Python numpy.pi方法代碼示例

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import pi [as 別名]
def periodic_hann(window_length):
  """Calculate a "periodic" Hann window.

  The classic Hann window is defined as a raised cosine that starts and
  ends on zero, and where every value appears twice, except the middle
  point for an odd-length window.  Matlab calls this a "symmetric" window
  and np.hanning() returns it.  However, for Fourier analysis, this
  actually represents just over one cycle of a period N-1 cosine, and
  thus is not compactly expressed on a length-N Fourier basis.  Instead,
  it's better to use a raised cosine that ends just before the final
  zero value - i.e. a complete cycle of a period-N cosine.  Matlab
  calls this a "periodic" window. This routine calculates it.

  Args:
    window_length: The number of points in the returned window.

  Returns:
    A 1D np.array containing the periodic hann window.
  """
  return 0.5 - (0.5 * np.cos(2 * np.pi / window_length *
                             np.arange(window_length))) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import pi [as 別名]
def to_radians(arr, is_delta=False):
    """Force data with units either degrees or radians to be radians."""
    # Infer the units from embedded metadata, if it's there.
    try:
        units = arr.units
    except AttributeError:
        pass
    else:
        if units.lower().startswith('degrees'):
            warn_msg = ("Conversion applied: degrees -> radians to array: "
                        "{}".format(arr))
            logging.debug(warn_msg)
            return np.deg2rad(arr)
    # Otherwise, assume degrees if the values are sufficiently large.
    threshold = 0.1*np.pi if is_delta else 4*np.pi
    if np.max(np.abs(arr)) > threshold:
        warn_msg = ("Conversion applied: degrees -> radians to array: "
                    "{}".format(arr))
        logging.debug(warn_msg)
        return np.deg2rad(arr)
    return arr 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import pi [as 別名]
def test_cross_phase_2d(self, dask):
        Ny, Nx = (32, 16)
        x = np.linspace(0, 1, num=Nx, endpoint=False)
        y = np.ones(Ny)
        f = 6
        phase_offset = np.pi/2
        signal1 = np.cos(2*np.pi*f*x)  # frequency = 1/(2*pi)
        signal2 = np.cos(2*np.pi*f*x - phase_offset)
        da1 = xr.DataArray(data=signal1*y[:,np.newaxis], name='a',
                          dims=['y','x'], coords={'y':y, 'x':x})
        da2 = xr.DataArray(data=signal2*y[:,np.newaxis], name='b',
                          dims=['y','x'], coords={'y':y, 'x':x})
        with pytest.raises(ValueError):
            xrft.cross_phase(da1, da2, dim=['y','x'])

        if dask:
            da1 = da1.chunk({'x': 16})
            da2 = da2.chunk({'x': 16})
        cp = xrft.cross_phase(da1, da2, dim=['x'])
        actual_phase_offset = cp.sel(freq_x=f).values
        npt.assert_almost_equal(actual_phase_offset, phase_offset) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import pi [as 別名]
def doa(self, receiver, source):
        ''' Computes the direction of arrival wrt a source and receiver '''

        s_ind = self.key2ind(source)
        r_ind = self.key2ind(receiver)

        # vector from receiver to source
        v = self.X[:,s_ind] - self.X[:,r_ind]

        azimuth = np.arctan2(v[1], v[0])
        elevation = np.arctan2(v[2], la.norm(v[:2]))

        azimuth = azimuth + 2*np.pi if azimuth < 0. else azimuth
        elevation = elevation + 2*np.pi if elevation < 0. else elevation

        return np.array([azimuth, elevation]) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import pi [as 別名]
def compute_mode(self):
        """
        Pre-compute mode vectors from candidate locations (in spherical 
        coordinates).
        """
        if self.num_loc is None:
            raise ValueError('Lookup table appears to be empty. \
                Run build_lookup().')
        self.mode_vec = np.zeros((self.max_bin,self.M,self.num_loc), 
            dtype='complex64')
        if (self.nfft % 2 == 1):
            raise ValueError('Signal length must be even.')
        f = 1.0 / self.nfft * np.linspace(0, self.nfft / 2, self.max_bin) \
            * 1j * 2 * np.pi
        for i in range(self.num_loc):
            p_s = self.loc[:, i]
            for m in range(self.M):
                p_m = self.L[:, m]
                if (self.mode == 'near'):
                    dist = np.linalg.norm(p_m - p_s, axis=1)
                if (self.mode == 'far'):
                    dist = np.dot(p_s, p_m)
                # tau = np.round(self.fs*dist/self.c) # discrete - jagged
                tau = self.fs * dist / self.c  # "continuous" - smoother
                self.mode_vec[:, m, i] = np.exp(f * tau) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import pi [as 別名]
def convert_image(self, filename):
        pic = img.imread(filename)
        # Set FFT size to be double the image size so that the edge of the spectrum stays clear
        # preventing some bandfilter artifacts
        self.NFFT = 2*pic.shape[1]

        # Repeat image lines until each one comes often enough to reach the desired line time
        ffts = (np.flipud(np.repeat(pic[:, :, 0], self.repetitions, axis=0) / 16.)**2.) / 256.

