Python tensorflow.python.ops.math_ops.reciprocal() Examples

def normalize_moments(counts, mean_ss, variance_ss, shift, name=None):
  """Calculate the mean and variance of based on the sufficient statistics.

  Args:
    counts: A `Tensor` containing a the total count of the data (one value).
    mean_ss: A `Tensor` containing the mean sufficient statistics: the (possibly
      shifted) sum of the elements to average over.
    variance_ss: A `Tensor` containing the variance sufficient statistics: the
      (possibly shifted) squared sum of the data to compute the variance over.
    shift: A `Tensor` containing the value by which the data is shifted for
      numerical stability, or `None` if no shift was performed.
    name: Name used to scope the operations that compute the moments.

  Returns:
    Two `Tensor` objects: `mean` and `variance`.
  """
  with ops.name_scope(name, "normalize", [counts, mean_ss, variance_ss, shift]):
    divisor = math_ops.reciprocal(counts, name="divisor")
    if shift is not None:
      shifted_mean = math_ops.multiply(mean_ss, divisor, name="shifted_mean")
      mean = math_ops.add(shifted_mean, shift, name="mean")
    else:  # no shift.
      shifted_mean = math_ops.multiply(mean_ss, divisor, name="mean")
      mean = shifted_mean
    variance = math_ops.subtract(
        math_ops.multiply(variance_ss, divisor),
        math_ops.square(shifted_mean),
        name="variance")
  return (mean, variance) 

def _LogGrad(op, grad):
  """Returns grad * (1/x)."""
  x = op.inputs[0]
  with ops.control_dependencies([grad]):
    x = math_ops.conj(x)
    return grad * math_ops.reciprocal(x) 

def _Log1pGrad(op, grad):
  """Returns grad * (1/(1 + x))."""
  x = op.inputs[0]
  with ops.control_dependencies([grad]):
    x = math_ops.conj(x)
    return grad * math_ops.reciprocal(1 + x) 

def _AtanhGrad(op, grad):
  """Returns grad * 1/ (1 - x^2)."""
  x = op.inputs[0]
  with ops.control_dependencies([grad]):
    x = math_ops.conj(x)
    x2 = math_ops.square(x)
    one = constant_op.constant(1, dtype=grad.dtype)
    inv = math_ops.reciprocal(math_ops.subtract(one, x2))
    return grad * inv 

def _TanGrad(op, grad):
  """Returns grad * 1/sec^2(x)."""
  x = op.inputs[0]
  with ops.control_dependencies([grad]):
    x = math_ops.conj(x)
    secx = math_ops.reciprocal(math_ops.cos(x))
    secx2 = math_ops.square(secx)
    return grad * secx2 

def _AcosGrad(op, grad):
  """Returns grad * -1/sqrt(1-x^2)."""
  x = op.inputs[0]
  with ops.control_dependencies([grad]):
    x = math_ops.conj(x)
    x2 = math_ops.square(x)
    one = constant_op.constant(1, dtype=grad.dtype)
    den = math_ops.sqrt(math_ops.subtract(one, x2))
    inv = math_ops.reciprocal(den)
    return -grad * inv 

def _AtanGrad(op, grad):
  """Returns grad * 1/ (1 + x^2)."""
  x = op.inputs[0]
  with ops.control_dependencies([grad]):
    x = math_ops.conj(x)
    x2 = math_ops.square(x)
    one = constant_op.constant(1, dtype=grad.dtype)
    inv = math_ops.reciprocal(math_ops.add(one, x2))
    return grad * inv 

def _AngleGrad(op, grad):
  """Returns -grad / (Im(x) + iRe(x))"""
  x = op.inputs[0]
  with ops.control_dependencies([grad]):
    re = math_ops.real(x)
    im = math_ops.imag(x)
    z = math_ops.reciprocal(math_ops.complex(im, re))
    zero = constant_op.constant(0, dtype=grad.dtype)
    complex_grad = math_ops.complex(grad, zero)
    return -complex_grad * z 

