/**
* Axiom: |x|∞ ≤ |x|₂ ≤ √n |x|∞
* Max norm is less than equal to l₂-norm which is less than equal to sqrt n * max norm.
*
* @dataProvider dataProviderForSingleVector
*/
public function testMaxNormLessThtanEQualL2NormLessThanEqualSqrtNMaxNorm(array $V)
{
$V = new Vector($V);
$n = $V->getN();
$max_norm = $V->maxNorm();
$l²norm = $V->l2Norm();
$√n_max_norm = $n * $max_norm;
$this->assertLessThanOrEqual($l²norm, $max_norm);
$this->assertLessThanOrEqual($√n_max_norm, $l²norm);
$this->assertLessThanOrEqual($√n_max_norm, $max_norm);
}
/**
* @dataProvider dataProviderForL2Norm
*/
public function testL2Norm(array $A, $l²norm)
{
$A = new Vector($A);
$this->assertEquals($l²norm, $A->l2Norm(), '', 0.0001);
}
