def huber(x,M):
"""
Huber penalty function with parameter M.
Convex.
:param x: Number or scalar object.
:param M: Positive constant.
:rtype: Number or :class:`cvxpy_tree`.
"""
# x must be scalar
if((not np.isscalar(x)) and
type(x).__name__ not in SCALAR_OBJS):
raise ValueError('Invalid first argument')
# M must be a positive constant
if((not np.isscalar(M)) or M <= 0):
raise ValueError('Invalid second argument')
# Construct and return program
v = var('v')
w = var('w')
a = param('a')
p = prog(minimize(2*v+square(w)),
[less(abs(a),w+v),
greater(v,0),
greater(w,0),
less(w,1)],
[a],None,'huber')
return square(M)*p((1.0/M)*x)
def huber(x, M):
"""
Huber penalty function with parameter M.
Convex.
:param x: Number or scalar object.
:param M: Positive constant.
:rtype: Number or :class:`cvxpy_tree`.
"""
# x must be scalar
if ((not np.isscalar(x)) and type(x).__name__ not in SCALAR_OBJS):
raise ValueError('Invalid first argument')
# M must be a positive constant
if ((not np.isscalar(M)) or M <= 0):
raise ValueError('Invalid second argument')
# Construct and return program
v = var('v')
w = var('w')
a = param('a')
p = prog(minimize(2 * v + square(w)),
[less(abs(a), w + v),
greater(v, 0),
greater(w, 0),
less(w, 1)], [a], None, 'huber')
return square(M) * p((1.0 / M) * x)
def quad_form(x, P):
"""
Quadratic form :math:`x^TPx`.
Convex.
:param x: Column vector.
:type x: :class:`cvxpy_matrix` or array object
:param P: Positive semidefinite matrix.
:type P: :class:`cvxpy_matrix`
:rtype: number or :class:`cvxpy_tree`.
"""
# P must be symmetric
if (not np.allclose(P, P.T)):
raise ValueError('Invalid second argument')
# P must be positive semidefinite
min_eig = np.min(np.linalg.eig(P)[0])
if (min_eig < 0.0):
raise ValueError('Invalid second argument')
P_half = sqrtm(P)
(m, n) = x.shape
# x must be a column vector
if (n != 1):
raise ValueError('Invalid first argument')
# Construct and return program
a = param('a', m, 1)
t = var('t')
p = prog(minimize(t), [less(sum(square(sqrtm(P) * a)), t)], [a], None,
'quad_form')
return p(x)
def quad_form(x,P):
"""
Quadratic form :math:`x^TPx`.
Convex.
:param x: Column vector.
:type x: :class:`cvxpy_matrix` or array object
:param P: Positive semidefinite matrix.
:type P: :class:`cvxpy_matrix`
:rtype: number or :class:`cvxpy_tree`.
"""
# P must be symmetric
if(not np.allclose(P,P.T)):
raise ValueError('Invalid second argument')
# P must be positive semidefinite
min_eig = np.min(np.linalg.eig(P)[0])
if(min_eig < 0.0):
raise ValueError('Invalid second argument')
P_half = sqrtm(P)
(m,n) = x.shape
# x must be a column vector
if(n!=1):
raise ValueError('Invalid first argument')
# Construct and return program
a = param('a',m,1)
t = var('t')
p = prog(minimize(t),
[less(sum(square(sqrtm(P)*a)),t)],
[a],
None,
'quad_form')
return p(x)
