Python numpy.pi() Examples

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))) 

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]) 

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 

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 

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)) 

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))) 

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) 

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) 

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 

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 

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)] 

def test_ffft_equal_to_bogoliubov(size):

    def fourier_transform_matrix():
        root_of_unity = np.exp(-2j * np.pi / size)
        return np.array([[root_of_unity ** (j * k) for k in range(size)]
                         for j in range(size)]) / np.sqrt(size)

    qubits = LineQubit.range(size)

    ffft_circuit = cirq.Circuit(
        ffft(qubits), strategy=cirq.InsertStrategy.EARLIEST)
    ffft_matrix = ffft_circuit.unitary(
        qubits_that_should_be_present=qubits)

    bogoliubov_circuit = cirq.Circuit(
        bogoliubov_transform(qubits, fourier_transform_matrix()),
        strategy=cirq.InsertStrategy.EARLIEST)
    bogoliubov_matrix = bogoliubov_circuit.unitary(
        qubits_that_should_be_present=qubits)

    cirq.testing.assert_allclose_up_to_global_phase(
        ffft_matrix, bogoliubov_matrix, atol=1e-8
    ) 

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) 

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) 

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) 

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()) 

def _get_export(self, frameIndex, propertiesLUT, format='%s'):
        # create data, metadata and header
        frame = propertiesLUT['frames-name'][frameIndex]
        data  = propertiesLUT['frames-data'][frameIndex]
        # compute categories
        names    = self.engine.get_original_data("allNames", frame=frame)
        elements = self.engine.get_original_data("allElements", frame=frame)
        atom2 = self.__anglesList[0]
        atom1 = self.__anglesList[1]
        atom3 = self.__anglesList[2]
        lower = self.__anglesList[3]*180./np.pi
        upper = self.__anglesList[4]*180./np.pi
        consData = data["angles"]*180./np.pi
        header = ['atom_1_index',   'atom_2_index', 'atom_3_index',
                  'atom_1_element', 'atom_2_element', 'atom_3_element',
                  'atom_1_name',     'atom_2_name', 'atom_3_name',
                  'lower_limit', 'upper_limit', 'value']
        data = []
        for idx in xrange(self.__anglesList[0].shape[0]):
            #if self._atomsCollector.is_collected(idx):
            #    continue
            if self._atomsCollector.is_collected(atom1[idx]):
                continue
            if self._atomsCollector.is_collected(atom2[idx]):
                continue
            if self._atomsCollector.is_collected(atom3[idx]):
                continue
            data.append([str(atom1[idx]),str(atom2[idx]),str(atom3[idx]),
                             elements[atom1[idx]],elements[atom2[idx]],elements[atom3[idx]],
                             names[atom1[idx]],names[atom2[idx]],names[atom3[idx]],
                             format%lower[idx], format%upper[idx],
                             format%consData[idx]] )
        # save
        return header, data 

def Ryxxy(rads: float) -> cirq.PhasedISwapPowGate:
    """Returns a gate with the matrix exp(-i rads (Y⊗X - X⊗Y) / 2)."""
    pi = sympy.pi if isinstance(rads, sympy.Basic) else np.pi
    return cirq.PhasedISwapPowGate(exponent=2 * rads / pi) 

def Rxxyy(rads: float) -> cirq.ISwapPowGate:
    """Returns a gate with the matrix exp(-i rads (X⊗X + Y⊗Y) / 2)."""
    pi = sympy.pi if isinstance(rads, sympy.Basic) else np.pi
    return cirq.ISwapPowGate(exponent=-2 * rads / pi) 

def _get_export(self, frameIndex, propertiesLUT, format='%s'):
        # create data, metadata and header
        frame = propertiesLUT['frames-name'][frameIndex]
        data  = propertiesLUT['frames-data'][frameIndex]
        # compute categories
        names    = self.engine.get_original_data("allNames", frame=frame)
        elements = self.engine.get_original_data("allElements", frame=frame)
        atom2 = self.__anglesList[0]
        atom1 = self.__anglesList[1]
        atom3 = self.__anglesList[2]
        atom4 = self.__anglesList[3]
        lower = self.__anglesList[4]*180./np.pi
        upper = self.__anglesList[5]*180./np.pi
        consData = data["angles"]*180./np.pi
        header = ['atom_1_index', 'atom_2_index', 'atom_3_index', 'atom_4_index',
                  'atom_1_element', 'atom_2_element', 'atom_3_element','atom_4_element',
                  'atom_1_name', 'atom_2_name', 'atom_3_name', 'atom_4_name',
                  'lower_limit', 'upper_limit', 'value']
        data = []
        for idx in xrange(self.__anglesList[0].shape[0]):
            #if self._atomsCollector.is_collected(idx):
            #    continue
            if self._atomsCollector.is_collected(atom1[idx]):
                continue
            if self._atomsCollector.is_collected(atom2[idx]):
                continue
            if self._atomsCollector.is_collected(atom3[idx]):
                continue
            if self._atomsCollector.is_collected(atom4[idx]):
                continue
            data.append([str(atom1[idx]),str(atom2[idx]),str(atom3[idx]),str(atom4[idx]),
                             elements[atom1[idx]],elements[atom2[idx]],elements[atom3[idx]],elements[atom4[idx]],
                             names[atom1[idx]],names[atom2[idx]],names[atom3[idx]],names[atom4[idx]],
                             format%lower[idx], format%upper[idx],
                             format%consData[idx]] )
        # save
        return header, data 

