text: #!/usr/bin/env python3
  # -*- coding: utf-8 -*-
  
  import torch.nn as nn
  import torch as T
  from torch.autograd import Variable as var
  import torch.nn.functional as F
  import numpy as np
  
  from .util import *
  
  
  class Memory(nn.Module):
  
    def __init__(self, input_size, mem_size=512, cell_size=32, read_heads=4, gpu_id=-1, independent_linears=True):
      super(Memory, self).__init__()
  
      self.mem_size = mem_size
      self.cell_size = cell_size
      self.read_heads = read_heads
      self.gpu_id = gpu_id
      self.input_size = input_size
      self.independent_linears = independent_linears
  
      m = self.mem_size
      w = self.cell_size
      r = self.read_heads
  
      if self.independent_linears:
        self.read_keys_transform = nn.Linear(self.input_size, w * r)
        self.read_strengths_transform = nn.Linear(self.input_size, r)
        self.write_key_transform = nn.Linear(self.input_size, w)
        self.write_strength_transform = nn.Linear(self.input_size, 1)
        self.erase_vector_transform = nn.Linear(self.input_size, w)
        self.write_vector_transform = nn.Linear(self.input_size, w)
        self.free_gates_transform = nn.Linear(self.input_size, r)
        self.allocation_gate_transform = nn.Linear(self.input_size, 1)
        self.write_gate_transform = nn.Linear(self.input_size, 1)
        self.read_modes_transform = nn.Linear(self.input_size, 3 * r)
      else:
        self.interface_size = (w * r) + (3 * w) + (5 * r) + 3
        self.interface_weights = nn.Linear(self.input_size, self.interface_size)
  
      self.I = (1 - T.eye(m).unsqueeze(0) ).cuda() # (1 * n * n)qqq
  
    def reset(self, batch_size=1, hidden=None, erase=False):
      m = self.mem_size
      w = self.cell_size
      r = self.read_heads
      b = batch_size
  
      if hidden is None:
        return {
            'memory': T.zeros(b, m, w).cuda(),
            'link_matrix': T.zeros(b, 1, m, m).cuda(),
            'precedence': T.zeros(b, 1, m).cuda() ,
            'read_weights': T.zeros(b, r, m).cuda() ,
            'write_weights': T.zeros(b, 1, m).cuda(),
            'usage_vector': T.zeros(b, m).cuda() 
        }
      else:
        hidden['memory'] = hidden['memory'].detach()
        hidden['link_matrix'] = hidden['link_matrix'].detach()
        hidden['precedence'] = hidden['precedence'].detach()
        hidden['read_weights'] = hidden['read_weights'].detach()
        hidden['write_weights'] = hidden['write_weights'].detach()
        hidden['usage_vector'] = hidden['usage_vector'].detach()
  
        if erase:
          hidden['memory'].data.fill_(0)
          hidden['link_matrix'].data.zero_()
          hidden['precedence'].data.zero_()
          hidden['read_weights'].data.fill_(0)
          hidden['write_weights'].data.fill_(0)
          hidden['usage_vector'].data.zero_()
      return hidden
  
    def get_usage_vector(self, usage, free_gates, read_weights, write_weights):
      # write_weights = write_weights.detach()  # detach from the computation graph
      usage = usage + (1 - usage) * (1 - T.prod(1 - write_weights, 1))
      ψ = T.prod(1 - free_gates.unsqueeze(2) * read_weights, 1)
      return usage * ψ
  
    def allocate(self, usage, write_gate):
      # ensure values are not too small prior to cumprod.
      usage = δ + (1 - δ) * usage
      batch_size = usage.size(0)
      # free list
      sorted_usage, φ = T.topk(usage, self.mem_size, dim=1, largest=False)
  
      # cumprod with exclusive=True
      # https://discuss.pytorch.org/t/cumprod-exclusive-true-equivalences/2614/8
      v = var(sorted_usage.data.new(batch_size, 1).fill_(1))
      cat_sorted_usage = T.cat((v, sorted_usage), 1)
      prod_sorted_usage = T.cumprod(cat_sorted_usage, 1)[:, :-1]
  
      sorted_allocation_weights = (1 - sorted_usage) * prod_sorted_usage.squeeze()
  
