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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.","# ==============================================================================","\"\"\"Math Operations.","","Note: Functions taking `Tensor` arguments can also take anything accepted by","`tf.convert_to_tensor`.","","Note: Elementwise binary operations in TensorFlow follow [numpy-style","broadcasting](http://docs.scipy.org/doc/numpy/user/basics.broadcasting.html).","","TensorFlow provides a variety of math functions including:","","* Basic arithmetic operators and trigonometric functions.","* Special math functions (like: `tf.math.igamma` and `tf.math.zeta`)","* Complex number functions (like: `tf.math.imag` and `tf.math.angle`)","* Reductions and scans (like: `tf.math.reduce_mean` and `tf.math.cumsum`)","* Segment functions (like: `tf.math.segment_sum`)","","See: `tf.linalg` for matrix and tensor functions.","","","","## About Segmentation","","TensorFlow provides several operations that you can use to perform common","math computations on tensor segments.","Here a segmentation is a partitioning of a tensor along","the first dimension, i.e. it defines a mapping from the first dimension onto","`segment_ids`. The `segment_ids` tensor should be the size of","the first dimension, `d0`, with consecutive IDs in the range `0` to `k`,","where `k [[0 0 0 0]","# [5 6 7 8]]","```","","The standard `segment_*` functions assert that the segment indices are sorted.","If you have unsorted indices use the equivalent `unsorted_segment_` function.","These functions take an additional argument `num_segments` so that the output","tensor can be efficiently allocated.","","``` python","c = tf.constant([[1,2,3,4], [-1,-2,-3,-4], [5,6,7,8]])","tf.math.unsorted_segment_sum(c, tf.constant([0, 1, 0]), num_segments=2)","# ==> [[ 6, 8, 10, 12],","# [-1, -2, -3, -4]]","```","","API docstring: tensorflow.math","\"\"\"","import builtins","import numpy as np","","from tensorflow.python.compat import compat as forward_compat","from tensorflow.python.eager import context","from tensorflow.python.framework import constant_op","from tensorflow.python.framework import dtypes","from tensorflow.python.framework import indexed_slices","from tensorflow.python.framework import ops","from tensorflow.python.framework import override_binary_operator","from tensorflow.python.framework import sparse_tensor","from tensorflow.python.framework import tensor as tensor_lib","from tensorflow.python.framework import tensor_conversion_registry","from tensorflow.python.framework import tensor_shape","from tensorflow.python.framework import tensor_util","from tensorflow.python.ops import array_ops","from tensorflow.python.ops import array_ops_stack","from tensorflow.python.ops import gen_array_ops","from tensorflow.python.ops import gen_bitwise_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 tensor_math_operator_overrides # pylint: disable=unused-import","# go/tf-wildcard-import","# pylint: disable=wildcard-import","from tensorflow.python.ops.gen_math_ops import *","# pylint: enable=wildcard-import","from tensorflow.python.platform import tf_logging as logging","from tensorflow.python.util import _pywrap_utils","from tensorflow.python.util import compat","from tensorflow.python.util import deprecation","from tensorflow.python.util import dispatch","from tensorflow.python.util import nest","from tensorflow.python.util.compat import collections_abc","from tensorflow.python.util.tf_export import tf_export","","","# Aliases for some automatically-generated names.","nextafter = gen_math_ops.next_after","","","@tf_export(\"linspace\", v1=[\"lin_space\", \"linspace\"])","@dispatch.add_dispatch_support","@deprecation.deprecated_endpoints(\"lin_space\")","def linspace_nd(start, stop, num, name=None, axis=0):"," r\"\"\"Generates evenly-spaced values in an interval along a given axis.",""," A sequence of `num` evenly-spaced values are generated beginning at `start`"," along a given `axis`."," If `num > 1`, the values in the sequence increase by"," `(stop - start) / (num - 1)`, so that the last one is exactly `stop`."," If `num <= 0`, `ValueError` is raised.",""," Matches"," [np.linspace](https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html)'s"," behaviour"," except when `num == 0`.",""," For example:",""," ```"," tf.linspace(10.0, 12.0, 3, name=\"linspace\") => [ 10.0 11.0 12.0]"," ```",""," `Start` and `stop` can be tensors of arbitrary size:",""," >>> tf.linspace([0., 5.], [10., 40.], 5, axis=0)"," ",""," `Axis` is where the values will be generated (the dimension in the"," returned tensor which corresponds to the axis will be equal to `num`)",""," >>> tf.linspace([0., 5.], [10., 40.], 5, axis=-1)"," ","","",""," Args:"," start: A `Tensor`. Must be one of the following types: `bfloat16`,"," `float32`, `float64`. N-D tensor. First entry in the range."," stop: A `Tensor`. Must have the same type and shape as `start`. N-D tensor."," Last entry in the range."," num: A `Tensor`. Must be one of the following types: `int32`, `int64`. 0-D"," tensor. Number of values to generate."," name: A name for the operation (optional)."," axis: Axis along which the operation is performed (used only when N-D"," tensors are provided).",""," Returns:"," A `Tensor`. Has the same type as `start`."," \"\"\"",""," with ops.name_scope(name, \"linspace\", [start, stop]):"," start = ops.convert_to_tensor(start, name=\"start\")"," # stop must be convertible to the same dtype as start"," stop = ops.convert_to_tensor(stop, name=\"stop\", dtype=start.dtype)"," num_int = array_ops.convert_to_int_tensor(num, name=\"num\")"," num = cast(num_int, dtype=start.dtype)",""," broadcast_shape = array_ops.broadcast_dynamic_shape("," array_ops.shape(start), array_ops.shape(stop))"," start = array_ops.broadcast_to(start, broadcast_shape)"," stop = array_ops.broadcast_to(stop, broadcast_shape)",""," expanded_start = array_ops.expand_dims(start, axis=axis)"," expanded_stop = array_ops.expand_dims(stop, axis=axis)",""," shape = array_ops.shape(expanded_start)"," ndims = array_ops.shape(shape)[0]",""," axis = array_ops.where_v2(axis >= 0, axis, ndims + axis)",""," # The purpose is to avoid having negative values when repeating."," num_fill = gen_math_ops.maximum(num_int - 2, 0)"," # To avoid having negative values in the range or zero division"," # the result is sliced in the end so a correct result is returned for"," # num == 1, and num == 0."," n_steps = gen_math_ops.maximum(num_int - 1, 1)"," delta = (expanded_stop - expanded_start) / cast(n_steps,"," expanded_stop.dtype)"," # Re-cast tensors as delta."," expanded_start = cast(expanded_start, delta.dtype)"," expanded_stop = cast(expanded_stop, delta.dtype)"," # If num < 0, we will throw exception in the range"," # otherwise use the same div for delta"," range_end = array_ops.where_v2(num_int >= 0, n_steps, -1)"," # Even though range supports an output dtype, its limited"," # (e.g. doesn't support half at the moment)."," desired_range = cast(range(1, range_end, dtype=dtypes.int64), delta.dtype)"," mask = gen_math_ops.equal(axis, range(ndims))"," # desired_range_shape is [1. 1. 1. ... 1. num_fill 1. 1. ... 1.], where the"," # index of num_fill is equal to axis."," desired_range_shape = array_ops.where_v2(mask, num_fill, 1)"," desired_range = array_ops.reshape(desired_range, desired_range_shape)",""," res = expanded_start + delta * desired_range",""," # Add the start and endpoints to the result, and slice out the desired"," # portion."," all_tensors = (expanded_start, res, expanded_stop)"," concatenated = array_ops.concat(all_tensors, axis=axis)"," begin = array_ops.zeros_like(shape)"," # Preserve shape information for final slice."," size = array_ops.concat("," (shape[0:axis], array_ops.reshape(num_int, [1]), shape[axis + 1 :]),"," axis=0,"," )"," return array_ops.slice(concatenated, begin, size)","","","linspace = linspace_nd","","arg_max = deprecation.deprecated(None, \"Use `tf.math.argmax` instead\")(arg_max) # pylint: disable=used-before-assignment","arg_min = deprecation.deprecated(None, \"Use `tf.math.argmin` instead\")(arg_min) # pylint: disable=used-before-assignment","tf_export(v1=[\"arg_max\"])(dispatch.add_dispatch_support(arg_max))","tf_export(v1=[\"arg_min\"])(dispatch.add_dispatch_support(arg_min))","","","def _set_doc(doc):",""," def _decorator(func):"," func.__doc__ = doc"," return func",""," return _decorator","","","# pylint: disable=redefined-builtin","@tf_export(v1=[\"math.argmax\", \"argmax\"])","@dispatch.add_dispatch_support","@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):"," axis = deprecation.deprecated_argument_lookup(\"axis\", axis, \"dimension\","," dimension)"," return argmax_v2(input, axis, output_type, name)","","","@tf_export(\"math.argmax\", \"argmax\", v1=[])","@dispatch.add_dispatch_support","def argmax_v2(input, axis=None, output_type=dtypes.int64, name=None):"," \"\"\"Returns the index with the largest value across axes of a tensor.",""," In case of identity returns the smallest index.",""," For example:",""," >>> A = tf.constant([2, 20, 30, 3, 6])"," >>> tf.math.argmax(A) # A[2] is maximum in tensor A"," "," >>> B = tf.constant([[2, 20, 30, 3, 6], [3, 11, 16, 1, 8],"," ... [14, 45, 23, 5, 27]])"," >>> tf.math.argmax(B, 0)"," "," >>> tf.math.argmax(B, 1)"," "," >>> C = tf.constant([0, 0, 0, 0])"," >>> tf.math.argmax(C) # Returns smallest index in case of ties"," ",""," Args:"," input: A `Tensor`."," axis: An integer, the axis to reduce across. Default to 0."," output_type: An optional output dtype (`tf.int32` or `tf.int64`). Defaults"," to `tf.int64`."," name: An optional name for the operation.",""," Returns:"," A `Tensor` of type `output_type`."," \"\"\""," if axis is None:"," axis = 0"," return gen_math_ops.arg_max(input, axis, name=name, output_type=output_type)","","","@tf_export(v1=[\"math.argmin\", \"argmin\"])","@dispatch.add_dispatch_support","@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):"," axis = deprecation.deprecated_argument_lookup(\"axis\", axis, \"dimension\","," dimension)"," return argmin_v2(input, axis, output_type, name)","","","@tf_export(\"math.argmin\", \"argmin\", v1=[])","@dispatch.add_dispatch_support","def argmin_v2(input, axis=None, output_type=dtypes.int64, name=None):"," \"\"\"Returns the index with the smallest value across axes of a tensor.",""," Returns the smallest index in case of ties.",""," Args:"," input: A `Tensor`. Must be one of the following types: `float32`, `float64`,"," `int32`, `uint8`, `int16`, `int8`, `complex64`, `int64`, `qint8`,"," `quint8`, `qint32`, `bfloat16`, `uint16`, `complex128`, `half`, `uint32`,"," `uint64`."," axis: A `Tensor`. Must be one of the following types: `int32`, `int64`."," int32 or int64, must be in the range `-rank(input), rank(input))`."," Describes which axis of the input Tensor to reduce across. For vectors,"," use axis = 0."," output_type: An optional `tf.DType` from: `tf.int32, tf.int64`. Defaults to"," `tf.int64`."," name: A name for the operation (optional).",""," Returns:"," A `Tensor` of type `output_type`.",""," Usage:"," ```python"," import tensorflow as tf"," a = [1, 10, 26.9, 2.8, 166.32, 62.3]"," b = tf.math.argmin(input = a)"," c = tf.keras.backend.eval(b)"," # c = 0"," # here a[0] = 1 which is the smallest element of a across axis 0"," ```"," \"\"\""," if 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(\"math.abs\", \"abs\")","@dispatch.register_unary_elementwise_api","@dispatch.add_dispatch_support","def abs(x, name=None): # pylint: disable=redefined-builtin"," r\"\"\"Computes the absolute value of a tensor.",""," Given a tensor of integer or floating-point values, this operation returns a"," tensor of the same type, where each element contains the absolute value of the"," corresponding element in the input.",""," 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`. For"," a complex number \\\\(a + bj\\\\), its absolute value is computed as"," \\\\(\\sqrt{a^2 + b^2}\\\\).",""," For example:",""," >>> # real number"," >>> x = tf.constant([-2.25, 3.25])"," >>> tf.abs(x)"," ",""," >>> # complex number"," >>> x = tf.constant([[-2.25 + 4.75j], [-3.25 + 5.75j]])"," >>> tf.abs(x)"," ",""," Args:"," x: A `Tensor` or `SparseTensor` of type `float16`, `float32`, `float64`,"," `int32`, `int64`, `complex64` or `complex128`."," name: A name for the operation (optional).",""," Returns:"," A `Tensor` or `SparseTensor` of the same size, type and sparsity 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:"," 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:"," \"\"\"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(\"math.divide\", \"divide\")","@dispatch.register_binary_elementwise_api","@dispatch.add_dispatch_support","def divide(x, y, name=None):"," \"\"\"Computes Python style division of `x` by `y`.",""," For example:",""," >>> x = tf.constant([16, 12, 11])"," >>> y = tf.constant([4, 6, 2])"," >>> tf.divide(x,y)"," ",""," Args:"," x: A `Tensor`"," y: A `Tensor`"," name: A name for the operation (optional).",""," Returns:"," A `Tensor` with same shape as input"," \"\"\"",""," 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:"," # We do conversion here to make sure at least x is a tensor."," if not tensor_util.is_tf_type(x):"," dtype = y.dtype.base_dtype if tensor_util.is_tf_type(y) else None"," x = ops.convert_to_tensor(x, dtype=dtype)"," return x / y","","","@tf_export(\"math.multiply\", \"multiply\")","@dispatch.register_binary_elementwise_api","@dispatch.add_dispatch_support","def multiply(x, y, name=None):"," \"\"\"Returns an element-wise x * y.",""," For example:",""," >>> x = tf.constant(([1, 2, 3, 4]))"," >>> tf.math.multiply(x, x)"," ",""," Since `tf.math.multiply` will convert its arguments to `Tensor`s, you can also"," pass in non-`Tensor` arguments:",""," >>> tf.math.multiply(7,6)"," ",""," If `x.shape` is not the same as `y.shape`, they will be broadcast to a"," compatible shape. (More about broadcasting"," [here](https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html).)",""," For example:",""," >>> x = tf.ones([1, 2]);"," >>> y = tf.ones([2, 1]);"," >>> x * y # Taking advantage of operator overriding"," ",""," The reduction version of this elementwise operation is `tf.math.reduce_prod`",""," Args:"," x: A Tensor. Must be one of the following types: `bfloat16`,"," `half`, `float32`, `float64`, `uint8`, `int8`, `uint16`,"," `int16`, `int32`, `int64`, `complex64`, `complex128`."," y: A `Tensor`. Must have the same type as `x`."," name: A name for the operation (optional).",""," Returns:",""," A `Tensor`. Has the same type as `x`.",""," Raises:",""," * InvalidArgumentError: When `x` and `y` have incompatible shapes or types."," \"\"\"",""," return gen_math_ops.mul(x, y, name)","","","# TODO(aselle): put deprecation in after another round of global code changes","@deprecation.deprecated("," \"2016-12-30\","," \"`tf.mul(x, y)` is deprecated; use `tf.math.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(\"math.subtract\", \"subtract\")","@dispatch.register_binary_elementwise_api","@dispatch.add_dispatch_support","def subtract(x, y, name=None):"," return gen_math_ops.sub(x, y, name)","","","subtract.__doc__ = gen_math_ops.sub.__doc__","","","# 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__))","","negative = gen_math_ops.neg","","","# 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(v1=[\"math.scalar_mul\", \"scalar_mul\"])","@dispatch.register_binary_elementwise_api","@dispatch.add_dispatch_support","def scalar_mul(scalar, x, name=None):"," \"\"\"Multiplies a scalar times a `Tensor` or `IndexedSlices` object.",""," This is a special case of `tf.math.multiply`, where the first value must be a"," `scalar`. Unlike the general form of `tf.math.multiply`, this is operation is"," guaranteed to be efficient for `tf.IndexedSlices`.",""," >>> x = tf.reshape(tf.range(30, dtype=tf.float32), [10, 3])"," >>> with tf.GradientTape() as g:"," ... g.watch(x)"," ... y = tf.gather(x, [1, 2]) # IndexedSlices"," ... z = tf.math.scalar_mul(10.0, y)",""," Args:"," scalar: A 0-D scalar `Tensor`. Must have known shape."," x: A `Tensor` or `IndexedSlices` to be scaled."," name: A name for the operation (optional).",""," Returns:"," `scalar * x` of the same type (`Tensor` or `IndexedSlices`) as `x`.",""," Raises:"," ValueError: if scalar is not a 0-D `scalar`."," \"\"\""," base_dtype = dtypes.as_dtype(x.dtype).base_dtype"," scalar = ops.convert_to_tensor("," scalar, dtype=base_dtype, name=\"scalar\")"," shape = scalar.get_shape()"," if shape.ndims == 0:"," if isinstance(x, indexed_slices.IndexedSlices):"," return indexed_slices.IndexedSlices("," gen_math_ops.mul(scalar, x.values, name), x.indices, x.dense_shape)"," else:"," return gen_math_ops.mul(scalar, x, name)"," else:"," raise ValueError("," f\"The input scalar must be a 0-D value. Received shape {shape}.