Python torch.sin() Examples

def embed(self, h, r, t):
        """Function to get the embedding value.

           Args:
               h (Tensor): Head entities ids.
               r (Tensor): Relation ids of the triple.
               t (Tensor): Tail entity ids of the triple.

            Returns:
                Tensors: Returns real and imaginary values of head, relation and tail embedding.
        """
        pi = 3.14159265358979323846
        h_e_r = self.ent_embeddings(h)
        h_e_i = self.ent_embeddings_imag(h)
        r_e_r = self.rel_embeddings(r)
        t_e_r = self.ent_embeddings(t)
        t_e_i = self.ent_embeddings_imag(t)
        r_e_r = r_e_r / (self.embedding_range / pi)
        r_e_i = torch.sin(r_e_r)
        r_e_r = torch.cos(r_e_r)
        return h_e_r, h_e_i, r_e_r, r_e_i, t_e_r, t_e_i 

def positional_encodings_like(x, t=None):
    if t is None:
        positions = torch.arange(0., x.size(1))
        if x.is_cuda:
            positions = positions.cuda(x.get_device())
    else:
        positions = t
    encodings = torch.zeros(*x.size()[1:])
    if x.is_cuda:
        encodings = encodings.cuda(x.get_device())
    for channel in range(x.size(-1)):
        if channel % 2 == 0:
            encodings[:, channel] = torch.sin(
                positions / 10000 ** (channel / x.size(2)))
        else:
            encodings[:, channel] = torch.cos(
                positions / 10000 ** ((channel - 1) / x.size(2)))
    return Variable(encodings)


# torch.matmul can't do (4, 3, 2) @ (4, 2) -> (4, 3) 

def get_embedding(num_embeddings, embedding_dim, padding_idx=None):
        """Build sinusoidal embeddings.

        This matches the implementation in tensor2tensor, but differs slightly
        from the description in Section 3.5 of "Attention Is All You Need".
        """
        half_dim = embedding_dim // 2
        emb = math.log(10000) / (half_dim - 1)
        emb = torch.exp(torch.arange(half_dim, dtype=torch.float) * -emb)
        emb = torch.arange(num_embeddings, dtype=torch.float).unsqueeze(1) * emb.unsqueeze(0)
        emb = torch.cat([torch.sin(emb), torch.cos(emb)], dim=1).view(num_embeddings, -1)
        if embedding_dim % 2 == 1:
            # zero pad
            emb = torch.cat([emb, torch.zeros(num_embeddings, 1)], dim=1)
        if padding_idx is not None:
            emb[padding_idx, :] = 0
        return emb 

def _test_istft_of_sine(self, amplitude, L, n):
        # stft of amplitude*sin(2*pi/L*n*x) with the hop length and window size equaling L
        x = torch.arange(2 * L + 1, dtype=torch.get_default_dtype())
        sound = amplitude * torch.sin(2 * math.pi / L * x * n)
        # stft = torch.stft(sound, L, hop_length=L, win_length=L,
        #                   window=torch.ones(L), center=False, normalized=False)
        stft = torch.zeros((L // 2 + 1, 2, 2))
        stft_largest_val = (amplitude * L) / 2.0
        if n < stft.size(0):
            stft[n, :, 1] = -stft_largest_val

        if 0 <= L - n < stft.size(0):
            # symmetric about L // 2
            stft[L - n, :, 1] = stft_largest_val

        estimate = torchaudio.functional.istft(stft, L, hop_length=L, win_length=L,
                                               window=torch.ones(L), center=False, normalized=False)
        # There is a larger error due to the scaling of amplitude
        _compare_estimate(sound, estimate, atol=1e-3) 

def _create_data_set(self):
        # used to generate the dataset to test on. this is not used in testing (offline procedure)
        test_filepath = common_utils.get_asset_path('kaldi_file.wav')
        sr = 16000
        x = torch.arange(0, 20).float()
        # between [-6,6]
        y = torch.cos(2 * math.pi * x) + 3 * torch.sin(math.pi * x) + 2 * torch.cos(x)
        # between [-2^30, 2^30]
        y = (y / 6 * (1 << 30)).long()
        # clear the last 16 bits because they aren't used anyways
        y = ((y >> 16) << 16).float()
        torchaudio.save(test_filepath, y, sr)
        sound, sample_rate = torchaudio.load(test_filepath, normalization=False)
        print(y >> 16)
        self.assertTrue(sample_rate == sr)
        torch.testing.assert_allclose(y, sound) 

