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math_ops.cc
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math_ops.cc
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/* Copyright 2015 The TensorFlow Authors. All Rights Reserved.
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
==============================================================================*/
#include "tensorflow/core/framework/common_shape_fns.h"
#include "tensorflow/core/framework/numeric_op.h"
#include "tensorflow/core/framework/op.h"
#include "tensorflow/core/framework/shape_inference.h"
namespace tensorflow {
using shape_inference::DimensionHandle;
using shape_inference::InferenceContext;
using shape_inference::ShapeHandle;
REGISTER_OP("AddN")
.Input("inputs: N * T")
.Output("sum: T")
.Attr("N: int >= 1")
.Attr("T: numbertype")
.SetIsCommutative()
.SetIsAggregate()
.SetShapeFn([](InferenceContext* c) {
ShapeHandle cur = c->input(c->num_inputs() - 1);
for (int i = c->num_inputs() - 2; i >= 0; --i) {
TF_RETURN_WITH_CONTEXT_IF_ERROR(c->Merge(c->input(i), cur, &cur),
"From merging shape ", i,
" with other shapes.");
}
c->set_output(0, cur);
return Status::OK();
})
.Doc(R"doc(
Add all input tensors element wise.
inputs: Must all be the same size and shape.
)doc");
// --------------------------------------------------------------------------
REGISTER_OP("BatchMatMul")
.Input("x: T")
.Input("y: T")
.Output("output: T")
.Attr("T: {half, float, double, int32, complex64, complex128}")
.Attr("adj_x: bool = false")
.Attr("adj_y: bool = false")
.SetShapeFn([](InferenceContext* c) {
ShapeHandle a_shape;
ShapeHandle b_shape;
TF_RETURN_IF_ERROR(c->WithRankAtLeast(c->input(0), 2, &a_shape));
TF_RETURN_IF_ERROR(c->WithRankAtLeast(c->input(1), 2, &b_shape));
// Determine output rows and cols.
bool adj_x;
bool adj_y;
TF_RETURN_IF_ERROR(c->GetAttr("adj_x", &adj_x));
TF_RETURN_IF_ERROR(c->GetAttr("adj_y", &adj_y));
DimensionHandle output_rows = c->Dim(a_shape, adj_x ? -1 : -2);
DimensionHandle output_cols = c->Dim(b_shape, adj_y ? -2 : -1);
// Batch dims match between inputs.
ShapeHandle a_batch_dims;
ShapeHandle b_batch_dims;
ShapeHandle batch_dims;
TF_RETURN_IF_ERROR(c->Subshape(a_shape, 0, -2, &a_batch_dims));
TF_RETURN_IF_ERROR(c->Subshape(b_shape, 0, -2, &b_batch_dims));
TF_RETURN_IF_ERROR(c->Merge(a_batch_dims, b_batch_dims, &batch_dims));
// Assert inner dims match.
DimensionHandle unused;
TF_RETURN_IF_ERROR(c->Merge(c->Dim(a_shape, adj_x ? -2 : -1),
c->Dim(b_shape, adj_y ? -1 : -2), &unused));
ShapeHandle out;
TF_RETURN_IF_ERROR(c->Concatenate(
batch_dims, c->Matrix(output_rows, output_cols), &out));
c->set_output(0, out);
return Status::OK();
})
.Doc(R"doc(
Multiplies slices of two tensors in batches.
Multiplies all slices of `Tensor` `x` and `y` (each slice can be
viewed as an element of a batch), and arranges the individual results
in a single output tensor of the same batch size. Each of the
individual slices can optionally be adjointed (to adjoint a matrix
means to transpose and conjugate it) before multiplication by setting
the `adj_x` or `adj_y` flag to `True`, which are by default `False`.
The input tensors `x` and `y` are 3-D or higher with shape `[..., r_x, c_x]`
and `[..., r_y, c_y]`.
The output tensor is 3-D or higher with shape `[..., r_o, c_o]`, where:
r_o = c_x if adj_x else r_x
c_o = r_y if adj_y else c_y
It is computed as:
output[..., :, :] = matrix(x[..., :, :]) * matrix(y[..., :, :])
x: 3-D or higher with shape `[..., r_x, c_x]`.
y: 3-D or higher with shape `[..., r_y, c_y]`.
output: 3-D or higher with shape `[..., r_o, c_o]`
adj_x: If `True`, adjoint the slices of `x`. Defaults to `False`.
adj_y: If `True`, adjoint the slices of `y`. Defaults to `False`.
