from typing import Dict
from scipy.stats import norm, gaussian_kde, rankdata

import numpy as np

from . import common_args
from ..util import read_param_file, ResultDict


def analyze(problem: Dict, X: np.array, Y: np.array, 
            num_resamples: int = 100, conf_level: float = 0.95,
            print_to_console: bool = False, seed: int = None) -> Dict:
    """Perform Delta Moment-Independent Analysis on model outputs.

    Returns a dictionary with keys 'delta', 'delta_conf', 'S1', and 'S1_conf',
    where each entry is a list of size D (the number of parameters) containing
    the indices in the same order as the parameter file.

    Parameters
    ----------
    problem : dict
        The problem definition
    X: numpy.matrix
        A NumPy matrix containing the model inputs
    Y : numpy.array
        A NumPy array containing the model outputs
    num_resamples : int
        The number of resamples when computing confidence intervals (default 10)
    conf_level : float
        The confidence interval level (default 0.95)
    print_to_console : bool
        Print results directly to console (default False)

    References
    ----------
    .. [1] Borgonovo, E. (2007). "A new uncertainty importance measure."
           Reliability Engineering & System Safety, 92(6):771-784,
           doi:10.1016/j.ress.2006.04.015.

    .. [2] Plischke, E., E. Borgonovo, and C. L. Smith (2013). "Global
           sensitivity measures from given data." European Journal of
           Operational Research, 226(3):536-550, doi:10.1016/j.ejor.2012.11.047.

    Examples
    --------
        >>> X = latin.sample(problem, 1000)
        >>> Y = Ishigami.evaluate(X)
        >>> Si = delta.analyze(problem, X, Y, print_to_console=True)
    """
    if seed:
        np.random.seed(seed)

    D = problem['num_vars']
    N = Y.size

    if not 0 < conf_level < 1:
        raise RuntimeError("Confidence level must be between 0-1.")

    # equal frequency partition
    exp = (2 / (7 + np.tanh((1500 - N) / 500)))
    M = int(np.round( min(int(np.ceil(N**exp)), 48) ))
    m = np.linspace(0, N, M + 1)
    Ygrid = np.linspace(np.min(Y), np.max(Y), 100)

    keys = ('delta', 'delta_conf', 'S1', 'S1_conf')
    S = ResultDict((k, np.zeros(D)) for k in keys)
    S['names'] = problem['names']

    if print_to_console:
        print("Parameter %s %s %s %s" % keys)

    try:
        for i in range(D):
            X_i = X[:, i]
            S['delta'][i], S['delta_conf'][i] = bias_reduced_delta(
                Y, Ygrid, X_i, m, num_resamples, conf_level)
            S['S1'][i] = sobol_first(Y, X_i, m)
            S['S1_conf'][i] = sobol_first_conf(
                Y, X_i, m, num_resamples, conf_level)
            if print_to_console:
                print("%s %f %f %f %f" % (S['names'][i], S['delta'][
                    i], S['delta_conf'][i], S['S1'][i], S['S1_conf'][i]))
    except np.linalg.LinAlgError as e:
        msg = "Singular matrix detected\n"
        msg += "This may be due to the sample size ({}) being too small\n".format(Y.size)
        msg += "If this is not the case, check Y values or raise an issue with the\n"
        msg += "SALib team"

        raise np.linalg.LinAlgError(msg)

    return S


def calc_delta(Y, Ygrid, X, m):
    """Plischke et al. (2013) delta index estimator (eqn 26) for d_hat."""
    N = len(Y)
    fy = gaussian_kde(Y, bw_method='silverman')(Ygrid)
    abs_fy = np.abs(fy)
    xr = rankdata(X, method='ordinal')

    d_hat = 0
    for j in range(len(m) - 1):
        ix = np.where((xr > m[j]) & (xr <= m[j + 1]))[0]
        nm = len(ix)

        Y_ix = Y[ix]
        if not np.all(np.equal(Y_ix, Y_ix[0])):
            fyc = gaussian_kde(Y_ix, bw_method='silverman')(Ygrid)
            fy_ = np.abs(fy - fyc)
        else:
            fy_ = abs_fy
        
        d_hat += (nm / (2 * N)) * np.trapz(fy_, Ygrid)

    return d_hat


def bias_reduced_delta(Y, Ygrid, X, m, num_resamples, conf_level):
    """Plischke et al. 2013 bias reduction technique (eqn 30)"""
    d = np.zeros(num_resamples)
    d_hat = calc_delta(Y, Ygrid, X, m)

    N = len(Y)
    r = np.random.randint(N, size=(num_resamples, N))
    for i in range(num_resamples):
        r_i = r[i, :]
        d[i] = calc_delta(Y[r_i], Ygrid, X[r_i], m)

    d = 2 * d_hat - d
    return (d.mean(), norm.ppf(0.5 + conf_level / 2) * d.std(ddof=1))


def sobol_first(Y, X, m):
    xr = rankdata(X, method='ordinal')
    Vi = 0
    N = len(Y)
    Y_mean = Y.mean()
    for j in range(len(m) - 1):
        ix = np.where((xr > m[j]) & (xr <= m[j + 1]))[0]
        nm = len(ix)
        Vi += (nm / N) * ((Y[ix].mean() - Y_mean)**2)
    return Vi / np.var(Y)


def sobol_first_conf(Y, X, m, num_resamples, conf_level):
    s = np.zeros(num_resamples)

    N = len(Y)
    r = np.random.randint(N, size=(num_resamples, N))
    for i in range(num_resamples):
        r_i = r[i, :]
        s[i] = sobol_first(Y[r_i], X[r_i], m)

    return norm.ppf(0.5 + conf_level / 2) * s.std(ddof=1)


def cli_parse(parser):
    parser.add_argument('-X', '--model-input-file', type=str, required=True,
                        default=None,
                        help='Model input file')
    parser.add_argument('-r', '--resamples', type=int, required=False,
                        default=10,
                        help='Number of bootstrap resamples for \
                           Sobol confidence intervals')
    return parser


def cli_action(args):
    problem = read_param_file(args.paramfile)
    Y = np.loadtxt(args.model_output_file,
                   delimiter=args.delimiter, usecols=(args.column,))
    X = np.loadtxt(args.model_input_file, delimiter=args.delimiter, ndmin=2)
    if len(X.shape) == 1:
        X = X.reshape((len(X), 1))

    analyze(problem, X, Y, num_resamples=args.resamples, print_to_console=True,
            seed=args.seed)


if __name__ == "__main__":
    common_args.run_cli(cli_parse, cli_action)