Python torch.lgamma方法代碼示例

# 需要導入模塊: import torch [as 別名]
# 或者: from torch import lgamma [as 別名]
def __init__(self, n, eta, validate_args=False):
        TModule.__init__(self)
        if not isinstance(n, int) or n < 1:
            raise ValueError("n must be a positive integer")
        if isinstance(eta, Number):
            eta = torch.tensor(float(eta))
        self.n = torch.tensor(n, dtype=torch.long, device=eta.device)
        batch_shape = eta.shape
        event_shape = torch.Size([n, n])
        # Normalization constant(s)
        i = torch.arange(n, dtype=eta.dtype, device=eta.device)
        C = (((2 * eta.view(-1, 1) - 2 + i) * i).sum(1) * math.log(2)).view_as(eta)
        C += n * torch.sum(2 * torch.lgamma(i / 2 + 1) - torch.lgamma(i + 2))
        # need to assign values before registering as buffers to make argument validation work
        self.eta = eta
        self.C = C
        super(LKJPrior, self).__init__(batch_shape, event_shape, validate_args=validate_args)
        # now need to delete to be able to register buffer
        del self.eta, self.C
        self.register_buffer("eta", eta)
        self.register_buffer("C", C) 

# 需要導入模塊: import torch [as 別名]
# 或者: from torch import lgamma [as 別名]
def forward(ctx, scale, c, dim):
        scale = scale.double()
        c = c.double()
        ctx.scale = scale.clone().detach()
        ctx.c = c.clone().detach()
        ctx.dim = dim

        device = scale.device
        output = .5 * (Constants.logpi - Constants.log2) + scale.log() -(int(dim) - 1) * (c.log() / 2 + Constants.log2)
        dim = torch.tensor(int(dim)).to(device).double()

        k_float = rexpand(torch.arange(int(dim)), *scale.size()).double().to(device)
        s = torch.lgamma(dim) - torch.lgamma(k_float + 1) - torch.lgamma(dim - k_float) \
            + (dim - 1 - 2 * k_float).pow(2) * c * scale.pow(2) / 2 \
            + torch.log1p(torch.erf((dim - 1 - 2 * k_float) * c.sqrt() * scale / math.sqrt(2)))
        signs = torch.tensor([1., -1.]).double().to(device).repeat(((int(dim)+1) // 2)*2)[:int(dim)]
        signs = rexpand(signs, *scale.size())
        ctx.log_sum_term = log_sum_exp_signs(s, signs, dim=0)
        output = output + ctx.log_sum_term

        return output.float() 

# 需要導入模塊: import torch [as 別名]
# 或者: from torch import lgamma [as 別名]
def backward(ctx, grad_output):
        grad_input = grad_output.clone()

        device = grad_input.device
        scale = ctx.scale
        c = ctx.c
        dim = torch.tensor(int(ctx.dim)).to(device).double()

        k_float = rexpand(torch.arange(int(dim)), *scale.size()).double().to(device)
        signs = torch.tensor([1., -1.]).double().to(device).repeat(((int(dim)+1) // 2)*2)[:int(dim)]
        signs = rexpand(signs, *scale.size())

        log_arg = (dim - 1 - 2 * k_float).pow(2) * c * scale * (1+torch.erf((dim - 1 - 2 * k_float) * c.sqrt() * scale / math.sqrt(2))) + \
            torch.exp(-(dim - 1 - 2 * k_float).pow(2) * c * scale.pow(2) / 2) * 2 / math.sqrt(math.pi) * (dim - 1 - 2 * k_float) * c.sqrt() / math.sqrt(2)
        log_arg_signs = torch.sign(log_arg)
        s = torch.lgamma(dim) - torch.lgamma(k_float + 1) - torch.lgamma(dim - k_float) \
            + (dim - 1 - 2 * k_float).pow(2) * c * scale.pow(2) / 2 \
            + torch.log(log_arg_signs * log_arg)
        log_grad_sum_sigma = log_sum_exp_signs(s, log_arg_signs * signs, dim=0)

        grad_scale = torch.exp(log_grad_sum_sigma - ctx.log_sum_term)
        grad_scale = 1 / ctx.scale + grad_scale

        grad_scale = (grad_input * grad_scale.float()).view(-1, *grad_input.shape).sum(0)
        return (grad_scale, None, None) 