def _fade_out(self, waveform_length: int) -> Tensor:
        fade = torch.linspace(0, 1, self.fade_out_len)
        ones = torch.ones(waveform_length - self.fade_out_len)

        if self.fade_shape == "linear":
            fade = - fade + 1

        if self.fade_shape == "exponential":
            fade = torch.pow(2, - fade) * (1 - fade)

        if self.fade_shape == "logarithmic":
            fade = torch.log10(1.1 - fade) + 1

        if self.fade_shape == "quarter_sine":
            fade = torch.sin(fade * math.pi / 2 + math.pi / 2)

        if self.fade_shape == "half_sine":
            fade = torch.sin(fade * math.pi + math.pi / 2) / 2 + 0.5

        return torch.cat((ones, fade)).clamp_(0, 1) 

def _fade_in(self, waveform_length: int) -> Tensor:
        fade = torch.linspace(0, 1, self.fade_in_len)
        ones = torch.ones(waveform_length - self.fade_in_len)

        if self.fade_shape == "linear":
            fade = fade

        if self.fade_shape == "exponential":
            fade = torch.pow(2, (fade - 1)) * fade

        if self.fade_shape == "logarithmic":
            fade = torch.log10(.1 + fade) + 1

        if self.fade_shape == "quarter_sine":
            fade = torch.sin(fade * math.pi / 2)

        if self.fade_shape == "half_sine":
            fade = torch.sin(fade * math.pi - math.pi / 2) / 2 + 0.5

        return torch.cat((fade, ones)).clamp_(0, 1) 

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 __init__(self, height, width, lr = 1, aux_loss = False):
        super(Depth3DGridGen, self).__init__()
        self.height, self.width = height, width
        self.aux_loss = aux_loss
        self.lr = lr

        self.grid = np.zeros( [self.height, self.width, 3], dtype=np.float32)
        self.grid[:,:,0] = np.expand_dims(np.repeat(np.expand_dims(np.arange(-1, 1, 2.0/self.height), 0), repeats = self.width, axis = 0).T, 0)
        self.grid[:,:,1] = np.expand_dims(np.repeat(np.expand_dims(np.arange(-1, 1, 2.0/self.width), 0), repeats = self.height, axis = 0), 0)
        self.grid[:,:,2] = np.ones([self.height, width])
        self.grid = torch.from_numpy(self.grid.astype(np.float32))

        self.theta = self.grid[:,:,0] * np.pi/2 + np.pi/2
        self.phi = self.grid[:,:,1] * np.pi

        self.x = torch.sin(self.theta) * torch.cos(self.phi)
        self.y = torch.sin(self.theta) * torch.sin(self.phi)
        self.z = torch.cos(self.theta)

        self.grid3d = torch.from_numpy(np.zeros( [self.height, self.width, 4], dtype=np.float32))

        self.grid3d[:,:,0] = self.x
        self.grid3d[:,:,1] = self.y
        self.grid3d[:,:,2] = self.z
        self.grid3d[:,:,3] = self.grid[:,:,2] 

def __init__(self, height, width, lr = 1, aux_loss = False):
        super(DenseAffine3DGridGen_rotate, self).__init__()
        self.height, self.width = height, width
        self.aux_loss = aux_loss
        self.lr = lr

        self.grid = np.zeros( [self.height, self.width, 3], dtype=np.float32)
        self.grid[:,:,0] = np.expand_dims(np.repeat(np.expand_dims(np.arange(-1, 1, 2.0/self.height), 0), repeats = self.width, axis = 0).T, 0)
        self.grid[:,:,1] = np.expand_dims(np.repeat(np.expand_dims(np.arange(-1, 1, 2.0/self.width), 0), repeats = self.height, axis = 0), 0)
        self.grid[:,:,2] = np.ones([self.height, width])
        self.grid = torch.from_numpy(self.grid.astype(np.float32))

        self.theta = self.grid[:,:,0] * np.pi/2 + np.pi/2
        self.phi = self.grid[:,:,1] * np.pi

        self.x = torch.sin(self.theta) * torch.cos(self.phi)
        self.y = torch.sin(self.theta) * torch.sin(self.phi)
        self.z = torch.cos(self.theta)

        self.grid3d = torch.from_numpy(np.zeros( [self.height, self.width, 4], dtype=np.float32))

