<?php
include_once('includes/LeastSquareRegression.php');

$wave = array();

for ($i=0; $i<1000; $i++  ){
    $wave[$i]['time']=$i+(rand(0,100)+0.01)/100;
    $wave[$i]['U']=(cos($i/62.83+(rand(0,100)+0.01)/100)+cos(3*$i/62.83+(rand(0,100)+0.01)/100)+cos(5*$i/62.83+(rand(0,100)+0.01)/100))>1?1:0;
}


$dataString = "";
$first = true;
$data =array();
$data_time = array();
$i=0;

foreach($wave as $point) {
    $x=$point['time'];
    $y=$point['U'];
    $dataString.=($first?"":",")."['".$x."',".$y."]";
    $first = false;
    $data[$i] = $y;
    $data_time[$i] = $x;
    $i++;
}
//set polinom rank
$k=7;
//define polinom function
function f1($x) {
  return cos($x/62.83);
}
//Clear all internal data and prepare for new calculation.
$x_Powers = array();
$xy_Powers = array();

$squares = ( $k - 1 ) * 2;

// Initialize power arrays.
for ( $index = 0; $index <= $squares; ++$index )
{
  $x_Powers[ $index ] = 0;
  $xy_Powers[ $index ] = 0;
}
//Add a data point to calculation
for($i=0;$i<count($data);$i++) {
  //$data[$i]['x'] - month # = 0,1,...,n, not month # in year, just sort# in data array
  $x=f1($data_time[$i]);
  $y=$data[$i];
  // Accumulate new data to power sums.
  for ( $index = 0; $index <= $squares; ++$index )
  {
    $x_Powers[ $index ] = $x_Powers[ $index ] + pow( $x, $index );
  
    $xy_Powers[ $index ] = $xy_Powers[ $index ] + $y * pow( $x, $index );
  }
}
//Calculate coefficients based on current data.

// Build a matrix.
// The matrix is made up of the sum of powers.  So if the number represents the power,
// the matrix will look like this for a 5th degree polynomial:
//     [ 0 1 2 3 4 ]
//     [ 1 2 3 4 5 ]
//     [ 2 3 4 5 6 ]
//     [ 3 4 5 6 7 ]
//     [ 4 5 6 7 8 ]
//
$matrix = array();
for ( $row = 0; $row < $k; ++$row )
{
  $matrix[ $row ] = array();
  for ( $column = 0; $column < $k; ++$column )
    $matrix[ $row ][ $column ] =
      $x_Powers[ $row + $column ];
}

// Create augmented matrix by adding X*Y powers.
for ( $row = 0; $row < $k; ++$row )
  $matrix[ $row ][ $k ] = $xy_Powers[ $row ];

// Initialize done.
$isDone = array();
for ( $column = 0; $column < $k; ++$column )
  $isDone[ $column ] = false;
  
// This loop will result in an upper-triangle matrix with the
// diagonals all 1--the first part of row-reduction--using 2
// elementary row operations: multiplying a row by a scalar, and
// subtracting a row by a multiple of an other row.
// NOTE: This loop can be done out-of-order.  That is, the first
// row may not begin with the first term.  Order is tracked in the
// "order" array.
$order = array();
for ( $column = 0; $column < $k; ++$column )
{
  // Find a row to work with.
  // A row that has a term in this column, and has not yet been
  // reduced.
  $activeRow = 0;
  while ( ( $activeRow < $k ) && ( ( 0 == $matrix[ $activeRow ][ $column ] )
         || ( $isDone[ $activeRow ] ) )
        )
  {
    ++$activeRow;
  }

  // Do we have a term in this row?
  if ( $activeRow < $k )
  {
    // Remember the order.
    $order[ $column ] = $activeRow;

    // Normalize row--results in the first term being 1.
    $firstTerm = $matrix[ $activeRow ][ $column ];
    for ( $subColumn = $column; $subColumn <= $k; ++$subColumn )
      $matrix[ $activeRow ][ $subColumn ] = $matrix[ $activeRow ][ $subColumn ]/$firstTerm;

    // This row is finished.
    $isDone[ $activeRow ] = true;

    // Subtract the active row from all rows that are not finished.
    for ( $row = 0; $row < $k; ++$row )
      if ( ( ! $isDone[ $row ] )
        && ( 0 != $matrix[ $row ][ $column ] ) )
      {
         // Get first term in row.
         $firstTerm = $matrix[ $row ][ $column ];
         for ( $subColumn = $column; $subColumn <= $k; ++$subColumn )
         {
           $accumulator =$firstTerm * $matrix[ $activeRow ][ $subColumn ];
           $matrix[ $row ][ $subColumn ] = $matrix[ $row ][ $subColumn ] - $accumulator;
         }
      }
  }
}

// Reset done.
for ( $row = 0; $row < $k; ++$row )
 $isDone[ $row ] = false;

$coefficients = array();

// Back-substitution.
// This will solve the matrix completely, resulting in the identity
// matrix in the x-locations, and the coefficients in the last column.
//   | 1  0  0 ... 0  c0 |
//   | 0  1  0 ... 0  c1 |
//   | .  .  .     .   . |
//   | .  .  .     .   . |
//   | 0  0  0 ... 1  cn |
for ( $column = ( $k - 1 ); $column >= 0; --$column )
{
  // The active row is based on order.
  $activeRow = $order[ $column ];

  // The active row is now finished.
  $isDone[ $activeRow ] = true;

  // For all rows not finished...
  for ( $row = 0; $row < $k; ++$row )
    if ( $isDone[ $row ]!=true )
    {
      $firstTerm = $matrix[ $row ][ $column ];

      // Back substitution.
      for ( $subColumn = $column; $subColumn <= $k; ++$subColumn )
      {
        $accumulator = $firstTerm * $matrix[ $activeRow ][ $subColumn ];
        $matrix[ $row ][ $subColumn ] = $matrix[ $row ][ $subColumn ] - $accumulator;
      }
    }

  // Save this coefficient.
  $coefficients[ $column ] = $matrix[ $activeRow ][ $k ];
}

$dataString6 = '';
for($m=$i;$m<=$i+10;$m++){
    $data[$m] = 0;
    $data_time[$m] = ' +'.($m-$i+1);
}
$first = true;
foreach($data as $x=>$y) {
        $yk2=0;
    for($j=0;$j<$k;$j++) {
        $yk2+=$coefficients[$j]*pow(f1($x),$j);
    }
    $dataString6.=($first?"":",")."['".$data_time[$x]."',".$yk2."]";
  $first = false;
}


    
?>
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<script type="text/javascript">
var myData = new Array(<?echo $dataString;?>);
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