MediumCalculusca-128

Legendre Transform Value

Problem

The Legendre transform of f(x) = a*x^2 / 2 with a > 0 is f*(p) = sup over x of (p*x - f(x)).

Maximizing gives x = p/a and f*(p) = p^2 / (2*a). Given a and p, return f*(p).

Hint

Set f'(x) = p and substitute back into p*x - f(x).

case 1

in: [1,2]

expected: 2

case 2

in: [2,3]

expected: 2.25

case 3

in: [4,0]

expected: 0

case 4

in: [0.5,1]

expected: 1

case 5

in: [1,-3]

expected: 4.5

Starter codePython

def legendre_transform(a, p):
    # Your code here
    pass

5 test cases · run your code against them in the editor