Python tensorflow.python.ops.array_ops.one_hot() Examples

def hardmax(logits, name=None):
  """Returns batched one-hot vectors.

  The depth index containing the `1` is that of the maximum logit value.

  Args:
    logits: A batch tensor of logit values.
    name: Name to use when creating ops.
  Returns:
    A batched one-hot tensor.
  """
  with ops.name_scope(name, "Hardmax", [logits]):
    logits = ops.convert_to_tensor(logits, name="logits")
    if logits.get_shape()[-1].value is not None:
      depth = logits.get_shape()[-1].value
    else:
      depth = array_ops.shape(logits)[-1]
    return array_ops.one_hot(
        math_ops.argmax(logits, -1), depth, dtype=logits.dtype) 

def _estimate_data_distribution(c, num_examples_per_class_seen):
  """Estimate data distribution as labels are seen.

  Args:
    c: The class labels.  Type `int32`, shape `[batch_size]`.
    num_examples_per_class_seen: A `ResourceVariable` containing counts.
      Type `int64`, shape `[num_classes]`.

  Returns:
    dist: The updated distribution.  Type `float32`, shape `[num_classes]`.
  """
  num_classes = num_examples_per_class_seen.get_shape()[0].value
  # Update the class-count based on what labels are seen in
  # batch.  But do this asynchronously to avoid performing a
  # cross-device round-trip.  Just use the cached value.
  num_examples_per_class_seen = num_examples_per_class_seen.assign_add(
      math_ops.reduce_sum(
          array_ops.one_hot(c, num_classes, dtype=dtypes.int64),
          0))
  init_prob_estimate = math_ops.truediv(
      num_examples_per_class_seen,
      math_ops.reduce_sum(num_examples_per_class_seen))
  return math_ops.cast(init_prob_estimate, dtypes.float32) 

def hardmax(logits, name=None):
  """Returns batched one-hot vectors.

  The depth index containing the `1` is that of the maximum logit value.

  Args:
    logits: A batch tensor of logit values.
    name: Name to use when creating ops.
  Returns:
    A batched one-hot tensor.
  """
  with ops.name_scope(name, "Hardmax", [logits]):
    logits = ops.convert_to_tensor(logits, name="logits")
    if logits.get_shape()[-1].value is not None:
      depth = logits.get_shape()[-1].value
    else:
      depth = array_ops.shape(logits)[-1]
    return array_ops.one_hot(
        math_ops.argmax(logits, -1), depth, dtype=logits.dtype) 

def initial_alignments(self, batch_size, dtype):
    """Creates the initial alignment values for the monotonic attentions.

    Initializes to dirac distributions, i.e. [1, 0, 0, ...memory length..., 0]
    for all entries in the batch.

    Args:
      batch_size: `int32` scalar, the batch_size.
      dtype: The `dtype`.

    Returns:
      A `dtype` tensor shaped `[batch_size, alignments_size]`
      (`alignments_size` is the values' `max_time`).
    """
    max_time = self._alignments_size
    return array_ops.one_hot(
        array_ops.zeros((batch_size,), dtype=dtypes.int32), max_time,
        dtype=dtype) 

def hardmax(logits, name=None):
  """Returns batched one-hot vectors.

  The depth index containing the `1` is that of the maximum logit value.

  Args:
    logits: A batch tensor of logit values.
    name: Name to use when creating ops.
  Returns:
    A batched one-hot tensor.
  """
  with ops.name_scope(name, "Hardmax", [logits]):
    logits = ops.convert_to_tensor(logits, name="logits")
    if logits.get_shape()[-1].value is not None:
      depth = logits.get_shape()[-1].value
    else:
      depth = array_ops.shape(logits)[-1]
    return array_ops.one_hot(
        math_ops.argmax(logits, -1), depth, dtype=logits.dtype) 

def one_hot(indices, num_classes):
  """Computes the one-hot representation of an integer tensor.

  Arguments:
      indices: nD integer tensor of shape
          `(batch_size, dim1, dim2, ... dim(n-1))`
      num_classes: Integer, number of classes to consider.