\")","","","@tf_export(\"math.softplus\", \"nn.softplus\", v1=[\"math.softplus\", \"nn.softplus\"])","@dispatch.register_unary_elementwise_api","@dispatch.add_dispatch_support","def softplus(features, name=None):"," \"\"\"Computes elementwise softplus: `softplus(x) = log(exp(x) + 1)`.",""," `softplus` is a smooth approximation of `relu`. Like `relu`, `softplus` always"," takes on positive values.",""," ",""," Example:",""," >>> import tensorflow as tf"," >>> tf.math.softplus(tf.range(0, 2, dtype=tf.float32)).numpy()"," array([0.6931472, 1.3132616], dtype=float32)",""," Args:"," features: `Tensor`"," name: Optional: name to associate with this operation."," Returns:"," `Tensor`"," \"\"\""," return gen_nn_ops.softplus(features, name)","","","@tf_export(\"math.scalar_mul\", \"scalar_mul\", v1=[])","@dispatch.register_binary_elementwise_api","@dispatch.add_dispatch_support","@_set_doc(scalar_mul.__doc__)","def scalar_mul_v2(scalar, x, name=None):"," with ops.name_scope(name, \"scalar_mul\", [x]) as name:"," return scalar_mul(scalar, x, name)","","","@tf_export(\"math.pow\", \"pow\")","@dispatch.register_binary_elementwise_api","@dispatch.add_dispatch_support","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 `float16`, `float32`, `float64`, `int32`, `int64`,"," `complex64`, or `complex128`."," y: A `Tensor` of type `float16`, `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(\"dtypes.complex\", \"complex\")","@dispatch.register_binary_elementwise_api","@dispatch.add_dispatch_support","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`.",""," Raises:"," TypeError: Real and imag must be correct types"," \"\"\""," 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("," f\"The `real` and `imag` components have incorrect types: \""," f\"{real.dtype.name} {imag.dtype.name}. They must be consistent, and \""," f\"one of {[dtypes.float32, dtypes.float64]}\")"," return gen_math_ops._complex(real, imag, Tout=Tout, name=name)","","","@tf_export(\"math.sign\", \"sign\")","@dispatch.register_unary_elementwise_api","@dispatch.add_dispatch_support","def sign(x, name=None):"," r\"\"\"Returns an element-wise indication of the sign of a number.",""," `y = sign(x) = -1 if x < 0; 0 if x == 0; 1 if x > 0`.",""," For complex numbers, `y = sign(x) = x / |x| if x != 0, otherwise y = 0`.",""," Example usage:",""," >>> # real number"," >>> tf.math.sign([0., 2., -3.])"," ",""," >>> # complex number"," >>> tf.math.sign([1 + 1j, 0 + 0j])"," ",""," Args:"," x: A Tensor. Must be one of the following types: bfloat16, half, float32,"," float64, int32, int64, complex64, complex128."," name: A name for the operation (optional).",""," Returns:"," A Tensor. Has the same type as x.",""," If x is a SparseTensor, returns SparseTensor(x.indices,"," tf.math.sign(x.values, ...), x.dense_shape)."," \"\"\""," x = ops.convert_to_tensor(x)"," if x.dtype.is_complex:"," return gen_math_ops.div_no_nan("," x,"," cast("," gen_math_ops.complex_abs("," x,"," Tout=dtypes.float32"," if x.dtype == dtypes.complex64 else dtypes.float64),"," dtype=x.dtype),"," name=name)"," return gen_math_ops.sign(x, name=name)","","","@tf_export(\"math.real\", v1=[\"math.real\", \"real\"])","@dispatch.register_unary_elementwise_api","@dispatch.add_dispatch_support","@deprecation.deprecated_endpoints(\"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.math.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:"," input = ops.convert_to_tensor(input, name=\"input\")"," if input.dtype.is_complex:"," real_dtype = input.dtype.real_dtype"," return gen_math_ops.real(input, Tout=real_dtype, name=name)"," elif input.dtype.is_numeric:"," return input"," else:"," raise TypeError("," \"input must be a numeric tensor, but got tensor with dtype {}\".format("," input.dtype"," )"," )","","","@tf_export(\"math.imag\", v1=[\"math.imag\", \"imag\"])","@dispatch.register_unary_elementwise_api","@dispatch.add_dispatch_support","@deprecation.deprecated_endpoints(\"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.math.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:"," input = ops.convert_to_tensor(input, name=\"input\")"," 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(\"math.angle\", v1=[\"math.angle\", \"angle\"])","@dispatch.register_unary_elementwise_api","@dispatch.add_dispatch_support","@deprecation.deprecated_endpoints(\"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:",""," ```"," input = tf.constant([-2.25 + 4.75j, 3.25 + 5.75j], dtype=tf.complex64)"," tf.math.angle(input).numpy()"," # ==> array([2.0131705, 1.056345 ], dtype=float32)"," ```",""," 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:"," input = ops.convert_to_tensor(input, name=\"input\")"," if input.dtype.is_complex:"," return gen_math_ops.angle(input, Tout=input.dtype.real_dtype, name=name)"," else:"," return array_ops.where(input < 0, np.pi * array_ops.ones_like(input),"," array_ops.zeros_like(input))","","","# pylint: enable=redefined-outer-name,redefined-builtin","","","@tf_export(\"math.round\", \"round\")","@dispatch.register_unary_elementwise_api","@dispatch.add_dispatch_support","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 `float16`, `float32`, `float64`, `int32`, or `int64`."," 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)","","","# TODO(mdan): Include a full_type argument to replace dtype.","@tf_export(\"cast\", \"dtypes.cast\")","@dispatch.register_unary_elementwise_api","@dispatch.add_dispatch_support","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` or `IndexedSlices`) to `dtype`.",""," For example:",""," >>> x = tf.constant([1.8, 2.2], dtype=tf.float32)"," >>> tf.cast(x, tf.int32)"," ",""," Notice `tf.cast` has an alias `tf.dtypes.cast`:",""," >>> x = tf.constant([1.8, 2.2], dtype=tf.float32)"," >>> tf.dtypes.cast(x, tf.int32)"," ",""," The operation supports data types (for `x` and `dtype`) of"," `uint8`, `uint16`, `uint32`, `uint64`, `int8`, `int16`, `int32`, `int64`,"," `float16`, `float32`, `float64`, `complex64`, `complex128`, `bfloat16`."," In case of casting from complex types (`complex64`, `complex128`) to real"," types, only the real part of `x` is returned. In case of casting from real"," types to complex types (`complex64`, `complex128`), the imaginary part of the"," returned value is set to `0`. The handling of complex types here matches the"," behavior of numpy.",""," Note casting nan and inf values to integral types has undefined behavior.",""," Note this operation can lead to a loss of precision when converting native"," Python `float` and `complex` variables to `tf.float64` or `tf.complex128`"," tensors, since the input is first converted to the `float32` data type and"," then widened. It is recommended to use `tf.convert_to_tensor` instead of"," `tf.cast` for any non-tensor inputs.",""," Args:"," x: A `Tensor` or `SparseTensor` or `IndexedSlices` of numeric type. It could"," be `uint8`, `uint16`, `uint32`, `uint64`, `int8`, `int16`, `int32`,"," `int64`, `float16`, `float32`, `float64`, `complex64`, `complex128`,"," `bfloat16`."," dtype: The destination type. The list of supported dtypes is the same as"," `x`."," name: A name for the operation (optional).",""," Returns:"," A `Tensor` or `SparseTensor` or `IndexedSlices` with same shape as `x` and"," same type as `dtype`.",""," Raises:"," TypeError: If `x` cannot be cast to the `dtype`.",""," \"\"\""," base_type = dtypes.as_dtype(dtype).base_dtype"," if ("," isinstance(x, tensor_lib.Tensor) or _pywrap_utils.IsResourceVariable(x)"," ) and base_type == x.dtype:"," return x"," 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)"," elif isinstance(x, indexed_slices.IndexedSlices):"," values_cast = cast(x.values, base_type, name=name)"," x = indexed_slices.IndexedSlices(values_cast, x.indices, 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.is_complex and base_type.is_floating:"," logging.warn("," f\"You are casting an input of type {x.dtype.name} to an \""," f\"incompatible dtype {base_type.name}. This will \""," \"discard the imaginary part and may not be what you \""," \"intended.\""," )"," if x.dtype != base_type:"," x = gen_math_ops.cast(x, base_type, name=name)"," return x","","","@tf_export(\"dtypes.saturate_cast\", \"saturate_cast\")","@dispatch.register_unary_elementwise_api","@dispatch.add_dispatch_support","def saturate_cast(value, dtype, name=None):"," \"\"\"Performs a safe saturating cast of `value` to `dtype`.",""," This function casts the input to `dtype` without overflow. If"," there is a danger that values would over or underflow in the cast, this op"," applies the appropriate clamping before the cast. See `tf.cast` for more"," details.",""," 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",""," in_dtype = value.dtype"," if in_dtype.is_complex:"," if dtype.is_complex:"," # Clamp real and imag components separately, if required."," real_in_dtype = in_dtype.real_dtype"," real_out_dtype = dtype.real_dtype"," if ("," real_in_dtype.min < real_out_dtype.min"," or real_in_dtype.max > real_out_dtype.max"," ):"," value = gen_math_ops._clip_by_value("," value,"," ops.convert_to_tensor("," builtins.complex(real_out_dtype.min, real_out_dtype.min),"," dtype=in_dtype),"," ops.convert_to_tensor("," builtins.complex(real_out_dtype.max, real_out_dtype.max),"," dtype=in_dtype),"," name=\"clamp\")"," return cast(value, dtype, name=name)"," else:"," # Extract real component and fall through to clamp+cast."," value = real(value)"," logging.warn(\"Casting complex to real discards imaginary part.\")"," in_dtype = in_dtype.real_dtype",""," # in_dtype is real, but out_dtype could be complex."," out_real_dtype = dtype.real_dtype",""," # TODO: b/288437118 - unconditionally apply `clip_by_value` to fix `inf`"," # behavior."," if ("," forward_compat.forward_compatible(2024, 11, 1)"," or in_dtype.min < out_real_dtype.min"," or in_dtype.max > out_real_dtype.max"," ):"," # The output min/max may not actually be representable in the"," # in_dtype (e.g. casting float32 to uint32). This can lead to undefined"," # behavior when trying to cast a value outside the valid range of the"," # target type. We work around this by nudging the min/max to fall within"," # the valid output range. The catch is that we may actually saturate"," # to a value less than the true saturation limit, but this is the best we"," # can do in order to avoid UB without introducing a separate SaturateCast"," # op."," np_dtype = in_dtype.as_numpy_dtype"," min_limit = np_dtype(np.maximum(in_dtype.min, out_real_dtype.min))"," if min_limit < out_real_dtype.min:"," min_limit = np.nextafter(min_limit, np_dtype(0), dtype=np_dtype)",""," max_limit = np_dtype(np.minimum(in_dtype.max, out_real_dtype.max))"," if max_limit > out_real_dtype.max:"," max_limit = np.nextafter(max_limit, np_dtype(0), dtype=np_dtype)",""," value = gen_math_ops._clip_by_value("," value,"," ops.convert_to_tensor(min_limit, dtype=in_dtype),"," ops.convert_to_tensor(max_limit, dtype=in_dtype),"," name=\"clamp\","," )"," return cast(value, dtype, name=name)","","","@tf_export(v1=[\"to_float\"])","@dispatch.register_unary_elementwise_api","@dispatch.add_dispatch_support","@deprecation.deprecated(date=None, instructions=\"Use `tf.cast` instead.\")","def to_float(x, name=\"ToFloat\"):"," \"\"\"Casts a tensor to type `float32`.",""," Args:"," x: A `Tensor` or `SparseTensor` or `IndexedSlices`."," name: A name for the operation (optional).",""," Returns:"," A `Tensor` or `SparseTensor` or `IndexedSlices` with same shape as `x` with"," type `float32`.",""," Raises:"," TypeError: If `x` cannot be cast to the `float32`.",""," @compatibility(TF2)",""," This name was deprecated and removed in TF2, but has an exact replacement"," `tf.cast(..., tf.float32)`. There are no further issues with eager execution"," or tf.function.",""," Before:",""," >>> tf.compat.v1.to_float(tf.constant(3.14, dtype=tf.double))"," ",""," After:",""," >>> tf.cast(tf.constant(3.14, dtype=tf.double), tf.float32)"," ",""," @end_compatibility",""," \"\"\""," return cast(x, dtypes.float32, name=name)","","","@tf_export(v1=[\"to_double\"])","@dispatch.register_unary_elementwise_api","@dispatch.add_dispatch_support","@deprecation.deprecated(date=None, instructions=\"Use `tf.cast` instead.\")","def to_double(x, name=\"ToDouble\"):"," \"\"\"Casts a tensor to type `float64`.",""," Args:"," x: A `Tensor` or `SparseTensor` or `IndexedSlices`."," name: A name for the operation (optional).",""," Returns:"," A `Tensor` or `SparseTensor` or `IndexedSlices` with same shape as `x` with"," type `float64`.",""," Raises:"," TypeError: If `x` cannot be cast to the `float64`.",""," @compatibility(TF2)",""," This name was deprecated and removed in TF2, but has an exact replacement"," `tf.cast(..., tf.double)`. There are no further issues with eager execution or"," tf.function.",""," Before:",""," >>> tf.compat.v1.to_double(tf.constant(3.14, dtype=tf.float32))"," ",""," After:",""," >>> tf.cast(tf.constant(3.14, dtype=tf.float32), tf.double)"," ",""," @end_compatibility",""," \"\"\""," return cast(x, dtypes.float64, name=name)","","","@tf_export(v1=[\"to_int32\"])","@dispatch.register_unary_elementwise_api","@dispatch.add_dispatch_support","@deprecation.deprecated(date=None, instructions=\"Use `tf.cast` instead.\")","def to_int32(x, name=\"ToInt32\"):"," \"\"\"Casts a tensor to type `int32`.",""," Args:"," x: A `Tensor` or `SparseTensor` or `IndexedSlices`."," name: A name for the operation (optional).",""," Returns:"," A `Tensor` or `SparseTensor` or `IndexedSlices` with same shape as `x` with"," type `int32`.",""," Raises:"," TypeError: If `x` cannot be cast to the `int32`.",""," @compatibility(TF2)",""," This name was deprecated and removed in TF2, but has an exact replacement"," `tf.cast(..., tf.int32)`. There are no further issues with eager execution or"," tf.function.",""," Before:",""," >>> tf.compat.v1.to_int32(tf.constant(1, dtype=tf.int64))"," ",""," After:",""," >>> tf.cast(tf.constant(1, dtype=tf.int64), tf.int32)"," ",""," @end_compatibility",""," \"\"\""," return cast(x, dtypes.int32, name=name)","","","@tf_export(v1=[\"to_int64\"])","@dispatch.register_unary_elementwise_api","@dispatch.add_dispatch_support","@deprecation.deprecated(date=None, instructions=\"Use `tf.cast` instead.\")","def to_int64(x, name=\"ToInt64\"):"," \"\"\"Casts a tensor to type `int64`.",""," Args:"," x: A `Tensor` or `SparseTensor` or `IndexedSlices`."," name: A name for the operation (optional).",""," Returns:"," A `Tensor` or `SparseTensor` or `IndexedSlices` with same shape as `x` with"," type `int64`.",""," Raises:"," TypeError: If `x` cannot be cast to the `int64`.",""," @compatibility(TF2)",""," This name was deprecated and removed in TF2, but has an exact replacement"," `tf.cast(..., tf.int64)`. There are no further issues with eager execution or"," tf.function.",""," Before:",""," >>> tf.compat.v1.to_int64(tf.constant(1, dtype=tf.int32))"," ",""," After:",""," >>> tf.cast(tf.constant(1, dtype=tf.int32), tf.int64)"," ",""," @end_compatibility",""," \"\"\""," return cast(x, dtypes.int64, name=name)","","","@tf_export(v1=[\"to_bfloat16\"])","@dispatch.register_unary_elementwise_api","@dispatch.add_dispatch_support","@deprecation.deprecated(date=None, instructions=\"Use `tf.cast` instead.\")","def to_bfloat16(x, name=\"ToBFloat16\"):"," \"\"\"Casts a tensor to type `bfloat16`.",""," Args:"," x: A `Tensor` or `SparseTensor` or `IndexedSlices`."," name: A name for the operation (optional).",""," Returns:"," A `Tensor` or `SparseTensor` or `IndexedSlices` with same shape as `x` with"," type `bfloat16`.",""," Raises:"," TypeError: If `x` cannot be cast to the `bfloat16`.",""," @compatibility(TF2)",""," This name was deprecated and removed in TF2, but has an exact replacement"," `tf.cast(..., tf.bfloat16)`. There are no further issues with eager execution"," or tf.function.",""," Before:",""," >>> tf.compat.v1.to_bfloat16(tf.constant(3.14, dtype=tf.float32))"," ",""," After:",""," >>> tf.cast(tf.constant(3.14, dtype=tf.float32), tf.bfloat16)"," ",""," @end_compatibility",""," \"\"\""," return cast(x, dtypes.bfloat16, name=name)","","","@tf_export(v1=[\"to_complex64\"])","@dispatch.register_unary_elementwise_api","@dispatch.add_dispatch_support","@deprecation.deprecated(date=None, instructions=\"Use `tf.cast` instead.\")","def to_complex64(x, name=\"ToComplex64\"):"," \"\"\"Casts a tensor to type `complex64`.",""," Args:"," x: A `Tensor` or `SparseTensor` or `IndexedSlices`."," name: A name for the operation (optional).",""," Returns:"," A `Tensor` or `SparseTensor` or `IndexedSlices` with same shape as `x` with"," type `complex64`.",""," Raises:"," TypeError: If `x` cannot be cast to the `complex64`.",""," @compatibility(TF2)",""," This name was deprecated and removed in TF2, but has an exact replacement"," `tf.cast(..., tf.complex64)`. There are no further issues with eager execution"," or tf.function.",""," Before:",""," >>> tf.compat.v1.to_complex64(tf.constant(1. + 2.j, dtype=tf.complex128))"," ",""," After:",""," >>> tf.cast(tf.constant(1. + 2.j, dtype=tf.complex128), tf.complex64)"," ",""," @end_compatibility",""," \"\"\""," return cast(x, dtypes.complex64, name=name)","","","@tf_export(v1=[\"to_complex128\"])","@dispatch.register_unary_elementwise_api","@dispatch.add_dispatch_support","@deprecation.deprecated(date=None, instructions=\"Use `tf.cast` instead.