def _SelfAdjointEigV2Grad(op, grad_e, grad_v):
  """Gradient for SelfAdjointEigV2."""
  e = op.outputs[0]
  compute_v = op.get_attr("compute_v")
  # a = op.inputs[0], which satisfies
  # a[...,:,:] * v[...,:,i] = e[...,i] * v[...,i]
  with ops.control_dependencies([grad_e, grad_v]):
    if compute_v:
      v = op.outputs[1]
      # Construct the matrix f(i,j) = (i != j ? 1 / (e_i - e_j) : 0).
      # Notice that because of the term involving f, the gradient becomes
      # infinite (or NaN in practice) when eigenvalues are not unique.
      # Mathematically this should not be surprising, since for (k-fold)
      # degenerate eigenvalues, the corresponding eigenvectors are only defined
      # up to arbitrary rotation in a (k-dimensional) subspace.
      f = array_ops.matrix_set_diag(
          math_ops.reciprocal(
              array_ops.expand_dims(e, -2) - array_ops.expand_dims(e, -1)),
          array_ops.zeros_like(e))
      grad_a = math_ops.matmul(
          v,
          math_ops.matmul(
              array_ops.matrix_diag(grad_e) +
              f * math_ops.matmul(v, grad_v, adjoint_a=True),
              v,
              adjoint_b=True))
    else:
      _, v = linalg_ops.self_adjoint_eig(op.inputs[0])
      grad_a = math_ops.matmul(v,
                               math_ops.matmul(
                                   array_ops.matrix_diag(grad_e),
                                   v,
                                   adjoint_b=True))
    # The forward op only depends on the lower triangular part of a, so here we
    # symmetrize and take the lower triangle
    grad_a = array_ops.matrix_band_part(
        grad_a + math_ops.conj(array_ops.matrix_transpose(grad_a)), -1, 0)
    grad_a = array_ops.matrix_set_diag(grad_a,
                                       0.5 * array_ops.matrix_diag_part(grad_a))
    return grad_a 

def _IRFFTGradHelper(rank, rfft_fn):
  """Returns a gradient function for an IRFFT of the provided rank."""
  # Can't happen because we don't register a gradient for IRFFT3D.
  assert rank in (1, 2), "Gradient for IRFFT3D is not implemented."

  def _Grad(op, grad):
    """A gradient function for IRFFT with the provided `rank` and `rfft_fn`."""
    # Generate a simple mask like [1.0, 2.0, ..., 2.0, 1.0] for even-length FFTs
    # and [1.0, 2.0, ..., 2.0] for odd-length FFTs. To reduce extra ops in the
    # graph we special-case the situation where the FFT length and last
    # dimension of the input are known at graph construction time.
    fft_length = op.inputs[1]
    is_odd = math_ops.mod(fft_length[-1], 2)
    input_last_dimension = array_ops.shape(op.inputs[0])[-1]
    mask = array_ops.concat(
        [[1.0], 2.0 * array_ops.ones([input_last_dimension - 2 + is_odd]),
         array_ops.ones([1 - is_odd])], 0)

    rsize = math_ops.reciprocal(math_ops.to_float(_FFTSizeForGrad(grad, rank)))

    # The gradient of IRFFT is the RFFT of the incoming gradient times a scaling
    # factor and a mask. The mask scales the gradient for the Hermitian
    # symmetric components of the RFFT by a factor of two, since these
    # components are de-duplicated in the RFFT.
    rfft = rfft_fn(grad, fft_length)
    return rfft * math_ops.cast(rsize * mask, dtypes.complex64), None

  return _Grad 

def _LogGrad(op, grad):
  """Returns grad * (1/x)."""
  x = op.inputs[0]
  with ops.control_dependencies([grad.op]):
    x = math_ops.conj(x)
    return grad * math_ops.reciprocal(x) 

def _Log1pGrad(op, grad):
  """Returns grad * (1/(1 + x))."""
  x = op.inputs[0]
  with ops.control_dependencies([grad.op]):
    x = math_ops.conj(x)
    return grad * math_ops.reciprocal(1 + x) 

def _TanGrad(op, grad):
  """Returns grad * 1/sec^2(x)."""
  x = op.inputs[0]
  with ops.control_dependencies([grad.op]):
    x = math_ops.conj(x)
    secx = math_ops.reciprocal(math_ops.cos(x))
    secx2 = math_ops.square(secx)
    return grad * secx2 

def _AsinGrad(op, grad):
  """Returns grad * 1/sqrt(1-x^2)."""
  x = op.inputs[0]
  with ops.control_dependencies([grad.op]):
    x = math_ops.conj(x)
    x2 = math_ops.square(x)
    one = constant_op.constant(1, dtype=grad.dtype)
    den = math_ops.sqrt(math_ops.subtract(one, x2))
    inv = math_ops.reciprocal(den)
    return grad * inv 

