# Copyright 2015 The TensorFlow Authors. All Rights Reserved. # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. # ============================================================================== """Basic arithmetic operators. See the @{$python/math_ops} guide. @@add @@subtract @@multiply @@scalar_mul @@div @@divide @@truediv @@floordiv @@realdiv @@truncatediv @@floor_div @@truncatemod @@floormod @@mod @@cross @@add_n @@abs @@negative @@sign @@reciprocal @@square @@round @@sqrt @@rsqrt @@pow @@exp @@expm1 @@log @@log1p @@sinh @@cosh @@asinh @@acosh @@atanh @@ceil @@floor @@maximum @@minimum @@cos @@sin @@lbeta @@tan @@acos @@asin @@atan @@atan2 @@lgamma @@digamma @@erf @@erfc @@squared_difference @@igamma @@igammac @@zeta @@polygamma @@betainc @@rint @@diag @@diag_part @@trace @@transpose @@eye @@matrix_diag @@matrix_diag_part @@matrix_band_part @@matrix_set_diag @@matrix_transpose @@matmul @@norm @@matrix_determinant @@matrix_inverse @@cholesky @@cholesky_solve @@matrix_solve @@matrix_triangular_solve @@matrix_solve_ls @@qr @@self_adjoint_eig @@self_adjoint_eigvals @@svd @@tensordot @@complex @@conj @@imag @@angle @@real @@fft @@ifft @@fft2d @@ifft2d @@fft3d @@ifft3d @@reduce_sum @@reduce_prod @@reduce_min @@reduce_max @@reduce_mean @@reduce_all @@reduce_any @@reduce_logsumexp @@count_nonzero @@accumulate_n @@einsum @@bincount @@cumsum @@cumprod @@segment_sum @@segment_prod @@segment_min @@segment_max @@segment_mean @@to_complex128 @@to_complex64 @@unsorted_segment_sum @@unsorted_segment_max @@unsorted_segment_mean @@unsorted_segment_min @@unsorted_segment_prod @@unsorted_segment_sqrt_n @@sparse_segment_sum @@sparse_segment_mean @@sparse_segment_sqrt_n @@argmin @@argmax @@setdiff1d @@where @@unique @@edit_distance @@invert_permutation """ from __future__ import absolute_import from __future__ import division from __future__ import print_function import numpy as np from six.moves import xrange # pylint: disable=redefined-builtin from tensorflow.python.eager import context from tensorflow.python.framework import common_shapes from tensorflow.python.framework import constant_op from tensorflow.python.framework import dtypes from tensorflow.python.framework import graph_util from tensorflow.python.framework import ops from tensorflow.python.framework import sparse_tensor from tensorflow.python.framework import tensor_shape from tensorflow.python.ops import array_ops from tensorflow.python.ops import gen_data_flow_ops from tensorflow.python.ops import gen_math_ops from tensorflow.python.ops import gen_nn_ops from tensorflow.python.ops import gen_sparse_ops from tensorflow.python.ops import gen_spectral_ops from tensorflow.python.platform import tf_logging as logging # go/tf-wildcard-import # pylint: disable=wildcard-import from tensorflow.python.ops.gen_math_ops import * # pylint: enable=wildcard-import from tensorflow.python.util import compat from tensorflow.python.util import deprecation from tensorflow.python.util import nest from tensorflow.python.util.tf_export import tf_export # Aliases for some automatically-generated names. linspace = gen_math_ops.lin_space arg_max = deprecation.deprecated(None, "Use argmax instead")(arg_max) # pylint: disable=used-before-assignment arg_min = deprecation.deprecated(None, "Use argmin instead")(arg_min) # pylint: disable=used-before-assignment tf_export("arg_max")(arg_max) tf_export("arg_min")(arg_min) # This is set by resource_variable_ops.py. It is included in this way since # there is a circular dependency between math_ops and resource_variable_ops _resource_variable_type = None def _set_doc(doc): def _decorator(func): func.__doc__ = doc return func return _decorator # pylint: disable=redefined-builtin @tf_export("argmax") @deprecation.deprecated_args(None, "Use the axis argument instead", "dimension") @_set_doc( gen_math_ops.arg_max.__doc__.replace("dimensions", "axes").replace( "dimension", "axis")) def argmax(input, axis=None, name=None, dimension=None, output_type=dtypes.int64): if dimension is not None: if axis is not None: raise ValueError("Cannot specify both 'axis' and 'dimension'") axis = dimension elif axis is None: axis = 0 return gen_math_ops.arg_max(input, axis, name=name, output_type=output_type) @tf_export("argmin") @deprecation.deprecated_args(None, "Use the axis argument instead", "dimension") @_set_doc( gen_math_ops.arg_min.__doc__.replace("dimensions", "axes").replace( "dimension", "axis")) def argmin(input, axis=None, name=None, dimension=None, output_type=dtypes.int64): if dimension is not None: if axis is not None: raise ValueError("Cannot specify both 'axis' and 'dimension'") axis = dimension elif axis is None: axis = 0 return gen_math_ops.arg_min(input, axis, name=name, output_type=output_type) # pylint: enable=redefined-builtin # pylint: disable=anomalous-backslash-in-string,protected-access # pylint: disable=g-docstring-has-escape @tf_export("abs") def abs(x, name=None): # pylint: disable=redefined-builtin r"""Computes the absolute value of a tensor. Given a tensor x of complex numbers, this operation returns a tensor of type float32 or float64 that is the absolute value of each element in x. All elements in x must be complex numbers of the form \$$a + bj\$$. The absolute value is computed as \$$\sqrt{a^2 + b^2}\$$. For example: python x = tf.constant([[-2.25 + 4.75j], [-3.25 + 5.75j]]) tf.abs(x) # [5.25594902, 6.60492229]  Args: x: A Tensor or SparseTensor of type float32, float64, int32, int64, complex64 or complex128. name: A name for the operation (optional). Returns: A Tensor or SparseTensor the same size and type as x with absolute values. Note, for complex64 or complex128 input, the returned Tensor will be of type float32 or float64, respectively. """ with ops.name_scope(name, "Abs", [x]) as name: if isinstance(x, sparse_tensor.SparseTensor): if x.values.dtype.is_complex: x_abs = gen_math_ops.complex_abs( x.values, Tout=x.values.dtype.real_dtype, name=name) return sparse_tensor.SparseTensor( indices=x.indices, values=x_abs, dense_shape=x.dense_shape) x_abs = gen_math_ops._abs(x.values, name=name) return sparse_tensor.SparseTensor( indices=x.indices, values=x_abs, dense_shape=x.dense_shape) else: x = ops.convert_to_tensor(x, name="x") if x.dtype.is_complex: return gen_math_ops.complex_abs(x, Tout=x.dtype.real_dtype, name=name) return gen_math_ops._abs(x, name=name) # pylint: enable=g-docstring-has-escape # pylint: disable=redefined-builtin def _bucketize(input, boundaries, name=None): return gen_math_ops.bucketize(input=input, boundaries=boundaries, name=name) # pylint: enable=redefined-builtin class DivideDelegateWithName(object): """Use Python2/Python3 division delegation to implement divide for tensors.""" def __init__(self, x, name): """Construct DivideDelegateWithName. Args: x: Tensor to use as left operand in operator overloads name: The name that is preferred for the op created. """ self.x = x self.name = name def __truediv__(self, y): return _truediv_python3(self.x, y, self.name) def __floordiv__(self, y): return floordiv(self.x, y, self.name) def __div__(self, y): return _div_python2(self.x, y, self.name) @tf_export("divide") def divide(x, y, name=None): """Computes Python style division of x by y.""" if name is not None: # Cannot use tensors operator overload, because it has no way to track # override names. Use a dummy class to track the runtime division behavior return DivideDelegateWithName(x, name) / y else: return x / y @tf_export("multiply") def multiply(x, y, name=None): return gen_math_ops.mul(x, y, name) multiply.__doc__ = gen_math_ops.mul.__doc__.replace("Multiply", "tf.multiply") # TODO(aselle): put deprecation in after another round of global code changes @deprecation.deprecated( "2016-12-30", "tf.mul(x, y) is deprecated, please use tf.multiply(x, y) or x * y") def _mul(x, y, name=None): return gen_math_ops.mul(x, y, name) _mul.__doc__ = ( gen_math_ops.mul.__doc__ + ("" if _mul.__doc__ is None else _mul.__doc__)) @tf_export("subtract") def subtract(x, y, name=None): return gen_math_ops.sub(x, y, name) subtract.__doc__ = gen_math_ops.sub.__doc__.replace("Sub", "tf.subtract") # TODO(aselle): put deprecation in after another round of global code changes @deprecation.deprecated( "2016-12-30", "tf.sub(x, y) is deprecated, please use tf.subtract(x, y) or x - y") def _sub(x, y, name=None): return gen_math_ops.sub(x, y, name) _sub.__doc__ = ( gen_math_ops.sub.__doc__ + ("" if _sub.__doc__ is None else _sub.__doc__)) # pylint: disable=g-docstring-has-escape @tf_export("negative") def negative(x, name=None): """Computes numerical negative value element-wise. I.e., \$$y = -x\$$. Args: x: A Tensor or SparseTensor. Must be one of the following types: half, float32, float64, int32, int64, complex64, complex128. name: A name for the operation (optional). Returns: A Tensor or SparseTensor, respectively. Has the same type as x. """ with ops.name_scope(name, "Neg", [x]) as name: if isinstance(x, sparse_tensor.SparseTensor): x_neg = gen_math_ops.neg(x.values, name=name) return sparse_tensor.SparseTensor( indices=x.indices, values=x_neg, dense_shape=x.dense_shape) else: return gen_math_ops.neg(x, name=name) # pylint: enable=g-docstring-has-escape # pylint: disable=g-docstring-has-escape @deprecation.deprecated( "2016-12-30", "tf.neg(x) is deprecated, please use tf.negative(x) or -x") def _neg(x, name=None): """Computes numerical negative value element-wise. I.e., \$$y = -x\$$. Args: x: A Tensor or SparseTensor. Must be one of the following types: half, float32, float64, int32, int64, complex64, complex128. name: A name for the operation (optional). Returns: A Tensor or SparseTensor, respectively. Has the same type as x. """ return negative(x, name) # pylint: enable=g-docstring-has-escape @tf_export("sign") def sign(x, name=None): """Returns an element-wise indication of the sign of a number. y = sign(x) = -1 if x < 0; 0 if x == 0 or tf.is_nan(x); 1 if x > 0. Zero is returned for NaN inputs. For complex numbers, y = sign(x) = x / |x| if x != 0, otherwise y = 0. Args: x: A Tensor or SparseTensor. Must be one of the following types: half, float32, float64, int32, int64, complex64, complex128. name: A name for the operation (optional). Returns: A Tensor or SparseTensor, respectively. Has the same type as x. @compatibility(numpy) Equivalent to numpy.sign except for the behavior for input values of NaN. @end_compatibility """ with ops.name_scope(name, "Sign", [x]) as name: if isinstance(x, sparse_tensor.SparseTensor): x_sign = gen_math_ops.sign(x.values, name=name) return sparse_tensor.SparseTensor( indices=x.indices, values=x_sign, dense_shape=x.dense_shape) else: return gen_math_ops.sign(x, name=name) @tf_export("square") def square(x, name=None): r"""Computes square of x element-wise. I.e., \$$y = x * x = x^2\$$. Args: x: A Tensor or SparseTensor. Must be one of the following types: half, float32, float64, int32, int64, complex64, complex128. name: A name for the operation (optional). Returns: A Tensor or SparseTensor. Has the same type as x. """ with