_grid_reverse[all_grid_ID[i]];
+      eventID_To_denseventID[i]=-1;
+      if (dense_grid_ID!=-1) //for point (i) belonging to dense grids
+        {
+          eventID_To_denseventID[i]=dense_event_ID;
+          dense_event_ID++;
+
+          if (densegridID_To_gridevent[dense_grid_ID]==-1) //for point i that hasn't been selected
+            densegridID_To_gridevent[dense_grid_ID]=i; //densegridID_To_gridevent maps dense_grid_ID to its representative point
+        }
+    }
+
+
+}
+
+/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+// Compute dense_grid_seq
+/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+//	generate_grid_seq(file_Len, num_dm, sorted_seq, num_dense_grids, densegridID_To_gridevent, position, dense_grid_rank, dense_grid_seq);
+/* Construct a table of binned data values for each dense grid.
+ *
+ * Output:
+ *
+ * dense_grid_seq  -- table of binned data values for each dense grid (recall that all members of a grid have identical binned data values)
+ */
+
+void generate_grid_seq(int num_dm, int num_dense_grids, int *densegridID_To_gridevent, int **position, int **dense_grid_seq)
+{
+
+  int i=0;
+  int j=0;
+  int ReventID=0; //representative event ID of the dense grid
+
+  for (i=0;i<num_dense_grids;i++)
+    {
+      ReventID = densegridID_To_gridevent[i];
+
+      for (j=0;j<num_dm;j++)
+        dense_grid_seq[i][j]=position[ReventID][j];
+    }
+}
+
+//compare two vectors
+int compare_value(int num_dm, int *search_value, int *seq_value)
+{
+  int i=0;
+
+  for (i=0;i<num_dm;i++)
+    {
+      if (search_value[i]<seq_value[i])
+        return 1;
+      if (search_value[i]>seq_value[i])
+        return -1;
+      if (search_value[i]==seq_value[i])
+        continue;
+    }
+  return 0;
+}
+
+//binary search the dense_grid_seq to return the dense grid ID if it exists
+int binary_search(int num_dense_grids, int num_dm, int *search_value, int **dense_grid_seq)
+{
+
+  int low=0;
+  int high=0;
+  int mid=0;
+  int comp_result=0;
+  int match=0;
+  //int found=0;
+
+  low = 0;
+  high = num_dense_grids-1;
+
+  while (low <= high)
+    {
+      mid = (int)((low + high)/2);
+
+      comp_result=compare_value(num_dm, search_value,dense_grid_seq[mid]);
+
+
+      switch(comp_result)
+        {
+        case 1:
+          high=mid-1;
+          break;
+        case -1:
+          low=mid+1;
+          break;
+        case 0:
+          match=1;
+          break;
+        }
+      if (match==1)
+        break;
+    }
+
+
+
+  if (match==1)
+    {
+      return mid;
+    }
+  else
+    return -1;
+}
+
+
+/********************************************** Computing Centers Using IDs **********************************************/
+
+void ID2Center(double **data_in, int file_Len, int num_dm, int *eventID_To_denseventID, int num_clust, int *cluster_ID, double **population_center)
+{
+  int i=0;
+  int j=0;
+  int ID=0;
+  int eventID=0;
+  int *size_c;
+
+
+
+  size_c=(int *)malloc(sizeof(int)*num_clust);
+  memset(size_c,0,sizeof(int)*num_clust);
+
+  for (i=0;i<num_clust;i++)
+    for (j=0;j<num_dm;j++)
+      population_center[i][j]=0;
+
+  for (i=0;i<file_Len;i++)
+    {
+      eventID=eventID_To_denseventID[i];
+
+      if (eventID!=-1) //only events in dense grids count
+        {
+          ID=cluster_ID[eventID];
+
+          if (ID==-1)
+            {
+              //modified on July 23, 2010
+			  //printf("ID==-1! in ID2Center\n");
+              //exit(0);
+			  fprintf(stderr,"Incorrect file format or input parameters (no dense regions found!)\n"); //modified on July 23, 2010
+			  abort();
+            }
+
+          for (j=0;j<num_dm;j++)
+            population_center[ID][j]=population_center[ID][j]+data_in[i][j];
+
+          size_c[ID]++;
+        }
+    }
+
+
+  for (i=0;i<num_clust;i++)
+    {
+      for (j=0;j<num_dm;j++)
+        if (size_c[i]!=0)
+          population_center[i][j]=(population_center[i][j]/(double)(size_c[i]));
+        else
+          population_center[i][j]=0;
+    }
+
+  free(size_c);
+
+}
+
+///////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+//  Compute Population Center with all events
+///////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+void ID2Center_all(double **data_in, int file_Len, int num_dm, int num_clust, int *cluster_ID, double **population_center)
+{
+  int i=0;
+  int j=0;
+  int ID=0;
+  int *size_c;
+
+
+
+  size_c=(int *)malloc(sizeof(int)*num_clust);
+  memset(size_c,0,sizeof(int)*num_clust);
+
+  for (i=0;i<num_clust;i++)
+    for (j=0;j<num_dm;j++)
+      population_center[i][j]=0;
+
+  for (i=0;i<file_Len;i++)
+    {
+         ID=cluster_ID[i];
+
+         if (ID==-1)
+         {
+            //commented on July 23, 2010
+			//printf("ID==-1! in ID2Center_all\n");
+            //exit(0);
+			fprintf(stderr,"Incorrect file format or input parameters (resulting in incorrect population IDs)\n"); //modified on July 23, 2010
+			abort();
+         }
+
+         for (j=0;j<num_dm;j++)
+           population_center[ID][j]=population_center[ID][j]+data_in[i][j];
+
+         size_c[ID]++;
+    }
+
+
+  for (i=0;i<num_clust;i++)
+    {
+      for (j=0;j<num_dm;j++)
+        if (size_c[i]!=0)
+          population_center[i][j]=(population_center[i][j]/(double)(size_c[i]));
+        else
+          population_center[i][j]=0;
+    }
+
+  free(size_c);
+
+}
+
+/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+// Merge neighboring grids to clusters
+/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+
+int merge_grids(double **normalized_data, double *interval, int file_Len, int num_dm, int num_bin, int **position, int num_dense_grids,
+                 int *dense_grid_reverse, int **dense_grid_seq, int *eventID_To_denseventID, int *densegridID_To_gridevent, int *all_grid_ID,
+                 int *cluster_ID, int *grid_ID, int *grid_clusterID)
+{
+
+
+  int i=0;
+  int j=0;
+  int t=0;
+  int p=0;
+  int num_clust=0;
+  int ReventID=0;
+  int denseID=0;
+  int neighbor_ID=0;
+  //int temp_grid=0;
+
+  int *grid_value;
+  int *search_value;
+
+  int **graph_of_grid; //the graph constructed for dense grids: each dense grid is a graph node
+
+  double real_dist=0;
+  double **norm_grid_center;
+
+  norm_grid_center=(double **)malloc(sizeof(double*)*num_dense_grids);
+  memset(norm_grid_center,0,sizeof(double*)*num_dense_grids);
+
+  for (i=0;i<num_dense_grids;i++)
+    {
+      norm_grid_center[i]=(double *)malloc(sizeof(double)*num_dm);
+      memset(norm_grid_center[i],0,sizeof(double)*num_dm);
+    }
+
+  for (i=0;i<file_Len;i++)
+    {
+      denseID=eventID_To_denseventID[i];
+      if (denseID!=-1) //only dense events can enter
+        {
+          grid_ID[denseID]=dense_grid_reverse[all_grid_ID[i]];
+
+          if (grid_ID[denseID]==-1)
+            {
+              fprintf(stderr,"Incorrect input file format or input parameters (no dense region found)!\n"); //modified on July 23, 2010
+              abort();
+            }
+        }
+    }
+
+
+  /* Find centroid (in the normalized data) for each dense grid */
+  ID2Center(normalized_data,file_Len,num_dm,eventID_To_denseventID,num_dense_grids,grid_ID,norm_grid_center);
+
+  //printf("pass the grid ID2 center\n"); //commmented on July 23, 2010
+
+
+  graph_of_grid=(int **)malloc(sizeof(int*)*num_dense_grids);
+  memset(graph_of_grid,0,sizeof(int*)*num_dense_grids);
+  for (i=0;i<num_dense_grids;i++)
+    {
+      graph_of_grid[i]=(int *)malloc(sizeof(int)*num_dm);
+      memset(graph_of_grid[i],0,sizeof(int)*num_dm);
+
+
+      for (j=0;j<num_dm;j++)
+        graph_of_grid[i][j]=-1;
+    }
+
+  grid_value=(int *)malloc(sizeof(int)*num_dm);
+  memset(grid_value,0,sizeof(int)*num_dm);
+
+  search_value=(int *)malloc(sizeof(int)*num_dm);
+  memset(search_value,0,sizeof(int)*num_dm);
+
+
+  for (i=0;i<num_dense_grids;i++)
+    {
+      ReventID=densegridID_To_gridevent[i];
+
+      for (j=0;j<num_dm;j++)
+        {
+          grid_value[j]=position[ReventID][j];
+
+        }
+
+
+      /* For each dimension, find the neighbor, if any, that is equal in all other dimensions and 1 greater in
+         the chosen dimension.  If the neighbor's centroid is not too far away, add it to this grid's neighbor
+         list. */
+      for (t=0;t<num_dm;t++)
+        {
+          for (p=0;p<num_dm;p++)
+            search_value[p]=grid_value[p];
+
+          if (grid_value[t]==num_bin-1)
+            continue;
+
+          search_value[t]=grid_value[t]+1; //we only consider the neighbor at the bigger side
+
+          neighbor_ID=binary_search(num_dense_grids, num_dm, search_value, dense_grid_seq);
+
+          if (neighbor_ID!=-1)
+            {
+              real_dist=norm_grid_center[i][t]-norm_grid_center[neighbor_ID][t];
+
+              if (real_dist<0)
+                real_dist=-real_dist;
+
+              if (real_dist<2*interval[t])
+                graph_of_grid[i][t]=neighbor_ID;
+            }
+        }
+      grid_clusterID[i]=i; //initialize grid_clusterID
+    }
+
+
+  //graph constructed
+  //DFS-based search begins
+
+  /* Use a depth-first search to construct a list of connected subgraphs (= "clusters").
+     Note our graph as we have constructed it is a DAG, so we can use that to our advantage
+     in our search. */
+  //  num_clust=dfs(graph_of_grid,num_dense_grids,num_dm,grid_clusterID);
+  num_clust=find_connected(graph_of_grid, num_dense_grids, num_dm, grid_clusterID);
+
+
+  //computes grid_ID and cluster_ID
+  for (i=0;i<file_Len;i++)
+    {
+      denseID=eventID_To_denseventID[i];
+      if (denseID!=-1) //only dense events can enter
+	  {
+        cluster_ID[denseID]=grid_clusterID[grid_ID[denseID]];
+		//if (cluster_ID[denseID]==-1)
+		//	printf("catch you!\n");
+	  }
+    }
+
+  free(search_value);
+  free(grid_value);
+
+  for (i=0;i<num_dense_grids;i++)
+    {
+      free(graph_of_grid[i]);
+      free(norm_grid_center[i]);
+    }
+  free(graph_of_grid);
+  free(norm_grid_center);
+
+  return num_clust;
+}
+
+/********************************************* Merge Clusters to Populations *******************************************/
+// This is the function future work can be on because it is about how to cluster the about 500 points accurately
+
+int merge_clusters(int num_clust, int num_dm, double *interval, double **cluster_center, int *cluster_populationID, int max_num_pop)
+{
+  int num_population=0;
+  int temp_num_population=0;
+
+  int i=0;
+  int j=0;
+  int t=0;
+  int merge=0;
+  int smid=0;
+  int bgid=0;
+  double merge_dist=1.1; //initial value of merge_dist*interval should be slightly larger than the bin width
+
+  int *map_ID;
+
+  double diff=0;
+
+  map_ID=(int*)malloc(sizeof(int)*num_clust);
+  memset(map_ID,0,sizeof(int)*num_clust);
+
+  while ((num_population>max_num_pop) || (num_population<=1))
+  {
+
+	  if (num_population<=1)
+	  	  merge_dist=merge_dist-0.1;
+
+	  if (num_population>max_num_pop)
+          merge_dist=merge_dist+0.1;
+
+
+	 for (i=0;i<num_clust;i++)
+		cluster_populationID[i]=i;
+
+    for (i=0;i<num_clust-1;i++)
+    {
+      for (j=i+1;j<num_clust;j++)
+        {
+          merge=1;
+
+          for (t=0;t<num_dm;t++)
+            {
+              diff=cluster_center[i][t]-cluster_center[j][t];
+
+              if (diff<0)
+                diff=-diff;
+              if (diff>(merge_dist*interval[t]))
+                merge=0;
+            }
+
+          if ((merge) && (cluster_populationID[i]!=cluster_populationID[j]))
+            {
+              if (cluster_populationID[i]<cluster_populationID[j])  //they could not be equal
+                {
+                  smid = cluster_populationID[i];
+                  bgid = cluster_populationID[j];
+                }
+              else
+                {
+                  smid = cluster_populationID[j];
+                  bgid = cluster_populationID[i];
+                }
+              for (t=0;t<num_clust;t++)
+                {
+                  if (cluster_populationID[t]==bgid)
+                    cluster_populationID[t]=smid;
+                }
+            }
+        }
+    }
+
+
+
+  for (i=0;i<num_clust;i++)
+    map_ID[i]=-1;
+
+  for (i=0;i<num_clust;i++)
+    map_ID[cluster_populationID[i]]=1;
+
+  num_population=0;
+  for (i=0;i<num_clust;i++)
+    {
+      if (map_ID[i]==1)
+        {
+          map_ID[i]=num_population;
+          num_population++;
+        }
+    }
+
+  if ((temp_num_population>max_num_pop) && (num_population==1))
+	  break;
+  else
+	  temp_num_population=num_population;
+
+  if (num_clust<=1)
+	break;
+  }
+
+  for (i=0;i<num_clust;i++)
+    cluster_populationID[i]=map_ID[cluster_populationID[i]];
+
+  free(map_ID);
+
+  return num_population;
+}
+
+///////////////////////////////////////////////////////
+/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+double kmeans(double **Matrix, int k, double kmean_term, int file_Len, int num_dm, int *shortest_id, double **center)
+{
+
+	int i=0;
+	int j=0;
+	int t=0;
+	int random=0;
+	int random1=0;
+	int random2=0;
+	int times=0;
+	int dist_used=0; //0 is Euclidean and 1 is Pearson
+	int random_init=0; //0: not use random seeds;
+	int real_Len=0;
+	int skipped=0;
+
+ 	int *num;  //num[i]=t means the ith cluster has t points
+
+	double vvv=1.0; // the biggest variation;
+	double distance=0.0;
+	double xv=0.0;
+	double variation=0.0;
+
+	double mean_dx=0;
+	double mean_dy=0;
+	double sum_var=0;
+	double dx=0;
+	double dy=0;
+	double sd_x=0;
+	double sd_y=0;
+	double diff=0;
+	double distortion=0;
+
+	double shortest_distance;
+
+	double *temp_center;
+
+	double **sum;
+
+	temp_center = (double *)malloc(sizeof(double)*num_dm);
+	memset(temp_center,0,sizeof(double)*num_dm);
+
+	if (random_init)
+	{
+		for (i=0;i<k;i++)
+		{
+			random1=rand()*rand();
+			random2=abs((random1%5)+1);
+			for (t=0;t<random2;t++)
+				random2=random2*rand()+rand();
+
+			random=abs(random2%file_Len);
+			for (j=0;j<num_dm;j++)
+				center[i][j]=Matrix[random][j];
+		}
+	}
+
+
+	num = (int *)malloc(sizeof(int)*k);
+	memset(num,0,sizeof(int)*k);
+
+	sum = (double **)malloc(sizeof(double*)*k);
+	memset(sum,0,sizeof(double*)*k);
+	for (i=0;i<k;i++)
+	{
+		sum[i] = (double *)malloc(sizeof(double)*num_dm);
+		memset(sum[i],0,sizeof(double)*num_dm);
+	}
+
+
+	times=0;
+	real_Len=0;
+
+	while (((vvv>kmean_term) && (kmean_term<1)) || ((times<kmean_term) && (kmean_term>=1)))
+	{
+		for (i=0;i<k;i++)
+		{
+			num[i]=0;
+			for (j=0;j<num_dm;j++)
+				sum[i][j]=0.0;
+		}
+
+		for (i=0;i<file_Len;i++)  //for each data point i, we compute the distance between Matrix[i] and center[j]
+		{
+			skipped = 0;
+			shortest_distance=MAX_VALUE;
+			for (j=0;j<k;j++)  //for each center j
+			{
+				distance=0.0;
+
+				if (dist_used==0)  //Euclidean distance
+				{
+					for (t=0;t<num_dm;t++) //for each dimension here num_dm is always 1 as we consider individual dimensions
+					{
+
+						diff=center[j][t]-Matrix[i][t];
+
+						diff=diff*diff;
+
+						distance = distance+diff; //here we have a weight for each dimension
+					}
+				}
+				else  //pearson correlation
+				{
+					mean_dx=0.0;
+					mean_dy=0.0;
+					sum_var=0.0;
+					dx=0.0;
+					dy=0.0;
+					sd_x=0.0;
+					sd_y=0.0;
+					for (t=0;t<num_dm;t++)
+					{
+						mean_dx+=center[j][t];
+						mean_dy+=Matrix[i][t];
+					}
+					mean_dx=mean_dx/(double)num_dm;
+					mean_dy=mean_dy/(double)num_dm;
+
+					for (t=0;t<num_dm;t++)
+					{
+						dx=center[j][t]-mean_dx;
+						dy=Matrix[i][t]-mean_dy;
+						sum_var+=dx*dy;
+						sd_x+=dx*dx;
+						sd_y+=dy*dy;
+					}
+					if (sqrt(sd_x*sd_y)==0)
+						distance = 1.0;
+					else
+						distance = 1.0 - (sum_var/(sqrt(sd_x*sd_y))); // distance ranges from 0 to 2;
+					//printf("distance=%f\n",distance);
+				}	//pearson correlation ends
+
+				if ((distance<shortest_distance) && (skipped == 0))
+				{
+					shortest_distance=distance;
+					shortest_id[i]=j;
+				}
+			}//end for j
+				real_Len++;
+				num[shortest_id[i]]=num[shortest_id[i]]+1;
+				for (t=0;t<num_dm;t++)
+					sum[shortest_id[i]][t]=sum[shortest_id[i]][t]+Matrix[i][t];
+		}//end for i
+	/* recompute the centers */
+	//compute_mean(group);
+		vvv=0.0;
+		for (j=0;j<k;j++)
+		{
+			memcpy(temp_center,center[j],sizeof(double)*num_dm);
+			variation=0.0;
+			if (num[j]!=0)
+			{
+				for (t=0;t<num_dm;t++)
+				{
+					center[j][t]=sum[j][t]/(double)num[j];
+					xv=(temp_center[t]-center[j][t]);
+					variation=variation+xv*xv;
+				}
+			}
+
+			if (variation>vvv)
+				vvv=variation;  //vvv is the biggest variation among the k clusters;
+		}
+	//compute_variation;
+		times++;
+	} //end for while
+
+
+
+
+	free(num);
+
+	for (i=0;i<k;i++)
+		free(sum[i]);
+	free(sum);
+	free(temp_center);
+
+
+	return distortion;
+
+}
+
+//////////////////////////////////////////////////////
+/*************************** Show *****************************/
+void show(double **Matrix, int *cluster_id, int file_Len, int k, int num_dm, char *name_string)
+{
+	int situ1=0;
+	int situ2=0;
+
+	int i=0;
+	int id=0;
+	int j=0;
+	int t=0;
+
+	int *size_c;
+
+
+
+	int **size_mybound_1;
+	int **size_mybound_2;
+	int **size_mybound_3;
+	int **size_mybound_0;
+
+	double interval=0.0;
+
+	double *big;
+	double *small;
+
+
+	double **center;
+	double **mybound;
+
+	int **prof; //prof[i][j]=1 means population i is + at parameter j
+
+	FILE *fpcnt_id; //proportion id
+	//FILE *fcent_id; //center_id, i.e., centers of clusters within the original data
+	FILE *fprof_id; //profile_id
+
+	big=(double *)malloc(sizeof(double)*num_dm);
+	memset(big,0,sizeof(double)*num_dm);
+
+	small=(double *)malloc(sizeof(double)*num_dm);
+	memset(small,0,sizeof(double)*num_dm);
+
+	for (i=0;i<num_dm;i++)
+	{
+		big[i]=0.0;
+		small[i]=(double)MAX_VALUE;
+	}
+
+
+	size_c=(int *)malloc(sizeof(int)*k);
+	memset(size_c,0,sizeof(int)*k);
+
+	center=(double**)malloc(sizeof(double*)*k);
+	memset(center,0,sizeof(double*)*k);
+	for (i=0;i<k;i++)
+	{
+		center[i]=(double*)malloc(sizeof(double)*num_dm);
+		memset(center[i],0,sizeof(double)*num_dm);
+	}
+
+	mybound=(double**)malloc(sizeof(double*)*num_dm);
+	memset(mybound,0,sizeof(double*)*num_dm);
+	for (i=0;i<num_dm;i++) //there are 3 mybounds for 4 categories
+	{
+		mybound[i]=(double*)malloc(sizeof(double)*3);
+		memset(mybound[i],0,sizeof(double)*3);
+	}
+
+	prof=(int **)malloc(sizeof(int*)*k);
+	memset(prof,0,sizeof(int*)*k);
+	for (i=0;i<k;i++)
+	{
+		prof[i]=(int *)malloc(sizeof(int)*num_dm);
+		memset(prof[i],0,sizeof(int)*num_dm);
+	}
+
+
+	for (i=0;i<file_Len;i++)
+	{
+		id=cluster_id[i];
+		for (j=0;j<num_dm;j++)
+		{
+			center[id][j]=center[id][j]+Matrix[i][j];
+			if (big[j]<Matrix[i][j])
+				big[j]=Matrix[i][j];
+			if (small[j]>Matrix[i][j])
+				small[j]=Matrix[i][j];
+		}
+
+		size_c[id]++;
+	}
+
+	for (i=0;i<k;i++)
+		for (j=0;j<num_dm;j++)
+		{
+			if (size_c[i]!=0)
+				center[i][j]=(center[i][j]/(double)(size_c[i]));
+			else
+				center[i][j]=0;
+		}
+
+	for (j=0;j<num_dm;j++)
+	{
+		interval=((big[j]-small[j])/4.0);
+		//printf("interval[%d] is %f\n",j,interval);
+		for (i=0;i<3;i++)
+			mybound[j][i]=small[j]+((double)(i+1)*interval);
+	}
+
+
+	size_mybound_0=(int **)malloc(sizeof(int*)*k);
+	memset(size_mybound_0,0,sizeof(int*)*k);
+
+	for (i=0;i<k;i++)
+	{
+		size_mybound_0[i]=(int*)malloc(sizeof(int)*num_dm);
+		memset(size_mybound_0[i],0,sizeof(int)*num_dm);
+	}
+
+	size_mybound_1=(int **)malloc(sizeof(int*)*k);
+	memset(size_mybound_1,0,sizeof(int*)*k);
+
+	for (i=0;i<k;i++)
+	{
+		size_mybound_1[i]=(int*)malloc(sizeof(int)*num_dm);
+		memset(size_mybound_1[i],0,sizeof(int)*num_dm);
+	}
+
+	size_mybound_2=(int **)malloc(sizeof(int*)*k);
+	memset(size_mybound_2,0,sizeof(int*)*k);
+
+	for (i=0;i<k;i++)
+	{
+		size_mybound_2[i]=(int*)malloc(sizeof(int)*num_dm);
+		memset(size_mybound_2[i],0,sizeof(int)*num_dm);
+	}
+
+	size_mybound_3=(int **)malloc(sizeof(int*)*k);
+	memset(size_mybound_3,0,sizeof(int*)*k);
+
+	for (i=0;i<k;i++)
+	{
+		size_mybound_3[i]=(int*)malloc(sizeof(int)*num_dm);
+		memset(size_mybound_3[i],0,sizeof(int)*num_dm);
+	}
+
+	for (i=0;i<file_Len;i++)
+		for (j=0;j<num_dm;j++)
+			{
+				if (Matrix[i][j]<mybound[j][0])// && ((Matrix[i][j]-small[j])>0)) //the smallest values excluded
+					size_mybound_0[cluster_id[i]][j]++;
+				else
+				{
+					if (Matrix[i][j]<mybound[j][1])
+						size_mybound_1[cluster_id[i]][j]++;
+					else
+					{
+						if (Matrix[i][j]<mybound[j][2])
+							size_mybound_2[cluster_id[i]][j]++;
+						else
+							//if (Matrix[i][j]!=big[j]) //the biggest values excluded
+								size_mybound_3[cluster_id[i]][j]++;
+					}
+
+				}
+			}
+
+	fprof_id=fopen("profile.txt","w");
+	fprintf(fprof_id,"Population_ID\t");
+	fprintf(fprof_id,"%s\n",name_string);
+
+	for (i=0;i<k;i++)
+	{
+		fprintf(fprof_id,"%d\t",i+1); //i changed to i+1 to start from 1 instead of 0: April 16, 2009
+		for (j=0;j<num_dm;j++)
+		{
+
+			if (size_mybound_0[i][j]>size_mybound_1[i][j])
+				situ1=0;
+			else
+				situ1=1;
+			if (size_mybound_2[i][j]>size_mybound_3[i][j])
+				situ2=2;
+			else
+				situ2=3;
+
+			if ((situ1==0) && (situ2==2))
+			{
+				if (size_mybound_0[i][j]>size_mybound_2[i][j])
+					prof[i][j]=0;
+				else
+					prof[i][j]=2;
+			}
+			if ((situ1==0) && (situ2==3))
+			{
+				if (size_mybound_0[i][j]>size_mybound_3[i][j])
+					prof[i][j]=0;
+				else
+					prof[i][j]=3;
+			}
+			if ((situ1==1) && (situ2==2))
+			{
+				if (size_mybound_1[i][j]>size_mybound_2[i][j])
+					prof[i][j]=1;
+				else
+					prof[i][j]=2;
+			}
+			if ((situ1==1) && (situ2==3))
+			{
+				if (size_mybound_1[i][j]>size_mybound_3[i][j])
+					prof[i][j]=1;
+				else
+					prof[i][j]=3;
+			}
+
+			//begin to output profile
+			if (j==num_dm-1)
+			{
+				if (prof[i][j]==0)
+					fprintf(fprof_id,"1\n");
+				if (prof[i][j]==1)
+					fprintf(fprof_id,"2\n");
+				if (prof[i][j]==2)
+					fprintf(fprof_id,"3\n");
+				if (prof[i][j]==3)
+					fprintf(fprof_id,"4\n");
+			}
+			else
+			{
+				if (prof[i][j]==0)
+					fprintf(fprof_id,"1\t");
+				if (prof[i][j]==1)
+					fprintf(fprof_id,"2\t");
+				if (prof[i][j]==2)
+					fprintf(fprof_id,"3\t");
+				if (prof[i][j]==3)
+					fprintf(fprof_id,"4\t");
+			}
+		}
+	}
+	fclose(fprof_id);
+
+	///////////////////////////////////////////////////////////
+
+
+	fpcnt_id=fopen("percentage.txt","w");
+	fprintf(fpcnt_id,"Population_ID\tPercentage\n");
+
+	for (t=0;t<k;t++)
+	{
+		fprintf(fpcnt_id,"%d\t%.2f\n",t+1,(double)size_c[t]*100.0/(double)file_Len);	//t changed to t+1 to start from 1 instead of 0: April 16, 2009
+	}
+	fclose(fpcnt_id);
+
+	free(big);
+	free(small);
+	free(size_c);
+
+	for (i=0;i<k;i++)
+	{
+		free(center[i]);
+		free(prof[i]);
+		free(size_mybound_0[i]);
+		free(size_mybound_1[i]);
+		free(size_mybound_2[i]);
+		free(size_mybound_3[i]);
+	}
+	free(center);
+	free(prof);
+	free(size_mybound_0);
+	free(size_mybound_1);
+	free(size_mybound_2);
+	free(size_mybound_3);
+
+	for (i=0;i<num_dm;i++)
+		free(mybound[i]);
+	free(mybound);
+
+}
+
+
+
+/******************************************************** Main Function **************************************************/
+//for normalized data, there are five variables:
+//cluster_ID
+//population_center
+//grid_clusterID
+//grid_ID
+//grid_Center
+
+//the same five variables exist for the original data
+//however, the three IDs (cluster_ID, grid_ID, grid_clusterID) don't change in either normalized or original data
+//also, data + cluster_ID -> population_center
+//data + grid_ID -> grid_Center
+
+/* what is the final output */
+//the final things we want are grid_Center in the original data and grid_clusterID //or population_center in the original data
+//Sparse grids will not be considered when computing the two centroids (centroids of grids and centroids of clusters)
+
+/*  what information should select_bin output */
+//the size of all IDs are unknown to function main because we only consider the events in dense grids, and also the number of dense grids
+//is unknown, therefore I must use a prescreening to output
+//how many bins I should use
+//the number of dense grids
+//total number of events in the dense grids
+
+/* basic procedure of main function */
+//1. read raw file and normalize the raw file
+//2. select_bin
+//3. allocate memory for eventID_To_denseventID, grid_clusterID, grid_ID, cluster_ID.
+//4. call select_dense and merge_grids with grid_clusterID, grid_ID, cluster_ID.