        # Embed image in center bins of the FFT
        fftall = np.zeros((ffts.shape[0], self.NFFT))
        startbin = int(self.NFFT/4)
        fftall[:, startbin:(startbin+pic.shape[1])] = ffts

        # Generate random phase vectors for the FFT bins, this is important to prevent high peaks in the output
        # The phases won't be visible in the spectrum
        phases = 2*np.pi*np.random.rand(*fftall.shape)
        rffts = fftall * np.exp(1j*phases)

        # Perform the FFT per image line, then concatenate them to form the final signal
        timedata = np.fft.ifft(np.fft.ifftshift(rffts, axes=1), axis=1) / np.sqrt(float(self.NFFT))
        linear = timedata.flatten()
        linear = linear / np.max(np.abs(linear))
        return linear 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import pi [as 別名]
def vertex_eccen(m, property=None):
    p = vertex_prop(m, property)
    if p is None:
        ecc0 = next((m[k]
                     for kk in _vertex_angle_prefixes
                     for k in [kk + 'eccentricity']
                     if k in m),
                    None)
        if ecc0 is not None: return ecc0
        ecc0 = next((m[k]
                     for kk in _vertex_angle_prefixes
                     for k in [kk + 'rho']
                     if k in m),
                    None)
        if ecc0 is not None:
            return 180.0/np.pi*ecc0
        return None
    return p 

# 需要導入模塊: import numpy [as 別名]
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def cos_well(f=Ellipsis, width=np.pi/2, offset=0, scale=1):
    '''
    cos_well() yields a potential function g(x) that calculates 0.5*(1 - cos(x)) for -pi/2 <= x
      <= pi/2 and is 1 outside of that range.
    
    The full formulat of the cosine well is, including optional arguments:
      scale / 2 * (1 - cos((x - offset) / (width/pi)))

    The following optional arguments may be given:
      * width (default: pi) specifies that the frequency of the cos-curve should be pi/width; the
        width is the distance between the points on the cos-curve with the value of 1.
      * offset (default: 0) specifies the offset of the minimum value of the coine curve on the
        x-axis.
      * scale (default: 1) specifies the height of the cosine well.
    '''
    f = to_potential(f)
    freq = np.pi/width*2
    (xmn,xmx) = (offset - width/2, offset + width/2)
    F = piecewise(scale, ((xmn,xmx), scale/2 * (1 - cos(freq * (identity - offset)))))
    if   is_const_potential(f):    return const_potential(F.value(f.c))
    elif is_identity_potential(f): return F
    else:                          return compose(F, f) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import pi [as 別名]
def cos_edge(f=Ellipsis, width=np.pi, offset=0, scale=1):
    '''
    cos_edge() yields a potential function g(x) that calculates 0 for x < pi/2, 1 for x > pi/2, and
      0.5*(1 + cos(pi/2*(1 - x))) for x between -pi/2 and pi/2.
    
    The full formulat of the cosine well is, including optional arguments:
      scale/2 * (1 + cos(pi*(0.5 - (x - offset)/width)

    The following optional arguments may be given:
      * width (default: pi) specifies that the frequency of the cos-curve should be pi/width; the
        width is the distance between the points on the cos-curve with the value of 1.
      * offset (default: 0) specifies the offset of the minimum value of the coine curve on the
        x-axis.
      * scale (default: 1) specifies the height of the cosine well.
    '''
    f = to_potential(f)
    freq = np.pi/2
    (xmn,xmx) = (offset - width/2, offset + width/2)
    F = piecewise(scale,
                  ((-np.inf, xmn), 0),
                  ((xmn,xmx), scale/2 * (1 + cos(np.pi*(0.5 - (identity - offset)/width)))))
    if   is_const_potential(f):    return const_potential(F.value(f.c))
    elif is_identity_potential(f): return F
    else:                          return compose(F, f) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import pi [as 別名]
def test_cmag(self):
        '''
        test_cmag() ensures that the neuropythy.vision cortical magnification function is working.
        '''
        import neuropythy.vision as vis
        logging.info('neuropythy: Testing areal cortical magnification...')
        dset = ny.data['benson_winawer_2018']
        sub = dset.subjects['S1202']
        hem = [sub.lh, sub.rh][np.random.randint(2)]
        cm = vis.areal_cmag(hem.midgray_surface, 'prf_',
                            mask=('inf-prf_visual_area', 1),
                            weight='prf_variance_explained')
        # cmag should get smaller in general
        ths = np.arange(0, 2*np.pi, np.pi/3)
        es = [0.5, 1, 2, 4]
        x = np.diff([np.mean(cm(e*np.cos(ths), e*np.sin(ths))) for e in es])
        self.assertTrue((x < 0).all()) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import pi [as 別名]
def rotate_camera_to_point_at(up_from, lookat_from, up_to, lookat_to):
  inputs = [up_from, lookat_from, up_to, lookat_to]
  for i in range(4):
    inputs[i] = normalize(np.array(inputs[i]).reshape((-1,)))
  up_from, lookat_from, up_to, lookat_to = inputs
  r1 = r_between(lookat_from, lookat_to)

