1 # Copyright 2015 The TensorFlow Authors. All Rights Reserved. 2 # 3 # Licensed under the Apache License, Version 2.0 (the "License"); 4 # you may not use this file except in compliance with the License. 5 # You may obtain a copy of the License at 6 # 7 # http://www.apache.org/licenses/LICENSE-2.0 8 # 9 # Unless required by applicable law or agreed to in writing, software 10 # distributed under the License is distributed on an "AS IS" BASIS, 11 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 12 # See the License for the specific language governing permissions and 13 # limitations under the License. 14 # ============================================================================== 15 """Basic arithmetic operators. 16 17 See the @{$python/math_ops} guide. 18 19 @@add 20 @@subtract 21 @@multiply 22 @@scalar_mul 23 @@div 24 @@divide 25 @@truediv 26 @@floordiv 27 @@realdiv 28 @@truncatediv 29 @@floor_div 30 @@truncatemod 31 @@floormod 32 @@mod 33 @@cross 34 @@add_n 35 @@abs 36 @@negative 37 @@sign 38 @@reciprocal 39 @@square 40 @@round 41 @@sqrt 42 @@rsqrt 43 @@pow 44 @@exp 45 @@expm1 46 @@log 47 @@log1p 48 @@sinh 49 @@cosh 50 @@asinh 51 @@acosh 52 @@atanh 53 @@ceil 54 @@floor 55 @@maximum 56 @@minimum 57 @@cos 58 @@sin 59 @@lbeta 60 @@tan 61 @@acos 62 @@asin 63 @@atan 64 @@atan2 65 @@lgamma 66 @@digamma 67 @@erf 68 @@erfc 69 @@squared_difference 70 @@igamma 71 @@igammac 72 @@zeta 73 @@polygamma 74 @@betainc 75 @@rint 76 @@diag 77 @@diag_part 78 @@trace 79 @@transpose 80 @@eye 81 @@matrix_diag 82 @@matrix_diag_part 83 @@matrix_band_part 84 @@matrix_set_diag 85 @@matrix_transpose 86 @@matmul 87 @@norm 88 @@matrix_determinant 89 @@matrix_inverse 90 @@cholesky 91 @@cholesky_solve 92 @@matrix_exponential 93 @@matrix_logarithm 94 @@matrix_solve 95 @@matrix_triangular_solve 96 @@matrix_solve_ls 97 @@qr 98 @@self_adjoint_eig 99 @@self_adjoint_eigvals 100 @@svd 101 @@tensordot 102 @@complex 103 @@conj 104 @@imag 105 @@angle 106 @@real 107 @@fft 108 @@ifft 109 @@fft2d 110 @@ifft2d 111 @@fft3d 112 @@ifft3d 113 @@reduce_sum 114 @@reduce_prod 115 @@reduce_min 116 @@reduce_max 117 @@reduce_mean 118 @@reduce_all 119 @@reduce_any 120 @@reduce_logsumexp 121 @@count_nonzero 122 @@accumulate_n 123 @@einsum 124 @@bincount 125 @@cumsum 126 @@cumprod 127 @@segment_sum 128 @@segment_prod 129 @@segment_min 130 @@segment_max 131 @@segment_mean 132 @@unsorted_segment_sum 133 @@unsorted_segment_max 134 @@unsorted_segment_min 135 @@unsorted_segment_prod 136 @@unsorted_segment_sqrt_n 137 @@sparse_segment_sum 138 @@sparse_segment_mean 139 @@sparse_segment_sqrt_n 140 @@argmin 141 @@argmax 142 @@setdiff1d 143 @@where 144 @@unique 145 @@edit_distance 146 @@invert_permutation 147 """ 148 from __future__ import absolute_import 149 from __future__ import division 150 from __future__ import print_function 151 152 import numpy as np 153 from six.moves import xrange # pylint: disable=redefined-builtin 154 155 from tensorflow.python.eager import context 156 from tensorflow.python.framework import common_shapes 157 from tensorflow.python.framework import constant_op 158 from tensorflow.python.framework import dtypes 159 from tensorflow.python.framework import graph_util 160 from tensorflow.python.framework import ops 161 from tensorflow.python.framework import sparse_tensor 162 from tensorflow.python.framework import tensor_shape 163 from tensorflow.python.ops import array_ops 164 from tensorflow.python.ops import gen_control_flow_ops 165 from tensorflow.python.ops import gen_data_flow_ops 166 from tensorflow.python.ops import gen_math_ops 167 from tensorflow.python.ops import gen_nn_ops 168 from tensorflow.python.ops import gen_sparse_ops 169 from tensorflow.python.ops import gen_spectral_ops 170 from tensorflow.python.ops import gen_state_ops 171 from tensorflow.python.ops import state_ops 172 # go/tf-wildcard-import 173 # pylint: disable=wildcard-import 174 from tensorflow.python.ops.gen_math_ops import * 175 # pylint: enable=wildcard-import 176 from tensorflow.python.util import compat 177 from tensorflow.python.util import deprecation 178 from tensorflow.python.util.tf_export import tf_export 179 180 # Aliases for some automatically-generated names. 181 linspace = gen_math_ops.lin_space 182 183 arg_max = deprecation.deprecated(None, "Use `argmax` instead")(arg_max) # pylint: disable=used-before-assignment 184 arg_min = deprecation.deprecated(None, "Use `argmin` instead")(arg_min) # pylint: disable=used-before-assignment 185 186 187 def _set_doc(doc): 188 189 def _decorator(func): 190 func.__doc__ = doc 191 return func 192 193 return _decorator 194 195 196 # pylint: disable=redefined-builtin 197 @tf_export("argmax") 198 @deprecation.deprecated_args(None, "Use the `axis` argument instead", 199 "dimension") 200 @_set_doc( 201 gen_math_ops.arg_max.__doc__.replace("dimensions", "axes").replace( 202 "dimension", "axis")) 203 def argmax(input, 204 axis=None, 205 name=None, 206 dimension=None, 207 output_type=dtypes.int64): 208 if dimension is not None: 209 if axis is not None: 210 raise ValueError("Cannot specify both 'axis' and 'dimension'") 211 axis = dimension 212 elif axis is None: 213 axis = 0 214 return gen_math_ops.arg_max(input, axis, name=name, output_type=output_type) 215 216 217 @tf_export("argmin") 218 @deprecation.deprecated_args(None, "Use the `axis` argument instead", 219 "dimension") 220 @_set_doc( 221 gen_math_ops.arg_min.__doc__.replace("dimensions", "axes").replace( 222 "dimension", "axis")) 223 def argmin(input, 224 axis=None, 225 name=None, 226 dimension=None, 227 output_type=dtypes.int64): 228 if dimension is not None: 229 if axis is not None: 230 raise ValueError("Cannot specify both 'axis' and 'dimension'") 231 axis = dimension 232 elif axis is None: 233 axis = 0 234 return gen_math_ops.arg_min(input, axis, name=name, output_type=output_type) 235 236 237 # pylint: enable=redefined-builtin 238 239 240 # pylint: disable=anomalous-backslash-in-string,protected-access 241 # pylint: disable=g-docstring-has-escape 242 @tf_export("abs") 243 def abs(x, name=None): # pylint: disable=redefined-builtin 244 r"""Computes the absolute value of a tensor. 245 246 Given a tensor `x` of complex numbers, this operation returns a tensor of type 247 `float32` or `float64` that is the absolute value of each element in `x`. All 248 elements in `x` must be complex numbers of the form \\(a + bj\\). The 249 absolute value is computed as \\( \sqrt{a^2 + b^2}\\). For example: 250 ```python 251 x = tf.constant([[-2.25 + 4.75j], [-3.25 + 5.75j]]) 252 tf.abs(x) # [5.25594902, 6.60492229] 253 ``` 254 255 Args: 256 x: A `Tensor` or `SparseTensor` of type `float32`, `float64`, `int32`, 257 `int64`, `complex64` or `complex128`. 258 name: A name for the operation (optional). 259 260 Returns: 261 A `Tensor` or `SparseTensor` the same size and type as `x` with absolute 262 values. 263 Note, for `complex64` or `complex128` input, the returned `Tensor` will be 264 of type `float32` or `float64`, respectively. 265 """ 266 with ops.name_scope(name, "Abs", [x]) as name: 267 if isinstance(x, sparse_tensor.SparseTensor): 268 if x.values.dtype.is_complex: 269 x_abs = gen_math_ops._complex_abs( 270 x.values, Tout=x.values.dtype.real_dtype, name=name) 271 return sparse_tensor.SparseTensor( 272 indices=x.indices, values=x_abs, dense_shape=x.dense_shape) 273 x_abs = gen_math_ops._abs(x.values, name=name) 274 return sparse_tensor.SparseTensor( 275 indices=x.indices, values=x_abs, dense_shape=x.dense_shape) 276 else: 277 x = ops.convert_to_tensor(x, name="x") 278 if x.dtype.is_complex: 279 return gen_math_ops._complex_abs(x, Tout=x.dtype.real_dtype, name=name) 280 return gen_math_ops._abs(x, name=name) 281 282 283 # pylint: enable=g-docstring-has-escape 284 285 286 # pylint: disable=redefined-builtin 287 def _bucketize(input, boundaries, name=None): 288 return gen_math_ops._bucketize(input=input, boundaries=boundaries, name=name) 289 290 291 # pylint: enable=redefined-builtin 292 293 294 class DivideDelegateWithName(object): 295 """Use Python2/Python3 division delegation to implement divide for tensors.""" 296 297 def __init__(self, x, name): 298 """Construct DivideDelegateWithName. 299 300 Args: 301 x: Tensor to use as left operand in operator overloads 302 name: The name that is preferred for the op created. 303 """ 304 self.x = x 305 self.name = name 306 307 def __truediv__(self, y): 308 return _truediv_python3(self.x, y, self.name) 309 310 def __floordiv__(self, y): 311 return floordiv(self.x, y, self.name) 312 313 def __div__(self, y): 314 return _div_python2(self.x, y, self.name) 315 316 317 @tf_export("divide") 318 def divide(x, y, name=None): 319 """Computes Python style division of `x` by `y`.""" 320 321 if name is not None: 322 # Cannot use tensors operator overload, because it has no way to track 323 # override names. Use a dummy class to track the runtime division behavior 324 return DivideDelegateWithName(x, name) / y 325 else: 326 return x / y 327 328 329 @tf_export("multiply") 330 def multiply(x, y, name=None): 331 return gen_math_ops._mul(x, y, name) 332 333 334 multiply.__doc__ = gen_math_ops._mul.__doc__.replace("Mul", "`tf.multiply`") 335 336 337 # TODO(aselle): put deprecation in after another round of global code changes 338 @deprecation.deprecated( 339 "2016-12-30", 340 "`tf.mul(x, y)` is deprecated, please use `tf.multiply(x, y)` or `x * y`") 341 def _mul(x, y, name=None): 342 return gen_math_ops._mul(x, y, name) 343 344 345 _mul.__doc__ = ( 346 gen_math_ops._mul.__doc__ + ("" if _mul.__doc__ is None else _mul.__doc__)) 347 348 349 @tf_export("subtract") 350 def subtract(x, y, name=None): 351 return gen_math_ops._sub(x, y, name) 352 353 354 subtract.__doc__ = gen_math_ops._sub.__doc__.replace("`Sub`", "`tf.subtract`") 355 356 357 # TODO(aselle): put deprecation in after another round of global code changes 358 @deprecation.deprecated( 359 "2016-12-30", 360 "`tf.sub(x, y)` is deprecated, please use `tf.subtract(x, y)` or `x - y`") 361 def _sub(x, y, name=None): 362 return gen_math_ops._sub(x, y, name) 363 364 365 _sub.__doc__ = ( 366 gen_math_ops._sub.__doc__ + ("" if _sub.__doc__ is None else _sub.__doc__)) 367 368 369 # pylint: disable=g-docstring-has-escape 370 @tf_export("negative") 371 def negative(x, name=None): 372 """Computes numerical negative value element-wise. 373 374 I.e., \\(y = -x\\). 375 376 Args: 377 x: A `Tensor` or `SparseTensor`. Must be one of the following types: `half`, 378 `float32`, `float64`, `int32`, `int64`, `complex64`, `complex128`. 379 name: A name for the operation (optional). 380 381 Returns: 382 A `Tensor` or `SparseTensor`, respectively. Has the same type as `x`. 383 """ 384 with ops.name_scope(name, "Neg", [x]) as name: 385 if isinstance(x, sparse_tensor.SparseTensor): 386 x_neg = gen_math_ops._neg(x.values, name=name) 387 return sparse_tensor.SparseTensor( 388 indices=x.indices, values=x_neg, dense_shape=x.dense_shape) 389 else: 390 return gen_math_ops._neg(x, name=name) 391 392 393 # pylint: enable=g-docstring-has-escape 394 395 396 # pylint: disable=g-docstring-has-escape 397 @deprecation.deprecated( 398 "2016-12-30", 399 "`tf.neg(x)` is deprecated, please use `tf.negative(x)` or `-x`") 400 def _neg(x, name=None): 401 """Computes numerical negative value element-wise. 402 403 I.e., \\(y = -x\\). 404 405 Args: 406 x: A `Tensor` or `SparseTensor`. Must be one of the following types: `half`, 407 `float32`, `float64`, `int32`, `int64`, `complex64`, `complex128`. 408 name: A name for the operation (optional). 409 410 Returns: 411 A `Tensor` or `SparseTensor`, respectively. Has the same type as `x`. 412 """ 413 return negative(x, name) 414 415 416 # pylint: enable=g-docstring-has-escape 417 418 419 @tf_export("sign") 420 def sign(x, name=None): 421 """Returns an element-wise indication of the sign of a number. 422 423 `y = sign(x) = -1` if `x < 0`; 0 if `x == 0` or `tf.is_nan(x)`; 1 if `x > 0`. 424 425 Zero is returned for NaN inputs. 426 427 For complex numbers, `y = sign(x) = x / |x|` if `x != 0`, otherwise `y = 0`. 428 429 Args: 430 x: A `Tensor` or `SparseTensor`. Must be one of the following types: `half`, 431 `float32`, `float64`, `int32`, `int64`, `complex64`, `complex128`. 432 name: A name for the operation (optional). 433 434 Returns: 435 A `Tensor` or `SparseTensor`, respectively. Has the same type as `x`. 436 437 @compatibility(numpy) 438 Equivalent to numpy.sign except for the behavior for input values of NaN. 439 @end_compatibility 440 """ 441 with ops.name_scope(name, "Sign", [x]) as name: 442 if isinstance(x, sparse_tensor.SparseTensor): 443 x_sign = gen_math_ops.sign(x.values, name=name) 444 return sparse_tensor.SparseTensor( 445 indices=x.indices, values=x_sign, dense_shape=x.dense_shape) 446 else: 447 return gen_math_ops.sign(x, name=name) 448 449 450 @tf_export("square") 451 def square(x, name=None): 452 r"""Computes square of x element-wise. 453 454 I.e., \\(y = x * x = x^2\\). 