idx = find(crit<=0.500) #rohs = rohs[idx[0]] rohs = rohs[idx[0]] A3 = vstack([A,identity(m)*sqrt(rohs)]) b3 = vstack([ones((n,1)),sqrt(rohs)*0.5*ones((m,1))]) p_ls_reg = np.linalg.lstsq(A3, b3)[0] val_ls_reg = np.max(np.abs(log(A*matrix(p_ls_reg)))) print p_ls_reg print val_ls_reg #solution 4 chebyshev approximation from cvxpy import Minimize, normInf, Variable, Problem, inv_pos x=Variable (m,1) objective = Minimize(normInf(matrix(A)*x-ones((n,1)))) constraints =[x>=0,x<=1] pro = Problem(objective, constraints) result = pro.solve() print x.value val_ls_chev = np.max(np.abs(log(A*matrix(x.value)))) print val_ls_chev #solution 5 cvxpy from cvxpy import max y=Variable (m,1) Am = matrix(A) qq = [max(Am[i,:]*y,inv_pos(Am[i,:]*y)) for i in range(n)] objective1 = Minimize(max(*qq)) constraints1 =[y>=0,y<=1]
Atot1 = hstack([Are, -Aim]) Atot2 = hstack([Aim, Are]) Atot = matrix(vstack([Atot1, Atot2])) btot = matrix(vstack([bre, bim])) z_2 = Atot.T * inv(Atot * Atot.T) * btot x2 = z_2[0:99] + 1j * z_2[100:199] print x2 # cvxpy from cvxpy import Variable, norm2, Problem, Minimize x = Variable(2 * n, 1) objective = Minimize(norm2(x)) constraints = [Atot * x == btot] pro = Problem(objective, constraints) result = pro.solve() xnorm = x.value[0:99] + 1j * x.value[100:199] print x2 - xnorm # cvxpy norminf from cvxpy import normInf, norm1 xinf = Variable(2 * n, 1) objective1 = Minimize(normInf(xinf)) constraints1 = [Atot * xinf == btot] pro1 = Problem(objective1, constraints1) result = pro1.solve() # print xinf.value[0:99]+1j*xinf.value[100:199] scatter(x.value[0:99], x.value[100:199]) scatter(xinf.value[0:99], xinf.value[100:199], c="r", marker="D")