ops.name_scope(name, "Square", [x]) as name: if isinstance(x, sparse_tensor.SparseTensor): x_square = gen_math_ops.square(x.values, name=name) return sparse_tensor.SparseTensor( indices=x.indices, values=x_square, dense_shape=x.dense_shape) else: return gen_math_ops.square(x, name=name) @tf_export("sqrt") def sqrt(x, name=None): r"""Computes square root of x element-wise. I.e., \$$y = \sqrt{x} = x^{1/2}\$$. Args: x: A Tensor or SparseTensor. Must be one of the following types: half, float32, float64, complex64, complex128. name: A name for the operation (optional). Returns: A Tensor or SparseTensor, respectively. Has the same type as x. """ with ops.name_scope(name, "Sqrt", [x]) as name: if isinstance(x, sparse_tensor.SparseTensor): x_sqrt = gen_math_ops.sqrt(x.values, name=name) return sparse_tensor.SparseTensor( indices=x.indices, values=x_sqrt, dense_shape=x.dense_shape) else: return gen_math_ops.sqrt(x, name=name) @tf_export("erf") def erf(x, name=None): """Computes the Gauss error function of x element-wise. Args: x: A Tensor of SparseTensor. Must be one of the following types: half, float32, float64. name: A name for the operation (optional). Returns: A Tensor or SparseTensor, respectively. Has the same type as x. """ with ops.name_scope(name, "Erf", [x]) as name: if isinstance(x, sparse_tensor.SparseTensor): x_erf = gen_math_ops.erf(x.values, name=name) return sparse_tensor.SparseTensor( indices=x.indices, values=x_erf, dense_shape=x.dense_shape) else: return gen_math_ops.erf(x, name=name) @tf_export("scalar_mul") def scalar_mul(scalar, x): """Multiplies a scalar times a Tensor or IndexedSlices object. Intended for use in gradient code which might deal with IndexedSlices objects, which are easy to multiply by a scalar but more expensive to multiply with arbitrary tensors. Args: scalar: A 0-D scalar Tensor. Must have known shape. x: A Tensor or IndexedSlices to be scaled. Returns: scalar * x of the same type (Tensor or IndexedSlices) as x. Raises: ValueError: if scalar is not a 0-D scalar. """ scalar = ops.convert_to_tensor( scalar, dtype=x.dtype.base_dtype, name="scalar") shape = scalar.get_shape() if shape.ndims == 0: if isinstance(x, ops.IndexedSlices): return ops.IndexedSlices(scalar * x.values, x.indices, x.dense_shape) else: return scalar * x else: raise ValueError("Only scalar multiply works, got shape %s" % shape) @tf_export("pow") def pow(x, y, name=None): # pylint: disable=redefined-builtin r"""Computes the power of one value to another. Given a tensor x and a tensor y, this operation computes \$$x^y\$$ for corresponding elements in x and y. For example: python x = tf.constant([[2, 2], [3, 3]]) y = tf.constant([[8, 16], [2, 3]]) tf.pow(x, y) # [[256, 65536], [9, 27]]  Args: x: A Tensor of type float32, float64, int32, int64, complex64, or complex128. y: A Tensor of type float32, float64, int32, int64, complex64, or complex128. name: A name for the operation (optional). Returns: A Tensor. """ with ops.name_scope(name, "Pow", [x]) as name: return gen_math_ops._pow(x, y, name=name) # pylint: disable=redefined-builtin,redefined-outer-name @tf_export("complex") def complex(real, imag, name=None): r"""Converts two real numbers to a complex number. Given a tensor real representing the real part of a complex number, and a tensor imag representing the imaginary part of a complex number, this operation returns complex numbers elementwise of the form \$$a + bj\$$, where *a* represents the real part and *b* represents the imag part. The input tensors real and imag must have the same shape. For example: python real = tf.constant([2.25, 3.25]) imag = tf.constant([4.75, 5.75]) tf.complex(real, imag) # [[2.25 + 4.75j], [3.25 + 5.75j]]  Args: real: A Tensor. Must be one of the following types: float32, float64. imag: A Tensor. Must have the same type as real. name: A name for the operation (optional). Returns: A Tensor of type complex64 or complex128. """ real = ops.convert_to_tensor(real, name="real") imag = ops.convert_to_tensor(imag, name="imag") with ops.name_scope(name, "Complex", [real, imag]) as name: input_types = (real.dtype, imag.dtype) if input_types == (dtypes.float64, dtypes.float64): Tout = dtypes.complex128 elif input_types == (dtypes.float32, dtypes.float32): Tout = dtypes.complex64 else: raise TypeError("real and imag have incorrect types: " "{} {}".format(real.dtype.name, imag.dtype.name)) return gen_math_ops._complex(real, imag, Tout=Tout, name=name) @tf_export("real") def real(input, name=None): r"""Returns the real part of a complex (or real) tensor. Given a tensor input, this operation returns a tensor of type float that is the real part of each element in input considered as a complex number. For example: python x = tf.constant([-2.25 + 4.75j, 3.25 + 5.75j]) tf.real(x) # [-2.25, 3.25]  If input is already real, it is returned unchanged. Args: input: A Tensor. Must have numeric type. name: A name for the operation (optional). Returns: A Tensor of type float32 or float64. """ with ops.name_scope(name, "Real", [input]) as name: if input.dtype.is_complex: real_dtype = input.dtype.real_dtype return gen_math_ops.real(input, Tout=real_dtype, name=name) else: return input @tf_export("imag") def imag(input, name=None): r"""Returns the imaginary part of a complex (or real) tensor. Given a tensor input, this operation returns a tensor of type float that is the imaginary part of each element in input considered as a complex number. If input is real, a tensor of all zeros is returned. For example: python x = tf.constant([-2.25 + 4.75j, 3.25 + 5.75j]) tf.imag(x) # [4.75, 5.75]  Args: input: A Tensor. Must be one of the following types: float, double, complex64, complex128. name: A name for the operation (optional). Returns: A Tensor of type float32 or float64. """ with ops.name_scope(name, "Imag", [input]) as name: if input.dtype.is_complex: return gen_math_ops.imag(input, Tout=input.dtype.real_dtype, name=name) else: return array_ops.zeros_like(input) @tf_export("angle") def angle(input, name=None): r"""Returns the element-wise argument of a complex (or real) tensor. Given a tensor input, this operation returns a tensor of type float that is the argument of each element in input considered as a complex number. The elements in input are considered to be complex numbers of the form \$$a + bj\$$, where *a* is the real part and *b* is the imaginary part. If input is real then *b* is zero by definition. The argument returned by this function is of the form \$$atan2(b, a)\$$. If input is real, a tensor of all zeros is returned. For example:  # tensor 'input' is [-2.25 + 4.75j, 3.25 + 5.75j] tf.angle(input) ==> [2.0132, 1.056]  Args: input: A Tensor. Must be one of the following types: float, double, complex64, complex128. name: A name for the operation (optional). Returns: A Tensor of type float32 or float64. """ with ops.name_scope(name, "Angle", [input]) as name: if input.dtype.is_complex: return gen_math_ops.angle(input, Tout=input.dtype.real_dtype, name=name) else: return array_ops.zeros_like(input) # pylint: enable=redefined-outer-name,redefined-builtin @tf_export("round") def round(x, name=None): # pylint: disable=redefined-builtin """Rounds the values of a tensor to the nearest integer, element-wise. Rounds half to even. Also known as bankers rounding. If you want to round according to the current system rounding mode use tf::cint. For example: python x = tf.constant([0.9, 2.5, 2.3, 1.5, -4.5]) tf.round(x) # [ 1.0, 2.0, 2.0, 2.0, -4.0 ]  Args: x: A Tensor of type float32 or float64. name: A name for the operation (optional). Returns: A Tensor of same shape and type as x. """ x = ops.convert_to_tensor(x, name="x") if x.dtype.is_integer: return x else: return gen_math_ops.round(x, name=name) @tf_export("cast") def cast(x, dtype, name=None): """Casts a tensor to a new type. The operation casts x (in case of Tensor) or x.values (in case of SparseTensor) to dtype. For example: python x = tf.constant([1.8, 2.2], dtype=tf.float32) tf.cast(x, tf.int32) # [1, 2], dtype=tf.int32  Args: x: A Tensor or SparseTensor. dtype: The destination type. name: A name for the operation (optional). Returns: A Tensor or SparseTensor with same shape as x. Raises: TypeError: If x cannot be cast to the dtype. """ base_type = dtypes.as_dtype(dtype).base_dtype with ops.name_scope(name, "Cast", [x]) as name: if isinstance(x, sparse_tensor.SparseTensor): values_cast = cast(x.values, base_type, name=name) x = sparse_tensor.SparseTensor(x.indices, values_cast, x.dense_shape) else: # TODO(josh11b): If x is not already a Tensor, we could return # ops.convert_to_tensor(x, dtype=dtype, ...) here, but that # allows some conversions that cast() can't do, e.g. casting numbers to # strings. x = ops.convert_to_tensor(x, name="x") if x.dtype.base_dtype != base_type: x = gen_math_ops.cast(x, base_type, name=name) if x.dtype.is_complex and base_type.is_floating: logging.warn("Casting complex to real discards imaginary part.") return x @tf_export("saturate_cast") def saturate_cast(value, dtype, name=None): """Performs a safe saturating cast of value to dtype. This function casts the input to dtype without applying any scaling. If there is a danger that values would over or underflow in the cast, this op applies the appropriate clamping before the cast. Args: value: A Tensor. dtype: The desired output DType. name: A name for the operation (optional). Returns: value safely cast to dtype. """ # When casting to a type with smaller representable range, clamp. # Note that this covers casting to unsigned types as well. with ops.name_scope(name, "saturate_cast", [value]) as name: value = ops.convert_to_tensor(value, name="value") dtype = dtypes.as_dtype(dtype).base_dtype if value.dtype.min < dtype.min: value = gen_math_ops.maximum(value, ops.convert_to_tensor( dtype.min, dtype=value.dtype, name="min")) if value.dtype.max > dtype.max: value = gen_math_ops.minimum(value, ops.convert_to_tensor( dtype.max, dtype=value.dtype, name="max")) return cast(value, dtype, name=name) @tf_export("to_float") def to_float(x, name="ToFloat"): """Casts a tensor to type float32. Args: x: A Tensor or SparseTensor. name: A name for the operation (optional). Returns: A Tensor or SparseTensor with same shape as x with type float32. Raises: TypeError: If x cannot be cast to the float32. """ return cast(x, dtypes.float32, name=name) @tf_export("to_double") def to_double(x, name="ToDouble"): """Casts a tensor to type float64. Args: x: A Tensor or SparseTensor. name: A name for the operation (optional). Returns: A Tensor or SparseTensor with same shape as x with type float64. Raises: TypeError: If x cannot be cast to the float64. """ return cast(x, dtypes.float64, name=name) @tf_export("to_int32") def to_int32(x, name="ToInt32"): """Casts a tensor to type int32. Args: x: A Tensor or SparseTensor. name: A name for the operation (optional). Returns: A Tensor or SparseTensor with same shape as x with type int32. Raises: TypeError: If x cannot be cast to the int32. """ return cast(x, dtypes.int32, name=name) @tf_export("to_int64") def