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 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 transform_quad_over_lin(expr):
assert len(expr.arg) == 2
x, y = expr.arg
assert dim(y) == 1
t = epi_var(expr, "qol", size=(1,1))
return t, [
expression.soc_constraint(
expression.add(y, t),
expression.vstack(
expression.add(y, expression.negate(t)),
expression.reshape(
expression.multiply(expression.scalar_constant(2), x),
dim(x), 1))),
expression.leq_constraint(expression.scalar_constant(0), y)]
def transform_quad_over_lin(expr):
assert len(expr.arg) == 2
x, y = expr.arg
assert dim(y) == 1
t = epi_var(expr, "qol", size=(1, 1))
return t, [
expression.soc_constraint(
expression.add(y, t),
expression.hstack(
expression.add(y, expression.negate(t)),
expression.reshape(
expression.multiply(expression.scalar_constant(2), x), 1,
dim(x)))),
expression.leq_constraint(expression.scalar_constant(0), y)
]