      # construct the reverse sorting index https://stackoverflow.com/questions/2483696/undo-or-reverse-argsort-python
      _, φ_rev = T.topk(φ, k=self.mem_size, dim=1, largest=False)
      allocation_weights = sorted_allocation_weights.gather(1, φ_rev.long())
  
      return allocation_weights.unsqueeze(1), usage
  
    def write_weighting(self, memory, write_content_weights, allocation_weights, write_gate, allocation_gate):
      ag = allocation_gate.unsqueeze(-1)
      wg = write_gate.unsqueeze(-1)
  
      return wg * (ag * allocation_weights + (1 - ag) * write_content_weights)
  
    def get_link_matrix(self, link_matrix, write_weights, precedence):
      precedence = precedence.unsqueeze(2)
      write_weights_i = write_weights.unsqueeze(3)
      write_weights_j = write_weights.unsqueeze(2)
  
      prev_scale = 1 - write_weights_i - write_weights_j
      new_link_matrix = write_weights_i * precedence
  
      link_matrix = prev_scale * link_matrix + new_link_matrix
      # trick to delete diag elems
      return self.I.expand_as(link_matrix) * link_matrix
  
    def update_precedence(self, precedence, write_weights):
      return (1 - T.sum(write_weights, 2, keepdim=True)) * precedence + write_weights
  
    def write(self, write_key, write_vector, erase_vector, free_gates, read_strengths, write_strength, write_gate, allocation_gate, hidden):
      # get current usage
      hidden['usage_vector'] = self.get_usage_vector(
          hidden['usage_vector'],
          free_gates,
          hidden['read_weights'],
          hidden['write_weights']
      )
  
      # lookup memory with write_key and write_strength
      write_content_weights = self.content_weightings(hidden['memory'], write_key, write_strength)
  
      # get memory allocation
      alloc, _ = self.allocate(
          hidden['usage_vector'],
          allocation_gate * write_gate
      )
  
      # get write weightings
      hidden['write_weights'] = self.write_weighting(
          hidden['memory'],
          write_content_weights,
          alloc,
          write_gate,
          allocation_gate
      )
  
      weighted_resets = hidden['write_weights'].unsqueeze(3) * erase_vector.unsqueeze(2)
      reset_gate = T.prod(1 - weighted_resets, 1)
      # Update memory
      hidden['memory'] = hidden['memory'] * reset_gate
  
      hidden['memory'] = hidden['memory'] + \
          T.bmm(hidden['write_weights'].transpose(1, 2), write_vector)
  
      # update link_matrix
      hidden['link_matrix'] = self.get_link_matrix(
          hidden['link_matrix'],
          hidden['write_weights'],
          hidden['precedence']
      )
      hidden['precedence'] = self.update_precedence(hidden['precedence'], hidden['write_weights'])
  
      return hidden
  
    def content_weightings(self, memory, keys, strengths):
      d = θ(memory, keys)
      return σ(d * strengths.unsqueeze(2), 2)
  
    def directional_weightings(self, link_matrix, read_weights):
      rw = read_weights.unsqueeze(1)
  
      f = T.matmul(link_matrix, rw.transpose(2, 3)).transpose(2, 3)
      b = T.matmul(rw, link_matrix)
      return f.transpose(1, 2), b.transpose(1, 2)
  
    def read_weightings(self, memory, content_weights, link_matrix, read_modes, read_weights):
      forward_weight, backward_weight = self.directional_weightings(link_matrix, read_weights)
  
      content_mode = read_modes[:, :, 2].contiguous().unsqueeze(2) * content_weights
      backward_mode = T.sum(read_modes[:, :, 0:1].contiguous().unsqueeze(3) * backward_weight, 2)
      forward_mode = T.sum(read_modes[:, :, 1:2].contiguous().unsqueeze(3) * forward_weight, 2)
  
