Python math_ops.rsqrt函数代码示例

  def _apply_noisy_update(self, mom, grad):
    # Compute and apply the gradient update following
    # preconditioned Langevin dynamics
    stddev = array_ops.where(
        array_ops.squeeze(self._counter > self._burnin),
        math_ops.cast(math_ops.rsqrt(self._learning_rate), grad.dtype),
        array_ops.zeros([], grad.dtype))

    preconditioner = math_ops.rsqrt(
        mom + math_ops.cast(self._diagonal_bias, grad.dtype))
    return (
        0.5 * preconditioner * grad * math_ops.cast(self._num_pseudo_batches,
                                                    grad.dtype) +
        random_ops.random_normal(array_ops.shape(grad), 1.0, dtype=grad.dtype) *
        stddev * math_ops.sqrt(preconditioner))

 def _batch_norm(self, x, mean, var, offset, scale, epsilon):
   # We compute the batch norm manually in this function because
   # nn_impl.batch_normalization does not support float16 yet.
   # TODO(reedwm): Add float16 support to nn_impl.batch_normalization.
   inv = math_ops.rsqrt(var + epsilon) * scale
   y = math_ops.cast(x, scale.dtype) * inv + (offset - mean * inv)
   return math_ops.cast(y, x.dtype)

def clip_by_norm(t, clip_norm, name=None):
  """Clips tensor values to a maximum L2-norm.

  Given a tensor `t`, and a maximum clip value `clip_norm`, this operation
  normalizes `t` so that its L2-norm is less than or equal to `clip_norm'.
  Specifically, if the L2-norm is already less than or equal to `clip_norm`,
  then `t` is not modified. If the L2-norm is greater than `clip_norm`, then
  this operation returns a tensor of the same type and shape as `t` with its
  values set to:

  `t * clip_norm / l2norm(t)`

  In this case, the L2-norm of the output tensor is `clip_norm`.

  This operation is typically used to clip gradients before applying them with
  an optimizer.

  Args:
    t: A `Tensor`.
    clip_norm: A 0-D (scalar) `Tensor` > 0. A maximum clipping value.
    name: A name for the operation (optional).

  Returns:
    A clipped `Tensor`.
  """
  with ops.op_scope([t, clip_norm], name, "clip_by_norm") as name:
    t = ops.convert_to_tensor(t, name="t")

    # Calculate L2-norm, clip elements by ratio of clip_norm to L2-norm
    l2norm_inv = math_ops.rsqrt(
        math_ops.reduce_sum(t * t, math_ops.range(array_ops.rank(t))))
    tclip = array_ops.identity(t * clip_norm * math_ops.minimum(
        l2norm_inv, constant_op.constant(1.0 / clip_norm)), name=name)

  return tclip

def l2_normalize(x, dim, epsilon=1e-12, name=None):
  """Normalizes along dimension `dim` using an L2 norm.

  For a 1-D tensor with `dim = 0`, computes

      output = x / sqrt(max(sum(x**2), epsilon))

  For `x` with more dimensions, independently normalizes each 1-D slice along
  dimension `dim`.

  Args:
    x: A `Tensor`.
    dim: Dimension along which to normalize.
    epsilon: A lower bound value for the norm. Will use `sqrt(epsilon)` as the
      divisor if `norm < sqrt(epsilon)`.
    name: A name for this operation (optional).

  Returns:
    A `Tensor` with the same shape as `x`.
  """
  with ops.op_scope([x], name, "l2_normalize") as name:
    x = ops.convert_to_tensor(x, name="x")
    square_sum = math_ops.reduce_sum(math_ops.square(x), [dim], keep_dims=True)
    x_inv_norm = math_ops.rsqrt(math_ops.maximum(square_sum, epsilon))
    return math_ops.mul(x, x_inv_norm, name=name)

 def _opsBatchNorm(self, x, m, v, beta, gamma, epsilon,
                   scale_after_normalization):
   y = (x - m) * math_ops.rsqrt(v + epsilon)
   if scale_after_normalization:
     y = gamma * y
   y += beta
   return y

def _sliced_wasserstein(a, b, random_sampling_count, random_projection_dim):
  """Compute the approximate sliced Wasserstein distance.