\")","def to_complex128(x, name=\"ToComplex128\"):"," \"\"\"Casts a tensor to type `complex128`.",""," Args:"," x: A `Tensor` or `SparseTensor` or `IndexedSlices`."," name: A name for the operation (optional).",""," Returns:"," A `Tensor` or `SparseTensor` or `IndexedSlices` with same shape as `x` with"," type `complex128`.",""," Raises:"," TypeError: If `x` cannot be cast to the `complex128`.",""," @compatibility(TF2)",""," This name was deprecated and removed in TF2, but has an exact replacement"," `tf.cast(..., tf.complex128)`. There are no further issues with eager"," execution or tf.function.",""," Before:",""," >>> tf.compat.v1.to_complex128(tf.constant(1. + 2.j, dtype=tf.complex64))"," ",""," After:",""," >>> tf.cast(tf.constant(1. + 2.j, dtype=tf.complex64), tf.complex128)"," ",""," @end_compatibility",""," \"\"\""," return cast(x, dtypes.complex128, name=name)","","","# 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.uint32: dtypes.float64,"," dtypes.int32: dtypes.float64,"," dtypes.uint64: dtypes.float64,"," dtypes.int64: dtypes.float64,"," dtypes.bfloat16: None,"," dtypes.float16: None,"," dtypes.float32: None,"," dtypes.float64: None,"," dtypes.complex64: None,"," dtypes.complex128: None,","}","","","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, dtype_hint=x.dtype.base_dtype, name=\"y\")"," x_dtype = x.dtype.base_dtype"," y_dtype = y.dtype.base_dtype"," if x_dtype != y_dtype:"," raise TypeError(f\"`x` and `y` must have the same dtype, \""," f\"got {x_dtype!r} != {y_dtype!r}.\")"," try:"," dtype = _TRUEDIV_TABLE[x_dtype]"," except KeyError:"," raise TypeError("," f\"Invalid dtype {x_dtype!r} in __truediv__. Expected one \""," f\"of {{{', '.join([repr(x) for x in _TRUEDIV_TABLE.keys()])}}}.\")"," 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(f\"`x` and `y` must have the same dtype, \""," f\"got {x_dtype!r} != {y_dtype!r}.\")"," 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(\"math.truediv\", \"truediv\")","@dispatch.register_binary_elementwise_api","@dispatch.add_dispatch_support","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.math.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(v1=[\"div\"])","@dispatch.register_binary_elementwise_api","@dispatch.add_dispatch_support","@deprecation.deprecated("," date=None,"," instructions=\"Deprecated in favor of operator or tf.math.divide.\")","def div(x, y, name=None):"," \"\"\"Divides x / y elementwise (using Python 2 division operator semantics).",""," @compatibility(TF2)"," This function is deprecated in TF2. Prefer using the Tensor division operator,"," `tf.divide`, or `tf.math.divide`, which obey the Python 3 division operator"," semantics."," @end_compatibility","",""," This function divides `x` and `y`, forcing Python 2 semantics. That is, if `x`"," and `y` are both integers then the result will be an integer. This is in"," contrast to Python 3, where division with `/` is always a float while division"," with `//` is always an integer.",""," 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)","","","@tf_export(\"math.divide_no_nan\", v1=[\"math.divide_no_nan\", \"div_no_nan\"])","@dispatch.register_binary_elementwise_api","@dispatch.add_dispatch_support","@deprecation.deprecated_endpoints(\"div_no_nan\")","def div_no_nan(x, y, name=None):"," \"\"\"Computes a safe divide which returns 0 if `y` (denominator) is zero.",""," For example:",""," >>> tf.constant(3.0) / 0.0"," "," >>> tf.math.divide_no_nan(3.0, 0.0)"," ",""," Note that 0 is returned if `y` is 0 even if `x` is nonfinite:",""," >>> tf.math.divide_no_nan(np.nan, 0.0)"," ",""," Args:"," x: A `Tensor` of a floating or integer dtype."," y: A `Tensor` with the same dtype as `x` and a compatible shape."," name: A name for the operation (optional).",""," Returns:"," The element-wise quotient as in `tf.math.divide(x, y)`,"," except that division by zero produces `0.0`, not `nan`."," \"\"\"",""," with ops.name_scope(name, \"div_no_nan\", [x, y]) as name:"," if not tensor_util.is_tf_type(x) and tensor_util.is_tf_type(y):"," # Treat this case specially like divide() does above."," y = ops.convert_to_tensor(y, name=\"y\")"," x = ops.convert_to_tensor(x, dtype=y.dtype.base_dtype, name=\"x\")"," else:"," x = ops.convert_to_tensor(x, name=\"x\")"," y = ops.convert_to_tensor(y, dtype_hint=x.dtype.base_dtype, name=\"y\")"," x_dtype = x.dtype.base_dtype"," y_dtype = y.dtype.base_dtype"," if x_dtype != y_dtype:"," raise TypeError(f\"`x` and `y` must have the same dtype, \""," f\"got {x_dtype!r} != {y_dtype!r}.\")"," try:"," dtype = _TRUEDIV_TABLE[x_dtype]"," except KeyError as e:"," raise TypeError("," f\"Invalid dtype {x_dtype!r} in tf.math.divide_no_nan. Expected one \""," f\"of {{{', '.join([repr(x) for x in _TRUEDIV_TABLE.keys()])}}}.\""," ) from e"," if dtype is not None:"," x = cast(x, dtype)"," y = cast(y, dtype)"," return gen_math_ops.div_no_nan(x, y, name=name)","","","@tf_export(\"math.multiply_no_nan\")","@dispatch.register_binary_elementwise_api","@dispatch.add_dispatch_support","def multiply_no_nan(x, y, name=None):"," \"\"\"Computes the product of x and y and returns 0 if the y is zero, even if x is NaN or infinite.",""," Note this is noncommutative: if y is NaN or infinite and x is 0, the result"," will be NaN.",""," Args:"," x: A `Tensor`. Must be one of the following types: `float32`, `float64`."," y: A `Tensor` whose dtype is compatible with `x`."," name: A name for the operation (optional).",""," Returns:"," The element-wise value of the x times y."," \"\"\"",""," with ops.name_scope(name, \"multiply_no_nan\", [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(f\"`x` and `y` must have the same dtype, \""," f\"got {x_dtype!r} != {y_dtype!r}\")"," return gen_math_ops.mul_no_nan(x, y, name=name)","","","def mod(x, y, name=None):"," r\"\"\"Returns element-wise remainder of division.",""," This follows Python semantics in that the"," result here is consistent with a flooring divide. E.g."," `floor(x / y) * y + floormod(x, y) = x`, regardless of the signs of x and y.",""," *NOTE*: `math.floormod` supports broadcasting. More about broadcasting"," [here](http://docs.scipy.org/doc/numpy/user/basics.broadcasting.html)",""," Args:"," x: A `Tensor`. Must be one of the following types: `int8`, `int16`, `int32`,"," `int64`, `uint8`, `uint16`, `uint32`, `uint64`, `bfloat16`, `half`,"," `float32`, `float64`."," y: A `Tensor`. Must have the same type as `x`."," name: A name for the operation (optional).",""," Returns:"," A `Tensor`. Has the same type as `x`."," \"\"\""," with ops.name_scope(name, \"mod\", [x, y]) as name:"," return gen_math_ops.floor_mod(x, y, name=name)","","","@tf_export(\"math.floordiv\", v1=[\"math.floordiv\", \"floordiv\"])","@dispatch.register_binary_elementwise_api","@dispatch.add_dispatch_support","@deprecation.deprecated_endpoints(\"floordiv\")","def floordiv(x, y, name=None):"," \"\"\"Divides `x / y` elementwise, rounding toward the most negative integer.",""," Mathematically, this is equivalent to floor(x / y). For example:"," floor(8.4 / 4.0) = floor(2.1) = 2.0"," floor(-8.4 / 4.0) = floor(-2.1) = -3.0"," This is equivalent to the '//' operator in Python 3.0 and above.",""," Note: `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 toward -infinity.",""," 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","truncatediv = gen_math_ops.truncate_div","floor_div = gen_math_ops.floor_div","truncatemod = gen_math_ops.truncate_mod","floormod = gen_math_ops.floor_mod","","","@tf_export(\"__operators__.add\", v1=[])","@dispatch.add_dispatch_support","def _add_dispatch(x, y, name=None):"," \"\"\"The operation invoked by the `Tensor.__add__` operator.",""," Purpose in the API:",""," This method is exposed in TensorFlow's API so that library developers"," can register dispatching for `Tensor.__add__` to allow it to handle"," custom composite tensors & other custom objects.",""," The API symbol is not intended to be called by users directly and does"," appear in TensorFlow's generated documentation.",""," Args:"," x: The left-hand side of the `+` operator."," y: The right-hand side of the `+` operator."," name: an optional name for the operation.",""," Returns:"," The result of the elementwise `+` operation."," \"\"\""," if ops.is_auto_dtype_conversion_enabled():"," return add(x, y, name=name)"," if not isinstance(y, tensor_lib.Tensor) and not isinstance("," y, sparse_tensor.SparseTensor):"," y = ops.convert_to_tensor(y, dtype_hint=x.dtype.base_dtype, name=\"y\")"," if x.dtype == dtypes.string:"," return gen_math_ops.add(x, y, name=name)"," else:"," return gen_math_ops.add_v2(x, y, name=name)","","","def _mul_dispatch(x, y, name=None):"," \"\"\"Dispatches cwise mul for \"Dense*Dense\" and \"Dense*Sparse\".\"\"\""," if 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)"," else:"," return multiply(x, y, name=name)","","","@tf_export(\"math.logical_xor\", v1=[\"math.logical_xor\", \"logical_xor\"])","@dispatch.register_binary_elementwise_api","@dispatch.add_dispatch_support","@deprecation.deprecated_endpoints(\"logical_xor\")","def logical_xor(x, y, name=\"LogicalXor\"):"," \"\"\"Logical XOR function.",""," x ^ y = (x | y) & ~(x & y)",""," Requires that `x` and `y` have the same shape or have"," [broadcast-compatible](http://docs.scipy.org/doc/numpy/user/basics.broadcasting.html)"," shapes. For example, `x` and `y` can be:",""," - Two single elements of type `bool`"," - One `tf.Tensor` of type `bool` and one single `bool`, where the result will"," be calculated by applying logical XOR with the single element to each"," element in the larger Tensor."," - Two `tf.Tensor` objects of type `bool` of the same shape. In this case,"," the result will be the element-wise logical XOR of the two input tensors.",""," Usage:",""," >>> a = tf.constant([True])"," >>> b = tf.constant([False])"," >>> tf.math.logical_xor(a, b)"," ",""," >>> c = tf.constant([True])"," >>> x = tf.constant([False, True, True, False])"," >>> tf.math.logical_xor(c, x)"," ",""," >>> y = tf.constant([False, False, True, True])"," >>> z = tf.constant([False, True, False, True])"," >>> tf.math.logical_xor(y, z)"," ",""," Args:"," x: A `tf.Tensor` type bool."," y: A `tf.Tensor` of type bool."," name: A name for the operation (optional).",""," Returns:"," A `tf.Tensor` of type bool with the same size as that of x or 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)","","","def and_(x, y, name=None):"," if x.dtype == dtypes.bool:"," return gen_math_ops.logical_and(x, y, name)"," return gen_bitwise_ops.bitwise_and(x, y)","","","def or_(x, y, name=None):"," if x.dtype == dtypes.bool:"," return gen_math_ops.logical_or(x, y, name)"," return gen_bitwise_ops.bitwise_or(x, y)","","","def xor_(x, y, name=None):"," if x.dtype == dtypes.bool:"," return logical_xor(x, y, name)"," return gen_bitwise_ops.bitwise_xor(x, y)","","","def invert_(x, name=None):"," if x.dtype == dtypes.bool:"," return gen_math_ops.logical_not(x, name=name)"," return gen_bitwise_ops.invert(x, name=name)","","","@tf_export(\"math.equal\", \"equal\")","@dispatch.register_binary_elementwise_api","@dispatch.add_dispatch_support","def equal(x, y, name=None):"," \"\"\"Returns the truth value of (x == y) element-wise.",""," Performs a [broadcast]("," https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html) with the"," arguments and then an element-wise equality comparison, returning a Tensor of"," boolean values.",""," For example:",""," >>> x = tf.constant([2, 4])"," >>> y = tf.constant(2)"," >>> tf.math.equal(x, y)"," ",""," >>> x = tf.constant([2, 4])"," >>> y = tf.constant([2, 4])"," >>> tf.math.equal(x, y)"," ",""," Args:"," x: A `tf.Tensor`."," y: A `tf.Tensor`."," name: A name for the operation (optional).",""," Returns:"," A `tf.Tensor` of type bool with the same size as that of x or y.",""," Raises:"," `tf.errors.InvalidArgumentError`: If shapes of arguments are incompatible"," \"\"\""," return gen_math_ops.equal(x, y, name=name)","","","@tf_export(\"math.not_equal\", \"not_equal\")","@dispatch.register_binary_elementwise_api","@dispatch.add_dispatch_support","def not_equal(x, y, name=None):"," \"\"\"Returns the truth value of (x != y) element-wise.",""," Performs a [broadcast]("," https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html) with the"," arguments and then an element-wise inequality comparison, returning a Tensor"," of boolean values.",""," For example:",""," >>> x = tf.constant([2, 4])"," >>> y = tf.constant(2)"," >>> tf.math.not_equal(x, y)"," ",""," >>> x = tf.constant([2, 4])"," >>> y = tf.constant([2, 4])"," >>> tf.math.not_equal(x, y)"," ",""," Args:"," x: A `tf.Tensor`."," y: A `tf.Tensor`."," name: A name for the operation (optional).",""," Returns:"," A `tf.Tensor` of type bool with the same size as that of x or y.",""," Raises:"," `tf.errors.InvalidArgumentError`: If shapes of arguments are incompatible"," \"\"\""," return gen_math_ops.not_equal(x, y, name=name)","","","@tf_export(\"__operators__.eq\", v1=[])","@dispatch.add_dispatch_support","def tensor_equals(self, other):"," \"\"\"The operation invoked by the `Tensor.__eq__` operator.",""," Compares two tensors element-wise for equality if they are"," broadcast-compatible; or returns False if they are not broadcast-compatible."," (Note that this behavior differs from `tf.math.equal`, which raises an"," exception if the two tensors are not broadcast-compatible.)",""," Purpose in the API:",""," This method is exposed in TensorFlow's API so that library developers"," can register dispatching for `Tensor.__eq__` to allow it to handle"," custom composite tensors & other custom objects.",""," The API symbol is not intended to be called by users directly and does"," appear in TensorFlow's generated documentation.",""," Args:"," self: The left-hand side of the `==` operator."," other: The right-hand side of the `==` operator.",""," Returns:"," The result of the elementwise `==` operation, or `False` if the arguments"," are not broadcast-compatible."," \"\"\""," if other is None:"," return False"," g = getattr(self, \"graph\", None)"," if ("," tensor_lib.Tensor._USE_EQUALITY"," and ops.executing_eagerly_outside_functions()"," and (g is None or g.building_function)"," ):"," self, other = override_binary_operator.maybe_promote_tensors(self, other)"," return gen_math_ops.equal(self, other, incompatible_shape_error=False)"," else:"," # In legacy graph mode, tensor equality is object equality"," return self is other","","","@tf_export(\"__operators__.ne\", v1=[])","@dispatch.add_dispatch_support","def tensor_not_equals(self, other):"," \"\"\"The operation invoked by the `Tensor.__ne__` operator.",""," Compares two tensors element-wise for inequality if they are"," broadcast-compatible; or returns True if they are not broadcast-compatible."," (Note that this behavior differs from `tf.math.not_equal`, which raises an"," exception if the two tensors are not broadcast-compatible.)",""," Purpose in the API:",""," This method is exposed in TensorFlow's API so that library developers"," can register dispatching for `Tensor.__ne__` to allow it to handle"," custom composite tensors & other custom objects.",""," The API symbol is not intended to be called by users directly and does"," appear in TensorFlow's generated documentation.",""," Args:"," self: The left-hand side of the `!=` operator."," other: The right-hand side of the `!=` operator.",""," Returns:"," The result of the elementwise `!=` operation, or `True` if the arguments"," are not broadcast-compatible."," \"\"\""," if other is None:"," return True"," if ("," tensor_lib.Tensor._USE_EQUALITY"," and ops.executing_eagerly_outside_functions()"," ):"," self, other = override_binary_operator.maybe_promote_tensors(self, other)"," return gen_math_ops.not_equal(self, other, incompatible_shape_error=False)"," else:"," # In legacy graph mode, tensor equality is object equality"," return self is not other","","","@tf_export(\"range\")","@dispatch.add_dispatch_support","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:",""," >>> start = 3"," >>> limit = 18"," >>> delta = 3"," >>> tf.range(start, limit, delta)"," ",""," >>> start = 3"," >>> limit = 1"," >>> delta = -0.5"," >>> tf.range(start, limit, delta)"," ",""," >>> limit = 5"," >>> tf.range(limit)"," ",""," 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:"," if not isinstance(start, tensor_lib.Tensor):"," start = ops.convert_to_tensor(start, dtype=dtype, name=\"start\")"," if not isinstance(limit, tensor_lib.Tensor):"," limit = ops.convert_to_tensor(limit, dtype=dtype, name=\"limit\")"," if not isinstance(delta, tensor_lib.Tensor):"," 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)"," else:"," inferred_dtype = dtype"," # Always try to perform a cast even when start/limit/delta are already"," # tensors. This will resolve the case where start/limit/delta's original's"," # dtype is different from provided dtype."," 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)","","","def _range_tensor_conversion_function(value, dtype=None, name=None,"," as_ref=False):"," del as_ref"," return range(value.start, value.stop, value.step, dtype=dtype, name=name)","","","tensor_conversion_registry.register_tensor_conversion_function("," builtins.range, _range_tensor_conversion_function)","","","# Reduction operations","def _ReductionDims(x, axis): # pylint: disable=invalid-name"," \"\"\"Returns range(0, rank(x)) if axis is None.