455 456 Args: 457 x: A `Tensor` or `SparseTensor`. Must be one of the following types: `half`, 458 `float32`, `float64`, `int32`, `int64`, `complex64`, `complex128`. 459 name: A name for the operation (optional). 460 461 Returns: 462 A `Tensor` or `SparseTensor`. Has the same type as `x`. 463 """ 464 with ops.name_scope(name, "Square", [x]) as name: 465 if isinstance(x, sparse_tensor.SparseTensor): 466 x_square = gen_math_ops.square(x.values, name=name) 467 return sparse_tensor.SparseTensor( 468 indices=x.indices, values=x_square, dense_shape=x.dense_shape) 469 else: 470 return gen_math_ops.square(x, name=name) 471 472 473 @tf_export("sqrt") 474 def sqrt(x, name=None): 475 r"""Computes square root of x element-wise. 476 477 I.e., \\(y = \sqrt{x} = x^{1/2}\\). 478 479 Args: 480 x: A `Tensor` or `SparseTensor`. Must be one of the following types: `half`, 481 `float32`, `float64`, `complex64`, `complex128`. 482 name: A name for the operation (optional). 483 484 Returns: 485 A `Tensor` or `SparseTensor`, respectively. Has the same type as `x`. 486 """ 487 with ops.name_scope(name, "Sqrt", [x]) as name: 488 if isinstance(x, sparse_tensor.SparseTensor): 489 x_sqrt = gen_math_ops.sqrt(x.values, name=name) 490 return sparse_tensor.SparseTensor( 491 indices=x.indices, values=x_sqrt, dense_shape=x.dense_shape) 492 else: 493 return gen_math_ops.sqrt(x, name=name) 494 495 496 @tf_export("erf") 497 def erf(x, name=None): 498 """Computes the Gauss error function of `x` element-wise. 499 500 Args: 501 x: A `Tensor` of `SparseTensor`. Must be one of the following types: `half`, 502 `float32`, `float64`. 503 name: A name for the operation (optional). 504 505 Returns: 506 A `Tensor` or `SparseTensor`, respectively. Has the same type as `x`. 507 """ 508 with ops.name_scope(name, "Erf", [x]) as name: 509 if isinstance(x, sparse_tensor.SparseTensor): 510 x_erf = gen_math_ops.erf(x.values, name=name) 511 return sparse_tensor.SparseTensor( 512 indices=x.indices, values=x_erf, dense_shape=x.dense_shape) 513 else: 514 return gen_math_ops.erf(x, name=name) 515 516 517 @tf_export("scalar_mul") 518 def scalar_mul(scalar, x): 519 """Multiplies a scalar times a `Tensor` or `IndexedSlices` object. 520 521 Intended for use in gradient code which might deal with `IndexedSlices` 522 objects, which are easy to multiply by a scalar but more expensive to 523 multiply with arbitrary tensors. 524 525 Args: 526 scalar: A 0-D scalar `Tensor`. Must have known shape. 527 x: A `Tensor` or `IndexedSlices` to be scaled. 528 529 Returns: 530 `scalar * x` of the same type (`Tensor` or `IndexedSlices`) as `x`. 531 532 Raises: 533 ValueError: if scalar is not a 0-D `scalar`. 534 """ 535 scalar = ops.convert_to_tensor( 536 scalar, dtype=x.dtype.base_dtype, name="scalar") 537 shape = scalar.get_shape() 538 if shape.ndims == 0: 539 if isinstance(x, ops.IndexedSlices): 540 return ops.IndexedSlices(scalar * x.values, x.indices, x.dense_shape) 541 else: 542 return scalar * x 543 else: 544 raise ValueError("Only scalar multiply works, got shape %s" % shape) 545 546 547 @tf_export("pow") 548 def pow(x, y, name=None): # pylint: disable=redefined-builtin 549 r"""Computes the power of one value to another. 550 551 Given a tensor `x` and a tensor `y`, this operation computes \\(x^y\\) for 552 corresponding elements in `x` and `y`. For example: 553 554 ```python 555 x = tf.constant([[2, 2], [3, 3]]) 556 y = tf.constant([[8, 16], [2, 3]]) 557 tf.pow(x, y) # [[256, 65536], [9, 27]] 558 ``` 559 560 Args: 561 x: A `Tensor` of type `float32`, `float64`, `int32`, `int64`, `complex64`, 562 or `complex128`. 563 y: A `Tensor` of type `float32`, `float64`, `int32`, `int64`, `complex64`, 564 or `complex128`. 565 name: A name for the operation (optional). 566 567 Returns: 568 A `Tensor`. 569 """ 570 with ops.name_scope(name, "Pow", [x]) as name: 571 return gen_math_ops._pow(x, y, name=name) 572 573 574 # pylint: disable=redefined-builtin,redefined-outer-name 575 @tf_export("complex") 576 def complex(real, imag, name=None): 577 r"""Converts two real numbers to a complex number. 578 579 Given a tensor `real` representing the real part of a complex number, and a 580 tensor `imag` representing the imaginary part of a complex number, this 581 operation returns complex numbers elementwise of the form \\(a + bj\\), where 582 *a* represents the `real` part and *b* represents the `imag` part. 583 584 The input tensors `real` and `imag` must have the same shape. 585 586 For example: 587 588 ```python 589 real = tf.constant([2.25, 3.25]) 590 imag = tf.constant([4.75, 5.75]) 591 tf.complex(real, imag) # [[2.25 + 4.75j], [3.25 + 5.75j]] 592 ``` 593 594 Args: 595 real: A `Tensor`. Must be one of the following types: `float32`, 596 `float64`. 597 imag: A `Tensor`. Must have the same type as `real`. 598 name: A name for the operation (optional). 599 600 Returns: 601 A `Tensor` of type `complex64` or `complex128`. 602 """ 603 real = ops.convert_to_tensor(real, name="real") 604 imag = ops.convert_to_tensor(imag, name="imag") 605 with ops.name_scope(name, "Complex", [real, imag]) as name: 606 input_types = (real.dtype, imag.dtype) 607 if input_types == (dtypes.float64, dtypes.float64): 608 Tout = dtypes.complex128 609 elif input_types == (dtypes.float32, dtypes.float32): 610 Tout = dtypes.complex64 611 else: 612 raise TypeError("real and imag have incorrect types: " 613 "{} {}".format(real.dtype.name, imag.dtype.name)) 614 return gen_math_ops._complex(real, imag, Tout=Tout, name=name) 615 616 617 @tf_export("real") 618 def real(input, name=None): 619 r"""Returns the real part of a complex (or real) tensor. 620 621 Given a tensor `input`, this operation returns a tensor of type `float` that 622 is the real part of each element in `input` considered as a complex number. 623 624 For example: 625 626 ```python 627 x = tf.constant([-2.25 + 4.75j, 3.25 + 5.75j]) 628 tf.real(x) # [-2.25, 3.25] 629 ``` 630 631 If `input` is already real, it is returned unchanged. 632 633 Args: 634 input: A `Tensor`. Must have numeric type. 635 name: A name for the operation (optional). 636 637 Returns: 638 A `Tensor` of type `float32` or `float64`. 639 """ 640 with ops.name_scope(name, "Real", [input]) as name: 641 if input.dtype.is_complex: 642 real_dtype = input.dtype.real_dtype 643 return gen_math_ops.real(input, Tout=real_dtype, name=name) 644 else: 645 return input 646 647 648 @tf_export("imag") 649 def imag(input, name=None): 650 r"""Returns the imaginary part of a complex (or real) tensor. 651 652 Given a tensor `input`, this operation returns a tensor of type `float` that 653 is the imaginary part of each element in `input` considered as a complex 654 number. If `input` is real, a tensor of all zeros is returned. 655 656 For example: 657 658 ```python 659 x = tf.constant([-2.25 + 4.75j, 3.25 + 5.75j]) 660 tf.imag(x) # [4.75, 5.75] 661 ``` 662 663 Args: 664 input: A `Tensor`. Must be one of the following types: `float`, `double`, 665 `complex64`, `complex128`. 666 name: A name for the operation (optional). 667 668 Returns: 669 A `Tensor` of type `float32` or `float64`. 670 """ 671 with ops.name_scope(name, "Imag", [input]) as name: 672 if input.dtype.is_complex: 673 return gen_math_ops.imag(input, Tout=input.dtype.real_dtype, name=name) 674 else: 675 return array_ops.zeros_like(input) 676 677 678 @tf_export("angle") 679 def angle(input, name=None): 680 r"""Returns the element-wise argument of a complex (or real) tensor. 681 682 Given a tensor `input`, this operation returns a tensor of type `float` that 683 is the argument of each element in `input` considered as a complex number. 684 685 The elements in `input` are considered to be complex numbers of the form 686 \\(a + bj\\), where *a* is the real part and *b* is the imaginary part. 687 If `input` is real then *b* is zero by definition. 688 689 The argument returned by this function is of the form \\(atan2(b, a)\\). 690 If `input` is real, a tensor of all zeros is returned. 691 692 For example: 693 694 ``` 695 # tensor 'input' is [-2.25 + 4.75j, 3.25 + 5.75j] 696 tf.angle(input) ==> [2.0132, 1.056] 697 ``` 698 699 Args: 700 input: A `Tensor`. Must be one of the following types: `float`, `double`, 701 `complex64`, `complex128`. 702 name: A name for the operation (optional). 703 704 Returns: 705 A `Tensor` of type `float32` or `float64`. 706 """ 707 with ops.name_scope(name, "Angle", [input]) as name: 708 if input.dtype.is_complex: 709 return gen_math_ops.angle(input, Tout=input.dtype.real_dtype, name=name) 710 else: 711 return array_ops.zeros_like(input) 712 713 714 # pylint: enable=redefined-outer-name,redefined-builtin 715 716 717 @tf_export("round") 718 def round(x, name=None): # pylint: disable=redefined-builtin 719 """Rounds the values of a tensor to the nearest integer, element-wise. 720 721 Rounds half to even. Also known as bankers rounding. If you want to round 722 according to the current system rounding mode use tf::cint. 723 For example: 724 725 ```python 726 x = tf.constant([0.9, 2.5, 2.3, 1.5, -4.5]) 727 tf.round(x) # [ 1.0, 2.0, 2.0, 2.0, -4.0 ] 728 ``` 729 730 Args: 731 x: A `Tensor` of type `float32` or `float64`. 732 name: A name for the operation (optional). 733 734 Returns: 735 A `Tensor` of same shape and type as `x`. 736 """ 737 x = ops.convert_to_tensor(x, name="x") 738 if x.dtype.is_integer: 739 return x 740 else: 741 return gen_math_ops.round(x, name=name) 742 743 744 @tf_export("cast") 745 def cast(x, dtype, name=None): 746 """Casts a tensor to a new type. 747 748 The operation casts `x` (in case of `Tensor`) or `x.values` 749 (in case of `SparseTensor`) to `dtype`. 750 751 For example: 752 753 ```python 754 x = tf.constant([1.8, 2.2], dtype=tf.float32) 755 tf.cast(x, tf.int32) # [1, 2], dtype=tf.int32 756 ``` 757 758 Args: 759 x: A `Tensor` or `SparseTensor`. 760 dtype: The destination type. 761 name: A name for the operation (optional). 762 763 Returns: 764 A `Tensor` or `SparseTensor` with same shape as `x`. 765 766 Raises: 767 TypeError: If `x` cannot be cast to the `dtype`. 768 """ 769 base_type = dtypes.as_dtype(dtype).base_dtype 770 with ops.name_scope(name, "Cast", [x]) as name: 771 if isinstance(x, sparse_tensor.SparseTensor): 772 values_cast = cast(x.values, base_type, name=name) 773 return sparse_tensor.SparseTensor(x.indices, values_cast, x.dense_shape) 774 else: 775 # TODO(josh11b): If x is not already a Tensor, we could return 776 # ops.convert_to_tensor(x, dtype=dtype, ...) here, but that 777 # allows some conversions that cast() can't do, e.g. casting numbers to 778 # strings. 779 x = ops.convert_to_tensor(x, name="x") 780 if x.dtype.base_dtype == base_type: 781 return x 782 return gen_math_ops.cast(x, base_type, name=name) 783 784 785 @tf_export("saturate_cast") 786 def saturate_cast(value, dtype, name=None): 787 """Performs a safe saturating cast of `value` to `dtype`. 788 789 This function casts the input to `dtype` without applying any scaling. If 790 there is a danger that values would over or underflow in the cast, this op 791 applies the appropriate clamping before the cast. 792 793 Args: 794 value: A `Tensor`. 795 dtype: The desired output `DType`. 796 name: A name for the operation (optional). 797 798 Returns: 799 `value` safely cast to `dtype`. 800 """ 801 # When casting to a type with smaller representable range, clamp. 802 # Note that this covers casting to unsigned types as well. 803 with ops.name_scope(name, "saturate_cast", [value]) as name: 804 value = ops.convert_to_tensor(value, name="value") 805 dtype = dtypes.as_dtype(dtype).base_dtype 806 if value.dtype.min < dtype.min: 807 value = gen_math_ops.maximum(value, 808 ops.convert_to_tensor( 809 dtype.min, dtype=value.dtype, 810 name="min")) 811 if value.dtype.max > dtype.max: 812 value = gen_math_ops.minimum(value, 813 ops.convert_to_tensor( 814 dtype.max, dtype=value.dtype, 815 name="max")) 816 return cast(value, dtype, name=name) 817 818 819 @tf_export("to_float") 820 def to_float(x, name="ToFloat"): 821 """Casts a tensor to type `float32`. 822 823 Args: 824 x: A `Tensor` or `SparseTensor`. 825 name: A name for the operation (optional). 826 827 Returns: 828 A `Tensor` or `SparseTensor` with same shape as `x` with type `float32`. 829 830 Raises: 831 TypeError: If `x` cannot be cast to the `float32`. 832 """ 833 return cast(x, dtypes.float32, name=name) 834 835 836 @tf_export("to_double") 837 def to_double(x, name="ToDouble"): 838 """Casts a tensor to type `float64`. 839 840 Args: 841 x: A `Tensor` or `SparseTensor`. 842 name: A name for the operation (optional). 843 844 Returns: 845 A `Tensor` or `SparseTensor` with same shape as `x` with type `float64`. 846 847 Raises: 848 TypeError: If `x` cannot be cast to the `float64`. 