Python numpy.fft.rfftfreq() Examples

def test_definition(self):
        x = [0, 1, 2, 3, 4]
        assert_array_almost_equal(9*fft.rfftfreq(9), x)
        assert_array_almost_equal(9*pi*fft.rfftfreq(9, pi), x)
        x = [0, 1, 2, 3, 4, 5]
        assert_array_almost_equal(10*fft.rfftfreq(10), x)
        assert_array_almost_equal(10*pi*fft.rfftfreq(10, pi), x) 

def test_definition(self):
        x = [0, 1, 2, 3, 4]
        assert_array_almost_equal(9*fft.rfftfreq(9), x)
        assert_array_almost_equal(9*pi*fft.rfftfreq(9, pi), x)
        x = [0, 1, 2, 3, 4, 5]
        assert_array_almost_equal(10*fft.rfftfreq(10), x)
        assert_array_almost_equal(10*pi*fft.rfftfreq(10, pi), x) 

def test_definition(self):
        x = [0, 1, 2, 3, 4]
        assert_array_almost_equal(9*fft.rfftfreq(9), x)
        assert_array_almost_equal(9*pi*fft.rfftfreq(9, pi), x)
        x = [0, 1, 2, 3, 4, 5]
        assert_array_almost_equal(10*fft.rfftfreq(10), x)
        assert_array_almost_equal(10*pi*fft.rfftfreq(10, pi), x) 

def test_definition(self):
        x = [0, 1, 2, 3, 4]
        assert_array_almost_equal(9*fft.rfftfreq(9), x)
        assert_array_almost_equal(9*pi*fft.rfftfreq(9, pi), x)
        x = [0, 1, 2, 3, 4, 5]
        assert_array_almost_equal(10*fft.rfftfreq(10), x)
        assert_array_almost_equal(10*pi*fft.rfftfreq(10, pi), x) 

def test_definition(self):
        x = [0, 1, 2, 3, 4]
        assert_array_almost_equal(9*fft.rfftfreq(9), x)
        assert_array_almost_equal(9*pi*fft.rfftfreq(9, pi), x)
        x = [0, 1, 2, 3, 4, 5]
        assert_array_almost_equal(10*fft.rfftfreq(10), x)
        assert_array_almost_equal(10*pi*fft.rfftfreq(10, pi), x) 

def test_definition(self):
        x = [0, 1, 2, 3, 4]
        assert_array_almost_equal(9*fft.rfftfreq(9), x)
        assert_array_almost_equal(9*pi*fft.rfftfreq(9, pi), x)
        x = [0, 1, 2, 3, 4, 5]
        assert_array_almost_equal(10*fft.rfftfreq(10), x)
        assert_array_almost_equal(10*pi*fft.rfftfreq(10, pi), x) 

def test_definition(self):
        x = [0, 1, 2, 3, 4]
        assert_array_almost_equal(9*fft.rfftfreq(9), x)
        assert_array_almost_equal(9*pi*fft.rfftfreq(9, pi), x)
        x = [0, 1, 2, 3, 4, 5]
        assert_array_almost_equal(10*fft.rfftfreq(10), x)
        assert_array_almost_equal(10*pi*fft.rfftfreq(10, pi), x) 

def test_definition(self):
        x = [0, 1, 2, 3, 4]
        assert_array_almost_equal(9*fft.rfftfreq(9), x)
        assert_array_almost_equal(9*pi*fft.rfftfreq(9, pi), x)
        x = [0, 1, 2, 3, 4, 5]
        assert_array_almost_equal(10*fft.rfftfreq(10), x)
        assert_array_almost_equal(10*pi*fft.rfftfreq(10, pi), x) 

def test_definition(self):
        x = [0, 1, 2, 3, 4]
        assert_array_almost_equal(9*fft.rfftfreq(9), x)
        assert_array_almost_equal(9*pi*fft.rfftfreq(9, pi), x)
        x = [0, 1, 2, 3, 4, 5]
        assert_array_almost_equal(10*fft.rfftfreq(10), x)
        assert_array_almost_equal(10*pi*fft.rfftfreq(10, pi), x) 

def test_definition(self):
        x = [0, 1, 2, 3, 4]
        assert_array_almost_equal(9*fft.rfftfreq(9), x)
        assert_array_almost_equal(9*pi*fft.rfftfreq(9, pi), x)
        x = [0, 1, 2, 3, 4, 5]
        assert_array_almost_equal(10*fft.rfftfreq(10), x)
        assert_array_almost_equal(10*pi*fft.rfftfreq(10, pi), x) 

def test_definition(self):
        x = [0, 1, 2, 3, 4]
        assert_array_almost_equal(9*fft.rfftfreq(9), x)
        assert_array_almost_equal(9*pi*fft.rfftfreq(9, pi), x)
        x = [0, 1, 2, 3, 4, 5]
        assert_array_almost_equal(10*fft.rfftfreq(10), x)
        assert_array_almost_equal(10*pi*fft.rfftfreq(10, pi), x) 

def main(args):
    pyfftw.interfaces.cache.enable()

    refmap = mrc.read(args.key, compat="relion")
    df = star.parse_star(args.input, keep_index=False)
    star.augment_star_ucsf(df)
    refmap_ft = vop.vol_ft(refmap, threads=args.threads)

    apix = star.calculate_apix(df)
    sz = refmap_ft.shape[0] // 2 - 1
    sx, sy = np.meshgrid(rfftfreq(sz), fftfreq(sz))
    s = np.sqrt(sx ** 2 + sy ** 2)
    r = s * sz
    r = np.round(r).astype(np.int64)
    r[r > sz // 2] = sz // 2 + 1
    a = np.arctan2(sy, sx)

    def1 = df["rlnDefocusU"].values
    def2 = df["rlnDefocusV"].values
    angast = df["rlnDefocusAngle"].values
    phase = df["rlnPhaseShift"].values
    kv = df["rlnVoltage"].values
    ac = df["rlnAmplitudeContrast"].values
    cs = df["rlnSphericalAberration"].values
    xshift = df["rlnOriginX"].values
    yshift = df["rlnOriginY"].values

    score = np.zeros(df.shape[0])

