<?php
// The following functions are used to construct a contigency table 
// and to calculate the Simpson's Index of Diversity and 95% Confidence Interval, 
// Rand, adjusted Rand, Wallace coefficients
//
//    Copyright (C) 2009  UMMI@IMM
//
//    This file is part of Comparing Partitions website <http://www.comparingpartitions.info/>.    
//    Comparing Partitions website is free software: you can redistribute it and/or modify
//    it under the terms of the GNU General Public License as published by
//    the Free Software Foundation, either version 3 of the License, or
//    (at your option) any later version.
//
//    This program is distributed in the hope that it will be useful,
//    but WITHOUT ANY WARRANTY; without even the implied warranty of
//    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//    GNU General Public License for more details.
//
//    You should have received a copy of the GNU General Public License
//    along with this program.  If not, see <http://www.gnu.org/licenses/>.
//
//The following functions are used to construct a contigency table array ($cont_table)
// from a 2 array ($ar1,$ar2) input each with a classification of a dataset
//input (full_cont_table): $ar1,$ar2
//output:$cont_table
function full_cont_table($ar1,$ar2){
	$table=cont_table($ar1,$ar2);
	$table_headers=cont_table_headers($table);
	list($sumrow,$sumcol,$total)=cont_table_totals($table,$table_headers);
	$cont_table[values]=$table;
	$cont_table[headers]=$table_headers;
	$cont_table[totals][rows]=$sumrow;
	$cont_table[totals][columns]=$sumcol;
	$cont_table[Total]=$total;
	return($cont_table);
}

function cont_table($ar1,$ar2){
	$n_ele=count($ar1);# TODO verify if size a1==size a2
	for ($i=0; $i<=$n_ele-1;$i++){
		$cont["$ar1[$i]"]["$ar2[$i]"]++;	
	}
return($cont); 
}

function cont_table_headers($cont){
	$xnames=array_keys($cont);
	foreach($xnames as $value ) {
		$piece=array_keys($cont[$value]);
		foreach($piece as $value2){
			$ynames[]=$value2;
		}
	}
	$ynames=array_unique($ynames);
	$ct_headers[x]=$xnames;
	$ct_headers[y]=$ynames;
	
	
	return($ct_headers);
}

function cont_table_totals($cont,$ct_headers){

	foreach($ct_headers[y] as $value){
		$sumrow[$value]=0;
		foreach($ct_headers[x] as $value2){
			if($cont["$value2"]["$value"]!=0) {$CV=$cont["$value2"]["$value"];} else {$CV=0;}
		    $sumrow["$value"]=$sumrow["$value"]+$cont["$value2"]["$value"];
		    $sumcol["$value2"]=$sumcol["$value2"]+$cont["$value2"]["$value"];
		}
	}
#TOTALS ROW
	foreach($ct_headers[x] as $value3){
		$total=$total+$sumcol[$value3];
	}
	return(array($sumrow,$sumcol,$total));
}

//This function calculates the mismatch matrix that are needed for the 
//partition agreement coeficients calculations 
//input: $cont_table (output from full_cont_table)
//output:$a,$b,$c,$d,$N
function mismatch_matrix($full_table_cont){
#Defining $a
	foreach($full_table_cont[headers][x] as $value){
		foreach($full_table_cont[headers][y] as $value2){
			$a=$a+($full_table_cont[values]["$value"]["$value2"]*($full_table_cont[values][$value][$value2]-1))/2;
			
		}
	}
	
	#Defining $A1
	foreach($full_table_cont[totals][columns] as $value){
		$A1=$A1+($value*($value-1))/2;
	}
	#Defining $b
	$b=$A1-$a;
	#Defining $A2
	foreach($full_table_cont[totals][rows] as $value){
		$A2=$A2+($value*($value-1))/2;
	}
	##Defining $c
	$c=$A2-$a;
	##defining d
	$N=$full_table_cont[Total];
	$d=($N*($N-1)/2)-$A1-$c;
	
	return(array($a,$b,$c,$d,$N));
}


// RAND, Adjusted RAnd and Wallace coefficient functions
function randcoef($a,$b,$c,$d){
	$Rand = ($a + $d)/($a + $b + $c + $d);
	return($Rand);
}

function adjust_rand($a,$b,$c,$d,$N){
	//$Rand = ($a + $d)/($a + $b + $c + $d);
    $ARand = (($N*($N-1)/2)*($a+$d)-(($a+$b)*($a+$c)+($c+$d)*($b+$d)))/(pow($N*($N-1)/2,2)-(($a+$b)*($a+$c)+($c+$d)*($b+$d)));	
    //return(array($Rand,$ARand));
    return($ARand);
}

function wallace($a,$b,$c){
	if($a+$b>0){
		$Wallace1=$a/($a+$b);
	} else $Wallace1=0;
	if($a+$c>0){
		$Wallace2=$a/($a+$c);
	}else $Wallace2=0;
	return(array($Wallace1,$Wallace2));
}

//Simpson's index of diversity and 95% confidence interval calculation 
//input is an array of calssification
//input: $ar1
//output: $SID  (array...see function for details)
function Simpsons_Index_Diversity($ar1){
	$N=count($ar1);
	$unique_entries=array_unique($ar1);
	$ngroups=count($unique_entries);
	foreach($unique_entries as $values){
		$freq[$values]=count(array_keys($ar1,$values));
	}
	foreach($freq as $values){		
		$sumtot=$sumtot+(($values)*(($values)-1));
		$sumFc2=$sumFc2+pow(($values/$N),2);
		$sumFc3=$sumFc3+pow(($values/$N),3);
	}
	if (($N*($N-1))>0){
		$SID[value]=1-($sumtot/($N*($N-1)));
	} else $SID[value]=1; 
	$sqrsumFc2=pow($sumFc2,2);
	$s2=(4/$N)*($sumFc3-$sqrsumFc2);

	$SID[low]=$SID[value]-2*sqrt($s2);
	$SID[high]=$SID[value]+2*sqrt($s2);
	$SID[ngroups]=count($freq);
	return($SID);
}

?>