)doc");
// --------------------------------------------------------------------------
// Casting Ops
//
// NOTE: Only a smaller number of types are supported by
// Cast. The exact casting rule is TBD. The current
// implementation uses C++ static cast rules for numeric
// types, which may be changed in the future.
REGISTER_OP("Cast")
.Input("x: SrcT")
.Output("y: DstT")
.Attr("SrcT: type")
.Attr("DstT: type")
.SetShapeFn(shape_inference::UnchangedShape)
.Doc(R"doc(
Cast x of type SrcT to y of DstT.
)doc");
REGISTER_OP("_HostCast")
.Input("x: SrcT")
.Output("y: DstT")
.Attr("SrcT: type")
.Attr("DstT: type")
.SetShapeFn(shape_inference::UnchangedShape)
.Doc(R"doc(
Cast x of type SrcT to y of DstT.
_HostCast requires its input and produces its output in host memory.
)doc");
// --------------------------------------------------------------------------
REGISTER_OP("Abs")
.Input("x: T")
.Output("y: T")
.Attr("T: {half, float, double, int32, int64}")
.SetShapeFn(shape_inference::UnchangedShape)
.Doc(R"doc(
Computes the absolute value of a tensor.
Given a tensor `x`, this operation returns a tensor containing the absolute
value of each element in `x`. For example, if x is an input element and y is
an output element, this operation computes \\(y = |x|\\).
)doc");
REGISTER_OP("ComplexAbs")
.Input("x: T")
.Output("y: Tout")
.Attr("T: {complex64, complex128} = DT_COMPLEX64")
.Attr("Tout: {float, double} = DT_FLOAT")
.SetShapeFn(shape_inference::UnchangedShape)
.Doc(R"doc(
Computes the complex absolute value of a tensor.
Given a tensor `x` of complex numbers, this operation returns a tensor of type
`float` or `double` that is the absolute value of each element in `x`. All
elements in `x` must be complex numbers of the form \\(a + bj\\). The absolute
value is computed as \\( \sqrt{a^2 + b^2}\\).
For example:
```
# tensor 'x' is [[-2.25 + 4.75j], [-3.25 + 5.75j]]
tf.complex_abs(x) ==> [5.25594902, 6.60492229]
```
)doc");
// Declares cwise unary operations signature: 't -> 't
#define UNARY() \
Input("x: T") \
.Output("y: T") \
.Attr("T: {half, float, double, int32, int64, complex64, complex128}") \
.SetShapeFn(shape_inference::UnchangedShape)
#define UNARY_REAL() \
Input("x: T") \
.Output("y: T") \
.Attr("T: {half, float, double}") \
.SetShapeFn(shape_inference::UnchangedShape)
#define UNARY_COMPLEX() \
Input("x: T") \
.Output("y: T") \
.Attr("T: {half, float, double, complex64, complex128}") \
.SetShapeFn(shape_inference::UnchangedShape)
#define UNARY_GRADIENT_COMPLEX() \
Input("x: T") \
.Input("y: T") \
.Output("z: T") \
.Attr("T: {half, float, double, complex64, complex128}") \
.SetShapeFn(shape_inference::UnchangedShape)
REGISTER_OP("Neg")
.UNARY()
.Doc(R"doc(
Computes numerical negative value element-wise.
I.e., \\(y = -x\\).
)doc");
REGISTER_OP("Inv")
.UNARY()
.Doc(R"doc(
Computes the reciprocal of x element-wise.
I.e., \\(y = 1 / x\\).
)doc")
.Deprecated(17, "Use Reciprocal");
REGISTER_OP("InvGrad")
.UNARY_GRADIENT_COMPLEX()
.Doc(R"doc(
Computes the gradient for the inverse of `x` wrt its input.
Specifically, `grad = -dy * y*y`, where `y = 1/x`, and `dy`
is the corresponding input gradient.
)doc")
.Deprecated(17, "Use ReciprocalGrad");
REGISTER_OP("Reciprocal").UNARY().Doc(R"doc(
Computes the reciprocal of x element-wise.
I.e., \\(y = 1 / x\\).
)doc");
REGISTER_OP("ReciprocalGrad").UNARY_GRADIENT_COMPLEX().Doc(R"doc(
Computes the gradient for the inverse of `x` wrt its input.
Specifically, `grad = -dy * y*y`, where `y = 1/x`, and `dy`
is the corresponding input gradient.
)doc");
REGISTER_OP("Square")
.UNARY()
.Doc(R"doc(
Computes square of x element-wise.
I.e., \\(y = x * x = x^2\\).