+//5. release normalized data; allocate memory for grid_Center and population_center
+//6. output grid_Center and population_center using ID2Center together with grid_clusterID //from IDs to centers
+
+int main (int argc, char **argv)
+{
+  //inputs
+  FILE *f_src; //source file pointer
+
+  FILE *f_out; //coordinates
+  FILE *f_cid; //population-ID of events
+  FILE *f_ctr; //centroids of populations
+  FILE *f_results; //coordinates file event and population column
+  FILE *f_mfi; //added April 16, 2009 for mean fluorescence intensity
+  FILE *f_parameters; //number of bins and density calculated by
+                      //the algorithm. Used to update the database
+  FILE *f_properties; //Properties file used by Image generation software
+
+  char para_name_string[LINE_LEN];
+
+  int time_ID=-1;
+  int num_bin=0; //the bins I will use on each dimension
+
+  int file_Len=0; //number of events
+  int num_dm=0;
+  int num_clust=0;
+  int num_dense_events=0;
+  int num_dense_grids=0;
+  int num_nonempty=0;
+  int num_population=0;
+  //int temp=0;
+
+  //below are read from configuration file
+  int i=0;
+  int j=0;
+  int max_num_pop=0;
+
+  int den_t_event=0;
+
+  int *grid_clusterID; //(dense)gridID to clusterID
+  int *grid_ID; //(dense)eventID to gridID
+  int *cluster_ID; //(dense)eventID to clusterID
+  int *eventID_To_denseventID; //eventID_To_denseventID[i]=k means event i is in a dense grid and its ID within dense events is k
+  int *all_grid_ID; //gridID for all events
+  int *densegridID_To_gridevent;
+  int *sorted_seq;
+  int *dense_grid_reverse;
+  int *population_ID; //denseeventID to populationID
+  int *cluster_populationID; //clusterID to populationID
+  int *grid_populationID; //gridID to populationID
+  int *all_population_ID; //populationID of event
+
+  int **position;
+  int **dense_grid_seq;
+
+  double *interval;
+
+  double **population_center; //population centroids in the raw/original data
+  double **cluster_center; //cluster centroids in the raw/original data
+
+  double **input_data;
+  double **normalized_data;
+
+  int min = 999999;
+  int max = 0;
+
+  printf( "Starting time:\t\t\t\t");
+  fflush(stdout);
+  system("/bin/date");
+  /////////////////////////////////////////////////////////////
+
+  if ((argc!=2) && (argc!=4) && (argc!=5))
+  {
+      //modified on Jul 23, 2010
+	  //printf("usage:\n");
+	  //printf("basic mode: flock data_file\n");
+	  //printf("advanced mode: flock data_file num_bin density_index\n");
+      //exit(0);
+
+	  fprintf(stderr,"Incorrect number of input parameters!\n"); //modified on July 23, 2010
+	  //fprintf(stderr,"basic mode: flock data_file\n"); //modified on July 23, 2010
+	  //fprintf(stderr,"advanced mode1: flock data_file num_bin density_index\n"); //modified on July 23, 2010
+	  fprintf(stderr,"advanced mode: flock data_file num_bin density_index max_num_pop\n"); //added on Dec 16, 2010 for GenePattern
+	  abort();
+  }
+
+  f_src=fopen(argv[1],"r");
+
+  if (argc==2)
+  {
+	 max_num_pop=30; //default value, maximum 30 clusters
+  }
+
+  if (argc==4)
+  {
+	 num_bin=atoi(argv[2]);
+	 printf("num_bin is %d\n",num_bin);
+
+	 den_t_event=atoi(argv[3]);
+	 printf("density_index is %d\n",den_t_event);
+
+	 max_num_pop=30;
+
+	 if (((num_bin<6) && (num_bin!=0)) || (num_bin>29))
+	 {
+		fprintf(stderr,"Incorrect input range of number of bins, which should be larger than 5 and smaller than 30\n");
+		abort();
+	  }
+
+	  if (((den_t_event<3) && (den_t_event!=0)) || (den_t_event>99))
+	  {
+		fprintf(stderr,"Incorrect input range of density threshold, which should be larger than 2 and smaller than 100\n");
+		abort();
+	  }
+  }
+
+  if (argc==5)
+  {
+	  num_bin=atoi(argv[2]);
+	  printf("num_bin is %d\n",num_bin);
+
+	  den_t_event=atoi(argv[3]);
+	  printf("density_index is %d\n",den_t_event);
+
+	  max_num_pop=atoi(argv[4]);
+	  printf("max number of clusters is %d\n",max_num_pop);
+
+	  if (((num_bin<6) && (num_bin!=0)) || (num_bin>29))
+	  {
+		fprintf(stderr,"Incorrect input range of number of bins, which should be larger than 5 and smaller than 30\n");
+		abort();
+	  }
+
+	  if (((den_t_event<3) && (den_t_event!=0)) || (den_t_event>99))
+	  {
+		fprintf(stderr,"Incorrect input range of density threshold, which should be larger than 2 and smaller than 100\n");
+		abort();
+	  }
+
+	  if ((max_num_pop<5) || (max_num_pop>999))
+	  {
+		fprintf(stderr,"Incorrect input range of maximum number of populations, which should be larger than 4 and smaller than 1000\n");
+		abort();
+	  }
+  }
+
+
+  getfileinfo(f_src, &file_Len, &num_dm, para_name_string, &time_ID); //get the filelength, number of dimensions, and num/name of parameters
+
+  /************************************************* Read the data *****************************************************/
+
+  rewind(f_src); //reset the file pointer
+
+  input_data = (double **)malloc(sizeof(double*)*file_Len);
+  memset(input_data,0,sizeof(double*)*file_Len);
+  for (i=0;i<file_Len;i++)
+  {
+     input_data[i]=(double *)malloc(sizeof(double)*num_dm);
+     memset(input_data[i],0,sizeof(double)*num_dm);
+  }
+
+  readsource(f_src, file_Len, num_dm, input_data, time_ID); //read the data;
+
+  fclose(f_src);
+
+  normalized_data=(double **)malloc(sizeof(double*)*file_Len);
+  memset(normalized_data,0,sizeof(double*)*file_Len);
+  for (i=0;i<file_Len;i++)
+    {
+      normalized_data[i]=(double *)malloc(sizeof(double)*num_dm);
+      memset(normalized_data[i],0,sizeof(double)*num_dm);
+    }
+
+  tran(input_data, file_Len, num_dm, NORM_METHOD, normalized_data);
+
+
+  position=(int **)malloc(sizeof(int*)*file_Len);
+  memset(position,0,sizeof(int*)*file_Len);
+  for (i=0;i<file_Len;i++)
+    {
+      position[i]=(int*)malloc(sizeof(int)*num_dm);
+      memset(position[i],0,sizeof(int)*num_dm);
+    }
+
+  all_grid_ID=(int *)malloc(sizeof(int)*file_Len);
+  memset(all_grid_ID,0,sizeof(int)*file_Len);
+
+  sorted_seq=(int*)malloc(sizeof(int)*file_Len);
+  memset(sorted_seq,0,sizeof(int)*file_Len);
+
+  interval=(double*)malloc(sizeof(double)*num_dm);
+  memset(interval,0,sizeof(double)*num_dm);
+
+  /************************************************* select_bin *************************************************/
+
+  if (num_bin>=1)  //num_bin has been selected by user
+  	select_bin(normalized_data, file_Len, num_dm, MIN_GRID, MAX_GRID, position, sorted_seq, all_grid_ID, &num_nonempty, interval,num_bin);
+  else  //num_bin has not been selected by user
+  {
+	num_bin=select_bin(normalized_data, file_Len, num_dm, MIN_GRID, MAX_GRID, position, sorted_seq, all_grid_ID, &num_nonempty, interval,num_bin);
+	printf("selected bin number is %d\n",num_bin);
+  }
+  printf("number of non-empty grids is %d\n",num_nonempty);
+
+
+
+  /* Although we return sorted_seq from select_bin(), we don't use it for anything, except possibly diagnostics */
+  free(sorted_seq);
+
+
+  dense_grid_reverse=(int*)malloc(sizeof(int)*num_nonempty);
+  memset(dense_grid_reverse,0,sizeof(int)*num_nonempty);
+
+  /************************************************* select_dense **********************************************/
+
+  if (den_t_event>=1) //den_t_event must be larger or equal to 2 if the user wants to set it
+	select_dense(file_Len, all_grid_ID, num_nonempty, &num_dense_grids, &num_dense_events, dense_grid_reverse, den_t_event);
+  else
+  {
+	den_t_event=select_dense(file_Len, all_grid_ID, num_nonempty, &num_dense_grids, &num_dense_events, dense_grid_reverse, den_t_event);
+	printf("automated selected density threshold is %d\n",den_t_event);
+  }
+
+  printf("Number of dense grids is %d\n",num_dense_grids);
+
+  densegridID_To_gridevent = (int *)malloc(sizeof(int)*num_dense_grids);
+  memset(densegridID_To_gridevent,0,sizeof(int)*num_dense_grids);
+
+  for (i=0;i<num_dense_grids;i++)
+    densegridID_To_gridevent[i]=-1; //initialize all densegridID_To_gridevent values to -1
+
+
+  eventID_To_denseventID=(int *)malloc(sizeof(int)*file_Len);
+  memset(eventID_To_denseventID,0,sizeof(int)*file_Len);     //eventID_To_denseventID[i]=k means event i is in a dense grid and its ID within dense events is k
+
+
+  grid_To_event(file_Len, dense_grid_reverse, all_grid_ID, eventID_To_denseventID, densegridID_To_gridevent);
+
+
+  dense_grid_seq=(int **)malloc(sizeof(int*)*num_dense_grids);
+  memset(dense_grid_seq,0,sizeof(int*)*num_dense_grids);
+  for (i=0;i<num_dense_grids;i++)
+    {
+      dense_grid_seq[i]=(int *)malloc(sizeof(int)*num_dm);
+      memset(dense_grid_seq[i],0,sizeof(int)*num_dm);
+    }
+
+
+  /* Look up the binned data values for each dense grid */
+  generate_grid_seq(num_dm, num_dense_grids, densegridID_To_gridevent, position, dense_grid_seq);
+
+
+  /************************************************* allocate memory *********************************************/
+
+  grid_clusterID=(int *)malloc(sizeof(int)*num_dense_grids);
+  memset(grid_clusterID,0,sizeof(int)*num_dense_grids);
+
+  grid_ID=(int *)malloc(sizeof(int)*num_dense_events);
+  memset(grid_ID,0,sizeof(int)*num_dense_events);
+
+  cluster_ID=(int *)malloc(sizeof(int)*num_dense_events);
+  memset(cluster_ID,0,sizeof(int)*num_dense_events);
+
+
+  /*********************************************** merge_grids ***********************************************/
+  //int merge_grids(int file_Len, int num_dm, int num_bin, int **position, int num_dense_grids, int *dense_grid_rank, int *dense_grid_reverse,
+  //			 int **dense_grid_seq, int *eventID_To_denseventID, int *densegridID_To_gridevent, int *all_grid_ID,
+  //			 int *cluster_ID, int *grid_ID, int *grid_clusterID)
+
+  num_clust = merge_grids(normalized_data, interval, file_Len, num_dm, num_bin, position, num_dense_grids, dense_grid_reverse, dense_grid_seq, eventID_To_denseventID, densegridID_To_gridevent, all_grid_ID, cluster_ID, grid_ID, grid_clusterID);
+
+  printf("computed number of groups is %d\n",num_clust);
+
+
+  /************************************** release unnecessary memory and allocate memory and compute centers **********************************/
+
+
+  for (i=0;i<file_Len;i++)
+    free(position[i]);
+  free(position);
+
+  for (i=0;i<num_dense_grids;i++)
+    free(dense_grid_seq[i]);
+  free(dense_grid_seq);
+
+  free(dense_grid_reverse);
+
+  free(densegridID_To_gridevent);
+  free(all_grid_ID);
+
+  // cluster_center ////////////////////////////////////////////////////////////////////////////////////////////////////////
+
+  cluster_center=(double **)malloc(sizeof(double*)*num_clust);
+  memset(cluster_center,0,sizeof(double*)*num_clust);
+  for (i=0;i<num_clust;i++)
+  {
+     cluster_center[i]=(double*)malloc(sizeof(double)*num_dm);
+     memset(cluster_center[i],0,sizeof(double)*num_dm);
+  }
+
+  ID2Center(normalized_data,file_Len,num_dm,eventID_To_denseventID,num_clust,cluster_ID,cluster_center); //produce the centers with normalized data
+
+  //printf("pass the first ID2center\n");  //commented on July 23, 2010
+
+  /*** population_ID and grid_populationID **/
+
+  cluster_populationID=(int*)malloc(sizeof(int)*num_clust);
+  memset(cluster_populationID,0,sizeof(int)*num_clust);
+
+  grid_populationID=(int*)malloc(sizeof(int)*num_dense_grids);
+  memset(grid_populationID,0,sizeof(int)*num_dense_grids);
+
+  population_ID=(int*)malloc(sizeof(int)*num_dense_events);
+  memset(population_ID,0,sizeof(int)*num_dense_events);
+
+  num_population = merge_clusters(num_clust, num_dm, interval, cluster_center, cluster_populationID,max_num_pop);
+
+
+
+  for (i=0;i<num_clust;i++)
+    free(cluster_center[i]);
+  free(cluster_center);
+
+  free(interval);
+
+  for (i=0;i<num_dense_grids;i++)
+    {
+      grid_populationID[i]=cluster_populationID[grid_clusterID[i]];
+    }
+
+  for (i=0;i<num_dense_events;i++)
+    {
+      population_ID[i]=cluster_populationID[cluster_ID[i]];
+    }
+
+  printf("computed number of populations is %d\n",num_population);
+
+
+
+  // population_center /////////////////////////////////////////////////////////////////////////////////////////////////////
+
+
+  population_center=(double **)malloc(sizeof(double*)*num_population);
+  memset(population_center,0,sizeof(double*)*num_population);
+  for (i=0;i<num_population;i++)
+    {
+      population_center[i]=(double*)malloc(sizeof(double)*num_dm);
+      memset(population_center[i],0,sizeof(double)*num_dm);
+    }
+
+
+
+  ID2Center(normalized_data,file_Len,num_dm,eventID_To_denseventID,num_population,population_ID,population_center); //produce population centers with normalized data
+
+
+  // show ////////////////////////////////////////////////////////////////////////////////
+  all_population_ID=(int*)malloc(sizeof(int)*file_Len);
+  memset(all_population_ID,0,sizeof(int)*file_Len);
+
+  kmeans(normalized_data, num_population, KMEANS_TERM, file_Len, num_dm, all_population_ID, population_center);
+  show(input_data, all_population_ID, file_Len, num_population, num_dm, para_name_string);
+
+  ID2Center_all(input_data,file_Len,num_dm,num_population,all_population_ID,population_center);
+
+
+  f_cid=fopen("population_id.txt","w");
+  f_ctr=fopen("population_center.txt","w");
+  f_out=fopen("coordinates.txt","w");
+  f_results=fopen("flock_results.txt","w");
+
+/*
+  f_parameters=fopen("parameters.txt","w");
+  fprintf(f_parameters,"Number_of_Bins\t%d\n",num_bin);
+  fprintf(f_parameters,"Density\t%f\n",aver_index);
+  fclose(f_parameters);
+*/
+
+  for (i=0;i<file_Len;i++)
+	fprintf(f_cid,"%d\n",all_population_ID[i]+1); //all_population_ID[i] changed to all_population_ID[i]+1 to start from 1 instead of 0: April 16, 2009
+
+  /*
+   * New to check for min/max to add to parameters.txt
+   *
+  */
+
+  fprintf(f_out,"%s\n",para_name_string);
+  //fprintf(f_results,"%s\tEvent\tPopulation\n",para_name_string);
+  fprintf(f_results,"%s\tPopulation\n",para_name_string);
+  for (i=0;i<file_Len;i++)
+  {
+	for (j=0;j<num_dm;j++)
+	{
+		if (input_data[i][j] < min) {
+			min = (int)input_data[i][j];
+		}
+		if (input_data[i][j] > max) {
+			max = (int)input_data[i][j];
+		}
+		if (j==num_dm-1)
+		{
+			fprintf(f_out,"%d\n",(int)input_data[i][j]);
+			fprintf(f_results,"%d\t",(int)input_data[i][j]);
+		}
+		else
+		{
+			fprintf(f_out,"%d\t",(int)input_data[i][j]);
+			fprintf(f_results,"%d\t",(int)input_data[i][j]);
+		}
+	}
+	//fprintf(f_results,"%d\t",i + 1);
+	fprintf(f_results,"%d\n",all_population_ID[i]+1); //all_population_ID[i] changed to all_population_ID[i]+1 to start from 1 instead of 0: April 16, 2009
+  }
+
+/*
+  f_parameters=fopen("parameters.txt","w");
+  fprintf(f_parameters,"Number_of_Bins\t%d\n",num_bin);
+  fprintf(f_parameters,"Density\t%d\n",den_t_event);
+  fprintf(f_parameters,"Min\t%d\n",min);
+  fprintf(f_parameters,"Max\t%d\n",max);
+  fclose(f_parameters);
+*/
+
+  f_properties=fopen("fcs.properties","w");
+  fprintf(f_properties,"Bins=%d\n",num_bin);
+  fprintf(f_properties,"Density=%d\n",den_t_event);
+  fprintf(f_properties,"Min=%d\n",min);
+  fprintf(f_properties,"Max=%d\n",max);
+  fprintf(f_properties,"Populations=%d\n",num_population);
+  fprintf(f_properties,"Events=%d\n",file_Len);
+  fprintf(f_properties,"Markers=%d\n",num_dm);
+  fclose(f_properties);
+
+
+  for (i=0;i<num_population;i++) {
+	/* Add if we want to include population id in the output
+	*/
+	fprintf(f_ctr,"%d\t",i+1);  //i changed to i+1 to start from 1 instead of 0: April 16, 2009
+
+	for (j=0;j<num_dm;j++) {
+		if (j==num_dm-1)
+			fprintf(f_ctr,"%.0f\n",population_center[i][j]);
+		else
+			fprintf(f_ctr,"%.0f\t",population_center[i][j]);
+	}
+  }
+
+  	//added April 16, 2009
+	f_mfi=fopen("MFI.txt","w");
+
+	for (i=0;i<num_population;i++)
+	{
+		fprintf(f_mfi,"%d\t",i+1);
+
+		for (j=0;j<num_dm;j++)
+		{
+			if (j==num_dm-1)
+				fprintf(f_mfi,"%.0f\n",population_center[i][j]);
+			else
+				fprintf(f_mfi,"%.0f\t",population_center[i][j]);
+		}
+	}
+	fclose(f_mfi);
+
+	//ended April 16, 2009
+
+  fclose(f_cid);
+  fclose(f_ctr);
+  fclose(f_out);
+  fclose(f_results);
+
+
+  for (i=0;i<num_population;i++)
+  {
+	free(population_center[i]);
+  }
+  free(population_center);
+
+
+  for (i=0;i<file_Len;i++)
+    free(normalized_data[i]);
+  free(normalized_data);
+
+  free(grid_populationID);
+
+  free(cluster_populationID);
+  free(grid_clusterID);
+  free(cluster_ID);
+
+  for (i=0;i<file_Len;i++)
+    free(input_data[i]);
+  free(input_data);
+
+  free(grid_ID);
+  free(population_ID);
+  free(all_population_ID);
+  free(eventID_To_denseventID);
+
+  ///////////////////////////////////////////////////////////
+  printf("Ending time:\t\t\t\t");
+  fflush(stdout);
+  system("/bin/date");
+
+  return 0;
+
+}
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/cross_sample/src/flock2.c	Mon Feb 27 13:29:54 2017 -0500
@@ -0,0 +1,3405 @@
+///////////
+// Changes made:
+// 1. Added another parameter: number of populations
+// 2. Added a hierarchical merging step based on density change between centroids of two hyper-regions
+// 3. Picked the longest dimensions between the population centroids to judge whether the two parts should be merged
+// 4. Removed checking time parameter
+// 5. Output error to stderr
+// 6. Fixed the bug of density threshold always = 3
+// 7. Added another error (select_num_bin<min_grid) || (select_num_bin>max_grid) to STDERR
+// 8. Fixed a bug for 2D data by using K=e*K
+// 9. Added some header files, may not be necessary
+// 10. Added a lower bound (at least two) for number of populations
+/***************************************************************************************************************************************
+
+	FLOCK: FLOw cytometry Clustering without K (Named by: Jamie A. Lee and Richard H. Scheuermann)
+
+	Author: (Max) Yu Qian, Ph.D.
+
+	Copyright: Scheuermann Lab, Dept. of Pathology, UTSW
+
+	Development: November 2005 ~ Forever
+
+	Status: July 2010: Release 2.0
+
+	Usage: flock data_file
+		    Note: the input file format must be channel values and the delimiter between two values must be a tab.
+
+
+
+****************************************************************************************************************************************/
+
+#include <time.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <string.h>
+#include <sys/stat.h>
+#include <unistd.h>
+#include <assert.h>
+
+
+
+#define DEBUG 0
+#define LINE_LEN 1024
+#define FILE_NAME_LEN 128
+#define PARA_NAME_LEN 64
+#define MAX_VALUE 1000000000
+#define MIN_GRID 6
+#define MAX_GRID 50
+#define E_T 1.0
+
+#define NORM_METHOD 2 //2 if z-score; 0 if no normalization; 1 if min-max
+#define KMEANS_TERM 10
+#define MAX_POP_NUM 128
+
+#ifndef max
+    #define max( a, b ) ( ((a) > (b)) ? (a) : (b) )
+#endif
+
+#ifndef min
+    #define min( a, b ) ( ((a) < (b)) ? (a) : (b) )
+#endif
+
+static long **Gr=0;
+static long *gcID = 0;          /* grid cluster IDs */
+static long *cluster_count=0;   /* count of nodes per cluster */
+static long ndense=0;
+static long ndim=0;
+/* cid changes between depth-first searches, but is constant within a
+   single search, so it goes here. */
+static long cid=0;
+/* Do a depth-first search for a single connected component in graph
+ * G.  Start from node, tag the nodes found with cid, and record
+ * the tags in grid_clusterID.  Also, record the node count in
+ * cluster_count.  If we find a node that has already been assigned to
+ * a cluster, that means we're merging two clusters, so zero out the
+ * old cid's node count.
+ *
+ * Note that our graph is constructed as a DAG, so we can be
+ * guaranteed to terminate without checking for cycles.
+ *
+ * Note2: this function can potentially recurse to depth = ndense.
+ * Plan stack size accordingly.
+ *
+ * Output:
+ *
+ * grid_clusterID[] -- array where we tag the nodes.
+ * cluster_count[]  -- count of the number of nodes per cluster.
+ */
+static void merge_cluster(long from, long into)
+{
+  int i;
+
+  for(i=0; i<ndense; ++i)
+    if(gcID[i] == from)
+      gcID[i] = into;
+}
+
+void depth_first(long node)
+{
+  long i;
+
+  if(gcID[node] == cid)         // we're guaranteed no cycles, but it is possible to reach a node
+    return;                     // through two different paths in the same cluster.  This early
+                                // return saves us some unneeded work.
+
+  /* Check to see if we are merging a cluster */
+  if(gcID[node] >= 0) {
+    /* We are, so zero the count for the old cluster. */
+    cluster_count[ gcID[node] ] = 0;
+    merge_cluster(gcID[node], cid);
+    return;
+  }
+
+  /* Update for this node */
+  gcID[node] = cid;
+  cluster_count[cid]++;
+
+  /* Recursively search the child nodes */
+  for(i=0; i<ndim; ++i)
+    if(Gr[node][i] >= 0)      /* This is a child node */
+      depth_first(Gr[node][i]);
+}
+
+void bail(const char *msg)
+{
+  fprintf(stderr,"%s",msg);
+  exit(0);
+}
+
+
+static void check_clusters(long *gcID, int ndense)
+{
+  int i;
+
+  for(i=0; i<ndense; ++i)
+    if(gcID[i] < 0) {
+      fprintf(stderr,"faulty cluster id at i= %d\n",i);
+      exit(0);
+    }
+}
+
+
+
+long find_connected(long **G, long n_dense_grids, long num_dm, long *grid_clusterID)
+{
+  long nclust=0;                  /* number of clusters found */
+  long i;
+  long *subfac;
+  long clustid=0;
+  int subval=0,nempty=0;
+
+  int sz = n_dense_grids*sizeof(long);
+  cluster_count = malloc(sz);
+  if(!cluster_count)
+    bail("find_connected: Unable to allocate %zd bytes.\n");
+  memset(cluster_count,0,sz);
+
+  /* set up the statics that will be used in the DFS */
+  Gr=G;
+  gcID = grid_clusterID;
+  ndense = n_dense_grids;
+  ndim = num_dm;
+
+  for(i=0;i<ndense;++i)
+    grid_clusterID[i] = -1;
+
+  for(i=0;i<ndense;++i) {
+    if(grid_clusterID[i] < 0) {  /* grid hasn't been assigned yet */
+      cid = nclust++;
+      depth_first(i);
+    }
+  }
+
+
+
+  /* At this point we probably have some clusters that are empty due to merging.
+     We want to compact the cluster numbering to eliminate the empty clusters. */
+
+  subfac = malloc(sz);
+  if(!subfac)
+    bail("find_connected: Unable to allocate %zd bytes.\n");
+  subval=0;
+  nempty=0;
+
+  /* cluster #i needs to have its ID decremented by 1 for each empty cluster with
+     ID < i.  Precaclulate the decrements in this loop: */
+  for(i=0;i<nclust;++i) {
+    //clustid = grid_clusterID[i];
+    if(cluster_count[i] == 0) {
+      subval++;
+      nempty++;
+    }
+    subfac[i] = subval;
+  }
+
+  //printf("nempty is %d\n",nempty);
+
+  /* Now apply the decrements to all of the dense grids */
+  for(i=0;i<ndense;++i) {
+    clustid = grid_clusterID[i];
+    grid_clusterID[i] -= subfac[clustid];
+  }
+
+
+
+  /* correct the number of clusters found */
+  nclust -= nempty;
+
+  //printf("nclust is %d\n",nclust);
+
+  return nclust;
+}
+
+/************************************* Read basic info of the source file **************************************/
+/************************************* Read basic info of the source file **************************************/
+void getfileinfo(FILE *f_src, long *file_Len, long *num_dm, char *name_string, long *time_ID)
+{
+  char src[LINE_LEN];
+  char current_name[64];
+  char prv;
+
+  long num_rows=0;
+  long num_columns=0;
+  long ch='\n';
+  long prev='\n';
+  long time_pos=0;
+  long i=0;
+  long j=0;
+  int sw=0;
+
+  src[0]='\0';
+  fgets(src, LINE_LEN, f_src);
+
+  name_string[0]='\0';
+  current_name[0]='\0';
+  prv='\n';
+
+  while ((src[i]==' ') || (src[i]=='\t')) //skip space and tab characters
+    i++;
+
+  while ((src[i]!='\0') && (src[i]!='\n')) //repeat until the end of the line
+    {
+      current_name[j]=src[i];
+
+      if ((src[i]=='\t') && (prv!='\t')) //a complete word
+        {
+          current_name[j]='\0';
+
+          if (0!=strcmp(current_name,"Time"))
+            {
+              num_columns++; //num_columns does not inlcude the column of Time
+              time_pos++;
+              if (sw) {
+                  strcat(name_string,"\t");
+              }
+              strcat(name_string,current_name);
+              sw = 1;
+            }
+          else
+            {
+              *time_ID=time_pos;
+            }
+
+          current_name[0]='\0';
+          j=0;
+        }
+
+      if ((src[i]=='\t') && (prv=='\t')) //a duplicate tab or space
+        {
+          current_name[0]='\0';
+          j=0;
+        }
+
+      if (src[i]!='\t')
+        j++;
+
+      prv=src[i];
+      i++;
+    }
+
+  //name_string[j]='\0';
+  if (prv!='\t') //the last one hasn't been retrieved
+    {
+      current_name[j]='\0';
+      if (0!=strcmp(current_name,"Time"))
+        {
+          num_columns++;
+          strcat(name_string,"\t");
+          strcat(name_string,current_name);
+          time_pos++;
+        }
+      else
+        {
+          *time_ID=time_pos;
+        }
+    }
+  if (DEBUG==1)
+    {
+      printf("time_ID is %ld\n",*time_ID);
+      printf("name_string is %s\n",name_string);
+    }
+
+  //start computing # of rows
+
+  while ((ch = fgetc(f_src))!= EOF )
+    {
+      if (ch == '\n')
+        {
+          ++num_rows;
+        }
+      prev = ch;
+    }
+  if (prev!='\n')
+    ++num_rows;
+
+   if (num_rows<50)
+  {
+    fprintf(stderr,"Number of events in the input file is too few and should not be processed!\n"); //modified on July 23, 2010
+	exit(0);
+  }
+
+  *file_Len=num_rows;
+  *num_dm=num_columns;
+
+  printf("original file size is %ld; number of dimensions is %ld\n", *file_Len, *num_dm);
+}
+
+
+
+/************************************* Read the source file into uncomp_data **************************************/
+void readsource(FILE *f_src, long file_Len, long num_dm, double **uncomp_data, long time_ID)
+{
+  //long time_pass=0; //to mark whether the time_ID has been passed
+  long index=0;
+
+  long i=0;
+  long j=0;
+  long t=0;
+
+  char src[LINE_LEN];
+  char xc[LINE_LEN/10];
+
+  src[0]='\0';
+  fgets(src,LINE_LEN, f_src); //skip the first line about parameter names
+
+  while (!feof(f_src) && (index<file_Len)) //index = 0, 1, ..., file_Len-1
+    {
+      src[0]='\0';
+      fgets(src,LINE_LEN,f_src);
+      i=0;
+      //time_pass=0;
+
+      //if (time_ID==-1)  //there is no time_ID
+      //  {
+          for (t=0;t<num_dm;t++)
+            {
+              xc[0]='\0';
+              j=0;
+              while ((src[i]!='\0') && (src[i]!='\n') && (src[i]!=' ') && (src[i]!='\t'))
+                {
+                  xc[j]=src[i];
+                  i++;
+                  j++;
+                }
+
+              xc[j]='\0';
+              i++;
+
+              uncomp_data[index][t]=atof(xc);
+            }
+       // }
+      /*else
+        {
+          for (t=0;t<=num_dm;t++) //the time column needs to be skipped, so there are num_dm+1 columns
+            {
+              xc[0]='\0';
+              j=0;
+              while ((src[i]!='\0') && (src[i]!='\n') && (src[i]!=' ') && (src[i]!='\t'))
+                {
+                  xc[j]=src[i];
+                  i++;
+                  j++;
+                }
+
+              xc[j]='\0';
+              i++;
+
+              if (t==time_ID)
+                {
+                  time_pass=1;
+                  continue;
+                }
+
+              if (time_pass)
+                uncomp_data[index][t-1]=atof(xc);
+              else
+                uncomp_data[index][t]=atof(xc);
+            }
+        }*/ //commented by Yu Qian on Aug 31, 2010 as we do not want to check time_ID anymore
+      index++;
+      //fprintf(fout_ID,"%s",src);
+    } //end of while
+
+  if (DEBUG == 1)
+    {
+      printf("the last line of the source data is:\n");
+      for (j=0;j<num_dm;j++)
+        printf("%f ",uncomp_data[index-1][j]);
+      printf("\n");
+    }
+}
+
+
+/**************************************** Normalization ******************************************/
+void tran(double **orig_data, long file_Len, long num_dm, long norm_used, double **matrix_to_cluster)
+{
+  long i=0;
+  long j=0;
+
+  double biggest=0;
+  double smallest=MAX_VALUE;
+
+  double *aver; //average of each column
+  double *std; //standard deviation of each column
+
+  aver=(double*)malloc(sizeof(double)*file_Len);
+  memset(aver,0,sizeof(double)*file_Len);
+
+  std=(double*)malloc(sizeof(double)*file_Len);
+  memset(std,0,sizeof(double)*file_Len);
+
+  if (norm_used==2) //z-score normalization
+    {
+      for (j=0;j<num_dm;j++)
+        {
+          aver[j]=0;
+          for (i=0;i<file_Len;i++)
+            aver[j]=aver[j]+orig_data[i][j];
+          aver[j]=aver[j]/(double)file_Len;
+
+          std[j]=0;
+          for (i=0;i<file_Len;i++)
+            std[j]=std[j]+((orig_data[i][j]-aver[j])*(orig_data[i][j]-aver[j]));
+          std[j]=sqrt(std[j]/(double)file_Len);
+
+          for (i=0;i<file_Len;i++)
+            matrix_to_cluster[i][j]=(orig_data[i][j]-aver[j])/std[j];  //z-score normalization
+        }
+    }
+
+  if (norm_used==1) //0-1 min-max normalization
+    {
+      for (j=0;j<num_dm;j++)
+        {
+          biggest=0;
+          smallest=MAX_VALUE;
+          for (i=0;i<file_Len;i++)
+            {
+              if (orig_data[i][j]>biggest)
+                biggest=orig_data[i][j];
+              if (orig_data[i][j]<smallest)
+                smallest=orig_data[i][j];
+            }
+
+          for (i=0;i<file_Len;i++)
+            {
+              if (biggest==smallest)
+                matrix_to_cluster[i][j]=biggest;
+              else
+                matrix_to_cluster[i][j]=(orig_data[i][j]-smallest)/(biggest-smallest);
+            }
+        }
+    }
+
+  if (norm_used==0) //no normalization
+    {
+      for (i=0;i<file_Len;i++)
+        for (j=0;j<num_dm;j++)
+          matrix_to_cluster[i][j]=orig_data[i][j];
+    }
+
+}
+
+
+
+/********************************************** RadixSort *******************************************/
+/* Perform a radix sort using each dimension from the original data as a radix.
+ * Outputs:
+ * sorted_seq   -- a permutation vector mapping the ordered list onto the original data.
+ *                  (sorted_seq[i] -> index in the original data of the ith element of the ordered list)
+ * grid_ID      -- mapping between the original data and the "grids" (see below) found as a byproduct
+ *                  of the sorting procedure.
+ * num_nonempty -- the number of grids that occur in the data (= the number of distinct values assumed
+ *                  by grid_ID)
+ */
+
+void radixsort_flock(long **position,long file_Len,long num_dm,long num_bin,long *sorted_seq,long *num_nonempty,long *grid_ID)
+{
+  long i=0;
+  long length=0;
+  long start=0;
+  long prev_ID=0;
+  long curr_ID=0;
+
+  long j=0;
+  long t=0;
+  long p=0;
+  long loc=0;
+  long temp=0;
+  long equal=0;
+
+  long *count; //count[i]=j means there are j numbers having value i at the processing digit
+  long *index; //index[i]=j means the starting position of grid i is j
+  long *cp; //current position
+  long *mark; //mark[i]=0 means it is not an ending point of a part, 1 means it is (a "part" is a group of items with identical bins for all dimensions)
+  long *seq; //temporary sequence
+
+  count=(long*)malloc(sizeof(long)*num_bin);
+  memset(count,0,sizeof(long)*num_bin);
+
+  cp=(long*)malloc(sizeof(long)*num_bin);
+  memset(cp,0,sizeof(long)*num_bin);
+
+  index=(long*)malloc(sizeof(long)*num_bin); // initialized below
+
+  seq=(long*)malloc(sizeof(long)*file_Len);
+  memset(seq,0,sizeof(long)*file_Len);
+
+  mark=(long*)malloc(sizeof(long)*file_Len);
+  memset(mark,0,sizeof(long)*file_Len);
+
+  for (i=0;i<file_Len;i++)
+    {
+      sorted_seq[i]=i;
+      mark[i]=0;
+      seq[i]=0;
+    }
+  for (i=0;i<num_bin;i++)
+    {
+      index[i]=0;
+      cp[i]=0;
+      count[i]=0;
+    }
+
+  for (j=0;j<num_dm;j++)
+    {
+      if (j==0) //compute the initial values of mark
+        {
+          for (i=0;i<file_Len;i++)
+            count[position[i][j]]++; // initialize the count to the number of items in each bin of the 0th dimension
+
+          index[0] = 0;
+          for (i=0;i<num_bin-1;i++)
+            {
+              index[i+1]=index[i]+count[i];  //index[k]=x means k segment starts at x (in the ordered list)
+              if ((index[i+1]>0) && (index[i+1]<=file_Len))
+                {
+                  mark[index[i+1]-1]=1; // Mark the end of the segment in the ordered list
+                }
+              else
+                {
+                  printf("out of myboundary for mark at index[i+1]-1.\n");
+                }
+            }
+          mark[file_Len-1]=1;
+
+          for (i=0;i<file_Len;i++)
+            {
+              /* Build a permutation vector for the partially ordered data.  Store the PV in sorted_seq */
+              loc=position[i][j];
+              temp=index[loc]+cp[loc]; //cp[i]=j means the offset from the starting position of grid i is j
+              sorted_seq[temp]=i;  //sorted_seq[i]=temp is also another way to sort
+              cp[loc]++;
+            }
+        }
+      else
+        {
+          //reset count, index, loc, temp, cp, start, and length
+          length=0;
+          loc=0;
+          temp=0;
+          start=0;
+          for (p=0;p<num_bin;p++)
+            {
+              cp[p]=0;
+              count[p]=0;
+              index[p]=0;
+            }
+
+          for (i=0;i<file_Len;i++)
+            {
+              long iperm = sorted_seq[i]; // iperm allows us to traverse the data in sorted order.
+              if (mark[i]!=1)
+                {
+                  /* Count the number of items in each bin of
+                     dimension j, BUT we are going to reset at the end
+                     of each "part".  Thus, the total effect is to do
+                     a sort by bin on the jth dimension for each group
+                     of data that has been identical for the
+                     dimensions processed up to this point.  This is
+                     the standard radix sort procedure, but doing it
+                     this way saves us having to allocate buckets to
+                     hold the data in each group of "identical-so-far"
+                     elements. */
+                  count[position[iperm][j]]++;  //count[position[i][j]]++;
+                  length++;                     // This is the total length of the part, irrespective of the value of the jth component
+                                                // (actually, less one, since we don't increment for the final element below)
+                }
+              if (mark[i]==1)
+                {
+                  //length++;
+                  count[position[iperm][j]]++;//count[position[i][j]]++;  //the current point must be counted in
+                  start=i-length; //this part starts from start to i: [start,i]
+                  /* Now we sort on the jth radix, just like we did for the 0th above, but we restrict it to just the current part.
+                     This would be a lot more clear if we broke this bit of code out into a separate function and processed recursively,
+                     plus we could multi-thread over the parts.  (Hmmm...)
+                  */
+                  index[0] = start; // Let index give the offset within the whole ordered list.
+                  for (t=0;t<num_bin-1;t++)
+                    {
+                      index[t+1]=index[t]+count[t];
+
+                      if ((index[t+1]<=file_Len) && (index[t+1]>0))
+                        {
+                          mark[index[t+1]-1]=1; // update the part boundaries to include the differences in the current radix.
