Python numpy.power() Examples

def class_balanced_weight(beta, samples_per_class):
    assert 0 <= beta < 1, 'Wrong rang of beta {}'.format(beta)
    if not isinstance(samples_per_class, np.ndarray):
        if isinstance(samples_per_class, (list, tuple)):
            samples_per_class = np.array(samples_per_class)
        elif torch.is_tensor(samples_per_class):
            samples_per_class = samples_per_class.numpy()
        else:
            raise NotImplementedError(
                'Type of samples_per_class should be {}, {} or {} but got {}'.format(
                    (list, tuple), np.ndarray, torch.Tensor, type(samples_per_class)))
    assert isinstance(samples_per_class, np.ndarray) \
        and isinstance(beta, numbers.Number)

    balanced_matrix = (1 - beta) / (1 - np.power(beta, samples_per_class))
    return torch.Tensor(balanced_matrix) 

def normalize_adj(A, is_sym=True, exponent=0.5):
  """
    Normalize adjacency matrix

    is_sym=True: D^{-1/2} A D^{-1/2}
    is_sym=False: D^{-1} A
  """
  rowsum = np.array(A.sum(1))

  if is_sym:
    r_inv = np.power(rowsum, -exponent).flatten()
  else:
    r_inv = np.power(rowsum, -1.0).flatten()

  r_inv[np.isinf(r_inv)] = 0.

  if sp.isspmatrix(A):
    r_mat_inv = sp.diags(r_inv.squeeze())
  else:
    r_mat_inv = np.diag(r_inv)

  if is_sym:
    return r_mat_inv.dot(A).dot(r_mat_inv)
  else:
    return r_mat_inv.dot(A) 

def cost(params, Y, R, num_features):
    Y = np.matrix(Y)  # (1682, 943)
    R = np.matrix(R)  # (1682, 943)
    num_movies = Y.shape[0]
    num_users = Y.shape[1]
    
    # reshape the parameter array into parameter matrices
    X = np.matrix(np.reshape(params[:num_movies * num_features], (num_movies, num_features)))  # (1682, 10)
    Theta = np.matrix(np.reshape(params[num_movies * num_features:], (num_users, num_features)))  # (943, 10)
    
    # initializations
    J = 0
    
    # compute the cost
    error = np.multiply((X * Theta.T) - Y, R)  # (1682, 943)
    squared_error = np.power(error, 2)  # (1682, 943)
    J = (1. / 2) * np.sum(squared_error)
    
    return J 

def prepare_poly_data(*args, power):
    """
    args: keep feeding in X, Xval, or Xtest
        will return in the same order
    """
    def prepare(x):
        # expand feature
        df = poly_features(x, power=power)

        # normalization
        ndarr = normalize_feature(df).as_matrix()

        # add intercept term
        return np.insert(ndarr, 0, np.ones(ndarr.shape[0]), axis=1)

    return [prepare(x) for x in args] 

def spectrogram2wav(mag):
    '''# Generate wave file from spectrogram'''
    # transpose
    mag = mag.T

    # de-noramlize
    mag = (np.clip(mag, 0, 1) * hp.max_db) - hp.max_db + hp.ref_db

    # to amplitude
    mag = np.power(10.0, mag * 0.05)

    # wav reconstruction
    wav = griffin_lim(mag)

    # de-preemphasis
    wav = signal.lfilter([1], [1, -hp.preemphasis], wav)

    # trim
    wav, _ = librosa.effects.trim(wav)

    return wav.astype(np.float32) 

def test_return_l2_regularizer_weights(self):
    conv_hyperparams_text_proto = """
      regularizer {
        l2_regularizer {
          weight: 0.42
        }
      }
      initializer {
        truncated_normal_initializer {
        }
      }
    """
    conv_hyperparams_proto = hyperparams_pb2.Hyperparams()
    text_format.Merge(conv_hyperparams_text_proto, conv_hyperparams_proto)
    scope = hyperparams_builder.build(conv_hyperparams_proto, is_training=True)
    conv_scope_arguments = scope.values()[0]