to_int64(x, name="ToInt64"): """Casts a tensor to type int64. Args: x: A Tensor or SparseTensor. name: A name for the operation (optional). Returns: A Tensor or SparseTensor with same shape as x with type int64. Raises: TypeError: If x cannot be cast to the int64. """ return cast(x, dtypes.int64, name=name) @tf_export("to_bfloat16") def to_bfloat16(x, name="ToBFloat16"): """Casts a tensor to type bfloat16. Args: x: A Tensor or SparseTensor. name: A name for the operation (optional). Returns: A Tensor or SparseTensor with same shape as x with type bfloat16. Raises: TypeError: If x cannot be cast to the bfloat16. """ return cast(x, dtypes.bfloat16, name=name) @tf_export("to_complex64") def to_complex64(x, name="ToComplex64"): """Casts a tensor to type complex64. Args: x: A Tensor or SparseTensor. name: A name for the operation (optional). Returns: A Tensor or SparseTensor with same shape as x with type complex64. Raises: TypeError: If x cannot be cast to the complex64. """ return cast(x, dtypes.complex64, name=name) @tf_export("to_complex128") def to_complex128(x, name="ToComplex128"): """Casts a tensor to type complex128. Args: x: A Tensor or SparseTensor. name: A name for the operation (optional). Returns: A Tensor or SparseTensor with same shape as x with type complex128. Raises: TypeError: If x cannot be cast to the complex128. """ return cast(x, dtypes.complex128, name=name) ops.Tensor._override_operator("__neg__", gen_math_ops.neg) ops.Tensor._override_operator("__abs__", abs) # __invert__ corresponds to the ~ operator. Here we follow the numpy convention # ~ marks an elementwise bit-wise inverse. This is only implemented for boolean # tensors and will throw a TypeError if used on nonboolean arrays ops.Tensor._override_operator("__invert__", gen_math_ops.logical_not) def _OverrideBinaryOperatorHelper(func, op_name, clazz_object=ops.Tensor): """Register operators with different tensor and scalar versions. If clazz_object is SparseTensor, assumes func takes (sp_indices, sp_values, sp_shape, dense) and outputs (new_sp_values). Args: func: the operator op_name: name of the operator being overridden clazz_object: class to override for. Either Tensor or SparseTensor. """ def binary_op_wrapper(x, y): with ops.name_scope(None, op_name, [x, y]) as name: if not isinstance(y, sparse_tensor.SparseTensor): try: y = ops.convert_to_tensor(y, dtype=x.dtype.base_dtype, name="y") except TypeError: # If the RHS is not a tensor, it might be a tensor aware object # that can implement the operator with knowledge of itself # and the tensor. if hasattr(type(y), "__r%s__" % op_name): return NotImplemented else: raise return func(x, y, name=name) def binary_op_wrapper_sparse(sp_x, y): with ops.name_scope(None, op_name, [sp_x, y]) as name: y = ops.convert_to_tensor(y, dtype=sp_x.dtype.base_dtype, name="y") return sparse_tensor.SparseTensor(sp_x.indices, func( sp_x.indices, sp_x.values, sp_x.dense_shape, y, name=name), sp_x.dense_shape) def r_binary_op_wrapper(y, x): with ops.name_scope(None, op_name, [x, y]) as name: x = ops.convert_to_tensor(x, dtype=y.dtype.base_dtype, name="x") return func(x, y, name=name) # Propagate func.__doc__ to the wrappers try: doc = func.__doc__ except AttributeError: doc = None binary_op_wrapper.__doc__ = doc r_binary_op_wrapper.__doc__ = doc binary_op_wrapper_sparse.__doc__ = doc if clazz_object is ops.Tensor: clazz_object._override_operator("__%s__" % op_name, binary_op_wrapper) del binary_op_wrapper clazz_object._override_operator("__r%s__" % op_name, r_binary_op_wrapper) del r_binary_op_wrapper else: clazz_object._override_operator("__%s__" % op_name, binary_op_wrapper_sparse) del binary_op_wrapper_sparse # Conversion table for __truediv__. None entries mean no conversion required. _TRUEDIV_TABLE = { dtypes.uint8: dtypes.float32, dtypes.int8: dtypes.float32, dtypes.uint16: dtypes.float32, dtypes.int16: dtypes.float32, dtypes.int32: dtypes.float64, dtypes.int64: dtypes.float64, dtypes.bfloat16: None, dtypes.float16: None, dtypes.float32: None, dtypes.float64: None, dtypes.complex64: None, dtypes.complex128: None, } # NOTE: the support of "sparse (true)div dense" is currently not baked in into # "tf.(true_)div()". Until such an API decision is made, the supported usage is # to explicitly use the "/" operator to invoke either truediv or div. def _sparse_dense_truediv(sp_indices, sp_values, sp_shape, y, name=None): """Internal helper function for 'sp_t / dense_t'.""" with ops.name_scope(name, "truediv", [sp_indices, sp_values, sp_shape, y]) as name: sp_values = ops.convert_to_tensor(sp_values, name="sp_values") y = ops.convert_to_tensor(y, name="y") x_dtype = sp_values.dtype.base_dtype y_dtype = y.dtype.base_dtype if x_dtype != y_dtype: raise TypeError("x and y must have the same dtype, got %r != %r" % (x_dtype, y_dtype)) try: dtype = _TRUEDIV_TABLE[x_dtype] except KeyError: raise TypeError("Invalid dtype %r in __truediv__" % x_dtype) if dtype is not None: sp_values = cast(sp_values, dtype) y = cast(y, dtype) return gen_sparse_ops.sparse_dense_cwise_div( sp_indices, sp_values, sp_shape, y, name=name) def _truediv_python3(x, y, name=None): with ops.name_scope(name, "truediv", [x, y]) as name: x = ops.convert_to_tensor(x, name="x") y = ops.convert_to_tensor(y, name="y") x_dtype = x.dtype.base_dtype y_dtype = y.dtype.base_dtype if x_dtype != y_dtype: raise TypeError("x and y must have the same dtype, got %r != %r" % (x_dtype, y_dtype)) try: dtype = _TRUEDIV_TABLE[x_dtype] except KeyError: raise TypeError("Invalid dtype %r in __truediv__" % x_dtype) if dtype is not None: x = cast(x, dtype) y = cast(y, dtype) return gen_math_ops.real_div(x, y, name=name) def _div_python2(x, y, name=None): """Divide two values using Python 2 semantics. Used for Tensor.__div__. Args: x: Tensor numerator of real numeric type. y: Tensor denominator of real numeric type. name: A name for the operation (optional). Returns: x / y returns the quotient of x and y. """ with ops.name_scope(name, "div", [x, y]) as name: x = ops.convert_to_tensor(x, name="x") y = ops.convert_to_tensor(y, name="y", dtype=x.dtype.base_dtype) x_dtype = x.dtype.base_dtype y_dtype = y.dtype.base_dtype if x_dtype != y_dtype: raise TypeError("x and y must have the same dtype, got %r != %r" % (x_dtype, y_dtype)) if x_dtype.is_floating or x_dtype.is_complex: return gen_math_ops.real_div(x, y, name=name) else: return gen_math_ops.floor_div(x, y, name=name) @tf_export("truediv") def truediv(x, y, name=None): """Divides x / y elementwise (using Python 3 division operator semantics). NOTE: Prefer using the Tensor operator or tf.divide which obey Python division operator semantics. This function forces Python 3 division operator semantics where all integer arguments are cast to floating types first. This op is generated by normal x / y division in Python 3 and in Python 2.7 with from __future__ import division. If you want integer division that rounds down, use x // y or tf.floordiv. x and y must have the same numeric type. If the inputs are floating point, the output will have the same type. If the inputs are integral, the inputs are cast to float32 for int8 and int16 and float64 for int32 and int64 (matching the behavior of Numpy). Args: x: Tensor numerator of numeric type. y: Tensor denominator of numeric type. name: A name for the operation (optional). Returns: x / y evaluated in floating point. Raises: TypeError: If x and y have different dtypes. """ return _truediv_python3(x, y, name) @tf_export("div") def div(x, y, name=None): """Divides x / y elementwise (using Python 2 division operator semantics). NOTE: Prefer using the Tensor division operator or tf.divide which obey Python division operator semantics. This function divides x and y, forcing Python 2.7 semantics. That is, if one of x or y is a float, then the result will be a float. Otherwise, the output will be an integer type. Flooring semantics are used for integer division. Args: x: Tensor numerator of real numeric type. y: Tensor denominator of real numeric type. name: A name for the operation (optional). Returns: x / y returns the quotient of x and y. """ return _div_python2(x, y, name) # TODO(aselle): This should be removed mod = gen_math_ops.floor_mod # TODO(aselle): Deprecate this once all internal functionality uses # tf.truncatediv @tf_export("floordiv") def floordiv(x, y, name=None): """Divides x / y elementwise, rounding toward the most negative integer. The same as tf.div(x,y) for integers, but uses tf.floor(tf.div(x,y)) for floating point arguments so that the result is always an integer (though possibly an integer represented as floating point). This op is generated by x // y floor division in Python 3 and in Python 2.7 with from __future__ import division. Note that for efficiency, floordiv uses C semantics for negative numbers (unlike Python and Numpy). x and y must have the same type, and the result will have the same type as well. Args: x: Tensor numerator of real numeric type. y: Tensor denominator of real numeric type. name: A name for the operation (optional). Returns: x / y rounded down (except possibly towards zero for negative integers). Raises: TypeError: If the inputs are complex. """ with ops.name_scope(name, "floordiv", [x, y]) as name: return gen_math_ops.floor_div(x, y, name=name) realdiv = gen_math_ops.real_div tf_export("realdiv")(realdiv) truncatediv = gen_math_ops.truncate_div tf_export("truncatediv")(truncatediv) # TODO(aselle): Rename this to floordiv when we can. floor_div = gen_math_ops.floor_div tf_export("floor_div")(floor_div) truncatemod = gen_math_ops.truncate_mod tf_export("truncatemod")(truncatemod) floormod = gen_math_ops.floor_mod tf_export("floormod", "mod")(floormod) def _mul_dispatch(x, y, name=None): """Dispatches cwise mul for "Dense*Dense" and "Dense*Sparse".""" is_tensor_y = isinstance(y, ops.Tensor) if is_tensor_y: return gen_math_ops.mul(x, y, name=name) else: assert isinstance(y, sparse_tensor.SparseTensor) # Case: Dense * Sparse. new_vals = gen_sparse_ops.sparse_dense_cwise_mul(y.indices, y.values, y.dense_shape, x, name) return sparse_tensor.SparseTensor(y.indices, new_vals, y.dense_shape) # NOTE(aselle): When integer division is added for sparse_dense_cwise, # div, truediv, and floordiv should be delegated appropriately for # Python sematnics, analogous to dense cwise tensor operations. _OverrideBinaryOperatorHelper(gen_sparse_ops.sparse_dense_cwise_div, "div", sparse_tensor.SparseTensor) _OverrideBinaryOperatorHelper(_sparse_dense_truediv, "truediv", sparse_tensor.SparseTensor) _OverrideBinaryOperatorHelper(gen_sparse_ops.sparse_dense_cwise_mul, "mul", sparse_tensor.SparseTensor) _OverrideBinaryOperatorHelper(gen_math_ops.add, "add") _OverrideBinaryOperatorHelper(gen_math_ops.sub, "sub") _OverrideBinaryOperatorHelper(_mul_dispatch, "mul") _OverrideBinaryOperatorHelper(_div_python2, "div") _OverrideBinaryOperatorHelper(_truediv_python3, "truediv") _OverrideBinaryOperatorHelper(floordiv, "floordiv") _OverrideBinaryOperatorHelper(gen_math_ops.floor_mod, "mod") _OverrideBinaryOperatorHelper(pow, "pow") @tf_export("logical_xor") def