+                        }
+
+                    }
+                  mark[i]=1;
+
+                  /* Update the permutation vector for the current part (i.e., from start to i).  By the time we finish the loop over i
+                     the PV will be completely updated for the partial ordering up to the current radix. */
+                  for (t=start;t<=i;t++)
+                    {
+                      loc=position[sorted_seq[t]][j];//loc=position[t][j];
+                      temp=index[loc]+cp[loc];
+                      if ((temp<file_Len) && (temp>=0))
+                        {
+                          // seq is a temporary because we have to maintain the old PV until we have finished this step.
+                          seq[temp]=sorted_seq[t];  //sorted_seq[i]=temp is also another way to sort
+                          cp[loc]++;
+                        }
+                      else
+                        {
+                          printf("out of myboundary for seq at temp.\n");
+                        }
+                    }
+
+                  for (t=start;t<=i;t++)
+                    {
+                      // copy the temporary back into sorted_seq.  sorted_seq is now updated for radix j up through
+                      // entry i in the ordered list.
+                      if ((t>=0) && (t<file_Len))
+                        sorted_seq[t]=seq[t];
+                      else
+                        printf("out of myboundary for seq and sorted_seq at t.\n");
+                    }
+                  //reset count, index, seq, length, and cp
+                  length=0;
+                  loc=0;
+                  temp=0;
+                  for (p=0;p<num_bin;p++)
+                    {
+                      cp[p]=0;
+                      count[p]=0;
+                      index[p]=0;
+                    }
+                }
+            }//end for i
+        }//end else
+    }//end for j
+
+  /* sorted_seq[] now contains the ordered list for all radices.  mark[] gives the boundaries between groups of elements that are
+     identical over all radices (= dimensions in the original data) (although it appears we aren't going to make use of this fact) */
+
+  for (i=0;i<file_Len;i++)
+    grid_ID[i]=0; //in case the initial value hasn't been assigned
+  *num_nonempty=1; //starting from 1!
+
+  /* assign the "grid" identifiers for all of the data.  A grid will be what we were calling a "part" above.  We will number them
+     serially and tag the *unordered* data with the grid IDs.  We will also count the number of populated grids (in general there will
+     be many possible combinations of bin values that simply never occur) */
+
+  for (i=1;i<file_Len;i++)
+    {
+      equal=1;
+      prev_ID=sorted_seq[i-1];
+      curr_ID=sorted_seq[i];
+      for (j=0;j<num_dm;j++)
+        {
+          if (position[prev_ID][j]!=position[curr_ID][j])
+            {
+              equal=0;  //not equal
+              break;
+            }
+        }
+
+      if (equal)
+        {
+          grid_ID[curr_ID]=grid_ID[prev_ID];
+        }
+      else
+        {
+          *num_nonempty=*num_nonempty+1;
+          grid_ID[curr_ID]=grid_ID[prev_ID]+1;
+        }
+      //all_grid_vol[grid_ID[curr_ID]]++;
+    }
+
+  //free memory
+  free(count);
+  free(index);
+  free(cp);
+  free(seq);
+  free(mark);
+
+}
+
+/********************************************** Compute Position of Events ************************************************/
+void compute_position(double **data_in, long file_Len, long num_dm, long num_bin, long **position, double *interval)
+{
+  /* What we are really doing here is binning the data, with the bins
+     spanning the range of the data and number of bins = num_bin */
+  long i=0;
+  long j=0;
+
+  double *small; //small[j] is the smallest value within dimension j
+  double *big; //big[j] is the biggest value within dimension j
+
+  small=(double*)malloc(sizeof(double)*num_dm);
+  memset(small,0,sizeof(double)*num_dm);
+
+  big=(double*)malloc(sizeof(double)*num_dm);
+  memset(big,0,sizeof(double)*num_dm);
+
+
+  for (j=0;j<num_dm;j++)
+    {
+      big[j]=MAX_VALUE*(-1);
+      small[j]=MAX_VALUE;
+      for (i=0;i<file_Len;i++)
+        {
+          if (data_in[i][j]>big[j])
+            big[j]=data_in[i][j];
+
+          if (data_in[i][j]<small[j])
+            small[j]=data_in[i][j];
+        }
+
+      interval[j]=(big[j]-small[j])/(double)num_bin;	//interval is computed using the biggest value and smallest value instead of the channel limit
+      /* XXX: I'm pretty sure the denominator of the fraction above should be num_bin-1. */
+    }
+
+  for (j=0;j<num_dm;j++)
+  {
+     for (i=0;i<file_Len;i++)
+     {
+        if (data_in[i][j]>=big[j])
+           position[i][j]=num_bin-1;
+        else
+        {
+           position[i][j]=(long)((data_in[i][j]-small[j])/interval[j]); //position[i][j]=t means point i is at the t grid of dimensional j
+           if ((position[i][j]>=num_bin) || (position[i][j]<0))
+           {
+               //printf("position mis-computed in density analysis!\n");
+               //exit(0);
+			   fprintf(stderr,"Incorrect input file format or input parameters (number of bins overflows)!\n"); //modified on July 23, 2010
+				exit(0);
+           }
+        }
+     }
+  }
+
+
+  free(small);
+  free(big);
+}
+
+/********************************************** select_bin to select the number of bins **********************************/
+//num_bin=select_bin(normalized_data, file_Len, num_dm, MIN_GRID, MAX_GRID, position, sorted_seq, all_grid_ID, &num_nonempty);
+/* Determine the number of bins to use in each dimension.  Additionally sort the data elements according to the binned
+ * values, and partition the data into "grids" with identical (binned) values.  We try progressively more bins until we
+ * maximize a merit function, then return the results obtained using the optimal number of bins.
+ *
+ * Outputs:
+ * position     -- binned data values
+ * sorted_seq   -- permutation vector mapping the ordered list to the original data
+ * all_grid_ID  -- grid to which each data element was assigned.
+ * num_nonempty -- number of distinct values assumed by all_grid_ID
+ * interval     -- bin width for each data dimension
+ * return value -- the number of bins selected.
+ */
+
+long select_bin(double **normalized_data, long file_Len, long num_dm, long min_grid, long max_grid, long **position, long *sorted_seq,
+                long *all_grid_ID, long *num_nonempty, double *interval, long user_num_bin)
+{
+
+  long num_bin=0;
+  long select_num_bin=0;
+  long m=0;
+  long n=0;
+
+  long i=0;
+  long bin_scope=0;
+  long temp_num_nonempty=0;
+
+  long *temp_grid_ID;
+  long *temp_sorted_seq;
+  long **temp_position;
+
+  //sorted_seq[i]=j means the event j ranks i
+
+  double temp_index=0;
+  double *bin_index;
+  double *temp_interval;
+
+
+  temp_grid_ID=(long *)malloc(sizeof(long)*file_Len);
+  memset(temp_grid_ID,0,sizeof(long)*file_Len);
+
+  temp_sorted_seq=(long *)malloc(sizeof(long)*file_Len);
+  memset(temp_sorted_seq,0,sizeof(long)*file_Len);
+
+  temp_position=(long **)malloc(sizeof(long*)*file_Len);
+  memset(temp_position,0,sizeof(long*)*file_Len);
+  for (m=0;m<file_Len;m++)
+    {
+      temp_position[m]=(long*)malloc(sizeof(long)*num_dm);
+      memset(temp_position[m],0,sizeof(long)*num_dm);
+    }
+
+  temp_interval=(double*)malloc(sizeof(double)*num_dm);
+  memset(temp_interval,0,sizeof(double)*num_dm);
+
+  bin_scope=max_grid-min_grid+1;
+  bin_index=(double *)malloc(sizeof(double)*bin_scope);
+  memset(bin_index,0,sizeof(double)*bin_scope);
+
+  i=0;
+
+  for (num_bin=min_grid;num_bin<=max_grid;num_bin++)
+    {
+
+	  temp_num_nonempty=0;
+	   /* compute_position bins the data into num_bin bins.  Each
+         dimension is binned independently.
+
+         Outputs:
+         temp_position[i][j] -- bin for the jth component of data element i.
+         temp_interval[j]    -- bin-width for the jth component
+      */
+      compute_position(normalized_data, file_Len, num_dm, num_bin, temp_position, temp_interval);
+      radixsort_flock(temp_position,file_Len,num_dm,num_bin,temp_sorted_seq,&temp_num_nonempty,temp_grid_ID);
+
+      /* our figure of merit is the number of non-empty grids divided by number of bins per dimension.
+         We declare victory when we have found a local maximum */
+      bin_index[i]=((double)temp_num_nonempty)/((double)num_bin);
+	  if ((double)(temp_num_nonempty)>=(double)(file_Len)*0.95)
+		  break;
+      if ((bin_index[i]<temp_index) && (user_num_bin==0))
+         break;
+	  if ((user_num_bin==num_bin-1) && (user_num_bin!=0))
+		 break;
+
+      /* Since we have accepted this trial bin, copy all the temporary results into
+         the output buffers */
+      memcpy(all_grid_ID,temp_grid_ID,sizeof(long)*file_Len);
+      memcpy(sorted_seq,temp_sorted_seq,sizeof(long)*file_Len);
+      memcpy(interval,temp_interval,sizeof(double)*num_dm);
+
+      for (m=0;m<file_Len;m++)
+        for (n=0;n<num_dm;n++)
+          position[m][n]=temp_position[m][n];
+
+      temp_index=bin_index[i];
+      select_num_bin=num_bin;
+      num_nonempty[0]=temp_num_nonempty;
+      i++;
+    }
+
+   if ((select_num_bin<min_grid) || (select_num_bin>max_grid))
+  {
+    fprintf(stderr,"Number of events collected is too few in terms of number of markers used. The file should not be processed!\n"); //modified on Nov 04, 2010
+	exit(0);
+  }
+
+  if (temp_index==0)
+  {
+	 fprintf(stderr,"Too many dimensions with too few events in the input file, or a too large number of bins used.\n"); //modified on July 23, 2010
+	 exit(0);
+  }
+
+  free(temp_grid_ID);
+  free(temp_sorted_seq);
+  free(bin_index);
+  free(temp_interval);
+
+  for (m=0;m<file_Len;m++)
+    free(temp_position[m]);
+  free(temp_position);
+
+  return select_num_bin;
+}
+
+/************************************* Select dense grids **********************************/
+// compute num_dense_grids, num_dense_events, dense_grid_reverse, and all_grid_vol
+// den_cutoff=select_dense(file_Len, all_grid_ID, num_nonempty, &num_dense_grids, &num_dense_events, dense_grid_reverse);
+/*
+ * Prune away grids that are insufficiently "dense" (i.e., contain too few data items)
+ *
+ * Outputs:
+ * num_dense_grids    -- number of dense grids
+ * num_dense_events   -- total number of data items in all dense grids
+ * dense_grid_reverse -- mapping from list of all grids to list of dense grids.
+ * return value       -- density cutoff for separating dense from non-dense grids.
+ */
+
+int select_dense(long file_Len, long *all_grid_ID, long num_nonempty, long *num_dense_grids, long *num_dense_events, long *dense_grid_reverse, int den_t_event)
+{
+
+
+  long i=0;
+  long vol_ID=0;
+  long biggest_size=0; //biggest grid_size, to define grid_size_index
+  long biggest_index=0;
+  //long actual_threshold=0; //the actual threshold on grid_size, e.g., 1 implies 1 event in the grid
+  //long num_remain=0; //number of remaining grids with different density thresholds
+  long temp_num_dense_grids=0;
+  long temp_num_dense_events=0;
+
+  long *grid_size_index;
+  long *all_grid_vol;
+  long *grid_density_index;
+
+  //double den_average=0;
+ // double avr_index=0;
+
+
+  /////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+  // Compute all_grid_vol
+  /////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+  all_grid_vol=(long *)malloc(sizeof(long)*num_nonempty);
+  memset(all_grid_vol,0,sizeof(long)*num_nonempty);
+
+  /* Grid "volume" is just the number of data contained in the grid. */
+  for (i=0;i<file_Len;i++)
+    {
+      vol_ID=all_grid_ID[i]; //vol_ID=all_grid_ID[sorted_seq[i]];
+      all_grid_vol[vol_ID]++;  //all_grid_vol[i]=j means grid i has j points
+    }
+
+
+
+  //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+  // Compute grid_size_index (histogram of grid sizes)
+  //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+
+  for (i=0;i<num_nonempty;i++)
+    {
+      if (biggest_size<all_grid_vol[i])
+        {
+          biggest_size=all_grid_vol[i];
+        }
+    }
+
+   if (biggest_size<3)
+  {
+	 fprintf(stderr,"Too many dimensions with too few events in the input file, or a too large number of bins used.\n"); //modified on July 23, 2010
+	 exit(0);
+  }
+
+
+  grid_size_index=(long*)malloc(sizeof(long)*biggest_size);
+  memset(grid_size_index,0,sizeof(long)*biggest_size);
+
+  for (i=0;i<num_nonempty;i++)
+    {
+      grid_size_index[all_grid_vol[i]-1]++; //grid_size_index[0]=5 means there are 5 grids having size 1
+    }
+
+
+
+  ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+  // Compute den_cutoff
+  ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+
+  grid_density_index=(long *)malloc(sizeof(long)*(biggest_size-2));//from event 2 to biggest_size-1, i.e., from 0 to biggest_size-3
+  memset(grid_density_index,0,sizeof(long)*(biggest_size-2));
+
+  if (den_t_event==0)
+  {
+	  biggest_index=0;
+
+	  for (i=2;i<biggest_size-1;i++) //the grid with 1 event will be skipped, i.e., grid_density_index[0] won't be defined
+	  {
+		  grid_density_index[i-1]=(grid_size_index[i-1]+grid_size_index[i+1]-2*grid_size_index[i]);
+		  if (biggest_index<grid_density_index[i-1])
+		  {
+			biggest_index=grid_density_index[i-1];
+			den_t_event=i+1;
+		  }
+	  }
+  }
+
+  if (den_t_event==0) //if biggest_size==3
+  {
+	 fprintf(stderr,"the densest hyperregion has only 3 events, smaller than the user-specified value. Therefore the density threshold is automatically changed to 3.\n");
+	 den_t_event=3;
+  }
+
+  for (i=0;i<num_nonempty;i++)
+	  if (all_grid_vol[i]>=den_t_event)
+		temp_num_dense_grids++;
+
+  if (temp_num_dense_grids<=1)
+  {
+	  //exit(0);
+	  //printf("a too high density threshold is set! Please decrease your density threshold.\n");
+	  fprintf(stderr,"a too high density threshold! Please decrease your density threshold.\n"); //modified on July 23, 2010
+	  exit(0);
+  }
+
+   if (temp_num_dense_grids>=100000)
+  {
+	  //modified on July 23, 2010
+	  //printf("a too low density threshold is set! Please increase your density threshold.\n");
+	  //exit(0);
+	  fprintf(stderr,"a too low density threshold! Please increase your density threshold.\n"); //modified on July 23, 2010
+	  exit(0);
+  }
+
+  ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+  // Compute dense_grid_reverse
+  ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+  temp_num_dense_grids=0;
+  temp_num_dense_events=0;
+  for (i=0;i<num_nonempty;i++)
+    {
+      dense_grid_reverse[i]=-1;
+
+      if (all_grid_vol[i]>=den_t_event)
+        {
+          dense_grid_reverse[i]=temp_num_dense_grids;  //dense_grid_reverse provides a mapping from all nonempty grids to dense grids.
+          temp_num_dense_grids++;
+          temp_num_dense_events+=all_grid_vol[i];
+        }
+    }
+
+  num_dense_grids[0]=temp_num_dense_grids;
+  num_dense_events[0]=temp_num_dense_events;
+
+  free(grid_size_index);
+  free(all_grid_vol);
+
+  return den_t_event;
+}
+
+/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+// Compute densegridID_To_gridevent and eventID_To_denseventID
+/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+//	grid_To_event(file_Len, dense_grid_reverse, all_grid_ID, eventID_To_denseventID, densegridID_To_gridevent);
+/*
+ * Filter the data so that only the data belonging to dense grids is left
+ *
+ * Output:
+ * eventID_To_denseeventID   -- mapping from original event ID to ID in list containing only events contained in dense grids.
+ * densegridID_To_gridevent  -- mapping from dense grids to prototype members of the grids.
+ *
+ */
+
+void grid_To_event(long file_Len, long *dense_grid_reverse, long *all_grid_ID, long *eventID_To_denseventID, long *densegridID_To_gridevent)
+{
+  long i=0;
+  long dense_grid_ID=0;
+  long dense_event_ID=0;
+
+  for (i=0;i<file_Len;i++)
+    {
+      dense_grid_ID=dense_grid_reverse[all_grid_ID[i]];
+      eventID_To_denseventID[i]=-1;
+      if (dense_grid_ID!=-1) //for point (i) belonging to dense grids
+        {
+          eventID_To_denseventID[i]=dense_event_ID;
+          dense_event_ID++;
+
+          if (densegridID_To_gridevent[dense_grid_ID]==-1) //for point i that hasn't been selected
+            densegridID_To_gridevent[dense_grid_ID]=i; //densegridID_To_gridevent maps dense_grid_ID to its representative point
+        }
+    }
+
+
+}
+
+/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+// Compute dense_grid_seq
+/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+//	generate_grid_seq(file_Len, num_dm, sorted_seq, num_dense_grids, densegridID_To_gridevent, position, dense_grid_rank, dense_grid_seq);
+/* Construct a table of binned data values for each dense grid.
+ *
+ * Output:
+ *
+ * dense_grid_seq  -- table of binned data values for each dense grid (recall that all members of a grid have identical binned data values)
+ */
+
+void generate_grid_seq(long num_dm, long num_dense_grids, long *densegridID_To_gridevent, long **position, long **dense_grid_seq)
+{
+
+  long i=0;
+  long j=0;
+  long ReventID=0; //representative event ID of the dense grid
+
+  for (i=0;i<num_dense_grids;i++)
+    {
+      ReventID = densegridID_To_gridevent[i];
+
+      for (j=0;j<num_dm;j++)
+        dense_grid_seq[i][j]=position[ReventID][j];
+    }
+}
+
+//compare two vectors
+long compare_value(long num_dm, long *search_value, long *seq_value)
+{
+  long i=0;
+
+  for (i=0;i<num_dm;i++)
+    {
+      if (search_value[i]<seq_value[i])
+        return 1;
+      if (search_value[i]>seq_value[i])
+        return -1;
+      if (search_value[i]==seq_value[i])
+        continue;
+    }
+  return 0;
+}
+
+//binary search the dense_grid_seq to return the dense grid ID if it exists
+long binary_search(long num_dense_grids, long num_dm, long *search_value, long **dense_grid_seq)
+{
+
+  long low=0;
+  long high=0;
+  long mid=0;
+  long comp_result=0;
+  long match=0;
+  //long found=0;
+
+  low = 0;
+  high = num_dense_grids-1;
+
+  while (low <= high)
+    {
+      mid = (long)((low + high)/2);
+
+      comp_result=compare_value(num_dm, search_value,dense_grid_seq[mid]);
+
+
+      switch(comp_result)
+        {
+        case 1:
+          high=mid-1;
+          break;
+        case -1:
+          low=mid+1;
+          break;
+        case 0:
+          match=1;
+          break;
+        }
+      if (match==1)
+        break;
+    }
+
+
+
+  if (match==1)
+    {
+      return mid;
+    }
+  else
+    return -1;
+}
+
+
+/********************************************** Computing Centers Using IDs **********************************************/
+
+void ID2Center(double **data_in, long file_Len, long num_dm, long *eventID_To_denseventID, long num_clust, long *cluster_ID, double **population_center)
+{
+  long i=0;
+  long j=0;
+  long ID=0;
+  long eventID=0;
+  long *size_c;
+
+
+
+  size_c=(long *)malloc(sizeof(long)*num_clust);
+  memset(size_c,0,sizeof(long)*num_clust);
+
+  for (i=0;i<num_clust;i++)
+    for (j=0;j<num_dm;j++)
+      population_center[i][j]=0;
+
+  for (i=0;i<file_Len;i++)
+    {
+      eventID=eventID_To_denseventID[i];
+
+      if (eventID!=-1) //only events in dense grids count
+        {
+          ID=cluster_ID[eventID];
+
+          if (ID==-1)
+            {
+              //printf("ID==-1! in ID2Center\n");
+              //exit(0);
+			  fprintf(stderr,"Incorrect file format or input parameters (no dense regions found!)\n"); //modified on July 23, 2010
+			  exit(0);
+            }
+
+          for (j=0;j<num_dm;j++)
+            population_center[ID][j]=population_center[ID][j]+data_in[i][j];
+
+          size_c[ID]++;
+        }
+    }
+
+
+  for (i=0;i<num_clust;i++)
+    {
+      for (j=0;j<num_dm;j++)
+        if (size_c[i]!=0)
+          population_center[i][j]=(population_center[i][j]/(double)(size_c[i]));
+        else
+		{
+          population_center[i][j]=0;
+		  printf("size_c[%ld]=0 in ID2center\n",i);
+		}
+    }
+
+  free(size_c);
+
+}
+
+///////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+//  Compute Population Center with all events
+///////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+void ID2Center_all(double **data_in, long file_Len, long num_dm, long num_clust, long *cluster_ID, double **population_center)
+{
+  long i=0;
+  long j=0;
+  long ID=0;
+  long *size_c;
+
+
+
+  size_c=(long *)malloc(sizeof(long)*num_clust);
+  memset(size_c,0,sizeof(long)*num_clust);
+
+  for (i=0;i<num_clust;i++)
+    for (j=0;j<num_dm;j++)
+      population_center[i][j]=0;
+
+
+  for (i=0;i<file_Len;i++)
+    {
+         ID=cluster_ID[i];
+
+         if (ID==-1)
+         {
+            //printf("ID==-1! in ID2Center_all\n");
+            //exit(0);
+			fprintf(stderr,"Incorrect file format or input parameters (resulting in incorrect population IDs)\n"); //modified on July 23, 2010
+			exit(0);
+         }
+
+         for (j=0;j<num_dm;j++)
+           population_center[ID][j]=population_center[ID][j]+data_in[i][j];
+
+         size_c[ID]++;
+    }
+
+
+  for (i=0;i<num_clust;i++)
+    {
+      for (j=0;j<num_dm;j++)
+        if (size_c[i]!=0)
+          population_center[i][j]=(population_center[i][j]/(double)(size_c[i]));
+        else
+		{
+          population_center[i][j]=0;
+		  printf("size_c[%ld]=0 in ID2center_all\n",i);
+		}
+    }
+
+
+  free(size_c);
+
+}
+
+/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+// Merge neighboring grids to clusters
+/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+
+long merge_grids(double **normalized_data, double *interval, long file_Len, long num_dm, long num_bin, long **position, long num_dense_grids,
+                 long *dense_grid_reverse, long **dense_grid_seq, long *eventID_To_denseventID, long *densegridID_To_gridevent, long *all_grid_ID,
+                 long *cluster_ID, long *grid_ID, long *grid_clusterID)
+{
+
+
+  long i=0;
+  long j=0;
+  long t=0;
+  long p=0;
+  long num_clust=0;
+  long ReventID=0;
+  long denseID=0;
+  long neighbor_ID=0;
+  //long temp_grid=0;
+
+  long *grid_value;
+  long *search_value;
+
+  long **graph_of_grid; //the graph constructed for dense grids: each dense grid is a graph node
+
+  double real_dist=0;
+  double **norm_grid_center;
+
+  norm_grid_center=(double **)malloc(sizeof(double*)*num_dense_grids);
+  memset(norm_grid_center,0,sizeof(double*)*num_dense_grids);
+
+  for (i=0;i<num_dense_grids;i++)
+    {
+      norm_grid_center[i]=(double *)malloc(sizeof(double)*num_dm);
+      memset(norm_grid_center[i],0,sizeof(double)*num_dm);
+    }
+
+  for (i=0;i<file_Len;i++)
+    {
+      denseID=eventID_To_denseventID[i];
+      if (denseID!=-1) //only dense events can enter
+        {
+          grid_ID[denseID]=dense_grid_reverse[all_grid_ID[i]];
+
+          if (grid_ID[denseID]==-1)
+            {
+              fprintf(stderr,"Incorrect input file format or input parameters (no dense region found)!\n");
+              exit(0);
+            }
+        }
+    }
+
+
+  /* Find centroid (in the normalized data) for each dense grid */
+  ID2Center(normalized_data,file_Len,num_dm,eventID_To_denseventID,num_dense_grids,grid_ID,norm_grid_center);
+
+  //printf("pass the grid ID2 center\n");
+
+
+  graph_of_grid=(long **)malloc(sizeof(long*)*num_dense_grids);
+  memset(graph_of_grid,0,sizeof(long*)*num_dense_grids);
+  for (i=0;i<num_dense_grids;i++)
+    {
+      graph_of_grid[i]=(long *)malloc(sizeof(long)*num_dm);
+      memset(graph_of_grid[i],0,sizeof(long)*num_dm);
+
+
+      for (j=0;j<num_dm;j++)
+        graph_of_grid[i][j]=-1;
+    }
+
+  grid_value=(long *)malloc(sizeof(long)*num_dm);
+  memset(grid_value,0,sizeof(long)*num_dm);
+
+  search_value=(long *)malloc(sizeof(long)*num_dm);
+  memset(search_value,0,sizeof(long)*num_dm);
+
+
+  for (i=0;i<num_dense_grids;i++)
+    {
+      ReventID=densegridID_To_gridevent[i];
+
+      for (j=0;j<num_dm;j++)
+        {
+          grid_value[j]=position[ReventID][j];
+
+        }
+
+
+      /* For each dimension, find the neighbor, if any, that is equal in all other dimensions and 1 greater in
+         the chosen dimension.  If the neighbor's centroid is not too far away, add it to this grid's neighbor
+         list. */
+      for (t=0;t<num_dm;t++)
+        {
+          for (p=0;p<num_dm;p++)
+            search_value[p]=grid_value[p];
+
+          if (grid_value[t]==num_bin-1)
+            continue;
+
+          search_value[t]=grid_value[t]+1; //we only consider the neighbor at the bigger side
+
+          neighbor_ID=binary_search(num_dense_grids, num_dm, search_value, dense_grid_seq);
+
+          if (neighbor_ID!=-1)
+            {
+              real_dist=norm_grid_center[i][t]-norm_grid_center[neighbor_ID][t];
+
+              if (real_dist<0)
+                real_dist=-real_dist;
+
+              if (real_dist<2*interval[t]) //by using 2*interval, this switch is void
+                graph_of_grid[i][t]=neighbor_ID;
+            }
+        }
+      grid_clusterID[i]=i; //initialize grid_clusterID
+    }
+
+
+  //graph constructed
+  //DFS-based search begins
+
+  /* Use a depth-first search to construct a list of connected subgraphs (= "clusters").