        self.grid3d[:,:,0] = self.x
        self.grid3d[:,:,1] = self.y
        self.grid3d[:,:,2] = self.z
        self.grid3d[:,:,3] = self.grid[:,:,2] 

def __init__(self, height, width, lr = 1, aux_loss = False):
        super(DenseAffine3DGridGen, self).__init__()
        self.height, self.width = height, width
        self.aux_loss = aux_loss
        self.lr = lr

        self.grid = np.zeros( [self.height, self.width, 3], dtype=np.float32)
        self.grid[:,:,0] = np.expand_dims(np.repeat(np.expand_dims(np.arange(-1, 1, 2.0/self.height), 0), repeats = self.width, axis = 0).T, 0)
        self.grid[:,:,1] = np.expand_dims(np.repeat(np.expand_dims(np.arange(-1, 1, 2.0/self.width), 0), repeats = self.height, axis = 0), 0)
        self.grid[:,:,2] = np.ones([self.height, width])
        self.grid = torch.from_numpy(self.grid.astype(np.float32))

        self.theta = self.grid[:,:,0] * np.pi/2 + np.pi/2
        self.phi = self.grid[:,:,1] * np.pi

        self.x = torch.sin(self.theta) * torch.cos(self.phi)
        self.y = torch.sin(self.theta) * torch.sin(self.phi)
        self.z = torch.cos(self.theta)

        self.grid3d = torch.from_numpy(np.zeros( [self.height, self.width, 4], dtype=np.float32))

        self.grid3d[:,:,0] = self.x
        self.grid3d[:,:,1] = self.y
        self.grid3d[:,:,2] = self.z
        self.grid3d[:,:,3] = self.grid[:,:,2] 

def get_embedding(
        num_embeddings: int, embedding_dim: int, padding_idx: Optional[int] = None
    ):
        """Build sinusoidal embeddings.

        This matches the implementation in tensor2tensor, but differs slightly
        from the description in Section 3.5 of "Attention Is All You Need".
        """
        half_dim = embedding_dim // 2
        emb = math.log(10000) / (half_dim - 1)
        emb = torch.exp(torch.arange(half_dim, dtype=torch.float) * -emb)
        emb = torch.arange(num_embeddings, dtype=torch.float).unsqueeze(
            1
        ) * emb.unsqueeze(0)
        emb = torch.cat([torch.sin(emb), torch.cos(emb)], dim=1).view(
            num_embeddings, -1
        )
        if embedding_dim % 2 == 1:
            # zero pad
            emb = torch.cat([emb, torch.zeros(num_embeddings, 1)], dim=1)
        if padding_idx is not None:
            emb[padding_idx, :] = 0
        return emb 

def sinc(band,t_right, cuda=False):
    y_right= torch.sin(2*math.pi*band*t_right)/(2*math.pi*band*t_right)
    y_left= flip(y_right,0)

    ones = torch.ones(1)
    if cuda:
        ones = ones.to('cuda')
    y=torch.cat([y_left, ones, y_right])

    return y
    
    
# Modified from https://github.com/mravanelli/SincNet 

def sinc(self, x):
        # Numerically stable definition
        x_left=x[:,0:int((x.shape[1]-1)/2)]
        y_left=torch.sin(x_left) / x_left
        y_right= torch.flip(y_left,dims=[1])
        
        sinc=torch.cat([y_left,torch.ones([x.shape[0],1]).to(x.device),y_right],dim=1)
        

        return sinc 

def forward(self, waveforms):
        """
        Parameters
        ----------
        waveforms : `torch.Tensor` (batch_size, 1, n_samples)
            Batch of waveforms.
        Returns
        -------
        features : `torch.Tensor` (batch_size, out_channels, n_samples_out)
            Batch of sinc filters activations.
        """

        self.n_ = self.n_.to(waveforms.device)

        self.window_ = self.window_.to(waveforms.device)

        low = self.min_low_hz  + torch.abs(self.low_hz_)
        
        high = torch.clamp(low + self.min_band_hz + torch.abs(self.band_hz_),self.min_low_hz,self.sample_rate/2)
        band=(high-low)[:,0]
        
        f_times_t_low = torch.matmul(low, self.n_)
        f_times_t_high = torch.matmul(high, self.n_)