    regularizer = conv_scope_arguments['weights_regularizer']
    weights = np.array([1., -1, 4., 2.])
    with self.test_session() as sess:
      result = sess.run(regularizer(tf.constant(weights)))
    self.assertAllClose(np.power(weights, 2).sum() / 2.0 * 0.42, result) 

def speech_aug_scheduler(step, s_r, s_i, s_f, peak_lr):
    # Starting from 0, ramp-up to set LR and  converge to 0.01*LR, w/ exp. decay
    final_lr_ratio = 0.01
    exp_decay_lambda = -np.log10(final_lr_ratio)/(s_f-s_i) # Approx. w/ 10-based
    cur_step = step+1

    if cur_step<s_r:
        # Ramp-up
        return peak_lr*float(cur_step)/s_r
    elif cur_step<s_i:
        # Hold
        return peak_lr
    elif cur_step<=s_f:
        # Decay
        return peak_lr*np.power(10,-exp_decay_lambda*(cur_step-s_i))
    else:
        # Converge
        return peak_lr*final_lr_ratio 

def zipf_distribution(nbr_symbols, alpha):
  """Helper function: Create a Zipf distribution.

  Args:
    nbr_symbols: number of symbols to use in the distribution.
    alpha: float, Zipf's Law Distribution parameter. Default = 1.5.
      Usually for modelling natural text distribution is in
      the range [1.1-1.6].

  Returns:
    distr_map: list of float, Zipf's distribution over nbr_symbols.

  """
  tmp = np.power(np.arange(1, nbr_symbols + 1), -alpha)
  zeta = np.r_[0.0, np.cumsum(tmp)]
  return [x / zeta[-1] for x in zeta] 

def test_return_l2_regularizer_weights(self):
    conv_hyperparams_text_proto = """
      regularizer {
        l2_regularizer {
          weight: 0.42
        }
      }
      initializer {
        truncated_normal_initializer {
        }
      }
    """
    conv_hyperparams_proto = hyperparams_pb2.Hyperparams()
    text_format.Merge(conv_hyperparams_text_proto, conv_hyperparams_proto)
    scope = hyperparams_builder.build(conv_hyperparams_proto, is_training=True)
    conv_scope_arguments = scope.values()[0]

    regularizer = conv_scope_arguments['weights_regularizer']
    weights = np.array([1., -1, 4., 2.])
    with self.test_session() as sess:
      result = sess.run(regularizer(tf.constant(weights)))
    self.assertAllClose(np.power(weights, 2).sum() / 2.0 * 0.42, result) 

def get_poly_cc(n, k, t):
    """ This is a helper function to get the coeffitient of coefficient for n-th
        order polynomial with k-th derivative at time t.
    """
    assert (n > 0 and k >= 0), "order and derivative must be positive."

    cc = np.ones(n)
    D  = np.linspace(0, n-1, n)

    for i in range(n):
        for j in range(k):
            cc[i] = cc[i] * D[i]
            D[i] = D[i] - 1
            if D[i] == -1:
                D[i] = 0

    for i, c in enumerate(cc):
        cc[i] = c * np.power(t, D[i])

    return cc

# Minimum Snap Trajectory 

def test_get_poly_cc_t(self):
        cc = trajGen3D.get_poly_cc(4, 0, 1)
        expected = [1, 1, 1, 1]
        np.testing.assert_array_equal(cc, expected)

        cc = trajGen3D.get_poly_cc(8, 0, 2)
        expected = [1, 2, 4, 8, 16, 32, 64, 128]
        np.testing.assert_array_equal(cc, expected)

        cc = trajGen3D.get_poly_cc(8, 1, 1)
        expected = np.linspace(0, 7, 8)
        np.testing.assert_array_equal(cc, expected)

        t = 2
        cc = trajGen3D.get_poly_cc(8, 1, t)
        expected = [0, 1, 2*t, 3*np.power(t,2), 4*np.power(t,3), 5*np.power(t,4), 6*np.power(t,5), 7*np.power(t,6)]
        np.testing.assert_array_equal(cc, expected) 

def impulseamp(self,tnow):
        """
        Apply impulsive wave to the system
        Args:
            tnow: float
                Current time in A.U.
        Returns:
            amp: float
                Amplitude of field at time
            ison: bool
                On whether field is on or off