  new_x = np.dot(r1, np.array([1, 0, 0]).reshape((-1, 1))).reshape((-1))
  to_x = normalize(np.cross(lookat_to, up_to))
  angle = np.arccos(np.dot(new_x, to_x))
  if angle > ANGLE_EPS:
    if angle < np.pi - ANGLE_EPS:
      ax = normalize(np.cross(new_x, to_x))
      flip = np.dot(lookat_to, ax)
      if flip > 0:
        r2 = get_r_matrix(lookat_to, angle)
      elif flip < 0:
        r2 = get_r_matrix(lookat_to, -1. * angle)
    else:
      # Angle of rotation is too close to 180 degrees, direction of rotation
      # does not matter.
      r2 = get_r_matrix(lookat_to, angle)
  else:
    r2 = np.eye(3)
  return np.dot(r2, r1) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import pi [as 別名]
def get_loc_axis(self, node, delta_theta, perturb=None):
    """Based on the node orientation returns X, and Y axis. Used to sample the
    map in egocentric coordinate frame.
    """
    if type(node) == tuple:
      node = np.array([node])
    if perturb is None:
      perturb = np.zeros((node.shape[0], 4))
    xyt = self.to_actual_xyt_vec(node)
    x = xyt[:,[0]] + perturb[:,[0]]
    y = xyt[:,[1]] + perturb[:,[1]]
    t = xyt[:,[2]] + perturb[:,[2]]
    theta = t*delta_theta
    loc = np.concatenate((x,y), axis=1)
    x_axis = np.concatenate((np.cos(theta), np.sin(theta)), axis=1)
    y_axis = np.concatenate((np.cos(theta+np.pi/2.), np.sin(theta+np.pi/2.)),
                            axis=1)
    # Flip the sampled map where need be.
    y_axis[np.where(perturb[:,3] > 0)[0], :] *= -1.
    return loc, x_axis, y_axis, theta 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import pi [as 別名]
def diag_gaussian_log_likelihood(z, mu=0.0, logvar=0.0):
  """Log-likelihood under a Gaussian distribution with diagonal covariance.
    Returns the log-likelihood for each dimension.  One should sum the
    results for the log-likelihood under the full multidimensional model.

  Args:
    z: The value to compute the log-likelihood.
    mu: The mean of the Gaussian
    logvar: The log variance of the Gaussian.

  Returns:
    The log-likelihood under the Gaussian model.
  """

  return -0.5 * (logvar + np.log(2*np.pi) + \
                 tf.square((z-mu)/tf.exp(0.5*logvar))) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import pi [as 別名]
def gaussian_pos_log_likelihood(unused_mean, logvar, noise):
  """Gaussian log-likelihood function for a posterior in VAE

  Note: This function is specialized for a posterior distribution, that has the
  form of z = mean + sigma * noise.

  Args:
    unused_mean: ignore
    logvar: The log variance of the distribution
    noise: The noise used in the sampling of the posterior.

  Returns:
    The log-likelihood under the Gaussian model.
  """
  # ln N(z; mean, sigma) = - ln(sigma) - 0.5 ln 2pi - noise^2 / 2
  return - 0.5 * (logvar + np.log(2 * np.pi) + tf.square(noise)) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import pi [as 別名]
def _fourier_transform_single_fermionic_modes(
        amplitudes: List[complex]) -> List[complex]:
    """Fermionic Fourier transform of a list of single Fermionic modes.

    Args:
        amplitudes: List of amplitudes for each Fermionic mode.

    Return:
        List representing a new, Fourier transformed amplitudes of the input
        amplitudes.
    """
    def fft(k, n):
        unit = np.exp(-2j * np.pi * k / n)
        return sum(unit**j * amplitudes[j] for j in range(n)) / np.sqrt(n)
    n = len(amplitudes)
    return [fft(k, n) for k in range(n)]