# -*- coding: utf-8 -*-
# _dsclansNTF.py
# Module providing the dsclansNTF function
# Copyright 2013 Giuseppe Venturini
# This file is part of python-deltasigma.
#
# python-deltasigma is a 1:1 Python replacement of Richard Schreier's 
# MATLAB delta sigma toolbox (aka "delsigma"), upon which it is heavily based.
# The delta sigma toolbox is (c) 2009, Richard Schreier.
#
# python-deltasigma is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# LICENSE file for the licensing terms.

"""Module providing the dsclansNTF() function
"""

import numpy as np
from ._utils import carray

def dsclansNTF(x, order, rmax, Hz):
    """ Conversion of clans parameters into a NTF.

    Translate x into H.
    I've changed the relationships between (zeta, wn) and x
    in order to guarantee LHP roots of the s-polynomial.
    
    Returns the NTF, a zpk tuple.
    """
    x = x.squeeze()
    Hz = carray(Hz)
    Hz = Hz.reshape((-1,))
    Hp = np.zeros((1,), dtype=np.complex128)
    odd = (order % 2 == 1)
    if odd:
        s = -x[0]**2.
        Hp[0] = rmax*(1. + s)/(1. - s)

    for i in range(0+1*odd, order, 2):
        Hp = np.hstack((Hp, np.zeros((2,))))
        zeta = x[i]**2
        wn = x[i + 1]**2
        s = np.roots(np.array((1, 2*zeta*wn, wn**2)))
        Hp[i:i+2] = rmax*(1. + s)/(1. - s)

    H = (Hz, Hp, 1.)
    return H

def test_dsclansNTF():
    """Test function for dsclansNTF()
    """
    x = dsclansNTF(np.arange(1, 100.001, .001), 3, .5, 100)
    rt = np.array(x[1][:])
    rt.sort()
    rp = np.array([0, -0.016805373426715, 0.014809370415763])
    rp.sort()
    rz = (100., )
    assert np.allclose(rp, rt, rtol=1e-5, atol=1e-6)
    assert np.allclose(rz, x[0], rtol=1e-5, atol=1e-8)
    rp = np.array([0.35378443 +0.j, 0.34187718 +0.22831019j,
                   0.34187718 -0.22831019j, 0.32978826 +0.59355161j,
                   0.32978826 -0.59355161j])
    x = np.array([0.67623674, 0.9277613, 0.70365961, 0.60374009, 0.78008118])
    Hz = np.array([0.99604531 - 0.08884669j, 0.99604531 +0.08884669j,
                   0.99860302 - 0.05283948j, 0.99860302 +0.05283948j,
                   1.00000000 +0.j])
    tp =  dsclansNTF(x, order=5, rmax=.95, Hz=Hz)[1]
    assert np.allclose(rp, tp, rtol=1e-5, atol=1e-6)