# 需要導入模塊: import torch [as 別名]
# 或者: from torch import lgamma [as 別名]
def mean(self):
        c = self.c.double()
        scale = self.scale.double()
        dim = torch.tensor(int(self.dim)).double().to(self.device)
        signs = torch.tensor([1., -1.]).double().to(self.device).repeat(((self.dim+1) // 2)*2)[:self.dim].unsqueeze(-1).unsqueeze(-1).expand(self.dim, *self.scale.size())
        
        k_float = rexpand(torch.arange(self.dim), *self.scale.size()).double().to(self.device)
        s2 = torch.lgamma(dim) - torch.lgamma(k_float + 1) - torch.lgamma(dim - k_float) \
                + (dim - 1 - 2 * k_float).pow(2) * c * scale.pow(2) / 2 \
                + torch.log1p(torch.erf((dim - 1 - 2 * k_float) * c.sqrt() * scale / math.sqrt(2)))
        S2 = log_sum_exp_signs(s2, signs, dim=0)

        log_arg = (dim - 1 - 2 * k_float) * c.sqrt() * scale.pow(2) * (1 + torch.erf((dim - 1 - 2 * k_float) * c.sqrt() * scale / math.sqrt(2))) + \
                torch.exp(-(dim - 1 - 2 * k_float).pow(2) * c * scale.pow(2) / 2) * scale * math.sqrt(2 / math.pi)
        log_arg_signs = torch.sign(log_arg)
        s1 = torch.lgamma(dim) - torch.lgamma(k_float + 1) - torch.lgamma(dim - k_float) \
                + (dim - 1 - 2 * k_float).pow(2) * c * scale.pow(2) / 2 \
                + torch.log(log_arg_signs * log_arg)
        S1 = log_sum_exp_signs(s1, signs * log_arg_signs, dim=0)

        output = torch.exp(S1 - S2)
        return output.float() 

# 需要導入模塊: import torch [as 別名]
# 或者: from torch import lgamma [as 別名]
def log_zinb_positive(x, mu, theta, pi, eps=1e-8):
    """Note: All inputs are torch Tensors
    log likelihood (scalar) of a minibatch according to a zinb model.
    Notes:
    We parametrize the bernoulli using the logits, hence the softplus functions appearing

    Variables:
    mu: mean of the negative binomial (has to be positive support) (shape: minibatch x genes)
    theta: inverse dispersion parameter (has to be positive support) (shape: minibatch x genes)
    pi: logit of the dropout parameter (real support) (shape: minibatch x genes)
    eps: numerical stability constant

    """

    # theta is the dispersion rate. If .ndimension() == 1, it is shared for all cells (regardless of batch or labels)
    if theta.ndimension() == 1:
        theta = theta.view(
            1, theta.size(0)
        )  # In this case, we reshape theta for broadcasting

    softplus_pi = F.softplus(-pi)  #  uses log(sigmoid(x)) = -softplus(-x)
    log_theta_eps = torch.log(theta + eps)
    log_theta_mu_eps = torch.log(theta + mu + eps)
    pi_theta_log = -pi + theta * (log_theta_eps - log_theta_mu_eps)

    case_zero = F.softplus(pi_theta_log) - softplus_pi
    mul_case_zero = torch.mul((x < eps).type(torch.float32), case_zero)

    case_non_zero = (
        -softplus_pi
        + pi_theta_log
        + x * (torch.log(mu + eps) - log_theta_mu_eps)
        + torch.lgamma(x + theta)
        - torch.lgamma(theta)
        - torch.lgamma(x + 1)
    )
    mul_case_non_zero = torch.mul((x > eps).type(torch.float32), case_non_zero)

    res = mul_case_zero + mul_case_non_zero

    return res 

# 需要導入模塊: import torch [as 別名]
# 或者: from torch import lgamma [as 別名]
def log_nb_positive(x, mu, theta, eps=1e-8):
    """Note: All inputs should be torch Tensors
    log likelihood (scalar) of a minibatch according to a nb model.

