discretize.tests.get_quadratic

discretize.tests.get_quadratic(A, b, c=0)

Return a function that evaluates the given quadratic.

Given A, b and c, this returns a function that evaluates the quadratic for a vector x. Where $\mathbf{A}\in {\mathbb{R}}^{NxN}$, $\mathbf{b}\in {\mathbb{R}}^N$ and $c$ is a constant, this function evaluates the following quadratic:

$$Q(\mathbf{x})=\frac{1}{2}{\mathbf{x}}^{\mathbf{T}}\mathbf{A}\mathbf{x}\mathbf{+}{\mathbf{b}}^{\mathbf{T}}\mathbf{x}+c$$

for a vector $\mathbf{x}$. It also optionally returns the gradient of the above equation, and its Hessian.

Parameters:

A(N, N) numpy.ndarray

A square matrix

b(N) numpy.ndarray

A vector

cfloat

A constant

Returns:

function

The callable function that returns the quadratic evaluation, and optionally its gradient, and Hessian.