Python torch.pow() Examples

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 pairwise_distance(features, query=None, gallery=None, metric=None):
    if query is None and gallery is None:
        n = len(features)
        x = torch.cat(list(features.values()))
        x = x.view(n, -1)
        if metric is not None:
            x = metric.transform(x)
        dist = torch.pow(x, 2).sum(dim=1, keepdim=True) * 2
        dist = dist.expand(n, n) - 2 * torch.mm(x, x.t())
        return dist

    x = torch.cat([features["".join(f)].unsqueeze(0) for f, _, _, _ in query], 0)
    y = torch.cat([features["".join(f)].unsqueeze(0) for f, _, _, _ in gallery], 0)
    m, n = x.size(0), y.size(0)
    x = x.view(m, -1)
    y = y.view(n, -1)
    if metric is not None:
        x = metric.transform(x)
        y = metric.transform(y)
    dist = torch.pow(x, 2).sum(dim=1, keepdim=True).expand(m, n) + \
           torch.pow(y, 2).sum(dim=1, keepdim=True).expand(n, m).t()
    dist.addmm_(1, -2, x, y.t())
    return dist 

def maskedNLL(y_pred, y_gt, mask):
    acc = torch.zeros_like(mask)
    muX = y_pred[:,:,0]
    muY = y_pred[:,:,1]
    sigX = y_pred[:,:,2]
    sigY = y_pred[:,:,3]
    rho = y_pred[:,:,4]
    ohr = torch.pow(1-torch.pow(rho,2),-0.5)
    x = y_gt[:,:, 0]
    y = y_gt[:,:, 1]
    # If we represent likelihood in feet^(-1):
    out = 0.5*torch.pow(ohr, 2)*(torch.pow(sigX, 2)*torch.pow(x-muX, 2) + torch.pow(sigY, 2)*torch.pow(y-muY, 2) - 2*rho*torch.pow(sigX, 1)*torch.pow(sigY, 1)*(x-muX)*(y-muY)) - torch.log(sigX*sigY*ohr) + 1.8379
    # If we represent likelihood in m^(-1):
    # out = 0.5 * torch.pow(ohr, 2) * (torch.pow(sigX, 2) * torch.pow(x - muX, 2) + torch.pow(sigY, 2) * torch.pow(y - muY, 2) - 2 * rho * torch.pow(sigX, 1) * torch.pow(sigY, 1) * (x - muX) * (y - muY)) - torch.log(sigX * sigY * ohr) + 1.8379 - 0.5160
    acc[:,:,0] = out
    acc[:,:,1] = out
    acc = acc*mask
    lossVal = torch.sum(acc)/torch.sum(mask)
    return lossVal

## NLL for sequence, outputs sequence of NLL values for each time-step, uses mask for variable output lengths, used for evaluation 

def focal_loss(self, x, y):
        '''Focal loss.
        Args:
          x: (tensor) sized [N,D].
          y: (tensor) sized [N,].
        Return:
          (tensor) focal loss.
        '''
        alpha = 0.25
        gamma = 2

        t = F.one_hot(y.data, 1+self.num_classes)  # [N,21]
        t = t[:,1:]  # exclude background
        t = Variable(t)
        
        p = x.sigmoid()
        pt = p*t + (1-p)*(1-t)         # pt = p if t > 0 else 1-p
        w = alpha*t + (1-alpha)*(1-t)  # w = alpha if t > 0 else 1-alpha
        w = w * (1-pt).pow(gamma)
        return F.binary_cross_entropy_with_logits(x, t, w, reduction='sum') 

def focal_loss(self, inputs, targets):
        '''Focal loss.
        mean of losses: L(x,c,l,g) = (Lconf(x, c) + αLloc(x,l,g)) / N
        '''
        N = inputs.size(0)
        C = inputs.size(1)
        P = F.softmax(inputs)
        
        class_mask = inputs.data.new(N, C).fill_(0)
        class_mask = Variable(class_mask)
        ids = targets.view(-1, 1)
        class_mask.scatter_(1, ids.data, 1.)

