| Метод |
Описание |
|
|
dataProviderForAdditiveInverse ( ) |
|
|
|
dataProviderForCrossProduct ( ) |
|
|
|
dataProviderForCrossProductThreeVectors ( ) |
|
|
|
dataProviderForDotProductZero ( ) |
|
|
|
dataProviderForOuterProduct ( ) |
|
|
|
dataProviderForPerpendicularIdentity ( ) |
|
|
|
dataProviderForProjPerp ( ) |
|
|
|
dataProviderForSingleVector ( ) |
|
|
|
dataProviderForTwoVectors ( ) |
|
|
|
testAdditivityInTheScalarForScalarMultiplication ( array $A ) |
Axiom: (c + d)A = cA + dA
Additivity in the scalar |
|
|
testAdditivityInTheVectorForScalarMultiplication ( array $A, array $B ) |
Axiom: c(A + B) = cA + cB
Additivity in the vector |
|
|
testCrossProductDistributivity ( array $A, array $B, array $C ) |
Axiom: A x (B + C) = (A x B) + (A x C)
Cross product distributivity |
|
|
testCrossProductInnerProductWithEitherVectorIsZero ( array $A, array $B ) |
Axiom: (A x B) ⋅ A = 0
Axiom: (A x B) ⋅ B = 0
Dot product of either vector with the cross product is always zero. |
|
|
testCrossProductLagrangeFormula ( array $A, array $B, array $C ) |
Axiom: A x (B x C) = (A ⋅ C)B - (A ⋅ B)C
Lagrange's formula |
|
|
testCrossProductPropertyOfZero ( array $A, array $_ ) |
Axiom: A x 0 = 0
Cross product property of 0 |
|
|
testCrossProductVolumeProperty ( array $A, array $B, array $C ) |
Axiom: A ⋅ (B x C) = (A x B) ⋅ C
Cross product volumn property |
|
|
testDotProductCommutative ( array $A, array $B ) |
Axiom: A⋅B = B⋅A
Dot product is commutative |
|
|
testDotProductZero ( array $A, array $zero ) |
Axiom: 0⋅A = A⋅0 = 0
Dot product of a vector and zero is zero. |
|
|
testL2NormLessThanL1NormLessThanSqrtNL2Norm ( array $V ) |
Axiom: |x|₂ ≤ |x|₁ ≤ √n |x|₂
l²-norm is less than equal to l₁-norm which is less than equal to sqrt n * l²-norm. |
|
|
testMaxNormLessThanEqualL1NormLessThanEqualSqrtNMaxNorm ( array $V ) |
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. |
|
|
testMaxNormLessThtanEQualL2NormLessThanEqualSqrtNMaxNorm ( array $V ) |
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. |
|
|
testOuterProductIsMatrixMultiplicationOfAAndBTranspose ( array $A, array $B ) |
Axiom: A⨂B = ABᵀ
Outer product is the same as matrix multiplication of A and transpose of B |
|
|
testPerpDotProdcutSwapOperandsChangeSign ( array $A ) |
Axiom: A⋅A⊥ = -A⊥⋅A
Swapping operands changes the sign of the perp dot product |
|
|
testPerpDotProductZero ( array $A ) |
Axiom: A⊥⋅A = 0
Perp dot product with itself will be zero. |
|
|
testPerpendicularDotProduct ( array $A ) |
Axiom: A⋅A⊥ = 0
Vector dot product with a vector perpendicular to it will be zero. |
|
|
testProjPerpDotProductEqualsZero ( array $A, array $B ) |
Axiom: projᵇA ⋅ perpᵇA = 0
Dot product of proj and perp of A on B is 0 |
|
|
testProjPerpPerpDotProductEqualsProductOfLengths ( array $A, array $B ) |
Axiom: |projᵇA⊥ ⋅ perpᵇA| = |projᵇA| |perpᵇA|
Absolute value of proj and perp dot product equals product of their lengths. |
|
|
testProjPerpSumEqualsA ( array $A, array $B ) |
Axiom: projᵇA + perpᵇA = A
Sum of the proj and perp of A on B equals A |
|
|
testProjPerpSumOfSquares ( array $A, array $B ) |
Axiom: |projᵇA|² + |perpᵇA|² = |A|²
Sum of squared lengths of proj and perp equals squared length of A |
|
|
testReverseCrossProduct ( array $A, array $B ) |
Axiom: A x B = -(B x A)
Anticommutivity: Reverse order cross product results in a negative cross product |
|
|
testScalarMultiplyNegativeOneIdentity ( array $A, array $R ) |
Axiom: -1A = -A
Additive inverse |
|
|
testScalarMultiplyOneIdentity ( array $A ) |
Axiom: 1A = A
Multiplying (scaling) by 1 does not change the vector |
|
|
testScalarMultiplyZeroIdentity ( array $A ) |
Axiom: 0A = 0
Multiplying (scaling) by 0 gives the zero vector |
|