        band_pass_left=((torch.sin(f_times_t_high)-torch.sin(f_times_t_low))/(self.n_/2))*self.window_ # Equivalent of Eq.4 of the reference paper (SPEAKER RECOGNITION FROM RAW WAVEFORM WITH SINCNET). I just have expanded the sinc and simplified the terms. This way I avoid several useless computations. 
        band_pass_center = 2*band.view(-1,1)
        band_pass_right= torch.flip(band_pass_left,dims=[1])
        
        
        band_pass=torch.cat([band_pass_left,band_pass_center,band_pass_right],dim=1)

        
        band_pass = band_pass / (2*band[:,None])
        

        self.filters = (band_pass).view(
            self.out_channels, 1, self.kernel_size)

        return F.conv1d(waveforms, self.filters, stride=self.stride,
                        padding=self.padding, dilation=self.dilation,
                         bias=None, groups=1) 

def sinc(self, x):
        # Numerically stable definition
        x_left=x[:,0:int((x.shape[1]-1)/2)]
        y_left=torch.sin(x_left) / x_left
        y_right= torch.flip(y_left,dims=[1])
        
        sinc=torch.cat([y_left,torch.ones([x.shape[0],1]).to(x.device),y_right],dim=1)
        

        return sinc 

def __init__(self, d_model, dropout, max_len=5000):
        super(PositionalEncoding, self).__init__()
        self.dropout = nn.Dropout(p=dropout)

        # Compute the positional encodings once in log space.
        pe = torch.zeros(max_len, d_model)
        position = torch.arange(0, max_len).unsqueeze(1)
        div_term = torch.exp(torch.arange(0, d_model, 2) *
                             -(math.log(10000.0) / d_model))
        pe[:, 0::2] = torch.sin(position * div_term)
        pe[:, 1::2] = torch.cos(position * div_term)
        pe = pe.unsqueeze(0)
        self.register_buffer('pe', pe) 

def __init__(self, dropout, dim, max_len=5000):
        pe = torch.zeros(max_len, dim)
        position = torch.arange(0, max_len).unsqueeze(1)
        div_term = torch.exp(torch.arange(0, dim, 2) *
                             -(math.log(10000.0) / dim))
        pe[:, 0::2] = torch.sin(position * div_term)
        pe[:, 1::2] = torch.cos(position * div_term)
        pe = pe.unsqueeze(1)
        super(PositionalEncoding, self).__init__()
        self.register_buffer('pe', pe)
        self.dropout = nn.Dropout(p=dropout)
        self.dim = dim 

def expmap(self, x: torch.Tensor, u: torch.Tensor) -> torch.Tensor:
        norm_u = u.norm(dim=-1, keepdim=True)
        exp = x * torch.cos(norm_u) + u * torch.sin(norm_u) / norm_u
        retr = self.projx(x + u)
        cond = norm_u > EPS[norm_u.dtype]
        return torch.where(cond, exp, retr) 

def __init__(self, dim_model, dropout, max_len=5000):
        super(PositionalEncoding, self).__init__()
        self.dropout = nn.Dropout(p=dropout)
        # Compute the positional encodings once in log space.
        pe = th.zeros(max_len, dim_model, dtype=th.float)
        position = th.arange(0, max_len, dtype=th.float).unsqueeze(1)
        div_term = th.exp(th.arange(0, dim_model, 2, dtype=th.float) *
                             -(np.log(10000.0) / dim_model))
        pe[:, 0::2] = th.sin(position * div_term)
        pe[:, 1::2] = th.cos(position * div_term)
        pe = pe.unsqueeze(0)
        self.register_buffer('pe', pe)  # Not a parameter but should be in state_dict 

def _create_data(self):
        n = torch.sqrt(torch.rand(self.num_points // 2)) * 540 * (2 * np.pi) / 360
        d1x = -torch.cos(n) * n + torch.rand(self.num_points // 2) * 0.5
        d1y = torch.sin(n) * n + torch.rand(self.num_points // 2) * 0.5
        x = torch.cat([torch.stack([d1x, d1y]).t(), torch.stack([-d1x, -d1y]).t()])
        self.data = x / 3 + torch.randn_like(x) * 0.1 

def create_circle(num_per_circle, std=0.1):
        u = torch.rand(num_per_circle)
        x1 = torch.cos(2 * np.pi * u)
        x2 = torch.sin(2 * np.pi * u)
        data = 2 * torch.stack((x1, x2)).t()
        data += std * torch.randn(data.shape)
        return data 

def _create_data(self):
        x1 = torch.randn(self.num_points)
        x2_mean = torch.sin(5 * x1)
        x2_var = torch.exp(-2 * torch.ones(x1.shape))
        x2 = x2_mean + x2_var ** 0.5 * torch.randn(self.num_points)
        self.data = torch.stack((x1, x2)).t() 

def RotBox2Polys_torch(dboxes):
    """