  Returns:
      (n + 1)D one hot representation of the input
      with shape `(batch_size, dim1, dim2, ... dim(n-1), num_classes)`

  Returns:
      The one-hot tensor.
  """
  return array_ops.one_hot(indices, depth=num_classes, axis=-1) 

def _sample_n(self, n, seed=None):
    n_draws = math_ops.cast(self.n, dtype=dtypes.int32)
    if self.n.get_shape().ndims is not None:
      if self.n.get_shape().ndims != 0:
        raise NotImplementedError(
            "Sample only supported for scalar number of draws.")
    elif self.validate_args:
      is_scalar = check_ops.assert_rank(
          n_draws, 0,
          message="Sample only supported for scalar number of draws.")
      n_draws = control_flow_ops.with_dependencies([is_scalar], n_draws)
    k = self.event_shape()[0]
    # Flatten batch dims so logits has shape [B, k],
    # where B = reduce_prod(self.batch_shape()).
    logits = array_ops.reshape(self.logits, [-1, k])
    draws = random_ops.multinomial(logits=logits,
                                   num_samples=n * n_draws,
                                   seed=seed)
    draws = array_ops.reshape(draws, shape=[-1, n, n_draws])
    x = math_ops.reduce_sum(array_ops.one_hot(draws, depth=k),
                            reduction_indices=-2)  # shape: [B, n, k]
    x = array_ops.transpose(x, perm=[1, 0, 2])
    final_shape = array_ops.concat([[n], self.batch_shape(), [k]], 0)
    return array_ops.reshape(x, final_shape) 

def _sample_n(self, n, seed=None):
    n_draws = math_ops.cast(self.total_count, dtype=dtypes.int32)
    if self.total_count.get_shape().ndims is not None:
      if self.total_count.get_shape().ndims != 0:
        raise NotImplementedError(
            "Sample only supported for scalar number of draws.")
    elif self.validate_args:
      is_scalar = check_ops.assert_rank(
          n_draws, 0,
          message="Sample only supported for scalar number of draws.")
      n_draws = control_flow_ops.with_dependencies([is_scalar], n_draws)
    k = self.event_shape_tensor()[0]
    # Flatten batch dims so logits has shape [B, k],
    # where B = reduce_prod(self.batch_shape_tensor()).
    x = random_ops.multinomial(
        logits=array_ops.reshape(self.logits, [-1, k]),
        num_samples=n * n_draws,
        seed=seed)
    x = array_ops.reshape(x, shape=[-1, n, n_draws])
    x = math_ops.reduce_sum(array_ops.one_hot(x, depth=k),
                            axis=-2)  # shape: [B, n, k]
    x = array_ops.transpose(x, perm=[1, 0, 2])
    final_shape = array_ops.concat([[n], self.batch_shape_tensor(), [k]], 0)
    x = array_ops.reshape(x, final_shape)
    return math_ops.cast(x, self.dtype) 

def _sample_n(self, n, seed=None):
    n_draws = math_ops.cast(self.total_count, dtype=dtypes.int32)
    k = self.event_shape_tensor()[0]
    unnormalized_logits = array_ops.reshape(
        math_ops.log(random_ops.random_gamma(
            shape=[n],
            alpha=self.concentration,
            dtype=self.dtype,
            seed=seed)),
        shape=[-1, k])
    draws = random_ops.multinomial(
        logits=unnormalized_logits,
        num_samples=n_draws,
        seed=distribution_util.gen_new_seed(seed, salt="dirichlet_multinomial"))
    x = math_ops.reduce_sum(array_ops.one_hot(draws, depth=k), -2)
    final_shape = array_ops.concat([[n], self.batch_shape_tensor(), [k]], 0)
    x = array_ops.reshape(x, final_shape)
    return math_ops.cast(x, self.dtype) 

def one_hot(indices, num_classes):
  """Computes the one-hot representation of an integer tensor.

  Arguments:
      indices: nD integer tensor of shape
          `(batch_size, dim1, dim2, ... dim(n-1))`
      num_classes: Integer, number of classes to consider.