    Variables:
    mu: mean of the negative binomial (has to be positive support) (shape: minibatch x genes)
    theta: inverse dispersion parameter (has to be positive support) (shape: minibatch x genes)
    eps: numerical stability constant

    """
    if theta.ndimension() == 1:
        theta = theta.view(
            1, theta.size(0)
        )  # In this case, we reshape theta for broadcasting

    log_theta_mu_eps = torch.log(theta + mu + eps)

    res = (
        theta * (torch.log(theta + eps) - log_theta_mu_eps)
        + x * (torch.log(mu + eps) - log_theta_mu_eps)
        + torch.lgamma(x + theta)
        - torch.lgamma(theta)
        - torch.lgamma(x + 1)
    )

    return res 

# 需要導入模塊: import torch [as 別名]
# 或者: from torch import lgamma [as 別名]
def __log_surface_area(self):
        if torch.__version__ >= "1.0.0":
            lgamma = torch.lgamma(torch.tensor([(self._dim + 1) / 2]).to(self.device))
        else:
            lgamma = torch.lgamma(
                torch.Tensor([(self._dim + 1) / 2], device=self.device)
            )
        return math.log(2) + ((self._dim + 1) / 2) * math.log(math.pi) - lgamma 

# 需要導入模塊: import torch [as 別名]
# 或者: from torch import lgamma [as 別名]
def cdf_r(value, scale, c, dim):
    value = value.double()
    scale = scale.double()
    c = c.double()

    if dim == 2:
        return 1 / torch.erf(c.sqrt() * scale / math.sqrt(2)) * .5 * \
    (2 * torch.erf(c.sqrt() * scale / math.sqrt(2)) + torch.erf((value - c.sqrt() * scale.pow(2)) / math.sqrt(2) / scale) - \
        torch.erf((c.sqrt() * scale.pow(2) + value) / math.sqrt(2) / scale))
    else:
        device = value.device

        k_float = rexpand(torch.arange(dim), *value.size()).double().to(device)
        dim = torch.tensor(dim).to(device).double()

        s1 = torch.lgamma(dim) - torch.lgamma(k_float + 1) - torch.lgamma(dim - k_float) \
            + (dim - 1 - 2 * k_float).pow(2) * c * scale.pow(2) / 2 \
            + torch.log( \
                torch.erf((value - (dim - 1 - 2 * k_float) * c.sqrt() * scale.pow(2)) / scale / math.sqrt(2)) \
                + torch.erf((dim - 1 - 2 * k_float) * c.sqrt() * scale / math.sqrt(2)) \
                )
        s2 = torch.lgamma(dim) - torch.lgamma(k_float + 1) - torch.lgamma(dim - k_float) \
            + (dim - 1 - 2 * k_float).pow(2) * c * scale.pow(2) / 2 \
            + torch.log1p(torch.erf((dim - 1 - 2 * k_float) * c.sqrt() * scale / math.sqrt(2)))

        signs = torch.tensor([1., -1.]).double().to(device).repeat(((int(dim)+1) // 2)*2)[:int(dim)]
        signs = rexpand(signs, *value.size())

        S1 = log_sum_exp_signs(s1, signs, dim=0)
        S2 = log_sum_exp_signs(s2, signs, dim=0)

        output = torch.exp(S1 - S2)
        zero_value_idx = value == 0.
        output[zero_value_idx] = 0.
        return output.float() 