\"\"\""," if axis is not None:"," return axis"," else:"," try:"," x_rank = x.shape.rank"," except AttributeError:"," x_rank = None",""," # Fast path: avoid creating Rank and Range ops if ndims is known."," if x_rank:"," return constant_op.constant(np.arange(x_rank, dtype=np.int32))"," else:"," # Otherwise, we rely on Range and Rank to do the right thing at run-time."," return range(0, array_ops.rank(x))","","","def _has_fully_defined_shape(tensor):"," \"\"\"Returns true if tensor has a fully defined shape.\"\"\""," return isinstance(tensor, ops.EagerTensor) or tensor.shape.is_fully_defined()","","","def _may_reduce_to_scalar(keepdims, axis, output):"," \"\"\"Set a reduction's output shape to be a scalar if we are certain.\"\"\""," if not _has_fully_defined_shape(output) and (not keepdims) and ("," axis is None):"," output.set_shape(())"," return output","","","@tf_export(v1=[\"math.reduce_sum\", \"reduce_sum\"])","@dispatch.add_dispatch_support","@deprecation.deprecated_args(None,"," \"keep_dims is deprecated, use keepdims instead\","," \"keep_dims\")","def reduce_sum_v1(input_tensor,"," axis=None,"," keepdims=None,"," name=None,"," reduction_indices=None,"," keep_dims=None):"," \"\"\"Computes the sum of elements across dimensions of a tensor.",""," This is the reduction operation for the elementwise `tf.math.add` op.",""," Reduces `input_tensor` along the dimensions given in `axis`."," Unless `keepdims` is true, the rank of the tensor is reduced by 1 for each"," of the entries in `axis`, which must be unique. If `keepdims` is true, the"," reduced dimensions are retained with length 1.",""," If `axis` is None, all dimensions are reduced, and a"," tensor with a single element is returned.",""," For example:",""," >>> # x has a shape of (2, 3) (two rows and three columns):"," >>> x = tf.constant([[1, 1, 1], [1, 1, 1]])"," >>> x.numpy()"," array([[1, 1, 1],"," [1, 1, 1]], dtype=int32)"," >>> # sum all the elements"," >>> # 1 + 1 + 1 + 1 + 1+ 1 = 6"," >>> tf.reduce_sum(x).numpy()"," 6"," >>> # reduce along the first dimension"," >>> # the result is [1, 1, 1] + [1, 1, 1] = [2, 2, 2]"," >>> tf.reduce_sum(x, 0).numpy()"," array([2, 2, 2], dtype=int32)"," >>> # reduce along the second dimension"," >>> # the result is [1, 1] + [1, 1] + [1, 1] = [3, 3]"," >>> tf.reduce_sum(x, 1).numpy()"," array([3, 3], dtype=int32)"," >>> # keep the original dimensions"," >>> tf.reduce_sum(x, 1, keepdims=True).numpy()"," array([[3],"," [3]], dtype=int32)"," >>> # reduce along both dimensions"," >>> # the result is 1 + 1 + 1 + 1 + 1 + 1 = 6"," >>> # or, equivalently, reduce along rows, then reduce the resultant array"," >>> # [1, 1, 1] + [1, 1, 1] = [2, 2, 2]"," >>> # 2 + 2 + 2 = 6"," >>> tf.reduce_sum(x, [0, 1]).numpy()"," 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 apart the fact that numpy upcast uint8 and int32 to"," int64 while tensorflow returns the same dtype as the input."," @end_compatibility"," \"\"\""," axis = deprecation.deprecated_argument_lookup(\"axis\", axis,"," \"reduction_indices\","," reduction_indices)"," keepdims = deprecation.deprecated_argument_lookup(\"keepdims\", keepdims,"," \"keep_dims\", keep_dims)"," return reduce_sum(input_tensor, axis, keepdims, name)","","","@tf_export(\"math.reduce_sum\", \"reduce_sum\", v1=[])","@dispatch.add_dispatch_support","def reduce_sum(input_tensor, axis=None, keepdims=False, name=None):"," \"\"\"Computes the sum of elements across dimensions of a tensor.",""," This is the reduction operation for the elementwise `tf.math.add` op.",""," Reduces `input_tensor` along the dimensions given in `axis`."," Unless `keepdims` is true, the rank of the tensor is reduced by 1 for each"," of the entries in `axis`, which must be unique. If `keepdims` is true, the"," reduced dimensions are retained with length 1.",""," If `axis` is None, all dimensions are reduced, and a"," tensor with a single element is returned.",""," For example:",""," >>> # x has a shape of (2, 3) (two rows and three columns):"," >>> x = tf.constant([[1, 1, 1], [1, 1, 1]])"," >>> x.numpy()"," array([[1, 1, 1],"," [1, 1, 1]], dtype=int32)"," >>> # sum all the elements"," >>> # 1 + 1 + 1 + 1 + 1+ 1 = 6"," >>> tf.reduce_sum(x).numpy()"," 6"," >>> # reduce along the first dimension"," >>> # the result is [1, 1, 1] + [1, 1, 1] = [2, 2, 2]"," >>> tf.reduce_sum(x, 0).numpy()"," array([2, 2, 2], dtype=int32)"," >>> # reduce along the second dimension"," >>> # the result is [1, 1] + [1, 1] + [1, 1] = [3, 3]"," >>> tf.reduce_sum(x, 1).numpy()"," array([3, 3], dtype=int32)"," >>> # keep the original dimensions"," >>> tf.reduce_sum(x, 1, keepdims=True).numpy()"," array([[3],"," [3]], dtype=int32)"," >>> # reduce along both dimensions"," >>> # the result is 1 + 1 + 1 + 1 + 1 + 1 = 6"," >>> # or, equivalently, reduce along rows, then reduce the resultant array"," >>> # [1, 1, 1] + [1, 1, 1] = [2, 2, 2]"," >>> # 2 + 2 + 2 = 6"," >>> tf.reduce_sum(x, [0, 1]).numpy()"," 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).",""," Returns:"," The reduced tensor, of the same dtype as the input_tensor.",""," @compatibility(numpy)"," Equivalent to np.sum apart the fact that numpy upcast uint8 and int32 to"," int64 while tensorflow returns the same dtype as the input."," @end_compatibility"," \"\"\"",""," return reduce_sum_with_dims(input_tensor, axis, keepdims, name,"," _ReductionDims(input_tensor, axis))","","","def reduce_sum_with_dims(input_tensor,"," axis=None,"," keepdims=False,"," name=None,"," dims=None):"," keepdims = False if keepdims is None else bool(keepdims)"," return _may_reduce_to_scalar("," keepdims, axis,"," gen_math_ops._sum(input_tensor, dims, keepdims, name=name))","","","@tf_export(\"math.reduce_euclidean_norm\")","@dispatch.add_dispatch_support","def reduce_euclidean_norm(input_tensor, axis=None, keepdims=False, name=None):"," \"\"\"Computes the Euclidean norm 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"," of the entries in `axis`, which must be unique. If `keepdims` is true, the"," reduced dimensions are retained with length 1.",""," If `axis` is None, all dimensions are reduced, and a"," tensor with a single element is returned.",""," For example:",""," ```python"," x = tf.constant([[1, 2, 3], [1, 1, 1]]) # x.dtype is tf.int32"," tf.math.reduce_euclidean_norm(x) # returns 4 as dtype is tf.int32"," y = tf.constant([[1, 2, 3], [1, 1, 1]], dtype = tf.float32)"," tf.math.reduce_euclidean_norm(y) # returns 4.1231055 which is sqrt(17)"," tf.math.reduce_euclidean_norm(y, 0) # [sqrt(2), sqrt(5), sqrt(10)]"," tf.math.reduce_euclidean_norm(y, 1) # [sqrt(14), sqrt(3)]"," tf.math.reduce_euclidean_norm(y, 1, keepdims=True) # [[sqrt(14)], [sqrt(3)]]"," tf.math.reduce_euclidean_norm(y, [0, 1]) # sqrt(17)"," ```",""," 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).",""," Returns:"," The reduced tensor, of the same dtype as the input_tensor."," \"\"\""," keepdims = bool(keepdims)"," return _may_reduce_to_scalar("," keepdims, axis,"," gen_math_ops.euclidean_norm("," input_tensor, _ReductionDims(input_tensor, axis), keepdims,"," name=name))","","","@tf_export(v1=[\"math.count_nonzero\", \"count_nonzero\"])","@dispatch.add_dispatch_support","@deprecation.deprecated_args(None,"," \"keep_dims is deprecated, use keepdims instead\","," \"keep_dims\")","@deprecation.deprecated_args("," None, \"reduction_indices is deprecated, use axis instead\","," \"reduction_indices\")","def count_nonzero(input_tensor=None,"," axis=None,"," keepdims=None,"," dtype=dtypes.int64,"," name=None,"," reduction_indices=None,"," keep_dims=None,"," input=None): # pylint: disable=redefined-builtin"," \"\"\"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.math.count_nonzero(x) # 3"," tf.math.count_nonzero(x, 0) # [1, 2, 0]"," tf.math.count_nonzero(x, 1) # [1, 2]"," tf.math.count_nonzero(x, 1, keepdims=True) # [[1], [2]]"," tf.math.count_nonzero(x, [0, 1]) # 3"," ```",""," **NOTE** Strings are compared against zero-length empty string `\"\"`. Any"," string with a size greater than zero is already considered as nonzero.",""," For example:"," ```python"," x = tf.constant([\"\", \"a\", \" \", \"b\", \"\"])"," tf.math.count_nonzero(x) # 3, with \"a\", \" \", and \"b\" as nonzero strings."," ```",""," Args:"," input_tensor: The tensor to reduce. Should be of numeric type, `bool`, or"," `string`."," 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`."," input: Overrides input_tensor. For compatibility.",""," Returns:"," The reduced tensor (number of nonzero values)."," \"\"\""," keepdims = deprecation.deprecated_argument_lookup(\"keepdims\", keepdims,"," \"keep_dims\", keep_dims)"," input_tensor = deprecation.deprecated_argument_lookup(\"input\", input,"," \"input_tensor\","," input_tensor)"," axis = deprecation.deprecated_argument_lookup(\"axis\", axis,"," \"reduction_indices\","," reduction_indices)",""," return count_nonzero_v2(input_tensor, axis, keepdims, dtype, name)","","","@tf_export(\"math.count_nonzero\", v1=[])","@dispatch.add_dispatch_support","def count_nonzero_v2("," input, # pylint: disable=redefined-builtin"," axis=None,"," keepdims=None,"," dtype=dtypes.int64,"," name=None):"," \"\"\"Computes number of nonzero elements across dimensions of a tensor.",""," Reduces `input` 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.math.count_nonzero(x) # 3"," tf.math.count_nonzero(x, 0) # [1, 2, 0]"," tf.math.count_nonzero(x, 1) # [1, 2]"," tf.math.count_nonzero(x, 1, keepdims=True) # [[1], [2]]"," tf.math.count_nonzero(x, [0, 1]) # 3"," ```",""," **NOTE** Strings are compared against zero-length empty string `\"\"`. Any"," string with a size greater than zero is already considered as nonzero.",""," For example:"," ```python"," x = tf.constant([\"\", \"a\", \" \", \"b\", \"\"])"," tf.math.count_nonzero(x) # 3, with \"a\", \" \", and \"b\" as nonzero strings."," ```",""," Args:"," input: The tensor to reduce. Should be of numeric type, `bool`, or `string`."," axis: The dimensions to reduce. If `None` (the default), reduces all"," dimensions. Must be in the range `[-rank(input), rank(input))`."," keepdims: If true, retains reduced dimensions with length 1."," dtype: The output dtype; defaults to `tf.int64`."," name: A name for the operation (optional).",""," Returns:"," The reduced tensor (number of nonzero values)."," \"\"\""," if keepdims is None:"," keepdims = False"," with ops.name_scope(name, \"count_nonzero\", [input]):"," input = ops.convert_to_tensor(input, name=\"input\")"," # if the input is already of type bool, then there is no need"," # to compare to zero."," if input.dtype == dtypes.bool:"," predicate = input"," else:"," # A scalar of 'zero' is enough as `not_equal` will broadcast."," zero = array_ops.zeros([], dtype=input.dtype)"," predicate = gen_math_ops.not_equal(input, zero)"," return cast("," reduce_sum("," # int64 reduction happens on GPU"," cast(predicate, dtypes.int64),"," axis=axis,"," keepdims=keepdims,"," ),"," dtype=dtype,"," )","","","@tf_export(v1=[\"math.reduce_mean\", \"reduce_mean\"])","@dispatch.add_dispatch_support","def reduce_mean_v1(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` by computing the"," mean of elements across the dimensions in `axis`."," Unless `keepdims` is true, the rank of the tensor is reduced by 1 for each"," the entries in `axis`, which must be unique. If `keepdims` is true, the"," reduced dimensions are retained with length 1.",""," If `axis` is None, all dimensions are reduced, and a tensor with a single"," element is returned.",""," For example:",""," >>> x = tf.constant([[1., 1.], [2., 2.]])"," >>> tf.reduce_mean(x)"," "," >>> tf.reduce_mean(x, 0)"," "," >>> tf.reduce_mean(x, 1)"," ",""," 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:",""," >>> x = tf.constant([1, 0, 1, 0])"," >>> tf.reduce_mean(x)"," "," >>> y = tf.constant([1., 0., 1., 0.])"," >>> tf.reduce_mean(y)"," ",""," @end_compatibility"," \"\"\""," axis = deprecation.deprecated_argument_lookup(\"axis\", axis,"," \"reduction_indices\","," reduction_indices)"," keepdims = deprecation.deprecated_argument_lookup(\"keepdims\", keepdims,"," \"keep_dims\", keep_dims)"," return reduce_mean(input_tensor, axis, keepdims, name)","","","@tf_export(\"math.reduce_mean\", \"reduce_mean\", v1=[])","@dispatch.add_dispatch_support","def reduce_mean(input_tensor, axis=None, keepdims=False, name=None):"," \"\"\"Computes the mean of elements across dimensions of a tensor.",""," Reduces `input_tensor` along the dimensions given in `axis` by computing the"," mean of elements across the dimensions in `axis`."," Unless `keepdims` is true, the rank of the tensor is reduced by 1 for each"," of the entries in `axis`, which must be unique. If `keepdims` is true, the"," reduced dimensions are retained with length 1.",""," If `axis` is None, all dimensions are reduced, and a tensor with a single"," element is returned.",""," For example:",""," >>> x = tf.constant([[1., 1.], [2., 2.]])"," >>> tf.reduce_mean(x)"," "," >>> tf.reduce_mean(x, 0)"," "," >>> tf.reduce_mean(x, 1)"," ",""," 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).",""," 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:",""," >>> x = tf.constant([1, 0, 1, 0])"," >>> tf.reduce_mean(x)"," "," >>> y = tf.constant([1., 0., 1., 0.])"," >>> tf.reduce_mean(y)"," ",""," @end_compatibility"," \"\"\""," keepdims = False if keepdims is None else bool(keepdims)"," return _may_reduce_to_scalar("," keepdims, axis,"," gen_math_ops.mean("," input_tensor, _ReductionDims(input_tensor, axis), keepdims,"," name=name))","","","@tf_export(\"math.reduce_variance\")","@dispatch.add_dispatch_support","def reduce_variance(input_tensor, axis=None, keepdims=False, name=None):"," \"\"\"Computes the variance 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"," of the entries in `axis`, which must be unique. If `keepdims` is true, the"," reduced dimensions are retained with length 1.",""," If `axis` is None, all dimensions are reduced, and a"," tensor with a single element is returned.",""," For example:",""," >>> x = tf.constant([[1., 2.], [3., 4.]])"," >>> tf.math.reduce_variance(x)"," "," >>> tf.math.reduce_variance(x, 0)"," "," >>> tf.math.reduce_variance(x, 1)"," ",""," Args:"," input_tensor: The tensor to reduce. Should have real or complex 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 scope for the associated operations (optional).",""," Returns:"," The reduced tensor, of the same dtype as the input_tensor. Note, for"," `complex64` or `complex128` input, the returned `Tensor` will be of type"," `float32` or `float64`, respectively.",""," @compatibility(numpy)"," Equivalent to np.var",""," Please note `np.var` has a `dtype` parameter that could be used to specify the"," output type. By default this is `dtype=float64`. On the other hand,"," `tf.math.reduce_variance` has aggressive type inference from `input_tensor`."," @end_compatibility"," \"\"\""," name = name if name else \"reduce_variance\""," with ops.name_scope(name):"," input_tensor = ops.convert_to_tensor(input_tensor)"," means = reduce_mean(input_tensor, axis=axis, keepdims=True)"," if means.dtype.is_integer:"," raise TypeError(f\"Input must be either real or complex. \""," f\"Received integer type {means.dtype}.