Numerical analysis (implemented in php) 1: Laplace Interpolation

 

In the field of numerical analysis, try to use php. If you are interested, stick it down and try again.

The Laplace interpolation is an interpolation process that gives n known points and uses polynomial functions to fit and obtain the fitting function, and then estimates the value of an unknown point function.

The interpolation function is f (x) = xigma (SUM) lk * yk

This class implements the function of displaying functional images after interpolation.

 

<? Php

/*

* Laplace Interpolation

* @ Wangbin

**/

Class lags {

Private $ dot = array ();

Public function _ construct ($ array ){

$ This-> dot = $ array;

}

 

/*

* Calculate lk

**/

Private function get_lk ($ x, $ k ){

$ Num = count ($ this-> dot ['X']);

$ Omiga_xk = 1;

$ Omiga_x = 1;

For ($ I = 0; $ I <$ num; $ I ++ ){

If ($ I! = $ K ){

$ Omiga_xk * = ($ this-> dot ['X'] [$ k]-$ this-> dot ['X'] [$ I]);

$ Omiga_x * = ($ x-$ this-> dot ['X'] [$ I]);

}

}

$ Lk = $ omiga_x/$ omiga_xk;

Return $ lk;

}

Public function get_y ($ x ){

$ Num = count ($ this-> dot ['X']);

$ L = 0;

For ($ k = 0; $ k <$ num; $ k ++ ){

$ Lk = $ this-> get_lk ($ x, $ k );

$ L + = ($ this-> dot ['y'] [$ k] * $ lk );

 

}

Return $ L;

}

Public function draw (){

$ Img = imagecreate (500,500 );

Imagecolorallocate ($ img, 255,255, 2 );

$ Num = count ($ this-> dot ['X']);

$ Max = 0;

For ($ I = 0; $ I <$ num; $ I ++) $ max = $ max <$ this-> dot ['X'] [$ I]? $ This-> dot ['X'] [$ I]: $ max;

$ R = 7; // the radius of the vertex

$ Step = 0.1; // step size

For ($ I = 0; $ I <$ num; $ I ++ ){

Imagefilledellipse ($ img, $ this-> dot ['X'] [$ I], $ this-> dot ['y'] [$ I], $ r, $ r, 1 );

}

For ($ I = $ this-> dot ['X'] [0]-10; $ I <$ max + 10; $ I + = $ step ){

$ Current_x = $ I;

$ Current_y = $ this-> get_y ($ current_x );

$ Next_x = $ I + $ step;

$ Next_y = $ this-> get_y ($ next_x );

Imageline ($ img, $ current_x, $ current_y, $ next_x, $ next_y, 1 );

}

Header ("Content-type: image/png ");

Imagepng ($ img );

Imagedestroy ($ img );

}

}

 

$ X = new Laplace (array ('x' => array (100,120,220, 240,220,340), 'y' => array )));

$ X-> draw ();

?>

 

From pcenshao