Source code for cvxpy.constraints.second_order

Copyright 2013 Steven Diamond

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from typing import List

import numpy as np

from cvxpy.constraints.constraint import Constraint
from cvxpy.expressions import cvxtypes
from cvxpy.utilities import scopes

[docs]class SOC(Constraint): """A second-order cone constraint for each row/column. Assumes ``t`` is a vector the same length as ``X``'s columns (rows) for ``axis == 0`` (``1``). Attributes: t: The scalar part of the second-order constraint. X: A matrix whose rows/columns are each a cone. axis: Slice by column 0 or row 1. """ def __init__(self, t, X, axis: int = 0, constr_id=None) -> None: t = cvxtypes.expression().cast_to_const(t) if len(t.shape) >= 2 or not t.is_real(): raise ValueError("Invalid first argument.") # Check t has one entry per cone. if (len(X.shape) <= 1 and t.size > 1) or \ (len(X.shape) == 2 and t.size != X.shape[1-axis]) or \ (len(X.shape) == 1 and axis == 1): raise ValueError( "Argument dimensions %s and %s, with axis=%i, are incompatible." % (t.shape, X.shape, axis) ) self.axis = axis if len(t.shape) == 0: t = t.flatten() super(SOC, self).__init__([t, X], constr_id) def __str__(self) -> str: return "SOC(%s, %s)" % (self.args[0], self.args[1]) @property def residual(self): t = self.args[0].value X = self.args[1].value if t is None or X is None: return None if self.axis == 0: X = X.T norms = np.linalg.norm(X, ord=2, axis=1) zero_indices = np.where(X <= -t)[0] averaged_indices = np.where(X >= np.abs(t))[0] X_proj = np.array(X) t_proj = np.array(t) X_proj[zero_indices] = 0 t_proj[zero_indices] = 0 avg_coeff = 0.5 * (1 + t/norms) X_proj[averaged_indices] = avg_coeff * X[averaged_indices] t_proj[averaged_indices] = avg_coeff * t[averaged_indices] return np.linalg.norm(np.concatenate([X, t], axis=1) - np.concatenate([X_proj, t_proj], axis=1), ord=2, axis=1) def get_data(self): """Returns info needed to reconstruct the object besides the args. Returns ------- list """ return [self.axis] def num_cones(self): """The number of elementwise cones. """ return self.args[0].size @property def size(self) -> int: """The number of entries in the combined cones. """ cone_size = 1 + self.args[1].shape[self.axis] return cone_size * self.num_cones() def cone_sizes(self) -> List[int]: """The dimensions of the second-order cones. Returns ------- list A list of the sizes of the elementwise cones. """ cone_size = 1 + self.args[1].shape[self.axis] return [cone_size] * self.num_cones()
[docs] def is_dcp(self, dpp: bool = False) -> bool: """An SOC constraint is DCP if each of its arguments is affine. """ if dpp: with scopes.dpp_scope(): return all(arg.is_affine() for arg in self.args) return all(arg.is_affine() for arg in self.args)
def is_dgp(self, dpp: bool = False) -> bool: return False def is_dqcp(self) -> bool: return self.is_dcp() def save_dual_value(self, value) -> None: cone_size = 1 + self.args[1].shape[self.axis] value = np.reshape(value, newshape=(-1, cone_size)) t = value[:, 0] X = value[:, 1:] if self.axis == 0: X = X.T self.dual_variables[0].save_value(t) self.dual_variables[1].save_value(X)