def _AcosGrad(op, grad):
  """Returns grad * -1/sqrt(1-x^2)."""
  x = op.inputs[0]
  with ops.control_dependencies([grad.op]):
    x = math_ops.conj(x)
    x2 = math_ops.square(x)
    one = constant_op.constant(1, dtype=grad.dtype)
    den = math_ops.sqrt(math_ops.subtract(one, x2))
    inv = math_ops.reciprocal(den)
    return -grad * inv 

def _SelfAdjointEigV2Grad(op, grad_e, grad_v):
  """Gradient for SelfAdjointEigV2."""
  e = op.outputs[0]
  v = op.outputs[1]
  # a = op.inputs[0], which satisfies
  # a[...,:,:] * v[...,:,i] = e[...,i] * v[...,i]
  with ops.control_dependencies([grad_e.op, grad_v.op]):
    if grad_v is not None:
      # Construct the matrix f(i,j) = (i != j ? 1 / (e_i - e_j) : 0).
      # Notice that because of the term involving f, the gradient becomes
      # infinite (or NaN in practice) when eigenvalues are not unique.
      # Mathematically this should not be surprising, since for (k-fold)
      # degenerate eigenvalues, the corresponding eigenvectors are only defined
      # up to arbitrary rotation in a (k-dimensional) subspace.
      f = array_ops.matrix_set_diag(
          math_ops.reciprocal(
              array_ops.expand_dims(e, -2) - array_ops.expand_dims(e, -1)),
          array_ops.zeros_like(e))
      grad_a = math_ops.matmul(
          v,
          math_ops.matmul(
              array_ops.matrix_diag(grad_e) + f * math_ops.matmul(
                  v, grad_v, adjoint_a=True),
              v,
              adjoint_b=True))
    else:
      grad_a = math_ops.matmul(
          v, math_ops.matmul(
              array_ops.matrix_diag(grad_e), v, adjoint_b=True))
    # The forward op only depends on the lower triangular part of a, so here we
    # symmetrize and take the lower triangle
    grad_a = array_ops.matrix_band_part(
        grad_a + array_ops.matrix_transpose(grad_a), -1, 0)
    grad_a = array_ops.matrix_set_diag(grad_a,
                                       0.5 * array_ops.matrix_diag_part(grad_a))
    return grad_a 

def normalize_moments(counts, mean_ss, variance_ss, shift, name=None):
  """Calculate the mean and variance of based on the sufficient statistics.

  Args:
    counts: A `Tensor` containing a the total count of the data (one value).
    mean_ss: A `Tensor` containing the mean sufficient statistics: the (possibly
      shifted) sum of the elements to average over.
    variance_ss: A `Tensor` containing the variance sufficient statistics: the
      (possibly shifted) squared sum of the data to compute the variance over.
    shift: A `Tensor` containing the value by which the data is shifted for
      numerical stability, or `None` if no shift was performed.
    name: Name used to scope the operations that compute the moments.

  Returns:
    Two `Tensor` objects: `mean` and `variance`.
  """
  with ops.name_scope(name, "normalize", [counts, mean_ss, variance_ss, shift]):
    divisor = math_ops.reciprocal(counts, name="divisor")
    if shift is not None:
      shifted_mean = math_ops.multiply(mean_ss, divisor, name="shifted_mean")
      mean = math_ops.add(shifted_mean, shift, name="mean")
    else:  # no shift.
      shifted_mean = math_ops.multiply(mean_ss, divisor, name="mean")
      mean = shifted_mean
    variance = math_ops.subtract(math_ops.multiply(variance_ss, divisor),
                                 math_ops.square(shifted_mean),
                                 name="variance")
  return (mean, variance) 

def setUp(self):
    super(CoreUnaryOpsTest, self).setUp()

