opt_utils.py

import numpy as np
from numpy import linalg

def null(A, eps=1e-15):
    """ Returns the null-space of matrix A (as column-vectors) """
    u, s, vT = np.linalg.svd(A, full_matrices=1, compute_uv=1)
    r = sum(s > eps)
    null_space = vT[r:,:]
    return null_space.T

def lcon_lsqr(A, b, C, d):
    """ Returns the solution of:
        argmin_x ||Ax - b||_2
        subject to Cx = d
    """
    x0 = np.linalg.lstsq(C, d)[0]
    N = null(C)
    z = np.linalg.lstsq(A.dot(N), b - A.dot(x0))[0]
    x = x0 + N.dot(z)
    return x