<?phprequire_once "PEAR.php"; class ArrayMath {   /**   * Determines whether the data object is a matrix   * or not.  Used in functions that emulate polymorphic   * java methods - if argument is matrix do one set of   * operations otherwise do another set.  See sumSquares   * method.   */   function isMatrix($data) {     $slice = $data[0];     return is_array($slice) ? 1 : 0;   }      /**   * Renormalizes the array so that its L2 norm is 1   * (up to computational errors).   */   function normalize($v) {     return $this->scalarMultiply(1.0 / $this->norm($v), $v);   }   /**   * Computes the L2 norm of an array (Euclidean norm or "length").   */   function norm($v) {     return sqrt($this->sumSquares($v));   }   /**   * Sums the squares of all components;   * also called the energy of the array.   */   function sumSquares($data) {     if ($this->isMatrix($data)) {       $ans = 0;       $nRows = count($data);       $nCols = count($data[0]);       for($i=0; $i < $nRows; $i++)         for($j=0; $j < $nCols; $j++)            $ans += $data[$i][$j] * $data[$i][$j];     } else {       $ans = 0;       $len = count($v);       for($i = 0; $i < $len; $i++)         $ans += $v[$i] * $v[$i];     }     return $ans;   }      /**   * Computes the variance.   */   function variance($v) {     $m   = $this->mean($v);     $ans = 0.0;     $len = count($v);     for($i=0; $i < $len; $i++)       $ans += pow($v[$i] - $m, 2);     return $ans /($len - 1);   }   /**   * Computes the covariance.   */   function covariance($v1, $v2) {     $len1 = count($v1);     $len2 = count($v2);     if($len1 != $len2)       die("Arrays must have the same length : $len1, $len2");     $m1  = $this->mean($v1);     $m2  = $this->mean($v2);     $ans = 0.0;     for($i=0; $i < $len1; $i++)       $ans += ($v1[$i]-$m1) * ($v2[$i]-$m2);     return $ans / ($len1 - 1);   }   /**   * Computes the (linear) correlation between two arrays.   * Squaring this result and multiply by 100 gives you   * the percentage of correlation.   */   function correlation($v1, $v2) {     $denom = sqrt($this->variance($v1) * $this->variance($v2));     if($denom != 0)       return($this->covariance($v1, $v2) / $denom);     else {       if ( ($this->variance($v1)==0) && ($this->variance($v2)==0) )         return 1.0;       else         return 0.0;  // impossible to correlate a null signal with another     }   }       /**   * Computes the mean.   */   function mean($v) {     $len = count($v);     if ($len==0)       die("Nothing to compute! The array must have at least one element.");     return $this->mass($v) / $len;   }   /**   * Returns the standard deviation of an array.   */   function stdev($v) {     return sqrt($this->variance($v));   }        /**   * Returns the sum of the elements of the array.   */   function mass($v) {     $sum = 0;     $len = count($v);     for($i=0; $i < $len; $i++)        $sum += $v[$i];     return $sum;   }        /**   * Multiplies every component of an array by a scalar.   */   function scalarMultiply($a, $v) {     $ans = array();     for($i=0; $i < $len; $i++)       $ans[$i] = $v[$i] * $a;     return $ans;   }   /**   * Fast scalar multiplication for sparse arrays.   */   function scalarMultiplyFast($a, $v) {     $len = count($v);     if ($a == 0.0)       return count($v);     $ans = array();               for($i=0; $i < $len; $i++) {       if ( ($a!=0) && ($v[$i]!=0) )         $ans[$i] = $v[$i] * $a;       else         $ans[$i] = 0.0;     }             for($i=0; $i < $len; $i++) {               if ( ($a!=0) && ($v[$i]!=0) )         $ans[$i] = $v[$i] * $a;       else         $ans[$i] = 0.0;     }     return $ans;   }            /**   * Adds the two arrays together (componentwise).   * @exception IllegalArgumentException if the   * two arrays don't have the same length.   */   function add($a, $b) {     $len1 = count($a);     $len2 = count($b);     if($len1 != $len2)       die("Arrays must have the same length : $len1, $len2");     $ans = $a;             for($i=0; $i < $len1; $i++)       $ans[$i] += $b[$i];     return $ans;   }      /**   * Subtracts the two arrays together (componentwise).   * @exception IllegalArgumentException if the   * two arrays don't have the same length.   */   function subtract($a, $b) {     $len1 = count($a);     $len2 = count($b);     if($len1 != $len2)       die("Arrays must have the same length : $len1, $len2");     $ans = $a;             for($i=0; $i < $len1; $i++)       $ans[$i] -= $b[$i];     return $ans;   }           } ?>