/** * 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); }