  Args:
      a: (matrix) Distribution "a" of samples (row, col).
      b: (matrix) Distribution "b" of samples (row, col).
      random_sampling_count: (int) Number of random projections to average.
      random_projection_dim: (int) Dimension of the random projection space.
  Returns:
      Float containing the approximate distance between "a" and "b".
  """
  s = array_ops.shape(a)
  means = []
  for _ in range(random_sampling_count):
    # Random projection matrix.
    proj = random_ops.random_normal(
        [array_ops.shape(a)[1], random_projection_dim])
    proj *= math_ops.rsqrt(
        math_ops.reduce_sum(math_ops.square(proj), 0, keepdims=True))
    # Project both distributions and sort them.
    proj_a = math_ops.matmul(a, proj)
    proj_b = math_ops.matmul(b, proj)
    proj_a = _sort_rows(proj_a, s[0])
    proj_b = _sort_rows(proj_b, s[0])
    # Pairwise Wasserstein distance.
    wdist = math_ops.reduce_mean(math_ops.abs(proj_a - proj_b))
    means.append(wdist)
  return math_ops.reduce_mean(means)

def _FoldFusedBatchNorms(graph):
  """Finds fused batch norm layers and folds them into preceding layers.

  Folding only affects the following layers: Conv2D, fully connected, depthwise
  convolution.

  Args:
    graph: Graph to walk and modify.

  Raises:
    ValueError: When batch norm folding fails.
  """
  for match in _FindFusedBatchNorms(graph):
    scope, sep, _ = match.layer_op.name.rpartition('/')
    # Make sure new ops are added to `graph` and put on the same device as
    # `bn_op`. The '/' (i.e. `sep`) ensures that we reuse the existing scope
    # named `scope`. Otherwise, TF creates a unique scope whose name starts with
    # `scope`.
    with graph.as_default(), graph.name_scope(scope + sep), ops.device(
        match.bn_op.device):
      with graph.name_scope(scope + sep + 'BatchNorm_Fold' + sep):
        # new weights = old weights * gamma / sqrt(variance + epsilon)
        # new biases = -mean * gamma / sqrt(variance + epsilon) + beta
        multiplier_tensor = match.gamma_tensor * math_ops.rsqrt(
            match.variance_tensor + match.bn_op.get_attr('epsilon'))
        bias_tensor = math_ops.subtract(
            match.beta_tensor,
            match.mean_tensor * multiplier_tensor,
            name='bias')

        # The shape of depthwise weights is different, so we need to reshape the
        # multiplier_tensor to ensure that the scaled_weight_tensor has the
        # expected shape.
        if match.layer_op.type == 'DepthwiseConv2dNative':
          new_shape = [
              match.weight_tensor.get_shape().as_list()[2],
              match.weight_tensor.get_shape().as_list()[3]
          ]
          multiplier_tensor = array_ops.reshape(
              multiplier_tensor, new_shape, name='scale_reshape')

      # TODO(suharshs): This naming of the following ops needs to carefully
      # follow the naming expected by quantize.py. Generalize the quantize code
      # to not require these delicate naming conventions.
      scaled_weight_tensor = math_ops.multiply(
          match.weight_tensor, multiplier_tensor, name='mul_fold')

      new_layer_tensor = _CloneWithNewOperands(
          match.layer_op, match.input_tensor, scaled_weight_tensor)

      bias_add_tensor = math_ops.add(
          new_layer_tensor, bias_tensor, name='add_fold')

      nodes_modified_count = graph_editor.reroute_ts(bias_add_tensor,
                                                     match.output_tensor)
      if nodes_modified_count != 1:
        raise ValueError(
            'Unexpected inputs to op: %s' % match.output_tensor.name)

def dct(input, type=2, n=None, axis=-1, norm=None, name=None):  # pylint: disable=redefined-builtin
  """Computes the 1D [Discrete Cosine Transform (DCT)][dct] of `input`.