    # TODO parallelize
    for i, row in df.iterrows():
        xcor = particle_xcorr(row, refmap_ft)

    if args.top is None:
        args.top = df.shape[0]

    top = df.iloc[np.argsort(score)][:args.top]
    star.simplify_star_ucsf(top)
    star.write_star(args.output, top)
    return 0 

def test_definition(self):
        x = [0, 1, 2, 3, 4]
        assert_array_almost_equal(9*fft.rfftfreq(9), x)
        assert_array_almost_equal(9*pi*fft.rfftfreq(9, pi), x)
        x = [0, 1, 2, 3, 4, 5]
        assert_array_almost_equal(10*fft.rfftfreq(10), x)
        assert_array_almost_equal(10*pi*fft.rfftfreq(10, pi), x) 

def test_definition(self):
        x = [0, 1, 2, 3, 4]
        assert_array_almost_equal(9*fft.rfftfreq(9), x)
        assert_array_almost_equal(9*pi*fft.rfftfreq(9, pi), x)
        x = [0, 1, 2, 3, 4, 5]
        assert_array_almost_equal(10*fft.rfftfreq(10), x)
        assert_array_almost_equal(10*pi*fft.rfftfreq(10, pi), x) 

def test_definition(self):
        x = [0, 1, 2, 3, 4]
        assert_array_almost_equal(9*fft.rfftfreq(9), x)
        assert_array_almost_equal(9*pi*fft.rfftfreq(9, pi), x)
        x = [0, 1, 2, 3, 4, 5]
        assert_array_almost_equal(10*fft.rfftfreq(10), x)
        assert_array_almost_equal(10*pi*fft.rfftfreq(10, pi), x) 

def test_definition(self):
        x = [0, 1, 2, 3, 4]
        assert_array_almost_equal(9*fft.rfftfreq(9), x)
        assert_array_almost_equal(9*pi*fft.rfftfreq(9, pi), x)
        x = [0, 1, 2, 3, 4, 5]
        assert_array_almost_equal(10*fft.rfftfreq(10), x)
        assert_array_almost_equal(10*pi*fft.rfftfreq(10, pi), x) 

def test_definition(self):
        x = [0, 1, 2, 3, 4]
        assert_array_almost_equal(9*fft.rfftfreq(9), x)
        assert_array_almost_equal(9*pi*fft.rfftfreq(9, pi), x)
        x = [0, 1, 2, 3, 4, 5]
        assert_array_almost_equal(10*fft.rfftfreq(10), x)
        assert_array_almost_equal(10*pi*fft.rfftfreq(10, pi), x) 

def falpha(length=8192, alpha=1.0, fl=None, fu=None, mean=0.0, var=1.0):
    """Generate (1/f)^alpha noise by inverting the power spectrum.

    Generates (1/f)^alpha noise by inverting the power spectrum.
    Follows the algorithm described by Voss (1988) to generate
    fractional Brownian motion.

    Parameters
    ----------
    length : int, optional (default = 8192)
        Length of the time series to be generated.
    alpha : float, optional (default = 1.0)
        Exponent in (1/f)^alpha.  Pink noise will be generated by
        default.
    fl : float, optional (default = None)
        Lower cutoff frequency.
    fu : float, optional (default = None)
        Upper cutoff frequency.
    mean : float, optional (default = 0.0)
        Mean of the generated noise.
    var : float, optional (default = 1.0)
        Variance of the generated noise.

    Returns
    -------
    x : array
        Array containing the time series.

    Notes
    -----
    As discrete Fourier transforms assume that the input data is
    periodic, the resultant series x_{i} (= x_{i + N}) is also periodic.
    To avoid this periodicity, it is recommended to always generate
    a longer series (two or three times longer) and trim it to the
    desired length.
    """
    freqs = fft.rfftfreq(length)
    power = freqs[1:] ** -alpha
    power = np.insert(power, 0, 0)  # P(0) = 0

    if fl:
        power[freqs < fl] = 0

    if fu:
        power[freqs > fu] = 0

    # Randomize complex phases.
    phase = 2 * np.pi * np.random.random(len(freqs))
    y = np.sqrt(power) * np.exp(1j * phase)

    # The last component (corresponding to the Nyquist frequency) of an
    # RFFT with even number of points is always real.  (We don't have to
    # make the mean real as P(0) = 0.)
    if length % 2 == 0:
        y[-1] = np.abs(y[-1] * np.sqrt(2))

    x = fft.irfft(y, n=length)

    # Rescale to proper variance and mean.
    x = np.sqrt(var) * x / np.std(x)
    return mean + x - np.mean(x)