      return backward_mode + content_mode + forward_mode
  
    def read_vectors(self, memory, read_weights):
      return T.bmm(read_weights, memory)
  
    def read(self, read_keys, read_strengths, read_modes, hidden):
      content_weights = self.content_weightings(hidden['memory'], read_keys, read_strengths)
  
      hidden['read_weights'] = self.read_weightings(
          hidden['memory'],
          content_weights,
          hidden['link_matrix'],
          read_modes,
          hidden['read_weights']
      )
      read_vectors = self.read_vectors(hidden['memory'], hidden['read_weights'])
      return read_vectors, hidden
  
    def forward(self, ξ, hidden):
  
      # ξ = ξ.detach()
      m = self.mem_size
      w = self.cell_size
      r = self.read_heads
      b = ξ.size()[0]
  
      if self.independent_linears:
        # r read keys (b * r * w)
        read_keys = F.tanh(self.read_keys_transform(ξ).view(b, r, w))
        # r read strengths (b * r)
        read_strengths = F.softplus(self.read_strengths_transform(ξ).view(b, r))
        # write key (b * 1 * w)
        write_key = F.tanh(self.write_key_transform(ξ).view(b, 1, w))
        # write strength (b * 1)
        write_strength = F.softplus(self.write_strength_transform(ξ).view(b, 1))
        # erase vector (b * 1 * w)
        erase_vector = F.sigmoid(self.erase_vector_transform(ξ).view(b, 1, w))
        # write vector (b * 1 * w)
        write_vector = F.tanh(self.write_vector_transform(ξ).view(b, 1, w))
        # r free gates (b * r)
        free_gates = F.sigmoid(self.free_gates_transform(ξ).view(b, r))
        # allocation gate (b * 1)
        allocation_gate = F.sigmoid(self.allocation_gate_transform(ξ).view(b, 1))
        # write gate (b * 1)
        write_gate = F.sigmoid(self.write_gate_transform(ξ).view(b, 1))
        # read modes (b * r * 3)
        read_modes = σ(self.read_modes_transform(ξ).view(b, r, 3), 1)
      else:
        ξ = self.interface_weights(ξ)
        # r read keys (b * w * r)
        read_keys = F.tanh(ξ[:, :r * w].contiguous().view(b, r, w))
        # r read strengths (b * r)
        read_strengths = F.softplus(ξ[:, r * w:r * w + r].contiguous().view(b, r))
        # write key (b * w * 1)
        write_key = F.tanh(ξ[:, r * w + r:r * w + r + w].contiguous().view(b, 1, w))
        # write strength (b * 1)
        write_strength = F.softplus(ξ[:, r * w + r + w].contiguous().view(b, 1))
        # erase vector (b * w)
        erase_vector = F.sigmoid(ξ[:, r * w + r + w + 1: r * w + r + 2 * w + 1].contiguous().view(b, 1, w))
        # write vector (b * w)
        write_vector = F.tanh(ξ[:, r * w + r + 2 * w + 1: r * w + r + 3 * w + 1].contiguous().view(b, 1, w))
        # r free gates (b * r)
        free_gates = F.sigmoid(ξ[:, r * w + r + 3 * w + 1: r * w + 2 * r + 3 * w + 1].contiguous().view(b, r))
        # allocation gate (b * 1)
        allocation_gate = F.sigmoid(ξ[:, r * w + 2 * r + 3 * w + 1].contiguous().unsqueeze(1).view(b, 1))
        # write gate (b * 1)
        write_gate = F.sigmoid(ξ[:, r * w + 2 * r + 3 * w + 2].contiguous()).unsqueeze(1).view(b, 1)
        # read modes (b * 3*r)
        read_modes = σ(ξ[:, r * w + 2 * r + 3 * w + 3: r * w + 5 * r + 3 * w + 3].contiguous().view(b, r, 3), 1)
  
      hidden = self.write(write_key, write_vector, erase_vector, free_gates,
                          read_strengths, write_strength, write_gate, allocation_gate, hidden)
      return self.read(read_keys, read_strengths, read_modes, hidden)
  