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 norm1(x)
elif p == "inf":
return normInf(x)
elif p == "nuc":
return normNuc(x)
elif p == "fro":
return norm2(x)
elif p == 2:
if x.is_matrix():
return sigma_max(x)
else:
return norm2(x)
else:
raise Exception("Invalid value %s for p." % p)
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 norm1(x)
elif p == "inf":
return normInf(x)
elif p == "nuc":
return normNuc(x)
elif p == "fro":
return norm2(x)
elif p == 2:
if x.is_matrix():
return sigma_max(x)
else:
return norm2(x)
else:
raise Exception("Invalid value %s for p." % p)
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 pnorm(x, p=2, axis=None, keepdims=False, max_denom=1024):
"""Factory function for a mathematical p-norm.
Parameters
----------
p : numeric type or string
The type of norm to construct; set this to np.inf or 'inf' to
construct an infinity norm.
Returns
-------
Atom
A norm1, norm_inf, or Pnorm object.
"""
if p == 1:
return norm1(x, axis=axis, keepdims=keepdims)
elif p in [np.inf, 'inf', 'Inf']:
return norm_inf(x, axis=axis, keepdims=keepdims)
else:
return Pnorm(x, p=p, axis=axis, keepdims=keepdims, max_denom=max_denom)