# 需要導入模塊: import torch [as 別名]
# 或者: from torch import lgamma [as 別名]
def _log_surface_area(self):
        return math.log(2) + ((self._dim + 1) / 2) * math.log(math.pi) - torch.lgamma(
            torch.Tensor([(self._dim + 1) / 2])) 

# 需要導入模塊: import torch [as 別名]
# 或者: from torch import lgamma [as 別名]
def students_t_nll(x, df, scale):
  """The NLL of a Generalized Student's T distribution (w/o including TFP)."""
  x = torch.as_tensor(x)
  df = torch.as_tensor(df)
  scale = torch.as_tensor(scale)
  log_partition = torch.log(torch.abs(scale)) + torch.lgamma(
      0.5 * df) - torch.lgamma(0.5 * df + torch.tensor(0.5)) + torch.tensor(
          0.5 * np.log(np.pi))
  return 0.5 * ((df + 1.) * torch.log1p(
      (x / scale)**2. / df) + torch.log(df)) + log_partition


# A constant scale that makes tf.image.rgb_to_yuv() volume preserving. 

# 需要導入模塊: import torch [as 別名]
# 或者: from torch import lgamma [as 別名]
def lbeta(a, b):
    return torch.lgamma(a) + torch.lgamma(b) - torch.lgamma(a + b) 

# 需要導入模塊: import torch [as 別名]
# 或者: from torch import lgamma [as 別名]
def kuma_moments(a, b, n):
    """
    Computes nth moment of Kumaraswamy using using torch.lgamma
    :param a:
    :param b:
    :param n:
    :return: nth moment
    """
    arg1 = 1 + n / a
    log_value = torch.lgamma(arg1) + torch.lgamma(b) - torch.lgamma(arg1 + b)
    return b * torch.exp(log_value) 

# 需要導入模塊: import torch [as 別名]
# 或者: from torch import lgamma [as 別名]
def log_mixture_nb(x, mu_1, mu_2, theta_1, theta_2, pi, eps=1e-8):
    """Note: All inputs should be torch Tensors
    log likelihood (scalar) of a minibatch according to a mixture nb model.
    pi is the probability to be in the first component.

    For totalVI, the first component should be background.

    Parameters
    ----------
    mu1: mean of the first negative binomial component (has to be positive support) (shape: minibatch x genes)
    theta1: first inverse dispersion parameter (has to be positive support) (shape: minibatch x genes)
    mu2: mean of the second negative binomial (has to be positive support) (shape: minibatch x genes)
    theta2: second inverse dispersion parameter (has to be positive support) (shape: minibatch x genes)
        If None, assume one shared inverse dispersion parameter.
    eps: numerical stability constant


    Returns
    -------

    """
    if theta_2 is not None:
        log_nb_1 = log_nb_positive(x, mu_1, theta_1)
        log_nb_2 = log_nb_positive(x, mu_2, theta_2)
    # this is intended to reduce repeated computations
    else:
        theta = theta_1
        if theta.ndimension() == 1:
            theta = theta.view(
                1, theta.size(0)
            )  # In this case, we reshape theta for broadcasting

        log_theta_mu_1_eps = torch.log(theta + mu_1 + eps)
        log_theta_mu_2_eps = torch.log(theta + mu_2 + eps)
        lgamma_x_theta = torch.lgamma(x + theta)
        lgamma_theta = torch.lgamma(theta)
        lgamma_x_plus_1 = torch.lgamma(x + 1)

        log_nb_1 = (
            theta * (torch.log(theta + eps) - log_theta_mu_1_eps)
            + x * (torch.log(mu_1 + eps) - log_theta_mu_1_eps)
            + lgamma_x_theta
            - lgamma_theta
            - lgamma_x_plus_1
        )
        log_nb_2 = (
            theta * (torch.log(theta + eps) - log_theta_mu_2_eps)
            + x * (torch.log(mu_2 + eps) - log_theta_mu_2_eps)
            + lgamma_x_theta
            - lgamma_theta
            - lgamma_x_plus_1
        )