+     Note our graph as we have constructed it is a DAG, so we can use that to our advantage
+     in our search. */
+  //  num_clust=dfs(graph_of_grid,num_dense_grids,num_dm,grid_clusterID);
+  num_clust=find_connected(graph_of_grid, num_dense_grids, num_dm, grid_clusterID);
+
+
+  //computes grid_ID and cluster_ID
+  for (i=0;i<file_Len;i++)
+    {
+      denseID=eventID_To_denseventID[i];
+      if (denseID!=-1) //only dense events can enter
+	  {
+        cluster_ID[denseID]=grid_clusterID[grid_ID[denseID]];
+		//if (cluster_ID[denseID]==-1)
+		//	printf("catch you!\n");
+	  }
+    }
+
+  free(search_value);
+  free(grid_value);
+
+  for (i=0;i<num_dense_grids;i++)
+    {
+      free(graph_of_grid[i]);
+      free(norm_grid_center[i]);
+    }
+  free(graph_of_grid);
+  free(norm_grid_center);
+
+  return num_clust;
+}
+
+/********************************************* Merge Clusters to Populations *******************************************/
+
+long merge_clusters(long num_clust, long num_dm, double *interval, double **cluster_center, long *cluster_populationID, long max_num_pop)
+{
+  long num_population=0;
+  long temp_num_population=0;
+
+  long i=0;
+  long j=0;
+  long t=0;
+  long merge=0;
+  long smid=0;
+  long bgid=0;
+  double merge_dist=1.1;
+
+  long *map_ID;
+
+  double diff=0;
+
+  map_ID=(long*)malloc(sizeof(long)*num_clust);
+  memset(map_ID,0,sizeof(long)*num_clust);
+
+  for (i=0;i<num_clust;i++)
+  {
+    	cluster_populationID[i]=i;
+		map_ID[i]=i;
+  }
+
+
+  while (((num_population>max_num_pop) && (merge_dist<5.0)) || ((num_population<=1) && (merge_dist>0.1)))
+  {
+
+	  if (num_population<=1)
+	  	  merge_dist=merge_dist-0.1;
+
+	  if (num_population>max_num_pop)
+          merge_dist=merge_dist+0.1;
+
+
+	 for (i=0;i<num_clust;i++)
+		cluster_populationID[i]=i;
+
+    for (i=0;i<num_clust-1;i++)
+    {
+      for (j=i+1;j<num_clust;j++)
+        {
+          merge=1;
+
+          for (t=0;t<num_dm;t++)
+            {
+              diff=cluster_center[i][t]-cluster_center[j][t];
+
+              if (diff<0)
+                diff=-diff;
+              if (diff>(merge_dist*interval[t]))
+                merge=0;
+            }
+
+          if ((merge) && (cluster_populationID[i]!=cluster_populationID[j]))
+            {
+              if (cluster_populationID[i]<cluster_populationID[j])  //they could not be equal
+                {
+                  smid = cluster_populationID[i];
+                  bgid = cluster_populationID[j];
+                }
+              else
+                {
+                  smid = cluster_populationID[j];
+                  bgid = cluster_populationID[i];
+                }
+              for (t=0;t<num_clust;t++)
+                {
+                  if (cluster_populationID[t]==bgid)
+                    cluster_populationID[t]=smid;
+                }
+            }
+        }
+    }
+
+
+
+  for (i=0;i<num_clust;i++)
+    map_ID[i]=-1;
+
+  for (i=0;i<num_clust;i++)
+    map_ID[cluster_populationID[i]]=1;
+
+  num_population=0;
+  for (i=0;i<num_clust;i++)
+    {
+      if (map_ID[i]==1)
+        {
+          map_ID[i]=num_population;
+          num_population++;
+        }
+    }
+
+  if ((temp_num_population>max_num_pop) && (num_population==1))
+	  break;
+  else
+	  temp_num_population=num_population;
+
+  if (num_clust<=1)
+	break;
+  } //end while
+
+  for (i=0;i<num_clust;i++)
+    cluster_populationID[i]=map_ID[cluster_populationID[i]];
+
+  free(map_ID);
+
+  return num_population;
+}
+
+///////////////////////////////////////////////////////
+/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+double kmeans(double **Matrix, long k, double kmean_term, long file_Len, long num_dm, long *shortest_id, double **center)
+{
+
+	long i=0;
+	long j=0;
+	long t=0;
+	long random=0;
+	long random1=0;
+	long random2=0;
+	long times=0;
+	long dist_used=0; //0 is Euclidean and 1 is Pearson
+	long random_init=0; //0: not use random seeds;
+	long real_Len=0;
+	long skipped=0;
+
+ 	long *num;  //num[i]=t means the ith cluster has t points
+
+	double vvv=1.0; // the biggest variation;
+	double distance=0.0;
+	double xv=0.0;
+	double variation=0.0;
+
+	double mean_dx=0;
+	double mean_dy=0;
+	double sum_var=0;
+	double dx=0;
+	double dy=0;
+	double sd_x=0;
+	double sd_y=0;
+	double diff=0;
+	double distortion=0;
+	double sd=0; //standard deviation
+	double shortest_distance;
+
+	double *temp_center;
+
+	double **sum;
+
+	temp_center = (double *)malloc(sizeof(double)*num_dm);
+	memset(temp_center,0,sizeof(double)*num_dm);
+
+	if (random_init)
+	{
+		for (i=0;i<k;i++)
+		{
+			random1=rand()*rand();
+			random2=abs((random1%5)+1);
+			for (t=0;t<random2;t++)
+				random2=random2*rand()+rand();
+
+			random=abs(random2%file_Len);
+			for (j=0;j<num_dm;j++)
+				center[i][j]=Matrix[random][j];
+		}
+	}
+
+
+	num = (long *)malloc(sizeof(long)*k);
+	memset(num,0,sizeof(long)*k);
+
+	sum = (double **)malloc(sizeof(double*)*k);
+	memset(sum,0,sizeof(double*)*k);
+	for (i=0;i<k;i++)
+	{
+		sum[i] = (double *)malloc(sizeof(double)*num_dm);
+		memset(sum[i],0,sizeof(double)*num_dm);
+	}
+
+
+	times=0;
+	real_Len=0;
+
+	while (((vvv>kmean_term) && (kmean_term<1)) || ((times<kmean_term) && (kmean_term>=1)))
+	{
+		for (i=0;i<k;i++)
+		{
+			num[i]=0;
+			for (j=0;j<num_dm;j++)
+				sum[i][j]=0.0;
+		}
+
+		for (i=0;i<file_Len;i++)  //for each data point i, we compute the distance between Matrix[i] and center[j]
+		{
+			skipped = 0;
+			shortest_distance=MAX_VALUE;
+			for (j=0;j<k;j++)  //for each center j
+			{
+				distance=0.0;
+
+				if (dist_used==0)  //Euclidean distance
+				{
+					for (t=0;t<num_dm;t++) //for each dimension here num_dm is always 1 as we consider individual dimensions
+					{
+
+						diff=center[j][t]-Matrix[i][t];
+
+						diff=diff*diff;
+						//this K-means is only used for dimension selection, and therefore for 1-dimensional data only, no need to use cube distance
+
+						distance = distance+diff; //here we have a weight for each dimension
+					}
+				}
+				else  //pearson correlation
+				{
+					mean_dx=0.0;
+					mean_dy=0.0;
+					sum_var=0.0;
+					dx=0.0;
+					dy=0.0;
+					sd_x=0.0;
+					sd_y=0.0;
+					for (t=0;t<num_dm;t++)
+					{
+						mean_dx+=center[j][t];
+						mean_dy+=Matrix[i][t];
+					}
+					mean_dx=mean_dx/(double)num_dm;
+					mean_dy=mean_dy/(double)num_dm;
+
+					for (t=0;t<num_dm;t++)
+					{
+						dx=center[j][t]-mean_dx;
+						dy=Matrix[i][t]-mean_dy;
+						sum_var+=dx*dy;
+						sd_x+=dx*dx;
+						sd_y+=dy*dy;
+					}
+					if (sqrt(sd_x*sd_y)==0)
+						distance = 1.0;
+					else
+						distance = 1.0 - (sum_var/(sqrt(sd_x*sd_y))); // distance ranges from 0 to 2;
+					//printf("distance=%f\n",distance);
+				}	//pearson correlation ends
+
+				if ((distance<shortest_distance) && (skipped == 0))
+				{
+					shortest_distance=distance;
+					shortest_id[i]=j;
+				}
+			}//end for j
+				real_Len++;
+				num[shortest_id[i]]=num[shortest_id[i]]+1;
+				for (t=0;t<num_dm;t++)
+					sum[shortest_id[i]][t]=sum[shortest_id[i]][t]+Matrix[i][t];
+		}//end for i
+	/* recompute the centers */
+	//compute_mean(group);
+		vvv=0.0;
+		for (j=0;j<k;j++)
+		{
+			memcpy(temp_center,center[j],sizeof(double)*num_dm);
+			variation=0.0;
+			if (num[j]!=0)
+			{
+				for (t=0;t<num_dm;t++)
+				{
+					center[j][t]=sum[j][t]/(double)num[j];
+					xv=(temp_center[t]-center[j][t]);
+					variation=variation+xv*xv;
+				}
+			}
+
+			if (variation>vvv)
+				vvv=variation;  //vvv is the biggest variation among the k clusters;
+		}
+	//compute_variation;
+		times++;
+	} //end for while
+
+
+
+
+	free(num);
+
+	for (i=0;i<k;i++)
+		free(sum[i]);
+	free(sum);
+	free(temp_center);
+
+
+	return distortion;
+
+}
+
+//////////////////////////////////////////////////////
+/*************************** Show *****************************/
+void show(double **Matrix, long *cluster_id, long file_Len, long k, long num_dm, char *name_string)
+{
+	int situ1=0;
+	int situ2=0;
+
+	long i=0;
+	long id=0;
+	long j=0;
+	long info_id=0;
+	long nearest_id=0;
+	long insert=0;
+	long temp=0;
+	long m=0;
+	long n=0;
+	long t=0;
+
+	long *size_c;
+
+
+
+	long **size_mybound_1;
+	long **size_mybound_2;
+	long **size_mybound_3;
+	long **size_mybound_0;
+
+	double interval=0.0;
+
+	double *big;
+	double *small;
+
+
+	double **center;
+	double **mybound;
+
+	long **prof; //prof[i][j]=1 means population i is + at parameter j
+
+	FILE *fpcnt_id; //proportion id
+	//FILE *fcent_id; //center_id, i.e., centers of clusters within the original data
+	FILE *fprof_id; //profile_id
+
+	big=(double *)malloc(sizeof(double)*num_dm);
+	memset(big,0,sizeof(double)*num_dm);
+
+	small=(double *)malloc(sizeof(double)*num_dm);
+	memset(small,0,sizeof(double)*num_dm);
+
+	for (i=0;i<num_dm;i++)
+	{
+		big[i]=0.0;
+		small[i]=(double)MAX_VALUE;
+	}
+
+
+	size_c=(long *)malloc(sizeof(long)*k);
+	memset(size_c,0,sizeof(long)*k);
+
+	center=(double**)malloc(sizeof(double*)*k);
+	memset(center,0,sizeof(double*)*k);
+	for (i=0;i<k;i++)
+	{
+		center[i]=(double*)malloc(sizeof(double)*num_dm);
+		memset(center[i],0,sizeof(double)*num_dm);
+	}
+
+	mybound=(double**)malloc(sizeof(double*)*num_dm);
+	memset(mybound,0,sizeof(double*)*num_dm);
+	for (i=0;i<num_dm;i++) //there are 3 mybounds for 4 categories
+	{
+		mybound[i]=(double*)malloc(sizeof(double)*3);
+		memset(mybound[i],0,sizeof(double)*3);
+	}
+
+	prof=(long **)malloc(sizeof(long*)*k);
+	memset(prof,0,sizeof(long*)*k);
+	for (i=0;i<k;i++)
+	{
+		prof[i]=(long *)malloc(sizeof(long)*num_dm);
+		memset(prof[i],0,sizeof(long)*num_dm);
+	}
+
+
+	for (i=0;i<file_Len;i++)
+	{
+		id=cluster_id[i];
+		for (j=0;j<num_dm;j++)
+		{
+			center[id][j]=center[id][j]+Matrix[i][j];
+			if (big[j]<Matrix[i][j])
+				big[j]=Matrix[i][j];
+			if (small[j]>Matrix[i][j])
+				small[j]=Matrix[i][j];
+		}
+
+		size_c[id]++;
+	}
+
+	for (i=0;i<k;i++)
+		for (j=0;j<num_dm;j++)
+		{
+			if (size_c[i]!=0)
+				center[i][j]=(center[i][j]/(double)(size_c[i]));
+			else
+				center[i][j]=0;
+		}
+
+	for (j=0;j<num_dm;j++)
+	{
+		interval=((big[j]-small[j])/4.0);
+		//printf("interval[%d] is %f\n",j,interval);
+		for (i=0;i<3;i++)
+			mybound[j][i]=small[j]+((double)(i+1)*interval);
+	}
+
+
+	size_mybound_0=(long **)malloc(sizeof(long*)*k);
+	memset(size_mybound_0,0,sizeof(long*)*k);
+
+	for (i=0;i<k;i++)
+	{
+		size_mybound_0[i]=(long*)malloc(sizeof(long)*num_dm);
+		memset(size_mybound_0[i],0,sizeof(long)*num_dm);
+	}
+
+	size_mybound_1=(long **)malloc(sizeof(long*)*k);
+	memset(size_mybound_1,0,sizeof(long*)*k);
+
+	for (i=0;i<k;i++)
+	{
+		size_mybound_1[i]=(long*)malloc(sizeof(long)*num_dm);
+		memset(size_mybound_1[i],0,sizeof(long)*num_dm);
+	}
+
+	size_mybound_2=(long **)malloc(sizeof(long*)*k);
+	memset(size_mybound_2,0,sizeof(long*)*k);
+
+	for (i=0;i<k;i++)
+	{
+		size_mybound_2[i]=(long*)malloc(sizeof(long)*num_dm);
+		memset(size_mybound_2[i],0,sizeof(long)*num_dm);
+	}
+
+	size_mybound_3=(long **)malloc(sizeof(long*)*k);
+	memset(size_mybound_3,0,sizeof(long*)*k);
+
+	for (i=0;i<k;i++)
+	{
+		size_mybound_3[i]=(long*)malloc(sizeof(long)*num_dm);
+		memset(size_mybound_3[i],0,sizeof(long)*num_dm);
+	}
+
+	for (i=0;i<file_Len;i++)
+		for (j=0;j<num_dm;j++)
+			{
+				if (Matrix[i][j]<mybound[j][0])// && ((Matrix[i][j]-small[j])>0)) //the smallest values excluded
+					size_mybound_0[cluster_id[i]][j]++;
+				else
+				{
+					if (Matrix[i][j]<mybound[j][1])
+						size_mybound_1[cluster_id[i]][j]++;
+					else
+					{
+						if (Matrix[i][j]<mybound[j][2])
+							size_mybound_2[cluster_id[i]][j]++;
+						else
+							//if (Matrix[i][j]!=big[j]) //the biggest values excluded
+								size_mybound_3[cluster_id[i]][j]++;
+					}
+
+				}
+			}
+
+	fprof_id=fopen("profile.txt","w");
+	fprintf(fprof_id,"Population_ID\t");
+	fprintf(fprof_id,"%s\n",name_string);
+
+	for (i=0;i<k;i++)
+	{
+		fprintf(fprof_id,"%ld\t",i+1); //i changed to i+1 to start from 1 instead of 0: April 16, 2009
+		for (j=0;j<num_dm;j++)
+		{
+
+			if (size_mybound_0[i][j]>size_mybound_1[i][j])
+				situ1=0;
+			else
+				situ1=1;
+			if (size_mybound_2[i][j]>size_mybound_3[i][j])
+				situ2=2;
+			else
+				situ2=3;
+
+			if ((situ1==0) && (situ2==2))
+			{
+				if (size_mybound_0[i][j]>size_mybound_2[i][j])
+					prof[i][j]=0;
+				else
+					prof[i][j]=2;
+			}
+			if ((situ1==0) && (situ2==3))
+			{
+				if (size_mybound_0[i][j]>size_mybound_3[i][j])
+					prof[i][j]=0;
+				else
+					prof[i][j]=3;
+			}
+			if ((situ1==1) && (situ2==2))
+			{
+				if (size_mybound_1[i][j]>size_mybound_2[i][j])
+					prof[i][j]=1;
+				else
+					prof[i][j]=2;
+			}
+			if ((situ1==1) && (situ2==3))
+			{
+				if (size_mybound_1[i][j]>size_mybound_3[i][j])
+					prof[i][j]=1;
+				else
+					prof[i][j]=3;
+			}
+
+			//begin to output profile
+			if (j==num_dm-1)
+			{
+				if (prof[i][j]==0)
+					fprintf(fprof_id,"1\n");
+				if (prof[i][j]==1)
+					fprintf(fprof_id,"2\n");
+				if (prof[i][j]==2)
+					fprintf(fprof_id,"3\n");
+				if (prof[i][j]==3)
+					fprintf(fprof_id,"4\n");
+			}
+			else
+			{
+				if (prof[i][j]==0)
+					fprintf(fprof_id,"1\t");
+				if (prof[i][j]==1)
+					fprintf(fprof_id,"2\t");
+				if (prof[i][j]==2)
+					fprintf(fprof_id,"3\t");
+				if (prof[i][j]==3)
+					fprintf(fprof_id,"4\t");
+			}
+		}
+	}
+	fclose(fprof_id);
+
+	///////////////////////////////////////////////////////////
+
+
+	fpcnt_id=fopen("percentage.txt","w");
+	fprintf(fpcnt_id,"Population_ID\tPercentage\n");
+
+	for (t=0;t<k;t++)
+	{
+		fprintf(fpcnt_id,"%ld\t%.2f\n",t+1,(double)size_c[t]*100.0/(double)file_Len);	//t changed to t+1 to start from 1 instead of 0: April 16, 2009
+	}
+	fclose(fpcnt_id);
+
+	free(big);
+	free(small);
+	free(size_c);
+
+	for (i=0;i<k;i++)
+	{
+		free(center[i]);
+		free(prof[i]);
+		free(size_mybound_0[i]);
+		free(size_mybound_1[i]);
+		free(size_mybound_2[i]);
+		free(size_mybound_3[i]);
+	}
+	free(center);
+	free(prof);
+	free(size_mybound_0);
+	free(size_mybound_1);
+	free(size_mybound_2);
+	free(size_mybound_3);
+
+	for (i=0;i<num_dm;i++)
+		free(mybound[i]);
+	free(mybound);
+
+}
+///////////////////////////////////////////////////////////////////////////
+
+double get_avg_dist(double *population_center, long smaller_pop_ID, long larger_pop_ID, long *population_ID, long num_population, long file_Len,
+				   long num_dm, double **normalized_data, long d1, long d2, long d3, long *size_c)
+{
+	long k=0;
+	long temp=0;
+	long i=0;
+	long j=0;
+	long t=0;
+	long current_biggest=0;
+
+
+	double total_dist=0.0;
+	double distance=0.0;
+	double dist=0.0;
+	double biggest_distance=0.0;
+
+	long *nearest_neighbors;
+	double *nearest_distance;
+
+	k=min(size_c[smaller_pop_ID],size_c[larger_pop_ID]);
+
+	if (k>0)
+	{
+		k=(long)sqrt((double)k);
+		if (num_dm<=3)
+			k=(long)(2.7183*(double)k);  //e*k for low-dimensional space, added Nov. 4, 2010
+		//printf("the k-nearest k is %d\n",k);
+	}
+	else
+	{
+		printf("error in k\n");
+		exit(0);
+	}
+
+	nearest_neighbors=(long *)malloc(sizeof(long)*k);
+	memset(nearest_neighbors,0,sizeof(long)*k);
+
+	nearest_distance=(double *)malloc(sizeof(double)*k);
+	memset(nearest_distance,0,sizeof(double)*k);
+
+	temp=0;
+
+	for (i=0;i<file_Len;i++)
+	{
+		if ((population_ID[i]==smaller_pop_ID) || (population_ID[i]==larger_pop_ID)) //the event belongs to the pair of populations
+		{
+			distance=0.0;
+			for (t=0;t<num_dm;t++)
+			{
+				if ((t!=d1) && (t!=d2) && (t!=d3))
+					continue;
+				else
+				{
+					dist=population_center[t]-normalized_data[i][t];
+					distance=distance+dist*dist;
+				}
+			}
+
+			if (temp<k)
+			{
+				nearest_neighbors[temp]=i;
+				nearest_distance[temp]=distance;
+				temp++;
+			}
+			else
+			{
+			    biggest_distance=0.0;
+				for (j=0;j<k;j++)
+				{
+					if (nearest_distance[j]>biggest_distance)
+					{
+						biggest_distance=nearest_distance[j];
+						current_biggest=j;
+					}
+				}
+
+				if (biggest_distance>distance)
+				{
+					nearest_neighbors[current_biggest]=i;
+					nearest_distance[current_biggest]=distance;
+				}
+			}
+		}
+	}
+
+    for (i=0;i<k;i++)
+		total_dist=total_dist+nearest_distance[i];
+
+	total_dist=total_dist/(double)k;
+
+	free(nearest_distance);
+	free(nearest_neighbors);
+
+	return total_dist;
+}
+
+
+/******************************************************** Main Function **************************************************/
+//for normalized data, there are five variables:
+//cluster_ID
+//population_center
+//grid_clusterID
+//grid_ID
+//grid_Center
+
+//the same five variables exist for the original data
+//however, the three IDs (cluster_ID, grid_ID, grid_clusterID) don't change in either normalized or original data
+//also, data + cluster_ID -> population_center
+//data + grid_ID -> grid_Center
+
+/* what is the final output */
+//the final things we want are grid_Center in the original data and grid_clusterID //or population_center in the original data
+//Sparse grids will not be considered when computing the two centroids (centroids of grids and centroids of clusters)
+
+/*  what information should select_bin output */
+//the size of all IDs are unknown to function main because we only consider the events in dense grids, and also the number of dense grids
+//is unknown, therefore I must use a prescreening to output
+//how many bins I should use
+//the number of dense grids
+//total number of events in the dense grids
+
+/* basic procedure of main function */
+//1. read raw file and normalize the raw file
+//2. select_bin
+//3. allocate memory for eventID_To_denseventID, grid_clusterID, grid_ID, cluster_ID.
+//4. call select_dense and merge_grids with grid_clusterID, grid_ID, cluster_ID.
+//5. release normalized data; allocate memory for grid_Center and population_center
+//6. output grid_Center and population_center using ID2Center together with grid_clusterID //from IDs to centers
+
+int main (int argc, char **argv)
+{
+  //inputs
+  FILE *f_src; //source file pointer
+
+  FILE *f_out; //coordinates
+  FILE *f_cid; //population-ID of events
+  FILE *f_ctr; //centroids of populations
+  FILE *f_results; //coordinates file event and population column
+  FILE *f_mfi; //added April 16, 2009 for mean fluorescence intensity
+  FILE *f_parameters; //number of bins and density calculated by
+                      //the algorithm. Used to update the database
+  FILE *f_properties; //Properties file used by Image generation software
+
+  //char tmpbuf[128];
+
+  char para_name_string[LINE_LEN];
+
+  long time_ID=-1;
+  long num_bin=0; //the bins I will use on each dimension
+  long num_pop=0;
+  long file_Len=0; //number of events
+  long num_dm=0;
+  long num_clust=0;
+  long num_dense_events=0;
+  long num_dense_grids=0;
+  long num_nonempty=0;
+  long num_population=0;
+  long num_real_pop=0;
+  long keep_merge=0;
+  long num_checked_range=0;
+
+  //below are read from configuration file
+  long i=0;
+  long j=0;
+  long p=0;
+  long t=0;
+  long q=0;
+  long temp_i=0;
+  long temp_j=0;
+  long first_i=0;
+  long first_j=0;
+  long d1=0;
+  long d2=0;
+  long d3=0;
+  long d_d=0;
+  long max_num_pop=0; //upperbound of the number of populations that is equal to 2^d
+  long index_id=0;
+  long num_computed_population=0;
+  long tot_size=0;
+
+  int den_t_event=0;
+
+  double distance=0.0;
+  double dist=0.0;
+  double current_smallest_dist=0;
+  double max_d_dist=0.0;
+  double Ei=0.0;
+  double Ej=0.0;
+  double E1=0.0;
+  double E2=0.0;
+  double E3=0.0;
+  double Ep=0.0;
+  double temp=0.0;
+  double tmp=0.0;
+
+  long *grid_clusterID; //(dense)gridID to clusterID
+  long *grid_ID; //(dense)eventID to gridID
+  long *cluster_ID; //(dense)eventID to clusterID
+  long *eventID_To_denseventID; //eventID_To_denseventID[i]=k means event i is in a dense grid and its ID within dense events is k
+  long *all_grid_ID; //gridID for all events
+  long *densegridID_To_gridevent;
+  long *sorted_seq;
+  long *dense_grid_reverse;
+  long *population_ID; //denseeventID to populationID
+  long *cluster_populationID; //clusterID to populationID
+  long *grid_populationID; //gridID to populationID
+  long *all_population_ID; //populationID of event
+  long *size_c;
+  long *size_p_2;
+  long *partit;
+  long *size_p;
+  long *temp_size_j;
+  long *all_computed_pop_ID;
+
+
+  long **position;
+  long **dense_grid_seq;
+  long **temp_population_ID;
+
+  double *interval;
+  double *center_1;
+  double *center_2;
+  double *center_3;
+  double *aver;
+  double *std;
+  double *center_p_1;
+  double *center_p_2;
+  double *center_p_3;
+
+  double **population_center; //population centroids in the raw/original data
+  double **cluster_center; //cluster centroids in the raw/original data
+  double **new_population_center;
+  double **temp_population_center;
+  double **min_pop;
+  double **max_pop;
+
+  double **input_data;
+  double **normalized_data;
+
+  double **real_pop_center;
+  double **distance_pop;
+
+  double ***ind_pop;
+  double ***ind_pop_3;
+
+  int min = 999999;
+  int max = 0;
+
+  printf( "Starting time:\t\t\t\t");
+  fflush(stdout);
+  system("/bin/date");
+
+  /*
+   * Windows Version
+  _strtime( tmpbuf );
+  printf( "Starting time:\t\t\t\t%s\n", tmpbuf );
+  _strdate( tmpbuf );
+  printf( "Starting date:\t\t\t\t%s\n", tmpbuf );
+  */
+
+  /////////////////////////////////////////////////////////////
+
+  if ((argc!=2) && (argc!=3) && (argc!=4) && (argc!=5) && (argc!=6))
+  {
+      fprintf(stderr,"Incorrect number of input parameters!\n");
+	  fprintf(stderr,"usage:\n");
+	  fprintf(stderr,"basic mode: flock data_file\n");
+	  fprintf(stderr,"advanced mode 0 (specify maximum # of pops): flock data_file max_num_pop\n");
+	  fprintf(stderr,"advanced mode 1 (without # of pops): flock data_file num_bin density_index\n");
+	  fprintf(stderr,"advanced mode 2 (specify # of pops): flock data_file num_bin density_index number_of_pop\n");
+	  fprintf(stderr,"advanced mode 3 (specify both # of pops): flock data_file num_bin density_index number_of_pop max_num_pop\n");
+      exit(0);
+  }
+
+  f_src=fopen(argv[1],"r");
+
+  if (argc==3)
+  {
+	max_num_pop=atoi(argv[2]);
+	printf("num of maximum pop is %ld\n",max_num_pop);
+  }
+
+  if (argc==4)
+  {
+	num_bin=atoi(argv[2]);
+	printf("num_bin is %ld\n",num_bin);
+
+	den_t_event=atoi(argv[3]);
+	printf("density_index is %d\n",den_t_event);
+  }
+
+  if (argc==5)
+  {
+	num_bin=atoi(argv[2]);
+	printf("num_bin is %ld\n",num_bin);
+
+	den_t_event=atoi(argv[3]);
+	printf("density_index is %d\n",den_t_event);
+
+	num_pop=atoi(argv[4]);
+	printf("num of pop is %ld\n",num_pop);
+  }
+
+  if (argc==6)
+  {
+	num_bin=atoi(argv[2]);
+	printf("num_bin is %ld\n",num_bin);
+
+	den_t_event=atoi(argv[3]);
+	printf("density_index is %d\n",den_t_event);
+
+	num_pop=atoi(argv[4]);
+	printf("num of pop is %ld\n",num_pop);
+
+	max_num_pop=atoi(argv[5]);
+	printf("num of pop is %ld\n",max_num_pop);
+  }
+
+
+  if (num_pop==1)
+  {
+	  printf("it is not allowed to specify only one population\n");
+	  exit(0);
+  }
+
+
+
+  getfileinfo(f_src, &file_Len, &num_dm, para_name_string, &time_ID); //get the filelength, number of dimensions, and num/name of parameters
+
+
+  if (max_num_pop==0)
+  {
+	  max_num_pop=(long)pow(2,num_dm);
+		if (max_num_pop>MAX_POP_NUM)
+			max_num_pop=MAX_POP_NUM;
+  }
+
+  /************************************************* Read the data *****************************************************/
+
+  rewind(f_src); //reset the file pointer
+
+  input_data = (double **)malloc(sizeof(double*)*file_Len);
+  memset(input_data,0,sizeof(double*)*file_Len);
+  for (i=0;i<file_Len;i++)
+  {
+     input_data[i]=(double *)malloc(sizeof(double)*num_dm);
+     memset(input_data[i],0,sizeof(double)*num_dm);
+  }
+
+  readsource(f_src, file_Len, num_dm, input_data, time_ID); //read the data;
+
+  fclose(f_src);
+
+  normalized_data=(double **)malloc(sizeof(double*)*file_Len);
+  memset(normalized_data,0,sizeof(double*)*file_Len);
+  for (i=0;i<file_Len;i++)
+    {
+      normalized_data[i]=(double *)malloc(sizeof(double)*num_dm);
+      memset(normalized_data[i],0,sizeof(double)*num_dm);
+    }
+
+  tran(input_data, file_Len, num_dm, NORM_METHOD, normalized_data);
+
+
+  position=(long **)malloc(sizeof(long*)*file_Len);
+  memset(position,0,sizeof(long*)*file_Len);
+  for (i=0;i<file_Len;i++)
+    {
+      position[i]=(long*)malloc(sizeof(long)*num_dm);
+      memset(position[i],0,sizeof(long)*num_dm);
+    }
+
+  all_grid_ID=(long *)malloc(sizeof(long)*file_Len);
+  memset(all_grid_ID,0,sizeof(long)*file_Len);
+
+  sorted_seq=(long*)malloc(sizeof(long)*file_Len);
+  memset(sorted_seq,0,sizeof(long)*file_Len);
+
+  interval=(double*)malloc(sizeof(double)*num_dm);
+  memset(interval,0,sizeof(double)*num_dm);
+
+  /************************************************* select_bin *************************************************/
+
+  if (num_bin>=1)  //num_bin has been selected by user
+  {
+  	select_bin(normalized_data, file_Len, num_dm, MIN_GRID, MAX_GRID, position, sorted_seq, all_grid_ID, &num_nonempty, interval,num_bin);
+	printf("user set bin number is %ld\n",num_bin);
+  }
+  else  //num_bin has not been selected by user
+  {
+	num_bin=select_bin(normalized_data, file_Len, num_dm, MIN_GRID, MAX_GRID, position, sorted_seq, all_grid_ID, &num_nonempty, interval,num_bin);
+	printf("selected bin number is %ld\n",num_bin);
+  }
+  printf("number of non-empty grids is %ld\n",num_nonempty);
+
+
+
+  /* Although we return sorted_seq from select_bin(), we don't use it for anything, except possibly diagnostics */
+  free(sorted_seq);
+
+
+  dense_grid_reverse=(long*)malloc(sizeof(long)*num_nonempty);
+  memset(dense_grid_reverse,0,sizeof(long)*num_nonempty);
+
+  /************************************************* select_dense **********************************************/
+
+  if (den_t_event>=1) //den_t_event must be larger or equal to 2 if the user wants to set it
+	den_t_event=select_dense(file_Len, all_grid_ID, num_nonempty, &num_dense_grids, &num_dense_events, dense_grid_reverse, den_t_event);
+  else
+  {
+	den_t_event=select_dense(file_Len, all_grid_ID, num_nonempty, &num_dense_grids, &num_dense_events, dense_grid_reverse, den_t_event);
+	printf("automated selected density threshold is %d\n",den_t_event);
+  }
+
+  printf("Number of dense grids is %ld\n",num_dense_grids);
+
+  densegridID_To_gridevent = (long *)malloc(sizeof(long)*num_dense_grids);
+  memset(densegridID_To_gridevent,0,sizeof(long)*num_dense_grids);
+
+  for (i=0;i<num_dense_grids;i++)
+    densegridID_To_gridevent[i]=-1; //initialize all densegridID_To_gridevent values to -1
+
+
+  eventID_To_denseventID=(long *)malloc(sizeof(long)*file_Len);
+  memset(eventID_To_denseventID,0,sizeof(long)*file_Len);     //eventID_To_denseventID[i]=k means event i is in a dense grid and its ID within dense events is k
+
+
+  grid_To_event(file_Len, dense_grid_reverse, all_grid_ID, eventID_To_denseventID, densegridID_To_gridevent);
+
+
+  dense_grid_seq=(long **)malloc(sizeof(long*)*num_dense_grids);
+  memset(dense_grid_seq,0,sizeof(long*)*num_dense_grids);
+  for (i=0;i<num_dense_grids;i++)
+    {
+      dense_grid_seq[i]=(long *)malloc(sizeof(long)*num_dm);
+      memset(dense_grid_seq[i],0,sizeof(long)*num_dm);
+    }
+
+
+  /* Look up the binned data values for each dense grid */
+  generate_grid_seq(num_dm, num_dense_grids, densegridID_To_gridevent, position, dense_grid_seq);
+
+
+  /************************************************* allocate memory *********************************************/
+
+  grid_clusterID=(long *)malloc(sizeof(long)*num_dense_grids);
+  memset(grid_clusterID,0,sizeof(long)*num_dense_grids);
+
+  grid_ID=(long *)malloc(sizeof(long)*num_dense_events);
+  memset(grid_ID,0,sizeof(long)*num_dense_events);
+
+  cluster_ID=(long *)malloc(sizeof(long)*num_dense_events);
+  memset(cluster_ID,0,sizeof(long)*num_dense_events);
+
+
+  /*********************************************** merge_grids ***********************************************/
+  //long merge_grids(long file_Len, long num_dm, long num_bin, long **position, long num_dense_grids, long *dense_grid_rank, long *dense_grid_reverse,
+  //			 long **dense_grid_seq, long *eventID_To_denseventID, long *densegridID_To_gridevent, long *all_grid_ID,
+  //			 long *cluster_ID, long *grid_ID, long *grid_clusterID)
+
+  num_clust = merge_grids(normalized_data, interval, file_Len, num_dm, num_bin, position, num_dense_grids, dense_grid_reverse, dense_grid_seq, eventID_To_denseventID, densegridID_To_gridevent, all_grid_ID, cluster_ID, grid_ID, grid_clusterID);
+