        """
        amp = self.fieldamp*np.sin(self.fieldfreq*tnow)*\
        (1.0/math.sqrt(2.0*3.1415*self.tau*self.tau))*\
        np.exp(-1.0*np.power(tnow-self.tOn,2.0)/(2.0*self.tau*self.tau))
        ison = False
        if (np.abs(amp)>self.field_tol):
            ison = True
        return amp,ison 

def __init__(self, n_head, d_model, d_k, d_v, dropout=0.1):
        super(AverageHeadAttention, self).__init__()

        self.n_head = n_head
        self.d_k = d_k
        self.d_v = d_v

        self.w_qs = nn.Linear(d_model, n_head * d_k)
        self.w_ks = nn.Linear(d_model, n_head * d_k)
        self.w_vs = nn.Linear(d_model, n_head * d_v)
        nn.init.normal_(self.w_qs.weight, mean=0, std=np.sqrt(2.0 / (d_model + d_k)))
        nn.init.normal_(self.w_ks.weight, mean=0, std=np.sqrt(2.0 / (d_model + d_k)))
        nn.init.normal_(self.w_vs.weight, mean=0, std=np.sqrt(2.0 / (d_model + d_v)))

        self.attention = ScaledDotProductAttention(temperature=np.power(d_k, 0.5))
        self.layer_norm = nn.LayerNorm(d_model)

        self.fc = nn.Linear(d_v, d_model)
        nn.init.xavier_normal_(self.fc.weight)

        self.dropout = nn.Dropout(dropout) 

def __init__(self, n_head, d_model, d_k, d_v, dropout=0.1):
        super(MultiHeadAttention, self).__init__()

        self.n_head = n_head
        self.d_k = d_k
        self.d_v = d_v

        self.w_qs = nn.Linear(d_model, n_head * d_k)
        self.w_ks = nn.Linear(d_model, n_head * d_k)
        self.w_vs = nn.Linear(d_model, n_head * d_v)
        nn.init.normal_(self.w_qs.weight, mean=0, std=np.sqrt(2.0 / (d_model + d_k)))
        nn.init.normal_(self.w_ks.weight, mean=0, std=np.sqrt(2.0 / (d_model + d_k)))
        nn.init.normal_(self.w_vs.weight, mean=0, std=np.sqrt(2.0 / (d_model + d_v)))

        self.attention = ScaledDotProductAttention(temperature=np.power(d_k, 0.5))
        self.layer_norm = nn.LayerNorm(d_model)

        self.fc = nn.Linear(n_head * d_v, d_model)
        nn.init.xavier_normal_(self.fc.weight)

        self.dropout = nn.Dropout(dropout) 

def get_sinusoid_encoding_table(n_position, d_hid, padding_idx=None):
    ''' Sinusoid position encoding table '''

    def cal_angle(position, hid_idx):
        return position / np.power(10000, 2 * (hid_idx // 2) / d_hid)

    def get_posi_angle_vec(position):
        return [cal_angle(position, hid_j) for hid_j in range(d_hid)]

    sinusoid_table = np.array([get_posi_angle_vec(pos_i) for pos_i in range(n_position)])

    sinusoid_table[:, 0::2] = np.sin(sinusoid_table[:, 0::2])  # dim 2i
    sinusoid_table[:, 1::2] = np.cos(sinusoid_table[:, 1::2])  # dim 2i+1

    if padding_idx is not None:
        # zero vector for padding dimension
        sinusoid_table[padding_idx] = 0.

    return torch.FloatTensor(sinusoid_table) 

def scotts_factor(self):
        return power(self.n, -1./(self.d+4)) 

def imcv2_recolor(im, a = .1):
	t = [np.random.uniform()]
	t += [np.random.uniform()]
	t += [np.random.uniform()]
	t = np.array(t) * 2. - 1.

