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_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_lambda_max(expr):
t = epi_var(expr, "lambda_max", size=(1,1))
X = only_arg(expr)
n = dim(X, 0)
tI = expression.diag_vec(expression.multiply(expression.ones(n, 1), t))
return t, [expression.psd_constraint(tI, X)]
def transform_lambda_max(expr):
t = epi_var(expr, "lambda_max", size=(1, 1))
X = only_arg(expr)
n = dim(X, 0)
tI = expression.diag_vec(expression.multiply(expression.ones(n, 1), t))
return t, [expression.psd_constraint(tI, X)]