import theano
import cascade_creation
from theano import tensor, function
import numpy as np
import timeout
import cvxopt


@timeout.timeout(10)
def sparse_recovery(M_val, w_val, lbda):
    """
    Solves:
        min lbda * |theta|_1 - 1/n_cascades*(
                sum w log(e^[M*theta]) + (1-w) log(1-e^[M*theta])
            )
        s.t theta_j <= 0

    The objective must be re-normalized:
    -> log(e^x - 1) = (1-k)x + log(e^[kx] - 1)
    with k chosen as : n_nodes*n_cascades
    """
    assert len(M_val) == len(w_val)

    if M_val.dtype == bool:
        M_val = M_val.astype('float32')

    if type(lbda) == int:
        lbda = np.array(lbda)

    m, n = M_val.shape

    theta = tensor.row().T
    theta_ = theta.flatten()

    M = theano.shared(M_val.astype(theano.config.floatX))
    w = theano.shared(w_val.astype(theano.config.floatX))
    lbda = theano.shared(lbda.astype(theano.config.floatX))

    #Objective
    y =  lbda * (theta_).norm(1) - 1./m*(
            tensor.dot(1-w, tensor.log(1-tensor.exp(M.dot(theta_ *1./(n*m)))))\
            + (1 - 1./(n*m)) * tensor.dot(1 - w, tensor.dot(M, theta_)) \
            + tensor.dot(w, tensor.dot(M, theta_)))  

    return diff_and_opt(theta, theta_, M, M_val, w, lbda, y)


@timeout.timeout(20)
def type_lasso(M_val, w_val, lbda):
    """
    Solves:
        min - sum_j theta_j + lbda*|e^{M*theta} - (1 - w)|_2
        s.t theta_j <= 0
    """
    assert len(M_val) == len(w_val)

    if M_val.dtype == bool:
        M_val = M_val.astype('float32')

    if type(lbda) == int:
        lbda = np.array(lbda)

    theta = tensor.row().T
    theta_ = theta.flatten()

    M = theano.shared(M_val.astype(theano.config.floatX))
    w = theano.shared(w_val.astype(theano.config.floatX))
    lbda = theano.shared(lbda.astype(theano.config.floatX))

    y = lbda * (theta_).norm(1) + (
        tensor.exp(M.dot(theta_)) - (1 - w)).norm(2)

    return diff_and_opt(theta, theta_, M, M_val, w, lbda, y)


def diff_and_opt(theta, theta_, M, M_val, w, lbda, y):
    z = tensor.row().T
    z_ = z.flatten()

    m, n = M_val.shape

    y_diff = tensor.grad(y, theta_)
    y_hess = z[0] * theano.gradient.hessian(y, theta_)
    f_x = theano.function([theta], [y, y_diff], allow_input_downcast=True)
    f_xz = theano.function([theta, z], [y, y_diff, y_hess],
                           allow_input_downcast=True)

    def F(x=None, z=None):
        if x is None:
            return 0, cvxopt.matrix(-.001, (n,1))
        elif z is None:
            y, y_diff = f_x(x)
            return cvxopt.matrix(float(y), (1, 1)),\
                   cvxopt.matrix(y_diff.astype("float64")).T
        else:
            y, y_diff, y_hess = f_xz(x, z)
            return cvxopt.matrix(float(y), (1, 1)), \
                    cvxopt.matrix(y_diff.astype("float64")).T, \
                    cvxopt.matrix(y_hess.astype("float64"))

    G = cvxopt.spdiag([1 for i in range(n)])
    h = cvxopt.matrix(0.0, (n,1))

    #Relaxing precision constraints
    cvxopt.solvers.options['feastol'] = 2e-5
    cvxopt.solvers.options['abstol'] = 2e-5
    #cvxopt.solvers.options['maxiters'] = 100
    cvxopt.solvers.options['show_progress'] = True
    try:
        theta = cvxopt.solvers.cp(F, G, h)['x']
    except ArithmeticError:
        print("ArithmeticError thrown, change initial point"+\
              " given to the solver")
    except 

    return 1 - np.exp(theta), theta


def test():
    """
    unit test
    """
    lbda = 1
    G = cascade_creation.InfluenceGraph(max_proba=.8)
    G.erdos_init(n=100, p = .1)
    A = cascade_creation.generate_cascades(G, .1, 100)
    M_val, w_val = cascade_creation.icc_matrixvector_for_node(A, 0)
    
    #Type lasso
    if 0:
        p_vec, theta = type_lasso(M_val, w_val, lbda)
        print(p_vec)

    #Sparse recovery
    if 1:
        p_vec, theta = sparse_recovery(M_val, w_val, lbda)
        print(p_vec)

if __name__=="__main__":
    test()