  Returns:
      (n + 1)D one hot representation of the input
      with shape `(batch_size, dim1, dim2, ... dim(n-1), num_classes)`

  Returns:
      The one-hot tensor.
  """
  return array_ops.one_hot(indices, depth=num_classes, axis=-1) 

def _sample_n(self, n, seed=None):
    n_draws = math_ops.cast(self.n, dtype=dtypes.int32)
    if self.n.get_shape().ndims is not None:
      if self.n.get_shape().ndims != 0:
        raise NotImplementedError(
            "Sample only supported for scalar number of draws.")
    elif self.validate_args:
      is_scalar = check_ops.assert_rank(
          n_draws, 0,
          message="Sample only supported for scalar number of draws.")
      n_draws = control_flow_ops.with_dependencies([is_scalar], n_draws)
    k = self.event_shape()[0]
    # Flatten batch dims so logits has shape [B, k],
    # where B = reduce_prod(self.batch_shape()).
    logits = array_ops.reshape(self.logits, [-1, k])
    draws = random_ops.multinomial(logits=logits,
                                   num_samples=n * n_draws,
                                   seed=seed)
    draws = array_ops.reshape(draws, shape=[-1, n, n_draws])
    x = math_ops.reduce_sum(array_ops.one_hot(draws, depth=k),
                            reduction_indices=-2)  # shape: [B, n, k]
    x = array_ops.transpose(x, perm=[1, 0, 2])
    final_shape = array_ops.concat([[n], self.batch_shape(), [k]], 0)
    return array_ops.reshape(x, final_shape) 

def hardmax(logits, name=None):
  """Returns batched one-hot vectors.

  The depth index containing the `1` is that of the maximum logit value.

  Args:
    logits: A batch tensor of logit values.
    name: Name to use when creating ops.
  Returns:
    A batched one-hot tensor.
  """
  with ops.name_scope(name, "Hardmax", [logits]):
    logits = ops.convert_to_tensor(logits, name="logits")
    if logits.get_shape()[-1].value is not None:
      depth = logits.get_shape()[-1].value
    else:
      depth = array_ops.shape(logits)[-1]
    return array_ops.one_hot(
        math_ops.argmax(logits, -1), depth, dtype=logits.dtype) 

def initial_alignments(self, batch_size, dtype):
    """Creates the initial alignment values for the monotonic attentions.

    Initializes to dirac distributions, i.e. [1, 0, 0, ...memory length..., 0]
    for all entries in the batch.

    Args:
      batch_size: `int32` scalar, the batch_size.
      dtype: The `dtype`.

    Returns:
      A `dtype` tensor shaped `[batch_size, alignments_size]`
      (`alignments_size` is the values' `max_time`).
    """
    max_time = self._alignments_size
    return array_ops.one_hot(
        array_ops.zeros((batch_size,), dtype=dtypes.int32), max_time,
        dtype=dtype) 

def one_hot_matrix(tensor_in, num_classes, on_value=1.0, off_value=0.0):
  """Encodes indices from given tensor as one-hot tensor.

  TODO(ilblackdragon): Ideally implementation should be
  part of TensorFlow with Eigen-native operation.

  Args:
    tensor_in: Input tensor of shape [N1, N2].
    num_classes: Number of classes to expand index into.
    on_value: Tensor or float, value to fill-in given index.
    off_value: Tensor or float, value to fill-in everything else.
  Returns:
    Tensor of shape [N1, N2, num_classes] with 1.0 for each id in original
    tensor.
  """
  return array_ops_.one_hot(
      math_ops.cast(tensor_in, dtypes.int64), num_classes, on_value, off_value) 

def hardmax(logits, name=None):
  """Returns batched one-hot vectors.

  The depth index containing the `1` is that of the maximum logit value.

  Args:
    logits: A batch tensor of logit values.
    name: Name to use when creating ops.
  Returns:
    A batched one-hot tensor.
  """
  with ops.name_scope(name, "Hardmax", [logits]):
    logits = ops.convert_to_tensor(logits, name="logits")
    if logits.get_shape()[-1].value is not None:
      depth = logits.get_shape()[-1].value
    else:
      depth = array_ops.shape(logits)[-1]
    return array_ops.one_hot(
        math_ops.argmax(logits, -1), depth, dtype=logits.dtype
    ) 

def initial_alignments(self, batch_size, dtype):
    """Creates the initial alignment values for the monotonic attentions.

    Initializes to dirac distributions, i.e. [1, 0, 0, ...memory length..., 0]
    for all entries in the batch.

    Args:
      batch_size: `int32` scalar, the batch_size.
      dtype: The `dtype`.