        if inputs.is_cuda and not self.alpha.is_cuda:
            self.alpha = self.alpha.cuda()
        alpha = self.alpha[ids.data.view(-1)]
        probs = (P*class_mask).sum(1).view(-1,1)
        log_p = probs.log()

        batch_loss = -alpha*(torch.pow((1-probs), self.gamma))*log_p 

        loss = batch_loss.mean()
        return loss 

def smooth_l1_loss_LW(bbox_pred, bbox_targets, bbox_inside_weights, bbox_outside_weights, beta=1.0):
    """
    SmoothL1(x) = 0.5 * x^2 / beta      if |x| < beta
                  |x| - 0.5 * beta      otherwise.
    1 / N * sum_i alpha_out[i] * SmoothL1(alpha_in[i] * (y_hat[i] - y[i])).
    N is the number of batch elements in the input predictions
    """
    box_diff = bbox_pred - bbox_targets
    in_box_diff = bbox_inside_weights * box_diff
    abs_in_box_diff = torch.abs(in_box_diff)
    smoothL1_sign = (abs_in_box_diff < beta).detach().float()
    in_loss_box = smoothL1_sign * 0.5 * torch.pow(in_box_diff, 2) / beta + \
                  (1 - smoothL1_sign) * (abs_in_box_diff - (0.5 * beta))
    out_loss_box = bbox_outside_weights * in_loss_box
    loss_box = out_loss_box
    N = loss_box.size(0)  # batch size
    loss_box = loss_box.view(-1).sum(0) / N
    return loss_box 

def DB_to_amplitude(
        x: Tensor,
        ref: float,
        power: float
) -> Tensor:
    r"""Turn a tensor from the decibel scale to the power/amplitude scale.

    Args:
        x (Tensor): Input tensor before being converted to power/amplitude scale.
        ref (float): Reference which the output will be scaled by.
        power (float): If power equals 1, will compute DB to power. If 0.5, will compute DB to amplitude.

    Returns:
        Tensor: Output tensor in power/amplitude scale.
    """
    return ref * torch.pow(torch.pow(10.0, 0.1 * x), power) 

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 forward(self, inputs, labels):
        cos_th = F.linear(inputs, F.normalize(self.weight))
        cos_th = cos_th.clamp(-1, 1)
        sin_th = torch.sqrt(1.0 - torch.pow(cos_th, 2))
        cos_th_m = cos_th * self.cos_m - sin_th * self.sin_m
        cos_th_m = torch.where(cos_th > self.th, cos_th_m, cos_th - self.mm)

        cond_v = cos_th - self.th
        cond = cond_v <= 0
        cos_th_m[cond] = (cos_th - self.mm)[cond]

        if labels.dim() == 1:
            labels = labels.unsqueeze(-1)
        onehot = torch.zeros(cos_th.size()).cuda()
        onehot.scatter_(1, labels, 1)
        outputs = onehot * cos_th_m + (1.0 - onehot) * cos_th
        outputs = outputs * self.s
        return outputs 

def _smooth_l1_loss(bbox_pred, bbox_targets, bbox_inside_weights, bbox_outside_weights, sigma=1.0, dim=[1]):

    sigma_2 = sigma ** 2
    box_diff = bbox_pred - bbox_targets
    in_box_diff = bbox_inside_weights * box_diff
    abs_in_box_diff = torch.abs(in_box_diff)
    smoothL1_sign = (abs_in_box_diff < 1. / sigma_2).detach().float()
    in_loss_box = torch.pow(in_box_diff, 2) * (sigma_2 / 2.) * smoothL1_sign \
                  + (abs_in_box_diff - (0.5 / sigma_2)) * (1. - smoothL1_sign)
    out_loss_box = bbox_outside_weights * in_loss_box
    loss_box = out_loss_box

    s = loss_box.size(0)
    loss_box = loss_box.view(s, -1).sum(1).mean()
    # for i in sorted(dim, reverse=True):
    #   loss_box = loss_box.sum(i)
    # loss_box = loss_box.mean()
    return loss_box 

def attention_image_summary(name, attn, step=0, writer=None):
    """Compute color image summary.
    Args:
    attn: a Tensor with shape [batch, num_heads, query_length, memory_length]
    image_shapes: optional tuple of integer scalars.
      If the query positions and memory positions represent the
      pixels of flattened images, then pass in their dimensions:
        (query_rows, query_cols, memory_rows, memory_cols).
      If the query positions and memory positions represent the
      pixels x channels of flattened images, then pass in their dimensions:
        (query_rows, query_cols, query_channels,
         memory_rows, memory_cols, memory_channels).
    """
    num_heads = attn.size(1)
    # [batch, query_length, memory_length, num_heads]
    image = attn.permute(0, 2, 3, 1)
    image = torch.pow(image, 0.2)  # for high-dynamic-range
    # Each head will correspond to one of RGB.
    # pad the heads to be a multiple of 3
    image = F.pad(image, [0,  -num_heads % 3, 0, 0, 0, 0, 0, 0,])
    image = split_last_dimension(image, 3)
    image = image.max(dim=4).values
    grid_image = torchvision.utils.make_grid(image.permute(0, 3, 1, 2))
    writer.add_image(name, grid_image, global_step=step, dataformats='CHW') 