\")"," diff = input_tensor - means"," if diff.dtype.is_complex:"," # For complex values we need to take the absolute value before squaring."," # This is achieved by multiplying with the conjugate."," real_dtype = diff.dtype.real_dtype"," squared_deviations = gen_math_ops.real("," gen_math_ops.mul(gen_math_ops.conj(diff), diff), Tout=real_dtype)"," else:"," squared_deviations = gen_math_ops.square(diff)"," return reduce_mean(squared_deviations, axis=axis, keepdims=keepdims)","","","@tf_export(\"math.reduce_std\")","@dispatch.add_dispatch_support","def reduce_std(input_tensor, axis=None, keepdims=False, name=None):"," \"\"\"Computes the standard deviation 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"," of the entries in `axis`, which must be unique. If `keepdims` is true, the"," reduced dimensions are retained with length 1.",""," If `axis` is None, all dimensions are reduced, and a"," tensor with a single element is returned.",""," For example:",""," >>> x = tf.constant([[1., 2.], [3., 4.]])"," >>> tf.math.reduce_std(x)"," "," >>> tf.math.reduce_std(x, 0)"," "," >>> tf.math.reduce_std(x, 1)"," ",""," Args:"," input_tensor: The tensor to reduce. Should have real or complex 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 scope for the associated operations (optional).",""," Returns:"," The reduced tensor, of the same dtype as the input_tensor. Note, for"," `complex64` or `complex128` input, the returned `Tensor` will be of type"," `float32` or `float64`, respectively.",""," @compatibility(numpy)"," Equivalent to np.std",""," Please note `np.std` has a `dtype` parameter that could be used to specify the"," output type. By default this is `dtype=float64`. On the other hand,"," `tf.math.reduce_std` has aggressive type inference from `input_tensor`."," @end_compatibility"," \"\"\""," name = name if name else \"reduce_std\""," with ops.name_scope(name):"," input_tensor = ops.convert_to_tensor(input_tensor)"," variance = reduce_variance(input_tensor, axis=axis, keepdims=keepdims)"," return gen_math_ops.sqrt(variance)","","","@tf_export(\"math.reduce_prod\", \"reduce_prod\", v1=[])","@dispatch.add_dispatch_support","def reduce_prod(input_tensor, axis=None, keepdims=False, name=None):"," \"\"\"Computes `tf.math.multiply` of elements across dimensions of a tensor.",""," This is the reduction operation for the elementwise `tf.math.multiply` op.",""," 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` is None, all dimensions are reduced, and a"," tensor with a single element is returned.",""," For example:",""," >>> x = tf.constant([[1., 2.], [3., 4.]])"," >>> tf.math.reduce_prod(x)"," "," >>> tf.math.reduce_prod(x, 0)"," "," >>> tf.math.reduce_prod(x, 1)"," ",""," 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).",""," Returns:"," The reduced tensor.",""," @compatibility(numpy)"," Equivalent to np.prod"," @end_compatibility"," \"\"\""," keepdims = False if keepdims is None else bool(keepdims)"," return _may_reduce_to_scalar("," keepdims, axis,"," gen_math_ops.prod("," input_tensor, _ReductionDims(input_tensor, axis), keepdims,"," name=name))","","","@tf_export(v1=[\"math.reduce_prod\", \"reduce_prod\"])","@dispatch.add_dispatch_support","@deprecation.deprecated_args(None,"," \"keep_dims is deprecated, use keepdims instead\","," \"keep_dims\")","def reduce_prod_v1(input_tensor,"," axis=None,"," keepdims=None,"," name=None,"," reduction_indices=None,"," keep_dims=None):"," \"\"\"Computes `tf.math.multiply` of elements across dimensions of a tensor.",""," This is the reduction operation for the elementwise `tf.math.multiply` op.",""," Reduces `input_tensor` along the dimensions given in `axis`."," Unless `keepdims` is true, the rank of the tensor is reduced by 1 for each"," of the entries in `axis`, which must be unique. If `keepdims` is true, the"," reduced dimensions are retained with length 1.",""," If `axis` is None, all dimensions are reduced, and a"," tensor with a single element is returned.",""," For example:",""," >>> x = tf.constant([[1., 2.], [3., 4.]])"," >>> tf.math.reduce_prod(x)"," "," >>> tf.math.reduce_prod(x, 0)"," "," >>> tf.math.reduce_prod(x, 1)"," ",""," 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"," \"\"\""," axis = deprecation.deprecated_argument_lookup(\"axis\", axis,"," \"reduction_indices\","," reduction_indices)"," keepdims = deprecation.deprecated_argument_lookup(\"keepdims\", keepdims,"," \"keep_dims\", keep_dims)"," return reduce_prod(input_tensor, axis, keepdims, name)","","","@tf_export(v1=[\"math.reduce_min\", \"reduce_min\"])","@dispatch.add_dispatch_support","@deprecation.deprecated_args(None,"," \"keep_dims is deprecated, use keepdims instead\","," \"keep_dims\")","def reduce_min_v1(input_tensor,"," axis=None,"," keepdims=None,"," name=None,"," reduction_indices=None,"," keep_dims=None):"," \"\"\"Computes the `tf.math.minimum` of elements across dimensions of a tensor.",""," This is the reduction operation for the elementwise `tf.math.minimum` op.",""," Reduces `input_tensor` along the dimensions given in `axis`."," Unless `keepdims` is true, the rank of the tensor is reduced by 1 for each"," of the entries in `axis`, which must be unique. If `keepdims` is true, the"," reduced dimensions are retained with length 1.",""," If `axis` is None, all dimensions are reduced, and a"," tensor with a single element is returned.",""," Usage example:",""," >>> x = tf.constant([5, 1, 2, 4])"," >>> tf.reduce_min(x)"," "," >>> x = tf.constant([-5, -1, -2, -4])"," >>> tf.reduce_min(x)"," "," >>> x = tf.constant([4, float('nan')])"," >>> tf.reduce_min(x)"," "," >>> x = tf.constant([float('nan'), float('nan')])"," >>> tf.reduce_min(x)"," "," >>> x = tf.constant([float('-inf'), float('inf')])"," >>> tf.reduce_min(x)"," ",""," See the numpy docs for `np.amin` and `np.nanmin` behavior.",""," Args:"," input_tensor: The tensor to reduce. Should have real 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."," \"\"\""," axis = deprecation.deprecated_argument_lookup(\"axis\", axis,"," \"reduction_indices\","," reduction_indices)"," keepdims = deprecation.deprecated_argument_lookup(\"keepdims\", keepdims,"," \"keep_dims\", keep_dims)"," return reduce_min(input_tensor, axis, keepdims, name)","","","@tf_export(\"math.reduce_min\", \"reduce_min\", v1=[])","@dispatch.add_dispatch_support","def reduce_min(input_tensor, axis=None, keepdims=False, name=None):"," \"\"\"Computes the `tf.math.minimum` of elements across dimensions of a tensor.",""," This is the reduction operation for the elementwise `tf.math.minimum` op.",""," Reduces `input_tensor` along the dimensions given in `axis`."," Unless `keepdims` is true, the rank of the tensor is reduced by 1 for each"," of the entries in `axis`, which must be unique. If `keepdims` is true, the"," reduced dimensions are retained with length 1.",""," If `axis` is None, all dimensions are reduced, and a"," tensor with a single element is returned.",""," For example:",""," >>> a = tf.constant(["," ... [[1, 2], [3, 4]],"," ... [[1, 2], [3, 4]]"," ... ])"," >>> tf.reduce_min(a)"," ",""," Choosing a specific axis returns minimum element in the given axis:",""," >>> b = tf.constant([[1, 2, 3], [4, 5, 6]])"," >>> tf.reduce_min(b, axis=0)"," "," >>> tf.reduce_min(b, axis=1)"," ",""," Setting `keepdims` to `True` retains the dimension of `input_tensor`:",""," >>> tf.reduce_min(a, keepdims=True)"," "," >>> tf.math.reduce_min(a, axis=0, keepdims=True)"," ",""," Args:"," input_tensor: The tensor to reduce. Should have real 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).",""," Returns:"," The reduced tensor.",""," @compatibility(numpy)"," Equivalent to np.min"," @end_compatibility"," \"\"\""," keepdims = False if keepdims is None else bool(keepdims)"," return _may_reduce_to_scalar("," keepdims, axis,"," gen_math_ops._min("," input_tensor, _ReductionDims(input_tensor, axis), keepdims,"," name=name))","","","@tf_export(v1=[\"math.reduce_max\", \"reduce_max\"])","@dispatch.add_dispatch_support","@deprecation.deprecated_args(None,"," \"keep_dims is deprecated, use keepdims instead\","," \"keep_dims\")","def reduce_max_v1(input_tensor,"," axis=None,"," keepdims=None,"," name=None,"," reduction_indices=None,"," keep_dims=None):"," \"\"\"Computes `tf.math.maximum` of elements across dimensions of a tensor.",""," This is the reduction operation for the elementwise `tf.math.maximum` op.",""," Reduces `input_tensor` along the dimensions given in `axis`."," Unless `keepdims` is true, the rank of the tensor is reduced by 1 for each"," of the entries in `axis`, which must be unique. If `keepdims` is true, the"," reduced dimensions are retained with length 1.",""," If `axis` is None, all dimensions are reduced, and a"," tensor with a single element is returned.",""," Usage example:",""," >>> x = tf.constant([5, 1, 2, 4])"," >>> tf.reduce_max(x)"," "," >>> x = tf.constant([-5, -1, -2, -4])"," >>> tf.reduce_max(x)"," "," >>> x = tf.constant([4, float('nan')])"," >>> tf.reduce_max(x)"," "," >>> x = tf.constant([float('nan'), float('nan')])"," >>> tf.reduce_max(x)"," "," >>> x = tf.constant([float('-inf'), float('inf')])"," >>> tf.reduce_max(x)"," ",""," See the numpy docs for `np.amax` and `np.nanmax` behavior.",""," Args:"," input_tensor: The tensor to reduce. Should have real 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."," \"\"\""," axis = deprecation.deprecated_argument_lookup(\"axis\", axis,"," \"reduction_indices\","," reduction_indices)"," keepdims = deprecation.deprecated_argument_lookup(\"keepdims\", keepdims,"," \"keep_dims\", keep_dims)"," return reduce_max(input_tensor, axis, keepdims, name)","","","@tf_export(\"math.reduce_max\", \"reduce_max\", v1=[])","@dispatch.add_dispatch_support","def reduce_max(input_tensor, axis=None, keepdims=False, name=None):"," \"\"\"Computes `tf.math.maximum` of elements across dimensions of a tensor.",""," This is the reduction operation for the elementwise `tf.math.maximum` op.",""," Reduces `input_tensor` along the dimensions given in `axis`."," Unless `keepdims` is true, the rank of the tensor is reduced by 1 for each"," of the entries in `axis`, which must be unique. If `keepdims` is true, the"," reduced dimensions are retained with length 1.",""," If `axis` is None, all dimensions are reduced, and a"," tensor with a single element is returned.",""," Usage example:",""," >>> x = tf.constant([5, 1, 2, 4])"," >>> tf.reduce_max(x)"," "," >>> x = tf.constant([-5, -1, -2, -4])"," >>> tf.reduce_max(x)"," "," >>> x = tf.constant([4, float('nan')])"," >>> tf.reduce_max(x)"," "," >>> x = tf.constant([float('nan'), float('nan')])"," >>> tf.reduce_max(x)"," "," >>> x = tf.constant([float('-inf'), float('inf')])"," >>> tf.reduce_max(x)"," ",""," See the numpy docs for `np.amax` and `np.nanmax` behavior.",""," Args:"," input_tensor: The tensor to reduce. Should have real 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).",""," Returns:"," The reduced tensor."," \"\"\""," return reduce_max_with_dims(input_tensor, axis, keepdims, name,"," _ReductionDims(input_tensor, axis))","","","def reduce_max_with_dims(input_tensor,"," axis=None,"," keepdims=False,"," name=None,"," dims=None):"," keepdims = False if keepdims is None else bool(keepdims)"," return _may_reduce_to_scalar("," keepdims, axis,"," gen_math_ops._max(input_tensor, dims, keepdims, name=name))","","","@tf_export(v1=[\"math.reduce_all\", \"reduce_all\"])","@dispatch.add_dispatch_support","@deprecation.deprecated_args(None,"," \"keep_dims is deprecated, use keepdims instead\","," \"keep_dims\")","def reduce_all_v1(input_tensor,"," axis=None,"," keepdims=None,"," name=None,"," reduction_indices=None,"," keep_dims=None):"," \"\"\"Computes `tf.math.logical_and` of elements across dimensions of a tensor.",""," This is the reduction operation for the elementwise `tf.math.logical_and` op.",""," Reduces `input_tensor` along the dimensions given in `axis`."," Unless `keepdims` is true, the rank of the tensor is reduced by 1 for each"," of the entries in `axis`, which must be unique. If `keepdims` is true, the"," reduced dimensions are retained with length 1.",""," If `axis` is None, all dimensions are reduced, and a"," tensor with a single element is returned.",""," For example:",""," >>> x = tf.constant([[True, True], [False, False]])"," >>> tf.math.reduce_all(x)"," "," >>> tf.math.reduce_all(x, 0)"," "," >>> tf.math.reduce_all(x, 1)"," ",""," 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"," \"\"\""," axis = deprecation.deprecated_argument_lookup(\"axis\", axis,"," \"reduction_indices\","," reduction_indices)"," keepdims = deprecation.deprecated_argument_lookup(\"keepdims\", keepdims,"," \"keep_dims\", keep_dims)"," return reduce_all(input_tensor, axis, keepdims, name)","","","@tf_export(\"math.reduce_all\", \"reduce_all\", v1=[])","@dispatch.add_dispatch_support","def reduce_all(input_tensor, axis=None, keepdims=False, name=None):"," \"\"\"Computes `tf.math.logical_and` of elements across dimensions of a tensor.",""," This is the reduction operation for the elementwise `tf.math.logical_and` op.",""," Reduces `input_tensor` along the dimensions given in `axis`."," Unless `keepdims` is true, the rank of the tensor is reduced by 1 for each"," of the entries in `axis`, which must be unique. If `keepdims` is true, the"," reduced dimensions are retained with length 1.",""," If `axis` is None, all dimensions are reduced, and a"," tensor with a single element is returned.",""," For example:",""," >>> x = tf.constant([[True, True], [False, False]])"," >>> tf.math.reduce_all(x)"," "," >>> tf.math.reduce_all(x, 0)"," "," >>> tf.math.reduce_all(x, 1)"," ",""," 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).",""," Returns:"," The reduced tensor.",""," @compatibility(numpy)"," Equivalent to np.all"," @end_compatibility"," \"\"\""," keepdims = False if keepdims is None else bool(keepdims)"," return _may_reduce_to_scalar("," keepdims, axis,"," gen_math_ops._all("," input_tensor, _ReductionDims(input_tensor, axis), keepdims,"," name=name))","","","@tf_export(v1=[\"math.reduce_any\", \"reduce_any\"])","@dispatch.add_dispatch_support","@deprecation.deprecated_args(None,"," \"keep_dims is deprecated, use keepdims instead\","," \"keep_dims\")","def reduce_any_v1(input_tensor,"," axis=None,"," keepdims=None,"," name=None,"," reduction_indices=None,"," keep_dims=None):"," \"\"\"Computes `tf.math.logical_or` of elements across dimensions of a tensor.",""," This is the reduction operation for the elementwise `tf.math.logical_or` op.",""," Reduces `input_tensor` along the dimensions given in `axis`."," Unless `keepdims` is true, the rank of the tensor is reduced by 1 for each"," of the entries in `axis`, which must be unique. If `keepdims` is true, the"," reduced dimensions are retained with length 1.",""," If `axis` is None, all dimensions are reduced, and a"," tensor with a single element is returned.",""," For example:",""," >>> x = tf.constant([[True, True], [False, False]])"," >>> tf.reduce_any(x)"," "," >>> tf.reduce_any(x, 0)"," "," >>> tf.reduce_any(x, 1)"," ",""," 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"," \"\"\""," axis = deprecation.deprecated_argument_lookup(\"axis\", axis,"," \"reduction_indices\","," reduction_indices)"," keepdims = deprecation.deprecated_argument_lookup(\"keepdims\", keepdims,"," \"keep_dims\", keep_dims)"," return reduce_any(input_tensor, axis, keepdims, name)","","","@tf_export(\"math.reduce_any\", \"reduce_any\", v1=[])","@dispatch.add_dispatch_support","def reduce_any(input_tensor, axis=None, keepdims=False, name=None):"," \"\"\"Computes `tf.math.logical_or` of elements across dimensions of a tensor.",""," This is the reduction operation for the elementwise `tf.math.logical_or` op.",""," Reduces `input_tensor` along the dimensions given in `axis`."," Unless `keepdims` is true, the rank of the tensor is reduced by 1 for each"," of the entries in `axis`, which must be unique. If `keepdims` is true, the"," reduced dimensions are retained with length 1.",""," If `axis` is None, all dimensions are reduced, and a"," tensor with a single element is returned.",""," For example:",""," >>> x = tf.constant([[True, True], [False, False]])"," >>> tf.reduce_any(x)"," "," >>> tf.reduce_any(x, 0)"," "," >>> tf.reduce_any(x, 1)"," ",""," 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).",""," Returns:"," The reduced tensor.",""," @compatibility(numpy)"," Equivalent to np.any"," @end_compatibility"," \"\"\""," keepdims = False if keepdims is None else bool(keepdims)"," return _may_reduce_to_scalar("," keepdims, axis,"," gen_math_ops._any("," input_tensor, _ReductionDims(input_tensor, axis), keepdims,"," name=name))","","","@tf_export(v1=[\"math.reduce_logsumexp\", \"reduce_logsumexp\"])","@dispatch.add_dispatch_support","@deprecation.deprecated_args(None,"," \"keep_dims is deprecated, use keepdims instead\","," \"keep_dims\")","def reduce_logsumexp_v1(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"," of the entries in `axis`, which must be unique. 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."," \"\"\""," axis = deprecation.deprecated_argument_lookup(\"axis\", axis,"," \"reduction_indices\","," reduction_indices)"," keepdims = deprecation.deprecated_argument_lookup(\"keepdims\", keepdims,"," \"keep_dims\", keep_dims)"," return reduce_logsumexp(input_tensor, axis, keepdims, name)","","","@tf_export(\"math.reduce_logsumexp\", \"reduce_logsumexp\", v1=[])","@dispatch.add_dispatch_support","def reduce_logsumexp(input_tensor, axis=None, keepdims=False, name=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"," of the entries in `axis`, which must be unique. 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).",""," Returns:"," The reduced tensor."," \"\"\""," with ops.name_scope(name, \"ReduceLogSumExp\", [input_tensor]) as name:"," raw_max = reduce_max(input_tensor, axis=axis, keepdims=True)"," my_max = array_ops.stop_gradient("," gen_math_ops.select("," gen_math_ops.is_finite(raw_max), raw_max,"," gen_array_ops.zeros_like(raw_max)))"," result = gen_math_ops.log("," reduce_sum("," exp(subtract(input_tensor, my_max)),"," axis=axis,"," keepdims=keepdims))"," if not keepdims:"," my_max = array_ops.reshape(my_max, gen_array_ops.shape(result))"," result = add(result, my_max, name=name)"," return _may_reduce_to_scalar(keepdims, axis, result)","","","@tf_export(\"linalg.trace\", v1=[\"linalg.trace\", \"trace\"])","@dispatch.add_dispatch_support","@deprecation.deprecated_endpoints(\"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, k, ..., l, :, :])`",""," For example:",""," ```python"," x = tf.constant([[1, 2], [3, 4]])"," tf.linalg.trace(x) # 5",""," x = tf.constant([[1, 2, 3],"," [4, 5, 6],"," [7, 8, 9]])"," tf.linalg.