    Returns:
      A `dtype` tensor shaped `[batch_size, alignments_size]`
      (`alignments_size` is the values' `max_time`).
    """
    max_time = self._alignments_size
    return array_ops.one_hot(
        array_ops.zeros((batch_size,), dtype=dtypes.int32),
        max_time,
        dtype=dtype
    ) 

def hardmax(logits, name=None):
  """Returns batched one-hot vectors.

  The depth index containing the `1` is that of the maximum logit value.

  Args:
    logits: A batch tensor of logit values.
    name: Name to use when creating ops.
  Returns:
    A batched one-hot tensor.
  """
  with ops.name_scope(name, "Hardmax", [logits]):
    logits = ops.convert_to_tensor(logits, name="logits")
    if logits.get_shape()[-1].value is not None:
      depth = logits.get_shape()[-1].value
    else:
      depth = array_ops.shape(logits)[-1]
    return array_ops.one_hot(
        math_ops.argmax(logits, -1), depth, dtype=logits.dtype) 

def _get_eval_ops(self, features, targets, metrics):
    features, spec = data_ops.ParseDataTensorOrDict(features)
    labels = data_ops.ParseLabelTensorOrDict(targets)

    graph_builder = self.graph_builder_class(
        self.params, device_assigner=self.device_assigner, training=False,
        **self.construction_args)

    probabilities = graph_builder.inference_graph(features, data_spec=spec)

    # One-hot the labels.
    if not self.params.regression:
      labels = math_ops.to_int64(array_ops.one_hot(math_ops.to_int64(
          array_ops.squeeze(labels)), self.params.num_classes, 1, 0))

    if metrics is None:
      metrics = {self.accuracy_metric:
                 eval_metrics.get_metric(self.accuracy_metric)}

    result = {}
    for name, metric in six.iteritems(metrics):
      result[name] = metric(probabilities, labels)

    return result 

def initial_alignments(self, batch_size, dtype):
        """Creates the initial alignment values for the monotonic attentions.

        Initializes to dirac distributions, i.e. [1, 0, 0, ...memory length..., 0]
        for all entries in the batch.

        Args:
          batch_size: `int32` scalar, the batch_size.
          dtype: The `dtype`.

        Returns:
          A `dtype` tensor shaped `[batch_size, alignments_size]`
          (`alignments_size` is the values' `max_time`).
        """
        max_time = self._alignments_size
        return array_ops.one_hot(
            array_ops.zeros((batch_size,), dtype=dtypes.int32), max_time,
            dtype=dtype) 

def hardmax(logits, name=None):
    """Returns batched one-hot vectors.

    The depth index containing the `1` is that of the maximum logit value.

    Args:
      logits: A batch tensor of logit values.
      name: Name to use when creating ops.
    Returns:
      A batched one-hot tensor.
    """
    with ops.name_scope(name, "Hardmax", [logits]):
        logits = ops.convert_to_tensor(logits, name="logits")
        if logits.get_shape()[-1].value is not None:
            depth = logits.get_shape()[-1].value
        else:
            depth = array_ops.shape(logits)[-1]
        return array_ops.one_hot(
            math_ops.argmax(logits, -1), depth, dtype=logits.dtype) 

def _sample_n(self, n, seed=None):
    n_draws = math_ops.cast(self.total_count, dtype=dtypes.int32)
    if self.total_count.get_shape().ndims is not None:
      if self.total_count.get_shape().ndims != 0:
        raise NotImplementedError(
            "Sample only supported for scalar number of draws.")
    elif self.validate_args:
      is_scalar = check_ops.assert_rank(
          n_draws, 0,
          message="Sample only supported for scalar number of draws.")
      n_draws = control_flow_ops.with_dependencies([is_scalar], n_draws)
    k = self.event_shape_tensor()[0]
    # Flatten batch dims so logits has shape [B, k],
    # where B = reduce_prod(self.batch_shape_tensor()).
    draws = random_ops.multinomial(
        logits=array_ops.reshape(self.logits, [-1, k]),
        num_samples=n * n_draws,
        seed=seed)
    draws = array_ops.reshape(draws, shape=[-1, n, n_draws])
    x = math_ops.reduce_sum(array_ops.one_hot(draws, depth=k),
                            axis=-2)  # shape: [B, n, k]
    x = array_ops.transpose(x, perm=[1, 0, 2])
    final_shape = array_ops.concat([[n], self.batch_shape_tensor(), [k]], 0)
    return array_ops.reshape(x, final_shape) 