  Currently only Type II is supported. Implemented using a length `2N` padded
  @{tf.spectral.rfft}, as described here: https://dsp.stackexchange.com/a/10606

  @compatibility(scipy)
  Equivalent to scipy.fftpack.dct for the Type-II DCT.
  https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.fftpack.dct.html
  @end_compatibility

  Args:
    input: A `[..., samples]` `float32` `Tensor` containing the signals to
      take the DCT of.
    type: The DCT type to perform. Must be 2.
    n: For future expansion. The length of the transform. Must be `None`.
    axis: For future expansion. The axis to compute the DCT along. Must be `-1`.
    norm: The normalization to apply. `None` for no normalization or `'ortho'`
      for orthonormal normalization.
    name: An optional name for the operation.

  Returns:
    A `[..., samples]` `float32` `Tensor` containing the DCT of `input`.

  Raises:
    ValueError: If `type` is not `2`, `n` is not `None, `axis` is not `-1`, or
      `norm` is not `None` or `'ortho'`.

  [dct]: https://en.wikipedia.org/wiki/Discrete_cosine_transform
  """
  _validate_dct_arguments(type, n, axis, norm)
  with _ops.name_scope(name, "dct", [input]):
    # We use the RFFT to compute the DCT and TensorFlow only supports float32
    # for FFTs at the moment.
    input = _ops.convert_to_tensor(input, dtype=_dtypes.float32)

    axis_dim = input.shape[-1].value or _array_ops.shape(input)[-1]
    axis_dim_float = _math_ops.to_float(axis_dim)
    scale = 2.0 * _math_ops.exp(_math_ops.complex(
        0.0, -_math.pi * _math_ops.range(axis_dim_float) /
        (2.0 * axis_dim_float)))

    # TODO(rjryan): Benchmark performance and memory usage of the various
    # approaches to computing a DCT via the RFFT.
    dct2 = _math_ops.real(
        rfft(input, fft_length=[2 * axis_dim])[..., :axis_dim] * scale)

    if norm == "ortho":
      n1 = 0.5 * _math_ops.rsqrt(axis_dim_float)
      n2 = n1 * _math_ops.sqrt(2.0)
      # Use tf.pad to make a vector of [n1, n2, n2, n2, ...].
      weights = _array_ops.pad(
          _array_ops.expand_dims(n1, 0), [[0, axis_dim - 1]],
          constant_values=n2)
      dct2 *= weights

    return dct2

def _FusedBatchNormGrad(op, *grad):
  """Return the gradients for the 3 inputs of BatchNorm.

  Args:
    op: The BatchNormOp for which we need to compute gradients.
    *grad: An argument list for tensors of gradients wrt the outputs
          with grad[0] as grad_y.

  Returns:
    grad_x: gradient for x, which is scale * rsqrt(variance + epsilon) *
            [grad_y - mean(grad_y) - (x - mean(x)) *
            mean(grad_y * (x - mean(x))) / (variance + epsilon)]
            in training mode; grad_y * scale * rsqrt(pop_variance + epsilon)
            in freeze mode.

    grad_scale: gradient for scale, which is sum(grad_y * (x - mean(x)) *
                rsqrt(variance + epsilon)) in training mode;
                sum(grad_y * (x - pop_mean) * rsqrt(pop_variance + epsilon))
                in freeze mode.