logical_xor(x, y, name="LogicalXor"): """x ^ y = (x | y) & ~(x & y).""" # TODO(alemi) Make this a cwise op if people end up relying on it. return gen_math_ops.logical_and( gen_math_ops.logical_or(x, y), gen_math_ops.logical_not(gen_math_ops.logical_and(x, y)), name=name) _OverrideBinaryOperatorHelper(gen_math_ops.logical_and, "and") _OverrideBinaryOperatorHelper(gen_math_ops.logical_or, "or") _OverrideBinaryOperatorHelper(logical_xor, "xor") ops.Tensor._override_operator("__lt__", gen_math_ops.less) ops.Tensor._override_operator("__le__", gen_math_ops.less_equal) ops.Tensor._override_operator("__gt__", gen_math_ops.greater) ops.Tensor._override_operator("__ge__", gen_math_ops.greater_equal) @tf_export("range") def range(start, limit=None, delta=1, dtype=None, name="range"): # pylint: disable=redefined-builtin """Creates a sequence of numbers. Creates a sequence of numbers that begins at start and extends by increments of delta up to but not including limit. The dtype of the resulting tensor is inferred from the inputs unless it is provided explicitly. Like the Python builtin range, start defaults to 0, so that range(n) = range(0, n). For example: python start = 3 limit = 18 delta = 3 tf.range(start, limit, delta) # [3, 6, 9, 12, 15] start = 3 limit = 1 delta = -0.5 tf.range(start, limit, delta) # [3, 2.5, 2, 1.5] limit = 5 tf.range(limit) # [0, 1, 2, 3, 4]  Args: start: A 0-D Tensor (scalar). Acts as first entry in the range if limit is not None; otherwise, acts as range limit and first entry defaults to 0. limit: A 0-D Tensor (scalar). Upper limit of sequence, exclusive. If None, defaults to the value of start while the first entry of the range defaults to 0. delta: A 0-D Tensor (scalar). Number that increments start. Defaults to 1. dtype: The type of the elements of the resulting tensor. name: A name for the operation. Defaults to "range". Returns: An 1-D Tensor of type dtype. @compatibility(numpy) Equivalent to np.arange @end_compatibility """ if limit is None: start, limit = 0, start with ops.name_scope(name, "Range", [start, limit, delta]) as name: start = ops.convert_to_tensor(start, dtype=dtype, name="start") limit = ops.convert_to_tensor(limit, dtype=dtype, name="limit") delta = ops.convert_to_tensor(delta, dtype=dtype, name="delta") # infer dtype if not explicitly provided if dtype is None: dtype_hierarchy = [ dtypes.int32, dtypes.int64, dtypes.float32, dtypes.float64 ] assert all(arg.dtype in dtype_hierarchy for arg in [start, limit, delta]) inferred_dtype = max( [arg.dtype for arg in [start, limit, delta]], key=dtype_hierarchy.index) start = cast(start, inferred_dtype) limit = cast(limit, inferred_dtype) delta = cast(delta, inferred_dtype) return gen_math_ops._range(start, limit, delta, name=name) # Reduction operations def _ReductionDims(x, axis, reduction_indices): """Returns range(0, rank(x)) if reduction_indices is None.""" # TODO(aselle): Remove this after deprecation if reduction_indices is not None: if axis is not None: raise ValueError("Can't specify both axis' and 'reduction_indices'.") axis = reduction_indices if axis is not None: return axis else: # Fast path: avoid creating Rank and Range ops if ndims is known. if isinstance(x, ops.Tensor) and x._rank() is not None: # pylint: disable=protected-access return constant_op.constant(np.arange(x._rank()), dtype=dtypes.int32) # pylint: disable=protected-access if (isinstance(x, sparse_tensor.SparseTensor) and x.dense_shape.get_shape().is_fully_defined()): rank = x.dense_shape.get_shape()[0].value # sparse.dense_shape is 1-D. return constant_op.constant(np.arange(rank), dtype=dtypes.int32) # Otherwise, we rely on Range and Rank to do the right thing at run-time. return range(0, array_ops.rank(x)) def _may_reduce_to_scalar(keepdims, axis, reduction_indices, output): """Set a reduction's output's shape to be a scalar if we are certain.""" if (not output.shape.is_fully_defined()) and (not keepdims) and ( axis is None) and (reduction_indices is None): output.set_shape(()) return output @tf_export("reduce_sum") @deprecation.deprecated_args( None, "keep_dims is deprecated, use keepdims instead", "keep_dims") def reduce_sum(input_tensor, axis=None, keepdims=None, name=None, reduction_indices=None, keep_dims=None): """Computes the sum of elements across dimensions of a tensor. Reduces input_tensor along the dimensions given in axis. Unless keepdims is true, the rank of the tensor is reduced by 1 for each entry in axis. If keepdims is true, the reduced dimensions are retained with length 1. If axis has no entries, all dimensions are reduced, and a tensor with a single element is returned. For example: python x = tf.constant([[1, 1, 1], [1, 1, 1]]) tf.reduce_sum(x) # 6 tf.reduce_sum(x, 0) # [2, 2, 2] tf.reduce_sum(x, 1) # [3, 3] tf.reduce_sum(x, 1, keepdims=True) # [[3], [3]] tf.reduce_sum(x, [0, 1]) # 6  Args: input_tensor: The tensor to reduce. Should have numeric type. axis: The dimensions to reduce. If None (the default), reduces all dimensions. Must be in the range [-rank(input_tensor), rank(input_tensor)). keepdims: If true, retains reduced dimensions with length 1. name: A name for the operation (optional). reduction_indices: The old (deprecated) name for axis. keep_dims: Deprecated alias for keepdims. Returns: The reduced tensor, of the same dtype as the input_tensor. @compatibility(numpy) Equivalent to np.sum appart the fact that numpy upcast uint8 and int32 to int64 while tensorflow returns the same dtype as the input. @end_compatibility """ keepdims = deprecation.deprecated_argument_lookup("keepdims", keepdims, "keep_dims", keep_dims) if keepdims is None: keepdims = False return _may_reduce_to_scalar(keepdims, axis, reduction_indices, gen_math_ops._sum( input_tensor, _ReductionDims(input_tensor, axis, reduction_indices), keepdims, name=name)) @tf_export("count_nonzero") @deprecation.deprecated_args( None, "keep_dims is deprecated, use keepdims instead", "keep_dims") def count_nonzero(input_tensor, axis=None, keepdims=None, dtype=dtypes.int64, name=None, reduction_indices=None, keep_dims=None): """Computes number of nonzero elements across dimensions of a tensor. Reduces input_tensor along the dimensions given in axis. Unless keepdims is true, the rank of the tensor is reduced by 1 for each entry in axis. If keepdims is true, the reduced dimensions are retained with length 1. If axis has no entries, all dimensions are reduced, and a tensor with a single element is returned. **NOTE** Floating point comparison to zero is done by exact floating point equality check. Small values are **not** rounded to zero for purposes of the nonzero check. For example: python x = tf.constant([[0, 1, 0], [1, 1, 0]]) tf.count_nonzero(x) # 3 tf.count_nonzero(x, 0) # [1, 2, 0] tf.count_nonzero(x, 1) # [1, 2] tf.count_nonzero(x, 1, keepdims=True) # [[1], [2]] tf.count_nonzero(x, [0, 1]) # 3  Args: input_tensor: The tensor to reduce. Should be of numeric type, or bool. axis: The dimensions to reduce. If None (the default), reduces all dimensions. Must be in the range [-rank(input_tensor), rank(input_tensor)). keepdims: If true, retains reduced dimensions with length 1. dtype: The output dtype; defaults to tf.int64. name: A name for the operation (optional). reduction_indices: The old (deprecated) name for axis. keep_dims: Deprecated alias for keepdims. Returns: The reduced tensor (number of nonzero values). """ keepdims = deprecation.deprecated_argument_lookup("keepdims", keepdims, "keep_dims", keep_dims) if keepdims is None: keepdims = False with ops.name_scope(name, "count_nonzero", [input_tensor]): input_tensor = ops.convert_to_tensor(input_tensor, name="input_tensor") zero = input_tensor.dtype.as_numpy_dtype() return cast( reduce_sum( # int64 reduction happens on GPU to_int64(gen_math_ops.not_equal(input_tensor, zero)), axis=axis, keepdims=keepdims, reduction_indices=reduction_indices), dtype=dtype) @tf_export("reduce_mean") @deprecation.deprecated_args( None, "keep_dims is deprecated, use keepdims instead", "keep_dims") def reduce_mean(input_tensor, axis=None, keepdims=None, name=None, reduction_indices=None, keep_dims=None): """Computes the mean of elements across dimensions of a tensor. Reduces input_tensor along the dimensions given in axis. Unless keepdims is true, the rank of the tensor is reduced by 1 for each entry in axis. If keepdims is true, the reduced dimensions are retained with length 1. If axis has no entries, all dimensions are reduced, and a tensor with a single element is returned. For example: python x = tf.constant([[1., 1.], [2., 2.]]) tf.reduce_mean(x) # 1.5 tf.reduce_mean(x, 0) # [1.5, 1.5] tf.reduce_mean(x, 1) # [1., 2.]  Args: input_tensor: The tensor to reduce. Should have numeric type. axis: The dimensions to reduce. If None (the default), reduces all dimensions. Must be in the range [-rank(input_tensor), rank(input_tensor)). keepdims: If true, retains reduced dimensions with length 1. name: A name for the operation (optional). reduction_indices: The old (deprecated) name for axis. keep_dims: Deprecated alias for keepdims. Returns: The reduced tensor. @compatibility(numpy) Equivalent to np.mean Please note that np.mean has a dtype parameter that could be used to specify the output type. By default this is dtype=float64. On the other hand, tf.reduce_mean has an aggressive type inference from input_tensor, for example: python x = tf.constant([1, 0, 1, 0]) tf.reduce_mean(x) # 0 y = tf.constant([1., 0., 1., 0.]) tf.reduce_mean(y) # 0.5  @end_compatibility """ keepdims = deprecation.deprecated_argument_lookup("keepdims", keepdims, "keep_dims", keep_dims) if keepdims is None: keepdims = False return _may_reduce_to_scalar(keepdims, axis, reduction_indices, gen_math_ops.mean( input_tensor, _ReductionDims(input_tensor, axis, reduction_indices), keepdims, name=name)) @tf_export("reduce_prod") @deprecation.deprecated_args( None, "keep_dims is deprecated, use keepdims instead", "keep_dims") def reduce_prod(input_tensor, axis=None, keepdims=None, name=None, reduction_indices=None, keep_dims=None): """Computes the product of elements across dimensions of a tensor. Reduces input_tensor along the dimensions given in axis. Unless keepdims is true, the rank of the tensor is reduced by 1 for each entry in axis. If keepdims is true, the reduced dimensions are retained with length 1. If axis has no entries, all dimensions are reduced, and a tensor with a single element is returned. Args: input_tensor: The tensor to reduce. Should have numeric type. axis: The dimensions to reduce. If None (the default), reduces all dimensions. Must be in the range [-rank(input_tensor), rank(input_tensor)). keepdims: If true, retains reduced dimensions with length 1. name: A name for the operation (optional). reduction_indices: The old (deprecated) name for axis. keep_dims: Deprecated alias for keepdims. Returns: The reduced tensor. @compatibility(numpy) Equivalent to np.prod @end_compatibility """ keepdims = deprecation.deprecated_argument_lookup("keepdims", keepdims, "keep_dims", keep_dims) if keepdims is None: keepdims = False return _may_reduce_to_scalar(keepdims, axis, reduction_indices, gen_math_ops.prod( input_tensor, _ReductionDims(input_tensor, axis, reduction_indices), keepdims, name=name)) @tf_export("reduce_min") @deprecation.deprecated_args( None, "keep_dims is deprecated, use keepdims instead", "keep_dims") def reduce_min(input_tensor, axis=None, keepdims=None, name=None, reduction_indices=None, keep_dims=None): """Computes the minimum of elements across dimensions of a tensor. Reduces input_tensor along the dimensions given in axis. Unless keepdims is true, the rank of the tensor is reduced by 1 for each entry in axis. If keepdims is true, the reduced dimensions are retained with length 1. If axis has no entries, all dimensions are reduced, and a tensor with a single element is returned. Args: input_tensor: The tensor to reduce. Should have numeric type. axis: The dimensions to reduce. If None (the default), reduces all dimensions. Must be in the range [-rank(input_tensor), rank(input_tensor)). keepdims: If true, retains reduced dimensions with length 1. name: A name for the operation (optional). reduction_indices: The old (deprecated) name for axis. keep_dims: Deprecated alias for keepdims. Returns: The reduced tensor. @compatibility(numpy) Equivalent to np.min @end_compatibility """ keepdims = deprecation.deprecated_argument_lookup("keepdims", keepdims, "keep_dims", keep_dims) if keepdims is None: keepdims = False return _may_reduce_to_scalar(keepdims, axis, reduction_indices, gen_math_ops._min( input_tensor, _ReductionDims(input_tensor, axis, reduction_indices), keepdims, name=name)) @tf_export("reduce_max") @deprecation.deprecated_args( None, "keep_dims is deprecated, use keepdims instead", "keep_dims") def reduce_max(input_tensor, axis=None, keepdims=None, name=None, reduction_indices=None, keep_dims=None): """Computes the maximum of elements across dimensions of a tensor. Reduces input_tensor along the dimensions given in axis. Unless keepdims is true, the rank of the tensor is reduced by 1 for each entry in axis. If keepdims is true, the reduced dimensions are retained with length 1. If axis has no entries, all dimensions are reduced, and a tensor with a single element is returned. Args: input_tensor: The tensor to reduce. Should have numeric type. axis: The dimensions to reduce. If None (the default), reduces all dimensions. Must be in the range [-rank(input_tensor), rank(input_tensor)). keepdims: If true, retains reduced dimensions with length 1. name: A name for the operation (optional). reduction_indices: The old (deprecated) name for axis. keep_dims: Deprecated alias for keepdims. Returns: The reduced tensor. @compatibility(numpy) Equivalent to np.max @end_compatibility """ keepdims = deprecation.deprecated_argument_lookup("keepdims", keepdims, "keep_dims", keep_dims) if keepdims is None: keepdims = False return _may_reduce_to_scalar(keepdims, axis, reduction_indices, gen_math_ops._max( input_tensor, _ReductionDims(input_tensor, axis, reduction_indices), keepdims, name=name)) @tf_export("reduce_all") @deprecation.deprecated_args( None, "keep_dims is deprecated, use keepdims instead", "keep_dims") def reduce_all(input_tensor, axis=None, keepdims=None, name=None, reduction_indices=None, keep_dims=None): """Computes the "logical and" of elements across dimensions of a tensor. Reduces input_tensor along the dimensions given in axis. Unless keepdims is true, the rank of the tensor is reduced by 1 for each entry in axis. If keepdims is true, the reduced dimensions are retained with length 1. If axis has no entries, all dimensions are reduced, and a tensor with a single element is returned. For example: python x = tf.constant([[True, True], [False, False]]) tf.reduce_all(x) # False tf.reduce_all(x, 0) # [False, False] tf.reduce_all(x, 1) # [True, False]  Args: input_tensor: The boolean tensor to reduce. axis: The dimensions to reduce. If None (the default), reduces all dimensions. Must be in the range [-rank(input_tensor), rank(input_tensor)). keepdims: If true, retains reduced dimensions with length 1. name: A name for the operation (optional). reduction_indices: The old (deprecated) name for axis. keep_dims: Deprecated alias for keepdims. Returns: The reduced tensor. @compatibility(numpy) Equivalent to np.all @end_compatibility """ keepdims = deprecation.deprecated_argument_lookup("keepdims", keepdims, "keep_dims", keep_dims) if keepdims is None: keepdims = False return _may_reduce_to_scalar(keepdims, axis, reduction_indices, gen_math_ops._all( input_tensor, _ReductionDims(input_tensor, axis, reduction_indices), keepdims, name=name)) @tf_export("reduce_any") @deprecation.deprecated_args( None, "keep_dims is deprecated, use keepdims instead", "keep_dims") def reduce_any(input_tensor, axis=None, keepdims=None, name=None, reduction_indices=None, keep_dims=None): """Computes the "logical or" of elements across dimensions of a tensor. Reduces input_tensor along the dimensions given in axis. Unless keepdims is true, the rank of the tensor is reduced by 1 for each entry in axis. If keepdims is true, the reduced dimensions are retained with length 1. If axis has no entries, all dimensions are reduced, and a tensor with a single element is returned. For example: python x = tf.constant([[True, True], [False, False]]) tf.reduce_any(x) # True tf.reduce_any(x, 0) # [True, True] tf.reduce_any(x, 1) # [True, False]  Args: input_tensor: The boolean tensor to reduce. axis: The dimensions to reduce. If None (the default), reduces all dimensions. Must be in the range [-rank(input_tensor), rank(input_tensor)). keepdims: If true, retains reduced dimensions with length 1. name: A name for the operation (optional). reduction_indices: The old (deprecated) name for axis. keep_dims: Deprecated alias for keepdims. Returns: The reduced tensor. @compatibility(numpy) Equivalent to np.any @end_compatibility """ keepdims = deprecation.deprecated_argument_lookup("keepdims", keepdims, "keep_dims", keep_dims) if keepdims is None: keepdims = False return _may_reduce_to_scalar(keepdims, axis, reduction_indices, gen_math_ops._any( input_tensor, _ReductionDims(input_tensor, axis, reduction_indices), keepdims, name=name)) @tf_export("reduce_logsumexp") @deprecation.deprecated_args( None, "keep_dims is deprecated, use keepdims instead", "keep_dims") def reduce_logsumexp(input_tensor, axis=None, keepdims=None, name=None, reduction_indices=None, keep_dims=None): """Computes log(sum(exp(elements across dimensions of a tensor))). Reduces input_tensor along the dimensions given in axis. Unless keepdims is true, the rank of the tensor is reduced by 1 for each entry in axis. If keepdims is true, the reduced dimensions are retained with length 1. If axis has no entries, all dimensions are reduced, and a tensor with a single element is returned. This function is more numerically stable than log(sum(exp(input))). It avoids overflows caused by taking the exp of large inputs and underflows caused by taking the log of small inputs. For example: python x = tf.constant([[0., 0., 0.], [0., 0., 0.]]) tf.reduce_logsumexp(x) # log(6) tf.reduce_logsumexp(x, 0) # [log(2), log(2), log(2)] tf.reduce_logsumexp(x, 1) # [log(3), log(3)] tf.reduce_logsumexp(x, 1, keepdims=True) # [[log(3)], [log(3)]] tf.reduce_logsumexp(x, [0, 1]) # log(6)  Args: input_tensor: The tensor to reduce. Should have numeric type. axis: The dimensions to reduce. If None (the default), reduces all dimensions. Must be in the range [-rank(input_tensor), rank(input_tensor)). keepdims: If true, retains reduced dimensions with length 1. name: A name for the operation (optional). reduction_indices: The old (deprecated) name for axis. keep_dims: Deprecated alias for keepdims. Returns: The reduced tensor. """ keepdims = deprecation.deprecated_argument_lookup("keepdims", keepdims, "keep_dims", keep_dims) if keepdims is None: keepdims = False with ops.name_scope(name, "ReduceLogSumExp", [input_tensor]) as name: raw_max = reduce_max( input_tensor, axis=axis, reduction_indices=reduction_indices, keepdims=True) my_max = array_ops.stop_gradient( array_ops.where( gen_math_ops.is_finite(raw_max), raw_max, array_ops.zeros_like(raw_max))) result = gen_math_ops.log( reduce_sum( gen_math_ops.exp(input_tensor - my_max), axis, keepdims=keepdims, reduction_indices=reduction_indices)) if not keepdims: my_max = array_ops.reshape(my_max, array_ops.shape(result)) result += my_max return _may_reduce_to_scalar(keepdims, axis, reduction_indices, result) @tf_export("trace", "linalg.trace") def trace(x, name=None): """Compute the trace of a tensor x. trace(x) returns the sum along the main diagonal of each inner-most matrix in x. If x is of rank k with shape [I, J, K, ..., L, M, N], then output is a tensor of rank k-2 with dimensions [I, J, K, ..., L] where output[i, j, k, ..., l] = trace(x[i, j, i, ..., l, :, :]) For example: python x = tf.constant([[1, 2], [3, 4]]) tf.trace(x) # 5 x = tf.constant([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) tf.trace(x) # 15 x = tf.constant([[[1, 2, 3], [4, 5, 6], [7, 8, 9]], [[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]]]) tf.trace(x) # [15, -15]  Args: x: tensor. name: A name for the operation (optional). Returns: The trace of input tensor. """ with ops.name_scope(name, "Trace", [x]) as name: x = ops.convert_to_tensor(x, name="x") return reduce_sum(array_ops.matrix_diag_part(x), [-1], name=name) @tf_export("matmul") def matmul(a, b, transpose_a=False, transpose_b=False, adjoint_a=False, adjoint_b=False, a_is_sparse=False, b_is_sparse=False, name=None): """Multiplies matrix a by matrix b, producing a * b. The inputs must, following any transpositions, be tensors of rank >= 2 where the inner 2 dimensions specify valid matrix multiplication arguments, and any further outer dimensions match. Both matrices must be of the same type. The supported types are: float16, float32, float64, int32, complex64, complex128. Either matrix can be transposed or adjointed (conjugated and transposed) on the fly by setting one of the corresponding flag to True. These are False by default. If one or both of the matrices contain a lot of zeros, a more efficient multiplication algorithm can be used by setting the corresponding a_is_sparse or b_is_sparse flag to True. These are False by default. This optimization is only available for plain matrices (rank-2 tensors) with datatypes bfloat16 or float32. For example: python # 2-D tensor a # [[1, 2, 3], # [4, 5, 6]] a = tf.constant([1, 2, 3, 4, 5, 6], shape=[2, 3]) # 2-D tensor b # [[ 7, 8], # [ 9, 10], # [11, 12]] b = tf.constant([7, 8, 9, 10, 11, 12], shape=[3, 2]) # a * b # [[ 58, 64], # [139, 154]] c = tf.matmul(a, b) # 3-D tensor a # [[[ 1, 2, 3], # [ 4, 5, 6]], # [[ 7, 8, 9], # [10, 11, 12]]] a = tf.constant(np.arange(1, 13, dtype=np.int32), shape=[2, 2, 3]) # 3-D tensor b # [[[13, 14], # [15, 16], # [17, 18]], # [[19, 20], # [21, 22], # [23, 24]]] b = tf.constant(np.arange(13, 25, dtype=np.int32), shape=[2, 3, 2]) # a * b # [[[ 94, 100], # [229, 244]], # [[508, 532], # [697, 730]]] c = tf.matmul(a, b) # Since python >= 3.5 the @ operator is supported (see PEP 465). # In TensorFlow, it simply calls the tf.matmul() function, so the # following lines are equivalent: d = a @ b @ [[10.], [11.]] d = tf.matmul(tf.matmul(a, b), [[10.], [11.]])  