849 """ 850 return cast(x, dtypes.float64, name=name) 851 852 853 @tf_export("to_int32") 854 def to_int32(x, name="ToInt32"): 855 """Casts a tensor to type `int32`. 856 857 Args: 858 x: A `Tensor` or `SparseTensor`. 859 name: A name for the operation (optional). 860 861 Returns: 862 A `Tensor` or `SparseTensor` with same shape as `x` with type `int32`. 863 864 Raises: 865 TypeError: If `x` cannot be cast to the `int32`. 866 """ 867 return cast(x, dtypes.int32, name=name) 868 869 870 @tf_export("to_int64") 871 def to_int64(x, name="ToInt64"): 872 """Casts a tensor to type `int64`. 873 874 Args: 875 x: A `Tensor` or `SparseTensor`. 876 name: A name for the operation (optional). 877 878 Returns: 879 A `Tensor` or `SparseTensor` with same shape as `x` with type `int64`. 880 881 Raises: 882 TypeError: If `x` cannot be cast to the `int64`. 883 """ 884 return cast(x, dtypes.int64, name=name) 885 886 887 @tf_export("to_bfloat16") 888 def to_bfloat16(x, name="ToBFloat16"): 889 """Casts a tensor to type `bfloat16`. 890 891 Args: 892 x: A `Tensor` or `SparseTensor`. 893 name: A name for the operation (optional). 894 895 Returns: 896 A `Tensor` or `SparseTensor` with same shape as `x` with type `bfloat16`. 897 898 Raises: 899 TypeError: If `x` cannot be cast to the `bfloat16`. 900 """ 901 return cast(x, dtypes.bfloat16, name=name) 902 903 904 ops.Tensor._override_operator("__neg__", gen_math_ops._neg) 905 ops.Tensor._override_operator("__abs__", abs) 906 # __invert__ corresponds to the ~ operator. Here we follow the numpy convention 907 # ~ marks an elementwise bit-wise inverse. This is only implemented for boolean 908 # tensors and will throw a TypeError if used on nonboolean arrays 909 ops.Tensor._override_operator("__invert__", gen_math_ops.logical_not) 910 911 912 def _OverrideBinaryOperatorHelper(func, op_name, clazz_object=ops.Tensor): 913 """Register operators with different tensor and scalar versions. 914 915 If `clazz_object` is `SparseTensor`, assumes `func` takes `(sp_indices, 916 sp_values, sp_shape, dense)` and outputs `(new_sp_values)`. 917 918 Args: 919 func: the operator 920 op_name: name of the operator being overridden 921 clazz_object: class to override for. Either `Tensor` or `SparseTensor`. 922 """ 923 924 def binary_op_wrapper(x, y): 925 with ops.name_scope(None, op_name, [x, y]) as name: 926 if not isinstance(y, sparse_tensor.SparseTensor): 927 try: 928 y = ops.convert_to_tensor(y, dtype=x.dtype.base_dtype, name="y") 929 except TypeError: 930 # If the RHS is not a tensor, it might be a tensor aware object 931 # that can implement the operator with knowledge of itself 932 # and the tensor. 933 if hasattr(type(y), "__r%s__" % op_name): 934 return NotImplemented 935 else: 936 raise 937 return func(x, y, name=name) 938 939 def binary_op_wrapper_sparse(sp_x, y): 940 with ops.name_scope(None, op_name, [sp_x, y]) as name: 941 y = ops.convert_to_tensor(y, dtype=sp_x.dtype.base_dtype, name="y") 942 return sparse_tensor.SparseTensor(sp_x.indices, 943 func( 944 sp_x.indices, 945 sp_x.values, 946 sp_x.dense_shape, 947 y, 948 name=name), sp_x.dense_shape) 949 950 def r_binary_op_wrapper(y, x): 951 with ops.name_scope(None, op_name, [x, y]) as name: 952 x = ops.convert_to_tensor(x, dtype=y.dtype.base_dtype, name="x") 953 return func(x, y, name=name) 954 955 # Propagate func.__doc__ to the wrappers 956 try: 957 doc = func.__doc__ 958 except AttributeError: 959 doc = None 960 binary_op_wrapper.__doc__ = doc 961 r_binary_op_wrapper.__doc__ = doc 962 binary_op_wrapper_sparse.__doc__ = doc 963 964 if clazz_object is ops.Tensor: 965 clazz_object._override_operator("__%s__" % op_name, binary_op_wrapper) 966 del binary_op_wrapper 967 clazz_object._override_operator("__r%s__" % op_name, r_binary_op_wrapper) 968 del r_binary_op_wrapper 969 else: 970 clazz_object._override_operator("__%s__" % op_name, 971 binary_op_wrapper_sparse) 972 del binary_op_wrapper_sparse 973 974 975 # Conversion table for __truediv__. None entries mean no conversion required. 976 _TRUEDIV_TABLE = { 977 dtypes.uint8: dtypes.float32, 978 dtypes.int8: dtypes.float32, 979 dtypes.uint16: dtypes.float32, 980 dtypes.int16: dtypes.float32, 981 dtypes.int32: dtypes.float64, 982 dtypes.int64: dtypes.float64, 983 dtypes.bfloat16: None, 984 dtypes.float16: None, 985 dtypes.float32: None, 986 dtypes.float64: None, 987 dtypes.complex64: None, 988 dtypes.complex128: None, 989 } 990 991 992 # NOTE: the support of "sparse (true)div dense" is currently not baked in into 993 # "tf.(true_)div()". Until such an API decision is made, the supported usage is 994 # to explicitly use the "/" operator to invoke either truediv or div. 995 def _sparse_dense_truediv(sp_indices, sp_values, sp_shape, y, name=None): 996 """Internal helper function for 'sp_t / dense_t'.""" 997 with ops.name_scope(name, "truediv", 998 [sp_indices, sp_values, sp_shape, y]) as name: 999 sp_values = ops.convert_to_tensor(sp_values, name="sp_values") 1000 y = ops.convert_to_tensor(y, name="y") 1001 x_dtype = sp_values.dtype.base_dtype 1002 y_dtype = y.dtype.base_dtype 1003 if x_dtype != y_dtype: 1004 raise TypeError("x and y must have the same dtype, got %r != %r" % 1005 (x_dtype, y_dtype)) 1006 try: 1007 dtype = _TRUEDIV_TABLE[x_dtype] 1008 except KeyError: 1009 raise TypeError("Invalid dtype %r in __truediv__" % x_dtype) 1010 if dtype is not None: 1011 sp_values = cast(sp_values, dtype) 1012 y = cast(y, dtype) 1013 return gen_sparse_ops.sparse_dense_cwise_div( 1014 sp_indices, sp_values, sp_shape, y, name=name) 1015 1016 1017 def _truediv_python3(x, y, name=None): 1018 with ops.name_scope(name, "truediv", [x, y]) as name: 1019 x = ops.convert_to_tensor(x, name="x") 1020 y = ops.convert_to_tensor(y, name="y") 1021 x_dtype = x.dtype.base_dtype 1022 y_dtype = y.dtype.base_dtype 1023 if x_dtype != y_dtype: 1024 raise TypeError("x and y must have the same dtype, got %r != %r" % 1025 (x_dtype, y_dtype)) 1026 try: 1027 dtype = _TRUEDIV_TABLE[x_dtype] 1028 except KeyError: 1029 raise TypeError("Invalid dtype %r in __truediv__" % x_dtype) 1030 if dtype is not None: 1031 x = cast(x, dtype) 1032 y = cast(y, dtype) 1033 return gen_math_ops._real_div(x, y, name=name) 1034 1035 1036 def _div_python2(x, y, name=None): 1037 """Divide two values using Python 2 semantics. Used for Tensor.__div__. 1038 1039 Args: 1040 x: `Tensor` numerator of real numeric type. 1041 y: `Tensor` denominator of real numeric type. 1042 name: A name for the operation (optional). 1043 Returns: 1044 `x / y` returns the quotient of x and y. 1045 """ 1046 1047 with ops.name_scope(name, "div", [x, y]) as name: 1048 x = ops.convert_to_tensor(x, name="x") 1049 y = ops.convert_to_tensor(y, name="y", dtype=x.dtype.base_dtype) 1050 x_dtype = x.dtype.base_dtype 1051 y_dtype = y.dtype.base_dtype 1052 if x_dtype != y_dtype: 1053 raise TypeError("x and y must have the same dtype, got %r != %r" % 1054 (x_dtype, y_dtype)) 1055 if x_dtype.is_floating or x_dtype.is_complex: 1056 return gen_math_ops._real_div(x, y, name=name) 1057 else: 1058 return gen_math_ops._floor_div(x, y, name=name) 1059 1060 1061 @tf_export("truediv") 1062 def truediv(x, y, name=None): 1063 """Divides x / y elementwise (using Python 3 division operator semantics). 1064 1065 NOTE: Prefer using the Tensor operator or tf.divide which obey Python 1066 division operator semantics. 1067 1068 This function forces Python 3 division operator semantics where all integer 1069 arguments are cast to floating types first. This op is generated by normal 1070 `x / y` division in Python 3 and in Python 2.7 with 1071 `from __future__ import division`. If you want integer division that rounds 1072 down, use `x // y` or `tf.floordiv`. 1073 1074 `x` and `y` must have the same numeric type. If the inputs are floating 1075 point, the output will have the same type. If the inputs are integral, the 1076 inputs are cast to `float32` for `int8` and `int16` and `float64` for `int32` 1077 and `int64` (matching the behavior of Numpy). 1078 1079 Args: 1080 x: `Tensor` numerator of numeric type. 1081 y: `Tensor` denominator of numeric type. 1082 name: A name for the operation (optional). 1083 1084 Returns: 1085 `x / y` evaluated in floating point. 1086 1087 Raises: 1088 TypeError: If `x` and `y` have different dtypes. 1089 """ 1090 return _truediv_python3(x, y, name) 1091 1092 1093 @tf_export("div") 1094 def div(x, y, name=None): 1095 """Divides x / y elementwise (using Python 2 division operator semantics). 1096 1097 NOTE: Prefer using the Tensor division operator or tf.divide which obey Python 1098 division operator semantics. 1099 1100 This function divides `x` and `y`, forcing Python 2.7 semantics. That is, 1101 if one of `x` or `y` is a float, then the result will be a float. 1102 Otherwise, the output will be an integer type. Flooring semantics are used 1103 for integer division. 1104 1105 Args: 1106 x: `Tensor` numerator of real numeric type. 1107 y: `Tensor` denominator of real numeric type. 1108 name: A name for the operation (optional). 1109 Returns: 1110 `x / y` returns the quotient of x and y. 1111 """ 1112 return _div_python2(x, y, name) 1113 1114 1115 # TODO(aselle): This should be removed 1116 mod = gen_math_ops._floor_mod 1117 1118 1119 # TODO(aselle): Deprecate this once all internal functionality uses 1120 # tf.truncatediv 1121 @tf_export("floordiv") 1122 def floordiv(x, y, name=None): 1123 """Divides `x / y` elementwise, rounding toward the most negative integer. 1124 1125 The same as `tf.div(x,y)` for integers, but uses `tf.floor(tf.div(x,y))` for 1126 floating point arguments so that the result is always an integer (though 1127 possibly an integer represented as floating point). This op is generated by 1128 `x // y` floor division in Python 3 and in Python 2.7 with 1129 `from __future__ import division`. 1130 1131 Note that for efficiency, `floordiv` uses C semantics for negative numbers 1132 (unlike Python and Numpy). 1133 1134 `x` and `y` must have the same type, and the result will have the same type 1135 as well. 1136 1137 Args: 1138 x: `Tensor` numerator of real numeric type. 1139 y: `Tensor` denominator of real numeric type. 1140 name: A name for the operation (optional). 1141 1142 Returns: 1143 `x / y` rounded down (except possibly towards zero for negative integers). 1144 1145 Raises: 1146 TypeError: If the inputs are complex. 1147 """ 1148 with ops.name_scope(name, "floordiv", [x, y]) as name: 1149 return gen_math_ops._floor_div(x, y, name=name) 1150 1151 1152 realdiv = gen_math_ops._real_div 1153 truncatediv = gen_math_ops._truncate_div 1154 # TODO(aselle): Rename this to floordiv when we can. 1155 floor_div = gen_math_ops._floor_div 1156 truncatemod = gen_math_ops._truncate_mod 1157 floormod = gen_math_ops._floor_mod 1158 1159 1160 def _mul_dispatch(x, y, name=None): 1161 """Dispatches cwise mul for "Dense*Dense" and "Dense*Sparse".""" 1162 is_tensor_y = isinstance(y, ops.Tensor) 1163 if is_tensor_y: 1164 return gen_math_ops._mul(x, y, name=name) 1165 else: 1166 assert isinstance(y, sparse_tensor.SparseTensor) # Case: Dense * Sparse. 1167 new_vals = gen_sparse_ops.sparse_dense_cwise_mul(y.indices, y.values, 1168 y.dense_shape, x, name) 1169 return sparse_tensor.SparseTensor(y.indices, new_vals, y.dense_shape) 1170 1171 1172 # NOTE(aselle): When integer division is added for sparse_dense_cwise, 1173 # div, truediv, and floordiv should be delegated appropriately for 1174 # Python sematnics, analogous to dense cwise tensor operations. 1175 _OverrideBinaryOperatorHelper(gen_sparse_ops.sparse_dense_cwise_div, "div", 1176 sparse_tensor.SparseTensor) 1177 _OverrideBinaryOperatorHelper(_sparse_dense_truediv, "truediv", 1178 sparse_tensor.SparseTensor) 1179 _OverrideBinaryOperatorHelper(gen_sparse_ops.sparse_dense_cwise_mul, "mul", 1180 sparse_tensor.SparseTensor) 1181 1182 _OverrideBinaryOperatorHelper(gen_math_ops.add, "add") 1183 _OverrideBinaryOperatorHelper(gen_math_ops._sub, "sub") 1184 _OverrideBinaryOperatorHelper(_mul_dispatch, "mul") 1185 _OverrideBinaryOperatorHelper(_div_python2, "div") 1186 _OverrideBinaryOperatorHelper(_truediv_python3, "truediv") 1187 _OverrideBinaryOperatorHelper(floordiv, "floordiv") 1188 _OverrideBinaryOperatorHelper(gen_math_ops._floor_mod, "mod") 1189 _OverrideBinaryOperatorHelper(pow, "pow") 1190 1191 1192 @tf_export("logical_xor") 1193 def logical_xor(x, y, name="LogicalXor"): 1194 """x ^ y = (x | y) & ~(x & y).""" 