def quad_form(x, P):
x,P = map(Expression.cast_to_const, (x,P))
# Check dimensions.
n = P.size[0]
if P.size[1] != n or x.size != (n,1):
raise Exception("Invalid dimensions for arguments.")
if x.is_constant():
return x.T*P*x
elif P.is_constant():
np_intf = intf.get_matrix_interface(np.ndarray)
P = np_intf.const_to_matrix(P.value)
# Replace P with symmetric version.
P = (P + P.T)/2
# Check if P is PSD.
eigvals, V = LA.eig(P)
eigvals = eigvals.real
if min(eigvals) >= 0:
diag_eig = np.diag(np.sqrt(eigvals))
P_sqrt = Constant(diag_eig.dot(V.T))
return square(norm2(P_sqrt*x))
elif max(eigvals) <= 0:
diag_eig = np.diag(np.sqrt(-eigvals))
P_sqrt = Constant(diag_eig.dot(V.T))
return -square(norm2(P_sqrt*x))
else:
raise Exception("P has both positive and negative eigenvalues.")
else:
raise Exception("At least one argument to quad_form must be constant.")
def norm(x, p=2):
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):
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 quad_form(x, P):
""" Alias for :math:`x^T P x`.
"""
x, P = map(Expression.cast_to_const, (x, P))
# Check dimensions.
n = P.size[0]
if P.size[1] != n or x.size != (n, 1):
raise Exception("Invalid dimensions for arguments.")
if x.is_constant():
return x.T * P * x
elif P.is_constant():
np_intf = intf.get_matrix_interface(np.ndarray)
P = np_intf.const_to_matrix(P.value)
sgn, scale, M = _decomp_quad(P)
return sgn * scale * square(norm2(Constant(M.T) * x))
else:
raise Exception("At least one argument to quad_form must be constant.")
def quad_form(x, P):
""" Alias for :math:`x^T P x`.
"""
x,P = map(Expression.cast_to_const, (x,P))
# Check dimensions.
n = P.size[0]
if P.size[1] != n or x.size != (n,1):
raise Exception("Invalid dimensions for arguments.")
if x.is_constant():
return x.T * P * x
elif P.is_constant():
np_intf = intf.get_matrix_interface(np.ndarray)
P = np_intf.const_to_matrix(P.value)
sgn, scale, M = _decomp_quad(P)
return sgn * scale * square(norm2(Constant(M.T) * x))
else:
raise Exception("At least one argument to quad_form must be constant.")
