def norm(x, p=2, axis=None):
"""Wrapper on the different norm atoms.
Parameters
----------
x : Expression or numeric constant
The value to take the norm of.
p : int or str, optional
The type of norm.
Returns
-------
Expression
An Expression representing the norm.
"""
x = Expression.cast_to_const(x)
if p == 1:
return pnorm(x, 1, axis)
elif p == "inf":
return pnorm(x, 'inf', axis)
elif p == "nuc":
return normNuc(x)
elif p == "fro":
return pnorm(x, 2, axis)
elif p == 2:
if x.is_matrix():
return sigma_max(x)
else:
return pnorm(x, 2, axis)
else:
return pnorm(x, p, axis)
def norm(x, p=2, axis=None):
"""Wrapper on the different norm atoms.
Parameters
----------
x : Expression or numeric constant
The value to take the norm of.
p : int or str, optional
The type of norm.
Returns
-------
Expression
An Expression representing the norm.
"""
x = Expression.cast_to_const(x)
# Norms for scalars same as absolute value.
if p == 1 or x.is_scalar():
return pnorm(x, 1, axis)
elif p == "inf":
return pnorm(x, 'inf', axis)
elif p == "nuc":
return normNuc(x)
elif p == "fro":
return pnorm(x, 2, axis)
elif p == 2:
if axis is None and x.is_matrix():
return sigma_max(x)
else:
return pnorm(x, 2, axis)
else:
return pnorm(x, p, axis)
def norm(x, p=2):
"""Wrapper on the different norm atoms.
Parameters
----------
x : Expression or numeric constant
The value to take the norm of.
p : int or str, optional
The type of norm.
Returns
-------
Expression
An Expression representing the norm.
"""
x = Expression.cast_to_const(x)
if p == 1:
return pnorm(x, 1)
elif p == "inf":
return pnorm(x, 'inf')
elif p == "nuc":
return normNuc(x)
elif p == "fro":
return pnorm(x, 2)
elif p == 2:
if x.is_matrix():
return sigma_max(x)
else:
return pnorm(x, 2)
else:
return pnorm(x, p)
def DCCP_ini(self):
dom_constr = self.objective.args[0].domain
for arg in self.constraints:
for dom in arg.args[0].domain:
dom_constr.append(dom)
for dom in arg.args[1].domain:
dom_constr.append(dom)
var_store = []
init_flag = []
for var in self.variables():
var_store.append(np.zeros((var._rows,var._cols)))
init_flag.append(var.value is None)
times = 3
for t in range(times):
ini_cost = 0
var_ind = 0
for var in self.variables():
if init_flag[var_ind]:
var.value = np.random.randn(var._rows,var._cols)*10
ini_cost += pnorm(var-var.value,2)
var_ind += 1
ini_obj = Minimize(ini_cost)
ini_prob = Problem(ini_obj,dom_constr)
ini_prob.solve()
var_ind = 0
for var in self.variables():
var_store[var_ind] = var_store[var_ind] + var.value/float(times)
var_ind += 1
var_ind = 0
for var in self.variables():
var.value = var_store[var_ind]
var_ind += 1
def norm(x, p=2, axis=None):
"""Wrapper on the different norm atoms.
Parameters
----------
x : Expression or numeric constant
The value to take the norm of. If `x` is 2D and `axis` is None,
this function constructs a matrix norm.
p : int or str, optional
The type of norm. Valid options include any positive integer,
'fro' (for frobenius), 'nuc' (sum of singular values), np.inf or
'inf' (infinity norm).
axis : The axis along which to apply the norm, if any.
Returns
-------
Expression
An Expression representing the norm.
"""
x = Expression.cast_to_const(x)
# matrix norms take precedence
num_nontrivial_idxs = sum([d > 1 for d in x.shape])
if axis is None and x.ndim == 2:
if p == 1: # matrix 1-norm
return cvxpy.atoms.max(norm1(x, axis=0))
# Frobenius norm
elif p == 'fro' or (p == 2 and num_nontrivial_idxs == 1):
return pnorm(vec(x), 2)
elif p == 2: # matrix 2-norm is largest singular value
return sigma_max(x)
elif p == 'nuc': # the nuclear norm (sum of singular values)
return normNuc(x)
elif p in [np.inf, "inf", "Inf"]: # the matrix infinity-norm
return cvxpy.atoms.max(norm1(x, axis=1))
else:
raise RuntimeError('Unsupported matrix norm.')
else:
if p == 1 or x.is_scalar():
return norm1(x, axis=axis)
elif p in [np.inf, "inf", "Inf"]:
return norm_inf(x, axis)
else:
return pnorm(x, p, axis)
def norm(x, p=2, axis=None):
"""Wrapper on the different norm atoms.
Parameters
----------
x : Expression or numeric constant
The value to take the norm of.
p : int or str, optional
The type of norm.
Returns
-------
Expression
An Expression representing the norm.
"""
x = Expression.cast_to_const(x)
# matrix norms take precedence
if axis is None and x.ndim == 2:
if p == 1: # matrix 1-norm
return cvxpy.atoms.max(norm1(x, axis=0))
elif p == 2: # matrix 2-norm is largest singular value
return sigma_max(x)
elif p == 'nuc': # the nuclear norm (sum of singular values)
return normNuc(x)
elif p == 'fro': # Frobenius norm
return pnorm(vec(x), 2)
elif p in [np.inf, "inf", "Inf"]: # the matrix infinity-norm
return cvxpy.atoms.max(norm1(x, axis=1))
else:
raise RuntimeError('Unsupported matrix norm.')
else:
if p == 1 or x.is_scalar():
return norm1(x, axis=axis)
elif p in [np.inf, "inf", "Inf"]:
return norm_inf(x, axis)
else:
return pnorm(x, p, axis)
def harmonic_mean(x):
"""The harmonic mean of ``x``.
Parameters
----------
x : Expression or numeric
The expression whose harmonic mean is to be computed. Must have
positive entries.
Returns
-------
Expression
.. math::
\\frac{n}{\\left(\\sum_{i=1}^{n} x_i^{-1} \\right)},
where :math:`n` is the length of :math:`x`.
"""
x = Expression.cast_to_const(x)
# TODO(akshayka): Behavior of the below is incorrect when x has negative
# entries. Either fail fast or provide a correct expression with
# unknown curvature.
return x.size*pnorm(x, -1)
def normInf(x, axis=None):
return pnorm(x, 'inf', axis)
def harmonic_mean(x):
return np.prod(x.size)*pnorm(x, -1)
def harmonic_mean(x):
x = Expression.cast_to_const(x)
return np.prod(x.size)*pnorm(x, -1)
def norm1(x, axis=None):
return pnorm(x, 1, axis)
def norm2(x):
return pnorm(x, 2)
def norm2(x, axis=None):
return pnorm(x, 2, axis)
def norm1(x, axis=None):
return pnorm(x, 1, axis)
def normInf(x):
return pnorm(x, 'inf')
def norm1(x):
return pnorm(x, 1)