    :param dboxes:
    :return:
    """
    cs = torch.cos(dboxes[:, 4])
    ss = torch.sin(dboxes[:, 4])
    w = dboxes[:, 2] - 1
    h = dboxes[:, 3] - 1

    x_ctr = dboxes[:, 0]
    y_ctr = dboxes[:, 1]
    x1 = x_ctr + cs * (w / 2.0) - ss * (-h / 2.0)
    x2 = x_ctr + cs * (w / 2.0) - ss * (h / 2.0)
    x3 = x_ctr + cs * (-w / 2.0) - ss * (h / 2.0)
    x4 = x_ctr + cs * (-w / 2.0) - ss * (-h / 2.0)

    y1 = y_ctr + ss * (w / 2.0) + cs * (-h / 2.0)
    y2 = y_ctr + ss * (w / 2.0) + cs * (h / 2.0)
    y3 = y_ctr + ss * (-w / 2.0) + cs * (h / 2.0)
    y4 = y_ctr + ss * (-w / 2.0) + cs * (-h / 2.0)

    polys = torch.cat((x1.unsqueeze(1),
                       y1.unsqueeze(1),
                       x2.unsqueeze(1),
                       y2.unsqueeze(1),
                       x3.unsqueeze(1),
                       y3.unsqueeze(1),
                       x4.unsqueeze(1),
                       y4.unsqueeze(1)), 1)

    return polys 

def RotBox2Polys(dboxes):
    """
    :param dboxes: (x_ctr, y_ctr, w, h, angle)
        (numboxes, 5)
    :return: quadranlges:
        (numboxes, 8)
    """
    cs = np.cos(dboxes[:, 4])
    ss = np.sin(dboxes[:, 4])
    w = dboxes[:, 2] - 1
    h = dboxes[:, 3] - 1

    ## change the order to be the initial definition
    x_ctr = dboxes[:, 0]
    y_ctr = dboxes[:, 1]
    x1 = x_ctr + cs * (w / 2.0) - ss * (-h / 2.0)
    x2 = x_ctr + cs * (w / 2.0) - ss * (h / 2.0)
    x3 = x_ctr + cs * (-w / 2.0) - ss * (h / 2.0)
    x4 = x_ctr + cs * (-w / 2.0) - ss * (-h / 2.0)

    y1 = y_ctr + ss * (w / 2.0) + cs * (-h / 2.0)
    y2 = y_ctr + ss * (w / 2.0) + cs * (h / 2.0)
    y3 = y_ctr + ss * (-w / 2.0) + cs * (h / 2.0)
    y4 = y_ctr + ss * (-w / 2.0) + cs * (-h / 2.0)

    x1 = x1[:, np.newaxis]
    y1 = y1[:, np.newaxis]
    x2 = x2[:, np.newaxis]
    y2 = y2[:, np.newaxis]
    x3 = x3[:, np.newaxis]
    y3 = y3[:, np.newaxis]
    x4 = x4[:, np.newaxis]
    y4 = y4[:, np.newaxis]

    polys = np.concatenate((x1, y1, x2, y2, x3, y3, x4, y4), axis=1)
    return polys 

def dbbox2delta_v3(proposals, gt, means = [0, 0, 0, 0, 0], stds=[1, 1, 1, 1, 1]):
    """
    This version removes the module operation
    :param proposals: (x_ctr, y_ctr, w, h, angle)
            shape (n, 5)
    :param gt: (x_ctr, y_ctr, w, h, angle)
    :param means:
    :param stds:
    :return: encoded targets: shape (n, 5)
    """
    proposals = proposals.float()
    gt = gt.float()
    gt_widths = gt[..., 2]
    gt_heights = gt[..., 3]
    gt_angle = gt[..., 4]

    proposals_widths = proposals[..., 2]
    proposals_heights = proposals[..., 3]
    proposals_angle = proposals[..., 4]

