def transform_matrix_frac(expr):
assert len(expr.arg) == 2
x, P = expr.arg
n = dim(P, 0)
M = epi_var(expr, "matrix_frac_M", size=(n+1,n+1))
t = epi_var(expr, "matrix_frac")
return t, [
expression.eq_constraint(expression.index(M, 0, n, 0, n), P),
expression.eq_constraint(expression.index(M, 0, n, n, n+1), x),
expression.eq_constraint(expression.index(M, n, n+1, n, n+1), t),
expression.semidefinite(M)]
def transform_sigma_max(expr):
X = only_arg(expr)
m, n = dims(X)
S = epi_var(expr, "sigma_max_S", size=(m+n, m+n))
t = epi_var(expr, "sigma_max")
t_In = expression.diag_vec(expression.multiply(expression.ones(n, 1), t))
t_Im = expression.diag_vec(expression.multiply(expression.ones(m, 1), t))
return t, [
expression.eq_constraint(expression.index(S, 0, n, 0, n), t_In),
expression.eq_constraint(expression.index(S, n, n+m, 0, n), X),
expression.eq_constraint(expression.index(S, n, n+m, n, n+m), t_Im),
expression.semidefinite(S)]
def transform_matrix_frac(expr):
assert len(expr.arg) == 2
x, P = expr.arg
n = dim(P, 0)
M = epi_var(expr, "matrix_frac_M", size=(n + 1, n + 1))
t = epi_var(expr, "matrix_frac")
return t, [
expression.eq_constraint(expression.index(M, 0, n, 0, n), P),
expression.eq_constraint(expression.index(M, 0, n, n, n + 1), x),
expression.eq_constraint(expression.index(M, n, n + 1, n, n + 1), t),
expression.semidefinite(M)
]
def transform_sigma_max(expr):
X = only_arg(expr)
m, n = dims(X)
S = epi_var(expr, "sigma_max_S", size=(m + n, m + n))
t = epi_var(expr, "sigma_max")
t_In = expression.diag_vec(expression.multiply(expression.ones(n, 1), t))
t_Im = expression.diag_vec(expression.multiply(expression.ones(m, 1), t))
return t, [
expression.eq_constraint(expression.index(S, 0, n, 0, n), t_In),
expression.eq_constraint(expression.index(S, n, n + m, 0, n), X),
expression.eq_constraint(expression.index(S, n, n + m, n, n + m),
t_Im),
expression.semidefinite(S)
]
def transform_geo_mean(expr):
w = [Fraction(x.a, x.b) for x in expr.geo_mean_params.w]
w_dyad = [Fraction(x.a, x.b) for x in expr.geo_mean_params.w_dyad]
tree = power_tools.decompose(w_dyad)
t = epi_var(expr, "geo_mean")
x = only_arg(expr)
x_list = [expression.index(x, i, i+1) for i in range(len(w))]
return t, gm_constrs(t, x_list, w)
def transform_geo_mean(expr):
w = [Fraction(x.a, x.b) for x in expr.geo_mean_params.w]
w_dyad = [Fraction(x.a, x.b) for x in expr.geo_mean_params.w_dyad]
tree = power_tools.decompose(w_dyad)
t = epi_var(expr, "geo_mean")
x = only_arg(expr)
x_list = [expression.index(x, i, i + 1) for i in range(len(w))]
return t, gm_constrs(t, x_list, w)
def transform_norm_nuc(expr):
X = only_arg(expr)
m, n = dims(X)
T = epi_var(expr, "norm_nuc", size=(m+n, m+n))
obj = expression.multiply(
expression.scalar_constant(0.5),
expression.trace(T))
return obj, [
expression.semidefinite(T),
expression.eq_constraint(expression.index(T, 0, m, m, m+n), X)]
def transform_norm_nuc(expr):
X = only_arg(expr)
m, n = dims(X)
T = epi_var(expr, "norm_nuc", size=(m + n, m + n))
obj = expression.multiply(expression.scalar_constant(0.5),
expression.trace(T))
return obj, [
expression.semidefinite(T),
expression.eq_constraint(expression.index(T, 0, m, m, m + n), X)
]
def convert_index(expr):
starts = []
stops = []
assert len(expr.key) == 2
for i, key in enumerate(expr.key):
size = expr.args[0].size[i]
starts.append(index_value(key.start, size) if key.start else 0)
stops.append(index_value(key.stop, size) if key.stop else size)
assert len(expr.args) == 1
return expression.index(convert_expression(expr.args[0]), starts[0],
stops[0], starts[1], stops[1])
def convert_index(expr):
starts = []
stops = []
assert len(expr.key) == 2
for i, key in enumerate(expr.key):
size = expr.args[0].size[i]
starts.append(index_value(key.start, size) if key.start else 0)
stops.append(index_value(key.stop, size) if key.stop else size)
assert len(expr.args) == 1
return expression.index(convert_expression(expr.args[0]),
starts[0], stops[0],
starts[1], stops[1])