+  printf("computed number of groups is %ld\n",num_clust);
+
+
+  /************************************** release unnecessary memory and allocate memory and compute centers **********************************/
+
+
+  for (i=0;i<file_Len;i++)
+    free(position[i]);
+  free(position);
+
+  for (i=0;i<num_dense_grids;i++)
+    free(dense_grid_seq[i]);
+  free(dense_grid_seq);
+
+  free(dense_grid_reverse);
+
+  free(densegridID_To_gridevent);
+  free(all_grid_ID);
+
+  // cluster_center ////////////////////////////////////////////////////////////////////////////////////////////////////////
+
+  cluster_center=(double **)malloc(sizeof(double*)*num_clust);
+  memset(cluster_center,0,sizeof(double*)*num_clust);
+  for (i=0;i<num_clust;i++)
+  {
+     cluster_center[i]=(double*)malloc(sizeof(double)*num_dm);
+     memset(cluster_center[i],0,sizeof(double)*num_dm);
+  }
+
+  ID2Center(normalized_data,file_Len,num_dm,eventID_To_denseventID,num_clust,cluster_ID,cluster_center); //produce the centers with normalized data
+
+  //printf("pass the first ID2center\n");
+
+  /*** population_ID and grid_populationID **/
+
+  cluster_populationID=(long*)malloc(sizeof(long)*num_clust);
+  memset(cluster_populationID,0,sizeof(long)*num_clust);
+
+  grid_populationID=(long*)malloc(sizeof(long)*num_dense_grids);
+  memset(grid_populationID,0,sizeof(long)*num_dense_grids);
+
+  population_ID=(long*)malloc(sizeof(long)*num_dense_events);
+  memset(population_ID,0,sizeof(long)*num_dense_events);
+
+  num_population = merge_clusters(num_clust, num_dm, interval, cluster_center, cluster_populationID, max_num_pop);
+
+
+
+  for (i=0;i<num_clust;i++)
+    free(cluster_center[i]);
+  free(cluster_center);
+
+  free(interval);
+
+  for (i=0;i<num_dense_grids;i++)
+    {
+      grid_populationID[i]=cluster_populationID[grid_clusterID[i]];
+    }
+
+  for (i=0;i<num_dense_events;i++)
+    {
+      population_ID[i]=cluster_populationID[cluster_ID[i]];
+    }
+
+  printf("Number of merged groups before second-run partitioning is %ld\n",num_population);
+
+
+
+  // population_center /////////////////////////////////////////////////////////////////////////////////////////////////////
+
+
+  population_center=(double **)malloc(sizeof(double*)*num_population);
+  memset(population_center,0,sizeof(double*)*num_population);
+  for (i=0;i<num_population;i++)
+  {
+     population_center[i]=(double*)malloc(sizeof(double)*num_dm);
+     memset(population_center[i],0,sizeof(double)*num_dm);
+  }
+
+
+
+  ID2Center(normalized_data,file_Len,num_dm,eventID_To_denseventID,num_population,population_ID,population_center); //produce population centers with normalized data
+
+
+  // show ////////////////////////////////////////////////////////////////////////////////
+  all_population_ID=(long*)malloc(sizeof(long)*file_Len);
+  memset(all_population_ID,0,sizeof(long)*file_Len);
+
+  kmeans(normalized_data, num_population, KMEANS_TERM, file_Len, num_dm, all_population_ID, population_center);
+
+  for (i=0;i<num_population;i++)
+	free(population_center[i]);
+
+  free(population_center);
+
+  ////// there needs to be another step to further partition the data
+
+
+	  center_p_1=(double *)malloc(sizeof(double)*3);
+	  memset(center_p_1,0,sizeof(double)*3);
+
+	  center_p_2=(double *)malloc(sizeof(double)*3);
+	  memset(center_p_2,0,sizeof(double)*3);
+
+	  center_p_3=(double *)malloc(sizeof(double)*3);
+	  memset(center_p_3,0,sizeof(double)*3);
+
+	  size_p=(long *)malloc(sizeof(long)*num_population);
+	  memset(size_p,0,sizeof(long)*num_population);
+
+	  temp_size_j=(long *)malloc(sizeof(long)*num_population);
+	  memset(temp_size_j,0,sizeof(long)*num_population);
+
+	  all_computed_pop_ID=(long *)malloc(sizeof(long)*file_Len);
+	  memset(all_computed_pop_ID,0,sizeof(long)*file_Len);
+
+	  for (i=0;i<file_Len;i++)
+	  {
+		size_p[all_population_ID[i]]++;
+		all_computed_pop_ID[i]=all_population_ID[i];
+	  }
+
+	  ind_pop=(double***)malloc(sizeof(double**)*num_population);
+	  memset(ind_pop,0,sizeof(double**)*num_population);
+
+	  ind_pop_3=(double***)malloc(sizeof(double**)*num_population);
+	  memset(ind_pop_3,0,sizeof(double**)*num_population);
+
+	  for (i=0;i<num_population;i++)
+	  {
+		  ind_pop[i]=(double**)malloc(sizeof(double*)*size_p[i]);
+		  memset(ind_pop[i],0,sizeof(double*)*size_p[i]);
+
+		  ind_pop_3[i]=(double**)malloc(sizeof(double*)*size_p[i]);
+		  memset(ind_pop_3[i],0,sizeof(double*)*size_p[i]);
+
+		  for (j=0;j<size_p[i];j++)
+		  {
+			  ind_pop[i][j]=(double*)malloc(sizeof(double)*num_dm);
+			  memset(ind_pop[i][j],0,sizeof(double)*num_dm);
+
+			  ind_pop_3[i][j]=(double*)malloc(sizeof(double)*3);
+			  memset(ind_pop_3[i][j],0,sizeof(double)*3);
+		  }
+		  temp_size_j[i]=0;
+	  }
+
+	  for (i=0;i<file_Len;i++) //to generate ind_pop[i]
+	  {
+		  index_id=all_population_ID[i];
+
+		  j=temp_size_j[index_id];
+
+		  for (t=0;t<num_dm;t++)
+		  {
+			ind_pop[index_id][j][t]=input_data[i][t];
+		  }
+		  temp_size_j[index_id]++;
+	  }
+
+	  aver=(double*)malloc(sizeof(double)*num_dm);
+	  memset(aver,0,sizeof(double)*num_dm);
+
+	  std=(double*)malloc(sizeof(double)*num_dm);
+	  memset(std,0,sizeof(double)*num_dm);
+
+	  temp_population_center=(double**)malloc(sizeof(double*)*2);
+	  memset(temp_population_center,0,sizeof(double*)*2);
+	  for (i=0;i<2;i++)
+	  {
+		temp_population_center[i]=(double*)malloc(sizeof(double)*3);
+		memset(temp_population_center[i],0,sizeof(double)*3);
+	  }
+
+	  size_p_2=(long*)malloc(sizeof(long)*2);
+	  memset(size_p_2,0,sizeof(long)*2);
+
+	  partit=(long*)malloc(sizeof(long)*num_population);
+	  memset(partit,0,sizeof(long)*num_population);
+
+	  num_computed_population=num_population;
+
+	  temp_population_ID=(long**)malloc(sizeof(long*)*num_population);
+	  memset(temp_population_ID,0,sizeof(long*)*num_population);
+
+	  for (i=0;i<num_population;i++)
+	  {
+		temp_population_ID[i]=(long*)malloc(sizeof(long)*size_p[i]);
+		memset(temp_population_ID[i],0,sizeof(long)*size_p[i]);
+	  }
+
+	  //printf("num_population=%d\n",num_population);
+
+	  for (i=0;i<num_population;i++)
+	  {
+		  partit[i]=0;
+		  tran(ind_pop[i], size_p[i], num_dm, 1, ind_pop[i]);//0-1 normalize ind_pop[i]
+
+		  //find the 3 dimensions with the largest std for ind_pop[i]
+		  d1=-1;
+		  d2=-1;
+		  d3=-1;
+
+		  for (t=0;t<num_dm;t++)
+		  {
+			aver[t]=0;
+			for (j=0;j<size_p[i];j++)
+			{
+				aver[t]=aver[t]+ind_pop[i][j][t];
+			}
+			aver[t]=aver[t]/(double)size_p[i];
+
+			std[t]=0;
+			for (j=0;j<size_p[i];j++)
+			{
+				std[t]=std[t]+((ind_pop[i][j][t]-aver[t])*(ind_pop[i][j][t]-aver[t]));
+			}
+			std[t]=sqrt(std[t]/(double)size_p[i]);
+		  }
+
+
+
+		  for (j=0;j<3;j++)
+		  {
+			max_d_dist=0;
+			for (t=0;t<num_dm;t++)
+			{
+				if ((t!=d1) && (t!=d2))
+				{
+					dist=std[t];
+				}
+				else
+					dist=-1;
+
+				if (dist>max_d_dist)
+				{
+					max_d_dist=dist;
+					d_d=t;
+				}
+			}
+
+			if (j==0)
+				d1=d_d;
+			if (j==1)
+				d2=d_d;
+			if (j==2)
+				d3=d_d;
+		  }
+
+
+		  for (t=0;t<size_p[i];t++)
+		  {
+				ind_pop_3[i][t][0]=ind_pop[i][t][d1];
+				ind_pop_3[i][t][1]=ind_pop[i][t][d2];
+				ind_pop_3[i][t][2]=ind_pop[i][t][d3];
+		  }
+
+
+		 temp_population_center[0][0]=(aver[d1])/2.0;
+
+		 temp_population_center[0][1]=aver[d2];
+	     temp_population_center[0][2]=aver[d3];
+
+		 temp_population_center[1][0]=(aver[d1]+1.0)/2.0;
+
+		 temp_population_center[1][1]=aver[d2];
+		 temp_population_center[1][2]=aver[d3];
+
+
+
+		 //run K-means with K=2
+		 kmeans(ind_pop_3[i], 2, KMEANS_TERM, size_p[i], 3, temp_population_ID[i], temp_population_center);
+
+		 for (j=0;j<2;j++)
+			 size_p_2[j]=0;
+
+		 for (j=0;j<size_p[i];j++)
+			 size_p_2[temp_population_ID[i][j]]++;
+
+		 for (j=0;j<2;j++)
+			 if (size_p_2[j]==0)
+				 printf("size_p_2=0 at i=%ld\n",i);
+
+
+		 //check whether the 2 parts should be merged
+
+
+		 Ei=get_avg_dist(temp_population_center[0], 0,1, temp_population_ID[i], 2,size_p[i], 3, ind_pop_3[i], 0,1,2,size_p_2);
+		 Ej=get_avg_dist(temp_population_center[1], 0,1, temp_population_ID[i], 2,size_p[i], 3, ind_pop_3[i], 0,1,2,size_p_2);
+
+		 for (t=0;t<3;t++)
+		 {
+			center_p_1[t]=temp_population_center[0][t]*0.25+temp_population_center[1][t]*0.75;
+			center_p_2[t]=temp_population_center[0][t]*0.5+temp_population_center[1][t]*0.5;
+			center_p_3[t]=temp_population_center[0][t]*0.75+temp_population_center[1][t]*0.25;
+		 }
+
+		 E1=get_avg_dist(center_p_1, 0,1, temp_population_ID[i], 2,size_p[i], 3, ind_pop_3[i], 0,1,2,size_p_2);
+
+		 E2=get_avg_dist(center_p_2, 0,1, temp_population_ID[i], 2,size_p[i], 3, ind_pop_3[i], 0,1,2,size_p_2);
+
+		 E3=get_avg_dist(center_p_3, 0,1, temp_population_ID[i], 2,size_p[i], 3, ind_pop_3[i], 0,1,2,size_p_2);
+
+		 //printf("i=%d;E1=%f;E2=%f;E3=%f\n",i,E1,E2,E3);
+
+		 if (E1<E2)
+			Ep=E2;
+		 else
+			Ep=E1;
+
+		 Ep=max(Ep,E3); //Ep is the most sparse area
+
+
+
+		 if ((Ep>Ei) && (Ep>Ej)) //the two parts should be partitioned
+		 {
+			 partit[i]=num_computed_population;
+			 num_computed_population++;
+		 }
+
+	  } //end for (i=0;i<num_population;i++)
+
+
+	  for (i=0;i<num_population;i++)
+		  temp_size_j[i]=0;
+
+	  for (i=0;i<file_Len;i++)
+	  {
+		index_id=all_population_ID[i];
+		if (partit[index_id]>0)
+		{
+			j=temp_size_j[index_id];
+			if (temp_population_ID[index_id][j]==1)
+				all_computed_pop_ID[i]=partit[index_id];
+
+			temp_size_j[index_id]++;
+		}
+	  }
+
+	  printf("Number of groups after partitioning is %ld\n", num_computed_population);
+
+
+      free(size_p_2);
+
+	  free(aver);
+	  free(std);
+	  free(partit);
+
+	  free(center_p_1);
+	  free(center_p_2);
+	  free(center_p_3);
+
+
+
+	  for (i=0;i<num_population;i++)
+		  free(temp_population_ID[i]);
+	  free(temp_population_ID);
+
+	  for (i=0;i<num_population;i++)
+	  {
+		for (j=0;j<size_p[i];j++)
+		{
+			  free(ind_pop[i][j]);
+			  free(ind_pop_3[i][j]);
+		}
+	  }
+
+
+
+	  for (i=0;i<num_population;i++)
+	  {
+		  free(ind_pop[i]);
+		  free(ind_pop_3[i]);
+	  }
+	  free(ind_pop);
+	  free(ind_pop_3);
+
+
+
+
+	  for (i=0;i<2;i++)
+		  free(temp_population_center[i]);
+
+	  free(temp_population_center);
+
+	  free(temp_size_j);
+	  free(size_p);
+
+
+
+	  //update the IDs, Centers, and # of populations
+	  for (i=0;i<file_Len;i++)
+	  {
+		  all_population_ID[i]=all_computed_pop_ID[i];
+		  if (all_population_ID[i]>=num_computed_population)
+			  printf("all_population_ID[%ld]=%ld\n",i,all_population_ID[i]);
+	  }
+
+	  num_population=num_computed_population;
+
+	  free(all_computed_pop_ID);
+    //end partitioning
+  // since the num_population has changed, population_center needs to be redefined as below
+
+  population_center=(double **)malloc(sizeof(double*)*num_population);
+  memset(population_center,0,sizeof(double*)*num_population);
+  for (i=0;i<num_population;i++)
+  {
+     population_center[i]=(double*)malloc(sizeof(double)*num_dm);
+     memset(population_center[i],0,sizeof(double)*num_dm);
+  }
+
+
+  ID2Center_all(normalized_data,file_Len,num_dm,num_population,all_population_ID,population_center);
+
+
+
+  ////// end of further partitioning
+
+  ////////////////////////////////////////////////////////////
+  //  to further merge populations to avoid overpartitioning
+  //  Added June 20, 2010
+  ////////////////////////////////////////////////////////////
+
+
+
+  num_real_pop=num_population;
+  keep_merge=1;
+
+  if (num_pop>num_real_pop)
+  {
+		fprintf(stderr,"number of populations specified too large\n");
+		exit(0);
+  }
+
+  center_1=(double *)malloc(sizeof(double)*num_dm);
+  memset(center_1,0,sizeof(double)*num_dm);
+
+  center_2=(double *)malloc(sizeof(double)*num_dm);
+  memset(center_2,0,sizeof(double)*num_dm);
+
+  center_3=(double *)malloc(sizeof(double)*num_dm);
+  memset(center_3,0,sizeof(double)*num_dm);
+
+
+
+  while (((num_real_pop>num_pop) && (num_pop!=0)) || ((keep_merge==1) && (num_pop==0) && (num_real_pop>2)))
+  {
+
+	keep_merge=0;  //so, if no entering merge function, while will exit when num_pop==0
+
+	real_pop_center=(double **)malloc(sizeof(double*)*num_real_pop);
+    memset(real_pop_center,0,sizeof(double*)*num_real_pop);
+    for (i=0;i<num_real_pop;i++)
+    {
+      real_pop_center[i]=(double*)malloc(sizeof(double)*num_dm);
+      memset(real_pop_center[i],0,sizeof(double)*num_dm);
+    }
+
+	min_pop=(double **)malloc(sizeof(double*)*num_real_pop);
+    memset(min_pop,0,sizeof(double*)*num_real_pop);
+    for (i=0;i<num_real_pop;i++)
+    {
+      min_pop[i]=(double*)malloc(sizeof(double)*num_dm);
+      memset(min_pop[i],0,sizeof(double)*num_dm);
+    }
+
+	max_pop=(double **)malloc(sizeof(double*)*num_real_pop);
+    memset(max_pop,0,sizeof(double*)*num_real_pop);
+    for (i=0;i<num_real_pop;i++)
+    {
+      max_pop[i]=(double*)malloc(sizeof(double)*num_dm);
+      memset(max_pop[i],0,sizeof(double)*num_dm);
+    }
+
+	if (num_real_pop==num_population)
+	{
+		for (i=0;i<num_real_pop;i++)
+			for (j=0;j<num_dm;j++)
+				real_pop_center[i][j]=population_center[i][j];
+	}
+	else
+	{
+		ID2Center_all(normalized_data,file_Len,num_dm,num_real_pop,all_population_ID,real_pop_center);
+	}
+
+	for (i=0;i<num_real_pop;i++)
+	{
+		for (j=0;j<num_dm;j++)
+		{
+			min_pop[i][j]=MAX_VALUE;
+
+			max_pop[i][j]=0;
+		}
+	}
+
+	for (i=0;i<file_Len;i++)
+	{
+		index_id=all_population_ID[i];
+		for (j=0;j<num_dm;j++)
+		{
+			if (normalized_data[i][j]<min_pop[index_id][j])
+				min_pop[index_id][j]=normalized_data[i][j];
+
+			if (normalized_data[i][j]>max_pop[index_id][j])
+				max_pop[index_id][j]=normalized_data[i][j];
+		}
+	}
+
+/*	for (i=0;i<num_real_pop;i++)
+	{
+		for (j=0;j<num_dm;j++)
+		{
+			printf("min_pop is %f\t",min_pop[i][j]);
+			//printf("max_pop is %f\n",max_pop[i][j]);
+		}
+		printf("\n");
+	}
+*/
+
+
+	distance_pop=(double **)malloc(sizeof(double*)*num_real_pop);
+    memset(distance_pop,0,sizeof(double*)*num_real_pop);
+    for (i=0;i<num_real_pop;i++)
+    {
+      distance_pop[i]=(double*)malloc(sizeof(double)*num_real_pop);
+      memset(distance_pop[i],0,sizeof(double)*num_real_pop);
+    }
+
+	for (i=0;i<num_real_pop-1;i++)
+	{
+		for (j=i+1;j<num_real_pop;j++)
+		{
+		  distance=0;
+
+		  for (t=0;t<num_dm;t++)
+		  {
+			dist=real_pop_center[i][t]-real_pop_center[j][t];
+			distance=distance+dist*dist;
+		  }
+		  distance_pop[i][j]=distance;
+		  distance_pop[j][i]=distance;
+		}
+	}
+
+	if (num_real_pop>2)
+		num_checked_range=(long)((double)num_real_pop*(num_real_pop-1)/2.0); //to find the mergeable pair among the num_checked_range pairs of smallest distances
+	else
+		num_checked_range=1;
+
+	size_c=(long *)malloc(sizeof(long)*num_real_pop);
+    memset(size_c,0,sizeof(long)*num_real_pop);
+
+	for (i=0;i<file_Len;i++)
+	  size_c[all_population_ID[i]]++;
+
+	for (p=0;p<num_checked_range;p++)
+	{
+		current_smallest_dist=MAX_VALUE;
+
+		for (i=0;i<num_real_pop-1;i++)
+		{
+			for (j=i+1;j<num_real_pop;j++)
+			{
+				if (distance_pop[i][j]<current_smallest_dist)
+				{
+					current_smallest_dist=distance_pop[i][j];
+
+					temp_i=i;
+					temp_j=j;
+				}
+			}
+		}
+
+		if (p==0)
+		{
+			first_i=temp_i;
+			first_j=temp_j;
+		}
+
+		distance_pop[temp_i][temp_j]=MAX_VALUE+1; //make sure this pair won't be selected next time
+
+		//normalize and calculate std for temp_i and temp_j
+
+		//pick the largest 3 dimensions on standard deviation
+		d1=-1;
+		d2=-1;
+		d3=-1;
+
+		for (i=0;i<3;i++)
+		{
+			max_d_dist=0;
+			for (j=0;j<num_dm;j++)
+			{
+				if ((j!=d1) && (j!=d2))
+				{
+					temp=min(min_pop[temp_i][j],min_pop[temp_j][j]);
+					tmp=max(max_pop[temp_i][j],max_pop[temp_j][j]);
+					if (tmp<=temp)
+					{
+						//printf("min_pop[%d][%d]=%f \t min_pop[%d][%d]=%f \t max_pop[%d][%d]=%f \t max_pop[%d][%d]=%f\n",temp_i,j,min_pop[temp_i][j],temp_j, j, min_pop[temp_j][j],temp_i,j,max_pop[temp_i][j],temp_j,j,max_pop[temp_j][j]);
+						dist=0;
+					}
+					else
+						dist=(real_pop_center[temp_i][j]-real_pop_center[temp_j][j])/(tmp-temp);
+					if (dist<0)
+						dist=-dist;
+				}
+				else
+					dist=-1;
+
+				if (dist>max_d_dist)
+				{
+					max_d_dist=dist;
+					d_d=j;
+				}
+			}
+
+			if (i==0)
+				d1=d_d;
+			if (i==1)
+				d2=d_d;
+			if (i==2)
+				d3=d_d;
+		}
+
+		//printf("d1=%d;d2=%d;d3=%d\n",d1,d2,d3);
+
+		Ei=get_avg_dist(real_pop_center[temp_i], temp_i,temp_j, all_population_ID, num_real_pop,file_Len, num_dm, normalized_data, d1,d2,d3,size_c);
+		Ej=get_avg_dist(real_pop_center[temp_j], temp_i,temp_j, all_population_ID, num_real_pop,file_Len, num_dm, normalized_data, d1,d2,d3,size_c);
+
+		for (t=0;t<num_dm;t++)
+		{
+			center_1[t]=real_pop_center[temp_i][t]*0.25+real_pop_center[temp_j][t]*0.75;
+			center_2[t]=real_pop_center[temp_i][t]*0.5+real_pop_center[temp_j][t]*0.5;
+			center_3[t]=real_pop_center[temp_i][t]*0.75+real_pop_center[temp_j][t]*0.25;
+		}
+
+		E1=get_avg_dist(center_1, temp_i,temp_j, all_population_ID, num_real_pop,file_Len, num_dm, normalized_data, d1,d2,d3,size_c);
+
+		E2=get_avg_dist(center_2, temp_i,temp_j, all_population_ID, num_real_pop,file_Len, num_dm, normalized_data, d1,d2,d3,size_c);
+
+		E3=get_avg_dist(center_3, temp_i,temp_j, all_population_ID, num_real_pop,file_Len, num_dm, normalized_data, d1,d2,d3,size_c);
+
+		if (E1<E2)
+			Ep=E2;
+		else
+			Ep=E1;
+
+		Ep=max(Ep,E3); //Ep is the most sparse area
+
+		Ep=Ep*E_T;
+		//printf("Ep=%f;Ei=%f;Ej=%f\n",Ep,Ei,Ej);
+
+		if ((Ep<=Ei) || (Ep<=Ej))//if the most sparse area between i and j are still denser than one of them, temp_i and temp_j should be merged
+		{
+			keep_merge=1;
+			break;
+		}//end if (Ep)
+	} //end for p
+
+	//printf("keep_merge=%d\n",keep_merge);
+
+	for (i=0;i<num_real_pop;i++)
+	{
+		free(real_pop_center[i]);
+		free(distance_pop[i]);
+		free(min_pop[i]);
+		free(max_pop[i]);
+	}
+	free(real_pop_center);
+	free(min_pop);
+	free(max_pop);
+	free(distance_pop);
+	free(size_c);
+
+	//printf("temp_i=%d;temp_j=%d\n",temp_i,temp_j);
+
+	if (keep_merge)  //found one within p loop
+	{
+		for (i=0;i<file_Len;i++)
+		{
+			if (all_population_ID[i]>temp_j)
+			{
+				all_population_ID[i]=all_population_ID[i]-1;
+			}
+			else
+			{
+				if (all_population_ID[i]==temp_j)
+				{
+					all_population_ID[i]=temp_i;
+				}
+			}
+		}
+
+		num_real_pop--;
+	}
+	else
+	{
+		if ((num_pop!=0) && (num_pop<num_real_pop)) //not reach the specified num of pop
+		{
+			for (i=0;i<file_Len;i++)
+			{
+				if (all_population_ID[i]>first_j)
+				{
+					all_population_ID[i]=all_population_ID[i]-1;
+				}
+				else
+				{
+					if (all_population_ID[i]==first_j)
+					{
+						all_population_ID[i]=first_i;
+					}
+				}
+			}
+
+			num_real_pop--;
+
+
+
+		}
+	}
+		//printf("num_real_pop is %d\n",num_real_pop);
+
+  } //end of while
+
+
+
+  free(center_1);
+  free(center_2);
+  free(center_3);
+  printf("Final number of populations is %ld\n",num_real_pop);
+
+  new_population_center=(double **)malloc(sizeof(double*)*num_real_pop);
+  memset(new_population_center,0,sizeof(double*)*num_real_pop);
+  for (i=0;i<num_real_pop;i++)
+  {
+      new_population_center[i]=(double*)malloc(sizeof(double)*num_dm);
+      memset(new_population_center[i],0,sizeof(double)*num_dm);
+  }
+
+
+  ///////////////////////////////////////////
+  //End of population mapping
+  ///////////////////////////////////////////
+
+  show(input_data, all_population_ID, file_Len, num_real_pop, num_dm, para_name_string);
+
+  ID2Center_all(input_data,file_Len,num_dm,num_real_pop,all_population_ID,new_population_center);
+
+
+  f_cid=fopen("population_id.txt","w");
+  f_ctr=fopen("population_center.txt","w");
+  f_out=fopen("coordinates.txt","w");
+  f_results=fopen("flock_results.txt","w");
+
+/*
+  f_parameters=fopen("parameters.txt","w");
+  fprintf(f_parameters,"Number_of_Bins\t%d\n",num_bin);
+  fprintf(f_parameters,"Density\t%f\n",aver_index);
+  fclose(f_parameters);
+*/
+
+  for (i=0;i<file_Len;i++)
+	fprintf(f_cid,"%ld\n",all_population_ID[i]+1); //all_population_ID[i] changed to all_population_ID[i]+1 to start from 1 instead of 0: April 16, 2009
+
+  /*
+   * New to check for min/max to add to parameters.txt
+   *
+  */
+
+  fprintf(f_out,"%s\n",para_name_string);
+  //fprintf(f_results,"%s\tEvent\tPopulation\n",para_name_string);
+  fprintf(f_results,"%s\tPopulation\n",para_name_string);
+  for (i=0;i<file_Len;i++)
+  {
+	for (j=0;j<num_dm;j++)
+	{
+		if (input_data[i][j] < min) {
+			min = (int)input_data[i][j];
+		}
+		if (input_data[i][j] > max) {
+			max = (int)input_data[i][j];
+		}
+		if (j==num_dm-1)
+		{
+			fprintf(f_out,"%d\n",(int)input_data[i][j]);
+			fprintf(f_results,"%d\t",(int)input_data[i][j]);
+		}
+		else
+		{
+			fprintf(f_out,"%d\t",(int)input_data[i][j]);
+			fprintf(f_results,"%d\t",(int)input_data[i][j]);
+		}
+	}
+	//fprintf(f_results,"%ld\t",i + 1);
+	fprintf(f_results,"%ld\n",all_population_ID[i]+1); //all_population_ID[i] changed to all_population_ID[i]+1 to start from 1 instead of 0: April 16, 2009
+  }
+
+/*
+  f_parameters=fopen("parameters.txt","w");
+  fprintf(f_parameters,"Number_of_Bins\t%ld\n",num_bin);
+  fprintf(f_parameters,"Density\t%d\n",den_t_event);
+  fprintf(f_parameters,"Min\t%d\n",min);
+  fprintf(f_parameters,"Max\t%d\n",max);
+  fclose(f_parameters);
+*/
+
+  f_properties=fopen("fcs.properties","w");
+  fprintf(f_properties,"Bins=%ld\n",num_bin);
+  fprintf(f_properties,"Density=%d\n",den_t_event);
+  fprintf(f_properties,"Min=%d\n",min);
+  fprintf(f_properties,"Max=%d\n",max);
+  fprintf(f_properties,"Populations=%ld\n",num_real_pop);
+  fprintf(f_properties,"Events=%ld\n",file_Len);
+  fprintf(f_properties,"Markers=%ld\n",num_dm);
+  fclose(f_properties);
+
+  for (i=0;i<num_real_pop;i++) {
+	/* Add if we want to include population id in the output
+	*/
+	fprintf(f_ctr,"%ld\t",i+1);  //i changed to i+1 to start from 1 instead of 0: April 16, 2009
+
+	for (j=0;j<num_dm;j++) {
+		if (j==num_dm-1)
+			fprintf(f_ctr,"%.0f\n",new_population_center[i][j]);
+		else
+			fprintf(f_ctr,"%.0f\t",new_population_center[i][j]);
+	}
+  }
+
+  	//added April 16, 2009
+	f_mfi=fopen("MFI.txt","w");
+
+	for (i=0;i<num_real_pop;i++)
+	{
+		fprintf(f_mfi,"%ld\t",i+1);
+
+		for (j=0;j<num_dm;j++)
+		{
+			if (j==num_dm-1)
+				fprintf(f_mfi,"%.0f\n",new_population_center[i][j]);
+			else
+				fprintf(f_mfi,"%.0f\t",new_population_center[i][j]);
+		}
+	}
+	fclose(f_mfi);
+
+	//ended April 16, 2009
+
+  fclose(f_cid);
+  fclose(f_ctr);
+  fclose(f_out);
+  fclose(f_results);
+
+
+  for (i=0;i<num_population;i++)
+  	free(population_center[i]);
+
+  free(population_center);
+
+  for (i=0;i<num_real_pop;i++)
+	  free(new_population_center[i]);
+
+  free(new_population_center);
+
+  for (i=0;i<file_Len;i++)
+    free(normalized_data[i]);
+  free(normalized_data);
+
+  free(grid_populationID);
+
+  free(cluster_populationID);
+  free(grid_clusterID);
+  free(cluster_ID);
+
+  for (i=0;i<file_Len;i++)
+    free(input_data[i]);
+  free(input_data);
+
+  free(grid_ID);
+  free(population_ID);
+  free(all_population_ID);
+  free(eventID_To_denseventID);
+
+  ///////////////////////////////////////////////////////////
+  printf("Ending time:\t\t\t\t");
+  fflush(stdout);
+  system("/bin/date");
+
+  /*
+   * Windows version
+  _strtime( tmpbuf );
+  printf( "Ending time:\t\t\t\t%s\n", tmpbuf );
+  _strdate( tmpbuf );
+  printf( "Ending date:\t\t\t\t%s\n", tmpbuf );
+ */
+
+  return 0;
+}
--- a/src/flock2.c	Mon Feb 27 13:27:43 2017 -0500
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,3405 +0,0 @@
-///////////
-// Changes made:
-// 1. Added another parameter: number of populations
-// 2. Added a hierarchical merging step based on density change between centroids of two hyper-regions
-// 3. Picked the longest dimensions between the population centroids to judge whether the two parts should be merged
-// 4. Removed checking time parameter
-// 5. Output error to stderr
-// 6. Fixed the bug of density threshold always = 3
-// 7. Added another error (select_num_bin<min_grid) || (select_num_bin>max_grid) to STDERR
-// 8. Fixed a bug for 2D data by using K=e*K
-// 9. Added some header files, may not be necessary
-// 10. Added a lower bound (at least two) for number of populations
-/***************************************************************************************************************************************
-
-	FLOCK: FLOw cytometry Clustering without K (Named by: Jamie A. Lee and Richard H. Scheuermann)
-
-	Author: (Max) Yu Qian, Ph.D.
-
-	Copyright: Scheuermann Lab, Dept. of Pathology, UTSW
-
-	Development: November 2005 ~ Forever
-
-	Status: July 2010: Release 2.0
-
-	Usage: flock data_file
-		    Note: the input file format must be channel values and the delimiter between two values must be a tab.
-
-
-
-****************************************************************************************************************************************/
-
-#include <time.h>
-#include <stdio.h>
-#include <stdlib.h>
-#include <math.h>
-#include <string.h>
-#include <sys/stat.h>
-#include <unistd.h>
-#include <assert.h>
-
-
-
-#define DEBUG 0
-#define LINE_LEN 1024
-#define FILE_NAME_LEN 128
-#define PARA_NAME_LEN 64
-#define MAX_VALUE 1000000000
-#define MIN_GRID 6
-#define MAX_GRID 50
-#define E_T 1.0
-
-#define NORM_METHOD 2 //2 if z-score; 0 if no normalization; 1 if min-max
-#define KMEANS_TERM 10
-#define MAX_POP_NUM 128
-
-#ifndef max
-    #define max( a, b ) ( ((a) > (b)) ? (a) : (b) )
-#endif
-
-#ifndef min
-    #define min( a, b ) ( ((a) < (b)) ? (a) : (b) )
-#endif
-
-static long **Gr=0;
-static long *gcID = 0;          /* grid cluster IDs */
-static long *cluster_count=0;   /* count of nodes per cluster */
-static long ndense=0;
-static long ndim=0;
-/* cid changes between depth-first searches, but is constant within a
-   single search, so it goes here. */
-static long cid=0;
-/* Do a depth-first search for a single connected component in graph
- * G.  Start from node, tag the nodes found with cid, and record
- * the tags in grid_clusterID.  Also, record the node count in
- * cluster_count.  If we find a node that has already been assigned to
- * a cluster, that means we're merging two clusters, so zero out the
- * old cid's node count.
- *
- * Note that our graph is constructed as a DAG, so we can be
- * guaranteed to terminate without checking for cycles.
- *
- * Note2: this function can potentially recurse to depth = ndense.
- * Plan stack size accordingly.
- *
- * Output:
- *
- * grid_clusterID[] -- array where we tag the nodes.
- * cluster_count[]  -- count of the number of nodes per cluster.
- */
-static void merge_cluster(long from, long into)
-{
-  int i;
-
-  for(i=0; i<ndense; ++i)
-    if(gcID[i] == from)
-      gcID[i] = into;
-}
-
-void depth_first(long node)
-{
-  long i;
-
-  if(gcID[node] == cid)         // we're guaranteed no cycles, but it is possible to reach a node
-    return;                     // through two different paths in the same cluster.  This early
-                                // return saves us some unneeded work.
-
-  /* Check to see if we are merging a cluster */
-  if(gcID[node] >= 0) {
-    /* We are, so zero the count for the old cluster. */
-    cluster_count[ gcID[node] ] = 0;
-    merge_cluster(gcID[node], cid);
-    return;
-  }
-
-  /* Update for this node */
-  gcID[node] = cid;
-  cluster_count[cid]++;
-
-  /* Recursively search the child nodes */
-  for(i=0; i<ndim; ++i)
-    if(Gr[node][i] >= 0)      /* This is a child node */
-      depth_first(Gr[node][i]);
-}
-
-void bail(const char *msg)
-{
-  fprintf(stderr,"%s",msg);
-  exit(0);
-}
-
-
-static void check_clusters(long *gcID, int ndense)
-{
-  int i;
-
-  for(i=0; i<ndense; ++i)
-    if(gcID[i] < 0) {
-      fprintf(stderr,"faulty cluster id at i= %d\n",i);
-      exit(0);
-    }
-}
-
-
-
-long find_connected(long **G, long n_dense_grids, long num_dm, long *grid_clusterID)
-{
-  long nclust=0;                  /* number of clusters found */
-  long i;
-  long *subfac;
-  long clustid=0;
-  int subval=0,nempty=0;
-
-  int sz = n_dense_grids*sizeof(long);
-  cluster_count = malloc(sz);
-  if(!cluster_count)
-    bail("find_connected: Unable to allocate %zd bytes.\n");
-  memset(cluster_count,0,sz);
-
-  /* set up the statics that will be used in the DFS */
-  Gr=G;
-  gcID = grid_clusterID;
-  ndense = n_dense_grids;
-  ndim = num_dm;
-
-  for(i=0;i<ndense;++i)
-    grid_clusterID[i] = -1;
-
-  for(i=0;i<ndense;++i) {
-    if(grid_clusterID[i] < 0) {  /* grid hasn't been assigned yet */
-      cid = nclust++;
-      depth_first(i);
-    }
-  }
-
-
-
-  /* At this point we probably have some clusters that are empty due to merging.
