Python numpy.roots方法代碼示例

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import roots [as 別名]
def fit_cubic(y0, y1, g0, g1):
    """Fit cubic polynomial to function values and derivatives at x = 0, 1.

    Returns position and function value of minimum if fit succeeds. Fit does
    not succeeds if

    1. polynomial doesn't have extrema or
    2. maximum is from (0,1) or
    3. maximum is closer to 0.5 than minimum
    """
    a = 2 * (y0 - y1) + g0 + g1
    b = -3 * (y0 - y1) - 2 * g0 - g1
    p = np.array([a, b, g0, y0])
    r = np.roots(np.polyder(p))
    if not np.isreal(r).all():
        return None, None
    r = sorted(x.real for x in r)
    if p[0] > 0:
        maxim, minim = r
    else:
        minim, maxim = r
    if 0 < maxim < 1 and abs(minim - 0.5) > abs(maxim - 0.5):
        return None, None
    return minim, np.polyval(p, minim) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import roots [as 別名]
def data_analysis(e_ph, flux, method="least"):

    if method == "least":
        coeffs = np.polyfit(x=e_ph, y=flux, deg=11)
        polynom = np.poly1d(coeffs)


        x = np.linspace(e_ph[0], e_ph[-1], num=100)
        pd = np.polyder(polynom, m=1)
        indx = np.argmax(np.abs(pd(x)))
        eph_c = x[indx]

        pd2 = np.polyder(polynom, m=2)
        p2_roots = np.roots(pd2)
        p2_roots = p2_roots[p2_roots[:].imag == 0]
        p2_roots = np.real(p2_roots)
        Eph_fin = find_nearest(p2_roots,eph_c)
        return Eph_fin, polynom

    elif method == "new method":
        pass

        #plt.plot(Etotal, total, "ro")
        #plt.plot(x, polynom(x)) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import roots [as 別名]
def impz(b,a):
    """Pseudo implementation of the impz method of MATLAB"""
#% Compute time vector
# M = 0;  NN = [];
# if isempty(N)
#   % if not specified, determine the length
#   if isTF
#     N = impzlength(b,a,.00005);
#   else
#     N  = impzlength(b,.00005);
#   end
    p = np.roots(a)
    N = stableNmarginal_length(p, 0.00005, 0)
    N = len(b) * len(b) * len(b) # MATLAB AUTOFINDS THE SIZE HERE... 
    #TODO: Implement some way of finding the autosieze of this... I used a couple of examples... matlab gave 43 as length we give 64
    x = zeros(N)
    x[0] = 1
    h = lfilter(b,a, x)
    return h 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import roots [as 別名]
def polyroots(p, realroots=False, condition=lambda r: True):
    """
    Returns the roots of a polynomial with coefficients given in p.
      p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n]
    INPUT:
    p - Rank-1 array-like object of polynomial coefficients.
    realroots - a boolean.  If true, only real roots will be returned  and the
        condition function can be written assuming all roots are real.
    condition - a boolean-valued function.  Only roots satisfying this will be
        returned.  If realroots==True, these conditions should assume the roots
        are real.
    OUTPUT:
    A list containing the roots of the polynomial.
    NOTE:  This uses np.isclose and np.roots"""
    roots = np.roots(p)
    if realroots:
        roots = [r.real for r in roots if isclose(r.imag, 0)]
    roots = [r for r in roots if condition(r)]

    duplicates = []
    for idx, (r1, r2) in enumerate(combinations(roots, 2)):
        if isclose(r1, r2):
            duplicates.append(idx)
    return [r for idx, r in enumerate(roots) if idx not in duplicates] 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import roots [as 別名]
def get_minimum_energy_path(self, pressure=None):
        """

        Args:
            pressure:

        Returns:

        """
        if pressure is not None:
            raise NotImplemented()
        v_min_lst = []
        for c in self._coeff.T:
            v_min = np.roots(np.polyder(c, 1))
            p_der2 = np.polyder(c, 2)
            p_val2 = np.polyval(p_der2, v_min)
            v_m_lst = v_min[p_val2 > 0]
            if len(v_m_lst) > 0:
                v_min_lst.append(v_m_lst[0])
            else:
                v_min_lst.append(np.nan)
        return np.array(v_min_lst) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import roots [as 別名]
def roots_of_characteristic(self):
        """
        This function calculates z_0 and the 2m roots of the characteristic equation 
        associated with the Euler equation (1.7)

        Note:
        ------
        numpy.poly1d(roots, True) defines a polynomial using its roots that can be
        evaluated at any point. If x_1, x_2, ... , x_m are the roots then
            p(x) = (x - x_1)(x - x_2)...(x - x_m)
        """
        m = self.m
        ϕ = self.ϕ
        