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.linalg.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(\"linalg.matmul\", \"matmul\")","@dispatch.add_dispatch_support","def matmul("," a,"," b,"," transpose_a=False,"," transpose_b=False,"," adjoint_a=False,"," adjoint_b=False,"," a_is_sparse=False,"," b_is_sparse=False,"," output_type=None,"," grad_a=False,"," grad_b=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 dimensions,"," and any further outer dimensions specify matching batch size.",""," Both matrices must be of the same type. The supported types are:"," `bfloat16`, `float16`, `float32`, `float64`, `int32`, `int64`,"," `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`.",""," A simple 2-D tensor matrix multiplication:",""," >>> a = tf.constant([1, 2, 3, 4, 5, 6], shape=[2, 3])"," >>> a # 2-D tensor"," "," >>> b = tf.constant([7, 8, 9, 10, 11, 12], shape=[3, 2])"," >>> b # 2-D tensor"," "," >>> c = tf.matmul(a, b)"," >>> c # `a` * `b`"," ",""," A batch matrix multiplication with batch shape [2]:",""," >>> a = tf.constant(np.arange(1, 13, dtype=np.int32), shape=[2, 2, 3])"," >>> a # 3-D tensor"," "," >>> b = tf.constant(np.arange(13, 25, dtype=np.int32), shape=[2, 3, 2])"," >>> b # 3-D tensor"," "," >>> c = tf.matmul(a, b)"," >>> c # `a` * `b`"," ",""," Since python >= 3.5 the @ operator is supported"," (see [PEP 465](https://www.python.org/dev/peps/pep-0465/)). 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: `tf.Tensor` of type `float16`, `float32`, `float64`, `int32`,"," `complex64`, `complex128` and rank > 1."," b: `tf.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. Notice, this"," **does not support `tf.sparse.SparseTensor`**, it just makes optimizations"," that assume most values in `a` are zero. See"," `tf.sparse.sparse_dense_matmul` for some support for"," `tf.sparse.SparseTensor` multiplication."," b_is_sparse: If `True`, `b` is treated as a sparse matrix. Notice, this"," **does not support `tf.sparse.SparseTensor`**, it just makes optimizations"," that assume most values in `b` are zero. See"," `tf.sparse.sparse_dense_matmul` for some support for"," `tf.sparse.SparseTensor` multiplication."," output_type: The output datatype if needed. Defaults to None in which case"," the output_type is the same as input type. Currently only works when input"," tensors are type (u)int8 and output_type can be int32."," grad_a: Set it to `True` to hint that Tensor `a` is for the backward pass."," grad_b: Set it to `True` to hint that Tensor `b` is for the backward pass."," name: Name for the operation (optional).",""," Returns:"," A `tf.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`."," TypeError: If output_type is specified but the types of `a`, `b` and"," `output_type` is not (u)int8, (u)int8 and int32."," \"\"\"",""," with ops.name_scope(name, \"MatMul\", [a, b]) as name:"," if transpose_a and adjoint_a:"," raise ValueError("," f\"Only one of `transpose_a` and `adjoint_a` can be True. \""," f\"Received `transpose_a`={transpose_a}, \""," f\"`adjoint_a`={adjoint_a}.\")"," if transpose_b and adjoint_b:"," raise ValueError("," f\"Only one of `transpose_b` and `adjoint_b` can be True. \""," f\"Received `transpose_b`={transpose_b}, \""," f\"`adjoint_b`={adjoint_b}.\")",""," if context.executing_eagerly():"," if not ("," isinstance(a, ops.EagerTensor) or _pywrap_utils.IsResourceVariable(a)"," ):"," a = ops.convert_to_tensor(a, name=\"a\")"," if not isinstance(b, ops.EagerTensor) or _pywrap_utils.IsResourceVariable("," b):"," b = ops.convert_to_tensor(b, dtype_hint=a.dtype.base_dtype, name=\"b\")"," else:"," a = ops.convert_to_tensor(a, name=\"a\")"," b = ops.convert_to_tensor(b, dtype_hint=a.dtype.base_dtype, 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",""," output_may_have_non_empty_batch_shape = ("," (a_shape is None or len(a_shape) > 2) or"," (b_shape is None or len(b_shape) > 2))",""," # TODO(b/178749687): remove this boolean and all related branches once the"," # bridges are ready."," # batch_matmul_v3 is for when input type is different from output type."," use_batch_matmul_v3 = False"," if output_type and (output_type != a.dtype or output_type != b.dtype):"," use_batch_matmul_v3 = True",""," if (not a_is_sparse and"," not b_is_sparse) and output_may_have_non_empty_batch_shape:"," # 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"," if use_batch_matmul_v3:"," return gen_math_ops.batch_mat_mul_v3("," a,"," b,"," adj_x=adjoint_a,"," adj_y=adjoint_b,"," Tout=output_type,"," grad_x=grad_a,"," grad_y=grad_b,"," name=name,"," )"," else:"," return gen_math_ops.batch_mat_mul_v2("," a,"," b,"," adj_x=adjoint_a,"," adj_y=adjoint_b,"," grad_x=grad_a,"," grad_y=grad_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 and"," b.dtype not in (dtypes.int8, dtypes.uint8)) or"," (b.dtype == dtypes.bfloat16 and"," a.dtype not in (dtypes.int8, dtypes.uint8))) and a.dtype != b.dtype):"," # matmul currently doesn't handle mixed-precision inputs other than"," # fp16 * int8 which is supported in BatchMatMulV3."," 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:"," if use_batch_matmul_v3:"," adjoint_a = adjoint_a or transpose_a"," adjoint_b = adjoint_b or transpose_b"," return gen_math_ops.batch_mat_mul_v3("," a,"," b,"," adj_x=adjoint_a,"," adj_y=adjoint_b,"," Tout=output_type,"," grad_x=grad_a,"," grad_y=grad_b,"," name=name,"," )"," else:"," return gen_math_ops.mat_mul("," a,"," b,"," transpose_a=transpose_a,"," transpose_b=transpose_b,"," grad_a=grad_a,"," grad_b=grad_b,"," name=name,"," )","","","@tf_export(\"linalg.matvec\")","@dispatch.add_dispatch_support","def matvec(a,"," b,"," transpose_a=False,"," adjoint_a=False,"," a_is_sparse=False,"," b_is_sparse=False,"," name=None):"," \"\"\"Multiplies matrix `a` by vector `b`, producing `a` * `b`.",""," The matrix `a` must, following any transpositions, be a tensor of rank >= 2,"," with `shape(a)[-1] == shape(b)[-1]`, and `shape(a)[:-2]` able to broadcast"," with `shape(b)[:-1]`.",""," Both `a` and `b` must be of the same type. The supported types are:"," `float16`, `float32`, `float64`, `int32`, `complex64`, `complex128`.",""," Matrix `a` 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 inputs 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/vectors (rank-2/1"," 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])",""," # 1-D tensor `b`"," # [7, 9, 11]"," b = tf.constant([7, 9, 11], shape=[3])",""," # `a` * `b`"," # [ 58, 139]"," c = tf.linalg.matvec(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])",""," # 2-D tensor `b`"," # [[13, 14, 15],"," # [16, 17, 18]]"," b = tf.constant(np.arange(13, 19, dtype=np.int32),"," shape=[2, 3])",""," # `a` * `b`"," # [[ 86, 212],"," # [410, 563]]"," c = tf.linalg.matvec(a, b)"," ```",""," Args:"," a: `Tensor` of type `float16`, `float32`, `float64`, `int32`, `complex64`,"," `complex128` and rank > 1."," b: `Tensor` with same type as `a` and compatible dimensions."," transpose_a: If `True`, `a` is transposed before multiplication."," adjoint_a: If `True`, `a` 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 vector is"," the product of the corresponding matrices in `a` and vectors in `b`, e.g. if"," all transpose or adjoint attributes are `False`:",""," `output`[..., i] = sum_k (`a`[..., i, k] * `b`[..., k]), for all indices i.",""," Note: This is matrix-vector product, not element-wise product.","",""," Raises:"," ValueError: If transpose_a and adjoint_a are both set to True."," \"\"\""," with ops.name_scope(name, \"MatVec\", [a, b]) as name:"," output = matmul("," a,"," array_ops.expand_dims(b, axis=-1),"," transpose_a=transpose_a,"," adjoint_a=adjoint_a,"," a_is_sparse=a_is_sparse,"," b_is_sparse=b_is_sparse)"," return array_ops.squeeze(output, axis=-1)","","","# TODO(b/178650720): Also support numpy-style type promotion in freestanding TF","# functions (e.g. tf.add).","def matmul_wrapper(a, b, name=None): # pylint: disable=missing-function-docstring"," if ops.is_numpy_style_type_promotion():"," return a._matmul(b)"," return matmul(a, b, name=name)","matmul_wrapper.__doc__ = matmul.__doc__","","sparse_matmul = deprecation.deprecated(None, \"Use `tf.linalg.matmul` instead\")("," gen_math_ops.sparse_mat_mul)","tf_export(v1=[\"sparse_matmul\"])(sparse_matmul)","@dispatch.add_dispatch_support","","","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, (tensor_lib.Tensor, indexed_slices.IndexedSlices)):"," raise TypeError(f\"Not a Tensor or IndexedSlices: {type(x)}.\")"," if isinstance(x, indexed_slices.IndexedSlices):"," return x"," x_shape = array_ops.shape_internal(x, optimize=optimize)"," return indexed_slices.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(f\"Expected a list or tuple, not {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("," indexed_slices.IndexedSlices(o.values, cast(o.indices, dtypes.int64),"," o.dense_shape))"," else:"," casted_outputs.append(o)"," return casted_outputs","","","@tf_export(\"math.add\", \"add\")","@dispatch.register_binary_elementwise_api","@dispatch.add_dispatch_support","def add(x, y, name=None):"," \"\"\"Returns x + y element-wise.",""," Example usages below.",""," Add a scalar and a list:",""," >>> x = [1, 2, 3, 4, 5]"," >>> y = 1"," >>> tf.add(x, y)"," ",""," Note that binary `+` operator can be used instead:",""," >>> x = tf.convert_to_tensor([1, 2, 3, 4, 5])"," >>> y = tf.convert_to_tensor(1)"," >>> x + y"," ",""," Add a tensor and a list of same shape:",""," >>> x = [1, 2, 3, 4, 5]"," >>> y = tf.constant([1, 2, 3, 4, 5])"," >>> tf.add(x, y)"," ",""," **Warning**: If one of the inputs (`x` or `y`) is a tensor and the other is a"," non-tensor, the non-tensor input will adopt (or get casted to) the data type"," of the tensor input. This can potentially cause unwanted overflow or underflow"," conversion.",""," For example,",""," >>> x = tf.constant([1, 2], dtype=tf.int8)"," >>> y = [2**7 + 1, 2**7 + 2]"," >>> tf.add(x, y)"," ",""," When adding two input values of different shapes, `Add` follows NumPy"," broadcasting rules. The two input array shapes are compared element-wise."," Starting with the trailing dimensions, the two dimensions either have to be"," equal or one of them needs to be `1`.",""," For example,",""," >>> x = np.ones(6).reshape(1, 2, 1, 3)"," >>> y = np.ones(6).reshape(2, 1, 3, 1)"," >>> tf.add(x, y).shape.as_list()"," [2, 2, 3, 3]",""," Another example with two arrays of different dimension.",""," >>> x = np.ones([1, 2, 1, 4])"," >>> y = np.ones([3, 4])"," >>> tf.add(x, y).shape.as_list()"," [1, 2, 3, 4]",""," The reduction version of this elementwise operation is `tf.math.reduce_sum`",""," Args:"," x: A `tf.Tensor`. Must be one of the following types: bfloat16, half,"," float16, float32, float64, uint8, uint16, uint32, uint64, int8, int16,"," int32, int64, complex64, complex128, string."," y: A `tf.Tensor`. Must have the same type as x."," name: A name for the operation (optional)"," \"\"\""," with ops.name_scope(name, \"Add\", [x]) as name:"," x = ops.convert_to_tensor(x, name=\"x\")"," y = ops.convert_to_tensor(y, dtype_hint=x.dtype.base_dtype, name=\"y\")"," if x.dtype == dtypes.string:"," return gen_math_ops.add(x, y, name=name)"," else:"," return gen_math_ops.add_v2(x, y, name=name)","","","@tf_export(\"math.add_n\", \"add_n\")","@dispatch.add_dispatch_support(iterable_parameters=[\"inputs\"])","def add_n(inputs, name=None):"," \"\"\"Returns the element-wise sum of a list of tensors.",""," All inputs in the list must have the same shape. This op does not"," [broadcast](https://docs.scipy.org/doc/numpy-1.13.0/user/basics.broadcasting.html)"," its inputs. If you need broadcasting, use `tf.math.add` (or the `+` operator)"," instead.",""," For example:",""," >>> a = tf.constant([[3, 5], [4, 8]])"," >>> b = tf.constant([[1, 6], [2, 9]])"," >>> tf.math.add_n([a, b, a]).numpy()"," array([[ 7, 16],"," [10, 25]], dtype=int32)",""," See Also:",""," * `tf.reduce_sum(inputs, axis=0)` - This performs the same mathematical"," operation, but `tf.add_n` may be more efficient because it sums the"," tensors directly. `reduce_sum` on the other hand calls"," `tf.convert_to_tensor` on the list of tensors, unnecessarily stacking them"," into a single tensor before summing.",""," Args:"," inputs: A list of `tf.Tensor` or `tf.IndexedSlices` objects, each with the"," same shape and type. `tf.IndexedSlices` objects will be converted into"," dense tensors prior to adding."," name: A name for the operation (optional).",""," Returns:"," A `tf.Tensor` of the 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, collections_abc.Iterable):"," raise ValueError(\"Inputs must be an iterable of at least one \""," \"Tensor/IndexedSlices with the same dtype and shape.\")"," inputs = indexed_slices.convert_n_to_tensor_or_indexed_slices(inputs)"," if not all("," isinstance(x, (tensor_lib.Tensor, indexed_slices.IndexedSlices))"," for x in inputs):"," raise ValueError(\"Inputs must be an iterable of at least one \""," \"Tensor/IndexedSlices with the same dtype and shape.\")",""," if len(inputs) == 1:"," if isinstance(inputs[0], indexed_slices.IndexedSlices):"," values = ops.convert_to_tensor(inputs[0])"," else:"," values = inputs[0]"," if name:"," return array_ops.identity(values, name=name)"," return values"," return gen_math_ops.add_n(inputs, name=name)","","","@tf_export(\"math.accumulate_n\", v1=[\"math.accumulate_n\", \"accumulate_n\"])","@dispatch.add_dispatch_support","@deprecation.deprecated(None, \"Use `tf.math.add_n` Instead\")","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.",""," For example:",""," >>> a = tf.constant([[1, 2], [3, 4]])"," >>> b = tf.constant([[5, 0], [0, 6]])"," >>> tf.math.accumulate_n([a, b, a]).numpy()"," array([[ 7, 4],"," [ 6, 14]], dtype=int32)",""," >>> # Explicitly pass shape and type"," >>> tf.math.accumulate_n("," ... [a, b, a], shape=[2, 2], tensor_dtype=tf.int32).numpy()"," array([[ 7, 4],"," [ 6, 14]], dtype=int32)",""," Note: The input must be a list or tuple. This function does not handle"," `IndexedSlices`",""," See Also:",""," * `tf.reduce_sum(inputs, axis=0)` - This performe the same mathematical"," operation, but `tf.add_n` may be more efficient because it sums the"," tensors directly. `reduce_sum` on the other hand calls"," `tf.convert_to_tensor` on the list of tensors, unncessairly stacking them"," into a single tensor before summing."," * `tf.add_n` - This is another python wrapper for the same Op. It has"," nearly identical functionality.",""," Args:"," inputs: A list of `Tensor` objects, each with same shape and type."," shape: Expected shape of elements of `inputs` (optional). Also controls the"," output shape of this op, which may affect type inference in other ops. A"," value of `None` means \"infer the input shape from the shapes in `inputs`\"."," tensor_dtype: Expected data type of `inputs` (optional). A value of `None`"," means \"infer the input dtype from `inputs[0]`\"."," 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 = indexed_slices.convert_n_to_tensor_or_indexed_slices(inputs)"," if not all(isinstance(x, tensor_lib.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, tensor_lib.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("," f\"The `tensor_dtype` argument is {tensor_dtype}, but `input` is of \""," f\"type {inputs[0].dtype}. These must be equal. Try casting the input \""," f\"to the desired type.