Square

class gob.benchmarks.square.Square

Bases: Benchmark

The d-square function.

\(f(x) = x \cdot x^\top\).

Its minimum is \(0\) achieved at \(x = 0\).

expr(x)

The expression of the function.

Parameters:

x (array-like) – The point at which to evaluate the function.

Returns:

The value of the function at x.

Return type:

float

gradient(x)

Estimate the gradient of a function at a given point using finite differences.

Parameters:

• f (callable) – The function to estimate the gradient of. It should take a single argument.

• x (array-like) – The point at which to estimate the gradient of f.

• eps (float, optional) – The perturbation used to estimate the gradient.

Returns:

The estimated gradient of f at x and the value of f at x.

Return type:

pair