1195 # TODO(alemi) Make this a cwise op if people end up relying on it. 1196 return gen_math_ops.logical_and( 1197 gen_math_ops.logical_or(x, y), 1198 gen_math_ops.logical_not(gen_math_ops.logical_and(x, y)), 1199 name=name) 1200 1201 1202 _OverrideBinaryOperatorHelper(gen_math_ops.logical_and, "and") 1203 _OverrideBinaryOperatorHelper(gen_math_ops.logical_or, "or") 1204 _OverrideBinaryOperatorHelper(logical_xor, "xor") 1205 1206 ops.Tensor._override_operator("__lt__", gen_math_ops.less) 1207 ops.Tensor._override_operator("__le__", gen_math_ops.less_equal) 1208 ops.Tensor._override_operator("__gt__", gen_math_ops.greater) 1209 ops.Tensor._override_operator("__ge__", gen_math_ops.greater_equal) 1210 1211 1212 @tf_export("range") 1213 def range(start, limit=None, delta=1, dtype=None, name="range"): # pylint: disable=redefined-builtin 1214 """Creates a sequence of numbers. 1215 1216 Creates a sequence of numbers that begins at `start` and extends by 1217 increments of `delta` up to but not including `limit`. 1218 1219 The dtype of the resulting tensor is inferred from the inputs unless 1220 it is provided explicitly. 1221 1222 Like the Python builtin `range`, `start` defaults to 0, so that 1223 `range(n) = range(0, n)`. 1224 1225 For example: 1226 1227 ```python 1228 start = 3 1229 limit = 18 1230 delta = 3 1231 tf.range(start, limit, delta) # [3, 6, 9, 12, 15] 1232 1233 start = 3 1234 limit = 1 1235 delta = -0.5 1236 tf.range(start, limit, delta) # [3, 2.5, 2, 1.5] 1237 1238 limit = 5 1239 tf.range(limit) # [0, 1, 2, 3, 4] 1240 ``` 1241 1242 Args: 1243 start: A 0-D `Tensor` (scalar). Acts as first entry in the range if 1244 `limit` is not None; otherwise, acts as range limit and first entry 1245 defaults to 0. 1246 limit: A 0-D `Tensor` (scalar). Upper limit of sequence, 1247 exclusive. If None, defaults to the value of `start` while the first 1248 entry of the range defaults to 0. 1249 delta: A 0-D `Tensor` (scalar). Number that increments 1250 `start`. Defaults to 1. 1251 dtype: The type of the elements of the resulting tensor. 1252 name: A name for the operation. Defaults to "range". 1253 1254 Returns: 1255 An 1-D `Tensor` of type `dtype`. 1256 1257 @compatibility(numpy) 1258 Equivalent to np.arange 1259 @end_compatibility 1260 """ 1261 if limit is None: 1262 start, limit = 0, start 1263 1264 with ops.name_scope(name, "Range", [start, limit, delta]) as name: 1265 start = ops.convert_to_tensor(start, dtype=dtype, name="start") 1266 limit = ops.convert_to_tensor(limit, dtype=dtype, name="limit") 1267 delta = ops.convert_to_tensor(delta, dtype=dtype, name="delta") 1268 1269 # infer dtype if not explicitly provided 1270 if dtype is None: 1271 dtype_hierarchy = [ 1272 dtypes.int32, dtypes.int64, dtypes.float32, dtypes.float64 1273 ] 1274 assert all(arg.dtype in dtype_hierarchy for arg in [start, limit, delta]) 1275 inferred_dtype = max( 1276 [arg.dtype for arg in [start, limit, delta]], 1277 key=dtype_hierarchy.index) 1278 1279 start = cast(start, inferred_dtype) 1280 limit = cast(limit, inferred_dtype) 1281 delta = cast(delta, inferred_dtype) 1282 1283 return gen_math_ops._range(start, limit, delta, name=name) 1284 1285 1286 # Reduction operations 1287 def _ReductionDims(x, axis, reduction_indices): 1288 """Returns range(0, rank(x)) if reduction_indices is None.""" 1289 # TODO(aselle): Remove this after deprecation 1290 if reduction_indices is not None: 1291 if axis is not None: 1292 raise ValueError("Can't specify both axis' and 'reduction_indices'.") 1293 axis = reduction_indices 1294 if axis is not None: 1295 return axis 1296 else: 1297 # Fast path: avoid creating Rank and Range ops if ndims is known. 1298 if isinstance(x, ops.Tensor) and x.get_shape().ndims is not None: 1299 return constant_op.constant( 1300 np.arange(x.get_shape().ndims), dtype=dtypes.int32) 1301 if (isinstance(x, sparse_tensor.SparseTensor) and 1302 x.dense_shape.get_shape().is_fully_defined()): 1303 rank = x.dense_shape.get_shape()[0].value # sparse.dense_shape is 1-D. 1304 return constant_op.constant(np.arange(rank), dtype=dtypes.int32) 1305 1306 # Otherwise, we rely on Range and Rank to do the right thing at run-time. 1307 return range(0, array_ops.rank(x)) 1308 1309 1310 def _may_reduce_to_scalar(keepdims, axis, reduction_indices, output): 1311 """Set a reduction's output's shape to be a scalar if we are certain.""" 1312 if (not output.shape.is_fully_defined()) and (not keepdims) and ( 1313 axis is None) and (reduction_indices is None): 1314 output.set_shape(()) 1315 return output 1316 1317 1318 @tf_export("reduce_sum") 1319 @deprecation.deprecated_args( 1320 None, "keep_dims is deprecated, use keepdims instead", "keep_dims") 1321 def reduce_sum(input_tensor, 1322 axis=None, 1323 keepdims=None, 1324 name=None, 1325 reduction_indices=None, 1326 keep_dims=None): 1327 """Computes the sum of elements across dimensions of a tensor. 1328 1329 Reduces `input_tensor` along the dimensions given in `axis`. 1330 Unless `keepdims` is true, the rank of the tensor is reduced by 1 for each 1331 entry in `axis`. If `keepdims` is true, the reduced dimensions 1332 are retained with length 1. 1333 1334 If `axis` has no entries, all dimensions are reduced, and a 1335 tensor with a single element is returned. 1336 1337 For example: 1338 1339 ```python 1340 x = tf.constant([[1, 1, 1], [1, 1, 1]]) 1341 tf.reduce_sum(x) # 6 1342 tf.reduce_sum(x, 0) # [2, 2, 2] 1343 tf.reduce_sum(x, 1) # [3, 3] 1344 tf.reduce_sum(x, 1, keepdims=True) # [[3], [3]] 1345 tf.reduce_sum(x, [0, 1]) # 6 1346 ``` 1347 1348 Args: 1349 input_tensor: The tensor to reduce. Should have numeric type. 1350 axis: The dimensions to reduce. If `None` (the default), 1351 reduces all dimensions. Must be in the range 1352 `[-rank(input_tensor), rank(input_tensor))`. 1353 keepdims: If true, retains reduced dimensions with length 1. 1354 name: A name for the operation (optional). 1355 reduction_indices: The old (deprecated) name for axis. 1356 keep_dims: Deprecated alias for `keepdims`. 1357 1358 Returns: 1359 The reduced tensor. 1360 1361 @compatibility(numpy) 1362 Equivalent to np.sum 1363 @end_compatibility 1364 """ 1365 keepdims = deprecation.deprecated_argument_lookup("keepdims", keepdims, 1366 "keep_dims", keep_dims) 1367 if keepdims is None: 1368 keepdims = False 1369 1370 return _may_reduce_to_scalar(keepdims, axis, reduction_indices, 1371 gen_math_ops._sum( 1372 input_tensor, 1373 _ReductionDims(input_tensor, axis, 1374 reduction_indices), 1375 keepdims, 1376 name=name)) 1377 1378 1379 @tf_export("count_nonzero") 1380 @deprecation.deprecated_args( 1381 None, "keep_dims is deprecated, use keepdims instead", "keep_dims") 1382 def count_nonzero(input_tensor, 1383 axis=None, 1384 keepdims=None, 1385 dtype=dtypes.int64, 1386 name=None, 1387 reduction_indices=None, 1388 keep_dims=None): 1389 """Computes number of nonzero elements across dimensions of a tensor. 1390 1391 Reduces `input_tensor` along the dimensions given in `axis`. 1392 Unless `keepdims` is true, the rank of the tensor is reduced by 1 for each 1393 entry in `axis`. If `keepdims` is true, the reduced dimensions 1394 are retained with length 1. 1395 1396 If `axis` has no entries, all dimensions are reduced, and a 1397 tensor with a single element is returned. 1398 1399 **NOTE** Floating point comparison to zero is done by exact floating point 1400 equality check. Small values are **not** rounded to zero for purposes of 1401 the nonzero check. 1402 1403 For example: 1404 1405 ```python 1406 x = tf.constant([[0, 1, 0], [1, 1, 0]]) 1407 tf.count_nonzero(x) # 3 1408 tf.count_nonzero(x, 0) # [1, 2, 0] 1409 tf.count_nonzero(x, 1) # [1, 2] 1410 tf.count_nonzero(x, 1, keepdims=True) # [[1], [2]] 1411 tf.count_nonzero(x, [0, 1]) # 3 1412 ``` 1413 1414 Args: 1415 input_tensor: The tensor to reduce. Should be of numeric type, or `bool`. 1416 axis: The dimensions to reduce. If `None` (the default), 1417 reduces all dimensions. Must be in the range 1418 `[-rank(input_tensor), rank(input_tensor))`. 1419 keepdims: If true, retains reduced dimensions with length 1. 1420 dtype: The output dtype; defaults to `tf.int64`. 1421 name: A name for the operation (optional). 1422 reduction_indices: The old (deprecated) name for axis. 1423 keep_dims: Deprecated alias for `keepdims`. 1424 1425 Returns: 1426 The reduced tensor (number of nonzero values). 1427 """ 1428 keepdims = deprecation.deprecated_argument_lookup("keepdims", keepdims, 1429 "keep_dims", keep_dims) 1430 if keepdims is None: 1431 keepdims = False 1432 1433 with ops.name_scope(name, "count_nonzero", [input_tensor]): 1434 input_tensor = ops.convert_to_tensor(input_tensor, name="input_tensor") 1435 zero = input_tensor.dtype.as_numpy_dtype() 1436 return cast( 1437 reduce_sum( 1438 # int64 reduction happens on GPU 1439 to_int64(gen_math_ops.not_equal(input_tensor, zero)), 1440 axis=axis, 1441 keepdims=keepdims, 1442 reduction_indices=reduction_indices), 1443 dtype=dtype) 1444 1445 1446 @tf_export("reduce_mean") 1447 @deprecation.deprecated_args( 1448 None, "keep_dims is deprecated, use keepdims instead", "keep_dims") 1449 def reduce_mean(input_tensor, 1450 axis=None, 1451 keepdims=None, 1452 name=None, 1453 reduction_indices=None, 1454 keep_dims=None): 1455 """Computes the mean of elements across dimensions of a tensor. 1456 1457 Reduces `input_tensor` along the dimensions given in `axis`. 1458 Unless `keepdims` is true, the rank of the tensor is reduced by 1 for each 1459 entry in `axis`. If `keepdims` is true, the reduced dimensions 1460 are retained with length 1. 1461 1462 If `axis` has no entries, all dimensions are reduced, and a 1463 tensor with a single element is returned. 1464 1465 For example: 1466 1467 ```python 1468 x = tf.constant([[1., 1.], [2., 2.]]) 1469 tf.reduce_mean(x) # 1.5 1470 tf.reduce_mean(x, 0) # [1.5, 1.5] 1471 tf.reduce_mean(x, 1) # [1., 2.] 1472 ``` 1473 1474 Args: 1475 input_tensor: The tensor to reduce. Should have numeric type. 1476 axis: The dimensions to reduce. If `None` (the default), 1477 reduces all dimensions. Must be in the range 1478 `[-rank(input_tensor), rank(input_tensor)]`. 1479 keepdims: If true, retains reduced dimensions with length 1. 1480 name: A name for the operation (optional). 1481 reduction_indices: The old (deprecated) name for axis. 1482 keep_dims: Deprecated alias for `keepdims`. 1483 1484 Returns: 1485 The reduced tensor. 1486 1487 @compatibility(numpy) 1488 Equivalent to np.mean 1489 1490 Please note that `np.mean` has a `dtype` parameter that could be used to 1491 specify the output type. By default this is `dtype=float64`. On the other 1492 hand, `tf.reduce_mean` has an aggressive type inference from `input_tensor`, 1493 for example: 1494 1495 ```python 1496 x = tf.constant([1, 0, 1, 0]) 1497 tf.reduce_mean(x) # 0 1498 y = tf.constant([1., 0., 1., 0.]) 1499 tf.reduce_mean(y) # 0.5 1500 ``` 1501 1502 @end_compatibility 1503 """ 1504 keepdims = deprecation.deprecated_argument_lookup("keepdims", keepdims, 1505 "keep_dims", keep_dims) 1506 1507 if keepdims is None: 1508 keepdims = False 1509 return _may_reduce_to_scalar(keepdims, axis, reduction_indices, 1510 gen_math_ops._mean( 1511 input_tensor, 1512 _ReductionDims(input_tensor, axis, 1513 reduction_indices), 1514 keepdims, 1515 name=name)) 1516 1517 1518 @tf_export("reduce_prod") 1519 @deprecation.deprecated_args( 1520 None, "keep_dims is deprecated, use keepdims instead", "keep_dims") 1521 def reduce_prod(input_tensor, 1522 axis=None, 1523 keepdims=None, 1524 name=None, 1525 reduction_indices=None, 1526 keep_dims=None): 1527 """Computes the product of elements across dimensions of a tensor. 1528 1529 Reduces `input_tensor` along the dimensions given in `axis`. 1530 Unless `keepdims` is true, the rank of the tensor is reduced by 1 for each 1531 entry in `axis`. If `keepdims` is true, the reduced dimensions 1532 are retained with length 1. 1533 1534 If `axis` has no entries, all dimensions are reduced, and a 1535 tensor with a single element is returned. 1536 1537 Args: 1538 input_tensor: The tensor to reduce. Should have numeric type. 1539 axis: The dimensions to reduce. If `None` (the default), 1540 reduces all dimensions. Must be in the range 1541 `[-rank(input_tensor), rank(input_tensor))`. 1542 keepdims: If true, retains reduced dimensions with length 1. 1543 name: A name for the operation (optional). 1544 reduction_indices: The old (deprecated) name for axis. 1545 keep_dims: Deprecated alias for `keepdims`. 1546 1547 Returns: 1548 The reduced tensor. 1549 1550 @compatibility(numpy) 1551 Equivalent to np.prod 1552 @end_compatibility 1553 """ 1554 keepdims = deprecation.deprecated_argument_lookup("keepdims", keepdims, 1555 "keep_dims", keep_dims) 1556 1557 if keepdims is None: 1558 keepdims = False 1559 return _may_reduce_to_scalar(keepdims, axis, reduction_indices, 1560 gen_math_ops._prod( 1561 input_tensor, 1562 _ReductionDims(input_tensor, axis, 1563 reduction_indices), 1564 keepdims, 1565 name=name)) 1566 1567 1568 @tf_export("reduce_min") 1569 @deprecation.deprecated_args( 1570 None, "keep_dims is deprecated, use keepdims instead", "keep_dims") 1571 def reduce_min(input_tensor, 1572 axis=None, 1573 keepdims=None, 1574 name=None, 1575 reduction_indices=None, 1576 keep_dims=None): 1577 """Computes the minimum of elements across dimensions of a tensor. 