\")",""," 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)"," return add_n(inputs, name=name)","","","@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(\"math.sigmoid\", \"nn.sigmoid\", \"sigmoid\")","@dispatch.register_unary_elementwise_api","@dispatch.add_dispatch_support","def sigmoid(x, name=None):"," r\"\"\"Computes sigmoid of `x` element-wise.",""," Formula for calculating $\\mathrm{sigmoid}(x) = y = 1 / (1 + \\exp(-x))$.",""," For $x \\in (-\\infty, \\infty)$, $\\mathrm{sigmoid}(x) \\in (0, 1)$.",""," Example Usage:",""," If a positive number is large, then its sigmoid will approach to 1 since the"," formula will be `y = / (1 + )`",""," >>> x = tf.constant([0.0, 1.0, 50.0, 100.0])"," >>> tf.math.sigmoid(x)"," ",""," If a negative number is large, its sigmoid will approach to 0 since the"," formula will be `y = 1 / (1 + )`",""," >>> x = tf.constant([-100.0, -50.0, -1.0, 0.0])"," >>> tf.math.sigmoid(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`.",""," Usage Example:",""," >>> x = tf.constant([-128.0, 0.0, 128.0], dtype=tf.float32)"," >>> tf.sigmoid(x)"," ",""," @compatibility(scipy)"," Equivalent to 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(\"math.log_sigmoid\", v1=[\"math.log_sigmoid\", \"log_sigmoid\"])","@dispatch.register_unary_elementwise_api","@dispatch.add_dispatch_support","@deprecation.deprecated_endpoints(\"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`.",""," Usage Example:",""," If a positive number is large, then its log_sigmoid will approach to 0 since"," the formula will be `y = log( / (1 + ) )` which"," approximates to `log (1)` which is 0.",""," >>> x = tf.constant([0.0, 1.0, 50.0, 100.0])"," >>> tf.math.log_sigmoid(x)"," ",""," If a negative number is large, its log_sigmoid will approach to the number"," itself since the formula will be `y = log( 1 / (1 + ) )` which is"," `log (1) - log ( (1 + ) )` which approximates to `- `"," that is the number itself.",""," >>> x = tf.constant([-100.0, -50.0, -1.0, 0.0])"," >>> tf.math.log_sigmoid(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) # pylint: disable=invalid-unary-operand-type","","","@tf_export(\"math.cumsum\", \"cumsum\")","@dispatch.add_dispatch_support","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:"," For example:",""," >>> # tf.cumsum([a, b, c]) # [a, a + b, a + b + c]"," >>> x = tf.constant([2, 4, 6, 8])"," >>> tf.cumsum(x)"," ",""," >>> # using varying `axis` values"," >>> y = tf.constant([[2, 4, 6, 8], [1,3,5,7]])"," >>> tf.cumsum(y, axis=0)"," "," >>> tf.cumsum(y, axis=1)"," ",""," By setting the `exclusive` kwarg to `True`, an exclusive cumsum is performed"," instead:",""," >>> # tf.cumsum([a, b, c], exclusive=True) => [0, a, a + b]"," >>> x = tf.constant([2, 4, 6, 8])"," >>> tf.cumsum(x, exclusive=True)"," ",""," By setting the `reverse` kwarg to `True`, the cumsum is performed in the"," opposite direction:",""," >>> # tf.cumsum([a, b, c], reverse=True) # [a + b + c, b + c, c]"," >>> x = tf.constant([2, 4, 6, 8])"," >>> tf.cumsum(x, reverse=True)"," ",""," This is more efficient than using separate `tf.reverse` ops."," The `reverse` and `exclusive` kwargs can also be combined:",""," >>> # tf.cumsum([a, b, c], exclusive=True, reverse=True) # [b + c, c, 0]"," >>> x = tf.constant([2, 4, 6, 8])"," >>> tf.cumsum(x, exclusive=True, reverse=True)"," ",""," 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(\"math.cumprod\", v1=[\"math.cumprod\", \"cumprod\"])","@dispatch.add_dispatch_support","@deprecation.deprecated_endpoints(\"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.math.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.math.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.math.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.math.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(\"math.cumulative_logsumexp\", v1=[\"math.cumulative_logsumexp\"])","@dispatch.add_dispatch_support","def cumulative_logsumexp(x, axis=0, exclusive=False, reverse=False, name=None):"," \"\"\"Compute the cumulative log-sum-exp of the tensor `x` along `axis`.",""," By default, this op performs an inclusive cumulative log-sum-exp, which means"," that the first element of the input is identical to the first element of"," the output.",""," This operation is significantly more numerically stable than the equivalent"," tensorflow operation `tf.math.log(tf.math.cumsum(tf.math.exp(x)))`, although"," computes the same result given infinite numerical precision. However, note"," that in some cases, it may be less stable than `tf.math.reduce_logsumexp`"," for a given element, as it applies the \"log-sum-exp trick\" in a different"," way.",""," More precisely, where `tf.math.reduce_logsumexp` uses the following trick:",""," ```"," log(sum(exp(x))) == log(sum(exp(x - max(x)))) + max(x)"," ```",""," it cannot be directly used here as there is no fast way of applying it"," to each prefix `x[:i]`. Instead, this function implements a prefix"," scan using pairwise log-add-exp, which is a commutative and associative"," (up to floating point precision) operator:",""," ```"," log_add_exp(x, y) = log(exp(x) + exp(y))"," = log(1 + exp(min(x, y) - max(x, y))) + max(x, y)"," ```",""," However, reducing using the above operator leads to a different computation"," tree (logs are taken repeatedly instead of only at the end), and the maximum"," is only computed pairwise instead of over the entire prefix. In general, this"," leads to a different and slightly less precise computation.",""," Args:"," x: A `Tensor`. Must be one of the following types: `float16`, `float32`,"," `float64`."," axis: A `Tensor` of type `int32` or `int64` (default: 0). Must be in the"," range `[-rank(x), rank(x))`."," exclusive: If `True`, perform exclusive cumulative log-sum-exp."," reverse: If `True`, performs the cumulative log-sum-exp in the reverse"," direction."," name: A name for the operation (optional).",""," Returns:"," A `Tensor`. Has the same shape and type as `x`."," \"\"\""," with ops.name_scope(name, \"CumulativeLogsumexp\", [x]) as name:"," x = ops.convert_to_tensor(x, name=\"x\")"," return gen_math_ops.cumulative_logsumexp("," x, axis, exclusive=exclusive, reverse=reverse, name=name)","","","@tf_export(\"math.conj\", v1=[\"math.conj\", \"conj\"])","@dispatch.register_unary_elementwise_api","@dispatch.add_dispatch_support","@deprecation.deprecated_endpoints(\"conj\")","def conj(x, name=None):"," r\"\"\"Returns the complex conjugate of a complex number.",""," Given a tensor `x` of complex numbers, this operation returns a tensor of"," complex numbers that are the complex conjugate of each element in `x`. The"," complex numbers in `x` 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:",""," >>> x = tf.constant([-2.25 + 4.75j, 3.25 + 5.75j])"," >>> tf.math.conj(x)"," ",""," If `x` is real, it is returned unchanged.",""," For example:",""," >>> x = tf.constant([-2.25, 3.25])"," >>> tf.math.conj(x)"," ",""," 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.",""," @compatibility(numpy)"," Equivalent to numpy.conj."," @end_compatibility"," \"\"\""," if isinstance(x, tensor_lib.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("," f\"Expected numeric or variant tensor, got dtype {x.dtype!r}.\")","","","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."," \"\"\""," # TODO(allenl): Refactor `reduced_shape` to take the tensor corresponding to"," # `input_shape` rather than `tf.shape` of it. Then we can check if the shape"," # is fully defined here, which may be faster executing eagerly than running"," # `tf.shape` and then fetching its constant value."," constant_input_shape = tensor_util.constant_value(input_shape)"," if constant_input_shape is not None:"," constant_axes = tensor_util.constant_value(axes)"," if constant_axes is not None:"," constant_axes = np.array(constant_axes, dtype=np.int32)"," constant_input_shape = np.array(constant_input_shape, dtype=np.int32)"," constant_input_shape[constant_axes] = 1"," return constant_input_shape",""," # Example:"," # cast needed for SparseTensor reductions"," input_shape = cast(input_shape, dtypes.int32) # [2, 3, 5, 7]"," axes = cast(axes, dtypes.int32) # [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.ones(axes_shape, dtype=dtypes.int32)"," ]) # [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."," \"\"\""," num_segments = ops.convert_to_tensor(num_segments)"," # bincount doesn't support negative indices so we use unsorted_segment_sum"," segment_ids_shape = array_ops.shape_internal(segment_ids)"," 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"," broadcastable_shape = array_ops.concat("," [num_segments[array_ops.newaxis],"," array_ops.ones([array_ops.rank(data)"," - array_ops.rank(segment_ids)],"," dtype=num_segments.dtype)],"," axis=0)"," n = array_ops.reshape(n, broadcastable_shape)"," return gen_math_ops.maximum(n, 1)","","","@tf_export("," \"math.unsorted_segment_mean\","," v1=[\"math.unsorted_segment_mean\", \"unsorted_segment_mean\"])","@dispatch.add_dispatch_support","@deprecation.deprecated_endpoints(\"unsorted_segment_mean\")","def unsorted_segment_mean(data, segment_ids, num_segments, name=None):"," r\"\"\"Computes the mean along segments of a tensor.",""," Read [the section on"," segmentation](https://www.tensorflow.org/versions/r2.0/api_docs/python/tf/math#about_segmentation)"," for an explanation of segments.",""," This operator is similar to the `tf.math.unsorted_segment_sum` operator."," 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_{j...} data[j...]\\\\) where the sum is over tuples"," `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.",""," If the given segment ID `i` is negative, the value is dropped and will not"," be added to the sum of the segment.",""," Caution: On CPU, values in `segment_ids` are always validated to be less than"," `num_segments`, and an error is thrown for out-of-bound indices. On GPU, this"," does not throw an error for out-of-bound indices. On Gpu, out-of-bound indices"," result in safe but unspecified behavior, which may include ignoring"," out-of-bound indices or outputting a tensor with a 0 stored in the first"," dimension of its shape if `num_segments` is 0.",""," Args:"," data: A `Tensor` with floating point or complex dtype."," segment_ids: An integer tensor whose shape is a prefix of `data.shape`."," The values must be less than `num_segments`."," The values are always validated to be in range on CPU,"," never validated on GPU."," num_segments: An integer scalar `Tensor`. The number of distinct segment"," IDs."," name: A name for the operation (optional).",""," Returns:"," A `Tensor`. Has same shape as data, except for the first `segment_ids.rank`"," dimensions, which are replaced with a single dimension 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("," \"math.unsorted_segment_sqrt_n\","," v1=[\"math.unsorted_segment_sqrt_n\", \"unsorted_segment_sqrt_n\"])","@dispatch.add_dispatch_support","@deprecation.deprecated_endpoints(\"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 [the section on"," segmentation](https://www.tensorflow.org/versions/r2.0/api_docs/python/tf/math#about_segmentation)"," for an explanation of segments.",""," This operator is similar to the `tf.math.unsorted_segment_sum` operator."," Additionally to computing the sum over segments, it divides the results by"," sqrt(N).",""," \\\\(output_i = 1/sqrt(N_i) \\sum_{j...} data[j...]\\\\) where the sum is over"," tuples `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.",""," If the given segment ID `i` is negative, the value is dropped and will not"," be added to the sum of the segment.",""," Caution: On CPU, values in `segment_ids` are always validated to be less than"," `num_segments`, and an error is thrown for out-of-bound indices. On GPU, this"," does not throw an error for out-of-bound indices. On Gpu, out-of-bound indices"," result in safe but unspecified behavior, which may include ignoring"," out-of-bound indices or outputting a tensor with a 0 stored in the first"," dimension of its shape if `num_segments` is 0.",""," Args:"," data: A `Tensor` with floating point or complex dtype."," segment_ids: An integer tensor whose shape is a prefix of `data.shape`."," The values must be in the range `[0, num_segments)`."," The values are always validated to be in range on CPU,"," never validated on GPU."," num_segments: An integer scalar `Tensor`. The number of distinct segment"," IDs."," name: A name for the operation (optional).",""," Returns:"," A `Tensor`. Has same shape as data, except for the first `segment_ids.rank`"," dimensions, which are replaced with a single dimension 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(v1=[\"sparse.segment_sum\", \"sparse_segment_sum\"])","@deprecation.deprecated_endpoints(\"sparse_segment_sum\")","def sparse_segment_sum("," data,"," indices,"," segment_ids,"," name=None,"," num_segments=None,"," sparse_gradient=False,","):"," r\"\"\"Computes the sum along sparse segments of a tensor.",""," Read [the section on"," segmentation](https://www.tensorflow.org/versions/r2.0/api_docs/python/tf/math#about_segmentation)"," for an explanation of segments.",""," Like `tf.math.segment_sum`, 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.math.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`."," sparse_gradient: An optional `bool`. Defaults to `False`. If `True`, the"," gradient of this function will be sparse (`IndexedSlices`) instead of"," dense (`Tensor`). The sparse gradient will contain one non-zero row for"," each unique index in `indices`.",""," 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,"," sparse_gradient=sparse_gradient,"," name=name,"," )"," else:"," return gen_math_ops.sparse_segment_sum("," data=data,"," indices=indices,"," segment_ids=segment_ids,"," sparse_gradient=sparse_gradient,"," name=name,"," )","","","@tf_export(\"sparse.segment_sum\", v1=[])","def sparse_segment_sum_v2("," data,"," indices,"," segment_ids,"," num_segments=None,"," name=None,"," sparse_gradient=False,","):"," r\"\"\"Computes the sum along sparse segments of a tensor.",""," Read [the section on"," segmentation](https://www.tensorflow.org/versions/r2.0/api_docs/python/tf/math#about_segmentation)"," for an explanation of segments.",""," Like `tf.math.segment_sum`, 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.math.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."," num_segments: An optional int32 scalar. Indicates the size of the output"," `Tensor`."," name: A name for the operation (optional)."," sparse_gradient: An optional `bool`. Defaults to `False`. If `True`, the"," gradient of this function will be sparse (`IndexedSlices`) instead of"," dense (`Tensor`). The sparse gradient will contain one non-zero row for"," each unique index in `indices`.",""," 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`."," \"\"\""," return sparse_segment_sum("," data,"," indices,"," segment_ids,"," name=name,"," num_segments=num_segments,"," sparse_gradient=sparse_gradient,"," )","","","@tf_export(v1=[\"sparse.segment_mean\", \"sparse_segment_mean\"])","@deprecation.deprecated_endpoints(\"sparse_segment_mean\")","def sparse_segment_mean("," data,"," indices,"," segment_ids,"," name=None,"," num_segments=None,"," sparse_gradient=False,","):"," r\"\"\"Computes the mean along sparse segments of a tensor.",""," Read [the section on"," segmentation](https://www.tensorflow.org/versions/r2.0/api_docs/python/tf/math#about_segmentation)"," for an explanation of segments.",""," Like `tf.math.segment_mean`, 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`."," sparse_gradient: An optional `bool`. Defaults to `False`. If `True`, the"," gradient of this function will be sparse (`IndexedSlices`) instead of"," dense (`Tensor`). The sparse gradient will contain one non-zero row for"," each unique index in `indices`.",""," 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,"," sparse_gradient=sparse_gradient,"," )"," else:"," return gen_math_ops.sparse_segment_mean("," data=data,"," indices=indices,"," segment_ids=segment_ids,"," name=name,"," sparse_gradient=sparse_gradient,"," )","","","@tf_export(\"sparse.segment_mean\", v1=[])","def sparse_segment_mean_v2("," data,"," indices,"," segment_ids,"," num_segments=None,"," name=None,"," sparse_gradient=False,","):"," r\"\"\"Computes the mean along sparse segments of a tensor.",""," Read [the section on"," segmentation](https://www.tensorflow.org/versions/r2.0/api_docs/python/tf/math#about_segmentation)"," for an explanation of segments.",""," Like `tf.math.segment_mean`, 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."," num_segments: An optional int32 scalar. Indicates the size of the output"," `Tensor`."," name: A name for the operation (optional)."," sparse_gradient: An optional `bool`. Defaults to `False`. If `True`, the"," gradient of this function will be sparse (`IndexedSlices`) instead of"," dense (`Tensor`). The sparse gradient will contain one non-zero row for"," each unique index in `indices`.",""," 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`."," \"\"\""," return sparse_segment_mean("," data,"," indices,"," segment_ids,"," name=name,"," num_segments=num_segments,"," sparse_gradient=sparse_gradient,"," )","","","@tf_export(v1=[\"sparse.segment_sqrt_n\", \"sparse_segment_sqrt_n\"])","@deprecation.deprecated_endpoints(\"sparse_segment_sqrt_n\")","def sparse_segment_sqrt_n("," data,"," indices,"," segment_ids,"," name=None,"," num_segments=None,"," sparse_gradient=False,","):"," 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`."," sparse_gradient: An optional `bool`. Defaults to `False`. If `True`, the"," gradient of this function will be sparse (IndexedSlices) instead of dense"," (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,"," sparse_gradient=sparse_gradient,"," )"," else:"," return gen_math_ops.sparse_segment_sqrt_n("," data=data,"," indices=indices,"," segment_ids=segment_ids,"," name=name,"," sparse_gradient=sparse_gradient,"," )","","","@tf_export(\"sparse.segment_sqrt_n\", v1=[])","def sparse_segment_sqrt_n_v2("," data,"," indices,"," segment_ids,"," num_segments=None,"," name=None,"," sparse_gradient=False,","):"," r\"\"\"Computes the sum along sparse segments of a tensor divided by the