-     We want to compact the cluster numbering to eliminate the empty clusters. */
-
-  subfac = malloc(sz);
-  if(!subfac)
-    bail("find_connected: Unable to allocate %zd bytes.\n");
-  subval=0;
-  nempty=0;
-
-  /* cluster #i needs to have its ID decremented by 1 for each empty cluster with
-     ID < i.  Precaclulate the decrements in this loop: */
-  for(i=0;i<nclust;++i) {
-    //clustid = grid_clusterID[i];
-    if(cluster_count[i] == 0) {
-      subval++;
-      nempty++;
-    }
-    subfac[i] = subval;
-  }
-
-  //printf("nempty is %d\n",nempty);
-
-  /* Now apply the decrements to all of the dense grids */
-  for(i=0;i<ndense;++i) {
-    clustid = grid_clusterID[i];
-    grid_clusterID[i] -= subfac[clustid];
-  }
-
-
-
-  /* correct the number of clusters found */
-  nclust -= nempty;
-
-  //printf("nclust is %d\n",nclust);
-
-  return nclust;
-}
-
-/************************************* Read basic info of the source file **************************************/
-/************************************* Read basic info of the source file **************************************/
-void getfileinfo(FILE *f_src, long *file_Len, long *num_dm, char *name_string, long *time_ID)
-{
-  char src[LINE_LEN];
-  char current_name[64];
-  char prv;
-
-  long num_rows=0;
-  long num_columns=0;
-  long ch='\n';
-  long prev='\n';
-  long time_pos=0;
-  long i=0;
-  long j=0;
-  int sw=0;
-
-  src[0]='\0';
-  fgets(src, LINE_LEN, f_src);
-
-  name_string[0]='\0';
-  current_name[0]='\0';
-  prv='\n';
-
-  while ((src[i]==' ') || (src[i]=='\t')) //skip space and tab characters
-    i++;
-
-  while ((src[i]!='\0') && (src[i]!='\n')) //repeat until the end of the line
-    {
-      current_name[j]=src[i];
-
-      if ((src[i]=='\t') && (prv!='\t')) //a complete word
-        {
-          current_name[j]='\0';
-
-          if (0!=strcmp(current_name,"Time"))
-            {
-              num_columns++; //num_columns does not inlcude the column of Time
-              time_pos++;
-              if (sw) {
-                  strcat(name_string,"\t");
-              }
-              strcat(name_string,current_name);
-              sw = 1;
-            }
-          else
-            {
-              *time_ID=time_pos;
-            }
-
-          current_name[0]='\0';
-          j=0;
-        }
-
-      if ((src[i]=='\t') && (prv=='\t')) //a duplicate tab or space
-        {
-          current_name[0]='\0';
-          j=0;
-        }
-
-      if (src[i]!='\t')
-        j++;
-
-      prv=src[i];
-      i++;
-    }
-
-  //name_string[j]='\0';
-  if (prv!='\t') //the last one hasn't been retrieved
-    {
-      current_name[j]='\0';
-      if (0!=strcmp(current_name,"Time"))
-        {
-          num_columns++;
-          strcat(name_string,"\t");
-          strcat(name_string,current_name);
-          time_pos++;
-        }
-      else
-        {
-          *time_ID=time_pos;
-        }
-    }
-  if (DEBUG==1)
-    {
-      printf("time_ID is %ld\n",*time_ID);
-      printf("name_string is %s\n",name_string);
-    }
-
-  //start computing # of rows
-
-  while ((ch = fgetc(f_src))!= EOF )
-    {
-      if (ch == '\n')
-        {
-          ++num_rows;
-        }
-      prev = ch;
-    }
-  if (prev!='\n')
-    ++num_rows;
-
-   if (num_rows<50)
-  {
-    fprintf(stderr,"Number of events in the input file is too few and should not be processed!\n"); //modified on July 23, 2010
-	exit(0);
-  }
-
-  *file_Len=num_rows;
-  *num_dm=num_columns;
-
-  printf("original file size is %ld; number of dimensions is %ld\n", *file_Len, *num_dm);
-}
-
-
-
-/************************************* Read the source file into uncomp_data **************************************/
-void readsource(FILE *f_src, long file_Len, long num_dm, double **uncomp_data, long time_ID)
-{
-  //long time_pass=0; //to mark whether the time_ID has been passed
-  long index=0;
-
-  long i=0;
-  long j=0;
-  long t=0;
-
-  char src[LINE_LEN];
-  char xc[LINE_LEN/10];
-
-  src[0]='\0';
-  fgets(src,LINE_LEN, f_src); //skip the first line about parameter names
-
-  while (!feof(f_src) && (index<file_Len)) //index = 0, 1, ..., file_Len-1
-    {
-      src[0]='\0';
-      fgets(src,LINE_LEN,f_src);
-      i=0;
-      //time_pass=0;
-
-      //if (time_ID==-1)  //there is no time_ID
-      //  {
-          for (t=0;t<num_dm;t++)
-            {
-              xc[0]='\0';
-              j=0;
-              while ((src[i]!='\0') && (src[i]!='\n') && (src[i]!=' ') && (src[i]!='\t'))
-                {
-                  xc[j]=src[i];
-                  i++;
-                  j++;
-                }
-
-              xc[j]='\0';
-              i++;
-
-              uncomp_data[index][t]=atof(xc);
-            }
-       // }
-      /*else
-        {
-          for (t=0;t<=num_dm;t++) //the time column needs to be skipped, so there are num_dm+1 columns
-            {
-              xc[0]='\0';
-              j=0;
-              while ((src[i]!='\0') && (src[i]!='\n') && (src[i]!=' ') && (src[i]!='\t'))
-                {
-                  xc[j]=src[i];
-                  i++;
-                  j++;
-                }
-
-              xc[j]='\0';
-              i++;
-
-              if (t==time_ID)
-                {
-                  time_pass=1;
-                  continue;
-                }
-
-              if (time_pass)
-                uncomp_data[index][t-1]=atof(xc);
-              else
-                uncomp_data[index][t]=atof(xc);
-            }
-        }*/ //commented by Yu Qian on Aug 31, 2010 as we do not want to check time_ID anymore
-      index++;
-      //fprintf(fout_ID,"%s",src);
-    } //end of while
-
-  if (DEBUG == 1)
-    {
-      printf("the last line of the source data is:\n");
-      for (j=0;j<num_dm;j++)
-        printf("%f ",uncomp_data[index-1][j]);
-      printf("\n");
-    }
-}
-
-
-/**************************************** Normalization ******************************************/
-void tran(double **orig_data, long file_Len, long num_dm, long norm_used, double **matrix_to_cluster)
-{
-  long i=0;
-  long j=0;
-
-  double biggest=0;
-  double smallest=MAX_VALUE;
-
-  double *aver; //average of each column
-  double *std; //standard deviation of each column
-
-  aver=(double*)malloc(sizeof(double)*file_Len);
-  memset(aver,0,sizeof(double)*file_Len);
-
-  std=(double*)malloc(sizeof(double)*file_Len);
-  memset(std,0,sizeof(double)*file_Len);
-
-  if (norm_used==2) //z-score normalization
-    {
-      for (j=0;j<num_dm;j++)
-        {
-          aver[j]=0;
-          for (i=0;i<file_Len;i++)
-            aver[j]=aver[j]+orig_data[i][j];
-          aver[j]=aver[j]/(double)file_Len;
-
-          std[j]=0;
-          for (i=0;i<file_Len;i++)
-            std[j]=std[j]+((orig_data[i][j]-aver[j])*(orig_data[i][j]-aver[j]));
-          std[j]=sqrt(std[j]/(double)file_Len);
-
-          for (i=0;i<file_Len;i++)
-            matrix_to_cluster[i][j]=(orig_data[i][j]-aver[j])/std[j];  //z-score normalization
-        }
-    }
-
-  if (norm_used==1) //0-1 min-max normalization
-    {
-      for (j=0;j<num_dm;j++)
-        {
-          biggest=0;
-          smallest=MAX_VALUE;
-          for (i=0;i<file_Len;i++)
-            {
-              if (orig_data[i][j]>biggest)
-                biggest=orig_data[i][j];
-              if (orig_data[i][j]<smallest)
-                smallest=orig_data[i][j];
-            }
-
-          for (i=0;i<file_Len;i++)
-            {
-              if (biggest==smallest)
-                matrix_to_cluster[i][j]=biggest;
-              else
-                matrix_to_cluster[i][j]=(orig_data[i][j]-smallest)/(biggest-smallest);
-            }
-        }
-    }
-
-  if (norm_used==0) //no normalization
-    {
-      for (i=0;i<file_Len;i++)
-        for (j=0;j<num_dm;j++)
-          matrix_to_cluster[i][j]=orig_data[i][j];
-    }
-
-}
-
-
-
-/********************************************** RadixSort *******************************************/
-/* Perform a radix sort using each dimension from the original data as a radix.
- * Outputs:
- * sorted_seq   -- a permutation vector mapping the ordered list onto the original data.
- *                  (sorted_seq[i] -> index in the original data of the ith element of the ordered list)
- * grid_ID      -- mapping between the original data and the "grids" (see below) found as a byproduct
- *                  of the sorting procedure.
- * num_nonempty -- the number of grids that occur in the data (= the number of distinct values assumed
- *                  by grid_ID)
- */
-
-void radixsort_flock(long **position,long file_Len,long num_dm,long num_bin,long *sorted_seq,long *num_nonempty,long *grid_ID)
-{
-  long i=0;
-  long length=0;
-  long start=0;
-  long prev_ID=0;
-  long curr_ID=0;
-
-  long j=0;
-  long t=0;
-  long p=0;
-  long loc=0;
-  long temp=0;
-  long equal=0;
-
-  long *count; //count[i]=j means there are j numbers having value i at the processing digit
-  long *index; //index[i]=j means the starting position of grid i is j
-  long *cp; //current position
-  long *mark; //mark[i]=0 means it is not an ending point of a part, 1 means it is (a "part" is a group of items with identical bins for all dimensions)
-  long *seq; //temporary sequence
-
-  count=(long*)malloc(sizeof(long)*num_bin);
-  memset(count,0,sizeof(long)*num_bin);
-
-  cp=(long*)malloc(sizeof(long)*num_bin);
-  memset(cp,0,sizeof(long)*num_bin);
-
-  index=(long*)malloc(sizeof(long)*num_bin); // initialized below
-
-  seq=(long*)malloc(sizeof(long)*file_Len);
-  memset(seq,0,sizeof(long)*file_Len);
-
-  mark=(long*)malloc(sizeof(long)*file_Len);
-  memset(mark,0,sizeof(long)*file_Len);
-
-  for (i=0;i<file_Len;i++)
-    {
-      sorted_seq[i]=i;
-      mark[i]=0;
-      seq[i]=0;
-    }
-  for (i=0;i<num_bin;i++)
-    {
-      index[i]=0;
-      cp[i]=0;
-      count[i]=0;
-    }
-
-  for (j=0;j<num_dm;j++)
-    {
-      if (j==0) //compute the initial values of mark
-        {
-          for (i=0;i<file_Len;i++)
-            count[position[i][j]]++; // initialize the count to the number of items in each bin of the 0th dimension
-
-          index[0] = 0;
-          for (i=0;i<num_bin-1;i++)
-            {
-              index[i+1]=index[i]+count[i];  //index[k]=x means k segment starts at x (in the ordered list)
-              if ((index[i+1]>0) && (index[i+1]<=file_Len))
-                {
-                  mark[index[i+1]-1]=1; // Mark the end of the segment in the ordered list
-                }
-              else
-                {
-                  printf("out of myboundary for mark at index[i+1]-1.\n");
-                }
-            }
-          mark[file_Len-1]=1;
-
-          for (i=0;i<file_Len;i++)
-            {
-              /* Build a permutation vector for the partially ordered data.  Store the PV in sorted_seq */
-              loc=position[i][j];
-              temp=index[loc]+cp[loc]; //cp[i]=j means the offset from the starting position of grid i is j
-              sorted_seq[temp]=i;  //sorted_seq[i]=temp is also another way to sort
-              cp[loc]++;
-            }
-        }
-      else
-        {
-          //reset count, index, loc, temp, cp, start, and length
-          length=0;
-          loc=0;
-          temp=0;
-          start=0;
-          for (p=0;p<num_bin;p++)
-            {
-              cp[p]=0;
-              count[p]=0;
-              index[p]=0;
-            }
-
-          for (i=0;i<file_Len;i++)
-            {
-              long iperm = sorted_seq[i]; // iperm allows us to traverse the data in sorted order.
-              if (mark[i]!=1)
-                {
-                  /* Count the number of items in each bin of
-                     dimension j, BUT we are going to reset at the end
-                     of each "part".  Thus, the total effect is to do
-                     a sort by bin on the jth dimension for each group
-                     of data that has been identical for the
-                     dimensions processed up to this point.  This is
-                     the standard radix sort procedure, but doing it
-                     this way saves us having to allocate buckets to
-                     hold the data in each group of "identical-so-far"
-                     elements. */
-                  count[position[iperm][j]]++;  //count[position[i][j]]++;
-                  length++;                     // This is the total length of the part, irrespective of the value of the jth component
-                                                // (actually, less one, since we don't increment for the final element below)
-                }
-              if (mark[i]==1)
-                {
-                  //length++;
-                  count[position[iperm][j]]++;//count[position[i][j]]++;  //the current point must be counted in
-                  start=i-length; //this part starts from start to i: [start,i]
-                  /* Now we sort on the jth radix, just like we did for the 0th above, but we restrict it to just the current part.
-                     This would be a lot more clear if we broke this bit of code out into a separate function and processed recursively,
-                     plus we could multi-thread over the parts.  (Hmmm...)
-                  */
-                  index[0] = start; // Let index give the offset within the whole ordered list.
-                  for (t=0;t<num_bin-1;t++)
-                    {
-                      index[t+1]=index[t]+count[t];
-
-                      if ((index[t+1]<=file_Len) && (index[t+1]>0))
-                        {
-                          mark[index[t+1]-1]=1; // update the part boundaries to include the differences in the current radix.
-                        }
-
-                    }
-                  mark[i]=1;
-
-                  /* Update the permutation vector for the current part (i.e., from start to i).  By the time we finish the loop over i
-                     the PV will be completely updated for the partial ordering up to the current radix. */
-                  for (t=start;t<=i;t++)
-                    {
-                      loc=position[sorted_seq[t]][j];//loc=position[t][j];
-                      temp=index[loc]+cp[loc];
-                      if ((temp<file_Len) && (temp>=0))
-                        {
-                          // seq is a temporary because we have to maintain the old PV until we have finished this step.
-                          seq[temp]=sorted_seq[t];  //sorted_seq[i]=temp is also another way to sort
-                          cp[loc]++;
-                        }
-                      else
-                        {
-                          printf("out of myboundary for seq at temp.\n");
-                        }
-                    }
-
-                  for (t=start;t<=i;t++)
-                    {
-                      // copy the temporary back into sorted_seq.  sorted_seq is now updated for radix j up through
-                      // entry i in the ordered list.
-                      if ((t>=0) && (t<file_Len))
-                        sorted_seq[t]=seq[t];
-                      else
-                        printf("out of myboundary for seq and sorted_seq at t.\n");
-                    }
-                  //reset count, index, seq, length, and cp
-                  length=0;
-                  loc=0;
-                  temp=0;
-                  for (p=0;p<num_bin;p++)
-                    {
-                      cp[p]=0;
-                      count[p]=0;
-                      index[p]=0;
-                    }
-                }
-            }//end for i
-        }//end else
-    }//end for j
-
-  /* sorted_seq[] now contains the ordered list for all radices.  mark[] gives the boundaries between groups of elements that are
-     identical over all radices (= dimensions in the original data) (although it appears we aren't going to make use of this fact) */
-
-  for (i=0;i<file_Len;i++)
-    grid_ID[i]=0; //in case the initial value hasn't been assigned
-  *num_nonempty=1; //starting from 1!
-
-  /* assign the "grid" identifiers for all of the data.  A grid will be what we were calling a "part" above.  We will number them
-     serially and tag the *unordered* data with the grid IDs.  We will also count the number of populated grids (in general there will
-     be many possible combinations of bin values that simply never occur) */
-
-  for (i=1;i<file_Len;i++)
-    {
-      equal=1;
-      prev_ID=sorted_seq[i-1];
-      curr_ID=sorted_seq[i];
-      for (j=0;j<num_dm;j++)
-        {
-          if (position[prev_ID][j]!=position[curr_ID][j])
-            {
-              equal=0;  //not equal
-              break;
-            }
-        }
-
-      if (equal)
-        {
-          grid_ID[curr_ID]=grid_ID[prev_ID];
-        }
-      else
-        {
-          *num_nonempty=*num_nonempty+1;
-          grid_ID[curr_ID]=grid_ID[prev_ID]+1;
-        }
-      //all_grid_vol[grid_ID[curr_ID]]++;
-    }
-
-  //free memory
-  free(count);
-  free(index);
-  free(cp);
-  free(seq);
-  free(mark);
-
-}
-
-/********************************************** Compute Position of Events ************************************************/
-void compute_position(double **data_in, long file_Len, long num_dm, long num_bin, long **position, double *interval)
-{
-  /* What we are really doing here is binning the data, with the bins
-     spanning the range of the data and number of bins = num_bin */
-  long i=0;
-  long j=0;
-
-  double *small; //small[j] is the smallest value within dimension j
-  double *big; //big[j] is the biggest value within dimension j
-
-  small=(double*)malloc(sizeof(double)*num_dm);
-  memset(small,0,sizeof(double)*num_dm);
-
-  big=(double*)malloc(sizeof(double)*num_dm);
-  memset(big,0,sizeof(double)*num_dm);
-
-
-  for (j=0;j<num_dm;j++)
-    {
-      big[j]=MAX_VALUE*(-1);
-      small[j]=MAX_VALUE;
-      for (i=0;i<file_Len;i++)
-        {
-          if (data_in[i][j]>big[j])
-            big[j]=data_in[i][j];
-
-          if (data_in[i][j]<small[j])
-            small[j]=data_in[i][j];
-        }
-
-      interval[j]=(big[j]-small[j])/(double)num_bin;	//interval is computed using the biggest value and smallest value instead of the channel limit
-      /* XXX: I'm pretty sure the denominator of the fraction above should be num_bin-1. */
-    }
-
-  for (j=0;j<num_dm;j++)
-  {
-     for (i=0;i<file_Len;i++)
-     {
-        if (data_in[i][j]>=big[j])
-           position[i][j]=num_bin-1;
-        else
-        {
-           position[i][j]=(long)((data_in[i][j]-small[j])/interval[j]); //position[i][j]=t means point i is at the t grid of dimensional j
-           if ((position[i][j]>=num_bin) || (position[i][j]<0))
-           {
-               //printf("position mis-computed in density analysis!\n");
-               //exit(0);
-			   fprintf(stderr,"Incorrect input file format or input parameters (number of bins overflows)!\n"); //modified on July 23, 2010
-				exit(0);
-           }
-        }
-     }
-  }
-
-
-  free(small);
-  free(big);
-}
-
-/********************************************** select_bin to select the number of bins **********************************/
-//num_bin=select_bin(normalized_data, file_Len, num_dm, MIN_GRID, MAX_GRID, position, sorted_seq, all_grid_ID, &num_nonempty);
-/* Determine the number of bins to use in each dimension.  Additionally sort the data elements according to the binned
- * values, and partition the data into "grids" with identical (binned) values.  We try progressively more bins until we
- * maximize a merit function, then return the results obtained using the optimal number of bins.
- *
- * Outputs:
- * position     -- binned data values
- * sorted_seq   -- permutation vector mapping the ordered list to the original data
- * all_grid_ID  -- grid to which each data element was assigned.
- * num_nonempty -- number of distinct values assumed by all_grid_ID
- * interval     -- bin width for each data dimension
- * return value -- the number of bins selected.
- */
-
-long select_bin(double **normalized_data, long file_Len, long num_dm, long min_grid, long max_grid, long **position, long *sorted_seq,
-                long *all_grid_ID, long *num_nonempty, double *interval, long user_num_bin)
-{
-
-  long num_bin=0;
-  long select_num_bin=0;
-  long m=0;
-  long n=0;
-
-  long i=0;
-  long bin_scope=0;
-  long temp_num_nonempty=0;
-
-  long *temp_grid_ID;
-  long *temp_sorted_seq;
-  long **temp_position;
-
-  //sorted_seq[i]=j means the event j ranks i
-
-  double temp_index=0;
-  double *bin_index;
-  double *temp_interval;
-
-
-  temp_grid_ID=(long *)malloc(sizeof(long)*file_Len);
-  memset(temp_grid_ID,0,sizeof(long)*file_Len);
-
-  temp_sorted_seq=(long *)malloc(sizeof(long)*file_Len);
-  memset(temp_sorted_seq,0,sizeof(long)*file_Len);
-
-  temp_position=(long **)malloc(sizeof(long*)*file_Len);
-  memset(temp_position,0,sizeof(long*)*file_Len);
-  for (m=0;m<file_Len;m++)
-    {
-      temp_position[m]=(long*)malloc(sizeof(long)*num_dm);
-      memset(temp_position[m],0,sizeof(long)*num_dm);
-    }
-
-  temp_interval=(double*)malloc(sizeof(double)*num_dm);
-  memset(temp_interval,0,sizeof(double)*num_dm);
-
-  bin_scope=max_grid-min_grid+1;
-  bin_index=(double *)malloc(sizeof(double)*bin_scope);
-  memset(bin_index,0,sizeof(double)*bin_scope);
-
-  i=0;
-
-  for (num_bin=min_grid;num_bin<=max_grid;num_bin++)
-    {
-
-	  temp_num_nonempty=0;
-	   /* compute_position bins the data into num_bin bins.  Each
-         dimension is binned independently.
-
-         Outputs:
-         temp_position[i][j] -- bin for the jth component of data element i.
-         temp_interval[j]    -- bin-width for the jth component
-      */
-      compute_position(normalized_data, file_Len, num_dm, num_bin, temp_position, temp_interval);
-      radixsort_flock(temp_position,file_Len,num_dm,num_bin,temp_sorted_seq,&temp_num_nonempty,temp_grid_ID);
-
-      /* our figure of merit is the number of non-empty grids divided by number of bins per dimension.
-         We declare victory when we have found a local maximum */
-      bin_index[i]=((double)temp_num_nonempty)/((double)num_bin);
-	  if ((double)(temp_num_nonempty)>=(double)(file_Len)*0.95)
-		  break;
-      if ((bin_index[i]<temp_index) && (user_num_bin==0))
-         break;
-	  if ((user_num_bin==num_bin-1) && (user_num_bin!=0))
-		 break;
-
-      /* Since we have accepted this trial bin, copy all the temporary results into
-         the output buffers */
-      memcpy(all_grid_ID,temp_grid_ID,sizeof(long)*file_Len);
-      memcpy(sorted_seq,temp_sorted_seq,sizeof(long)*file_Len);
-      memcpy(interval,temp_interval,sizeof(double)*num_dm);
-
-      for (m=0;m<file_Len;m++)
-        for (n=0;n<num_dm;n++)
-          position[m][n]=temp_position[m][n];
-
-      temp_index=bin_index[i];
-      select_num_bin=num_bin;
-      num_nonempty[0]=temp_num_nonempty;
-      i++;
-    }
-
-   if ((select_num_bin<min_grid) || (select_num_bin>max_grid))
-  {
-    fprintf(stderr,"Number of events collected is too few in terms of number of markers used. The file should not be processed!\n"); //modified on Nov 04, 2010
-	exit(0);
-  }
-
-  if (temp_index==0)
-  {
-	 fprintf(stderr,"Too many dimensions with too few events in the input file, or a too large number of bins used.\n"); //modified on July 23, 2010
-	 exit(0);
-  }
-
-  free(temp_grid_ID);
-  free(temp_sorted_seq);
-  free(bin_index);
-  free(temp_interval);
-
-  for (m=0;m<file_Len;m++)
-    free(temp_position[m]);
-  free(temp_position);
-
-  return select_num_bin;
-}
-
-/************************************* Select dense grids **********************************/
-// compute num_dense_grids, num_dense_events, dense_grid_reverse, and all_grid_vol
-// den_cutoff=select_dense(file_Len, all_grid_ID, num_nonempty, &num_dense_grids, &num_dense_events, dense_grid_reverse);
-/*
- * Prune away grids that are insufficiently "dense" (i.e., contain too few data items)
- *
- * Outputs:
- * num_dense_grids    -- number of dense grids
- * num_dense_events   -- total number of data items in all dense grids
- * dense_grid_reverse -- mapping from list of all grids to list of dense grids.
- * return value       -- density cutoff for separating dense from non-dense grids.
- */
-
-int select_dense(long file_Len, long *all_grid_ID, long num_nonempty, long *num_dense_grids, long *num_dense_events, long *dense_grid_reverse, int den_t_event)
-{
-
-
-  long i=0;
-  long vol_ID=0;
-  long biggest_size=0; //biggest grid_size, to define grid_size_index
-  long biggest_index=0;
-  //long actual_threshold=0; //the actual threshold on grid_size, e.g., 1 implies 1 event in the grid
-  //long num_remain=0; //number of remaining grids with different density thresholds
-  long temp_num_dense_grids=0;
-  long temp_num_dense_events=0;
-
-  long *grid_size_index;
-  long *all_grid_vol;
-  long *grid_density_index;
-
-  //double den_average=0;
- // double avr_index=0;
-
-
-  /////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
-  // Compute all_grid_vol
-  /////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
-  all_grid_vol=(long *)malloc(sizeof(long)*num_nonempty);
-  memset(all_grid_vol,0,sizeof(long)*num_nonempty);
-
-  /* Grid "volume" is just the number of data contained in the grid. */
-  for (i=0;i<file_Len;i++)
-    {
-      vol_ID=all_grid_ID[i]; //vol_ID=all_grid_ID[sorted_seq[i]];
-      all_grid_vol[vol_ID]++;  //all_grid_vol[i]=j means grid i has j points
-    }
-
-
-
-  //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
-  // Compute grid_size_index (histogram of grid sizes)
-  //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
-
-  for (i=0;i<num_nonempty;i++)
-    {
-      if (biggest_size<all_grid_vol[i])
-        {
-          biggest_size=all_grid_vol[i];
-        }
-    }
-
-   if (biggest_size<3)
-  {
-	 fprintf(stderr,"Too many dimensions with too few events in the input file, or a too large number of bins used.\n"); //modified on July 23, 2010
-	 exit(0);
-  }
-
-
-  grid_size_index=(long*)malloc(sizeof(long)*biggest_size);
-  memset(grid_size_index,0,sizeof(long)*biggest_size);
-
-  for (i=0;i<num_nonempty;i++)
-    {
-      grid_size_index[all_grid_vol[i]-1]++; //grid_size_index[0]=5 means there are 5 grids having size 1
-    }
-
-
-
-  ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
-  // Compute den_cutoff
-  ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
-
-  grid_density_index=(long *)malloc(sizeof(long)*(biggest_size-2));//from event 2 to biggest_size-1, i.e., from 0 to biggest_size-3
-  memset(grid_density_index,0,sizeof(long)*(biggest_size-2));
-
-  if (den_t_event==0)
-  {
-	  biggest_index=0;
-
-	  for (i=2;i<biggest_size-1;i++) //the grid with 1 event will be skipped, i.e., grid_density_index[0] won't be defined
-	  {
-		  grid_density_index[i-1]=(grid_size_index[i-1]+grid_size_index[i+1]-2*grid_size_index[i]);
-		  if (biggest_index<grid_density_index[i-1])
-		  {
-			biggest_index=grid_density_index[i-1];
-			den_t_event=i+1;
-		  }
-	  }
-  }
-
-  if (den_t_event==0) //if biggest_size==3
-  {
-	 fprintf(stderr,"the densest hyperregion has only 3 events, smaller than the user-specified value. Therefore the density threshold is automatically changed to 3.\n");
-	 den_t_event=3;
-  }
-
-  for (i=0;i<num_nonempty;i++)
-	  if (all_grid_vol[i]>=den_t_event)
-		temp_num_dense_grids++;
-
-  if (temp_num_dense_grids<=1)
-  {
-	  //exit(0);
-	  //printf("a too high density threshold is set! Please decrease your density threshold.\n");
-	  fprintf(stderr,"a too high density threshold! Please decrease your density threshold.\n"); //modified on July 23, 2010
-	  exit(0);
-  }
-
-   if (temp_num_dense_grids>=100000)
-  {
-	  //modified on July 23, 2010
-	  //printf("a too low density threshold is set! Please increase your density threshold.\n");
-	  //exit(0);
-	  fprintf(stderr,"a too low density threshold! Please increase your density threshold.\n"); //modified on July 23, 2010
-	  exit(0);
-  }
-
-  ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
-  // Compute dense_grid_reverse
-  ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
-  temp_num_dense_grids=0;
-  temp_num_dense_events=0;
-  for (i=0;i<num_nonempty;i++)
-    {
-      dense_grid_reverse[i]=-1;
-
-      if (all_grid_vol[i]>=den_t_event)
-        {
-          dense_grid_reverse[i]=temp_num_dense_grids;  //dense_grid_reverse provides a mapping from all nonempty grids to dense grids.
-          temp_num_dense_grids++;
-          temp_num_dense_events+=all_grid_vol[i];
-        }
-    }
-
-  num_dense_grids[0]=temp_num_dense_grids;
-  num_dense_events[0]=temp_num_dense_events;
-
-  free(grid_size_index);
-  free(all_grid_vol);
-
-  return den_t_event;
-}
-
-/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
-// Compute densegridID_To_gridevent and eventID_To_denseventID
-/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
-//	grid_To_event(file_Len, dense_grid_reverse, all_grid_ID, eventID_To_denseventID, densegridID_To_gridevent);
-/*
- * Filter the data so that only the data belonging to dense grids is left
- *
- * Output:
- * eventID_To_denseeventID   -- mapping from original event ID to ID in list containing only events contained in dense grids.
- * densegridID_To_gridevent  -- mapping from dense grids to prototype members of the grids.
- *
- */
-
-void grid_To_event(long file_Len, long *dense_grid_reverse, long *all_grid_ID, long *eventID_To_denseventID, long *densegridID_To_gridevent)
-{
-  long i=0;
-  long dense_grid_ID=0;
-  long dense_event_ID=0;
-
-  for (i=0;i<file_Len;i++)
-    {
-      dense_grid_ID=dense_grid_reverse[all_grid_ID[i]];
-      eventID_To_denseventID[i]=-1;
-      if (dense_grid_ID!=-1) //for point (i) belonging to dense grids
-        {
-          eventID_To_denseventID[i]=dense_event_ID;
-          dense_event_ID++;
-
-          if (densegridID_To_gridevent[dense_grid_ID]==-1) //for point i that hasn't been selected
-            densegridID_To_gridevent[dense_grid_ID]=i; //densegridID_To_gridevent maps dense_grid_ID to its representative point
-        }
-    }
-
-
-}
-
-/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
-// Compute dense_grid_seq
-/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
-//	generate_grid_seq(file_Len, num_dm, sorted_seq, num_dense_grids, densegridID_To_gridevent, position, dense_grid_rank, dense_grid_seq);
-/* Construct a table of binned data values for each dense grid.
- *
- * Output:
- *
- * dense_grid_seq  -- table of binned data values for each dense grid (recall that all members of a grid have identical binned data values)
- */
-
-void generate_grid_seq(long num_dm, long num_dense_grids, long *densegridID_To_gridevent, long **position, long **dense_grid_seq)
-{
-
-  long i=0;
-  long j=0;
-  long ReventID=0; //representative event ID of the dense grid
-
-  for (i=0;i<num_dense_grids;i++)
-    {
-      ReventID = densegridID_To_gridevent[i];
-
-      for (j=0;j<num_dm;j++)
-        dense_grid_seq[i][j]=position[ReventID][j];
-    }
-}
-
-//compare two vectors
-long compare_value(long num_dm, long *search_value, long *seq_value)
-{
-  long i=0;
-
-  for (i=0;i<num_dm;i++)
-    {
-      if (search_value[i]<seq_value[i])
-        return 1;
-      if (search_value[i]>seq_value[i])
-        return -1;
-      if (search_value[i]==seq_value[i])
-        continue;
-    }
-  return 0;
-}
-
-//binary search the dense_grid_seq to return the dense grid ID if it exists
-long binary_search(long num_dense_grids, long num_dm, long *search_value, long **dense_grid_seq)
-{
-
-  long low=0;
-  long high=0;
-  long mid=0;
-  long comp_result=0;
-  long match=0;
-  //long found=0;
-
-  low = 0;
-  high = num_dense_grids-1;
-
-  while (low <= high)
-    {
-      mid = (long)((low + high)/2);
-
-      comp_result=compare_value(num_dm, search_value,dense_grid_seq[mid]);
-
-
-      switch(comp_result)
-        {
-        case 1:
-          high=mid-1;
-          break;
-        case -1:
-          low=mid+1;
-          break;
-        case 0:
-          match=1;
-          break;
-        }
-      if (match==1)
-        break;
-    }
-
-
-
-  if (match==1)
-    {
-      return mid;
-    }
-  else
-    return -1;
-}
-
-
-/********************************************** Computing Centers Using IDs **********************************************/
-
-void ID2Center(double **data_in, long file_Len, long num_dm, long *eventID_To_denseventID, long num_clust, long *cluster_ID, double **population_center)
-{
-  long i=0;
-  long j=0;
-  long ID=0;
-  long eventID=0;
-  long *size_c;
-
-
-
-  size_c=(long *)malloc(sizeof(long)*num_clust);
-  memset(size_c,0,sizeof(long)*num_clust);
-
-  for (i=0;i<num_clust;i++)
-    for (j=0;j<num_dm;j++)
-      population_center[i][j]=0;
-
-  for (i=0;i<file_Len;i++)
-    {
-      eventID=eventID_To_denseventID[i];
-
-      if (eventID!=-1) //only events in dense grids count
-        {
-          ID=cluster_ID[eventID];
-
-          if (ID==-1)
-            {
-              //printf("ID==-1! in ID2Center\n");
-              //exit(0);
-			  fprintf(stderr,"Incorrect file format or input parameters (no dense regions found!)\n"); //modified on July 23, 2010
-			  exit(0);
-            }
-
-          for (j=0;j<num_dm;j++)
-            population_center[ID][j]=population_center[ID][j]+data_in[i][j];
-
-          size_c[ID]++;
-        }
-    }
-
-
-  for (i=0;i<num_clust;i++)
-    {
-      for (j=0;j<num_dm;j++)
-        if (size_c[i]!=0)
-          population_center[i][j]=(population_center[i][j]/(double)(size_c[i]));
-        else
-		{
-          population_center[i][j]=0;
-		  printf("size_c[%ld]=0 in ID2center\n",i);
-		}
-    }
-
-  free(size_c);
-
-}
-
-///////////////////////////////////////////////////////////////////////////////////////////////////////////////////
-//  Compute Population Center with all events
-///////////////////////////////////////////////////////////////////////////////////////////////////////////////////
-void ID2Center_all(double **data_in, long file_Len, long num_dm, long num_clust, long *cluster_ID, double **population_center)
-{
-  long i=0;
-  long j=0;
-  long ID=0;
-  long *size_c;
-
-
-
-  size_c=(long *)malloc(sizeof(long)*num_clust);
-  memset(size_c,0,sizeof(long)*num_clust);
-
-  for (i=0;i<num_clust;i++)
-    for (j=0;j<num_dm;j++)
-      population_center[i][j]=0;
-
-
-  for (i=0;i<file_Len;i++)
-    {
-         ID=cluster_ID[i];
-
-         if (ID==-1)
-         {
-            //printf("ID==-1! in ID2Center_all\n");
-            //exit(0);
-			fprintf(stderr,"Incorrect file format or input parameters (resulting in incorrect population IDs)\n"); //modified on July 23, 2010
-			exit(0);
-         }
-
-         for (j=0;j<num_dm;j++)
-           population_center[ID][j]=population_center[ID][j]+data_in[i][j];
-
-         size_c[ID]++;
-    }
-
-
-  for (i=0;i<num_clust;i++)
-    {
-      for (j=0;j<num_dm;j++)
-        if (size_c[i]!=0)
-          population_center[i][j]=(population_center[i][j]/(double)(size_c[i]));
-        else
-		{
-          population_center[i][j]=0;
-		  printf("size_c[%ld]=0 in ID2center_all\n",i);
-		}
-    }
-
-
-  free(size_c);
-
-}
-
-/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
-// Merge neighboring grids to clusters
-/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
-
-long merge_grids(double **normalized_data, double *interval, long file_Len, long num_dm, long num_bin, long **position, long num_dense_grids,
-                 long *dense_grid_reverse, long **dense_grid_seq, long *eventID_To_denseventID, long *densegridID_To_gridevent, long *all_grid_ID,
-                 long *cluster_ID, long *grid_ID, long *grid_clusterID)
-{
-
-
-  long i=0;
-  long j=0;
-  long t=0;
-  long p=0;
-  long num_clust=0;
-  long ReventID=0;
-  long denseID=0;
-  long neighbor_ID=0;
-  //long temp_grid=0;
-
-  long *grid_value;
-  long *search_value;
-
-  long **graph_of_grid; //the graph constructed for dense grids: each dense grid is a graph node
-
-  double real_dist=0;
-  double **norm_grid_center;
-
-  norm_grid_center=(double **)malloc(sizeof(double*)*num_dense_grids);
-  memset(norm_grid_center,0,sizeof(double*)*num_dense_grids);
-
-  for (i=0;i<num_dense_grids;i++)
-    {
-      norm_grid_center[i]=(double *)malloc(sizeof(double)*num_dm);
-      memset(norm_grid_center[i],0,sizeof(double)*num_dm);
-    }
-
-  for (i=0;i<file_Len;i++)
-    {
-      denseID=eventID_To_denseventID[i];
-      if (denseID!=-1) //only dense events can enter
-        {
-          grid_ID[denseID]=dense_grid_reverse[all_grid_ID[i]];
-
-          if (grid_ID[denseID]==-1)
-            {
-              fprintf(stderr,"Incorrect input file format or input parameters (no dense region found)!\n");
-              exit(0);
-            }
-        }
-    }
-
-
-  /* Find centroid (in the normalized data) for each dense grid */
-  ID2Center(normalized_data,file_Len,num_dm,eventID_To_denseventID,num_dense_grids,grid_ID,norm_grid_center);
-
-  //printf("pass the grid ID2 center\n");
-
-
-  graph_of_grid=(long **)malloc(sizeof(long*)*num_dense_grids);
-  memset(graph_of_grid,0,sizeof(long*)*num_dense_grids);
-  for (i=0;i<num_dense_grids;i++)
-    {
-      graph_of_grid[i]=(long *)malloc(sizeof(long)*num_dm);
-      memset(graph_of_grid[i],0,sizeof(long)*num_dm);
-
-
-      for (j=0;j<num_dm;j++)
-        graph_of_grid[i][j]=-1;
-    }
-
-  grid_value=(long *)malloc(sizeof(long)*num_dm);
-  memset(grid_value,0,sizeof(long)*num_dm);
-
-  search_value=(long *)malloc(sizeof(long)*num_dm);
-  memset(search_value,0,sizeof(long)*num_dm);
-
-
-  for (i=0;i<num_dense_grids;i++)
-    {
-      ReventID=densegridID_To_gridevent[i];
-
-      for (j=0;j<num_dm;j++)
-        {
-          grid_value[j]=position[ReventID][j];
-
-        }
-
-
-      /* For each dimension, find the neighbor, if any, that is equal in all other dimensions and 1 greater in
-         the chosen dimension.  If the neighbor's centroid is not too far away, add it to this grid's neighbor
-         list. */
-      for (t=0;t<num_dm;t++)
-        {
-          for (p=0;p<num_dm;p++)
-            search_value[p]=grid_value[p];
-
-          if (grid_value[t]==num_bin-1)
-            continue;
-
-          search_value[t]=grid_value[t]+1; //we only consider the neighbor at the bigger side
-
-          neighbor_ID=binary_search(num_dense_grids, num_dm, search_value, dense_grid_seq);
-
-          if (neighbor_ID!=-1)
-            {
-              real_dist=norm_grid_center[i][t]-norm_grid_center[neighbor_ID][t];
-
-              if (real_dist<0)
-                real_dist=-real_dist;
-
-              if (real_dist<2*interval[t]) //by using 2*interval, this switch is void
-                graph_of_grid[i][t]=neighbor_ID;
-            }
-        }
-      grid_clusterID[i]=i; //initialize grid_clusterID
-    }
-
-
-  //graph constructed
-  //DFS-based search begins
-
-  /* Use a depth-first search to construct a list of connected subgraphs (= "clusters").