    self.ops = [
        ('abs', operator.abs, math_ops.abs, core.abs_function),
        ('neg', operator.neg, math_ops.negative, core.neg),
        # TODO(shoyer): add unary + to core TensorFlow
        ('pos', None, None, None),
        ('sign', None, math_ops.sign, core.sign),
        ('reciprocal', None, math_ops.reciprocal, core.reciprocal),
        ('square', None, math_ops.square, core.square),
        ('round', None, math_ops.round, core.round_function),
        ('sqrt', None, math_ops.sqrt, core.sqrt),
        ('rsqrt', None, math_ops.rsqrt, core.rsqrt),
        ('log', None, math_ops.log, core.log),
        ('exp', None, math_ops.exp, core.exp),
        ('log', None, math_ops.log, core.log),
        ('ceil', None, math_ops.ceil, core.ceil),
        ('floor', None, math_ops.floor, core.floor),
        ('cos', None, math_ops.cos, core.cos),
        ('sin', None, math_ops.sin, core.sin),
        ('tan', None, math_ops.tan, core.tan),
        ('acos', None, math_ops.acos, core.acos),
        ('asin', None, math_ops.asin, core.asin),
        ('atan', None, math_ops.atan, core.atan),
        ('lgamma', None, math_ops.lgamma, core.lgamma),
        ('digamma', None, math_ops.digamma, core.digamma),
        ('erf', None, math_ops.erf, core.erf),
        ('erfc', None, math_ops.erfc, core.erfc),
        ('lgamma', None, math_ops.lgamma, core.lgamma),
    ]
    total_size = np.prod([v.size for v in self.original_lt.axes.values()])
    self.test_lt = core.LabeledTensor(
        math_ops.cast(self.original_lt, dtypes.float32) / total_size,
        self.original_lt.axes) 

def _Log1pGrad(op, grad):
  """Returns grad * (1/(1 + x))."""
  x = op.inputs[0]
  with ops.control_dependencies([grad.op]):
    x = math_ops.conj(x)
    return grad * math_ops.reciprocal(1 + x) 

def _LogGrad(op, grad):
  """Returns grad * (1/x)."""
  x = op.inputs[0]
  with ops.control_dependencies([grad.op]):
    x = math_ops.conj(x)
    return grad * math_ops.reciprocal(x) 

def _Log1pGrad(op, grad):
  """Returns grad * (1/(1 + x))."""
  x = op.inputs[0]
  with ops.control_dependencies([grad.op]):
    x = math_ops.conj(x)
    return grad * math_ops.reciprocal(1 + x) 

def _TanGrad(op, grad):
  """Returns grad * 1/sec^2(x)."""
  x = op.inputs[0]
  with ops.control_dependencies([grad.op]):
    x = math_ops.conj(x)
    secx = math_ops.reciprocal(math_ops.cos(x))
    secx2 = math_ops.square(secx)
    return grad * secx2 

def _AsinGrad(op, grad):
  """Returns grad * 1/sqrt(1-x^2)."""
  x = op.inputs[0]
  with ops.control_dependencies([grad.op]):
    x = math_ops.conj(x)
    x2 = math_ops.square(x)
    one = constant_op.constant(1, dtype=grad.dtype)
    den = math_ops.sqrt(math_ops.subtract(one, x2))
    inv = math_ops.reciprocal(den)
    return grad * inv 

def _AtanGrad(op, grad):
  """Returns grad * 1/ (1 + x^2)."""
  x = op.inputs[0]
  with ops.control_dependencies([grad.op]):
    x = math_ops.conj(x)
    x2 = math_ops.square(x)
    one = constant_op.constant(1, dtype=grad.dtype)
    inv = math_ops.reciprocal(math_ops.add(one, x2))
    return grad * inv 

def _SelfAdjointEigV2Grad(op, grad_e, grad_v):
  """Gradient for SelfAdjointEigV2."""
  e = op.outputs[0]
  v = op.outputs[1]
  # a = op.inputs[0], which satisfies
  # a[...,:,:] * v[...,:,i] = e[...,i] * v[...,i]
  with ops.control_dependencies([grad_e.op, grad_v.op]):
    if grad_v is not None:
      # Construct the matrix f(i,j) = (i != j ? 1 / (e_i - e_j) : 0).
      # Notice that because of the term involving f, the gradient becomes
      # infinite (or NaN in practice) when eigenvalues are not unique.
      # Mathematically this should not be surprising, since for (k-fold)
      # degenerate eigenvalues, the corresponding eigenvectors are only defined
      # up to arbitrary rotation in a (k-dimensional) subspace.
      f = array_ops.matrix_set_diag(
          math_ops.reciprocal(
              array_ops.expand_dims(e, -2) - array_ops.expand_dims(e, -1)),
          array_ops.zeros_like(e))
      grad_a = math_ops.matmul(
          v,
          math_ops.matmul(
              array_ops.matrix_diag(grad_e) + f * math_ops.matmul(
                  v, grad_v, adjoint_a=True),
              v,
              adjoint_b=True))
    else:
      grad_a = math_ops.matmul(
          v, math_ops.matmul(
              array_ops.matrix_diag(grad_e), v, adjoint_b=True))
    # The forward op only depends on the lower triangular part of a, so here we
    # symmetrize and take the lower triangle
    grad_a = array_ops.matrix_band_part(
        grad_a + array_ops.matrix_transpose(grad_a), -1, 0)
    grad_a = array_ops.matrix_set_diag(grad_a,
                                       0.5 * array_ops.matrix_diag_part(grad_a))
    return grad_a 

def normalize_moments(counts, mean_ss, variance_ss, shift, name=None):
  """Calculate the mean and variance of based on the sufficient statistics.