1578 1579 Reduces `input_tensor` along the dimensions given in `axis`. 1580 Unless `keepdims` is true, the rank of the tensor is reduced by 1 for each 1581 entry in `axis`. If `keepdims` is true, the reduced dimensions 1582 are retained with length 1. 1583 1584 If `axis` has no entries, all dimensions are reduced, and a 1585 tensor with a single element is returned. 1586 1587 Args: 1588 input_tensor: The tensor to reduce. Should have numeric type. 1589 axis: The dimensions to reduce. If `None` (the default), 1590 reduces all dimensions. Must be in the range 1591 `[-rank(input_tensor), rank(input_tensor))`. 1592 keepdims: If true, retains reduced dimensions with length 1. 1593 name: A name for the operation (optional). 1594 reduction_indices: The old (deprecated) name for axis. 1595 keep_dims: Deprecated alias for `keepdims`. 1596 1597 Returns: 1598 The reduced tensor. 1599 1600 @compatibility(numpy) 1601 Equivalent to np.min 1602 @end_compatibility 1603 """ 1604 keepdims = deprecation.deprecated_argument_lookup("keepdims", keepdims, 1605 "keep_dims", keep_dims) 1606 if keepdims is None: 1607 keepdims = False 1608 return _may_reduce_to_scalar(keepdims, axis, reduction_indices, 1609 gen_math_ops._min( 1610 input_tensor, 1611 _ReductionDims(input_tensor, axis, 1612 reduction_indices), 1613 keepdims, 1614 name=name)) 1615 1616 1617 @tf_export("reduce_max") 1618 @deprecation.deprecated_args( 1619 None, "keep_dims is deprecated, use keepdims instead", "keep_dims") 1620 def reduce_max(input_tensor, 1621 axis=None, 1622 keepdims=None, 1623 name=None, 1624 reduction_indices=None, 1625 keep_dims=None): 1626 """Computes the maximum of elements across dimensions of a tensor. 1627 1628 Reduces `input_tensor` along the dimensions given in `axis`. 1629 Unless `keepdims` is true, the rank of the tensor is reduced by 1 for each 1630 entry in `axis`. If `keepdims` is true, the reduced dimensions 1631 are retained with length 1. 1632 1633 If `axis` has no entries, all dimensions are reduced, and a 1634 tensor with a single element is returned. 1635 1636 Args: 1637 input_tensor: The tensor to reduce. Should have numeric type. 1638 axis: The dimensions to reduce. If `None` (the default), 1639 reduces all dimensions. Must be in the range 1640 `[-rank(input_tensor), rank(input_tensor))`. 1641 keepdims: If true, retains reduced dimensions with length 1. 1642 name: A name for the operation (optional). 1643 reduction_indices: The old (deprecated) name for axis. 1644 keep_dims: Deprecated alias for `keepdims`. 1645 1646 Returns: 1647 The reduced tensor. 1648 1649 @compatibility(numpy) 1650 Equivalent to np.max 1651 @end_compatibility 1652 """ 1653 keepdims = deprecation.deprecated_argument_lookup("keepdims", keepdims, 1654 "keep_dims", keep_dims) 1655 if keepdims is None: 1656 keepdims = False 1657 return _may_reduce_to_scalar(keepdims, axis, reduction_indices, 1658 gen_math_ops._max( 1659 input_tensor, 1660 _ReductionDims(input_tensor, axis, 1661 reduction_indices), 1662 keepdims, 1663 name=name)) 1664 1665 1666 @tf_export("reduce_all") 1667 @deprecation.deprecated_args( 1668 None, "keep_dims is deprecated, use keepdims instead", "keep_dims") 1669 def reduce_all(input_tensor, 1670 axis=None, 1671 keepdims=None, 1672 name=None, 1673 reduction_indices=None, 1674 keep_dims=None): 1675 """Computes the "logical and" of elements across dimensions of a tensor. 1676 1677 Reduces `input_tensor` along the dimensions given in `axis`. 1678 Unless `keepdims` is true, the rank of the tensor is reduced by 1 for each 1679 entry in `axis`. If `keepdims` is true, the reduced dimensions 1680 are retained with length 1. 1681 1682 If `axis` has no entries, all dimensions are reduced, and a 1683 tensor with a single element is returned. 1684 1685 For example: 1686 1687 ```python 1688 x = tf.constant([[True, True], [False, False]]) 1689 tf.reduce_all(x) # False 1690 tf.reduce_all(x, 0) # [False, False] 1691 tf.reduce_all(x, 1) # [True, False] 1692 ``` 1693 1694 Args: 1695 input_tensor: The boolean tensor to reduce. 1696 axis: The dimensions to reduce. If `None` (the default), 1697 reduces all dimensions. Must be in the range 1698 `[-rank(input_tensor), rank(input_tensor))`. 1699 keepdims: If true, retains reduced dimensions with length 1. 1700 name: A name for the operation (optional). 1701 reduction_indices: The old (deprecated) name for axis. 1702 keep_dims: Deprecated alias for `keepdims`. 1703 1704 Returns: 1705 The reduced tensor. 1706 1707 @compatibility(numpy) 1708 Equivalent to np.all 1709 @end_compatibility 1710 """ 1711 keepdims = deprecation.deprecated_argument_lookup("keepdims", keepdims, 1712 "keep_dims", keep_dims) 1713 if keepdims is None: 1714 keepdims = False 1715 return _may_reduce_to_scalar(keepdims, axis, reduction_indices, 1716 gen_math_ops._all( 1717 input_tensor, 1718 _ReductionDims(input_tensor, axis, 1719 reduction_indices), 1720 keepdims, 1721 name=name)) 1722 1723 1724 @tf_export("reduce_any") 1725 @deprecation.deprecated_args( 1726 None, "keep_dims is deprecated, use keepdims instead", "keep_dims") 1727 def reduce_any(input_tensor, 1728 axis=None, 1729 keepdims=None, 1730 name=None, 1731 reduction_indices=None, 1732 keep_dims=None): 1733 """Computes the "logical or" of elements across dimensions of a tensor. 1734 1735 Reduces `input_tensor` along the dimensions given in `axis`. 1736 Unless `keepdims` is true, the rank of the tensor is reduced by 1 for each 1737 entry in `axis`. If `keepdims` is true, the reduced dimensions 1738 are retained with length 1. 1739 1740 If `axis` has no entries, all dimensions are reduced, and a 1741 tensor with a single element is returned. 1742 1743 For example: 1744 1745 ```python 1746 x = tf.constant([[True, True], [False, False]]) 1747 tf.reduce_any(x) # True 1748 tf.reduce_any(x, 0) # [True, True] 1749 tf.reduce_any(x, 1) # [True, False] 1750 ``` 1751 1752 Args: 1753 input_tensor: The boolean tensor to reduce. 1754 axis: The dimensions to reduce. If `None` (the default), 1755 reduces all dimensions. Must be in the range 1756 `[-rank(input_tensor), rank(input_tensor))`. 1757 keepdims: If true, retains reduced dimensions with length 1. 1758 name: A name for the operation (optional). 1759 reduction_indices: The old (deprecated) name for axis. 1760 keep_dims: Deprecated alias for `keepdims`. 1761 1762 Returns: 1763 The reduced tensor. 1764 1765 @compatibility(numpy) 1766 Equivalent to np.any 1767 @end_compatibility 1768 """ 1769 keepdims = deprecation.deprecated_argument_lookup("keepdims", keepdims, 1770 "keep_dims", keep_dims) 1771 if keepdims is None: 1772 keepdims = False 1773 return _may_reduce_to_scalar(keepdims, axis, reduction_indices, 1774 gen_math_ops._any( 1775 input_tensor, 1776 _ReductionDims(input_tensor, axis, 1777 reduction_indices), 1778 keepdims, 1779 name=name)) 1780 1781 1782 @tf_export("reduce_logsumexp") 1783 @deprecation.deprecated_args( 1784 None, "keep_dims is deprecated, use keepdims instead", "keep_dims") 1785 def reduce_logsumexp(input_tensor, 1786 axis=None, 1787 keepdims=None, 1788 name=None, 1789 reduction_indices=None, 1790 keep_dims=None): 1791 """Computes log(sum(exp(elements across dimensions of a tensor))). 1792 1793 Reduces `input_tensor` along the dimensions given in `axis`. 1794 Unless `keepdims` is true, the rank of the tensor is reduced by 1 for each 1795 entry in `axis`. If `keepdims` is true, the reduced dimensions 1796 are retained with length 1. 1797 1798 If `axis` has no entries, all dimensions are reduced, and a 1799 tensor with a single element is returned. 1800 1801 This function is more numerically stable than log(sum(exp(input))). It avoids 1802 overflows caused by taking the exp of large inputs and underflows caused by 1803 taking the log of small inputs. 1804 1805 For example: 1806 1807 ```python 1808 x = tf.constant([[0., 0., 0.], [0., 0., 0.]]) 1809 tf.reduce_logsumexp(x) # log(6) 1810 tf.reduce_logsumexp(x, 0) # [log(2), log(2), log(2)] 1811 tf.reduce_logsumexp(x, 1) # [log(3), log(3)] 1812 tf.reduce_logsumexp(x, 1, keepdims=True) # [[log(3)], [log(3)]] 1813 tf.reduce_logsumexp(x, [0, 1]) # log(6) 1814 ``` 1815 1816 Args: 1817 input_tensor: The tensor to reduce. Should have numeric type. 1818 axis: The dimensions to reduce. If `None` (the default), 1819 reduces all dimensions. Must be in the range 1820 `[-rank(input_tensor), rank(input_tensor))`. 1821 keepdims: If true, retains reduced dimensions with length 1. 1822 name: A name for the operation (optional). 1823 reduction_indices: The old (deprecated) name for axis. 1824 keep_dims: Deprecated alias for `keepdims`. 1825 1826 Returns: 1827 The reduced tensor. 1828 """ 1829 keepdims = deprecation.deprecated_argument_lookup("keepdims", keepdims, 1830 "keep_dims", keep_dims) 1831 if keepdims is None: 1832 keepdims = False 1833 with ops.name_scope(name, "ReduceLogSumExp", [input_tensor]) as name: 1834 raw_max = reduce_max( 1835 input_tensor, 1836 axis=axis, 1837 reduction_indices=reduction_indices, 1838 keepdims=True) 1839 my_max = array_ops.stop_gradient( 1840 array_ops.where( 1841 gen_math_ops.is_finite(raw_max), raw_max, 1842 array_ops.zeros_like(raw_max))) 1843 result = gen_math_ops.log( 1844 reduce_sum( 1845 gen_math_ops.exp(input_tensor - my_max), 1846 axis, 1847 keepdims=keepdims, 1848 reduction_indices=reduction_indices)) 1849 if not keepdims: 1850 my_max = array_ops.reshape(my_max, array_ops.shape(result)) 1851 result += my_max 1852 return _may_reduce_to_scalar(keepdims, axis, reduction_indices, result) 1853 1854 1855 @tf_export("trace", "linalg.trace") 1856 def trace(x, name=None): 1857 """Compute the trace of a tensor `x`. 1858 1859 `trace(x)` returns the sum along the main diagonal of each inner-most matrix 1860 in x. If x is of rank `k` with shape `[I, J, K, ..., L, M, N]`, then output 1861 is a tensor of rank `k-2` with dimensions `[I, J, K, ..., L]` where 1862 1863 `output[i, j, k, ..., l] = trace(x[i, j, i, ..., l, :, :])` 1864 1865 For example: 1866 1867 ```python 1868 x = tf.constant([[1, 2], [3, 4]]) 1869 tf.trace(x) # 5 1870 1871 x = tf.constant([[1, 2, 3], 1872 [4, 5, 6], 1873 [7, 8, 9]]) 1874 tf.trace(x) # 15 1875 1876 x = tf.constant([[[1, 2, 3], 1877 [4, 5, 6], 1878 [7, 8, 9]], 1879 [[-1, -2, -3], 1880 [-4, -5, -6], 1881 [-7, -8, -9]]]) 1882 tf.trace(x) # [15, -15] 1883 ``` 1884 1885 Args: 1886 x: tensor. 1887 name: A name for the operation (optional). 1888 1889 Returns: 1890 The trace of input tensor. 1891 """ 1892 with ops.name_scope(name, "Trace", [x]) as name: 1893 x = ops.convert_to_tensor(x, name="x") 1894 return reduce_sum(array_ops.matrix_diag_part(x), [-1], name=name) 1895 1896 1897 @tf_export("matmul") 1898 def matmul(a, 1899 b, 1900 transpose_a=False, 1901 transpose_b=False, 1902 adjoint_a=False, 1903 adjoint_b=False, 1904 a_is_sparse=False, 1905 b_is_sparse=False, 1906 name=None): 1907 """Multiplies matrix `a` by matrix `b`, producing `a` * `b`. 1908 1909 The inputs must, following any transpositions, be tensors of rank >= 2 1910 where the inner 2 dimensions specify valid matrix multiplication arguments, 1911 and any further outer dimensions match. 1912 1913 Both matrices must be of the same type. The supported types are: 1914 `float16`, `float32`, `float64`, `int32`, `complex64`, `complex128`. 1915 1916 Either matrix can be transposed or adjointed (conjugated and transposed) on 1917 the fly by setting one of the corresponding flag to `True`. These are `False` 1918 by default. 1919 1920 If one or both of the matrices contain a lot of zeros, a more efficient 1921 multiplication algorithm can be used by setting the corresponding 1922 `a_is_sparse` or `b_is_sparse` flag to `True`. These are `False` by default. 1923 This optimization is only available for plain matrices (rank-2 tensors) with 1924 datatypes `bfloat16` or `float32`. 1925 1926 For example: 1927 1928 ```python 1929 # 2-D tensor `a` 1930 # [[1, 2, 3], 1931 # [4, 5, 6]] 1932 a = tf.constant([1, 2, 3, 4, 5, 6], shape=[2, 3]) 1933 1934 # 2-D tensor `b` 1935 # [[ 7, 8], 1936 # [ 9, 10], 1937 # [11, 12]] 1938 b = tf.constant([7, 8, 9, 10, 11, 12], shape=[3, 2]) 1939 1940 # `a` * `b` 1941 # [[ 58, 64], 1942 # [139, 154]] 1943 c = tf.matmul(a, b) 1944 1945 1946 # 3-D tensor `a` 1947 # [[[ 1, 2, 3], 1948 # [ 4, 5, 6]], 1949 # [[ 7, 8, 9], 1950 # [10, 11, 12]]] 1951 a = tf.constant(np.arange(1, 13, dtype=np.int32), 1952 shape=[2, 2, 3]) 1953 1954 # 3-D tensor `b` 1955 # [[[13, 14], 1956 # [15, 16], 1957 # [17, 18]], 1958 # [[19, 20], 1959 # [21, 22], 1960 # [23, 24]]] 1961 b = tf.constant(np.arange(13, 25, dtype=np.int32), 1962 shape=[2, 3, 2]) 1963 1964 # `a` * `b` 1965 # [[[ 94, 100], 1966 # [229, 244]], 1967 # [[508, 532], 1968 # [697, 730]]] 1969 c = tf.matmul(a, b) 1970 1971 # Since python >= 3.5 the @ operator is supported (see PEP 465). 