        # Calculate the roots of the 2m-polynomial
        roots = np.roots(ϕ)
        # sort the roots according to their length (in descending order)
        roots_sorted = roots[np.argsort(abs(roots))[::-1]]

        z_0 = ϕ.sum() / np.poly1d(roots, True)(1)
        z_1_to_m = roots_sorted[:m]     # we need only those outside the unit circle

        λ = 1 / z_1_to_m

        return z_1_to_m, z_0, λ 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import roots [as 別名]
def test_output_order(self):
        zc, zr = _cplxreal(np.roots(array([1, 0, 0, 1])))
        assert_allclose(np.append(zc, zr), [1/2 + 1j*sin(pi/3), -1])

        eps = spacing(1)

        a = [0+1j, 0-1j, eps + 1j, eps - 1j, -eps + 1j, -eps - 1j,
             1, 4, 2, 3, 0, 0,
             2+3j, 2-3j,
             1-eps + 1j, 1+2j, 1-2j, 1+eps - 1j,  # sorts out of order
             3+1j, 3+1j, 3+1j, 3-1j, 3-1j, 3-1j,
             2-3j, 2+3j]
        zc, zr = _cplxreal(a)
        assert_allclose(zc, [1j, 1j, 1j, 1+1j, 1+2j, 2+3j, 2+3j, 3+1j, 3+1j,
                             3+1j])
        assert_allclose(zr, [0, 0, 1, 2, 3, 4])

        z = array([1-eps + 1j, 1+2j, 1-2j, 1+eps - 1j, 1+eps+3j, 1-2*eps-3j,
                   0+1j, 0-1j, 2+4j, 2-4j, 2+3j, 2-3j, 3+7j, 3-7j, 4-eps+1j,
                   4+eps-2j, 4-1j, 4-eps+2j])

        zc, zr = _cplxreal(z)
        assert_allclose(zc, [1j, 1+1j, 1+2j, 1+3j, 2+3j, 2+4j, 3+7j, 4+1j,
                             4+2j])
        assert_equal(zr, []) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import roots [as 別名]
def __init__(self, recording, freq_min=300, freq_max=6000, freq_wid=1000, filter_type='fft', order=3,
                 chunk_size=30000, cache_chunks=False):
        assert HAVE_BFR, "To use the BandpassFilterRecording, install scipy: \n\n pip install scipy\n\n"
        self._freq_min = freq_min
        self._freq_max = freq_max
        self._freq_wid = freq_wid
        self._type = filter_type
        self._order = order
        self._chunk_size = chunk_size

        if self._type == 'butter':
            fn = recording.get_sampling_frequency() / 2.
            band = np.array([self._freq_min, self._freq_max]) / fn

            self._b, self._a = ss.butter(self._order, band, btype='bandpass')

            if not np.all(np.abs(np.roots(self._a)) < 1):
                raise ValueError('Filter is not stable')
        FilterRecording.__init__(self, recording=recording, chunk_size=chunk_size, cache_chunks=cache_chunks)
        self.copy_channel_properties(recording)

        self.is_filtered = True
        self._kwargs = {'recording': recording.make_serialized_dict(), 'freq_min': freq_min, 'freq_max': freq_max,
                        'freq_wid': freq_wid, 'filter_type': filter_type, 'order': order,
                        'chunk_size': chunk_size, 'cache_chunks': cache_chunks} 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import roots [as 別名]
def _v(self, P, T, phi_w):
        """Calculate the real volume of a humid air using the virial equation
        of state

        Parameters
        ----------
        T : float
            Temperature, [K]
        phi_w : float
            Molar fraction of water, [-]

        Returns
        -------
        """
        vir = self._virialMixture(T, phi_w)
        Bm = vir["Bm"]
        Cm = vir["Cm"]

        vm = roots([1, -R*T/P, -R*T*Bm/P, -R*T*Cm/P])
        if vm[0].imag == 0.0:
            v = vm[0].real
        else:
            v = vm[2].real

        return v 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import roots [as 別名]
def poly2lsf(a):
    a = a / a[0]        
    A = np.r_[a, 0.0]
    B = A[::-1]
    P = A - B  
    Q = A + B  
    
    P = deconvolve(P, np.array([1.0, -1.0]))[0]
    Q = deconvolve(Q, np.array([1.0, 1.0]))[0]
    
    roots_P = np.roots(P)
    roots_Q = np.roots(Q)
    
    angles_P = np.angle(roots_P[::2])
    angles_Q = np.angle(roots_Q[::2])
    angles_P[angles_P < 0.0] += np.pi
    angles_Q[angles_Q < 0.0] += np.pi
    lsf = np.sort(np.r_[angles_P, angles_Q])
    return lsf 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import roots [as 別名]
def get_mu_tensor(self):
    const_fact = self._dist_to_opt_avg**2 * self._h_min**2 / 2 / self._grad_var
    coef = tf.Variable([-1.0, 3.0, 0.0, 1.0], dtype=tf.float32, name="cubic_solver_coef")
    coef = tf.scatter_update(coef, tf.constant(2), -(3 + const_fact) )        
    roots = tf.py_func(np.roots, [coef], Tout=tf.complex64, stateful=False)
    
