content: #!/usr/bin/env python3
  #
  # Copyright 2019 Intel AI, CMU, Bosch AI
  
  # Permission is hereby granted, free of charge, to any person obtaining
  # a copy of this software and associated documentation files (the
  # "Software"), to deal in the Software without restriction, including
  # without limitation the rights to use, copy, modify, merge, publish,
  # distribute, sublicense, and/or sell copies of the Software, and to
  # permit persons to whom the Software is furnished to do so, subject to
  # the following conditions:
  
  # The above copyright notice and this permission notice shall be
  # included in all copies or substantial portions of the Software.
  
  # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
  # EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
  # MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
  # NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
  # LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
  # OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
  # WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
  import numpy as np
  import numpy.random as npr
  import torch
  from torch.autograd import Function, Variable, grad
  from torch.nn import Module
  
  from theseus._version import lt_version
  
  old_torch = lt_version(torch.__version__, "0.4.0")
  
  
  def bdot(x, y):
      return torch.bmm(x.unsqueeze(1), y.unsqueeze(2)).squeeze()
  
  
  class LML(Module):
      def __init__(self, N, eps=1e-4, n_iter=100, branch=None, verbose=0):
          super().__init__()
          self.N = N
          self.eps = eps
          self.n_iter = n_iter
          self.branch = branch
          self.verbose = verbose
  
      def forward(self, x):
          return LML_Function.apply(
              x, self.N, self.eps, self.n_iter, self.branch, self.verbose
          )
  
  
  class LML_Function(Function):
      @staticmethod
      def forward(ctx, x, N, eps, n_iter, branch, verbose):
          ctx.N = N
          ctx.eps = eps
          ctx.n_iter = n_iter
          ctx.branch = branch
          ctx.verbose = verbose
  
          branch = ctx.branch
          if branch is None:
              if not x.is_cuda:
                  branch = 10
              else:
                  branch = 100
  
          single = x.ndimension() == 1
          orig_x = x
          if single:
              x = x.unsqueeze(0)
          assert x.ndimension() == 2
  
          n_batch, nx = x.shape
          if nx <= ctx.N:
              y = (1.0 - 1e-5) * torch.ones(n_batch, nx).type_as(x)
              if single:
                  y = y.squeeze(0)
              if old_torch:
                  ctx.save_for_backward(orig_x)
                  ctx.y = y
                  ctx.nu = torch.Tensor()
              else:
                  ctx.save_for_backward(orig_x, y, torch.Tensor())
              return y
  
          x_sorted, _ = torch.sort(x, dim=1, descending=True)
  
          # The sigmoid saturates the interval [-7, 7]
          nu_lower = -x_sorted[:, ctx.N - 1] - 7.0
          nu_upper = -x_sorted[:, ctx.N] + 7.0
  
          ls = torch.linspace(0, 1, branch).type_as(x)
  
          for i in range(ctx.n_iter):
              r = nu_upper - nu_lower
              I = r > ctx.eps  # noqa: E741
              n_update = I.sum()
              if n_update == 0:
                  break
  
              Ix = I.unsqueeze(1).expand_as(x) if old_torch else I
  
              nus = r[I].unsqueeze(1) * ls + nu_lower[I].unsqueeze(1)
              _xs = x[Ix].view(n_update, 1, nx) + nus.unsqueeze(2)
              fs = torch.sigmoid(_xs).sum(dim=2) - ctx.N
              # assert torch.all(fs[:,0] < 0) and torch.all(fs[:,-1] > 0)
  
              i_lower = ((fs < 0).sum(dim=1) - 1).long()
              J = i_lower < 0
              if J.sum() > 0:
                  print("LML Warning: An example has all positive iterates.")
                  i_lower[J] = 0
  
              i_upper = i_lower + 1
  
              nu_lower[I] = nus.gather(1, i_lower.unsqueeze(1)).squeeze()
              nu_upper[I] = nus.gather(1, i_upper.unsqueeze(1)).squeeze()
  
              if J.sum() > 0:
                  nu_lower[J] -= 7.0
  
          if ctx.verbose >= 0 and np.any(I.cpu().numpy()):
              print("LML Warning: Did not converge.")
              # import ipdb; ipdb.set_trace()
  
          nu = nu_lower + r / 2.0
          y = torch.sigmoid(x + nu.unsqueeze(1))
          if single:
              y = y.squeeze(0)
  
          if old_torch:
              # Storing these in the object may cause memory leaks.
              ctx.save_for_backward(orig_x)
              ctx.y = y
              ctx.nu = nu
          else:
              ctx.save_for_backward(orig_x, y, nu)
          return y
  
      @staticmethod
      def backward(ctx, grad_output):
          if old_torch:
              (x,) = ctx.saved_tensors
              y = ctx.y
              nu = ctx.nu
          else:
              x, y, nu = ctx.saved_tensors
  
          single = x.ndimension() == 1
          if single:
              x = x.unsqueeze(0)
              y = y.unsqueeze(0)
              grad_output = grad_output.unsqueeze(0)
  
          assert x.ndimension() == 2
          assert y.ndimension() == 2
          assert grad_output.ndimension() == 2
  
          n_batch, nx = x.shape
          if nx <= ctx.N:
              dx = torch.zeros_like(x)
              if single:
                  dx = dx.squeeze()
              grads = tuple([dx] + [None] * 5)
              return grads
  
          Hinv = 1.0 / (1.0 / y + 1.0 / (1.0 - y))
          dnu = bdot(Hinv, grad_output) / Hinv.sum(dim=1)
          dx = -Hinv * (-grad_output + dnu.unsqueeze(1))
  
          if single:
              dx = dx.squeeze()
  
          grads = tuple([dx] + [None] * 5)
          return grads
  
  
  if __name__ == "__main__":
      import sys
  
      from IPython.core import ultratb
  
      sys.excepthook = ultratb.FormattedTB(
          mode="Verbose", color_scheme="Linux", call_pdb=1
      )
  
      m = 10
      n = 2
  
      npr.seed(0)
      x = npr.random(m)
  
      import cvxpy as cp
      import numdifftools as nd
  
      y = cp.Variable(m)
      obj = cp.Minimize(-x * y - cp.sum(cp.entr(y)) - cp.sum(cp.entr(1.0 - y)))
      cons = [0 <= y, y <= 1, cp.sum(y) == n]
      prob = cp.Problem(obj, cons)
      prob.solve(cp.SCS, verbose=True)
      assert "optimal" in prob.status
      y_cp = y.value
  
      x = Variable(torch.from_numpy(x), requires_grad=True)
      x = torch.stack([x, x])
      y = LML(N=n)(x)
  
      np.testing.assert_almost_equal(y[0].data.numpy(), y_cp, decimal=3)
  
      (dy0,) = grad(y[0, 0], x)
      dy0 = dy0.squeeze()
  
      def f(x):
          x = Variable(torch.from_numpy(x).clone())
          y = LML(N=n)(x)
          return y.data.numpy()
  
      x = x.data[0].numpy().copy()
      df = nd.Jacobian(f)
  
      dy0_fd = df(x)[0]
  
      np.testing.assert_almost_equal(dy0[0].data.numpy(), dy0_fd, decimal=3)
  