def focal_loss(labels, logits, gamma=2.0):
    r"""
    Multi-class focal loss implementation: https://arxiv.org/abs/1708.02002
    :param labels: [batch_size, ] - Tensor of the correct class ids
    :param logits: [batch_size, num_classes] - Unscaled logits
    :param gamma: focal loss weight
    :return: [batch_size, ] - Tensor of average costs for each batch element
    """

    num_classes = array_ops.shape(logits)[1]
    onehot_labels = array_ops.one_hot(labels, num_classes, dtype=logits.dtype)

    p = nn_ops.softmax(logits)
    p = clip_ops.clip_by_value(p, 1e-7, 1.0 - 1e-7)

    f_loss = - onehot_labels * math_ops.pow(1.0 - p, gamma) * math_ops.log(p) \
             - (1 - onehot_labels) * math_ops.pow(p, gamma) * math_ops.log(1.0 - p)

    cost = math_ops.reduce_sum(f_loss, axis=1)
    return cost 

def mc_loss(labels, logits):
    r"""
    A multi-class cross-entropy loss
    :param labels: [batch_size, ] - Tensor of the correct class ids
    :param logits: [batch_size, num_classes] - Unscaled logits
    :return: [batch_size, ] - Tensor of average costs for each batch element
    """

    num_classes = array_ops.shape(logits)[1]
    onehot_labels = array_ops.one_hot(labels, num_classes, dtype=logits.dtype)

    p = nn_ops.softmax(logits)
    p = clip_ops.clip_by_value(p, 1e-7, 1.0 - 1e-7)

    ce_loss = - onehot_labels * math_ops.log(p) - (1 - onehot_labels) * math_ops.log(1.0-p)

    cost = math_ops.reduce_sum(ce_loss, axis=1)
    return cost 

def initial_alignments(self, batch_size, dtype):
    """Creates the initial alignment values for the monotonic attentions.

    Initializes to dirac distributions, i.e. [1, 0, 0, ...memory length..., 0]
    for all entries in the batch.

    Args:
      batch_size: `int32` scalar, the batch_size.
      dtype: The `dtype`.

    Returns:
      A `dtype` tensor shaped `[batch_size, alignments_size]`
      (`alignments_size` is the values' `max_time`).
    """
    max_time = self._alignments_size
    return array_ops.one_hot(
        array_ops.zeros((batch_size,), dtype=dtypes.int32), max_time,
        dtype=dtype) 

def initial_alignments(self, batch_size, dtype):
    """Creates the initial alignment values for the monotonic attentions.

    Initializes to dirac distributions, i.e. [1, 0, 0, ...memory length..., 0]
    for all entries in the batch.

    Args:
      batch_size: `int32` scalar, the batch_size.
      dtype: The `dtype`.

    Returns:
      A `dtype` tensor shaped `[batch_size, alignments_size]`
      (`alignments_size` is the values' `max_time`).
    """
    max_time = self._alignments_size
    return array_ops.one_hot(
        array_ops.zeros((batch_size,), dtype=dtypes.int32), max_time,
        dtype=dtype) 

def _sample_n(self, n, seed=None):
    n_draws = math_ops.cast(self.total_count, dtype=dtypes.int32)
    k = self.event_shape_tensor()[0]
    unnormalized_logits = array_ops.reshape(
        math_ops.log(random_ops.random_gamma(
            shape=[n],
            alpha=self.concentration,
            dtype=self.dtype,
            seed=seed)),
        shape=[-1, k])
    draws = random_ops.multinomial(
        logits=unnormalized_logits,
        num_samples=n_draws,
        seed=distribution_util.gen_new_seed(seed, salt="dirichlet_multinomial"))
    x = math_ops.reduce_sum(array_ops.one_hot(draws, depth=k), -2)
    final_shape = array_ops.concat([[n], self.batch_shape_tensor(), [k]], 0)
    return array_ops.reshape(x, final_shape) 

def _mode(self):
    ret = math_ops.argmax(self.logits, axis=self._batch_rank)
    ret = array_ops.one_hot(ret, self.num_classes, dtype=self.dtype)
    ret.set_shape(self.logits.get_shape())
    return ret 