    grad_offset: gradient for offset, which is sum(grad_y) in training mode;
                 sum(grad_y) in freeze mode.
  """
  x = op.inputs[0]
  grad_y = grad[0]
  scale = op.inputs[1]
  epsilon = op.get_attr("epsilon")
  data_format = op.get_attr("data_format")
  is_training = op.get_attr("is_training")
  if is_training:
    return gen_nn_ops.fused_batch_norm_grad(
        grad_y,
        x,
        scale,
        op.outputs[3],
        op.outputs[4],
        epsilon=epsilon,
        data_format=data_format,
        is_training=is_training)
  else:
    pop_mean = op.inputs[3]
    pop_var = op.inputs[4]
    if data_format == b"NHWC":
      reduce_axis = [0, 1, 2]
    else:
      reduce_axis = [0, 2, 3]
      shape = [1, array_ops.size(pop_mean), 1, 1]
      pop_mean = array_ops.reshape(pop_mean, shape)
      pop_var = array_ops.reshape(pop_var, shape)
      scale = array_ops.reshape(scale, shape)

    grad_offset = math_ops.reduce_sum(grad_y, axis=reduce_axis)
    var_rsqrt = math_ops.rsqrt(pop_var + epsilon)
    grad_scale = math_ops.reduce_sum(
        grad_y * (x - pop_mean) * var_rsqrt, axis=reduce_axis)
    grad_x = grad_y * scale * var_rsqrt
    return grad_x, grad_scale, grad_offset, None, None

def batch_normalization(x,
                        mean,
                        variance,
                        offset,
                        scale,
                        variance_epsilon,
                        name=None):
  r"""Batch normalization.

  As described in http://arxiv.org/abs/1502.03167.
  Normalizes a tensor by `mean` and `variance`, and applies (optionally) a
  `scale` \\(\gamma\\) to it, as well as an `offset` \\(\beta\\):

  \\(\frac{\gamma(x-\mu)}{\sigma}+\beta\\)

  `mean`, `variance`, `offset` and `scale` are all expected to be of one of two
  shapes:

    * In all generality, they can have the same number of dimensions as the
      input `x`, with identical sizes as `x` for the dimensions that are not
      normalized over (the 'depth' dimension(s)), and dimension 1 for the
      others which are being normalized over.
      `mean` and `variance` in this case would typically be the outputs of
      `tf.nn.moments(..., keep_dims=True)` during training, or running averages
      thereof during inference.
    * In the common case where the 'depth' dimension is the last dimension in
      the input tensor `x`, they may be one dimensional tensors of the same
      size as the 'depth' dimension.
      This is the case for example for the common `[batch, depth]` layout of
      fully-connected layers, and `[batch, height, width, depth]` for
      convolutions.
      `mean` and `variance` in this case would typically be the outputs of
      `tf.nn.moments(..., keep_dims=False)` during training, or running averages
      thereof during inference.

  Args:
    x: Input `Tensor` of arbitrary dimensionality.
    mean: A mean `Tensor`.
    variance: A variance `Tensor`.
    offset: An offset `Tensor`, often denoted \\(\beta\\) in equations, or
      None. If present, will be added to the normalized tensor.
    scale: A scale `Tensor`, often denoted \\(\gamma\\) in equations, or
      `None`. If present, the scale is applied to the normalized tensor.
    variance_epsilon: A small float number to avoid dividing by 0.
    name: A name for this operation (optional).

  Returns:
    the normalized, scaled, offset tensor.
  """
  with ops.name_scope(name, "batchnorm", [x, mean, variance, scale, offset]):
    inv = math_ops.rsqrt(variance + variance_epsilon)
    if scale is not None:
      inv *= scale
    return x * inv + (offset - mean * inv
                      if offset is not None else -mean * inv)

def _BatchNormGrad(grad_y, x, scale, epsilon, data_format):
  """Returns the gradients for the 3 inputs of BatchNorm.

  Args:
    grad_y: A `Tensor` of 4 dimensions for gradient for y.
    x: A `Tensor` of 4 dimensions for x.
    scale: A `Tensor` of 1 dimension for scaling.
    epsilon: A small float number added to the variance of x.
    data_format: The data format for input. Either b"NHWC" or b"NCHW".

