code: def general_loss_with_squared_residual(squared_x, alpha, scale):
      r"""The general loss that takes a squared residual.
  
      This fuses the sqrt operation done to compute many residuals while preserving
      the square in the loss formulation.
  
      This implements the rho(x, \alpha, c) function described in "A General and
      Adaptive Robust Loss Function", Jonathan T. Barron,
      https://arxiv.org/abs/1701.03077.
  
      Args:
        squared_x: The residual for which the loss is being computed. x can have
          any shape, and alpha and scale will be broadcasted to match x's shape if
          necessary.
        alpha: The shape parameter of the loss (\alpha in the paper), where more
          negative values produce a loss with more robust behavior (outliers "cost"
          less), and more positive values produce a loss with less robust behavior
          (outliers are penalized more heavily). Alpha can be any value in
          [-infinity, infinity], but the gradient of the loss with respect to alpha
          is 0 at -infinity, infinity, 0, and 2. Varying alpha allows for smooth
          interpolation between several discrete robust losses:
            alpha=-Infinity: Welsch/Leclerc Loss.
            alpha=-2: Geman-McClure loss.
            alpha=0: Cauchy/Lortentzian loss.
            alpha=1: Charbonnier/pseudo-Huber loss.
            alpha=2: L2 loss.
        scale: The scale parameter of the loss. When |x| < scale, the loss is an
          L2-like quadratic bowl, and when |x| > scale the loss function takes on a
          different shape according to alpha.
  
      Returns:
        The losses for each element of x, in the same shape as x.
      """
      eps = jnp.finfo(jnp.float32).eps
  
      # This will be used repeatedly.
      squared_scaled_x = squared_x / (scale**2)
  
      # The loss when alpha == 2.
      loss_two = 0.5 * squared_scaled_x
      # The loss when alpha == 0.
      loss_zero = log1p_safe(0.5 * squared_scaled_x)
      # The loss when alpha == -infinity.
      loss_neginf = -jnp.expm1(-0.5 * squared_scaled_x)
      # The loss when alpha == +infinity.
      loss_posinf = expm1_safe(0.5 * squared_scaled_x)
  
      # The loss when not in one of the above special cases.
      # Clamp |2-alpha| to be >= machine epsilon so that it's safe to divide by.
      beta_safe = jnp.maximum(eps, jnp.abs(alpha - 2.0))
      # Clamp |alpha| to be >= machine epsilon so that it's safe to divide by.
      alpha_safe = jnp.where(
          jnp.greater_equal(alpha, 0.0),
          jnp.ones_like(alpha),
          -jnp.ones_like(alpha),
      ) * jnp.maximum(eps, jnp.abs(alpha))
      loss_otherwise = (beta_safe / alpha_safe) * (
          jnp.power(squared_scaled_x / beta_safe + 1.0, 0.5 * alpha)
          - 1.0
      )
  
      # Select which of the cases of the loss to return.
      loss = jnp.where(
          alpha == -jnp.inf,
          loss_neginf,
          jnp.where(
              alpha == 0,
              loss_zero,
              jnp.where(
                  alpha == 2,
                  loss_two,
                  jnp.where(
                      alpha == jnp.inf, loss_posinf, loss_otherwise
                  ),
              ),
          ),
      )
  
      return scale * loss
  
imports: import collections
  from concurrent import futures
  import contextlib
  import functools
  import time
  from typing import List, Union
  import jax
  from jax import tree_util
  import jax.numpy
  import numpy
  from scipy import interpolate
  from scipy.spatial import transform
  import tqdm
label_desc: Use image node_id 20 for calling a global function with example usage: general_loss_with_squared_residual(squared_x, alpha, scale) and returns: unknown