Args: a: Tensor of type float16, float32, float64, int32, complex64, complex128 and rank > 1. b: Tensor with same type and rank as a. transpose_a: If True, a is transposed before multiplication. transpose_b: If True, b is transposed before multiplication. adjoint_a: If True, a is conjugated and transposed before multiplication. adjoint_b: If True, b is conjugated and transposed before multiplication. a_is_sparse: If True, a is treated as a sparse matrix. b_is_sparse: If True, b is treated as a sparse matrix. name: Name for the operation (optional). Returns: A Tensor of the same type as a and b where each inner-most matrix is the product of the corresponding matrices in a and b, e.g. if all transpose or adjoint attributes are False: output[..., i, j] = sum_k (a[..., i, k] * b[..., k, j]), for all indices i, j. Note: This is matrix product, not element-wise product. Raises: ValueError: If transpose_a and adjoint_a, or transpose_b and adjoint_b are both set to True. """ with ops.name_scope(name, "MatMul", [a, b]) as name: if transpose_a and adjoint_a: raise ValueError("Only one of transpose_a and adjoint_a can be True.") if transpose_b and adjoint_b: raise ValueError("Only one of transpose_b and adjoint_b can be True.") if context.executing_eagerly(): if not isinstance(a, (ops.EagerTensor, _resource_variable_type)): a = ops.convert_to_tensor(a, name="a") if not isinstance(b, (ops.EagerTensor, _resource_variable_type)): b = ops.convert_to_tensor(b, name="b") else: a = ops.convert_to_tensor(a, name="a") b = ops.convert_to_tensor(b, name="b") # TODO(apassos) remove _shape_tuple here when it is not needed. a_shape = a._shape_tuple() # pylint: disable=protected-access b_shape = b._shape_tuple() # pylint: disable=protected-access if (not a_is_sparse and not b_is_sparse) and ((a_shape is None or len(a_shape) > 2) and (b_shape is None or len(b_shape) > 2)): # BatchMatmul does not support transpose, so we conjugate the matrix and # use adjoint instead. Conj() is a noop for real matrices. if transpose_a: a = conj(a) adjoint_a = True if transpose_b: b = conj(b) adjoint_b = True return gen_math_ops.batch_mat_mul( a, b, adj_x=adjoint_a, adj_y=adjoint_b, name=name) # Neither matmul nor sparse_matmul support adjoint, so we conjugate # the matrix and use transpose instead. Conj() is a noop for real # matrices. if adjoint_a: a = conj(a) transpose_a = True if adjoint_b: b = conj(b) transpose_b = True use_sparse_matmul = False if a_is_sparse or b_is_sparse: sparse_matmul_types = [dtypes.bfloat16, dtypes.float32] use_sparse_matmul = ( a.dtype in sparse_matmul_types and b.dtype in sparse_matmul_types) if (a.dtype == dtypes.bfloat16 or b.dtype == dtypes.bfloat16 and a.dtype != b.dtype): # matmul currently doesn't handle mixed-precision inputs. use_sparse_matmul = True if use_sparse_matmul: ret = sparse_matmul( a, b, transpose_a=transpose_a, transpose_b=transpose_b, a_is_sparse=a_is_sparse, b_is_sparse=b_is_sparse, name=name) # sparse_matmul always returns float32, even with # bfloat16 inputs. This prevents us from configuring bfloat16 training. # casting to bfloat16 also matches non-sparse matmul behavior better. if a.dtype == dtypes.bfloat16 and b.dtype == dtypes.bfloat16: ret = cast(ret, dtypes.bfloat16) return ret else: return gen_math_ops.mat_mul( a, b, transpose_a=transpose_a, transpose_b=transpose_b, name=name) _OverrideBinaryOperatorHelper(matmul, "matmul") sparse_matmul = gen_math_ops.sparse_mat_mul tf_export("sparse_matmul")(sparse_matmul) @ops.RegisterStatistics("MatMul", "flops") def _calc_mat_mul_flops(graph, node): """Calculates the compute resources needed for MatMul.""" transpose_a = node.attr["transpose_a"].b a_shape = graph_util.tensor_shape_from_node_def_name(graph, node.input[0]) a_shape.assert_is_fully_defined() if transpose_a: k = int(a_shape[0]) else: k = int(a_shape[1]) output_shape = graph_util.tensor_shape_from_node_def_name(graph, node.name) output_shape.assert_is_fully_defined() output_count = np.prod(output_shape.as_list()) return ops.OpStats("flops", (k * output_count * 2)) def _as_indexed_slices(x, optimize=True): """Convert 'x' to IndexedSlices. Convert a dense Tensor to a block-sparse IndexedSlices. Args: x: Either a Tensor object, or an IndexedSlices object. optimize: if true, attempt to optimize the conversion of 'x'. Returns: An IndexedSlices object. Raises: TypeError: If 'x' is not a Tensor or an IndexedSlices object. """ # TODO(touts): op_scope if not isinstance(x, (ops.Tensor, ops.IndexedSlices)): raise TypeError("Not a Tensor or IndexedSlices: %s" % type(x)) if isinstance(x, ops.IndexedSlices): return x x_shape = array_ops.shape_internal(x, optimize=optimize) return ops.IndexedSlices(x, range(0, x_shape[0]), x_shape) def _as_indexed_slices_list(inputs, optimize=True): """Convert all elements of 'inputs' to IndexedSlices. Additionally, homogenize the types of all the indices to either int32 or int64. Args: inputs: List containing either Tensor or IndexedSlices objects. optimize: if true, attempt to optimize the conversion of each input. Returns: A list of IndexedSlices objects. Raises: TypeError: If 'inputs' is not a list or a tuple. """ if not isinstance(inputs, (list, tuple)): raise TypeError("Expected a list or tuple, not a %s" % type(inputs)) outputs = [_as_indexed_slices(i, optimize=optimize) for i in inputs] with_int32_index = [ o.indices for o in outputs if o.indices.dtype == dtypes.int32 ] if not with_int32_index or len(with_int32_index) == len(outputs): return outputs casted_outputs = [] for o in outputs: if o.indices.dtype == dtypes.int32: casted_outputs.append( ops.IndexedSlices(o.values, cast(o.indices, dtypes.int64), o.dense_shape)) else: casted_outputs.append(o) return casted_outputs @tf_export("add_n") def add_n(inputs, name=None): """Adds all input tensors element-wise. Args: inputs: A list of Tensor objects, each with same shape and type. name: A name for the operation (optional). Returns: A Tensor of same shape and type as the elements of inputs. Raises: ValueError: If inputs don't all have same shape and dtype or the shape cannot be inferred. """ if not inputs or not isinstance(inputs, (list, tuple)): raise ValueError("inputs must be a list of at least one Tensor with the " "same dtype and shape") inputs = ops.convert_n_to_tensor_or_indexed_slices(inputs) if not all(isinstance(x, ops.Tensor) for x in inputs): raise ValueError("inputs must be a list of at least one Tensor with the " "same dtype and shape") if len(inputs) == 1: if name: return array_ops.identity(inputs[0], name=name) return inputs[0] return gen_math_ops.add_n(inputs, name=name) @tf_export("accumulate_n") def accumulate_n(inputs, shape=None, tensor_dtype=None, name=None): """Returns the element-wise sum of a list of tensors. Optionally, pass shape and tensor_dtype for shape and type checking, otherwise, these are inferred. tf.accumulate_n performs the same operation as tf.add_n, but does not wait for all of its inputs to be ready before beginning to sum. This can save memory if inputs are ready at different times, since minimum temporary storage is proportional to the output size rather than the inputs size. accumulate_n is differentiable (but wasn't previous to TensorFlow 1.7). For example: python a = tf.constant([[1, 2], [3, 4]]) b = tf.constant([[5, 0], [0, 6]]) tf.accumulate_n([a, b, a]) # [[7, 4], [6, 14]] # Explicitly pass shape and type tf.accumulate_n([a, b, a], shape=[2, 2], tensor_dtype=tf.int32) # [[7, 4], # [6, 14]]  Args: inputs: A list of Tensor objects, each with same shape and type. shape: Shape of elements of inputs. tensor_dtype: The type of inputs. name: A name for the operation (optional). Returns: A Tensor of same shape and type as the elements of inputs. Raises: ValueError: If inputs don't all have same shape and dtype or the shape cannot be inferred. """ def _input_error(): return ValueError("inputs must be a list of at least one Tensor with the " "same dtype and shape") if not inputs or not isinstance(inputs, (list, tuple)): raise _input_error() inputs = ops.convert_n_to_tensor_or_indexed_slices(inputs) if not all(isinstance(x, ops.Tensor) for x in inputs): raise _input_error() if not all(x.dtype == inputs[0].dtype for x in inputs): raise _input_error() if shape is not None: shape = tensor_shape.as_shape(shape) else: shape = tensor_shape.unknown_shape() for input_tensor in inputs: if isinstance(input_tensor, ops.Tensor): shape = shape.merge_with(input_tensor.get_shape()) # tensor_dtype is for safety only; operator's output type computed in C++ if tensor_dtype is not None and tensor_dtype != inputs[0].dtype: raise TypeError("tensor_dtype is {}, but input is of type {}".format( tensor_dtype, inputs[0].dtype)) if len(inputs) == 1 and name is None: return inputs[0] elif len(inputs) == 1 and name is not None: return array_ops.identity(inputs[0], name=name) elif context.executing_eagerly(): # TemporaryVariable not currently supported in eager mode; fall back # onto AddN for now. # TODO(frreiss) remove this once the lifetime of eager variables gets # addressed return add_n(inputs, name=name) else: return gen_math_ops.accumulate_nv2(inputs, name=name, shape=shape) # pylint: disable=protected-access @ops.RegisterGradient("AccumulateNV2") def _accumulate_n_grad(op, grad): """Same as gradient for AddN. Copies the gradient to all inputs.""" # Not broadcasting. return [grad] * len(op.inputs) @tf_export("nn.sigmoid", "sigmoid") def sigmoid(x, name=None): """Computes sigmoid of x element-wise. Specifically, y = 1 / (1 + exp(-x)). Args: x: A Tensor with type float16, float32, float64, complex64, or complex128. name: A name for the operation (optional). Returns: A Tensor with the same type as x. @compatibility(numpy) Equivalent to np.scipy.special.expit @end_compatibility """ with ops.name_scope(name, "Sigmoid", [x]) as name: x = ops.convert_to_tensor(x, name="x") return gen_math_ops.sigmoid(x, name=name) @tf_export("log_sigmoid") def log_sigmoid(x, name=None): """Computes log sigmoid of x element-wise. Specifically, y = log(1 / (1 + exp(-x))). For numerical stability, we use y = -tf.nn.softplus(-x). Args: x: A Tensor with type float32 or float64. name: A name for the operation (optional). Returns: A Tensor with the same type as x. """ with ops.name_scope(name, "LogSigmoid", [x]) as name: x = ops.convert_to_tensor(x, name="x") return gen_math_ops.neg(gen_nn_ops.softplus(-x), name=name) @tf_export("nn.tanh", "tanh") def tanh(x, name=None): """Computes hyperbolic tangent of x element-wise. Args: x: A Tensor or SparseTensor with type float16, float32, double, complex64, or complex128. name: A name for the operation (optional). Returns: A Tensor or SparseTensor