* // Equivalent to: x^2 + .5 * $polynom = new ezcGraphPolynom( array( 2 => 1, 0 => .5 ) ); * * // Calculate result for x = 1, echos: 1.5 * echo $polynom->evaluate( 1 ), PHP_EOL; * * // Build the sum with another polynom * $polynom->add( new ezcGraphPolynom( array( 1 => 1 ) ) ); * * // Print polynom, echos: * // x^2 + x + 5.00e-1 * echo $polynom, PHP_EOL; * * * @version 1.5 * @package Graph */ class ezcGraphPolynom { /** * Factors of the polynom * * An example: * Polynom: * 2 * x^3 + .5 * x - 3 * Array: * array ( * (int) 3 => (float) 2, * (int) 1 => (float) .5, * (int) 0 => (float) -3, * ) * * @var array */ protected $values; // @TODO: Introduce precision option for string output? /** * Constructor * * Constructs a polynom object from given array, where the key is the * exponent and the value the factor. * An example: * Polynom: * 2 * x^3 + .5 * x - 3 * Array: * array ( * (int) 3 => (float) 2, * (int) 1 => (float) .5, * (int) 0 => (float) -3, * ) * * @param array $values Array with values * @return ezcGraphPolynom */ public function __construct( array $values = array() ) { foreach ( $values as $exponent => $factor ) { $this->values[(int) $exponent] = (float) $factor; } } /** * Initialise a polygon * * Initialise a polygon of the given order. Sets all factors to 0. * * @param int $order Order of polygon * @return ezcGraphPolynom Created polynom */ public function init( $order ) { for ( $i = 0; $i <= $order; ++$i ) { $this->values[$i] = 0; } return $this; } /** * Return factor for one exponent * * @param int $exponent Exponent * @return float Factor */ public function get( $exponent ) { if ( !isset( $this->values[$exponent] ) ) { return 0; } else { return $this->values[$exponent]; } } /** * Set the factor for one exponent * * @param int $exponent Exponent * @param float $factor Factor * @return ezcGraphPolynom Modified polynom */ public function set( $exponent, $factor ) { $this->values[(int) $exponent] = (float) $factor; return $this; } /** * Returns the order of the polynom * * @return int Polynom order */ public function getOrder() { return max( array_keys( $this->values ) ); } /** * Adds polynom to current polynom * * @param ezcGraphPolynom $polynom Polynom to add * @return ezcGraphPolynom Modified polynom */ public function add( ezcGraphPolynom $polynom ) { $order = max( $this->getOrder(), $polynom->getOrder() ); for ( $i = 0; $i <= $order; ++$i ) { $this->set( $i, $this->get( $i ) + $polynom->get( $i ) ); } return $this; } /** * Evaluate Polynom with a given value * * @param float $x Value * @return float Result */ public function evaluate( $x ) { $value = 0; foreach ( $this->values as $exponent => $factor ) { $value += $factor * pow( $x, $exponent ); } return $value; } /** * Returns a string represenation of the polynom * * @return string String representation of polynom */ public function __toString() { krsort( $this->values ); $string = ''; foreach ( $this->values as $exponent => $factor ) { if ( $factor == 0 ) { continue; } $string .= ( $factor < 0 ? ' - ' : ' + ' ); $factor = abs( $factor ); switch ( true ) { case abs( 1 - $factor ) < .0001: // No not append, if factor is ~1 break; case $factor < 1: case $factor >= 1000: $string .= sprintf( '%.2e ', $factor ); break; case $factor >= 100: $string .= sprintf( '%.0f ', $factor ); break; case $factor >= 10: $string .= sprintf( '%.1f ', $factor ); break; default: $string .= sprintf( '%.2f ', $factor ); break; } switch ( true ) { case $exponent > 1: $string .= sprintf( 'x^%d', $exponent ); break; case $exponent === 1: $string .= 'x'; break; case $exponent === 0: if ( abs( 1 - $factor ) < .0001 ) { $string .= '1'; } break; } } if ( substr( $string, 0, 3 ) === ' + ' ) { $string = substr( $string, 3 ); } else { $string = '-' . substr( $string, 3 ); } return trim( $string ); } } ?>