	# random amplify each channel
	im = im * (1 + t * a)
	mx = 255. * (1 + a)
	up = np.random.uniform() * 2 - 1
# 	im = np.power(im/mx, 1. + up * .5)
	im = cv2.pow(im/mx, 1. + up * .5)
	return np.array(im * 255., np.uint8) 

def spectrogram2wav(mag):
    '''# Generate wave file from linear magnitude spectrogram

    Args:
      mag: A numpy array of (T, 1+n_fft//2)

    Returns:
      wav: A 1-D numpy array.
    '''
    # transpose
    mag = mag.T

    # de-noramlize
    mag = (np.clip(mag, 0, 1) * hp.max_db) - hp.max_db + hp.ref_db

    # to amplitude
    mag = np.power(10.0, mag * 0.05)

    # wav reconstruction
    wav = griffin_lim(mag**hp.power)

    # de-preemphasis
    wav = signal.lfilter([1], [1, -hp.preemphasis], wav)

    # trim
    wav, _ = librosa.effects.trim(wav)

    return wav.astype(np.float32) 

def generate_regnet(self,
                        initial_width,
                        width_slope,
                        width_parameter,
                        depth,
                        divisor=8):
        """Generates per block width from RegNet parameters.

        Args:
            initial_width ([int]): Initial width of the backbone
            width_slope ([float]): Slope of the quantized linear function
            width_parameter ([int]): Parameter used to quantize the width.
            depth ([int]): Depth of the backbone.
            divisor (int, optional): The divisor of channels. Defaults to 8.

        Returns:
            list, int: return a list of widths of each stage and the number of
                stages
        """
        assert width_slope >= 0
        assert initial_width > 0
        assert width_parameter > 1
        assert initial_width % divisor == 0
        widths_cont = np.arange(depth) * width_slope + initial_width
        ks = np.round(
            np.log(widths_cont / initial_width) / np.log(width_parameter))
        widths = initial_width * np.power(width_parameter, ks)
        widths = np.round(np.divide(widths, divisor)) * divisor
        num_stages = len(np.unique(widths))
        widths, widths_cont = widths.astype(int).tolist(), widths_cont.tolist()
        return widths, num_stages 

def inv_spectrogram(spectrogram):
    S = _db_to_amp(_denormalize(spectrogram) + hparams.ref_level_db)  # Convert back to linear
    return _inv_preemphasis(_griffin_lim(S ** hparams.power))  # Reconstruct phase 

def _db_to_amp(x):
    return np.power(10.0, x * 0.05) 

def sign_log_func_inverse(x):
    return np.sign(x) * (np.power(10, np.abs(x)) - 1) 

def computeCost(X, y, theta):
    inner = np.power((X * theta.T - y), 2)
    return np.sum(inner) / (2 * len(X)) 

def cost0(params, Y, R, num_features):
    Y = np.matrix(Y)  # (1682, 943)
    R = np.matrix(R)  # (1682, 943)
    num_movies = Y.shape[0]
    num_users = Y.shape[1]
    
    # reshape the parameter array into parameter matrices
    X = np.matrix(np.reshape(params[:num_movies * num_features], (num_movies, num_features)))  # (1682, 10)
    Theta = np.matrix(np.reshape(params[num_movies * num_features:], (num_users, num_features)))  # (943, 10)
    
    # initializations
    J = 0
    X_grad = np.zeros(X.shape)  # (1682, 10)
    Theta_grad = np.zeros(Theta.shape)  # (943, 10)
    
    # compute the cost
    error = np.multiply((X * Theta.T) - Y, R)  # (1682, 943)
    squared_error = np.power(error, 2)  # (1682, 943)
    J = (1. / 2) * np.sum(squared_error)
    
    # calculate the gradients
    X_grad = error * Theta
    Theta_grad = error.T * X
    
    # unravel the gradient matrices into a single array
    grad = np.concatenate((np.ravel(X_grad), np.ravel(Theta_grad)))
    
    return J, grad 

def cost1(params, Y, R, num_features, learning_rate):
    Y = np.matrix(Y)  # (1682, 943)
    R = np.matrix(R)  # (1682, 943)
    num_movies = Y.shape[0]
    num_users = Y.shape[1]
    