  Returns:
    A tuple (grad_x, grad_scale, grad_offset), where grad_x is the gradient
    for x, grad_scale the gradient for scale, and grad_offset the gradient
    for offset.
  """
  if data_format == b"NHWC":
    keep_dims = False
    reduce_axis = [0, 1, 2]
  else:
    keep_dims = True
    reduce_axis = [0, 2, 3]
    shape = [1, array_ops.size(scale), 1, 1]
    scale = array_ops.reshape(scale, shape)
  mean_grad_y = math_ops.reduce_mean(grad_y, reduce_axis, keep_dims=keep_dims)
  mean_x = math_ops.reduce_mean(x, reduce_axis, keep_dims=keep_dims)
  var_x = math_ops.reduce_mean(
      math_ops.squared_difference(x, array_ops.stop_gradient(mean_x)),
      reduce_axis,
      keep_dims=keep_dims)
  grad_y_offset = grad_y - mean_grad_y
  x_offset = x - mean_x
  mean = math_ops.reduce_mean(
      grad_y * x_offset, axis=reduce_axis, keep_dims=keep_dims)
  grad_x = scale * math_ops.rsqrt(var_x + epsilon) * (
      grad_y_offset - math_ops.reciprocal(var_x + epsilon) * mean * x_offset)
  grad_scale = math_ops.rsqrt(var_x + epsilon) * math_ops.reduce_sum(
      grad_y * x_offset, axis=reduce_axis, keep_dims=keep_dims)
  if data_format == b"NCHW":
    grad_scale = array_ops.squeeze(grad_scale)
  grad_offset = math_ops.reduce_sum(grad_y, axis=reduce_axis)
  return grad_x, grad_scale, grad_offset

def _bahdanau_score(processed_query, keys, normalize):
  """Implements Bahdanau-style (additive) scoring function.

  This attention has two forms.  The first is Bhandanau attention,
  as described in:

  Dzmitry Bahdanau, Kyunghyun Cho, Yoshua Bengio.
  "Neural Machine Translation by Jointly Learning to Align and Translate."
  ICLR 2015. https://arxiv.org/abs/1409.0473

  The second is the normalized form.  This form is inspired by the
  weight normalization article:

  Tim Salimans, Diederik P. Kingma.
  "Weight Normalization: A Simple Reparameterization to Accelerate
   Training of Deep Neural Networks."
  https://arxiv.org/abs/1602.07868

  To enable the second form, set `normalize=True`.

  Args:
    processed_query: Tensor, shape `[batch_size, num_units]` to compare to keys.
    keys: Processed memory, shape `[batch_size, max_time, num_units]`.
    normalize: Whether to normalize the score function.

  Returns:
    A `[batch_size, max_time]` tensor of unnormalized score values.
  """
  dtype = processed_query.dtype
  # Get the number of hidden units from the trailing dimension of keys
  num_units = keys.shape[2].value or array_ops.shape(keys)[2]
  # Reshape from [batch_size, ...] to [batch_size, 1, ...] for broadcasting.
  processed_query = array_ops.expand_dims(processed_query, 1)
  v = variable_scope.get_variable(
      "attention_v", [num_units], dtype=dtype)
  if normalize:
    # Scalar used in weight normalization
    g = variable_scope.get_variable(
        "attention_g", dtype=dtype,
        initializer=math.sqrt((1. / num_units)))
    # Bias added prior to the nonlinearity
    b = variable_scope.get_variable(
        "attention_b", [num_units], dtype=dtype,
        initializer=init_ops.zeros_initializer())
    # normed_v = g * v / ||v||
    normed_v = g * v * math_ops.rsqrt(
        math_ops.reduce_sum(math_ops.square(v)))
    return math_ops.reduce_sum(
        normed_v * math_ops.tanh(keys + processed_query + b), [2])
  else:
    return math_ops.reduce_sum(v * math_ops.tanh(keys + processed_query), [2])

def clip_by_norm(t, clip_norm, axes=None, name=None):
  """Clips tensor values to a maximum L2-norm.

