Source code for cvxpy.atoms.norm_nuc

Copyright 2013 Steven Diamond

This file is part of CVXPY.

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from cvxpy.atoms.atom import Atom
import numpy as np
import scipy.sparse as sp

[docs]class normNuc(Atom): """Sum of the singular values. """ _allow_complex = True def __init__(self, A): super(normNuc, self).__init__(A) def numeric(self, values): """Returns the nuclear norm (i.e. the sum of the singular values) of A. """ return np.linalg.norm(values[0], 'nuc') def _grad(self, values): """Gives the (sub/super)gradient of the atom w.r.t. each argument. Matrix expressions are vectorized, so the gradient is a matrix. Args: values: A list of numeric values for the arguments. Returns: A list of SciPy CSC sparse matrices or None. """ # Grad UV^T U, _, V = np.linalg.svd(values[0]) D = return [sp.csc_matrix(D.ravel(order='F')).T] def shape_from_args(self): """Returns the (row, col) shape of the expression. """ return tuple() def sign_from_args(self): """Returns sign (is positive, is negative) of the expression. """ return (True, False) def is_atom_convex(self): """Is the atom convex? """ return True def is_atom_concave(self): """Is the atom concave? """ return False def is_incr(self, idx): """Is the composition non-decreasing in argument idx? """ return False def is_decr(self, idx): """Is the composition non-increasing in argument idx? """ return False