respectively with the same type as x. """ with ops.name_scope(name, "Tanh", [x]) as name: if isinstance(x, sparse_tensor.SparseTensor): x_tanh = gen_math_ops.tanh(x.values, name=name) return sparse_tensor.SparseTensor( indices=x.indices, values=x_tanh, dense_shape=x.dense_shape) else: return gen_math_ops.tanh(x, name=name) @tf_export("bincount") def bincount(arr, weights=None, minlength=None, maxlength=None, dtype=dtypes.int32): """Counts the number of occurrences of each value in an integer array. If minlength and maxlength are not given, returns a vector with length tf.reduce_max(arr) + 1 if arr is non-empty, and length 0 otherwise. If weights are non-None, then index i of the output stores the sum of the value in weights at each index where the corresponding value in arr is i. Args: arr: An int32 tensor of non-negative values. weights: If non-None, must be the same shape as arr. For each value in arr, the bin will be incremented by the corresponding weight instead of 1. minlength: If given, ensures the output has length at least minlength, padding with zeros at the end if necessary. maxlength: If given, skips values in arr that are equal or greater than maxlength, ensuring that the output has length at most maxlength. dtype: If weights is None, determines the type of the output bins. Returns: A vector with the same dtype as weights or the given dtype. The bin values. """ arr = ops.convert_to_tensor(arr, name="arr", dtype=dtypes.int32) array_is_nonempty = reduce_prod(array_ops.shape(arr)) > 0 output_size = cast(array_is_nonempty, dtypes.int32) * (reduce_max(arr) + 1) if minlength is not None: minlength = ops.convert_to_tensor( minlength, name="minlength", dtype=dtypes.int32) output_size = gen_math_ops.maximum(minlength, output_size) if maxlength is not None: maxlength = ops.convert_to_tensor( maxlength, name="maxlength", dtype=dtypes.int32) output_size = gen_math_ops.minimum(maxlength, output_size) if weights is not None: weights = ops.convert_to_tensor(weights, name="weights") return gen_math_ops.unsorted_segment_sum(weights, arr, output_size) weights = constant_op.constant([], dtype) return gen_math_ops.bincount(arr, output_size, weights) @tf_export("cumsum") def cumsum(x, axis=0, exclusive=False, reverse=False, name=None): """Compute the cumulative sum of the tensor x along axis. By default, this op performs an inclusive cumsum, which means that the first element of the input is identical to the first element of the output: python tf.cumsum([a, b, c]) # [a, a + b, a + b + c]  By setting the exclusive kwarg to True, an exclusive cumsum is performed instead: python tf.cumsum([a, b, c], exclusive=True) # [0, a, a + b]  By setting the reverse kwarg to True, the cumsum is performed in the opposite direction: python tf.cumsum([a, b, c], reverse=True) # [a + b + c, b + c, c]  This is more efficient than using separate tf.reverse ops. The reverse and exclusive kwargs can also be combined: python tf.cumsum([a, b, c], exclusive=True, reverse=True) # [b + c, c, 0]  Args: x: A Tensor. Must be one of the following types: float32, float64, int64, int32, uint8, uint16, int16, int8, complex64, complex128, qint8, quint8, qint32, half. axis: A Tensor of type int32 (default: 0). Must be in the range [-rank(x), rank(x)). exclusive: If True, perform exclusive cumsum. reverse: A bool (default: False). name: A name for the operation (optional). Returns: A Tensor. Has the same type as x. """ with ops.name_scope(name, "Cumsum", [x]) as name: x = ops.convert_to_tensor(x, name="x") return gen_math_ops.cumsum( x, axis, exclusive=exclusive, reverse=reverse, name=name) @tf_export("cumprod") def cumprod(x, axis=0, exclusive=False, reverse=False, name=None): """Compute the cumulative product of the tensor x along axis. By default, this op performs an inclusive cumprod, which means that the first element of the input is identical to the first element of the output: python tf.cumprod([a, b, c]) # [a, a * b, a * b * c]  By setting the exclusive kwarg to True, an exclusive cumprod is performed instead: python tf.cumprod([a, b, c], exclusive=True) # [1, a, a * b]  By setting the reverse kwarg to True, the cumprod is performed in the opposite direction: python tf.cumprod([a, b, c], reverse=True) # [a * b * c, b * c, c]  This is more efficient than using separate tf.reverse ops. The reverse and exclusive kwargs can also be combined: python tf.cumprod([a, b, c], exclusive=True, reverse=True) # [b * c, c, 1]  Args: x: A Tensor. Must be one of the following types: float32, float64, int64, int32, uint8, uint16, int16, int8, complex64, complex128, qint8, quint8, qint32, half. axis: A Tensor of type int32 (default: 0). Must be in the range [-rank(x), rank(x)). exclusive: If True, perform exclusive cumprod. reverse: A bool (default: False). name: A name for the operation (optional). Returns: A Tensor. Has the same type as x. """ with ops.name_scope(name, "Cumprod", [x]) as name: x = ops.convert_to_tensor(x, name="x") return gen_math_ops.cumprod( x, axis, exclusive=exclusive, reverse=reverse, name=name) @tf_export("conj") def conj(x, name=None): r"""Returns the complex conjugate of a complex number. Given a tensor input of complex numbers, this operation returns a tensor of complex numbers that are the complex conjugate of each element in input. The complex numbers in input must be of the form \$$a + bj\$$, where *a* is the real part and *b* is the imaginary part. The complex conjugate returned by this operation is of the form \$$a - bj\$$. For example: # tensor 'input' is [-2.25 + 4.75j, 3.25 + 5.75j] tf.conj(input) ==> [-2.25 - 4.75j, 3.25 - 5.75j] If x is real, it is returned unchanged. Args: x: Tensor to conjugate. Must have numeric or variant type. name: A name for the operation (optional). Returns: A Tensor that is the conjugate of x (with the same type). Raises: TypeError: If x is not a numeric tensor. """ if isinstance(x, ops.Tensor): dt = x.dtype if dt.is_floating or dt.is_integer: return x with ops.name_scope(name, "Conj", [x]) as name: x = ops.convert_to_tensor(x, name="x") if x.dtype.is_complex or x.dtype == dtypes.variant: return gen_math_ops.conj(x, name=name) elif x.dtype.is_floating or x.dtype.is_integer: return x else: raise TypeError( "Expected numeric or variant tensor, got dtype %r" % x.dtype) def _BroadcastShape(op): """Common shape function for binary operators that broadcast their inputs.""" return [ common_shapes.broadcast_shape(op.inputs[0].get_shape(), op.inputs[1].get_shape()) ] def reduced_shape(input_shape, axes): """Helper function for reduction ops. Args: input_shape: 1-D Tensor, the shape of the Tensor being reduced. axes: 1-D Tensor, the reduction axes. Returns: A 1-D Tensor, the output shape as if keepdims were set to True. """ # Example: # cast needed for SparseTensor reductions input_shape = to_int32(input_shape) # [2, 3, 5, 7] axes = to_int32(axes) # [1, 2] input_rank = array_ops.size(input_shape) # 4 axes = (axes + input_rank) % input_rank axes_shape = array_ops.shape(axes) # [2] return gen_data_flow_ops.dynamic_stitch( # [2, 1, 1, 7] [ range(input_rank), # [0, 1, 2, 3] axes ], # [1, 2] [ input_shape, # [2, 3, 5, 7] array_ops.fill(axes_shape, 1) ]) # [1, 1] def _unsorted_segment_N(data, segment_ids, num_segments): """ Helper function for unsorted_segment_mean/_sqrtN. Computes the number of segment entries with 0-entries set to 1 to allow division by N. """ # bincount doesn't support negative indices so we use unsorted_segment_sum ones_tensor = array_ops.ones(segment_ids.shape, dtype=data.dtype) N = gen_math_ops.unsorted_segment_sum(ones_tensor, segment_ids, num_segments) # add dimensions for all non-reduced axes ndims_output = data.shape.ndims - segment_ids.shape.ndims broadcast_shape = [num_segments] + [1] * ndims_output N = array_ops.reshape(N, broadcast_shape) return gen_math_ops.maximum(N, 1) @tf_export("unsorted_segment_mean") def unsorted_segment_mean(data, segment_ids, num_segments, name=None): r""" Computes the mean along segments of a tensor. Read @{$math_ops#segmentation$the section on segmentation} for an explanation of segments. This operator is similar to the unsorted segment sum operator found [here](../../../api_docs/python/math_ops.md#UnsortedSegmentSum). Instead of computing the sum over segments, it computes the mean of all entries belonging to a segment such that: \$$output_i = 1/N_i \sum data_j\$$ where the sum is over j such that segment_ids[j] == i with \\N_i\\ being the number of occurrences of id \\i\\. If there is no entry for a given segment ID i, it outputs 0. segment_ids: A 1-D tensor whose rank is equal to the rank of data's first dimension. output: Has same shape as data, except for dimension 0 which has size num_segments. """ with ops.name_scope(name, "UnsortedSegmentMean"): data = ops.convert_to_tensor(data) segment_ids = ops.convert_to_tensor(segment_ids) N = _unsorted_segment_N(data, segment_ids, num_segments) summed = gen_math_ops.unsorted_segment_sum(data, segment_ids, num_segments) return summed / N @tf_export("unsorted_segment_sqrt_n") def unsorted_segment_sqrt_n(data, segment_ids, num_segments, name=None): r"""Computes the sum along segments of a tensor divided by the sqrt(N). Read @{$math_ops#segmentation$the section on segmentation} for an explanation of segments. This operator is similar to the unsorted segment sum operator found [here](../../../api_docs/python/math_ops.md#UnsortedSegmentSum). Additionally to computing the sum over segments, it divides the results by sqrt(N). \$$output_i = 1/sqrt(N_i) \sum data_j\$$ where the sum is over j such that segment_ids[j] == i with \\N_i\\ being the number of occurrences of id \\i\\. If there is no entry for a given segment ID i, it outputs 0. Note that this op only supports floating point and complex dtypes, due to tf.sqrt only supporting these types. segment_ids: A 1-D tensor whose rank is equal to the rank of data's first dimension. output: Has same shape as data, except for dimension 0 which has size num_segments. """ with ops.name_scope(name, "UnsortedSegmentSqrtN"): data = ops.convert_to_tensor(data) segment_ids = ops.convert_to_tensor(segment_ids) N = _unsorted_segment_N(data, segment_ids, num_segments) summed = gen_math_ops.unsorted_segment_sum(data, segment_ids, num_segments) return summed / gen_math_ops.sqrt(N) @tf_export("sparse_segment_sum") def sparse_segment_sum(data, indices, segment_ids, name=None, num_segments=None): r"""Computes the sum along sparse segments of a tensor. Read @{$math_ops#Segmentation$the section on segmentation} for an explanation of segments. Like SegmentSum, but segment_ids can have rank less than data's first dimension, selecting a subset of dimension 0, specified by indices. segment_ids is allowed to have missing ids, in which case the output will be zeros at those indices. In those cases num_segments is used to determine the size of the output. For example: python c = tf.constant([[1,2,3,4], [-1,-2,-3,-4], [5,6,7,8]]) # Select two rows, one segment. tf.sparse_segment_sum(c, tf.constant([0, 1]), tf.constant([0, 