  Given a tensor `t`, and a maximum clip value `clip_norm`, this operation
  normalizes `t` so that its L2-norm is less than or equal to `clip_norm`,
  along the dimensions given in `axes`. Specifically, in the default case
  where all dimensions are used for calculation, if the L2-norm of `t` is
  already less than or equal to `clip_norm`, then `t` is not modified. If
  the L2-norm is greater than `clip_norm`, then this operation returns a
  tensor of the same type and shape as `t` with its values set to:

  `t * clip_norm / l2norm(t)`

  In this case, the L2-norm of the output tensor is `clip_norm`.

  As another example, if `t` is a matrix and `axes == [1]`, then each row
  of the output will have L2-norm equal to `clip_norm`. If `axes == [0]`
  instead, each column of the output will be clipped.

  This operation is typically used to clip gradients before applying them with
  an optimizer.

  Args:
    t: A `Tensor`.
    clip_norm: A 0-D (scalar) `Tensor` > 0. A maximum clipping value.
    axes: A 1-D (vector) `Tensor` of type int32 containing the dimensions
      to use for computing the L2-norm. If `None` (the default), uses all
      dimensions.
    name: A name for the operation (optional).

  Returns:
    A clipped `Tensor`.
  """
  with ops.name_scope(name, "clip_by_norm", [t, clip_norm]) as name:
    t = ops.convert_to_tensor(t, name="t")

    # Calculate L2-norm, clip elements by ratio of clip_norm to L2-norm
    l2norm_inv = math_ops.rsqrt(
        math_ops.reduce_sum(t * t, axes, keep_dims=True))
    intermediate = t * clip_norm
    # Assert that the shape is compatible with the initial shape,
    # to prevent unintentional broadcasting.
    _ = t.shape.merge_with(intermediate.shape)
    tclip = array_ops.identity(intermediate * math_ops.minimum(
        l2norm_inv, constant_op.constant(1.0, dtype=t.dtype) / clip_norm),
                               name=name)

  return tclip

def batch_normalization(x, mean, variance, offset, scale, variance_epsilon, data_format, name=None):
    """Data Format aware version of tf.nn.batch_normalization."""
    with ops.name_scope(name, 'batchnorm', [x, mean, variance, scale, offset]):
        inv = math_ops.rsqrt(variance + variance_epsilon)
        if scale is not None:
            inv *= scale

        a = math_ops.cast(inv, x.dtype)
        b = math_ops.cast(offset - mean * inv if offset is not None else -mean * inv, x.dtype)

        # Return a * x + b with customized data_format.
        # Currently TF doesn't have bias_scale, and tensorRT has bug in converting tf.nn.bias_add
        # So we reimplemted them to allow make the model work with tensorRT.
        # See https://github.com/tensorlayer/openpose-plus/issues/75 for more details.
        df = {'channels_first': 'NCHW', 'channels_last': 'NHWC'}
        return _bias_add(_bias_scale(x, a, df[data_format]), b, df[data_format])

 def _sample_n(self, n, seed=None):
   # The sampling method comes from the fact that if:
   #   X ~ Normal(0, 1)
   #   Z ~ Chi2(df)
   #   Y = X / sqrt(Z / df)
   # then:
   #   Y ~ StudentT(df).
   shape = array_ops.concat([[n], self.batch_shape_tensor()], 0)
   normal_sample = random_ops.random_normal(shape, dtype=self.dtype, seed=seed)
   df = self.df * array_ops.ones(self.batch_shape_tensor(), dtype=self.dtype)
   gamma_sample = random_ops.random_gamma(
       [n],
       0.5 * df,
       beta=0.5,
       dtype=self.dtype,
       seed=distribution_util.gen_new_seed(seed, salt="student_t"))
   samples = normal_sample * math_ops.rsqrt(gamma_sample / df)
   return samples * self.scale + self.loc  # Abs(scale) not wanted.