-     Note our graph as we have constructed it is a DAG, so we can use that to our advantage
-     in our search. */
-  //  num_clust=dfs(graph_of_grid,num_dense_grids,num_dm,grid_clusterID);
-  num_clust=find_connected(graph_of_grid, num_dense_grids, num_dm, grid_clusterID);
-
-
-  //computes grid_ID and cluster_ID
-  for (i=0;i<file_Len;i++)
-    {
-      denseID=eventID_To_denseventID[i];
-      if (denseID!=-1) //only dense events can enter
-	  {
-        cluster_ID[denseID]=grid_clusterID[grid_ID[denseID]];
-		//if (cluster_ID[denseID]==-1)
-		//	printf("catch you!\n");
-	  }
-    }
-
-  free(search_value);
-  free(grid_value);
-
-  for (i=0;i<num_dense_grids;i++)
-    {
-      free(graph_of_grid[i]);
-      free(norm_grid_center[i]);
-    }
-  free(graph_of_grid);
-  free(norm_grid_center);
-
-  return num_clust;
-}
-
-/********************************************* Merge Clusters to Populations *******************************************/
-
-long merge_clusters(long num_clust, long num_dm, double *interval, double **cluster_center, long *cluster_populationID, long max_num_pop)
-{
-  long num_population=0;
-  long temp_num_population=0;
-
-  long i=0;
-  long j=0;
-  long t=0;
-  long merge=0;
-  long smid=0;
-  long bgid=0;
-  double merge_dist=1.1;
-
-  long *map_ID;
-
-  double diff=0;
-
-  map_ID=(long*)malloc(sizeof(long)*num_clust);
-  memset(map_ID,0,sizeof(long)*num_clust);
-
-  for (i=0;i<num_clust;i++)
-  {
-    	cluster_populationID[i]=i;
-		map_ID[i]=i;
-  }
-
-
-  while (((num_population>max_num_pop) && (merge_dist<5.0)) || ((num_population<=1) && (merge_dist>0.1)))
-  {
-
-	  if (num_population<=1)
-	  	  merge_dist=merge_dist-0.1;
-
-	  if (num_population>max_num_pop)
-          merge_dist=merge_dist+0.1;
-
-
-	 for (i=0;i<num_clust;i++)
-		cluster_populationID[i]=i;
-
-    for (i=0;i<num_clust-1;i++)
-    {
-      for (j=i+1;j<num_clust;j++)
-        {
-          merge=1;
-
-          for (t=0;t<num_dm;t++)
-            {
-              diff=cluster_center[i][t]-cluster_center[j][t];
-
-              if (diff<0)
-                diff=-diff;
-              if (diff>(merge_dist*interval[t]))
-                merge=0;
-            }
-
-          if ((merge) && (cluster_populationID[i]!=cluster_populationID[j]))
-            {
-              if (cluster_populationID[i]<cluster_populationID[j])  //they could not be equal
-                {
-                  smid = cluster_populationID[i];
-                  bgid = cluster_populationID[j];
-                }
-              else
-                {
-                  smid = cluster_populationID[j];
-                  bgid = cluster_populationID[i];
-                }
-              for (t=0;t<num_clust;t++)
-                {
-                  if (cluster_populationID[t]==bgid)
-                    cluster_populationID[t]=smid;
-                }
-            }
-        }
-    }
-
-
-
-  for (i=0;i<num_clust;i++)
-    map_ID[i]=-1;
-
-  for (i=0;i<num_clust;i++)
-    map_ID[cluster_populationID[i]]=1;
-
-  num_population=0;
-  for (i=0;i<num_clust;i++)
-    {
-      if (map_ID[i]==1)
-        {
-          map_ID[i]=num_population;
-          num_population++;
-        }
-    }
-
-  if ((temp_num_population>max_num_pop) && (num_population==1))
-	  break;
-  else
-	  temp_num_population=num_population;
-
-  if (num_clust<=1)
-	break;
-  } //end while
-
-  for (i=0;i<num_clust;i++)
-    cluster_populationID[i]=map_ID[cluster_populationID[i]];
-
-  free(map_ID);
-
-  return num_population;
-}
-
-///////////////////////////////////////////////////////
-/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
-double kmeans(double **Matrix, long k, double kmean_term, long file_Len, long num_dm, long *shortest_id, double **center)
-{
-
-	long i=0;
-	long j=0;
-	long t=0;
-	long random=0;
-	long random1=0;
-	long random2=0;
-	long times=0;
-	long dist_used=0; //0 is Euclidean and 1 is Pearson
-	long random_init=0; //0: not use random seeds;
-	long real_Len=0;
-	long skipped=0;
-
- 	long *num;  //num[i]=t means the ith cluster has t points
-
-	double vvv=1.0; // the biggest variation;
-	double distance=0.0;
-	double xv=0.0;
-	double variation=0.0;
-
-	double mean_dx=0;
-	double mean_dy=0;
-	double sum_var=0;
-	double dx=0;
-	double dy=0;
-	double sd_x=0;
-	double sd_y=0;
-	double diff=0;
-	double distortion=0;
-	double sd=0; //standard deviation
-	double shortest_distance;
-
-	double *temp_center;
-
-	double **sum;
-
-	temp_center = (double *)malloc(sizeof(double)*num_dm);
-	memset(temp_center,0,sizeof(double)*num_dm);
-
-	if (random_init)
-	{
-		for (i=0;i<k;i++)
-		{
-			random1=rand()*rand();
-			random2=abs((random1%5)+1);
-			for (t=0;t<random2;t++)
-				random2=random2*rand()+rand();
-
-			random=abs(random2%file_Len);
-			for (j=0;j<num_dm;j++)
-				center[i][j]=Matrix[random][j];
-		}
-	}
-
-
-	num = (long *)malloc(sizeof(long)*k);
-	memset(num,0,sizeof(long)*k);
-
-	sum = (double **)malloc(sizeof(double*)*k);
-	memset(sum,0,sizeof(double*)*k);
-	for (i=0;i<k;i++)
-	{
-		sum[i] = (double *)malloc(sizeof(double)*num_dm);
-		memset(sum[i],0,sizeof(double)*num_dm);
-	}
-
-
-	times=0;
-	real_Len=0;
-
-	while (((vvv>kmean_term) && (kmean_term<1)) || ((times<kmean_term) && (kmean_term>=1)))
-	{
-		for (i=0;i<k;i++)
-		{
-			num[i]=0;
-			for (j=0;j<num_dm;j++)
-				sum[i][j]=0.0;
-		}
-
-		for (i=0;i<file_Len;i++)  //for each data point i, we compute the distance between Matrix[i] and center[j]
-		{
-			skipped = 0;
-			shortest_distance=MAX_VALUE;
-			for (j=0;j<k;j++)  //for each center j
-			{
-				distance=0.0;
-
-				if (dist_used==0)  //Euclidean distance
-				{
-					for (t=0;t<num_dm;t++) //for each dimension here num_dm is always 1 as we consider individual dimensions
-					{
-
-						diff=center[j][t]-Matrix[i][t];
-
-						diff=diff*diff;
-						//this K-means is only used for dimension selection, and therefore for 1-dimensional data only, no need to use cube distance
-
-						distance = distance+diff; //here we have a weight for each dimension
-					}
-				}
-				else  //pearson correlation
-				{
-					mean_dx=0.0;
-					mean_dy=0.0;
-					sum_var=0.0;
-					dx=0.0;
-					dy=0.0;
-					sd_x=0.0;
-					sd_y=0.0;
-					for (t=0;t<num_dm;t++)
-					{
-						mean_dx+=center[j][t];
-						mean_dy+=Matrix[i][t];
-					}
-					mean_dx=mean_dx/(double)num_dm;
-					mean_dy=mean_dy/(double)num_dm;
-
-					for (t=0;t<num_dm;t++)
-					{
-						dx=center[j][t]-mean_dx;
-						dy=Matrix[i][t]-mean_dy;
-						sum_var+=dx*dy;
-						sd_x+=dx*dx;
-						sd_y+=dy*dy;
-					}
-					if (sqrt(sd_x*sd_y)==0)
-						distance = 1.0;
-					else
-						distance = 1.0 - (sum_var/(sqrt(sd_x*sd_y))); // distance ranges from 0 to 2;
-					//printf("distance=%f\n",distance);
-				}	//pearson correlation ends
-
-				if ((distance<shortest_distance) && (skipped == 0))
-				{
-					shortest_distance=distance;
-					shortest_id[i]=j;
-				}
-			}//end for j
-				real_Len++;
-				num[shortest_id[i]]=num[shortest_id[i]]+1;
-				for (t=0;t<num_dm;t++)
-					sum[shortest_id[i]][t]=sum[shortest_id[i]][t]+Matrix[i][t];
-		}//end for i
-	/* recompute the centers */
-	//compute_mean(group);
-		vvv=0.0;
-		for (j=0;j<k;j++)
-		{
-			memcpy(temp_center,center[j],sizeof(double)*num_dm);
-			variation=0.0;
-			if (num[j]!=0)
-			{
-				for (t=0;t<num_dm;t++)
-				{
-					center[j][t]=sum[j][t]/(double)num[j];
-					xv=(temp_center[t]-center[j][t]);
-					variation=variation+xv*xv;
-				}
-			}
-
-			if (variation>vvv)
-				vvv=variation;  //vvv is the biggest variation among the k clusters;
-		}
-	//compute_variation;
-		times++;
-	} //end for while
-
-
-
-
-	free(num);
-
-	for (i=0;i<k;i++)
-		free(sum[i]);
-	free(sum);
-	free(temp_center);
-
-
-	return distortion;
-
-}
-
-//////////////////////////////////////////////////////
-/*************************** Show *****************************/
-void show(double **Matrix, long *cluster_id, long file_Len, long k, long num_dm, char *name_string)
-{
-	int situ1=0;
-	int situ2=0;
-
-	long i=0;
-	long id=0;
-	long j=0;
-	long info_id=0;
-	long nearest_id=0;
-	long insert=0;
-	long temp=0;
-	long m=0;
-	long n=0;
-	long t=0;
-
-	long *size_c;
-
-
-
-	long **size_mybound_1;
-	long **size_mybound_2;
-	long **size_mybound_3;
-	long **size_mybound_0;
-
-	double interval=0.0;
-
-	double *big;
-	double *small;
-
-
-	double **center;
-	double **mybound;
-
-	long **prof; //prof[i][j]=1 means population i is + at parameter j
-
-	FILE *fpcnt_id; //proportion id
-	//FILE *fcent_id; //center_id, i.e., centers of clusters within the original data
-	FILE *fprof_id; //profile_id
-
-	big=(double *)malloc(sizeof(double)*num_dm);
-	memset(big,0,sizeof(double)*num_dm);
-
-	small=(double *)malloc(sizeof(double)*num_dm);
-	memset(small,0,sizeof(double)*num_dm);
-
-	for (i=0;i<num_dm;i++)
-	{
-		big[i]=0.0;
-		small[i]=(double)MAX_VALUE;
-	}
-
-
-	size_c=(long *)malloc(sizeof(long)*k);
-	memset(size_c,0,sizeof(long)*k);
-
-	center=(double**)malloc(sizeof(double*)*k);
-	memset(center,0,sizeof(double*)*k);
-	for (i=0;i<k;i++)
-	{
-		center[i]=(double*)malloc(sizeof(double)*num_dm);
-		memset(center[i],0,sizeof(double)*num_dm);
-	}
-
-	mybound=(double**)malloc(sizeof(double*)*num_dm);
-	memset(mybound,0,sizeof(double*)*num_dm);
-	for (i=0;i<num_dm;i++) //there are 3 mybounds for 4 categories
-	{
-		mybound[i]=(double*)malloc(sizeof(double)*3);
-		memset(mybound[i],0,sizeof(double)*3);
-	}
-
-	prof=(long **)malloc(sizeof(long*)*k);
-	memset(prof,0,sizeof(long*)*k);
-	for (i=0;i<k;i++)
-	{
-		prof[i]=(long *)malloc(sizeof(long)*num_dm);
-		memset(prof[i],0,sizeof(long)*num_dm);
-	}
-
-
-	for (i=0;i<file_Len;i++)
-	{
-		id=cluster_id[i];
-		for (j=0;j<num_dm;j++)
-		{
-			center[id][j]=center[id][j]+Matrix[i][j];
-			if (big[j]<Matrix[i][j])
-				big[j]=Matrix[i][j];
-			if (small[j]>Matrix[i][j])
-				small[j]=Matrix[i][j];
-		}
-
-		size_c[id]++;
-	}
-
-	for (i=0;i<k;i++)
-		for (j=0;j<num_dm;j++)
-		{
-			if (size_c[i]!=0)
-				center[i][j]=(center[i][j]/(double)(size_c[i]));
-			else
-				center[i][j]=0;
-		}
-
-	for (j=0;j<num_dm;j++)
-	{
-		interval=((big[j]-small[j])/4.0);
-		//printf("interval[%d] is %f\n",j,interval);
-		for (i=0;i<3;i++)
-			mybound[j][i]=small[j]+((double)(i+1)*interval);
-	}
-
-
-	size_mybound_0=(long **)malloc(sizeof(long*)*k);
-	memset(size_mybound_0,0,sizeof(long*)*k);
-
-	for (i=0;i<k;i++)
-	{
-		size_mybound_0[i]=(long*)malloc(sizeof(long)*num_dm);
-		memset(size_mybound_0[i],0,sizeof(long)*num_dm);
-	}
-
-	size_mybound_1=(long **)malloc(sizeof(long*)*k);
-	memset(size_mybound_1,0,sizeof(long*)*k);
-
-	for (i=0;i<k;i++)
-	{
-		size_mybound_1[i]=(long*)malloc(sizeof(long)*num_dm);
-		memset(size_mybound_1[i],0,sizeof(long)*num_dm);
-	}
-
-	size_mybound_2=(long **)malloc(sizeof(long*)*k);
-	memset(size_mybound_2,0,sizeof(long*)*k);
-
-	for (i=0;i<k;i++)
-	{
-		size_mybound_2[i]=(long*)malloc(sizeof(long)*num_dm);
-		memset(size_mybound_2[i],0,sizeof(long)*num_dm);
-	}
-
-	size_mybound_3=(long **)malloc(sizeof(long*)*k);
-	memset(size_mybound_3,0,sizeof(long*)*k);
-
-	for (i=0;i<k;i++)
-	{
-		size_mybound_3[i]=(long*)malloc(sizeof(long)*num_dm);
-		memset(size_mybound_3[i],0,sizeof(long)*num_dm);
-	}
-
-	for (i=0;i<file_Len;i++)
-		for (j=0;j<num_dm;j++)
-			{
-				if (Matrix[i][j]<mybound[j][0])// && ((Matrix[i][j]-small[j])>0)) //the smallest values excluded
-					size_mybound_0[cluster_id[i]][j]++;
-				else
-				{
-					if (Matrix[i][j]<mybound[j][1])
-						size_mybound_1[cluster_id[i]][j]++;
-					else
-					{
-						if (Matrix[i][j]<mybound[j][2])
-							size_mybound_2[cluster_id[i]][j]++;
-						else
-							//if (Matrix[i][j]!=big[j]) //the biggest values excluded
-								size_mybound_3[cluster_id[i]][j]++;
-					}
-
-				}
-			}
-
-	fprof_id=fopen("profile.txt","w");
-	fprintf(fprof_id,"Population_ID\t");
-	fprintf(fprof_id,"%s\n",name_string);
-
-	for (i=0;i<k;i++)
-	{
-		fprintf(fprof_id,"%ld\t",i+1); //i changed to i+1 to start from 1 instead of 0: April 16, 2009
-		for (j=0;j<num_dm;j++)
-		{
-
-			if (size_mybound_0[i][j]>size_mybound_1[i][j])
-				situ1=0;
-			else
-				situ1=1;
-			if (size_mybound_2[i][j]>size_mybound_3[i][j])
-				situ2=2;
-			else
-				situ2=3;
-
-			if ((situ1==0) && (situ2==2))
-			{
-				if (size_mybound_0[i][j]>size_mybound_2[i][j])
-					prof[i][j]=0;
-				else
-					prof[i][j]=2;
-			}
-			if ((situ1==0) && (situ2==3))
-			{
-				if (size_mybound_0[i][j]>size_mybound_3[i][j])
-					prof[i][j]=0;
-				else
-					prof[i][j]=3;
-			}
-			if ((situ1==1) && (situ2==2))
-			{
-				if (size_mybound_1[i][j]>size_mybound_2[i][j])
-					prof[i][j]=1;
-				else
-					prof[i][j]=2;
-			}
-			if ((situ1==1) && (situ2==3))
-			{
-				if (size_mybound_1[i][j]>size_mybound_3[i][j])
-					prof[i][j]=1;
-				else
-					prof[i][j]=3;
-			}
-
-			//begin to output profile
-			if (j==num_dm-1)
-			{
-				if (prof[i][j]==0)
-					fprintf(fprof_id,"1\n");
-				if (prof[i][j]==1)
-					fprintf(fprof_id,"2\n");
-				if (prof[i][j]==2)
-					fprintf(fprof_id,"3\n");
-				if (prof[i][j]==3)
-					fprintf(fprof_id,"4\n");
-			}
-			else
-			{
-				if (prof[i][j]==0)
-					fprintf(fprof_id,"1\t");
-				if (prof[i][j]==1)
-					fprintf(fprof_id,"2\t");
-				if (prof[i][j]==2)
-					fprintf(fprof_id,"3\t");
-				if (prof[i][j]==3)
-					fprintf(fprof_id,"4\t");
-			}
-		}
-	}
-	fclose(fprof_id);
-
-	///////////////////////////////////////////////////////////
-
-
-	fpcnt_id=fopen("percentage.txt","w");
-	fprintf(fpcnt_id,"Population_ID\tPercentage\n");
-
-	for (t=0;t<k;t++)
-	{
-		fprintf(fpcnt_id,"%ld\t%.2f\n",t+1,(double)size_c[t]*100.0/(double)file_Len);	//t changed to t+1 to start from 1 instead of 0: April 16, 2009
-	}
-	fclose(fpcnt_id);
-
-	free(big);
-	free(small);
-	free(size_c);
-
-	for (i=0;i<k;i++)
-	{
-		free(center[i]);
-		free(prof[i]);
-		free(size_mybound_0[i]);
-		free(size_mybound_1[i]);
-		free(size_mybound_2[i]);
-		free(size_mybound_3[i]);
-	}
-	free(center);
-	free(prof);
-	free(size_mybound_0);
-	free(size_mybound_1);
-	free(size_mybound_2);
-	free(size_mybound_3);
-
-	for (i=0;i<num_dm;i++)
-		free(mybound[i]);
-	free(mybound);
-
-}
-///////////////////////////////////////////////////////////////////////////
-
-double get_avg_dist(double *population_center, long smaller_pop_ID, long larger_pop_ID, long *population_ID, long num_population, long file_Len,
-				   long num_dm, double **normalized_data, long d1, long d2, long d3, long *size_c)
-{
-	long k=0;
-	long temp=0;
-	long i=0;
-	long j=0;
-	long t=0;
-	long current_biggest=0;
-
-
-	double total_dist=0.0;
-	double distance=0.0;
-	double dist=0.0;
-	double biggest_distance=0.0;
-
-	long *nearest_neighbors;
-	double *nearest_distance;
-
-	k=min(size_c[smaller_pop_ID],size_c[larger_pop_ID]);
-
-	if (k>0)
-	{
-		k=(long)sqrt((double)k);
-		if (num_dm<=3)
-			k=(long)(2.7183*(double)k);  //e*k for low-dimensional space, added Nov. 4, 2010
-		//printf("the k-nearest k is %d\n",k);
-	}
-	else
-	{
-		printf("error in k\n");
-		exit(0);
-	}
-
-	nearest_neighbors=(long *)malloc(sizeof(long)*k);
-	memset(nearest_neighbors,0,sizeof(long)*k);
-
-	nearest_distance=(double *)malloc(sizeof(double)*k);
-	memset(nearest_distance,0,sizeof(double)*k);
-
-	temp=0;
-
-	for (i=0;i<file_Len;i++)
-	{
-		if ((population_ID[i]==smaller_pop_ID) || (population_ID[i]==larger_pop_ID)) //the event belongs to the pair of populations
-		{
-			distance=0.0;
-			for (t=0;t<num_dm;t++)
-			{
-				if ((t!=d1) && (t!=d2) && (t!=d3))
-					continue;
-				else
-				{
-					dist=population_center[t]-normalized_data[i][t];
-					distance=distance+dist*dist;
-				}
-			}
-
-			if (temp<k)
-			{
-				nearest_neighbors[temp]=i;
-				nearest_distance[temp]=distance;
-				temp++;
-			}
-			else
-			{
-			    biggest_distance=0.0;
-				for (j=0;j<k;j++)
-				{
-					if (nearest_distance[j]>biggest_distance)
-					{
-						biggest_distance=nearest_distance[j];
-						current_biggest=j;
-					}
-				}
-
-				if (biggest_distance>distance)
-				{
-					nearest_neighbors[current_biggest]=i;
-					nearest_distance[current_biggest]=distance;
-				}
-			}
-		}
-	}
-
-    for (i=0;i<k;i++)
-		total_dist=total_dist+nearest_distance[i];
-
-	total_dist=total_dist/(double)k;
-
-	free(nearest_distance);
-	free(nearest_neighbors);
-
-	return total_dist;
-}
-
-
-/******************************************************** Main Function **************************************************/
-//for normalized data, there are five variables:
-//cluster_ID
-//population_center
-//grid_clusterID
-//grid_ID
-//grid_Center
-
-//the same five variables exist for the original data
-//however, the three IDs (cluster_ID, grid_ID, grid_clusterID) don't change in either normalized or original data
-//also, data + cluster_ID -> population_center
-//data + grid_ID -> grid_Center
-
-/* what is the final output */
-//the final things we want are grid_Center in the original data and grid_clusterID //or population_center in the original data
-//Sparse grids will not be considered when computing the two centroids (centroids of grids and centroids of clusters)
-
-/*  what information should select_bin output */
-//the size of all IDs are unknown to function main because we only consider the events in dense grids, and also the number of dense grids
-//is unknown, therefore I must use a prescreening to output
-//how many bins I should use
-//the number of dense grids
-//total number of events in the dense grids
-
-/* basic procedure of main function */
-//1. read raw file and normalize the raw file
-//2. select_bin
-//3. allocate memory for eventID_To_denseventID, grid_clusterID, grid_ID, cluster_ID.
-//4. call select_dense and merge_grids with grid_clusterID, grid_ID, cluster_ID.
