/**
* Axiom: |x|∞ ≤ |x|₁ ≤ √n |x|∞
* Max norm is less than equal to l₁-norm which is less than equal to sqrt n * max norm.
*
* @dataProvider dataProviderForSingleVector
*/
public function testMaxNormLessThanEqualL1NormLessThanEqualSqrtNMaxNorm(array $V)
{
$V = new Vector($V);
$n = $V->getN();
$max_norm = $V->maxNorm();
$l₁norm = $V->l1Norm();
$√n_max_norm = $n * $max_norm;
$this->assertLessThanOrEqual($l₁norm, $max_norm);
$this->assertLessThanOrEqual($√n_max_norm, $l₁norm);
$this->assertLessThanOrEqual($√n_max_norm, $max_norm);
}
/**
* @dataProvider dataProviderForMaxNorm
*/
public function testMaxNorm(array $A, $maxnorm)
{
$A = new Vector($A);
$this->assertEquals($maxnorm, $A->maxNorm(), '', 0.0001);
}