def __init__(self, x, p, max_denom=1024):
p_old = p
# how we convert p to a rational depends on the branch of the function
if p > 1:
p, w = pow_high(p, max_denom)
elif 0 < p < 1:
p, w = pow_mid(p, max_denom)
elif p < 0:
p, w = pow_neg(p, max_denom)
# note: if, after making the rational approximation, p ends up being 0 or 1,
# we default to using the 0 or 1 behavior of the atom, which affects the curvature, domain, etc...
# maybe unexpected behavior to the user if they put in 1.00001?
if p == 1:
# in case p is a fraction equivalent to 1
p = 1
w = None
if p == 0:
p = 0
w = None
self.p, self.w = p, w
self.approx_error = float(abs(self.p - p_old))
super(power, self).__init__(x)
def __init__(self, x, p, max_denom=1024):
p_old = p
# how we convert p to a rational depends on the branch of the function
if p > 1:
p, w = pow_high(p, max_denom)
elif 0 < p < 1:
p, w = pow_mid(p, max_denom)
elif p < 0:
p, w = pow_neg(p, max_denom)
# note: if, after making the rational approximation, p ends up being 0 or 1,
# we default to using the 0 or 1 behavior of the atom, which affects the curvature, domain, etc...
# maybe unexpected behavior to the user if they put in 1.00001?
if p == 1:
# in case p is a fraction equivalent to 1
p = 1
w = None
if p == 0:
p = 0
w = None
self.p, self.w = p, w
self.approx_error = float(abs(self.p - p_old))
super(power, self).__init__(x)
def transform_norm_p(expr):
p = expr.p
x = only_arg(expr)
t = epi_var(expr, "norm_p", size=(1,1))
if p == float("inf"):
return t, [expression.leq_constraint(x, t),
expression.leq_constraint(expression.negate(x), t)]
if p == 1:
return transform_expr(expression.sum_entries(expression.abs_val(x)))
if p == 2:
return t, [expression.soc_constraint(t, x)]
r = epi_var(expr, "norm_p_r", size=dims(x))
t1 = expression.multiply(expression.ones(*dims(x)), t)
if p < 0:
p, _ = power_tools.pow_neg(p)
p = Fraction(p)
constrs = gm_constrs(t1, [x, r], (-p/(1-p), 1/(1-p)))
elif 0 < p < 1:
p, _ = power_tools.pow_mid(p)
p = Fraction(p)
constrs = gm_constrs(r, [x, t1], (p, 1-p))
elif p > 1:
abs_x, constrs = transform_expr(expression.abs_val(x))
p, _ = power_tools.pow_high(p)
p = Fraction(p)
constrs += gm_constrs(abs_x, [r, t1], (1/p, 1-1/p))
constrs.append(expression.eq_constraint(expression.sum_entries(r), t))
return t, constrs
def __init__(self, x, p, max_denom: int = 1024) -> None:
self._p_orig = p
# NB: It is important that the exponent is an attribute, not
# an argument. This prevents parametrized exponents from being replaced
# with their logs in Dgp2Dcp.
self.p = cvxtypes.expression().cast_to_const(p)
if not (isinstance(self.p, cvxtypes.constant())
or isinstance(self.p, cvxtypes.parameter())):
raise ValueError(
"The exponent `p` must be either a Constant or "
"a Parameter; received ", type(p))
self.max_denom = max_denom
self.p_rational = None
if isinstance(self.p, cvxtypes.constant()):
# Compute a rational approximation to p, for DCP (DGP doesn't need
# an approximation).
if not isinstance(self._p_orig, cvxtypes.expression()):
# converting to a CVXPY Constant loses the dtype (eg, int),
# so fetch the original exponent when possible
p = self._p_orig
else:
p = self.p.value
# how we convert p to a rational depends on the branch of the function
if p > 1:
p, w = pow_high(p, max_denom)
elif 0 < p < 1:
p, w = pow_mid(p, max_denom)
elif p < 0:
p, w = pow_neg(p, max_denom)
# note: if, after making the rational approximation, p ends up
# being 0 or 1, we default to using the 0 or 1 behavior of the
# atom, which affects the curvature, domain, etc... maybe
# unexpected behavior to the user if they put in 1.00001?
if p == 1:
# in case p is a fraction equivalent to 1
p = 1
w = None
if p == 0:
p = 0
w = None
self.p_rational, self.w = p, w
self.approx_error = float(abs(self.p_rational - p))
super(power, self).__init__(x)
def __init__(self, x, p=2, axis=None, keepdims=False, max_denom=1024):
if p < 0:
# TODO(akshayka): Why do we accept p < 0?
self.p, _ = pow_neg(p, max_denom)
elif 0 < p < 1:
self.p, _ = pow_mid(p, max_denom)
elif p > 1:
self.p, _ = pow_high(p, max_denom)
elif p == 1:
raise ValueError('Use the norm1 class to instantiate a one norm.')