-//5. release normalized data; allocate memory for grid_Center and population_center
-//6. output grid_Center and population_center using ID2Center together with grid_clusterID //from IDs to centers
-
-int main (int argc, char **argv)
-{
-  //inputs
-  FILE *f_src; //source file pointer
-
-  FILE *f_out; //coordinates
-  FILE *f_cid; //population-ID of events
-  FILE *f_ctr; //centroids of populations
-  FILE *f_results; //coordinates file event and population column
-  FILE *f_mfi; //added April 16, 2009 for mean fluorescence intensity
-  FILE *f_parameters; //number of bins and density calculated by
-                      //the algorithm. Used to update the database
-  FILE *f_properties; //Properties file used by Image generation software
-
-  //char tmpbuf[128];
-
-  char para_name_string[LINE_LEN];
-
-  long time_ID=-1;
-  long num_bin=0; //the bins I will use on each dimension
-  long num_pop=0;
-  long file_Len=0; //number of events
-  long num_dm=0;
-  long num_clust=0;
-  long num_dense_events=0;
-  long num_dense_grids=0;
-  long num_nonempty=0;
-  long num_population=0;
-  long num_real_pop=0;
-  long keep_merge=0;
-  long num_checked_range=0;
-
-  //below are read from configuration file
-  long i=0;
-  long j=0;
-  long p=0;
-  long t=0;
-  long q=0;
-  long temp_i=0;
-  long temp_j=0;
-  long first_i=0;
-  long first_j=0;
-  long d1=0;
-  long d2=0;
-  long d3=0;
-  long d_d=0;
-  long max_num_pop=0; //upperbound of the number of populations that is equal to 2^d
-  long index_id=0;
-  long num_computed_population=0;
-  long tot_size=0;
-
-  int den_t_event=0;
-
-  double distance=0.0;
-  double dist=0.0;
-  double current_smallest_dist=0;
-  double max_d_dist=0.0;
-  double Ei=0.0;
-  double Ej=0.0;
-  double E1=0.0;
-  double E2=0.0;
-  double E3=0.0;
-  double Ep=0.0;
-  double temp=0.0;
-  double tmp=0.0;
-
-  long *grid_clusterID; //(dense)gridID to clusterID
-  long *grid_ID; //(dense)eventID to gridID
-  long *cluster_ID; //(dense)eventID to clusterID
-  long *eventID_To_denseventID; //eventID_To_denseventID[i]=k means event i is in a dense grid and its ID within dense events is k
-  long *all_grid_ID; //gridID for all events
-  long *densegridID_To_gridevent;
-  long *sorted_seq;
-  long *dense_grid_reverse;
-  long *population_ID; //denseeventID to populationID
-  long *cluster_populationID; //clusterID to populationID
-  long *grid_populationID; //gridID to populationID
-  long *all_population_ID; //populationID of event
-  long *size_c;
-  long *size_p_2;
-  long *partit;
-  long *size_p;
-  long *temp_size_j;
-  long *all_computed_pop_ID;
-
-
-  long **position;
-  long **dense_grid_seq;
-  long **temp_population_ID;
-
-  double *interval;
-  double *center_1;
-  double *center_2;
-  double *center_3;
-  double *aver;
-  double *std;
-  double *center_p_1;
-  double *center_p_2;
-  double *center_p_3;
-
-  double **population_center; //population centroids in the raw/original data
-  double **cluster_center; //cluster centroids in the raw/original data
-  double **new_population_center;
-  double **temp_population_center;
-  double **min_pop;
-  double **max_pop;
-
-  double **input_data;
-  double **normalized_data;
-
-  double **real_pop_center;
-  double **distance_pop;
-
-  double ***ind_pop;
-  double ***ind_pop_3;
-
-  int min = 999999;
-  int max = 0;
-
-  printf( "Starting time:\t\t\t\t");
-  fflush(stdout);
-  system("/bin/date");
-
-  /*
-   * Windows Version
-  _strtime( tmpbuf );
-  printf( "Starting time:\t\t\t\t%s\n", tmpbuf );
-  _strdate( tmpbuf );
-  printf( "Starting date:\t\t\t\t%s\n", tmpbuf );
-  */
-
-  /////////////////////////////////////////////////////////////
-
-  if ((argc!=2) && (argc!=3) && (argc!=4) && (argc!=5) && (argc!=6))
-  {
-      fprintf(stderr,"Incorrect number of input parameters!\n");
-	  fprintf(stderr,"usage:\n");
-	  fprintf(stderr,"basic mode: flock data_file\n");
-	  fprintf(stderr,"advanced mode 0 (specify maximum # of pops): flock data_file max_num_pop\n");
-	  fprintf(stderr,"advanced mode 1 (without # of pops): flock data_file num_bin density_index\n");
-	  fprintf(stderr,"advanced mode 2 (specify # of pops): flock data_file num_bin density_index number_of_pop\n");
-	  fprintf(stderr,"advanced mode 3 (specify both # of pops): flock data_file num_bin density_index number_of_pop max_num_pop\n");
-      exit(0);
-  }
-
-  f_src=fopen(argv[1],"r");
-
-  if (argc==3)
-  {
-	max_num_pop=atoi(argv[2]);
-	printf("num of maximum pop is %ld\n",max_num_pop);
-  }
-
-  if (argc==4)
-  {
-	num_bin=atoi(argv[2]);
-	printf("num_bin is %ld\n",num_bin);
-
-	den_t_event=atoi(argv[3]);
-	printf("density_index is %d\n",den_t_event);
-  }
-
-  if (argc==5)
-  {
-	num_bin=atoi(argv[2]);
-	printf("num_bin is %ld\n",num_bin);
-
-	den_t_event=atoi(argv[3]);
-	printf("density_index is %d\n",den_t_event);
-
-	num_pop=atoi(argv[4]);
-	printf("num of pop is %ld\n",num_pop);
-  }
-
-  if (argc==6)
-  {
-	num_bin=atoi(argv[2]);
-	printf("num_bin is %ld\n",num_bin);
-
-	den_t_event=atoi(argv[3]);
-	printf("density_index is %d\n",den_t_event);
-
-	num_pop=atoi(argv[4]);
-	printf("num of pop is %ld\n",num_pop);
-
-	max_num_pop=atoi(argv[5]);
-	printf("num of pop is %ld\n",max_num_pop);
-  }
-
-
-  if (num_pop==1)
-  {
-	  printf("it is not allowed to specify only one population\n");
-	  exit(0);
-  }
-
-
-
-  getfileinfo(f_src, &file_Len, &num_dm, para_name_string, &time_ID); //get the filelength, number of dimensions, and num/name of parameters
-
-
-  if (max_num_pop==0)
-  {
-	  max_num_pop=(long)pow(2,num_dm);
-		if (max_num_pop>MAX_POP_NUM)
-			max_num_pop=MAX_POP_NUM;
-  }
-
-  /************************************************* Read the data *****************************************************/
-
-  rewind(f_src); //reset the file pointer
-
-  input_data = (double **)malloc(sizeof(double*)*file_Len);
-  memset(input_data,0,sizeof(double*)*file_Len);
-  for (i=0;i<file_Len;i++)
-  {
-     input_data[i]=(double *)malloc(sizeof(double)*num_dm);
-     memset(input_data[i],0,sizeof(double)*num_dm);
-  }
-
-  readsource(f_src, file_Len, num_dm, input_data, time_ID); //read the data;
-
-  fclose(f_src);
-
-  normalized_data=(double **)malloc(sizeof(double*)*file_Len);
-  memset(normalized_data,0,sizeof(double*)*file_Len);
-  for (i=0;i<file_Len;i++)
-    {
-      normalized_data[i]=(double *)malloc(sizeof(double)*num_dm);
-      memset(normalized_data[i],0,sizeof(double)*num_dm);
-    }
-
-  tran(input_data, file_Len, num_dm, NORM_METHOD, normalized_data);
-
-
-  position=(long **)malloc(sizeof(long*)*file_Len);
-  memset(position,0,sizeof(long*)*file_Len);
-  for (i=0;i<file_Len;i++)
-    {
-      position[i]=(long*)malloc(sizeof(long)*num_dm);
-      memset(position[i],0,sizeof(long)*num_dm);
-    }
-
-  all_grid_ID=(long *)malloc(sizeof(long)*file_Len);
-  memset(all_grid_ID,0,sizeof(long)*file_Len);
-
-  sorted_seq=(long*)malloc(sizeof(long)*file_Len);
-  memset(sorted_seq,0,sizeof(long)*file_Len);
-
-  interval=(double*)malloc(sizeof(double)*num_dm);
-  memset(interval,0,sizeof(double)*num_dm);
-
-  /************************************************* select_bin *************************************************/
-
-  if (num_bin>=1)  //num_bin has been selected by user
-  {
-  	select_bin(normalized_data, file_Len, num_dm, MIN_GRID, MAX_GRID, position, sorted_seq, all_grid_ID, &num_nonempty, interval,num_bin);
-	printf("user set bin number is %ld\n",num_bin);
-  }
-  else  //num_bin has not been selected by user
-  {
-	num_bin=select_bin(normalized_data, file_Len, num_dm, MIN_GRID, MAX_GRID, position, sorted_seq, all_grid_ID, &num_nonempty, interval,num_bin);
-	printf("selected bin number is %ld\n",num_bin);
-  }
-  printf("number of non-empty grids is %ld\n",num_nonempty);
-
-
-
-  /* Although we return sorted_seq from select_bin(), we don't use it for anything, except possibly diagnostics */
-  free(sorted_seq);
-
-
-  dense_grid_reverse=(long*)malloc(sizeof(long)*num_nonempty);
-  memset(dense_grid_reverse,0,sizeof(long)*num_nonempty);
-
-  /************************************************* select_dense **********************************************/
-
-  if (den_t_event>=1) //den_t_event must be larger or equal to 2 if the user wants to set it
-	den_t_event=select_dense(file_Len, all_grid_ID, num_nonempty, &num_dense_grids, &num_dense_events, dense_grid_reverse, den_t_event);
-  else
-  {
-	den_t_event=select_dense(file_Len, all_grid_ID, num_nonempty, &num_dense_grids, &num_dense_events, dense_grid_reverse, den_t_event);
-	printf("automated selected density threshold is %d\n",den_t_event);
-  }
-
-  printf("Number of dense grids is %ld\n",num_dense_grids);
-
-  densegridID_To_gridevent = (long *)malloc(sizeof(long)*num_dense_grids);
-  memset(densegridID_To_gridevent,0,sizeof(long)*num_dense_grids);
-
-  for (i=0;i<num_dense_grids;i++)
-    densegridID_To_gridevent[i]=-1; //initialize all densegridID_To_gridevent values to -1
-
-
-  eventID_To_denseventID=(long *)malloc(sizeof(long)*file_Len);
-  memset(eventID_To_denseventID,0,sizeof(long)*file_Len);     //eventID_To_denseventID[i]=k means event i is in a dense grid and its ID within dense events is k
-
-
-  grid_To_event(file_Len, dense_grid_reverse, all_grid_ID, eventID_To_denseventID, densegridID_To_gridevent);
-
-
-  dense_grid_seq=(long **)malloc(sizeof(long*)*num_dense_grids);
-  memset(dense_grid_seq,0,sizeof(long*)*num_dense_grids);
-  for (i=0;i<num_dense_grids;i++)
-    {
-      dense_grid_seq[i]=(long *)malloc(sizeof(long)*num_dm);
-      memset(dense_grid_seq[i],0,sizeof(long)*num_dm);
-    }
-
-
-  /* Look up the binned data values for each dense grid */
-  generate_grid_seq(num_dm, num_dense_grids, densegridID_To_gridevent, position, dense_grid_seq);
-
-
-  /************************************************* allocate memory *********************************************/
-
-  grid_clusterID=(long *)malloc(sizeof(long)*num_dense_grids);
-  memset(grid_clusterID,0,sizeof(long)*num_dense_grids);
-
-  grid_ID=(long *)malloc(sizeof(long)*num_dense_events);
-  memset(grid_ID,0,sizeof(long)*num_dense_events);
-
-  cluster_ID=(long *)malloc(sizeof(long)*num_dense_events);
-  memset(cluster_ID,0,sizeof(long)*num_dense_events);
-
-
-  /*********************************************** merge_grids ***********************************************/
-  //long merge_grids(long file_Len, long num_dm, long num_bin, long **position, long num_dense_grids, long *dense_grid_rank, long *dense_grid_reverse,
-  //			 long **dense_grid_seq, long *eventID_To_denseventID, long *densegridID_To_gridevent, long *all_grid_ID,
-  //			 long *cluster_ID, long *grid_ID, long *grid_clusterID)
-
-  num_clust = merge_grids(normalized_data, interval, file_Len, num_dm, num_bin, position, num_dense_grids, dense_grid_reverse, dense_grid_seq, eventID_To_denseventID, densegridID_To_gridevent, all_grid_ID, cluster_ID, grid_ID, grid_clusterID);
-
-  printf("computed number of groups is %ld\n",num_clust);
-
-
-  /************************************** release unnecessary memory and allocate memory and compute centers **********************************/
-
-
-  for (i=0;i<file_Len;i++)
-    free(position[i]);
-  free(position);
-
-  for (i=0;i<num_dense_grids;i++)
-    free(dense_grid_seq[i]);
-  free(dense_grid_seq);
-
-  free(dense_grid_reverse);
-
-  free(densegridID_To_gridevent);
-  free(all_grid_ID);
-
-  // cluster_center ////////////////////////////////////////////////////////////////////////////////////////////////////////
-
-  cluster_center=(double **)malloc(sizeof(double*)*num_clust);
-  memset(cluster_center,0,sizeof(double*)*num_clust);
-  for (i=0;i<num_clust;i++)
-  {
-     cluster_center[i]=(double*)malloc(sizeof(double)*num_dm);
-     memset(cluster_center[i],0,sizeof(double)*num_dm);
-  }
-
-  ID2Center(normalized_data,file_Len,num_dm,eventID_To_denseventID,num_clust,cluster_ID,cluster_center); //produce the centers with normalized data
-
-  //printf("pass the first ID2center\n");
-
-  /*** population_ID and grid_populationID **/
-
-  cluster_populationID=(long*)malloc(sizeof(long)*num_clust);
-  memset(cluster_populationID,0,sizeof(long)*num_clust);
-
-  grid_populationID=(long*)malloc(sizeof(long)*num_dense_grids);
-  memset(grid_populationID,0,sizeof(long)*num_dense_grids);
-
-  population_ID=(long*)malloc(sizeof(long)*num_dense_events);
-  memset(population_ID,0,sizeof(long)*num_dense_events);
-
-  num_population = merge_clusters(num_clust, num_dm, interval, cluster_center, cluster_populationID, max_num_pop);
-
-
-
-  for (i=0;i<num_clust;i++)
-    free(cluster_center[i]);
-  free(cluster_center);
-
-  free(interval);
-
-  for (i=0;i<num_dense_grids;i++)
-    {
-      grid_populationID[i]=cluster_populationID[grid_clusterID[i]];
-    }
-
-  for (i=0;i<num_dense_events;i++)
-    {
-      population_ID[i]=cluster_populationID[cluster_ID[i]];
-    }
-
-  printf("Number of merged groups before second-run partitioning is %ld\n",num_population);
-
-
-
-  // population_center /////////////////////////////////////////////////////////////////////////////////////////////////////
-
-
-  population_center=(double **)malloc(sizeof(double*)*num_population);
-  memset(population_center,0,sizeof(double*)*num_population);
-  for (i=0;i<num_population;i++)
-  {
-     population_center[i]=(double*)malloc(sizeof(double)*num_dm);
-     memset(population_center[i],0,sizeof(double)*num_dm);
-  }
-
-
-
-  ID2Center(normalized_data,file_Len,num_dm,eventID_To_denseventID,num_population,population_ID,population_center); //produce population centers with normalized data
-
-
-  // show ////////////////////////////////////////////////////////////////////////////////
-  all_population_ID=(long*)malloc(sizeof(long)*file_Len);
-  memset(all_population_ID,0,sizeof(long)*file_Len);
-
-  kmeans(normalized_data, num_population, KMEANS_TERM, file_Len, num_dm, all_population_ID, population_center);
-
-  for (i=0;i<num_population;i++)
-	free(population_center[i]);
-
-  free(population_center);
-
-  ////// there needs to be another step to further partition the data
-
-
-	  center_p_1=(double *)malloc(sizeof(double)*3);
-	  memset(center_p_1,0,sizeof(double)*3);
-
-	  center_p_2=(double *)malloc(sizeof(double)*3);
-	  memset(center_p_2,0,sizeof(double)*3);
-
-	  center_p_3=(double *)malloc(sizeof(double)*3);
-	  memset(center_p_3,0,sizeof(double)*3);
-
-	  size_p=(long *)malloc(sizeof(long)*num_population);
-	  memset(size_p,0,sizeof(long)*num_population);
-
-	  temp_size_j=(long *)malloc(sizeof(long)*num_population);
-	  memset(temp_size_j,0,sizeof(long)*num_population);
-
-	  all_computed_pop_ID=(long *)malloc(sizeof(long)*file_Len);
-	  memset(all_computed_pop_ID,0,sizeof(long)*file_Len);
-
-	  for (i=0;i<file_Len;i++)
-	  {
-		size_p[all_population_ID[i]]++;
-		all_computed_pop_ID[i]=all_population_ID[i];
-	  }
-
-	  ind_pop=(double***)malloc(sizeof(double**)*num_population);
-	  memset(ind_pop,0,sizeof(double**)*num_population);
-
-	  ind_pop_3=(double***)malloc(sizeof(double**)*num_population);
-	  memset(ind_pop_3,0,sizeof(double**)*num_population);
-
-	  for (i=0;i<num_population;i++)
-	  {
-		  ind_pop[i]=(double**)malloc(sizeof(double*)*size_p[i]);
-		  memset(ind_pop[i],0,sizeof(double*)*size_p[i]);
-
-		  ind_pop_3[i]=(double**)malloc(sizeof(double*)*size_p[i]);
-		  memset(ind_pop_3[i],0,sizeof(double*)*size_p[i]);
-
-		  for (j=0;j<size_p[i];j++)
-		  {
-			  ind_pop[i][j]=(double*)malloc(sizeof(double)*num_dm);
-			  memset(ind_pop[i][j],0,sizeof(double)*num_dm);
-
-			  ind_pop_3[i][j]=(double*)malloc(sizeof(double)*3);
-			  memset(ind_pop_3[i][j],0,sizeof(double)*3);
-		  }
-		  temp_size_j[i]=0;
-	  }
-
-	  for (i=0;i<file_Len;i++) //to generate ind_pop[i]
-	  {
-		  index_id=all_population_ID[i];
-
-		  j=temp_size_j[index_id];
-
-		  for (t=0;t<num_dm;t++)
-		  {
-			ind_pop[index_id][j][t]=input_data[i][t];
-		  }
-		  temp_size_j[index_id]++;
-	  }
-
-	  aver=(double*)malloc(sizeof(double)*num_dm);
-	  memset(aver,0,sizeof(double)*num_dm);
-
-	  std=(double*)malloc(sizeof(double)*num_dm);
-	  memset(std,0,sizeof(double)*num_dm);
-
-	  temp_population_center=(double**)malloc(sizeof(double*)*2);
-	  memset(temp_population_center,0,sizeof(double*)*2);
-	  for (i=0;i<2;i++)
-	  {
-		temp_population_center[i]=(double*)malloc(sizeof(double)*3);
-		memset(temp_population_center[i],0,sizeof(double)*3);
-	  }
-
-	  size_p_2=(long*)malloc(sizeof(long)*2);
-	  memset(size_p_2,0,sizeof(long)*2);
-
-	  partit=(long*)malloc(sizeof(long)*num_population);
-	  memset(partit,0,sizeof(long)*num_population);
-
-	  num_computed_population=num_population;
-
-	  temp_population_ID=(long**)malloc(sizeof(long*)*num_population);
-	  memset(temp_population_ID,0,sizeof(long*)*num_population);
-
-	  for (i=0;i<num_population;i++)
-	  {
-		temp_population_ID[i]=(long*)malloc(sizeof(long)*size_p[i]);
-		memset(temp_population_ID[i],0,sizeof(long)*size_p[i]);
-	  }
-
-	  //printf("num_population=%d\n",num_population);
-
-	  for (i=0;i<num_population;i++)
-	  {
-		  partit[i]=0;
-		  tran(ind_pop[i], size_p[i], num_dm, 1, ind_pop[i]);//0-1 normalize ind_pop[i]
-
-		  //find the 3 dimensions with the largest std for ind_pop[i]
-		  d1=-1;
-		  d2=-1;
-		  d3=-1;
-
-		  for (t=0;t<num_dm;t++)
-		  {
-			aver[t]=0;
-			for (j=0;j<size_p[i];j++)
-			{
-				aver[t]=aver[t]+ind_pop[i][j][t];
-			}
-			aver[t]=aver[t]/(double)size_p[i];
-
-			std[t]=0;
-			for (j=0;j<size_p[i];j++)
-			{
-				std[t]=std[t]+((ind_pop[i][j][t]-aver[t])*(ind_pop[i][j][t]-aver[t]));
-			}
-			std[t]=sqrt(std[t]/(double)size_p[i]);
-		  }
-
-
-
-		  for (j=0;j<3;j++)
-		  {
-			max_d_dist=0;
-			for (t=0;t<num_dm;t++)
-			{
-				if ((t!=d1) && (t!=d2))
-				{
-					dist=std[t];
-				}
-				else
-					dist=-1;
-
-				if (dist>max_d_dist)
-				{
-					max_d_dist=dist;
-					d_d=t;
-				}
-			}
-
-			if (j==0)
-				d1=d_d;
-			if (j==1)
-				d2=d_d;
-			if (j==2)
-				d3=d_d;
-		  }
-
-
-		  for (t=0;t<size_p[i];t++)
-		  {
-				ind_pop_3[i][t][0]=ind_pop[i][t][d1];
-				ind_pop_3[i][t][1]=ind_pop[i][t][d2];
-				ind_pop_3[i][t][2]=ind_pop[i][t][d3];
-		  }
-
-
-		 temp_population_center[0][0]=(aver[d1])/2.0;
-
-		 temp_population_center[0][1]=aver[d2];
-	     temp_population_center[0][2]=aver[d3];
-
-		 temp_population_center[1][0]=(aver[d1]+1.0)/2.0;
-
-		 temp_population_center[1][1]=aver[d2];
-		 temp_population_center[1][2]=aver[d3];
-
-
-
-		 //run K-means with K=2
-		 kmeans(ind_pop_3[i], 2, KMEANS_TERM, size_p[i], 3, temp_population_ID[i], temp_population_center);
-
-		 for (j=0;j<2;j++)
-			 size_p_2[j]=0;
-
-		 for (j=0;j<size_p[i];j++)
-			 size_p_2[temp_population_ID[i][j]]++;
-
-		 for (j=0;j<2;j++)
-			 if (size_p_2[j]==0)
-				 printf("size_p_2=0 at i=%ld\n",i);
-
-
-		 //check whether the 2 parts should be merged
-
-
-		 Ei=get_avg_dist(temp_population_center[0], 0,1, temp_population_ID[i], 2,size_p[i], 3, ind_pop_3[i], 0,1,2,size_p_2);
-		 Ej=get_avg_dist(temp_population_center[1], 0,1, temp_population_ID[i], 2,size_p[i], 3, ind_pop_3[i], 0,1,2,size_p_2);
-
-		 for (t=0;t<3;t++)
-		 {
-			center_p_1[t]=temp_population_center[0][t]*0.25+temp_population_center[1][t]*0.75;
-			center_p_2[t]=temp_population_center[0][t]*0.5+temp_population_center[1][t]*0.5;
-			center_p_3[t]=temp_population_center[0][t]*0.75+temp_population_center[1][t]*0.25;
-		 }
-
-		 E1=get_avg_dist(center_p_1, 0,1, temp_population_ID[i], 2,size_p[i], 3, ind_pop_3[i], 0,1,2,size_p_2);
-
-		 E2=get_avg_dist(center_p_2, 0,1, temp_population_ID[i], 2,size_p[i], 3, ind_pop_3[i], 0,1,2,size_p_2);
-
-		 E3=get_avg_dist(center_p_3, 0,1, temp_population_ID[i], 2,size_p[i], 3, ind_pop_3[i], 0,1,2,size_p_2);
-
-		 //printf("i=%d;E1=%f;E2=%f;E3=%f\n",i,E1,E2,E3);
-
-		 if (E1<E2)
-			Ep=E2;
-		 else
-			Ep=E1;
-
-		 Ep=max(Ep,E3); //Ep is the most sparse area
-
-
-
-		 if ((Ep>Ei) && (Ep>Ej)) //the two parts should be partitioned
-		 {
-			 partit[i]=num_computed_population;
-			 num_computed_population++;
-		 }
-
-	  } //end for (i=0;i<num_population;i++)
-
-
-	  for (i=0;i<num_population;i++)
-		  temp_size_j[i]=0;
-
-	  for (i=0;i<file_Len;i++)
-	  {
-		index_id=all_population_ID[i];
-		if (partit[index_id]>0)
-		{
-			j=temp_size_j[index_id];
-			if (temp_population_ID[index_id][j]==1)
-				all_computed_pop_ID[i]=partit[index_id];
-
-			temp_size_j[index_id]++;
-		}
-	  }
-
-	  printf("Number of groups after partitioning is %ld\n", num_computed_population);
-
-
-      free(size_p_2);
-
-	  free(aver);
-	  free(std);
-	  free(partit);
-
-	  free(center_p_1);
-	  free(center_p_2);
-	  free(center_p_3);
-
-
-
-	  for (i=0;i<num_population;i++)
-		  free(temp_population_ID[i]);
-	  free(temp_population_ID);
-
-	  for (i=0;i<num_population;i++)
-	  {
-		for (j=0;j<size_p[i];j++)
-		{
-			  free(ind_pop[i][j]);
-			  free(ind_pop_3[i][j]);
-		}
-	  }
-
-
-
-	  for (i=0;i<num_population;i++)
-	  {
-		  free(ind_pop[i]);
-		  free(ind_pop_3[i]);
-	  }
-	  free(ind_pop);
-	  free(ind_pop_3);
-
-
-
-
-	  for (i=0;i<2;i++)
-		  free(temp_population_center[i]);
-
-	  free(temp_population_center);
-
-	  free(temp_size_j);
-	  free(size_p);
-
-
-
-	  //update the IDs, Centers, and # of populations
-	  for (i=0;i<file_Len;i++)
-	  {
-		  all_population_ID[i]=all_computed_pop_ID[i];
-		  if (all_population_ID[i]>=num_computed_population)
-			  printf("all_population_ID[%ld]=%ld\n",i,all_population_ID[i]);
-	  }
-
-	  num_population=num_computed_population;
-
-	  free(all_computed_pop_ID);
-    //end partitioning
-  // since the num_population has changed, population_center needs to be redefined as below
-
-  population_center=(double **)malloc(sizeof(double*)*num_population);
-  memset(population_center,0,sizeof(double*)*num_population);
-  for (i=0;i<num_population;i++)
-  {
-     population_center[i]=(double*)malloc(sizeof(double)*num_dm);
-     memset(population_center[i],0,sizeof(double)*num_dm);
-  }
-
-
-  ID2Center_all(normalized_data,file_Len,num_dm,num_population,all_population_ID,population_center);
-
-
-
-  ////// end of further partitioning
-
-  ////////////////////////////////////////////////////////////
-  //  to further merge populations to avoid overpartitioning
-  //  Added June 20, 2010
-  ////////////////////////////////////////////////////////////
-
-
-
-  num_real_pop=num_population;
-  keep_merge=1;
-
-  if (num_pop>num_real_pop)
-  {
-		fprintf(stderr,"number of populations specified too large\n");
-		exit(0);
-  }
-
-  center_1=(double *)malloc(sizeof(double)*num_dm);
-  memset(center_1,0,sizeof(double)*num_dm);
-
-  center_2=(double *)malloc(sizeof(double)*num_dm);
-  memset(center_2,0,sizeof(double)*num_dm);
-
-  center_3=(double *)malloc(sizeof(double)*num_dm);
-  memset(center_3,0,sizeof(double)*num_dm);
-
-
-
-  while (((num_real_pop>num_pop) && (num_pop!=0)) || ((keep_merge==1) && (num_pop==0) && (num_real_pop>2)))
-  {
-
-	keep_merge=0;  //so, if no entering merge function, while will exit when num_pop==0
-
-	real_pop_center=(double **)malloc(sizeof(double*)*num_real_pop);
-    memset(real_pop_center,0,sizeof(double*)*num_real_pop);
-    for (i=0;i<num_real_pop;i++)
-    {
-      real_pop_center[i]=(double*)malloc(sizeof(double)*num_dm);
-      memset(real_pop_center[i],0,sizeof(double)*num_dm);
-    }
-
-	min_pop=(double **)malloc(sizeof(double*)*num_real_pop);
-    memset(min_pop,0,sizeof(double*)*num_real_pop);
-    for (i=0;i<num_real_pop;i++)
-    {
-      min_pop[i]=(double*)malloc(sizeof(double)*num_dm);
-      memset(min_pop[i],0,sizeof(double)*num_dm);
-    }
-
-	max_pop=(double **)malloc(sizeof(double*)*num_real_pop);
-    memset(max_pop,0,sizeof(double*)*num_real_pop);
-    for (i=0;i<num_real_pop;i++)
-    {
-      max_pop[i]=(double*)malloc(sizeof(double)*num_dm);
-      memset(max_pop[i],0,sizeof(double)*num_dm);
-    }
-
-	if (num_real_pop==num_population)
-	{
-		for (i=0;i<num_real_pop;i++)
-			for (j=0;j<num_dm;j++)
-				real_pop_center[i][j]=population_center[i][j];
-	}
-	else
-	{
-		ID2Center_all(normalized_data,file_Len,num_dm,num_real_pop,all_population_ID,real_pop_center);
-	}
-
-	for (i=0;i<num_real_pop;i++)
-	{
-		for (j=0;j<num_dm;j++)
-		{
-			min_pop[i][j]=MAX_VALUE;
-
-			max_pop[i][j]=0;
-		}
-	}
-
-	for (i=0;i<file_Len;i++)
-	{
-		index_id=all_population_ID[i];
-		for (j=0;j<num_dm;j++)
-		{
-			if (normalized_data[i][j]<min_pop[index_id][j])
-				min_pop[index_id][j]=normalized_data[i][j];
-
-			if (normalized_data[i][j]>max_pop[index_id][j])
-				max_pop[index_id][j]=normalized_data[i][j];
-		}
-	}
-
-/*	for (i=0;i<num_real_pop;i++)
-	{
-		for (j=0;j<num_dm;j++)
-		{
-			printf("min_pop is %f\t",min_pop[i][j]);
-			//printf("max_pop is %f\n",max_pop[i][j]);
-		}
-		printf("\n");
-	}
-*/
-
-
-	distance_pop=(double **)malloc(sizeof(double*)*num_real_pop);
-    memset(distance_pop,0,sizeof(double*)*num_real_pop);
-    for (i=0;i<num_real_pop;i++)
-    {
-      distance_pop[i]=(double*)malloc(sizeof(double)*num_real_pop);
-      memset(distance_pop[i],0,sizeof(double)*num_real_pop);
-    }
-
-	for (i=0;i<num_real_pop-1;i++)
-	{
-		for (j=i+1;j<num_real_pop;j++)
-		{
-		  distance=0;
-
-		  for (t=0;t<num_dm;t++)
-		  {
-			dist=real_pop_center[i][t]-real_pop_center[j][t];
-			distance=distance+dist*dist;
-		  }
-		  distance_pop[i][j]=distance;
-		  distance_pop[j][i]=distance;
-		}
-	}
-
-	if (num_real_pop>2)
-		num_checked_range=(long)((double)num_real_pop*(num_real_pop-1)/2.0); //to find the mergeable pair among the num_checked_range pairs of smallest distances
-	else
-		num_checked_range=1;
-
-	size_c=(long *)malloc(sizeof(long)*num_real_pop);
-    memset(size_c,0,sizeof(long)*num_real_pop);
-
-	for (i=0;i<file_Len;i++)
-	  size_c[all_population_ID[i]]++;
-
-	for (p=0;p<num_checked_range;p++)
-	{
-		current_smallest_dist=MAX_VALUE;
-
-		for (i=0;i<num_real_pop-1;i++)
-		{
-			for (j=i+1;j<num_real_pop;j++)
-			{
-				if (distance_pop[i][j]<current_smallest_dist)
-				{
-					current_smallest_dist=distance_pop[i][j];
-
-					temp_i=i;
-					temp_j=j;
-				}
-			}
-		}
-
-		if (p==0)
-		{
-			first_i=temp_i;
-			first_j=temp_j;
-		}
-
-		distance_pop[temp_i][temp_j]=MAX_VALUE+1; //make sure this pair won't be selected next time
-
-		//normalize and calculate std for temp_i and temp_j
-
-		//pick the largest 3 dimensions on standard deviation
-		d1=-1;
-		d2=-1;
-		d3=-1;
-
-		for (i=0;i<3;i++)
-		{
-			max_d_dist=0;
-			for (j=0;j<num_dm;j++)
-			{
-				if ((j!=d1) && (j!=d2))
-				{
-					temp=min(min_pop[temp_i][j],min_pop[temp_j][j]);
-					tmp=max(max_pop[temp_i][j],max_pop[temp_j][j]);
-					if (tmp<=temp)
-					{
-						//printf("min_pop[%d][%d]=%f \t min_pop[%d][%d]=%f \t max_pop[%d][%d]=%f \t max_pop[%d][%d]=%f\n",temp_i,j,min_pop[temp_i][j],temp_j, j, min_pop[temp_j][j],temp_i,j,max_pop[temp_i][j],temp_j,j,max_pop[temp_j][j]);
-						dist=0;
-					}
-					else
-						dist=(real_pop_center[temp_i][j]-real_pop_center[temp_j][j])/(tmp-temp);
-					if (dist<0)
-						dist=-dist;
-				}
-				else
-					dist=-1;
-
-				if (dist>max_d_dist)
-				{
-					max_d_dist=dist;
-					d_d=j;
-				}
-			}
-
-			if (i==0)
-				d1=d_d;
-			if (i==1)
-				d2=d_d;
-			if (i==2)
-				d3=d_d;
-		}
-
-		//printf("d1=%d;d2=%d;d3=%d\n",d1,d2,d3);
-
-		Ei=get_avg_dist(real_pop_center[temp_i], temp_i,temp_j, all_population_ID, num_real_pop,file_Len, num_dm, normalized_data, d1,d2,d3,size_c);
-		Ej=get_avg_dist(real_pop_center[temp_j], temp_i,temp_j, all_population_ID, num_real_pop,file_Len, num_dm, normalized_data, d1,d2,d3,size_c);
-
-		for (t=0;t<num_dm;t++)
-		{
-			center_1[t]=real_pop_center[temp_i][t]*0.25+real_pop_center[temp_j][t]*0.75;
-			center_2[t]=real_pop_center[temp_i][t]*0.5+real_pop_center[temp_j][t]*0.5;
-			center_3[t]=real_pop_center[temp_i][t]*0.75+real_pop_center[temp_j][t]*0.25;
-		}
-
-		E1=get_avg_dist(center_1, temp_i,temp_j, all_population_ID, num_real_pop,file_Len, num_dm, normalized_data, d1,d2,d3,size_c);
-
-		E2=get_avg_dist(center_2, temp_i,temp_j, all_population_ID, num_real_pop,file_Len, num_dm, normalized_data, d1,d2,d3,size_c);
-
-		E3=get_avg_dist(center_3, temp_i,temp_j, all_population_ID, num_real_pop,file_Len, num_dm, normalized_data, d1,d2,d3,size_c);
-
-		if (E1<E2)
-			Ep=E2;
-		else
-			Ep=E1;
-
-		Ep=max(Ep,E3); //Ep is the most sparse area
-
-		Ep=Ep*E_T;
-		//printf("Ep=%f;Ei=%f;Ej=%f\n",Ep,Ei,Ej);
-
-		if ((Ep<=Ei) || (Ep<=Ej))//if the most sparse area between i and j are still denser than one of them, temp_i and temp_j should be merged
-		{
-			keep_merge=1;
-			break;
-		}//end if (Ep)
-	} //end for p
-
-	//printf("keep_merge=%d\n",keep_merge);
-
-	for (i=0;i<num_real_pop;i++)
-	{
-		free(real_pop_center[i]);
-		free(distance_pop[i]);
-		free(min_pop[i]);
-		free(max_pop[i]);
-	}
-	free(real_pop_center);
-	free(min_pop);
-	free(max_pop);
-	free(distance_pop);
-	free(size_c);
-
-	//printf("temp_i=%d;temp_j=%d\n",temp_i,temp_j);
-
-	if (keep_merge)  //found one within p loop
-	{
-		for (i=0;i<file_Len;i++)
-		{
-			if (all_population_ID[i]>temp_j)
-			{
-				all_population_ID[i]=all_population_ID[i]-1;
-			}
-			else
-			{
-				if (all_population_ID[i]==temp_j)
-				{
-					all_population_ID[i]=temp_i;
-				}
-			}
-		}
-
-		num_real_pop--;
-	}
-	else
-	{
-		if ((num_pop!=0) && (num_pop<num_real_pop)) //not reach the specified num of pop
-		{
-			for (i=0;i<file_Len;i++)
-			{
-				if (all_population_ID[i]>first_j)
-				{
-					all_population_ID[i]=all_population_ID[i]-1;
-				}
-				else
-				{
-					if (all_population_ID[i]==first_j)
-					{
-						all_population_ID[i]=first_i;
-					}
-				}
-			}
-
-			num_real_pop--;
-
-
-
-		}
-	}
-		//printf("num_real_pop is %d\n",num_real_pop);
-
-  } //end of while
-
-
-
-  free(center_1);
-  free(center_2);
-  free(center_3);
-  printf("Final number of populations is %ld\n",num_real_pop);
-
-  new_population_center=(double **)malloc(sizeof(double*)*num_real_pop);
-  memset(new_population_center,0,sizeof(double*)*num_real_pop);
-  for (i=0;i<num_real_pop;i++)
-  {
-      new_population_center[i]=(double*)malloc(sizeof(double)*num_dm);
-      memset(new_population_center[i],0,sizeof(double)*num_dm);
-  }
-
-
-  ///////////////////////////////////////////
-  //End of population mapping
-  ///////////////////////////////////////////
-
-  show(input_data, all_population_ID, file_Len, num_real_pop, num_dm, para_name_string);
-
-  ID2Center_all(input_data,file_Len,num_dm,num_real_pop,all_population_ID,new_population_center);
-
-
-  f_cid=fopen("population_id.txt","w");
-  f_ctr=fopen("population_center.txt","w");
-  f_out=fopen("coordinates.txt","w");
-  f_results=fopen("flock_results.txt","w");
-
-/*
-  f_parameters=fopen("parameters.txt","w");
-  fprintf(f_parameters,"Number_of_Bins\t%d\n",num_bin);
-  fprintf(f_parameters,"Density\t%f\n",aver_index);
-  fclose(f_parameters);
-*/
-
-  for (i=0;i<file_Len;i++)
-	fprintf(f_cid,"%ld\n",all_population_ID[i]+1); //all_population_ID[i] changed to all_population_ID[i]+1 to start from 1 instead of 0: April 16, 2009
-
-  /*
-   * New to check for min/max to add to parameters.txt
-   *
-  */
-
-  fprintf(f_out,"%s\n",para_name_string);
-  //fprintf(f_results,"%s\tEvent\tPopulation\n",para_name_string);
-  fprintf(f_results,"%s\tPopulation\n",para_name_string);
-  for (i=0;i<file_Len;i++)
-  {
-	for (j=0;j<num_dm;j++)
-	{
-		if (input_data[i][j] < min) {
-			min = (int)input_data[i][j];
-		}
-		if (input_data[i][j] > max) {
-			max = (int)input_data[i][j];
-		}
-		if (j==num_dm-1)
-		{
-			fprintf(f_out,"%d\n",(int)input_data[i][j]);
-			fprintf(f_results,"%d\t",(int)input_data[i][j]);
-		}
-		else
-		{
-			fprintf(f_out,"%d\t",(int)input_data[i][j]);
-			fprintf(f_results,"%d\t",(int)input_data[i][j]);
-		}
-	}
-	//fprintf(f_results,"%ld\t",i + 1);
-	fprintf(f_results,"%ld\n",all_population_ID[i]+1); //all_population_ID[i] changed to all_population_ID[i]+1 to start from 1 instead of 0: April 16, 2009
-  }
-
-/*
-  f_parameters=fopen("parameters.txt","w");
-  fprintf(f_parameters,"Number_of_Bins\t%ld\n",num_bin);
-  fprintf(f_parameters,"Density\t%d\n",den_t_event);
-  fprintf(f_parameters,"Min\t%d\n",min);
-  fprintf(f_parameters,"Max\t%d\n",max);
-  fclose(f_parameters);
-*/
-
-  f_properties=fopen("fcs.properties","w");
-  fprintf(f_properties,"Bins=%ld\n",num_bin);
-  fprintf(f_properties,"Density=%d\n",den_t_event);
-  fprintf(f_properties,"Min=%d\n",min);
-  fprintf(f_properties,"Max=%d\n",max);
-  fprintf(f_properties,"Populations=%ld\n",num_real_pop);
-  fprintf(f_properties,"Events=%ld\n",file_Len);
-  fprintf(f_properties,"Markers=%ld\n",num_dm);
-  fclose(f_properties);
-
-  for (i=0;i<num_real_pop;i++) {
-	/* Add if we want to include population id in the output
-	*/
-	fprintf(f_ctr,"%ld\t",i+1);  //i changed to i+1 to start from 1 instead of 0: April 16, 2009
-
-	for (j=0;j<num_dm;j++) {
-		if (j==num_dm-1)
-			fprintf(f_ctr,"%.0f\n",new_population_center[i][j]);
-		else
-			fprintf(f_ctr,"%.0f\t",new_population_center[i][j]);
-	}
-  }
-
-  	//added April 16, 2009
-	f_mfi=fopen("MFI.txt","w");
-
-	for (i=0;i<num_real_pop;i++)
-	{
-		fprintf(f_mfi,"%ld\t",i+1);
-
-		for (j=0;j<num_dm;j++)
-		{
-			if (j==num_dm-1)
-				fprintf(f_mfi,"%.0f\n",new_population_center[i][j]);
-			else
-				fprintf(f_mfi,"%.0f\t",new_population_center[i][j]);
-		}
-	}
-	fclose(f_mfi);
-
-	//ended April 16, 2009
-
-  fclose(f_cid);
-  fclose(f_ctr);
-  fclose(f_out);
-  fclose(f_results);
-
-
-  for (i=0;i<num_population;i++)
-  	free(population_center[i]);
-
-  free(population_center);
-
-  for (i=0;i<num_real_pop;i++)
-	  free(new_population_center[i]);
-
-  free(new_population_center);
-
-  for (i=0;i<file_Len;i++)
-    free(normalized_data[i]);
-  free(normalized_data);
-
-  free(grid_populationID);
-
-  free(cluster_populationID);
-  free(grid_clusterID);
-  free(cluster_ID);
-
-  for (i=0;i<file_Len;i++)
-    free(input_data[i]);
-  free(input_data);
-
-  free(grid_ID);
-  free(population_ID);
-  free(all_population_ID);
-  free(eventID_To_denseventID);
-
-  ///////////////////////////////////////////////////////////
-  printf("Ending time:\t\t\t\t");
-  fflush(stdout);
-  system("/bin/date");
-
-  /*
-   * Windows version
-  _strtime( tmpbuf );
-  printf( "Ending time:\t\t\t\t%s\n", tmpbuf );
-  _strdate( tmpbuf );
-  printf( "Ending date:\t\t\t\t%s\n", tmpbuf );
- */
-
-  return 0;
-}