Numerical Analysis (implemented in php) 1: Laplace interpolation

In the course of numerical analysis, I tried to use php to implement it. if you are interested, you can stick it down and try using the Laplace interpolation to give n known points. use polynomial functions to fit and find the fitting function, then, an interpolation process for estimating the value of the unknown point function is f (x) xigma (sum) lk * yk... syntaxHighlighter. all ();

 

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.

 

/*

* 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