sqrt(N).",""," Read [the section on"," segmentation](https://www.tensorflow.org/versions/r2.0/api_docs/python/tf/math#about_segmentation)"," for an explanation of segments.",""," Like `tf.sparse.segment_mean`, but instead of dividing by the size of the"," segment, `N`, divide by `sqrt(N)` instead.",""," 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."," num_segments: An optional int32 scalar. Indicates the size of the output"," `Tensor`."," name: A name for the operation (optional)."," sparse_gradient: An optional `bool`. Defaults to `False`. If `True`, the"," gradient of this function will be sparse (`IndexedSlices`) instead of"," dense (`Tensor`). The sparse gradient will contain one non-zero row for"," each unique index in `indices`.",""," 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`."," \"\"\""," return sparse_segment_sqrt_n("," data,"," indices,"," segment_ids,"," name=name,"," num_segments=num_segments,"," sparse_gradient=sparse_gradient,"," )","","","@tf_export(\"tensordot\", \"linalg.tensordot\")","@dispatch.add_dispatch_support","def tensordot(a, b, axes, name=None):"," r\"\"\"Tensor contraction of a and b along specified axes and outer product.",""," Tensordot (also known as tensor contraction) sums the product of elements"," from `a` and `b` over the indices specified by `axes`.",""," 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: When `a` and `b` are matrices (order 2), the case `axes=0` gives"," the outer product, a tensor of order 4.",""," Example 4: 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])`.",""," For example:"," "," ```python"," import numpy as np"," import tensorflow as tf",""," a = np.arange(60).reshape(3,4,5)"," b = np.arange(24).reshape(4,3,2)"," c = tf.tensordot(a,b, axes=([1,0],[0,1]))"," c"," "," "," "," # Another example"," d = tf.random.uniform((3,4,5))"," e = tf.random.uniform((5,3,2))"," f = tf.tensordot(d,e, axes=([2,0],[0,1]))"," f"," "," "," "," ```"," "," 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. If `axes=0`, computes the outer product between `a` and"," `b`."," 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 builtins.range(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]"," if (perm != np.arange(len(shape_a))).any():"," a_trans = array_ops.transpose(a, perm)"," else:"," a_trans = a"," if a_trans.get_shape().as_list() != new_shape:"," reshaped_a = array_ops.reshape(a_trans, new_shape)"," else:"," reshaped_a = a_trans"," 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 builtins.range(len(shape_a)) if i not in axes]"," axes_dims = [shape_a[i] for i in axes]"," free_dims = [shape_a[i] for i in free]"," free_dims_static = free_dims"," axes = ops.convert_to_tensor(axes, dtype=dtypes.int32, name=\"axes\")"," free = ops.convert_to_tensor(free, dtype=dtypes.int32, name=\"free\")"," shape_a = array_ops.shape(a)"," 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 = array_ops.where(axes >= 0, axes, axes + rank_a)"," free, _ = gen_array_ops.list_diff(range(rank_a), axes, dtypes.int32)"," 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)"," if flipped:"," perm = array_ops.concat([axes, free], 0)"," new_shape = array_ops_stack.stack([prod_axes_dims, prod_free_dims])"," else:"," perm = array_ops.concat([free, axes], 0)"," new_shape = array_ops_stack.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(f\"`axes` must be at least 0. Received: {axes}.\")"," if a_shape.ndims is not None:"," if axes > a_shape.ndims:"," raise ValueError(f\"`axes` must not be larger than the number of \""," f\"dimensions of tensor {a}. Received {axes}, vs \""," f\"tensor dimensions {a_shape.ndims}.\")"," return (list(builtins.range(a_shape.ndims - axes,"," a_shape.ndims)), list(builtins.range(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("," f\"`axes` must be an integer or have length 2. Received {axes}.\")"," 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(f\"Different number of contraction axes `a` and `b`, \""," f\"{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):"," if (ab_matmul.get_shape().is_fully_defined() and"," ab_matmul.get_shape().as_list() == a_free_dims + b_free_dims):"," return ab_matmul"," else:"," 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\")","@dispatch.add_dispatch_support","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.",""," ```python"," p(x) = coeffs[n-1] + x * (coeffs[n-2] + ... + x * (coeffs[1] + x * coeffs[0]))"," ```",""," Usage Example:",""," >>> coefficients = [1.0, 2.5, -4.2]"," >>> x = 5.0"," >>> y = tf.math.polyval(coefficients, x)"," >>> y"," ",""," Usage Example:",""," >>> tf.math.polyval([2, 1, 0], 3) # evaluates 2 * (3**2) + 1 * (3**1) + 0 * (3**0)"," ",""," `tf.math.polyval` can also be used in polynomial regression. Taking"," advantage of this function can facilitate writing a polynomial equation"," as compared to explicitly writing it out, especially for higher degree"," polynomials.",""," >>> x = tf.constant(3)"," >>> theta1 = tf.Variable(2)"," >>> theta2 = tf.Variable(1)"," >>> theta3 = tf.Variable(0)"," >>> tf.math.polyval([theta1, theta2, theta3], x)"," ",""," Args:"," coeffs: A list of `Tensor` representing the coefficients of the polynomial."," x: A `Tensor` representing the variable of the polynomial."," name: A name for the operation (optional).",""," Returns:"," A `tensor` of the shape as the expression p(x) with usual broadcasting"," rules for element-wise addition and multiplication applied.",""," @compatibility(numpy)"," Equivalent to numpy.polyval."," @end_compatibility"," \"\"\""," if not isinstance(coeffs, list):"," raise ValueError("," f\"Argument coeffs must be list type. Received type {type(coeffs)}.\")",""," with ops.name_scope(name, \"polyval\", nest.flatten(coeffs) + [x]) as name:"," x = ops.convert_to_tensor(x, name=\"x\")"," if len(coeffs) < 1:"," return array_ops.zeros_like(x, name=name)"," coeffs = ["," ops.convert_to_tensor(coeff, name=(\"coeff_%d\" % index))"," for index, coeff in enumerate(coeffs)"," ]"," p = coeffs[0]"," for c in coeffs[1:]:"," p = c + p * x"," return p","","","@tf_export(\"math.reciprocal_no_nan\")","@dispatch.register_unary_elementwise_api","@dispatch.add_dispatch_support","def reciprocal_no_nan(x, name=None):"," \"\"\"Performs a safe reciprocal operation, element wise.",""," If a particular element is zero, the reciprocal for that element is"," also set to zero.",""," For example:"," ```python"," x = tf.constant([2.0, 0.5, 0, 1], dtype=tf.float32)"," tf.math.reciprocal_no_nan(x) # [ 0.5, 2, 0.0, 1.0 ]"," ```",""," Args:"," x: A `Tensor` of type `float16`, `float32`, `float64` `complex64` or"," `complex128`."," name: A name for the operation (optional).",""," Returns:"," A `Tensor` of same shape and type as `x`.",""," Raises:"," TypeError: x must be of a valid dtype.",""," \"\"\"",""," with ops.name_scope(name, \"reciprocal_no_nan\", [x]) as scope:"," x = ops.convert_to_tensor(x, name=\"x\")"," one = constant_op.constant(1, dtype=x.dtype.base_dtype, name=\"one\")"," return gen_math_ops.div_no_nan(one, x, name=scope)","","","@tf_export(\"math.xdivy\")","@dispatch.register_binary_elementwise_api","@dispatch.add_dispatch_support","def xdivy(x, y, name=None):"," \"\"\"Computes `x / y`.",""," Given `x` and `y`, computes `x / y`. This function safely returns"," zero when `x = 0`, no matter what the value of `y` is.",""," Example:",""," >>> tf.math.xdivy(1., 2.)"," "," >>> tf.math.xdivy(0., 1.)"," "," >>> tf.math.xdivy(0., 0.)"," "," >>> tf.math.xdivy(1., 0.)"," ",""," Args:"," x: A `tf.Tensor` of type `half`, `float32`, `float64`, `complex64`,"," `complex128`"," y: A `tf.Tensor` of type `half`, `float32`, `float64`, `complex64`,"," `complex128`"," name: A name for the operation (optional).",""," Returns:"," `x / y`."," \"\"\""," with ops.name_scope(name, \"xdivy\", [x]):"," return gen_math_ops.xdivy(x, y)","","","@tf_export(\"math.xlog1py\")","@dispatch.register_binary_elementwise_api","@dispatch.add_dispatch_support","def xlog1py(x, y, name=None):"," r\"\"\"Compute x * log1p(y).",""," Given `x` and `y`, compute `x * log1p(y)`. This function safely returns"," zero when `x = 0`, no matter what the value of `y` is.",""," Example:",""," >>> tf.math.xlog1py(0., 1.)"," "," >>> tf.math.xlog1py(1., 1.)"," "," >>> tf.math.xlog1py(2., 2.)"," "," >>> tf.math.xlog1py(0., -1.)"," ",""," Args:"," x: A `tf.Tensor` of type `half`, `float32`, `float64`, `complex64`,"," `complex128`"," y: A `tf.Tensor` of type `half`, `float32`, `float64`, `complex64`,"," `complex128`"," name: A name for the operation (optional).",""," Returns:"," `x * log1p(y)`.",""," @compatibility(scipy)"," Equivalent to scipy.special.xlog1py"," @end_compatibility"," \"\"\""," with ops.name_scope(name, \"xlog1py\", [x]):"," return gen_math_ops.xlog1py(x, y)","","","@tf_export(\"math.erfinv\")","@dispatch.register_unary_elementwise_api","@dispatch.add_dispatch_support","def erfinv(x, name=None):"," \"\"\"Compute inverse error function.",""," Given `x`, compute the inverse error function of `x`. This function"," is the inverse of `tf.math.erf`.",""," Args:"," x: `Tensor` with type `float` or `double`."," name: A name for the operation (optional)."," Returns:"," Inverse error function of `x`."," \"\"\""," with ops.name_scope(name, \"erfinv\", [x]):"," return gen_math_ops.erfinv(x)","","","@tf_export(\"math.ndtri\")","@dispatch.register_unary_elementwise_api","@dispatch.add_dispatch_support","def ndtri(x, name=None):"," \"\"\"Compute quantile of Standard Normal.",""," Args:"," x: `Tensor` with type `float` or `double`."," name: A name for the operation (optional)."," Returns:"," Inverse error function of `x`."," \"\"\""," with ops.name_scope(name, \"ndtri\", [x]):"," return gen_math_ops.ndtri(x)","","","@tf_export(\"math.erfcinv\")","@dispatch.register_unary_elementwise_api","@dispatch.add_dispatch_support","def erfcinv(x, name=None):"," \"\"\"Computes the inverse of complementary error function.",""," Given `x`, compute the inverse complementary error function of `x`."," This function is the inverse of `tf.math.erfc`, and is defined on"," `[0, 2]`.",""," >>> tf.math.erfcinv([0., 0.2, 1., 1.5, 2.])"," ",""," Args:"," x: `Tensor` with type `float` or `double`."," name: A name for the operation (optional)."," Returns:"," Inverse complementary error function of `x`.",""," @compatibility(numpy)"," Equivalent to scipy.special.erfcinv"," @end_compatibility"," \"\"\""," with ops.name_scope(name, \"erfcinv\", [x]):"," x = ops.convert_to_tensor(x, name=\"start\")"," return -ndtri(0.5 * x) * np.sqrt(0.5)","","","@tf_export(\"math.ceil\", v1=[\"math.ceil\", \"ceil\"])","@dispatch.register_unary_elementwise_api","@dispatch.add_dispatch_support","@deprecation.deprecated_endpoints(\"ceil\")","def ceil(x, name=None):"," \"\"\"Return the ceiling of the input, element-wise.",""," For example:",""," >>> tf.math.ceil([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0])"," ",""," Args:"," x: A `tf.Tensor`. Must be one of the following types: `bfloat16`, `half`,"," `float32`, `float64`. `int32`"," name: A name for the operation (optional).",""," Returns:"," A `tf.Tensor`. Has the same type as `x`.",""," @compatibility(numpy)"," Equivalent to np.ceil"," @end_compatibility"," \"\"\""," return gen_math_ops.ceil(x, name)","","","@tf_export(\"math.sqrt\", \"sqrt\")","@dispatch.register_unary_elementwise_api","@dispatch.add_dispatch_support","def sqrt(x, name=None): # pylint: disable=redefined-builtin"," r\"\"\"Computes element-wise square root of the input tensor.",""," Note: This operation does not support integer types.",""," >>> x = tf.constant([[4.0], [16.0]])"," >>> tf.sqrt(x)"," "," >>> y = tf.constant([[-4.0], [16.0]])"," >>> tf.sqrt(y)"," "," >>> z = tf.constant([[-1.0], [16.0]], dtype=tf.complex128)"," >>> tf.sqrt(z)"," ",""," Note: In order to support complex type, please provide an input tensor"," of `complex64` or `complex128`.",""," Args:"," x: A `tf.Tensor` of type `bfloat16`, `half`, `float32`, `float64`,"," `complex64`, `complex128`"," name: A name for the operation (optional).",""," Returns:"," A `tf.Tensor` of same size, type and sparsity as `x`."," \"\"\""," return gen_math_ops.sqrt(x, name)","","","# pylint: disable=g-docstring-has-escape","@tf_export(\"math.exp\", \"exp\")","@dispatch.register_unary_elementwise_api","@dispatch.add_dispatch_support","def exp(x, name=None):"," r\"\"\"Computes exponential of x element-wise. \\\\(y = e^x\\\\).",""," This function computes the exponential of the input tensor element-wise."," i.e. `math.exp(x)` or \\\\(e^x\\\\), where `x` is the input tensor."," \\\\(e\\\\) denotes Euler's number and is approximately equal to 2.718281."," Output is positive for any real input.",""," >>> x = tf.constant(2.0)"," >>> tf.math.exp(x)"," ",""," >>> x = tf.constant([2.0, 8.0])"," >>> tf.math.exp(x)"," ",""," For complex numbers, the exponential value is calculated as"," $$"," e^{x+iy} = {e^x} {e^{iy}} = {e^x} ({\\cos (y) + i \\sin (y)})"," $$",""," For `1+1j` the value would be computed as:"," $$"," e^1 (\\cos (1) + i \\sin (1)) = 2.7182817 \\times (0.5403023+0.84147096j)"," $$",""," >>> x = tf.constant(1 + 1j)"," >>> tf.math.exp(x)"," ",""," Args:"," x: A `tf.Tensor`. Must be one of the following types: `bfloat16`, `half`,"," `float32`, `float64`, `complex64`, `complex128`."," name: A name for the operation (optional).",""," Returns:"," A `tf.Tensor`. Has the same type as `x`.",""," @compatibility(numpy)"," Equivalent to np.exp"," @end_compatibility"," \"\"\""," return gen_math_ops.exp(x, name)","","","# pylint: enable=g-docstring-has-escape","","","@tf_export(\"math.sobol_sample\")","@dispatch.add_dispatch_support","def sobol_sample(dim, num_results, skip=0, dtype=dtypes.float32, name=None):"," \"\"\"Generates points from the Sobol sequence.",""," Creates a Sobol sequence with `num_results` samples. Each sample has dimension"," `dim`. Skips the first `skip` samples.",""," Args:"," dim: Positive scalar `Tensor` representing each sample's dimension."," num_results: Positive scalar `Tensor` of dtype int32. The number of Sobol"," points to return in the output."," skip: (Optional) Positive scalar `Tensor` of dtype int32. The number of"," initial points of the Sobol sequence to skip. Default value is 0."," dtype: (Optional) The `tf.Dtype` of the sample. One of: `tf.float32` or"," `tf.float64`. Defaults to `tf.float32`."," name: (Optional) Python `str` name prefixed to ops created by this function.",""," Returns:"," `Tensor` of samples from Sobol sequence with `shape` [num_results, dim]."," \"\"\""," with ops.name_scope(name, \"sobol\", [dim, num_results, skip]):"," return gen_math_ops.sobol_sample(dim, num_results, skip, dtype=dtype)","","","@tf_export(\"math.rsqrt\", v1=[\"math.rsqrt\", \"rsqrt\"])","@dispatch.register_unary_elementwise_api","@dispatch.add_dispatch_support","@deprecation.deprecated_endpoints(\"rsqrt\")","def rsqrt(x, name=None):"," \"\"\"Computes reciprocal of square root of x element-wise.",""," For example:",""," >>> x = tf.constant([2., 0., -2.])"," >>> tf.math.rsqrt(x)"," ",""," Args:"," x: A `tf.Tensor`. Must be one of the following types: `bfloat16`, `half`,"," `float32`, `float64`."," name: A name for the operation (optional).",""," Returns:"," A `tf.Tensor`. Has the same type as `x`."," \"\"\""," return gen_math_ops.rsqrt(x, name)","","","@tf_export(\"math.acos\", \"acos\")","@dispatch.register_unary_elementwise_api","@dispatch.add_dispatch_support","def acos(x, name=None):"," \"\"\"Computes acos of x element-wise.",""," Provided an input tensor, the `tf.math.acos` operation"," returns the inverse cosine of each element of the tensor."," If `y = tf.math.cos(x)` then, `x = tf.math.acos(y)`.",""," Input range is `[-1, 1]` and the output has a range of `[0, pi]`.",""," For example:",""," >>> x = tf.constant([1.0, -0.5, 3.4, 0.2, 0.0, -2], dtype = tf.float32)"," >>> tf.math.acos(x)"," ",""," Args:"," x: A `Tensor`. Must be one of the following types: `bfloat16`, `half`,"," `float32`, `float64`, `complex64`, `complex128`."," name: A name for the operation (optional).",""," Returns:"," A `Tensor`. Has the same type as x."," \"\"\""," return gen_math_ops.acos(x, name)","","","@tf_export(\"math.floor\", \"floor\")","@dispatch.register_unary_elementwise_api","@dispatch.add_dispatch_support","def floor(x, name=None):"," \"\"\"Returns element-wise largest integer not greater than x.",""," Both input range is `(-inf, inf)` and the"," output range consists of all integer values.",""," For example:",""," >>> x = tf.constant([1.3324, -1.5, 5.555, -2.532, 0.99, float(\"inf\")])"," >>> tf.floor(x).numpy()"," array([ 1., -2., 5., -3., 0., inf], dtype=float32)",""," Args:"," x: A `Tensor`. Must be one of the following types: `bfloat16`, `half`,"," `float32`, `float64`."," name: A name for the operation (optional).",""," Returns:"," A `Tensor`. Has the same type as x."," \"\"\""," return gen_math_ops.floor(x, name)","","","# Register elementwise ops that don't have Python wrappers.","# Binary elementwise 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