Numerical Analysis (PHP implementation) One: Lagrange interpolation _php Tutorial

Learning numerical analysis, try to implement with PHP, interested friends can stick down to try

Lagrange interpolation is to give n known points, to fit the polynomial function, to find out the fitted function, and then to estimate the value of an unknown point function interpolation process

The interpolation function is f (x) = Xigma (sum) Lk*yk

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

/*

* Lagrange interpolation

* @wangbin

* */

Class lagrange{

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 = radius of the 7;//point

$step = 0.1;//Step

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 +; $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 Lagrange (Array (' X ' =>array (10,30,100,120,220), ' Y ' =>array (20,40,240,220,340)));

$x->draw ();

?>

Excerpted from Pcenshao

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