1972 # In TensorFlow, it simply calls the `tf.matmul()` function, so the 1973 # following lines are equivalent: 1974 d = a @ b @ [[10.], [11.]] 1975 d = tf.matmul(tf.matmul(a, b), [[10.], [11.]]) 1976 ``` 1977 1978 Args: 1979 a: `Tensor` of type `float16`, `float32`, `float64`, `int32`, `complex64`, 1980 `complex128` and rank > 1. 1981 b: `Tensor` with same type and rank as `a`. 1982 transpose_a: If `True`, `a` is transposed before multiplication. 1983 transpose_b: If `True`, `b` is transposed before multiplication. 1984 adjoint_a: If `True`, `a` is conjugated and transposed before 1985 multiplication. 1986 adjoint_b: If `True`, `b` is conjugated and transposed before 1987 multiplication. 1988 a_is_sparse: If `True`, `a` is treated as a sparse matrix. 1989 b_is_sparse: If `True`, `b` is treated as a sparse matrix. 1990 name: Name for the operation (optional). 1991 1992 Returns: 1993 A `Tensor` of the same type as `a` and `b` where each inner-most matrix is 1994 the product of the corresponding matrices in `a` and `b`, e.g. if all 1995 transpose or adjoint attributes are `False`: 1996 1997 `output`[..., i, j] = sum_k (`a`[..., i, k] * `b`[..., k, j]), 1998 for all indices i, j. 1999 2000 Note: This is matrix product, not element-wise product. 2001 2002 2003 Raises: 2004 ValueError: If transpose_a and adjoint_a, or transpose_b and adjoint_b 2005 are both set to True. 2006 """ 2007 with ops.name_scope(name, "MatMul", [a, b]) as name: 2008 if transpose_a and adjoint_a: 2009 raise ValueError("Only one of transpose_a and adjoint_a can be True.") 2010 if transpose_b and adjoint_b: 2011 raise ValueError("Only one of transpose_b and adjoint_b can be True.") 2012 2013 a = ops.convert_to_tensor(a, name="a") 2014 b = ops.convert_to_tensor(b, name="b") 2015 # TODO(apassos) remove _shape_tuple here when it is not needed. 2016 a_shape = a._shape_tuple() # pylint: disable=protected-access 2017 b_shape = b._shape_tuple() # pylint: disable=protected-access 2018 if (not a_is_sparse and 2019 not b_is_sparse) and ((a_shape is None or len(a_shape) > 2) and 2020 (b_shape is None or len(b_shape) > 2)): 2021 # BatchMatmul does not support transpose, so we conjugate the matrix and 2022 # use adjoint instead. Conj() is a noop for real matrices. 2023 if transpose_a: 2024 a = conj(a) 2025 adjoint_a = True 2026 if transpose_b: 2027 b = conj(b) 2028 adjoint_b = True 2029 return gen_math_ops._batch_mat_mul( 2030 a, b, adj_x=adjoint_a, adj_y=adjoint_b, name=name) 2031 2032 # Neither matmul nor sparse_matmul support adjoint, so we conjugate 2033 # the matrix and use transpose instead. Conj() is a noop for real 2034 # matrices. 2035 if adjoint_a: 2036 a = conj(a) 2037 transpose_a = True 2038 if adjoint_b: 2039 b = conj(b) 2040 transpose_b = True 2041 2042 use_sparse_matmul = False 2043 if a_is_sparse or b_is_sparse: 2044 sparse_matmul_types = [dtypes.bfloat16, dtypes.float32] 2045 use_sparse_matmul = ( 2046 a.dtype in sparse_matmul_types and b.dtype in sparse_matmul_types) 2047 if a.dtype == dtypes.bfloat16 or b.dtype == dtypes.bfloat16: 2048 # matmul currently doesn't handle bfloat16 inputs. 2049 use_sparse_matmul = True 2050 if use_sparse_matmul: 2051 ret = sparse_matmul( 2052 a, 2053 b, 2054 transpose_a=transpose_a, 2055 transpose_b=transpose_b, 2056 a_is_sparse=a_is_sparse, 2057 b_is_sparse=b_is_sparse, 2058 name=name) 2059 # sparse_matmul always returns float32, even with 2060 # bfloat16 inputs. This prevents us from configuring bfloat16 training. 2061 # casting to bfloat16 also matches non-sparse matmul behavior better. 2062 if a.dtype == dtypes.bfloat16 and b.dtype == dtypes.bfloat16: 2063 ret = cast(ret, dtypes.bfloat16) 2064 return ret 2065 else: 2066 return gen_math_ops._mat_mul( 2067 a, b, transpose_a=transpose_a, transpose_b=transpose_b, name=name) 2068 2069 2070 _OverrideBinaryOperatorHelper(matmul, "matmul") 2071 2072 sparse_matmul = gen_math_ops._sparse_mat_mul 2073 2074 2075 @ops.RegisterStatistics("MatMul", "flops") 2076 def _calc_mat_mul_flops(graph, node): 2077 """Calculates the compute resources needed for MatMul.""" 2078 transpose_a = node.attr["transpose_a"].b 2079 a_shape = graph_util.tensor_shape_from_node_def_name(graph, node.input[0]) 2080 a_shape.assert_is_fully_defined() 2081 if transpose_a: 2082 k = int(a_shape[0]) 2083 else: 2084 k = int(a_shape[1]) 2085 output_shape = graph_util.tensor_shape_from_node_def_name(graph, node.name) 2086 output_shape.assert_is_fully_defined() 2087 output_count = np.prod(output_shape.as_list()) 2088 return ops.OpStats("flops", (k * output_count * 2)) 2089 2090 2091 def _as_indexed_slices(x, optimize=True): 2092 """Convert 'x' to IndexedSlices. 2093 2094 Convert a dense Tensor to a block-sparse IndexedSlices. 2095 2096 Args: 2097 x: Either a Tensor object, or an IndexedSlices object. 2098 optimize: if true, attempt to optimize the conversion of 'x'. 2099 2100 Returns: 2101 An IndexedSlices object. 2102 2103 Raises: 2104 TypeError: If 'x' is not a Tensor or an IndexedSlices object. 2105 """ 2106 # TODO(touts): op_scope 2107 if not isinstance(x, (ops.Tensor, ops.IndexedSlices)): 2108 raise TypeError("Not a Tensor or IndexedSlices: %s" % type(x)) 2109 if isinstance(x, ops.IndexedSlices): 2110 return x 2111 x_shape = array_ops.shape_internal(x, optimize=optimize) 2112 return ops.IndexedSlices(x, range(0, x_shape[0]), x_shape) 2113 2114 2115 def _as_indexed_slices_list(inputs, optimize=True): 2116 """Convert all elements of 'inputs' to IndexedSlices. 2117 2118 Additionally, homogenize the types of all the indices to 2119 either int32 or int64. 2120 2121 Args: 2122 inputs: List containing either Tensor or IndexedSlices objects. 2123 optimize: if true, attempt to optimize the conversion of each input. 2124 2125 Returns: 2126 A list of IndexedSlices objects. 2127 2128 Raises: 2129 TypeError: If 'inputs' is not a list or a tuple. 2130 """ 2131 if not isinstance(inputs, (list, tuple)): 2132 raise TypeError("Expected a list or tuple, not a %s" % type(inputs)) 2133 outputs = [_as_indexed_slices(i, optimize=optimize) for i in inputs] 2134 with_int32_index = [ 2135 o.indices for o in outputs if o.indices.dtype == dtypes.int32 2136 ] 2137 if not with_int32_index or len(with_int32_index) == len(outputs): 2138 return outputs 2139 casted_outputs = [] 2140 for o in outputs: 2141 if o.indices.dtype == dtypes.int32: 2142 casted_outputs.append( 2143 ops.IndexedSlices(o.values, cast(o.indices, dtypes.int64), 2144 o.dense_shape)) 2145 else: 2146 casted_outputs.append(o) 2147 return casted_outputs 2148 2149 2150 @tf_export("add_n") 2151 def add_n(inputs, name=None): 2152 """Adds all input tensors element-wise. 2153 2154 Args: 2155 inputs: A list of `Tensor` objects, each with same shape and type. 2156 name: A name for the operation (optional). 2157 2158 Returns: 2159 A `Tensor` of same shape and type as the elements of `inputs`. 2160 2161 Raises: 2162 ValueError: If `inputs` don't all have same shape and dtype or the shape 2163 cannot be inferred. 2164 """ 2165 if not inputs or not isinstance(inputs, (list, tuple)): 2166 raise ValueError("inputs must be a list of at least one Tensor with the " 2167 "same dtype and shape") 2168 inputs = ops.convert_n_to_tensor_or_indexed_slices(inputs) 2169 if not all(isinstance(x, ops.Tensor) for x in inputs): 2170 raise ValueError("inputs must be a list of at least one Tensor with the " 2171 "same dtype and shape") 2172 2173 if len(inputs) == 1: 2174 if name: 2175 return array_ops.identity(inputs[0], name=name) 2176 return inputs[0] 2177 return gen_math_ops._add_n(inputs, name=name) 2178 2179 2180 @tf_export("accumulate_n") 2181 def accumulate_n(inputs, shape=None, tensor_dtype=None, name=None): 2182 """Returns the element-wise sum of a list of tensors. 2183 2184 Optionally, pass `shape` and `tensor_dtype` for shape and type checking, 2185 otherwise, these are inferred. 2186 2187 NOTE: This operation is not differentiable and cannot be used if inputs depend 2188 on trainable variables. Please use `tf.add_n` for such cases. 2189 2190 Aside from differentiability, `tf.accumulate_n` performs the same operation as 2191 `tf.add_n`, but does not wait for all of its inputs to be ready before 2192 beginning to sum. This can save memory if inputs are ready at different times, 2193 since minimum temporary storage is proportional to the output size rather than 2194 the inputs size. 2195 2196 For example: 2197 2198 ```python 2199 a = tf.constant([[1, 2], [3, 4]]) 2200 b = tf.constant([[5, 0], [0, 6]]) 2201 tf.accumulate_n([a, b, a]) # [[7, 4], [6, 14]] 2202 2203 # Explicitly pass shape and type 2204 tf.accumulate_n([a, b, a], shape=[2, 2], tensor_dtype=tf.int32) # [[7, 4], 2205 # [6, 14]] 2206 ``` 2207 2208 Args: 2209 inputs: A list of `Tensor` objects, each with same shape and type. 2210 shape: Shape of elements of `inputs`. 2211 tensor_dtype: The type of `inputs`. 2212 name: A name for the operation (optional). 2213 2214 Returns: 2215 A `Tensor` of same shape and type as the elements of `inputs`. 2216 2217 Raises: 2218 ValueError: If `inputs` don't all have same shape and dtype or the shape 2219 cannot be inferred. 2220 """ 2221 if context.in_eager_mode(): 2222 # TODO(apassos) remove this once the lifetime of eager variables gets 2223 # addressed. 2224 raise ValueError("accumulate_n not supported in eager mode") 2225 if not inputs or not isinstance(inputs, (list, tuple)): 2226 raise ValueError("inputs must be a list of at least one Tensor with the " 2227 "same dtype and shape") 2228 inputs = ops.convert_n_to_tensor_or_indexed_slices(inputs) 2229 if not all(isinstance(x, ops.Tensor) for x in inputs): 2230 raise ValueError("inputs must be a list of at least one Tensor with the " 2231 "same dtype and shape") 2232 if not all(x.dtype == inputs[0].dtype for x in inputs): 2233 raise ValueError("inputs must be a list of at least one Tensor with the " 2234 "same dtype and shape") 2235 if shape is not None: 2236 shape = tensor_shape.as_shape(shape) 2237 else: 2238 shape = tensor_shape.unknown_shape() 2239 for input_tensor in inputs: 2240 if isinstance(input_tensor, ops.Tensor): 2241 shape = shape.merge_with(input_tensor.get_shape()) 2242 if tensor_dtype is None: 2243 tensor_dtype = inputs[0].dtype 2244 if tensor_dtype != inputs[0].dtype: 2245 raise TypeError("tensor_dtype is {}, but input is of type {}".format( 2246 tensor_dtype, inputs[0].dtype)) 2247 if len(inputs) == 1: 2248 return inputs[0] 2249 with ops.name_scope(name, "AccumulateN", inputs) as name: 2250 var = gen_state_ops._temporary_variable( 2251 shape=tensor_shape.vector(0), dtype=tensor_dtype) 2252 with ops.colocate_with(var): 2253 zeros = array_ops.zeros_like(gen_control_flow_ops._merge(inputs)[0]) 2254 zeros.set_shape(shape) 2255 ref = state_ops.assign(var, zeros, validate_shape=False) 2256 update_ops = [ 2257 state_ops.assign_add(ref, input_tensor, use_locking=True) 2258 for input_tensor in inputs 2259 ] 2260 with ops.control_dependencies(update_ops): 2261 return gen_state_ops._destroy_temporary_variable( 2262 ref, var_name=var.op.name, name=name) 2263 2264 2265 @tf_export("nn.sigmoid", "sigmoid") 2266 def sigmoid(x, name=None): 2267 """Computes sigmoid of `x` element-wise. 2268 2269 Specifically, `y = 1 / (1 + exp(-x))`. 2270 2271 Args: 2272 x: A Tensor with type `float16`, `float32`, `float64`, `complex64`, 2273 or `complex128`. 2274 name: A name for the operation (optional). 2275 2276 Returns: 2277 A Tensor with the same type as `x`. 2278 2279 @compatibility(numpy) 2280 Equivalent to np.scipy.special.expit 2281 @end_compatibility 2282 """ 2283 with ops.name_scope(name, "Sigmoid", [x]) as name: 2284 x = ops.convert_to_tensor(x, name="x") 2285 return gen_math_ops._sigmoid(x, name=name) 2286 2287 2288 @tf_export("log_sigmoid") 2289 def log_sigmoid(x, name=None): 2290 """Computes log sigmoid of `x` element-wise. 2291 2292 Specifically, `y = log(1 / (1 + exp(-x)))`. For numerical stability, 2293 we use `y = -tf.nn.softplus(-x)`. 2294 2295 Args: 2296 x: A Tensor with type `float32` or `float64`. 2297 name: A name for the operation (optional). 2298 2299 Returns: 2300 A Tensor with the same type as `x`. 2301 """ 2302 with ops.name_scope(name, "LogSigmoid", [x]) as name: 2303 x = ops.convert_to_tensor(x, name="x") 2304 return gen_math_ops._neg(gen_nn_ops.softplus(-x), name=name) 2305 2306 2307 @tf_export("nn.tanh", "tanh") 2308 def tanh(x, name=None): 2309 """Computes hyperbolic tangent of `x` element-wise. 2310 2311 Args: 2312 x: A Tensor or SparseTensor with type `float16`, `float32`, `double`, 2313 `complex64`, or `complex128`. 2314 name: A name for the operation (optional). 2315 2316 Returns: 2317 A Tensor or SparseTensor respectively with the same type as `x`. 