def _decompose_(self, qubits):
        r = 2 * abs(self.weights[0]) / np.pi
        theta = _arg(self.weights[0]) / np.pi
        yield cirq.Z(qubits[0])**-theta
        yield cirq.ISwapPowGate(exponent=-r * self.exponent)(*qubits)
        yield cirq.Z(qubits[0])**theta
        yield cirq.CZPowGate(exponent=-self.weights[1] * self.exponent /
                             np.pi)(*qubits) 

def compute_standard_error(self, data):
        """
        Compute the standard error (StdErr) of data not satisfying constraint
        conditions.

        .. math::
            StdErr = \\sum \\limits_{i}^{C}
            ( \\theta_{i} - \\theta_{i}^{min} ) ^{2}
            \\int_{0}^{\\theta_{i}^{min}} \\delta(\\theta-\\theta_{i}) d \\theta
            +
            ( \\theta_{i} - \\theta_{i}^{max} ) ^{2}
            \\int_{\\theta_{i}^{max}}^{\\pi} \\delta(\\theta-\\theta_{i}) d \\theta

        Where:\n
        :math:`C` is the total number of defined angles constraints. \n
        :math:`\\theta_{i}^{min}` is the angle constraint lower limit set for constraint i. \n
        :math:`\\theta_{i}^{max}` is the angle constraint upper limit set for constraint i. \n
        :math:`\\theta_{i}` is the angle computed for constraint i. \n
        :math:`\\delta` is the Dirac delta function. \n
        :math:`\\int_{0}^{\\theta_{i}^{min}} \\delta(\\theta-\\theta_{i}) d \\theta`
        is equal to 1 if :math:`0 \\leqslant \\theta_{i} \\leqslant \\theta_{i}^{min}` and 0 elsewhere.\n
        :math:`\\int_{\\theta_{i}^{max}}^{\\pi} \\delta(\\theta-\\theta_{i}) d \\theta`
        is equal to 1 if :math:`\\theta_{i}^{max} \\leqslant \\theta_{i} \\leqslant \\pi` and 0 elsewhere.\n

        :Parameters:
            #. data (numpy.array): Constraint's data to compute standardError.

        :Returns:
            #. standardError (number): The calculated standardError of the
               given data.
        """
        return FLOAT_TYPE( np.sum(data["reducedAngles"]**2) ) 

def pre(self, inputs):
    inputs['imgs'] = image_pre(inputs['imgs'], self.task_params.modalities)
    if inputs['loc_on_map'] is not None:
      inputs['loc_on_map'] = inputs['loc_on_map'] - inputs['loc_on_map'][:,[0],:]
    if inputs['theta_on_map'] is not None:
      inputs['theta_on_map'] = np.pi/2. - inputs['theta_on_map']
    return inputs 

def __init__(self, in_dataset, grid_size, rotate_aug = False, flip_aug = False, ignore_label = 255, return_test = False,
               fixed_volume_space= False, max_volume_space = [50,np.pi,1.5], min_volume_space = [3,-np.pi,-3]):
        'Initialization'
        self.point_cloud_dataset = in_dataset
        self.grid_size = np.asarray(grid_size)
        self.rotate_aug = rotate_aug
        self.flip_aug = flip_aug
        self.ignore_label = ignore_label
        self.return_test = return_test
        self.fixed_volume_space = fixed_volume_space
        self.max_volume_space = max_volume_space
        self.min_volume_space = min_volume_space 

def _get_relative_goal_loc(goal_loc, loc, theta):
  r = np.sqrt(np.sum(np.square(goal_loc - loc), axis=1))
  t = np.arctan2(goal_loc[:,1] - loc[:,1], goal_loc[:,0] - loc[:,0])
  t = t-theta[:,0] + np.pi/2
  return np.expand_dims(r,axis=1), np.expand_dims(t, axis=1) 

def get_map_to_predict(src_locs, src_x_axiss, src_y_axiss, map, map_size,
                       interpolation=cv2.INTER_LINEAR):
  fss = []
  valids = []

