def meshy_one(x,y,m,k=1,interp=1,mesh=None,lnorm=1,tune=50,eps=0.01,cvx_solver=0):
# interp = 0 for natural splines
# interp = 1 for banded piecewise polynomials
# possible solvers to choose from: typically CVXOPT works better for simulations thus far.
solvers = [cvx.SCS,cvx.CVXOPT] # 0 is SCS, 1 CVXOPT
default_iter = [160000,3200][cvx_solver] # defaults are 2500 and 100
n = x.size
# Create D-matrix: specify n and k
if mesh==None:
mesh = np.linspace(min(x)-eps,max(x)+eps,m)
delta = np.diff(mesh)[0]
D = utils.form_Dk(n=m,k=k)*(delta**(1/lnorm-k))
# Create O-matrix: specify x and number of desired cuts
O = utils.interpO(data=x,mesh=mesh,k=k,key=interp)
# Solve convex problem.
theta = cvx.Variable(m)
obj = cvx.Minimize(0.5 * cvx.sum_squares(y - O*theta)
+ tune * cvx.norm(D*theta, lnorm) )
prob = cvx.Problem(obj)
prob.solve(solver=solvers[cvx_solver],verbose=False,max_iters = default_iter)
counter = 0
while prob.status != cvx.OPTIMAL:
maxit = 2*default_iter
prob.solve(solver=solvers[cvx_solver],verbose=False,max_iters=maxit)
default_iter = maxit
counter = counter +1
if counter>4:
raise Exception("Solver did not converge with %s iterations! (N=%s,d=%s,k=%s)" % (default_iter,n,m,k) )
output = {'mesh': mesh, 'theta.hat': np.array(theta.value),'fitted':O.dot(np.array(theta.value)),'x':x,'y':y,'k':k,'interp':interp,'eps':eps,'m':m}
return output
def meshy_predict(meshy_one_object,x): O = utils.interpO(data=x,mesh=meshy_one_object['mesh'],k=meshy_one_object['k'],key=meshy_one_object['interp']) return O.dot(meshy_one_object['theta.hat'])