elif p == 'inf' or p == 'Inf' or p == np.inf:
raise ValueError('Use the norm_inf class to instantiate an '
'infinity norm.')
else:
raise ValueError('Invalid p: {}'.format(p))
self.approx_error = float(abs(self.p - p))
super(Pnorm, self).__init__(x, axis=axis, keepdims=keepdims)
def transform_norm_p(expr):
p = expr.p
x = only_arg(expr)
t = epi_var(expr, "norm_p")
if p == float("inf"):
return t, [
expression.leq_constraint(x, t),
expression.leq_constraint(expression.negate(x), t)
]
if p == 1:
return transform_expr(expression.sum_entries(expression.abs_val(x)))
if p == 2:
if not expr.has_axis:
return t, [
expression.soc_constraint(t, expression.reshape(x, 1, dim(x)))
]
if expr.axis == 0:
return t, [
expression.soc_constraint(expression.reshape(t, dim(x, 1), 1),
expression.transpose(x))
]
if expr.axis == 1:
return t, [expression.soc_constraint(t, x)]
r = epi_var(expr, "norm_p_r", size=dims(x))
t1 = expression.multiply(expression.ones(*dims(x)), t)
if p < 0:
p, _ = power_tools.pow_neg(p)
p = Fraction(p)
constrs = gm_constrs(t1, [x, r], (-p / (1 - p), 1 / (1 - p)))
elif 0 < p < 1:
p, _ = power_tools.pow_mid(p)
p = Fraction(p)
constrs = gm_constrs(r, [x, t1], (p, 1 - p))
elif p > 1:
abs_x, constrs = transform_expr(expression.abs_val(x))
p, _ = power_tools.pow_high(p)
p = Fraction(p)
constrs += gm_constrs(abs_x, [r, t1], (1 / p, 1 - 1 / p))
constrs.append(expression.eq_constraint(expression.sum_entries(r), t))
return t, constrs
def __init__(self, x, p=2, axis=None, max_denom=1024):
p_old = p
if p in ('inf', 'Inf', np.inf):
self.p = np.inf
elif p < 0:
self.p, _ = pow_neg(p, max_denom)
elif 0 < p < 1:
self.p, _ = pow_mid(p, max_denom)
elif p > 1:
self.p, _ = pow_high(p, max_denom)
elif p == 1:
self.p = 1
else:
raise ValueError('Invalid p: {}'.format(p))
super(pnorm, self).__init__(x, axis=axis)
if self.p == np.inf:
self.approx_error = 0
else:
self.approx_error = float(abs(self.p - p_old))
def __init__(self, x, p=2, axis=None, max_denom=1024):
p_old = p
if p in ('inf', 'Inf', np.inf):
self.p = np.inf
elif p < 0:
self.p, _ = pow_neg(p, max_denom)
elif 0 < p < 1:
self.p, _ = pow_mid(p, max_denom)
elif p > 1:
self.p, _ = pow_high(p, max_denom)
elif p == 1:
self.p = 1
else:
raise ValueError('Invalid p: {}'.format(p))
super(pnorm, self).__init__(x, axis=axis)
if self.p == np.inf:
self.approx_error = 0
else:
self.approx_error = float(abs(self.p - p_old))
def transform_power(expr):
p = expr.p
if p == 1:
return only_arg(expr)
one = expression.scalar_constant(1, size=dims(expr))
if p == 0:
return one, []
t = epi_var(expr, "power")
x = only_arg(expr)
if p < 0:
p, w = power_tools.pow_neg(p)
constrs = gm_constrs(one, [x, t], w)
if 0 < p < 1:
p, w = power_tools.pow_mid(p)
constrs = gm_constrs(t, [x, one], w)
if p > 1:
p, w = power_tools.pow_high(p)
constrs = gm_constrs(x, [t, one], w)
return t, constrs
def transform_power(expr):
p = expr.p
if p == 1:
return only_arg(expr)
one = expression.scalar_constant(1, size=dims(expr))
if p == 0:
return one, []
t = epi_var(expr, "power")
x = only_arg(expr)
if p < 0:
p, w = power_tools.pow_neg(p)
constrs = gm_constrs(one, [x, t], w)
if 0 < p < 1:
p, w = power_tools.pow_mid(p)
constrs = gm_constrs(t, [x, one], w)
if p > 1:
p, w = power_tools.pow_high(p)
constrs = gm_constrs(x, [t, one], w)
return t, constrs