def _focal_loss(preds, gt):
    pos_inds = gt.eq(1)
    neg_inds = gt.lt(1)

    neg_weights = torch.pow(1 - gt[neg_inds], 4)

    loss = 0
    for pred in preds:
        pos_pred = pred[pos_inds]
        neg_pred = pred[neg_inds]

        pos_loss = torch.log(pos_pred) * torch.pow(1 - pos_pred, 2)
        neg_loss = torch.log(1 - neg_pred) * torch.pow(neg_pred, 2) * neg_weights

        num_pos  = pos_inds.float().sum()
        pos_loss = pos_loss.sum()
        neg_loss = neg_loss.sum()

        if pos_pred.nelement() == 0:
            loss = loss - neg_loss
        else:
            loss = loss - (pos_loss + neg_loss) / num_pos
    return loss

# 扫视的损失函数 

def __init__(self, field_size, conv_kernel_width, conv_filters, device='cpu'):
        super(ConvLayer, self).__init__()
        self.device = device
        module_list = []
        n = int(field_size)
        l = len(conv_filters)
        filed_shape = n
        for i in range(1, l + 1):
            if i == 1:
                in_channels = 1
            else:
                in_channels = conv_filters[i - 2]
            out_channels = conv_filters[i - 1]
            width = conv_kernel_width[i - 1]
            k = max(1, int((1 - pow(i / l, l - i)) * n)) if i < l else 3
            module_list.append(Conv2dSame(in_channels=in_channels, out_channels=out_channels, kernel_size=(width, 1),
                                          stride=1).to(self.device))
            module_list.append(torch.nn.Tanh().to(self.device))

            # KMaxPooling, extract top_k, returns tensors values
            module_list.append(KMaxPooling(k=min(k, filed_shape), axis=2, device=self.device).to(self.device))
            filed_shape = min(k, filed_shape)
        self.conv_layer = nn.Sequential(*module_list)
        self.to(device)
        self.filed_shape = filed_shape 

def forward(self, inputs):
        fm_input = inputs

        square_of_sum = torch.pow(torch.sum(fm_input, dim=1, keepdim=True), 2)
        sum_of_square = torch.sum(fm_input * fm_input, dim=1, keepdim=True)
        cross_term = square_of_sum - sum_of_square
        cross_term = 0.5 * torch.sum(cross_term, dim=2, keepdim=False)

        return cross_term 

def gelu_new(x):
    """ Implementation of the gelu activation function currently in Google Bert repo (identical to OpenAI GPT).
        Also see https://arxiv.org/abs/1606.08415
    """
    return 0.5 * x * (1 + torch.tanh(math.sqrt(2 / math.pi) * (x + 0.044715 * torch.pow(x, 3)))) 

def forward(self, x):
        u = x.mean(-1, keepdim=True)
        s = (x - u).pow(2).mean(-1, keepdim=True)
        x = (x - u) / torch.sqrt(s + self.variance_epsilon)
        return self.weight * x + self.bias 

def forward(self, y, y_):  # y, y_ must be same type float (*)
        loss = y * torch.pow(1-y_, 2) + (1 - y) * torch.pow(y_-self.margin, 2)
        loss = torch.sum(loss) / 2.0 / len(y)   #y.size()[0]
        return loss 

def gelu(x):
    return 0.5 * x * (1 + torch.tanh(math.sqrt(2 / math.pi) * (x + 0.044715 * torch.pow(x, 3)))) 

def forward(self, x1, x2):
        out1 = self.embedding_net(x1)
        out2 = self.embedding_net(x2)

        # out1_norm = torch.sqrt(torch.sum(torch.pow(out1, 2), dim=1))
        # out2_norm = torch.sqrt(torch.sum(torch.pow(out2, 2), dim=1))
        # cosine = (out1*out2).sum(1) / (out1_norm*out2_norm)
        sim = F.cosine_similarity(out1, out2, dim=1)
        # pdist = F.pairwise_distance(out1, out2, p=2, eps=1e-06, keepdim=False)

        return out1, out2, sim 

def _ae_loss(tag0, tag1, mask):
    # squeeze去掉numpy数组里的shape中为1的维度
    num  = mask.sum(dim=1, keepdim=True).float()
    tag0 = tag0.squeeze()
    tag1 = tag1.squeeze()

    tag_mean = (tag0 + tag1) / 2

    # 返回方差/n，再求和[得，我们得到了方差和]
    tag0 = torch.pow(tag0 - tag_mean, 2) / (num + 1e-4)
    tag0 = tag0[mask].sum()
    tag1 = torch.pow(tag1 - tag_mean, 2) / (num + 1e-4)
    tag1 = tag1[mask].sum()
    pull = tag0 + tag1

