query_param_map.php

<?php

$params = array(
  'key1' => array( 'k1v1', 'k1v2'),
  'key2' => array( 'k2v1', 'k2v2'),
  'key3' => array( 'k3v1', 'k3v2'),
);

function query_param_map( array $input_arr )
{
  // declare output var
  $output = array();
  // intput array is not array so return empty array
  if( !is_array( $input_arr ) ) return $output;
    // keep count of object
    $obj_i = 0;
    // loop over object and it's values
    foreach ($input_arr as $key => $values) {
      // declare temp output
      $temp_output = array();
      // loop over values of given key
      for ( $i = 0; $i < count( $values ); $i++ ) {
        // first key output
        if( 0 === $obj_i ){
          $temp_output[] = sprintf( "%s=%s", $key, $values[ $i ] );
        }
        // other keys output
        else{
          // loop over output and append new key value into temp_output
          for ($j=0; $j < count( $output ); $j++) {
            $temp_output[] = sprintf( "%s&%s=%s", $output[ $j ], $key, $values[ $i ] );
          }
        }
      }
      // incress the index of the object
      $obj_i++;
      // copy the temp output into the output
      $output = $temp_output;
    }
  // return the output
  return $output;
}

$output = query_param_map( $params );
print_r( $output );

Output:

Array
(
    [0] => key1=k1v1&key2=k2v1&key3=k3v1
    [1] => key1=k1v2&key2=k2v1&key3=k3v1
    [2] => key1=k1v1&key2=k2v2&key3=k3v1
    [3] => key1=k1v2&key2=k2v2&key3=k3v1
    [4] => key1=k1v1&key2=k2v1&key3=k3v2
    [5] => key1=k1v2&key2=k2v1&key3=k3v2
    [6] => key1=k1v1&key2=k2v2&key3=k3v2
    [7] => key1=k1v2&key2=k2v2&key3=k3v2
)