public static function ex4()
{
header('Content-type: application/json; charset=utf-8');
//input matricea A , A init
$A = self::getMatrixFromString($_POST['matrice']);
$n = $_POST['n'];
$epsilon = $_POST['epsilon'];
$arrayS = self::getArrayFromString($_POST['arr']);
$b = self::getB($A, $arrayS, $n, $epsilon);
$QR = self::HouseholderDecomposition($A, $epsilon, $n, $b);
$x = self::getX($QR["r"], $n, $QR["b"]);
$matrix = new Matrix($n, $n);
$matrix->fromArray($A);
$QRlibf = array();
$QRlib = new QRGivens($matrix);
$QRlibf['Qlib'] = $QRlib->getQ()->asArray();
$QRlibf['rlib'] = $QRlib->getR()->asArray();
$xlib = self::getX($QR["r"], $n, $QR["b"]);
$vector1 = array();
$ainit = Util::getInit($A);
for ($i = 0; $i < $n; $i++) {
$vector1[$i] = $ainit[$i] * $x[$i] - $b[$i];
}
$norm1 = Util::getNorm($vector1, $n);
$vector2 = array();
for ($i = 0; $i < $n; $i++) {
$vector2[$i] = $ainit[$i] * $xlib[$i] - $b[$i];
}
$norm2 = Util::getNorm($vector2, $n);
$vector3 = array();
for ($i = 0; $i < $n; $i++) {
$vector3[$i] = $x[$i] - $arrayS[$i];
}
$norm3 = Util::getNorm($vector3, $n) / Util::getNorm($arrayS, $n);
$vector4 = array();
for ($i = 0; $i < $n; $i++) {
$vector4[$i] = $xlib[$i] - $arrayS[$i];
}
$norm4 = Util::getNorm($vector4, $n) / Util::getNorm($arrayS, $n);
echo json_encode(array("A" => Util::getStringFromMatrix($A), "epsilon" => $epsilon, "Q" => self::getStringFromMatrix($QR['Q']), "r" => self::getStringFromMatrix($QR['r']), "Qlib" => self::getStringFromMatrix($QRlibf['Qlib']), "rlib" => self::getStringFromMatrix($QRlibf['rlib']), "x" => Util::getStringFromArray($x), "xlib" => Util::getStringFromArray($xlib), "norm1" => $norm1, "norm2" => $norm2, "norm3" => $norm3, "norm4" => $norm4));
}
public function testMultiply()
{
$matrix = Matrix::fromArray([[1, 2, 3], [4, 5, 6]])->multiply(Matrix::fromArray([[7, 8], [9, 10], [11, 12]]));
$this->assertInstanceOf(Matrix::class, $matrix);
$this->assertSame([[58.0, 64.0], [139.0, 154.0]], $matrix->toArray());
}