2318 """ 2319 with ops.name_scope(name, "Tanh", [x]) as name: 2320 if isinstance(x, sparse_tensor.SparseTensor): 2321 x_tanh = gen_math_ops._tanh(x.values, name=name) 2322 return sparse_tensor.SparseTensor( 2323 indices=x.indices, values=x_tanh, dense_shape=x.dense_shape) 2324 else: 2325 return gen_math_ops._tanh(x, name=name) 2326 2327 2328 @tf_export("bincount") 2329 def bincount(arr, 2330 weights=None, 2331 minlength=None, 2332 maxlength=None, 2333 dtype=dtypes.int32): 2334 """Counts the number of occurrences of each value in an integer array. 2335 2336 If `minlength` and `maxlength` are not given, returns a vector with length 2337 `tf.reduce_max(arr) + 1` if `arr` is non-empty, and length 0 otherwise. 2338 If `weights` are non-None, then index `i` of the output stores the sum of the 2339 value in `weights` at each index where the corresponding value in `arr` is 2340 `i`. 2341 2342 Args: 2343 arr: An int32 tensor of non-negative values. 2344 weights: If non-None, must be the same shape as arr. For each value in 2345 `arr`, the bin will be incremented by the corresponding weight instead 2346 of 1. 2347 minlength: If given, ensures the output has length at least `minlength`, 2348 padding with zeros at the end if necessary. 2349 maxlength: If given, skips values in `arr` that are equal or greater than 2350 `maxlength`, ensuring that the output has length at most `maxlength`. 2351 dtype: If `weights` is None, determines the type of the output bins. 2352 2353 Returns: 2354 A vector with the same dtype as `weights` or the given `dtype`. The bin 2355 values. 2356 """ 2357 arr = ops.convert_to_tensor(arr, name="arr", dtype=dtypes.int32) 2358 array_is_nonempty = reduce_prod(array_ops.shape(arr)) > 0 2359 output_size = cast(array_is_nonempty, dtypes.int32) * (reduce_max(arr) + 1) 2360 if minlength is not None: 2361 minlength = ops.convert_to_tensor( 2362 minlength, name="minlength", dtype=dtypes.int32) 2363 output_size = gen_math_ops.maximum(minlength, output_size) 2364 if maxlength is not None: 2365 maxlength = ops.convert_to_tensor( 2366 maxlength, name="maxlength", dtype=dtypes.int32) 2367 output_size = gen_math_ops.minimum(maxlength, output_size) 2368 if weights is not None: 2369 weights = ops.convert_to_tensor(weights, name="weights") 2370 return gen_math_ops.unsorted_segment_sum(weights, arr, output_size) 2371 weights = constant_op.constant([], dtype) 2372 return gen_math_ops.bincount(arr, output_size, weights) 2373 2374 2375 @tf_export("cumsum") 2376 def cumsum(x, axis=0, exclusive=False, reverse=False, name=None): 2377 """Compute the cumulative sum of the tensor `x` along `axis`. 2378 2379 By default, this op performs an inclusive cumsum, which means that the first 2380 element of the input is identical to the first element of the output: 2381 2382 ```python 2383 tf.cumsum([a, b, c]) # [a, a + b, a + b + c] 2384 ``` 2385 2386 By setting the `exclusive` kwarg to `True`, an exclusive cumsum is performed 2387 instead: 2388 2389 ```python 2390 tf.cumsum([a, b, c], exclusive=True) # [0, a, a + b] 2391 ``` 2392 2393 By setting the `reverse` kwarg to `True`, the cumsum is performed in the 2394 opposite direction: 2395 2396 ```python 2397 tf.cumsum([a, b, c], reverse=True) # [a + b + c, b + c, c] 2398 ``` 2399 2400 This is more efficient than using separate `tf.reverse` ops. 2401 2402 The `reverse` and `exclusive` kwargs can also be combined: 2403 2404 ```python 2405 tf.cumsum([a, b, c], exclusive=True, reverse=True) # [b + c, c, 0] 2406 ``` 2407 2408 Args: 2409 x: A `Tensor`. Must be one of the following types: `float32`, `float64`, 2410 `int64`, `int32`, `uint8`, `uint16`, `int16`, `int8`, `complex64`, 2411 `complex128`, `qint8`, `quint8`, `qint32`, `half`. 2412 axis: A `Tensor` of type `int32` (default: 0). Must be in the range 2413 `[-rank(x), rank(x))`. 2414 exclusive: If `True`, perform exclusive cumsum. 2415 reverse: A `bool` (default: False). 2416 name: A name for the operation (optional). 2417 2418 Returns: 2419 A `Tensor`. Has the same type as `x`. 2420 """ 2421 with ops.name_scope(name, "Cumsum", [x]) as name: 2422 x = ops.convert_to_tensor(x, name="x") 2423 return gen_math_ops.cumsum( 2424 x, axis, exclusive=exclusive, reverse=reverse, name=name) 2425 2426 2427 @tf_export("cumprod") 2428 def cumprod(x, axis=0, exclusive=False, reverse=False, name=None): 2429 """Compute the cumulative product of the tensor `x` along `axis`. 2430 2431 By default, this op performs an inclusive cumprod, which means that the 2432 first element of the input is identical to the first element of the output: 2433 2434 ```python 2435 tf.cumprod([a, b, c]) # [a, a * b, a * b * c] 2436 ``` 2437 2438 By setting the `exclusive` kwarg to `True`, an exclusive cumprod is 2439 performed 2440 instead: 2441 2442 ```python 2443 tf.cumprod([a, b, c], exclusive=True) # [1, a, a * b] 2444 ``` 2445 2446 By setting the `reverse` kwarg to `True`, the cumprod is performed in the 2447 opposite direction: 2448 2449 ```python 2450 tf.cumprod([a, b, c], reverse=True) # [a * b * c, b * c, c] 2451 ``` 2452 2453 This is more efficient than using separate `tf.reverse` ops. 2454 The `reverse` and `exclusive` kwargs can also be combined: 2455 2456 ```python 2457 tf.cumprod([a, b, c], exclusive=True, reverse=True) # [b * c, c, 1] 2458 ``` 2459 2460 Args: 2461 x: A `Tensor`. Must be one of the following types: `float32`, `float64`, 2462 `int64`, `int32`, `uint8`, `uint16`, `int16`, `int8`, `complex64`, 2463 `complex128`, `qint8`, `quint8`, `qint32`, `half`. 2464 axis: A `Tensor` of type `int32` (default: 0). Must be in the range 2465 `[-rank(x), rank(x))`. 2466 exclusive: If `True`, perform exclusive cumprod. 2467 reverse: A `bool` (default: False). 2468 name: A name for the operation (optional). 2469 2470 Returns: 2471 A `Tensor`. Has the same type as `x`. 2472 """ 2473 with ops.name_scope(name, "Cumprod", [x]) as name: 2474 x = ops.convert_to_tensor(x, name="x") 2475 return gen_math_ops.cumprod( 2476 x, axis, exclusive=exclusive, reverse=reverse, name=name) 2477 2478 2479 @tf_export("conj") 2480 def conj(x, name=None): 2481 r"""Returns the complex conjugate of a complex number. 2482 2483 Given a tensor `input` of complex numbers, this operation returns a tensor of 2484 complex numbers that are the complex conjugate of each element in `input`. The 2485 complex numbers in `input` must be of the form \\(a + bj\\), where *a* is the 2486 real part and *b* is the imaginary part. 2487 2488 The complex conjugate returned by this operation is of the form \\(a - bj\\). 2489 2490 For example: 2491 2492 # tensor 'input' is [-2.25 + 4.75j, 3.25 + 5.75j] 2493 tf.conj(input) ==> [-2.25 - 4.75j, 3.25 - 5.75j] 2494 2495 If `x` is real, it is returned unchanged. 2496 2497 Args: 2498 x: `Tensor` to conjugate. Must have numeric or variant type. 2499 name: A name for the operation (optional). 2500 2501 Returns: 2502 A `Tensor` that is the conjugate of `x` (with the same type). 2503 2504 Raises: 2505 TypeError: If `x` is not a numeric tensor. 2506 """ 2507 if isinstance(x, ops.Tensor): 2508 dt = x.dtype 2509 if dt.is_floating or dt.is_integer: 2510 return x 2511 with ops.name_scope(name, "Conj", [x]) as name: 2512 x = ops.convert_to_tensor(x, name="x") 2513 if x.dtype.is_complex or x.dtype == dtypes.variant: 2514 return gen_math_ops._conj(x, name=name) 2515 elif x.dtype.is_floating or x.dtype.is_integer: 2516 return x 2517 else: 2518 raise TypeError( 2519 "Expected numeric or variant tensor, got dtype %r" % x.dtype) 2520 2521 2522 def _BroadcastShape(op): 2523 """Common shape function for binary operators that broadcast their inputs.""" 2524 return [ 2525 common_shapes.broadcast_shape(op.inputs[0].get_shape(), 2526 op.inputs[1].get_shape()) 2527 ] 2528 2529 2530 def reduced_shape(input_shape, axes): 2531 """Helper function for reduction ops. 2532 2533 Args: 2534 input_shape: 1-D Tensor, the shape of the Tensor being reduced. 2535 axes: 1-D Tensor, the reduction axes. 2536 Returns: 2537 A 1-D Tensor, the output shape as if keepdims were set to True. 2538 """ 2539 # Example: 2540 # cast needed for SparseTensor reductions 2541 input_shape = to_int32(input_shape) # [2, 3, 5, 7] 2542 axes = to_int32(axes) # [1, 2] 2543 2544 input_rank = array_ops.size(input_shape) # 4 2545 axes = (axes + input_rank) % input_rank 2546 axes_shape = array_ops.shape(axes) # [2] 2547 return gen_data_flow_ops.dynamic_stitch( # [2, 1, 1, 7] 2548 [ 2549 range(input_rank), # [0, 1, 2, 3] 2550 axes 2551 ], # [1, 2] 2552 [ 2553 input_shape, # [2, 3, 5, 7] 2554 array_ops.fill(axes_shape, 1) 2555 ]) # [1, 1] 2556 2557 2558 def _unsorted_segment_N(data, segment_ids, num_segments): 2559 """ Helper function for unsorted_segment_mean/_sqrtN. Computes the number 2560 of segment entries with 0-entries set to 1 to allow division by N. 2561 """ 2562 # bincount doesn't support negative indices so we use unsorted_segment_sum 2563 ones_tensor = array_ops.ones(segment_ids.shape, dtype=data.dtype) 2564 N = gen_math_ops.unsorted_segment_sum(ones_tensor, segment_ids, num_segments) 2565 # add dimensions for all non-reduced axes 2566 ndims_output = data.shape.ndims - segment_ids.shape.ndims 2567 broadcast_shape = [num_segments] + [1] * ndims_output 2568 N = array_ops.reshape(N, broadcast_shape) 2569 return gen_math_ops.maximum(N, 1) 2570 2571 2572 @tf_export("unsorted_segment_mean") 2573 def unsorted_segment_mean(data, segment_ids, num_segments, name=None): 2574 r""" Computes the mean along segments of a tensor. 2575 2576 Read @{$math_ops#segmentation$the section on segmentation} for an explanation 2577 of segments. 2578 2579 This operator is similar to the unsorted segment sum operator found 2580 [here](../../../api_docs/python/math_ops.md#UnsortedSegmentSum). 2581 Instead of computing the sum over segments, it computes the mean of all 2582 entries belonging to a segment such that: 2583 2584 \\(output_i = 1/N_i \sum data_j\\) where the sum is over `j` such 2585 that `segment_ids[j] == i` with \\N_i\\ being the number of occurrences 2586 of id \\i\\. 2587 2588 If there is no entry for a given segment ID `i`, it outputs 0. 2589 2590 segment_ids: A 1-D tensor whose rank is equal to the rank of `data`'s 2591 first dimension. 2592 2593 output: Has same shape as data, except for dimension 0 which 2594 has size `num_segments`. 2595 """ 2596 with ops.name_scope(name, "UnsortedSegmentMean"): 2597 data = ops.convert_to_tensor(data) 2598 segment_ids = ops.convert_to_tensor(segment_ids) 2599 N = _unsorted_segment_N(data, segment_ids, num_segments) 2600 summed = gen_math_ops.unsorted_segment_sum(data, segment_ids, num_segments) 2601 return summed / N 2602 2603 2604 @tf_export("unsorted_segment_sqrt_n") 2605 def unsorted_segment_sqrt_n(data, segment_ids, num_segments, name=None): 2606 r"""Computes the sum along segments of a tensor divided by the sqrt(N). 2607 2608 Read @{$math_ops#segmentation$the section on segmentation} for an explanation 2609 of segments. 2610 2611 This operator is similar to the unsorted segment sum operator found 2612 [here](../../../api_docs/python/math_ops.md#UnsortedSegmentSum). 2613 Additionally to computing the sum over segments, it divides the results by 2614 sqrt(N). 2615 2616 \\(output_i = 1/sqrt(N_i) \sum data_j\\) where the sum is over `j` such 2617 that `segment_ids[j] == i` with \\N_i\\ being the number of occurrences 2618 of id \\i\\. 2619 2620 If there is no entry for a given segment ID `i`, it outputs 0. 2621 2622 Note that this op only supports floating point and complex dtypes, 2623 due to tf.sqrt only supporting these types. 2624 2625 segment_ids: A 1-D tensor whose rank is equal to the rank of `data`'s 2626 first dimension. 2627 2628 output: Has same shape as data, except for dimension 0 which 2629 has size `num_segments`. 2630 """ 2631 with ops.name_scope(name, "UnsortedSegmentSqrtN"): 2632 data = ops.convert_to_tensor(data) 2633 segment_ids = ops.convert_to_tensor(segment_ids) 2634 N = _unsorted_segment_N(data, segment_ids, num_segments) 2635 summed = gen_math_ops.unsorted_segment_sum(data, segment_ids, num_segments) 2636 return summed / gen_math_ops.sqrt(N) 2637 2638 2639 @tf_export("sparse_segment_sum") 2640 def sparse_segment_sum(data, indices, segment_ids, name=None, 2641 num_segments=None): 2642 r"""Computes the sum along sparse segments of a tensor. 2643 2644 Read @{$math_ops#Segmentation$the section on segmentation} for an explanation 2645 of segments. 2646 2647 Like `SegmentSum`, but `segment_ids` can have rank less than `data`'s first 2648 dimension, selecting a subset of dimension 0, specified by `indices`. 2649 `segment_ids` is allowed to have missing ids, in which case the output will 2650 be zeros at those indices. In those cases `num_segments` is used to determine 2651 the size of the output. 2652 2653 For example: 2654 2655 ```python 2656 c = tf.constant([[1,2,3,4], [-1,-2,-3,-4], [5,6,7,8]]) 2657 2658 # Select two rows, one segment. 