vector-structure 2.2.0

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vector-structure

Lightweight utilities for working with structured flat vectors and block matrices in NumPy.

Example usage

Consider a Newton algorithm for solving the KKT conditions, as described here:

$$\begin{pmatrix} \nabla^2 f(x) & \color{gray}{Df(x)^T} & A^T \ \color{gray}{-diag(\lambda) Df(x)} & \color{gray}{-diag(f(x))} & \color{gray}{0} \ A & \color{gray}{0} & 0 \end{pmatrix} \begin{pmatrix} x^* \ \color{gray}{\lambda^*} \ v^* \end{pmatrix} = \begin{pmatrix} \ \dots \ \end{pmatrix}$$

where the grey components are only required when inequality constraints are present.

from vector_structure import VectorStructure

structure = [("x", n)]
if ineq_constraints:
    structure.append(("lambda", m))
structure.append(("mu", p))

vs = VectorStructure(structure)

M = np.zeros((vs.size, vs.size))
M[vs["x"], vs["x"]] = nabla2(f)(x)
if ineq_constraints:
    M[vs["x"], vs["lambda"]] = Df(x).T
M[vs["x"], vs["mu"]] = A
...

x_lambda_mu = np.linalg.solve(M, r)
x = x_lambda_mu[vs["x"]]
if ineq_constraints:
    lambda = x_lambda_mu[vs["lambda"]]