  Args:
    counts: A `Tensor` containing a the total count of the data (one value).
    mean_ss: A `Tensor` containing the mean sufficient statistics: the (possibly
      shifted) sum of the elements to average over.
    variance_ss: A `Tensor` containing the variance sufficient statistics: the
      (possibly shifted) squared sum of the data to compute the variance over.
    shift: A `Tensor` containing the value by which the data is shifted for
      numerical stability, or `None` if no shift was performed.
    name: Name used to scope the operations that compute the moments.

  Returns:
    Two `Tensor` objects: `mean` and `variance`.
  """
  with ops.name_scope(name, "normalize", [counts, mean_ss, variance_ss, shift]):
    divisor = math_ops.reciprocal(counts, name="divisor")
    if shift is not None:
      shifted_mean = math_ops.multiply(mean_ss, divisor, name="shifted_mean")
      mean = math_ops.add(shifted_mean, shift, name="mean")
    else:  # no shift.
      shifted_mean = math_ops.multiply(mean_ss, divisor, name="mean")
      mean = shifted_mean
    variance = math_ops.subtract(math_ops.multiply(variance_ss, divisor),
                                 math_ops.square(shifted_mean),
                                 name="variance")
  return (mean, variance) 

def _LogGrad(op, grad):
  """Returns grad * (1/x)."""
  x = op.inputs[0]
  with ops.control_dependencies([grad.op]):
    x = math_ops.conj(x)
    return grad * math_ops.reciprocal(x) 

def _IRFFTGradHelper(rank, rfft_fn):
  """Returns a gradient function for an IRFFT of the provided rank."""
  # Can't happen because we don't register a gradient for IRFFT3D.
  assert rank in (1, 2), "Gradient for IRFFT3D is not implemented."

  def _Grad(op, grad):
    """A gradient function for IRFFT with the provided `rank` and `rfft_fn`."""
    # Generate a simple mask like [1.0, 2.0, ..., 2.0, 1.0] for even-length FFTs
    # and [1.0, 2.0, ..., 2.0] for odd-length FFTs. To reduce extra ops in the
    # graph we special-case the situation where the FFT length and last
    # dimension of the input are known at graph construction time.
    fft_length = op.inputs[1]
    is_odd = math_ops.mod(fft_length[-1], 2)
    input_last_dimension = array_ops.shape(op.inputs[0])[-1]
    mask = array_ops.concat(
        [[1.0], 2.0 * array_ops.ones([input_last_dimension - 2 + is_odd]),
         array_ops.ones([1 - is_odd])], 0)

    rsize = math_ops.reciprocal(math_ops.to_float(_FFTSizeForGrad(grad, rank)))

    # The gradient of IRFFT is the RFFT of the incoming gradient times a scaling
    # factor and a mask. The mask scales the gradient for the Hermitian
    # symmetric components of the RFFT by a factor of two, since these
    # components are de-duplicated in the RFFT.
    rfft = rfft_fn(grad, fft_length)
    return rfft * math_ops.cast(rsize * mask, dtypes.complex64), None

  return _Grad 

def _TanGrad(op, grad):
  """Returns grad * 1/sec^2(x)."""
  x = op.inputs[0]
  with ops.control_dependencies([grad.op]):
    x = math_ops.conj(x)
    secx = math_ops.reciprocal(math_ops.cos(x))
    secx2 = math_ops.square(secx)
    return grad * secx2 

def _AsinGrad(op, grad):
  """Returns grad * 1/sqrt(1-x^2)."""
  x = op.inputs[0]
  with ops.control_dependencies([grad.op]):
    x = math_ops.conj(x)
    x2 = math_ops.square(x)
    one = constant_op.constant(1, dtype=grad.dtype)
    den = math_ops.sqrt(math_ops.subtract(one, x2))
    inv = math_ops.reciprocal(den)
    return grad * inv