def _sample_n(self, n, seed=None):
    sample_shape = array_ops.concat(([n], array_ops.shape(self.logits)), 0)
    logits = self.logits
    if logits.get_shape().ndims == 2:
      logits_2d = logits
    else:
      logits_2d = array_ops.reshape(logits, [-1, self.num_classes])
    samples = random_ops.multinomial(logits_2d, n, seed=seed)
    samples = array_ops.transpose(samples)
    samples = array_ops.one_hot(samples, self.num_classes, dtype=self.dtype)
    ret = array_ops.reshape(samples, sample_shape)
    return ret 

def __init__(self, loc, scale, validate_args=False, allow_nan_stats=True, name="von-Mises-Fisher"):
        """Construct von-Mises-Fisher distributions with mean and concentration `loc` and `scale`.

        Args:
          loc: Floating point tensor; the mean of the distribution(s).
          scale: Floating point tensor; the concentration of the distribution(s).
            Must contain only non-negative values.
          validate_args: Python `bool`, default `False`. When `True` distribution
            parameters are checked for validity despite possibly degrading runtime
            performance. When `False` invalid inputs may silently render incorrect
            outputs.
          allow_nan_stats: Python `bool`, default `True`. When `True`,
            statistics (e.g., mean, mode, variance) use the value "`NaN`" to
            indicate the result is undefined. When `False`, an exception is raised
            if one or more of the statistic's batch members are undefined.
          name: Python `str` name prefixed to Ops created by this class.

        Raises:
          TypeError: if `loc` and `scale` have different `dtype`.
        """
        parameters = locals()
        with ops.name_scope(name, values=[loc, scale]):
            with ops.control_dependencies([check_ops.assert_positive(scale),
                                           check_ops.assert_near(linalg_ops.norm(loc, axis=-1), 1, atol=1e-7)]
                                          if validate_args else []):
                self._loc = array_ops.identity(loc, name="loc")
                self._scale = array_ops.identity(scale, name="scale")
                check_ops.assert_same_float_dtype([self._loc, self._scale])

        super(VonMisesFisher, self).__init__(
            dtype=self._scale.dtype,
            reparameterization_type=distribution.FULLY_REPARAMETERIZED,
            validate_args=validate_args,
            allow_nan_stats=allow_nan_stats,
            parameters=parameters,
            graph_parents=[self._loc, self._scale],
            name=name)

        self.__m = math_ops.cast(self._loc.shape[-1], dtypes.int32)
        self.__mf = math_ops.cast(self.__m, dtype=self.dtype)
        self.__e1 = array_ops.one_hot([0], self.__m, dtype=self.dtype) 

def _estimate_data_distribution(labels, num_classes, smoothing_constant=10):
  """Estimate data distribution as labels are seen."""
  # Variable to track running count of classes. Smooth by a nonzero value to
  # avoid division-by-zero. Higher values provide more stability at the cost of
  # slower convergence.
  if smoothing_constant <= 0:
    raise ValueError('smoothing_constant must be nonzero.')
  num_examples_per_class_seen = variables.Variable(
      initial_value=[smoothing_constant] * num_classes,
      trainable=False,
      name='class_count',
      dtype=dtypes.int64)

  # Update the class-count based on what labels are seen in batch.
  num_examples_per_class_seen = num_examples_per_class_seen.assign_add(
      math_ops.reduce_sum(
          array_ops.one_hot(
              labels, num_classes, dtype=dtypes.int64), 0))

  # Normalize count into a probability.
  # NOTE: Without the `+= 0` line below, the test
  # `testMultiThreadedEstimateDataDistribution` fails. The reason is that
  # before this line, `num_examples_per_class_seen` is a Tensor that shares a
  # buffer with an underlying `ref` object. When the `ref` is changed by another
  # thread, `num_examples_per_class_seen` changes as well. Since this can happen
  # in the middle of the normalization computation, we get probabilities that
  # are very far from summing to one. Adding `+= 0` copies the contents of the
  # tensor to a new buffer, which will be consistent from the start to the end
  # of the normalization computation.
  num_examples_per_class_seen += 0
  init_prob_estimate = math_ops.truediv(
      num_examples_per_class_seen,
      math_ops.reduce_sum(num_examples_per_class_seen))

  # Must return float32 (not float64) to agree with downstream `_verify_input`
  # checks.
  return math_ops.cast(init_prob_estimate, dtypes.float32)