  center = (map_size-1.0)/2.0
  dst_theta = np.pi/2.0
  dst_loc = np.array([center, center])
  dst_x_axis = np.array([np.cos(dst_theta), np.sin(dst_theta)])
  dst_y_axis = np.array([np.cos(dst_theta+np.pi/2), np.sin(dst_theta+np.pi/2)])

  def compute_points(center, x_axis, y_axis):
    points = np.zeros((3,2),dtype=np.float32)
    points[0,:] = center
    points[1,:] = center + x_axis
    points[2,:] = center + y_axis
    return points

  dst_points = compute_points(dst_loc, dst_x_axis, dst_y_axis)
  for i in range(src_locs.shape[0]):
    src_loc = src_locs[i,:]
    src_x_axis = src_x_axiss[i,:]
    src_y_axis = src_y_axiss[i,:]
    src_points = compute_points(src_loc, src_x_axis, src_y_axis)
    M = cv2.getAffineTransform(src_points, dst_points)

    fs = cv2.warpAffine(map, M, (map_size, map_size), None, flags=interpolation,
                        borderValue=np.NaN)
    valid = np.invert(np.isnan(fs))
    valids.append(valid)
    fss.append(fs)
  return fss, valids 

def hybrid_forward(self, F, pred, target, sample_weight=None, epsilon=1e-08):
        target = _reshape_like(F, target, pred)
        if self._from_logits:
            loss = F.exp(pred) - target * pred
        else:
            loss = pred - target * F.log(pred + epsilon)
        if self._compute_full:
            # Using numpy's pi value
            stirling_factor = target * F.log(target)- target + 0.5 * F.log(2 * target * np.pi)
            target_gt_1 = target > 1
            stirling_factor *= target_gt_1
            loss += stirling_factor
        loss = _apply_weighting(F, loss, self._weight, sample_weight)
        return F.mean(loss) 

def __call__(self, src):
        """Augmenter body.
        Using approximate linear transfomation described in:
        https://beesbuzz.biz/code/hsv_color_transforms.php
        """
        alpha = random.uniform(-self.hue, self.hue)
        u = np.cos(alpha * np.pi)
        w = np.sin(alpha * np.pi)
        bt = np.array([[1.0, 0.0, 0.0],
                       [0.0, u, -w],
                       [0.0, w, u]])
        t = np.dot(np.dot(self.ityiq, bt), self.tyiq).T
        src = nd.dot(src, nd.array(t))
        return src 

def test_poisson_nllloss():
    pred = mx.nd.random.normal(shape=(3, 4))
    min_pred = mx.nd.min(pred)
    #This is necessary to ensure only positive random values are generated for prediction,
    # to avoid ivalid log calculation
    pred[:] = pred + mx.nd.abs(min_pred)
    target = mx.nd.random.normal(shape=(3, 4))
    min_target = mx.nd.min(target)
    #This is necessary to ensure only positive random values are generated for prediction,
    # to avoid ivalid log calculation
    target[:] += mx.nd.abs(min_target)

    Loss = gluon.loss.PoissonNLLLoss(from_logits=True)
    Loss_no_logits = gluon.loss.PoissonNLLLoss(from_logits=False)
    #Calculating by brute formula for default value of from_logits = True

    # 1) Testing for flag logits = True
    brute_loss = np.mean(np.exp(pred.asnumpy()) - target.asnumpy() * pred.asnumpy())
    loss_withlogits = Loss(pred, target)
    assert_almost_equal(brute_loss, loss_withlogits.asscalar())

    #2) Testing for flag logits = False
    loss_no_logits = Loss_no_logits(pred, target)
    np_loss_no_logits = np.mean(pred.asnumpy() - target.asnumpy() * np.log(pred.asnumpy() + 1e-08))
    if np.isnan(loss_no_logits.asscalar()):
        assert_almost_equal(np.isnan(np_loss_no_logits), np.isnan(loss_no_logits.asscalar()))
    else:
        assert_almost_equal(np_loss_no_logits, loss_no_logits.asscalar())

    #3) Testing for Sterling approximation
    np_pred = np.random.uniform(1, 5, (2, 3))
    np_target = np.random.uniform(1, 5, (2, 3))
    np_compute_full = np.mean((np_pred - np_target * np.log(np_pred + 1e-08)) + ((np_target * np.log(np_target)-\
     np_target + 0.5 * np.log(2 * np_target * np.pi))*(np_target > 1)))
    Loss_compute_full = gluon.loss.PoissonNLLLoss(from_logits=False, compute_full=True)
    loss_compute_full = Loss_compute_full(mx.nd.array(np_pred), mx.nd.array(np_target))
    assert_almost_equal(np_compute_full, loss_compute_full.asscalar()) 

def standard_normal_ll(input_):
    """Log-likelihood of standard Gaussian distribution."""
    res = -.5 * (tf.square(input_) + numpy.log(2. * numpy.pi))

    return res