    coord = gt[..., 0:2] - proposals[..., 0:2]
    dx = (torch.cos(proposals[..., 4]) * coord[..., 0] +
          torch.sin(proposals[..., 4]) * coord[..., 1]) / proposals_widths
    dy = (-torch.sin(proposals[..., 4]) * coord[..., 0] +
          torch.cos(proposals[..., 4]) * coord[..., 1]) / proposals_heights
    dw = torch.log(gt_widths / proposals_widths)
    dh = torch.log(gt_heights / proposals_heights)
    # import pdb
    # print('in dbbox2delta v3')
    # pdb.set_trace()
    # dangle = (gt_angle - proposals_angle) % (2 * math.pi) / (2 * math.pi)
    # TODO: debug for it, proposals_angle are -1.5708, gt_angle should close to -1.57, actully they close to 5.0153
    dangle = gt_angle - proposals_angle
    deltas = torch.stack((dx, dy, dw, dh, dangle), -1)

    means = deltas.new_tensor(means).unsqueeze(0)
    stds = deltas.new_tensor(stds).unsqueeze(0)
    deltas = deltas.sub_(means).div_(stds)

    return deltas 

def dbbox2delta(proposals, gt, means = [0, 0, 0, 0, 0], stds=[1, 1, 1, 1, 1]):
    """
    :param proposals: (x_ctr, y_ctr, w, h, angle)
            shape (n, 5)
    :param gt: (x_ctr, y_ctr, w, h, angle)
    :param means:
    :param stds:
    :return: encoded targets: shape (n, 5)
    """
    proposals = proposals.float()
    gt = gt.float()
    gt_widths = gt[..., 2]
    gt_heights = gt[..., 3]
    gt_angle = gt[..., 4]

    proposals_widths = proposals[..., 2]
    proposals_heights = proposals[..., 3]
    proposals_angle = proposals[..., 4]

    coord = gt[..., 0:2] - proposals[..., 0:2]
    dx = (torch.cos(proposals[..., 4]) * coord[..., 0] +
          torch.sin(proposals[..., 4]) * coord[..., 1]) / proposals_widths
    dy = (-torch.sin(proposals[..., 4]) * coord[..., 0] +
          torch.cos(proposals[..., 4]) * coord[..., 1]) / proposals_heights
    dw = torch.log(gt_widths / proposals_widths)
    dh = torch.log(gt_heights / proposals_heights)
    dangle = (gt_angle - proposals_angle) % (2 * math.pi) / (2 * math.pi)
    deltas = torch.stack((dx, dy, dw, dh, dangle), -1)

    means = deltas.new_tensor(means).unsqueeze(0)
    stds = deltas.new_tensor(stds).unsqueeze(0)
    deltas = deltas.sub_(means).div_(stds)

    # TODO: expand bbox regression
    return deltas 

def get_timecode(dim,t,tframe,size=None,maxlen=10000,collapse=False):
    if size is None: size=tframe
    n=t.float().view(-1,1,1)+torch.linspace(0,tframe-1,steps=size).view(1,1,-1).to(t.device)
    f=(10**(torch.arange(1,dim+1).float()/dim)).view(1,-1,1).to(t.device)
    tc=torch.sin(TWOPI*f*n/maxlen)
    if collapse:
        tc=tc.mean(1).unsqueeze(1)
    return tc 

def __init__(self, d_model, dropout, max_len=5000):
        super(PositionalEncoding, self).__init__()
        self.dropout = nn.Dropout(p=dropout)

        # Compute the positional encodings once in log space.
        pe = torch.zeros(max_len, d_model)
        position = torch.arange(0, max_len).unsqueeze(1)
        div_term = torch.exp(torch.arange(0, d_model, 2) *
                             -(math.log(10000.0) / d_model))
        pe[:, 0::2] = torch.sin(position * div_term)
        pe[:, 1::2] = torch.cos(position * div_term)
        pe = pe.unsqueeze(0)
        self.register_buffer('pe', pe) 

def rotz_batch_pytorch(t):
    """Rotation about the y-axis.
    t: (x1,x2,...xn)
    return: (x1,x2,...,xn,3,3)
    """
    input_shape = t.shape
    output = torch.zeros(tuple(list(input_shape)+[3,3])).cuda()
    c = torch.cos(t)
    s = torch.sin(t)
    output[...,0,0] = c
    output[...,0,1] = -s
    output[...,1,0] = s
    output[...,1,1] = c
    output[...,2,2] = 1
    return output