2659 tf.sparse_segment_sum(c, tf.constant([0, 1]), tf.constant([0, 0])) 2660 # => [[0 0 0 0]] 2661 2662 # Select two rows, two segment. 2663 tf.sparse_segment_sum(c, tf.constant([0, 1]), tf.constant([0, 1])) 2664 # => [[ 1 2 3 4] 2665 # [-1 -2 -3 -4]] 2666 2667 # With missing segment ids. 2668 tf.sparse_segment_sum(c, tf.constant([0, 1]), tf.constant([0, 2]), 2669 num_segments=4) 2670 # => [[ 1 2 3 4] 2671 # [ 0 0 0 0] 2672 # [-1 -2 -3 -4] 2673 # [ 0 0 0 0]] 2674 2675 # Select all rows, two segments. 2676 tf.sparse_segment_sum(c, tf.constant([0, 1, 2]), tf.constant([0, 0, 1])) 2677 # => [[0 0 0 0] 2678 # [5 6 7 8]] 2679 2680 # Which is equivalent to: 2681 tf.segment_sum(c, tf.constant([0, 0, 1])) 2682 ``` 2683 2684 Args: 2685 data: A `Tensor` with data that will be assembled in the output. 2686 indices: A 1-D `Tensor` with indices into `data`. Has same rank as 2687 `segment_ids`. 2688 segment_ids: A 1-D `Tensor` with indices into the output `Tensor`. 2689 Values should be sorted and can be repeated. 2690 name: A name for the operation (optional). 2691 num_segments: An optional int32 scalar. Indicates the size of the output 2692 `Tensor`. 2693 2694 Returns: 2695 A `tensor` of the shape as data, except for dimension 0 which 2696 has size `k`, the number of segments specified via `num_segments` or 2697 inferred for the last element in `segments_ids`. 2698 """ 2699 if num_segments is not None: 2700 return gen_math_ops.sparse_segment_sum_with_num_segments( 2701 data=data, 2702 indices=indices, 2703 segment_ids=segment_ids, 2704 num_segments=num_segments, 2705 name=name) 2706 else: 2707 return gen_math_ops.sparse_segment_sum( 2708 data=data, 2709 indices=indices, 2710 segment_ids=segment_ids, 2711 name=name) 2712 2713 2714 @tf_export("sparse_segment_mean") 2715 def sparse_segment_mean(data, indices, segment_ids, name=None, 2716 num_segments=None): 2717 r"""Computes the mean along sparse segments of a tensor. 2718 2719 Read @{$math_ops#Segmentation$the section on segmentation} for an explanation 2720 of segments. 2721 2722 Like `SegmentMean`, but `segment_ids` can have rank less than `data`'s first 2723 dimension, selecting a subset of dimension 0, specified by `indices`. 2724 `segment_ids` is allowed to have missing ids, in which case the output will 2725 be zeros at those indices. In those cases `num_segments` is used to determine 2726 the size of the output. 2727 2728 Args: 2729 data: A `Tensor` with data that will be assembled in the output. 2730 indices: A 1-D `Tensor` with indices into `data`. Has same rank as 2731 `segment_ids`. 2732 segment_ids: A 1-D `Tensor` with indices into the output `Tensor`. 2733 Values should be sorted and can be repeated. 2734 name: A name for the operation (optional). 2735 num_segments: An optional int32 scalar. Indicates the size of the output 2736 `Tensor`. 2737 2738 Returns: 2739 A `tensor` of the shape as data, except for dimension 0 which 2740 has size `k`, the number of segments specified via `num_segments` or 2741 inferred for the last element in `segments_ids`. 2742 """ 2743 if num_segments is not None: 2744 return gen_math_ops.sparse_segment_mean_with_num_segments( 2745 data=data, 2746 indices=indices, 2747 segment_ids=segment_ids, 2748 num_segments=num_segments, 2749 name=name) 2750 else: 2751 return gen_math_ops.sparse_segment_mean( 2752 data=data, 2753 indices=indices, 2754 segment_ids=segment_ids, 2755 name=name) 2756 2757 2758 @tf_export("sparse_segment_sqrt_n") 2759 def sparse_segment_sqrt_n(data, indices, segment_ids, name=None, 2760 num_segments=None): 2761 r"""Computes the sum along sparse segments of a tensor divided by the sqrt(N). 2762 2763 `N` is the size of the segment being reduced. 2764 2765 Args: 2766 data: A `Tensor` with data that will be assembled in the output. 2767 indices: A 1-D `Tensor` with indices into `data`. Has same rank as 2768 `segment_ids`. 2769 segment_ids: A 1-D `Tensor` with indices into the output `Tensor`. 2770 Values should be sorted and can be repeated. 2771 name: A name for the operation (optional). 2772 num_segments: An optional int32 scalar. Indicates the size of the output 2773 `Tensor`. 2774 2775 Returns: 2776 A `tensor` of the shape as data, except for dimension 0 which 2777 has size `k`, the number of segments specified via `num_segments` or 2778 inferred for the last element in `segments_ids`. 2779 """ 2780 if num_segments is not None: 2781 return gen_math_ops.sparse_segment_sqrt_n_with_num_segments( 2782 data=data, 2783 indices=indices, 2784 segment_ids=segment_ids, 2785 num_segments=num_segments, 2786 name=name) 2787 else: 2788 return gen_math_ops.sparse_segment_sqrt_n( 2789 data=data, 2790 indices=indices, 2791 segment_ids=segment_ids, 2792 name=name) 2793 2794 2795 @tf_export("tensordot", "linalg.tensordot") 2796 def tensordot(a, b, axes, name=None): 2797 r"""Tensor contraction of a and b along specified axes. 2798 2799 Tensordot (also known as tensor contraction) sums the product of elements 2800 from `a` and `b` over the indices specified by `a_axes` and `b_axes`. 2801 The lists `a_axes` and `b_axes` specify those pairs of axes along which to 2802 contract the tensors. The axis `a_axes[i]` of `a` must have the same dimension 2803 as axis `b_axes[i]` of `b` for all `i` in `range(0, len(a_axes))`. The lists 2804 `a_axes` and `b_axes` must have identical length and consist of unique 2805 integers that specify valid axes for each of the tensors. 2806 2807 This operation corresponds to `numpy.tensordot(a, b, axes)`. 2808 2809 Example 1: When `a` and `b` are matrices (order 2), the case `axes = 1` 2810 is equivalent to matrix multiplication. 2811 2812 Example 2: When `a` and `b` are matrices (order 2), the case 2813 `axes = [[1], [0]]` is equivalent to matrix multiplication. 2814 2815 Example 3: Suppose that \\(a_{ijk}\\) and \\(b_{lmn}\\) represent two 2816 tensors of order 3. Then, `contract(a, b, [[0], [2]])` is the order 4 tensor 2817 \\(c_{jklm}\\) whose entry 2818 corresponding to the indices \\((j,k,l,m)\\) is given by: 2819 2820 \\( c_{jklm} = \sum_i a_{ijk} b_{lmi} \\). 2821 2822 In general, `order(c) = order(a) + order(b) - 2*len(axes[0])`. 2823 2824 Args: 2825 a: `Tensor` of type `float32` or `float64`. 2826 b: `Tensor` with the same type as `a`. 2827 axes: Either a scalar `N`, or a list or an `int32` `Tensor` of shape [2, k]. 2828 If axes is a scalar, sum over the last N axes of a and the first N axes 2829 of b in order. 2830 If axes is a list or `Tensor` the first and second row contain the set of 2831 unique integers specifying axes along which the contraction is computed, 2832 for `a` and `b`, respectively. The number of axes for `a` and `b` must 2833 be equal. 2834 name: A name for the operation (optional). 2835 2836 Returns: 2837 A `Tensor` with the same type as `a`. 2838 2839 Raises: 2840 ValueError: If the shapes of `a`, `b`, and `axes` are incompatible. 2841 IndexError: If the values in axes exceed the rank of the corresponding 2842 tensor. 2843 """ 2844 2845 def _tensordot_reshape(a, axes, flipped=False): 2846 """Helper method to perform transpose and reshape for contraction op. 2847 2848 This method is helpful in reducing `math_ops.tensordot` to `math_ops.matmul` 2849 using `array_ops.transpose` and `array_ops.reshape`. The method takes a 2850 tensor and performs the correct transpose and reshape operation for a given 2851 set of indices. It returns the reshaped tensor as well as a list of indices 2852 necessary to reshape the tensor again after matrix multiplication. 2853 2854 Args: 2855 a: `Tensor`. 2856 axes: List or `int32` `Tensor` of unique indices specifying valid axes of 2857 `a`. 2858 flipped: An optional `bool`. Defaults to `False`. If `True`, the method 2859 assumes that `a` is the second argument in the contraction operation. 2860 2861 Returns: 2862 A tuple `(reshaped_a, free_dims, free_dims_static)` where `reshaped_a` is 2863 the tensor `a` reshaped to allow contraction via `matmul`, `free_dims` is 2864 either a list of integers or an `int32` `Tensor`, depending on whether 2865 the shape of a is fully specified, and free_dims_static is either a list 2866 of integers and None values, or None, representing the inferred 2867 static shape of the free dimensions 2868 """ 2869 if a.get_shape().is_fully_defined() and isinstance(axes, (list, tuple)): 2870 shape_a = a.get_shape().as_list() 2871 axes = [i if i >= 0 else i + len(shape_a) for i in axes] 2872 free = [i for i in xrange(len(shape_a)) if i not in axes] 2873 free_dims = [shape_a[i] for i in free] 2874 prod_free = int(np.prod([shape_a[i] for i in free])) 2875 prod_axes = int(np.prod([shape_a[i] for i in axes])) 2876 perm = list(axes) + free if flipped else free + list(axes) 2877 new_shape = [prod_axes, prod_free] if flipped else [prod_free, prod_axes] 2878 reshaped_a = array_ops.reshape(array_ops.transpose(a, perm), new_shape) 2879 return reshaped_a, free_dims, free_dims 2880 else: 2881 if a.get_shape().ndims is not None and isinstance(axes, (list, tuple)): 2882 shape_a = a.get_shape().as_list() 2883 axes = [i if i >= 0 else i + len(shape_a) for i in axes] 2884 free = [i for i in xrange(len(shape_a)) if i not in axes] 2885 free_dims_static = [shape_a[i] for i in free] 2886 else: 2887 free_dims_static = None 2888 shape_a = array_ops.shape(a) 2889 rank_a = array_ops.rank(a) 2890 axes = ops.convert_to_tensor(axes, dtype=dtypes.int32, name="axes") 2891 axes = cast(axes >= 0, dtypes.int32) * axes + cast( 2892 axes < 0, dtypes.int32) * ( 2893 axes + rank_a) 2894 free, _ = array_ops.setdiff1d(range(rank_a), axes) 2895 free_dims = array_ops.gather(shape_a, free) 2896 axes_dims = array_ops.gather(shape_a, axes) 2897 prod_free_dims = reduce_prod(free_dims) 2898 prod_axes_dims = reduce_prod(axes_dims) 2899 perm = array_ops.concat([axes_dims, free_dims], 0) 2900 if flipped: 2901 perm = array_ops.concat([axes, free], 0) 2902 new_shape = array_ops.stack([prod_axes_dims, prod_free_dims]) 2903 else: 2904 perm = array_ops.concat([free, axes], 0) 2905 new_shape = array_ops.stack([prod_free_dims, prod_axes_dims]) 2906 reshaped_a = array_ops.reshape(array_ops.transpose(a, perm), new_shape) 2907 return reshaped_a, free_dims, free_dims_static 2908 2909 def _tensordot_axes(a, axes): 2910 """Generates two sets of contraction axes for the two tensor arguments.""" 2911 a_shape = a.get_shape() 2912 if isinstance(axes, compat.integral_types): 2913 if axes < 0: 2914 raise ValueError("'axes' must be at least 0.") 2915 if a_shape.ndims is not None: 2916 if axes > a_shape.ndims: 2917 raise ValueError("'axes' must not be larger than the number of " 2918 "dimensions of tensor %s." % a) 2919 return (list(xrange(a_shape.ndims - axes, a_shape.ndims)), 2920 list(xrange(axes))) 2921 else: 2922 rank = array_ops.rank(a) 2923 return (range(rank - axes, rank, dtype=dtypes.int32), 2924 range(axes, dtype=dtypes.int32)) 2925 elif isinstance(axes, (list, tuple)): 2926 if len(axes) != 2: 2927 raise ValueError("'axes' must be an integer or have length 2.") 2928 a_axes = axes[0] 2929 b_axes = axes[1] 2930 if isinstance(a_axes, compat.integral_types) and \ 2931 isinstance(b_axes, compat.integral_types): 2932 a_axes = [a_axes] 2933 b_axes = [b_axes] 2934 if len(a_axes) != len(b_axes): 2935 raise ValueError( 2936 "Different number of contraction axes 'a' and 'b', %s != %s." % 2937 (len(a_axes), len(b_axes))) 2938 return a_axes, b_axes 2939 else: 2940 axes = ops.convert_to_tensor(axes, name="axes", dtype=dtypes.int32) 2941 return axes[0], axes[1] 2942 2943 with ops.name_scope(name, "Tensordot", [a, b, axes]) as name: 2944 a = ops.convert_to_tensor(a, name="a") 2945 b = ops.convert_to_tensor(b, name="b") 2946 a_axes, b_axes = _tensordot_axes(a, axes) 2947 a_reshape, a_free_dims, a_free_dims_static = _tensordot_reshape(a, a_axes) 2948 b_reshape, b_free_dims, b_free_dims_static = _tensordot_reshape( 2949 b, b_axes, True) 2950 ab_matmul = matmul(a_reshape, b_reshape) 2951 if isinstance(a_free_dims, list) and isinstance(b_free_dims, list): 2952 return array_ops.reshape(ab_matmul, a_free_dims + b_free_dims, name=name) 2953 else: 2954 a_free_dims = ops.convert_to_tensor(a_free_dims, dtype=dtypes.int32) 2955 b_free_dims = ops.convert_to_tensor(b_free_dims, dtype=dtypes.int32) 2956 product = array_ops.reshape( 2957 ab_matmul, array_ops.concat([a_free_dims, b_free_dims], 0), name=name) 2958 if a_free_dims_static is not None and b_free_dims_static is not None: 2959 product.set_shape(a_free_dims_static + b_free_dims_static) 2960 return product 2961 2962 2963 # FFT ops were moved to tf.spectral. tf.fft symbols were part of the TensorFlow 2964 # 1.0 API so we leave these here for backwards compatibility. 2965 fft = gen_spectral_ops.fft 2966 ifft = gen_spectral_ops.ifft 2967 fft2d = gen_spectral_ops.fft2d 2968 ifft2d = gen_spectral_ops.ifft2d 2969 fft3d = gen_spectral_ops.fft3d 2970 ifft3d = gen_spectral_ops.ifft3d 2971