    logsumexp = torch.logsumexp(torch.stack((log_nb_1, log_nb_2 - pi)), dim=0)
    softplus_pi = F.softplus(-pi)

    log_mixture_nb = logsumexp - softplus_pi

    return log_mixture_nb 

# 需要導入模塊: import torch [as 別名]
# 或者: from torch import lgamma [as 別名]
def grad_cdf_value_scale(value, scale, c, dim):
    device = value.device

    dim = torch.tensor(int(dim)).to(device).double()

    signs = torch.tensor([1., -1.]).double().to(device).repeat(((int(dim)+1) // 2)*2)[:int(dim)]
    signs = rexpand(signs, *value.size())
    k_float = rexpand(torch.arange(dim), *value.size()).double().to(device)

    log_arg1 = (dim - 1 - 2 * k_float).pow(2) * c * scale * \
    (\
        torch.erf((value - (dim - 1 - 2 * k_float) * c.sqrt() * scale.pow(2)) / scale / math.sqrt(2)) \
        + torch.erf((dim - 1 - 2 * k_float) * c.sqrt() * scale / math.sqrt(2)) \
    )
    
    log_arg2 = math.sqrt(2 / math.pi) * ( \
        (dim - 1 - 2 * k_float) * c.sqrt() * torch.exp(-(dim - 1 - 2 * k_float).pow(2) * c * scale.pow(2) / 2) \
        - ((value / scale.pow(2) + (dim - 1 - 2 * k_float) * c.sqrt()) * torch.exp(-(value - (dim - 1 - 2 * k_float) * c.sqrt() * scale.pow(2)).pow(2) / (2 * scale.pow(2)))) \
        )

    log_arg = log_arg1 + log_arg2
    sign_log_arg = torch.sign(log_arg)

    s = torch.lgamma(dim) - torch.lgamma(k_float + 1) - torch.lgamma(dim - k_float) \
            + (dim - 1 - 2 * k_float).pow(2) * c * scale.pow(2) / 2 \
            + torch.log(sign_log_arg * log_arg)

    log_grad_sum_sigma = log_sum_exp_signs(s, signs * sign_log_arg, dim=0)
    grad_sum_sigma = torch.sum(signs * sign_log_arg * torch.exp(s), dim=0)

    s1 = torch.lgamma(dim) - torch.lgamma(k_float + 1) - torch.lgamma(dim - k_float) \
        + (dim - 1 - 2 * k_float).pow(2) * c * scale.pow(2) / 2 \
        + torch.log( \
            torch.erf((value - (dim - 1 - 2 * k_float) * c.sqrt() * scale.pow(2)) / scale / math.sqrt(2)) \
            + torch.erf((dim - 1 - 2 * k_float) * c.sqrt() * scale / math.sqrt(2)) \
        )

    S1 = log_sum_exp_signs(s1, signs, dim=0)
    grad_log_cdf_scale = grad_sum_sigma / S1.exp()
    log_unormalised_prob = - value.pow(2) / (2 * scale.pow(2)) + (dim - 1) * logsinh(c.sqrt() * value) - (dim - 1) / 2 * c.log()
    
    with torch.autograd.enable_grad():
        scale = scale.float()
        logZ = _log_normalizer_closed_grad.apply(scale, c, dim)
        grad_logZ_scale = grad(logZ, scale, grad_outputs=torch.ones_like(scale))

    grad_log_cdf_scale = - grad_logZ_scale[0] + 1 / scale + grad_log_cdf_scale.float()
    cdf = cdf_r(value.double(), scale.double(), c.double(), int(dim)).float().squeeze(0)
    grad_scale = cdf * grad_log_cdf_scale

    grad_value = (log_unormalised_prob.float() - logZ).exp()
    return grad_value, grad_scale