    # filter out the correct root
    root_idx = tf.logical_and(tf.logical_and(tf.greater(tf.real(roots), tf.constant(0.0) ),
      tf.less(tf.real(roots), tf.constant(1.0) ) ), tf.less(tf.abs(tf.imag(roots) ), 1e-5) )
    # in case there are two duplicated roots satisfying the above condition
    root = tf.reshape(tf.gather(tf.gather(roots, tf.where(root_idx) ), tf.constant(0) ), shape=[] )
    tf.assert_equal(tf.size(root), tf.constant(1) )

    dr = self._h_max / self._h_min
    mu = tf.maximum(tf.real(root)**2, ( (tf.sqrt(dr) - 1)/(tf.sqrt(dr) + 1) )**2)    
    return mu 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import roots [as 別名]
def get_speed(power,Cx,f,W,slope,headwind,elevation):
    # slope in percent
    # headwind in m/s at 10 m high
    # elevation in meters
    air_pressure = 1 - 0.000104 * elevation
    Cx = Cx*air_pressure
    G = 9.81
    headwind = (0.1**0.143) * headwind
    roots = np.roots([Cx, 2*Cx*headwind, Cx*headwind**2 + W*G*(slope/100.0+f), -power])
    roots = np.real(roots[np.imag(roots) == 0])
    roots = roots[roots>0]
    speed = np.min(roots)
    if speed + headwind < 0:
        roots = np.roots([-Cx, -2*Cx*headwind, -Cx*headwind**2 + W*G*(slope/100.0+f), -power])
        roots = np.real(roots[np.imag(roots) == 0])
        roots = roots[roots>0]
        if len(roots) > 0:
            speed = np.min(roots)  
    return speed 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import roots [as 別名]
def stroud_1966_2(n):
    degree = 3
    # r is a smallest real-valued root of a polynomial of degree 3
    rts = numpy.roots(
        [2 * (n - 2) * (n + 1) * (n + 3), -(5 * n ** 2 + 5 * n - 18), 4 * n, -1]
    )
    r = numpy.min([r.real for r in rts if abs(r.imag) < 1.0e-15])

    s = 1 - n * r
    t = 0.5

    B = (n - 2) / (1 - 2 * n * r ** 2 - 2 * (1 - n * r) ** 2) / (n + 1) / (n + 2)
    C = 2 * (1 / (n + 1) - B) / n

    data = [(B, rd(n + 1, [(r, n), (s, 1)])), (C, rd(n + 1, [(t, 2)]))]

    points, weights = untangle(data)
    return TnScheme("Stroud 1966-II", n, weights, points, degree, source) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import roots [as 別名]
def phormants(x, sampling_rate):
    N = len(x)
    w = np.hamming(N)

    # Apply window and high pass filter.
    x1 = x * w
    x1 = lfilter([1], [1., 0.63], x1)

    # Get LPC.
    ncoeff = 2 + sampling_rate / 1000
    A, e, k = lpc(x1, ncoeff)
    # A, e, k = lpc(x1, 8)

    # Get roots.
    rts = np.roots(A)
    rts = [r for r in rts if np.imag(r) >= 0]

    # Get angles.
    angz = np.arctan2(np.imag(rts), np.real(rts))

    # Get frequencies.
    frqs = sorted(angz * (sampling_rate / (2 * math.pi)))

    return frqs 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import roots [as 別名]
def tune_everything(self, x0squared, c, t, gmin, gmax):
    del t
    # First tune based on dynamic range
    if c == 0:
      dr = gmax / gmin
      mustar = ((np.sqrt(dr) - 1) / (np.sqrt(dr) + 1))**2
      alpha_star = (1 + np.sqrt(mustar))**2/gmax

      return alpha_star, mustar

    dist_to_opt = x0squared
    grad_var = c
    max_curv = gmax
    min_curv = gmin
    const_fact = dist_to_opt * min_curv**2 / 2 / grad_var
    coef = [-1, 3, -(3 + const_fact), 1]
    roots = np.roots(coef)
    roots = roots[np.real(roots) > 0]
    roots = roots[np.real(roots) < 1]
    root = roots[np.argmin(np.imag(roots))]

    assert root > 0 and root < 1 and np.absolute(root.imag) < 1e-6

    dr = max_curv / min_curv
    assert max_curv >= min_curv
    mu = max(((np.sqrt(dr) - 1) / (np.sqrt(dr) + 1))**2, root**2)

    lr_min = (1 - np.sqrt(mu))**2 / min_curv

    alpha_star = lr_min
    mustar = mu

    return alpha_star, mustar