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|
levelSet1= {x | f(x) <= 1} with f=
NumericalMathFunction :
input : [x,y]
output : [y0]
evaluation : x^4 + y^4
gradient :
| d(y0) / d(x) = 4*x^3
| d(y0) / d(y) = 4*y^3
hessian :
| d^2(y0) / d(x)^2 = 12*x^2
| d^2(y0) / d(y)d(x) = 0
| d^2(y0) / d(y)^2 = 12*y^2
levelSet1 contains [-0.5, -0.5] ? True
levelSet1 contains [0.5, 0.0] ? True
levelSet1 contains [1.5, 0.0] ? False
levelSet2= {x | f(x) <= 1} with f=
NumericalMathFunction :
input : [x,y]
output : [y0]
evaluation : (x-1)^2 + y^2
gradient :
| d(y0) / d(x) = (-2)+(2*x)
| d(y0) / d(y) = 2*y
hessian :
| d^2(y0) / d(x)^2 = 2
| d^2(y0) / d(y)d(x) = 0
| d^2(y0) / d(y)^2 = 2
levelSet2 contains [-0.5, -0.5] ? False
levelSet2 contains [0.5, 0.0] ? True
levelSet2 contains [1.5, 0.0] ? True
intersection of {x | f(x) <= 1} with f=
NumericalMathFunction :
input : [x,y]
output : [y0]
evaluation : x^4 + y^4
gradient :
| d(y0) / d(x) = 4*x^3
| d(y0) / d(y) = 4*y^3
hessian :
| d^2(y0) / d(x)^2 = 12*x^2
| d^2(y0) / d(y)d(x) = 0
| d^2(y0) / d(y)^2 = 12*y^2
and {x | f(x) <= 1} with f=
NumericalMathFunction :
input : [x,y]
output : [y0]
evaluation : (x-1)^2 + y^2
gradient :
| d(y0) / d(x) = (-2)+(2*x)
| d(y0) / d(y) = 2*y
hessian :
| d^2(y0) / d(x)^2 = 2
| d^2(y0) / d(y)d(x) = 0
| d^2(y0) / d(y)^2 = 2
equals {x | f(x) <= 0} with f=
NumericalMathFunction :
input : [x,y]
output : [y0]
evaluation : (x0 > 1) + (x1 > 1) > 0.0
o
[NumericalMathFunction :
input : [x,y]
output : [y0]
evaluation : x^4 + y^4
gradient :
| d(y0) / d(x) = 4*x^3
| d(y0) / d(y) = 4*y^3
hessian :
| d^2(y0) / d(x)^2 = 12*x^2
| d^2(y0) / d(y)d(x) = 0
| d^2(y0) / d(y)^2 = 12*y^2
,NumericalMathFunction :
input : [x,y]
output : [y0]
evaluation : (x-1)^2 + y^2
gradient :
| d(y0) / d(x) = (-2)+(2*x)
| d(y0) / d(y) = 2*y
hessian :
| d^2(y0) / d(x)^2 = 2
| d^2(y0) / d(y)d(x) = 0
| d^2(y0) / d(y)^2 = 2
]
gradient : NumericalMathGradientImplementation
hessian : NumericalMathHessianImplementation
intersection contains [-0.5, -0.5] ? False
intersection contains [0.5, 0.0] ? True
intersection contains [1.5, 0.0] ? False
join of {x | f(x) <= 1} with f=
NumericalMathFunction :
input : [x,y]
output : [y0]
evaluation : x^4 + y^4
gradient :
| d(y0) / d(x) = 4*x^3
| d(y0) / d(y) = 4*y^3
hessian :
| d^2(y0) / d(x)^2 = 12*x^2
| d^2(y0) / d(y)d(x) = 0
| d^2(y0) / d(y)^2 = 12*y^2
and {x | f(x) <= 1} with f=
NumericalMathFunction :
input : [x,y]
output : [y0]
evaluation : (x-1)^2 + y^2
gradient :
| d(y0) / d(x) = (-2)+(2*x)
| d(y0) / d(y) = 2*y
hessian :
| d^2(y0) / d(x)^2 = 2
| d^2(y0) / d(y)d(x) = 0
| d^2(y0) / d(y)^2 = 2
equals {x | f(x) <= 0} with f=
NumericalMathFunction :
input : [x,y]
output : [y0]
evaluation : (x0 > 1) * (x1 > 1) > 0.0
o
[NumericalMathFunction :
input : [x,y]
output : [y0]
evaluation : x^4 + y^4
gradient :
| d(y0) / d(x) = 4*x^3
| d(y0) / d(y) = 4*y^3
hessian :
| d^2(y0) / d(x)^2 = 12*x^2
| d^2(y0) / d(y)d(x) = 0
| d^2(y0) / d(y)^2 = 12*y^2
,NumericalMathFunction :
input : [x,y]
output : [y0]
evaluation : (x-1)^2 + y^2
gradient :
| d(y0) / d(x) = (-2)+(2*x)
| d(y0) / d(y) = 2*y
hessian :
| d^2(y0) / d(x)^2 = 2
| d^2(y0) / d(y)d(x) = 0
| d^2(y0) / d(y)^2 = 2
]
gradient : NumericalMathGradientImplementation
hessian : NumericalMathHessianImplementation
join contains [-0.5, -0.5] ? True
join contains [0.5, 0.0] ? True
join contains [1.5, 0.0] ? True
|