    # 在第2维上[我们0开始应该是1]上增加一个维度
    mask = mask.unsqueeze(1) + mask.unsqueeze(2)
    mask = mask.eq(2)
    num  = num.unsqueeze(2)
    num2 = (num - 1) * num
    dist = tag_mean.unsqueeze(1) - tag_mean.unsqueeze(2)
    dist = 1 - torch.abs(dist)
    dist = nn.functional.relu(dist, inplace=True)
    dist = dist - 1 / (num + 1e-4)
    dist = dist / (num2 + 1e-4)
    dist = dist[mask]
    push = dist.sum()
    return pull, push 

def forward(self, x):
        batch_size = x.size()[0]
        h_x = x.size()[2]
        w_x = x.size()[3]
        count_h = self.tensor_size(x[:, :, 1:, :])
        count_w = self.tensor_size(x[:, :, :, 1:])
        h_tv = torch.pow((x[:, :, 1:, :] - x[:, :, :h_x - 1, :]), 2).sum()
        w_tv = torch.pow((x[:, :, :, 1:] - x[:, :, :, :w_x - 1]), 2).sum()
        return self.tv_loss_weight * 2 * (h_tv / count_h + w_tv / count_w) / batch_size 

def cabs(x):
    # modulus of a complex number
    return torch.pow(x[..., 0]**2+x[..., 1]**2, 0.5) 

def cabs(x):
    return torch.pow(x[..., 0]**2+x[..., 1]**2, 0.5) 

def cabs(x):
    return torch.pow(x[..., 0]**2+x[..., 1]**2, 0.5) 

def forward(self, inputs, targets):
        N = inputs.size(0)
        print(N)
        C = inputs.size(1)
        P = F.softmax(inputs)

        class_mask = inputs.data.new(N, C).fill_(0)
        ids = targets.view(-1, 1)
        class_mask.scatter_(1, ids.data, 1.)
        #print(class_mask)
        

        if inputs.is_cuda and not self.alpha.is_cuda:
            self.alpha = self.alpha.cuda()
        alpha = self.alpha[ids.data.view(-1)]
        
        probs = (P*class_mask).sum(1).view(-1,1)

        log_p = probs.log()
        #print('probs size= {}'.format(probs.size()))
        #print(probs)

        batch_loss = -alpha*(torch.pow((1-probs), self.gamma))*log_p 
        #print('-----bacth_loss------')
        #print(batch_loss)

        
        if self.size_average:
            loss = batch_loss.mean()
        else:
            loss = batch_loss.sum()
        return loss 

def forward(self, dist):
        dist = dist.view(-1, 1) - self.offset.view(1, -1)
        return torch.exp(self.coeff * torch.pow(dist, 2)) 

def forward(self, x):
        u = x.mean(-1, keepdim=True)
        s = (x - u).pow(2).mean(-1, keepdim=True)
        x = (x - u) / torch.sqrt(s + self.e)
        return self.g * x + self.b 

def gelu(x: torch.Tensor) -> torch.Tensor:
    return 0.5 * x * (1 + torch.tanh(math.sqrt(2 / math.pi) * (x + 0.044715 * torch.pow(x, 3)))) 

def _focal_loss_mask(preds, gt, mask):
    pos_inds = gt.eq(1)
    neg_inds = gt.lt(1)

    neg_weights = torch.pow(1 - gt[neg_inds], 4)

    pos_mask = mask[pos_inds]
    neg_mask = mask[neg_inds]

    loss = 0
    for pred in preds:
        pos_pred = pred[pos_inds]
        neg_pred = pred[neg_inds]

        pos_loss = torch.log(pos_pred) * torch.pow(1 - pos_pred, 2) * pos_mask
        neg_loss = torch.log(1 - neg_pred) * torch.pow(neg_pred, 2) * neg_weights * neg_mask

        num_pos  = pos_inds.float().sum()
        pos_loss = pos_loss.sum()
        neg_loss = neg_loss.sum()

        if pos_pred.nelement() == 0:
            loss = loss - neg_loss
        else:
            loss = loss - (pos_loss + neg_loss) / num_pos
    return loss 

def l2norm(X, dim, eps=1e-8):
    """L2-normalize columns of X"""
    norm = (torch.pow(X, 2).sum(dim=dim, keepdim=True) + eps).sqrt()
    X = torch.div(X, norm)
    return X