0])) # => [[0 0 0 0]] # Select two rows, two segment. tf.sparse_segment_sum(c, tf.constant([0, 1]), tf.constant([0, 1])) # => [[ 1 2 3 4] # [-1 -2 -3 -4]] # With missing segment ids. tf.sparse_segment_sum(c, tf.constant([0, 1]), tf.constant([0, 2]), num_segments=4) # => [[ 1 2 3 4] # [ 0 0 0 0] # [-1 -2 -3 -4] # [ 0 0 0 0]] # Select all rows, two segments. tf.sparse_segment_sum(c, tf.constant([0, 1, 2]), tf.constant([0, 0, 1])) # => [[0 0 0 0] # [5 6 7 8]] # Which is equivalent to: tf.segment_sum(c, tf.constant([0, 0, 1]))  Args: data: A Tensor with data that will be assembled in the output. indices: A 1-D Tensor with indices into data. Has same rank as segment_ids. segment_ids: A 1-D Tensor with indices into the output Tensor. Values should be sorted and can be repeated. name: A name for the operation (optional). num_segments: An optional int32 scalar. Indicates the size of the output Tensor. Returns: A tensor of the shape as data, except for dimension 0 which has size k, the number of segments specified via num_segments or inferred for the last element in segments_ids. """ if num_segments is not None: return gen_math_ops.sparse_segment_sum_with_num_segments( data=data, indices=indices, segment_ids=segment_ids, num_segments=num_segments, name=name) else: return gen_math_ops.sparse_segment_sum( data=data, indices=indices, segment_ids=segment_ids, name=name) @tf_export("sparse_segment_mean") def sparse_segment_mean(data, indices, segment_ids, name=None, num_segments=None): r"""Computes the mean along sparse segments of a tensor. Read @{$math_ops#Segmentation\$the section on segmentation} for an explanation of segments. Like SegmentMean, but segment_ids can have rank less than data's first dimension, selecting a subset of dimension 0, specified by indices. segment_ids is allowed to have missing ids, in which case the output will be zeros at those indices. In those cases num_segments is used to determine the size of the output. Args: data: A Tensor with data that will be assembled in the output. indices: A 1-D Tensor with indices into data. Has same rank as segment_ids. segment_ids: A 1-D Tensor with indices into the output Tensor. Values should be sorted and can be repeated. name: A name for the operation (optional). num_segments: An optional int32 scalar. Indicates the size of the output Tensor. Returns: A tensor of the shape as data, except for dimension 0 which has size k, the number of segments specified via num_segments or inferred for the last element in segments_ids. """ if num_segments is not None: return gen_math_ops.sparse_segment_mean_with_num_segments( data=data, indices=indices, segment_ids=segment_ids, num_segments=num_segments, name=name) else: return gen_math_ops.sparse_segment_mean( data=data, indices=indices, segment_ids=segment_ids, name=name) @tf_export("sparse_segment_sqrt_n") def sparse_segment_sqrt_n(data, indices, segment_ids, name=None, num_segments=None): r"""Computes the sum along sparse segments of a tensor divided by the sqrt(N). N is the size of the segment being reduced. Args: data: A Tensor with data that will be assembled in the output. indices: A 1-D Tensor with indices into data. Has same rank as segment_ids. segment_ids: A 1-D Tensor with indices into the output Tensor. Values should be sorted and can be repeated. name: A name for the operation (optional). num_segments: An optional int32 scalar. Indicates the size of the output Tensor. Returns: A tensor of the shape as data, except for dimension 0 which has size k, the number of segments specified via num_segments or inferred for the last element in segments_ids. """ if num_segments is not None: return gen_math_ops.sparse_segment_sqrt_n_with_num_segments( data=data, indices=indices, segment_ids=segment_ids, num_segments=num_segments, name=name) else: return gen_math_ops.sparse_segment_sqrt_n( data=data, indices=indices, segment_ids=segment_ids, name=name) @tf_export("tensordot", "linalg.tensordot") def tensordot(a, b, axes, name=None): r"""Tensor contraction of a and b along specified axes. Tensordot (also known as tensor contraction) sums the product of elements from a and b over the indices specified by a_axes and b_axes. The lists a_axes and b_axes specify those pairs of axes along which to contract the tensors. The axis a_axes[i] of a must have the same dimension as axis b_axes[i] of b for all i in range(0, len(a_axes)). The lists a_axes and b_axes must have identical length and consist of unique integers that specify valid axes for each of the tensors. This operation corresponds to numpy.tensordot(a, b, axes). Example 1: When a and b are matrices (order 2), the case axes = 1 is equivalent to matrix multiplication. Example 2: When a and b are matrices (order 2), the case axes = [[1], [0]] is equivalent to matrix multiplication. Example 3: Suppose that \$$a_{ijk}\$$ and \$$b_{lmn}\$$ represent two tensors of order 3. Then, contract(a, b, [[0], [2]]) is the order 4 tensor \$$c_{jklm}\$$ whose entry corresponding to the indices \$$(j,k,l,m)\$$ is given by: \$$c_{jklm} = \sum_i a_{ijk} b_{lmi} \$$. In general, order(c) = order(a) + order(b) - 2*len(axes[0]). Args: a: Tensor of type float32 or float64. b: Tensor with the same type as a. axes: Either a scalar N, or a list or an int32 Tensor of shape [2, k]. If axes is a scalar, sum over the last N axes of a and the first N axes of b in order. If axes is a list or Tensor the first and second row contain the set of unique integers specifying axes along which the contraction is computed, for a and b, respectively. The number of axes for a and b must be equal. name: A name for the operation (optional). Returns: A Tensor with the same type as a. Raises: ValueError: If the shapes of a, b, and axes are incompatible. IndexError: If the values in axes exceed the rank of the corresponding tensor. """ def _tensordot_reshape(a, axes, flipped=False): """Helper method to perform transpose and reshape for contraction op. This method is helpful in reducing math_ops.tensordot to math_ops.matmul using array_ops.transpose and array_ops.reshape. The method takes a tensor and performs the correct transpose and reshape operation for a given set of indices. It returns the reshaped tensor as well as a list of indices necessary to reshape the tensor again after matrix multiplication. Args: a: Tensor. axes: List or int32 Tensor of unique indices specifying valid axes of a. flipped: An optional bool. Defaults to False. If True, the method assumes that a is the second argument in the contraction operation. Returns: A tuple (reshaped_a, free_dims, free_dims_static) where reshaped_a is the tensor a reshaped to allow contraction via matmul, free_dims is either a list of integers or an int32 Tensor, depending on whether the shape of a is fully specified, and free_dims_static is either a list of integers and None values, or None, representing the inferred static shape of the free dimensions """ if a.get_shape().is_fully_defined() and isinstance(axes, (list, tuple)): shape_a = a.get_shape().as_list() axes = [i if i >= 0 else i + len(shape_a) for i in axes] free = [i for i in xrange(len(shape_a)) if i not in axes] free_dims = [shape_a[i] for i in free] prod_free = int(np.prod([shape_a[i] for i in free])) prod_axes = int(np.prod([shape_a[i] for i in axes])) perm = list(axes) + free if flipped else free + list(axes) new_shape = [prod_axes, prod_free] if flipped else [prod_free, prod_axes] reshaped_a = array_ops.reshape(array_ops.transpose(a, perm), new_shape) return reshaped_a, free_dims, free_dims else: if a.get_shape().ndims is not None and isinstance(axes, (list, tuple)): shape_a = a.get_shape().as_list() axes = [i if i >= 0 else i + len(shape_a) for i in axes] free = [i for i in xrange(len(shape_a)) if i not in axes] free_dims_static = [shape_a[i] for i in free] else: free_dims_static = None shape_a = array_ops.shape(a) rank_a = array_ops.rank(a) axes = ops.convert_to_tensor(axes, dtype=dtypes.int32, name="axes") axes = cast(axes >= 0, dtypes.int32) * axes + cast( axes < 0, dtypes.int32) * ( axes + rank_a) free, _ = array_ops.setdiff1d(range(rank_a), axes) free_dims = array_ops.gather(shape_a, free) axes_dims = array_ops.gather(shape_a, axes) prod_free_dims = reduce_prod(free_dims) prod_axes_dims = reduce_prod(axes_dims) perm = array_ops.concat([axes_dims, free_dims], 0) if flipped: perm = array_ops.concat([axes, free], 0) new_shape = array_ops.stack([prod_axes_dims, prod_free_dims]) else: perm = array_ops.concat([free, axes], 0) new_shape = array_ops.stack([prod_free_dims, prod_axes_dims]) reshaped_a = array_ops.reshape(array_ops.transpose(a, perm), new_shape) return reshaped_a, free_dims, free_dims_static def _tensordot_axes(a, axes): """Generates two sets of contraction axes for the two tensor arguments.""" a_shape = a.get_shape() if isinstance(axes, compat.integral_types): if axes < 0: raise ValueError("'axes' must be at least 0.") if a_shape.ndims is not None: if axes > a_shape.ndims: raise ValueError("'axes' must not be larger than the number of " "dimensions of tensor %s." % a) return (list(xrange(a_shape.ndims - axes, a_shape.ndims)), list(xrange(axes))) else: rank = array_ops.rank(a) return (range(rank - axes, rank, dtype=dtypes.int32), range(axes, dtype=dtypes.int32)) elif isinstance(axes, (list, tuple)): if len(axes) != 2: raise ValueError("'axes' must be an integer or have length 2.") a_axes = axes[0] b_axes = axes[1] if isinstance(a_axes, compat.integral_types) and \ isinstance(b_axes, compat.integral_types): a_axes = [a_axes] b_axes = [b_axes] if len(a_axes) != len(b_axes): raise ValueError( "Different number of contraction axes 'a' and 'b', %s != %s." % (len(a_axes), len(b_axes))) return a_axes, b_axes else: axes = ops.convert_to_tensor(axes, name="axes", dtype=dtypes.int32) return axes[0], axes[1] with ops.name_scope(name, "Tensordot", [a, b, axes]) as name: a = ops.convert_to_tensor(a, name="a") b = ops.convert_to_tensor(b, name="b") a_axes, b_axes = _tensordot_axes(a, axes) a_reshape, a_free_dims, a_free_dims_static = _tensordot_reshape(a, a_axes) b_reshape, b_free_dims, b_free_dims_static = _tensordot_reshape( b, b_axes, True) ab_matmul = matmul(a_reshape, b_reshape) if isinstance(a_free_dims, list) and isinstance(b_free_dims, list): return array_ops.reshape(ab_matmul, a_free_dims + b_free_dims, name=name) else: a_free_dims = ops.convert_to_tensor(a_free_dims, dtype=dtypes.int32) b_free_dims = ops.convert_to_tensor(b_free_dims, dtype=dtypes.int32) product = array_ops.reshape( ab_matmul, array_ops.concat([a_free_dims, b_free_dims], 0), name=name) if a_free_dims_static is not None and b_free_dims_static is not None: product.set_shape(a_free_dims_static + b_free_dims_static) return product @tf_export("math.polyval") def polyval(coeffs, x, name=None): r"""Computes the elementwise value of a polynomial. If x is a tensor and coeffs is a list n + 1 tensors, this function returns the value of the n-th order polynomial p(x) = coeffs[n-1] + coeffs[n-2] * x + ... + coeffs[0] * x**(n-1) evaluated using Horner's method, i.e. p(x) =