    # reshape the parameter array into parameter matrices
    X = np.matrix(np.reshape(params[:num_movies * num_features], (num_movies, num_features)))  # (1682, 10)
    Theta = np.matrix(np.reshape(params[num_movies * num_features:], (num_users, num_features)))  # (943, 10)
    
    # initializations
    J = 0
    X_grad = np.zeros(X.shape)  # (1682, 10)
    Theta_grad = np.zeros(Theta.shape)  # (943, 10)
    
    # compute the cost
    error = np.multiply((X * Theta.T) - Y, R)  # (1682, 943)
    squared_error = np.power(error, 2)  # (1682, 943)
    J = (1. / 2) * np.sum(squared_error)
    
    # add the cost regularization
    J = J + ((learning_rate / 2) * np.sum(np.power(Theta, 2)))
    J = J + ((learning_rate / 2) * np.sum(np.power(X, 2)))
    
    # calculate the gradients with regularization
    X_grad = (error * Theta) + (learning_rate * X)
    Theta_grad = (error.T * X) + (learning_rate * Theta)
    
    # unravel the gradient matrices into a single array
    grad = np.concatenate((np.ravel(X_grad), np.ravel(Theta_grad)))
    
    return J, grad 

def costReg(theta, X, y, learningRate):
    theta = np.matrix(theta)
    X = np.matrix(X)
    y = np.matrix(y)
    first = np.multiply(-y, np.log(sigmoid(X * theta.T)))
    second = np.multiply((1 - y), np.log(1 - sigmoid(X * theta.T)))
    reg = (learningRate / (2 * len(X))) * np.sum(np.power(theta[:,1:theta.shape[1]], 2))
    return np.sum(first - second) / len(X) + reg 

def poly_features(x, power, as_ndarray=False):
    data = {'f{}'.format(i): np.power(x, i) for i in range(1, power + 1)}
    df = pd.DataFrame(data)

    return df.as_matrix() if as_ndarray else df 

def _tanh(x, deriv=False):
        """
        Hyperbolic tangent activation
        """
        if deriv:
            return 1.0 - np.power(np.tanh(x), 2)
        return np.tanh(x) 

def _tanhpos(x, deriv=False):
        """
        Positive hyperbolic tangent activation
        """
        if deriv:
            return (1.0 - np.power(np.tanh(x), 2)) / 2.0
        return (np.tanh(x) + 1.0) / 2.0 

def __init__(self, obj_file, material_file=None, load_materials=True,
               name_prefix='', name_suffix=''):
    if material_file is not None:
      logging.error('Ignoring material file input, reading them off obj file.')
    load_flags = self.get_pyassimp_load_options()
    scene = assimp.load(obj_file, processing=load_flags)
    filter_ind = self._filter_triangles(scene.meshes)
    self.meshes = [scene.meshes[i] for i in filter_ind]
    for m in self.meshes:
      m.name = name_prefix + m.name + name_suffix

    dir_name = os.path.dirname(obj_file)
    # Load materials
    materials = None
    if load_materials:
      materials = []
      for m in self.meshes:
        file_name = os.path.join(dir_name, m.material.properties[('file', 1)])
        assert(os.path.exists(file_name)), \
            'Texture file {:s} foes not exist.'.format(file_name)
        img_rgb = cv2.imread(file_name)[::-1,:,::-1]
        if img_rgb.shape[0] != img_rgb.shape[1]:
          logging.warn('Texture image not square.')
          sz = np.maximum(img_rgb.shape[0], img_rgb.shape[1])
          sz = int(np.power(2., np.ceil(np.log2(sz))))
          img_rgb = cv2.resize(img_rgb, (sz,sz), interpolation=cv2.INTER_LINEAR)
        else:
          sz = img_rgb.shape[0]
          sz_ = int(np.power(2., np.ceil(np.log2(sz))))
          if sz != sz_:
            logging.warn('Texture image not square of power of 2 size. ' +
                         'Changing size from %d to %d.', sz, sz_)
            sz = sz_
            img_rgb = cv2.resize(img_rgb, (sz,sz), interpolation=cv2.INTER_LINEAR)
        materials.append(img_rgb)
    self.scene = scene
    self.materials = materials