)doc");
REGISTER_OP("Sqrt")
.UNARY_COMPLEX()
.Doc(R"doc(
Computes square root of x element-wise.
I.e., \\(y = \sqrt{x} = x^{1/2}\\).
)doc");
REGISTER_OP("SqrtGrad").UNARY_GRADIENT_COMPLEX().Doc(R"doc(
Computes the gradient for the sqrt of `x` wrt its input.
Specifically, `grad = dy * 0.5 / y`, where `y = sqrt(x)`, and `dy`
is the corresponding input gradient.
)doc");
REGISTER_OP("Rsqrt")
.UNARY_COMPLEX()
.Doc(R"doc(
Computes reciprocal of square root of x element-wise.
I.e., \\(y = 1 / \sqrt{x}\\).
)doc");
REGISTER_OP("Round").UNARY().Doc(R"doc(
Rounds the values of a tensor to the nearest integer, element-wise.
Rounds half to even. Also known as bankers rounding. If you want to round
according to the current system rounding mode use std::cint.
)doc");
REGISTER_OP("RsqrtGrad").UNARY_GRADIENT_COMPLEX().Doc(R"doc(
Computes the gradient for the rsqrt of `x` wrt its input.
Specifically, `grad = dy * -0.5 * y^3`, where `y = rsqrt(x)`, and `dy`
is the corresponding input gradient.
)doc");
REGISTER_OP("Exp")
.UNARY_COMPLEX()
.Doc(R"doc(
Computes exponential of x element-wise. \\(y = e^x\\).
)doc");
REGISTER_OP("Log")
.UNARY_COMPLEX()
.Doc(R"doc(
Computes natural logarithm of x element-wise.
I.e., \\(y = \log_e x\\).
)doc");
REGISTER_OP("Log1p")
.UNARY_COMPLEX()
.Doc(R"doc(
Computes natural logarithm of (1 + x) element-wise.
I.e., \\(y = \log_e (1 + x)\\).
)doc");
REGISTER_OP("Tanh")
.UNARY_COMPLEX()
.Doc(R"doc(
Computes hyperbolic tangent of `x` element-wise.
)doc");
REGISTER_OP("TanhGrad").UNARY_GRADIENT_COMPLEX().Doc(R"doc(
Computes the gradient for the tanh of `x` wrt its input.
Specifically, `grad = dy * (1 - y*y)`, where `y = tanh(x)`, and `dy`
is the corresponding input gradient.
)doc");
REGISTER_OP("Lgamma")
.UNARY_REAL()
.Doc(R"doc(
Computes the log of the absolute value of `Gamma(x)` element-wise.
)doc");
REGISTER_OP("Digamma")
.UNARY_REAL()
.Doc(R"doc(
Computes Psi, the derivative of Lgamma (the log of the absolute value of
`Gamma(x)`), element-wise.
)doc");
REGISTER_OP("Erf")
.UNARY_REAL()
.Doc(R"doc(
Computes the Gauss error function of `x` element-wise.
)doc");
REGISTER_OP("Erfc")
.UNARY_REAL()
.Doc(R"doc(
Computes the complementary error function of `x` element-wise.
)doc");
REGISTER_OP("Sigmoid")
.UNARY_COMPLEX()
.Doc(R"doc(
Computes sigmoid of `x` element-wise.
Specifically, `y = 1 / (1 + exp(-x))`.
)doc");
REGISTER_OP("SigmoidGrad").UNARY_GRADIENT_COMPLEX().Doc(R"doc(
Computes the gradient of the sigmoid of `x` wrt its input.
Specifically, `grad = dy * y * (1 - y)`, where `y = sigmoid(x)`, and
`dy` is the corresponding input gradient.
)doc");
REGISTER_OP("Sin")
.UNARY_COMPLEX()
.Doc(R"doc(
Computes sin of x element-wise.
)doc");
REGISTER_OP("Cos")
.UNARY_COMPLEX()
.Doc(R"doc(
Computes cos of x element-wise.
)doc");
REGISTER_OP("Tan")
.UNARY()
.Doc(R"doc(
Computes tan of x element-wise.
)doc");
REGISTER_OP("Asin")
.UNARY()
.Doc(R"doc(
Computes asin of x element-wise.
)doc");
REGISTER_OP("Acos")
.UNARY()
.Doc(R"doc(
Computes acos of x element-wise.
)doc");
REGISTER_OP("Atan")
.UNARY()
.Doc(R"doc(
Computes atan of x element-wise.
)doc");
#undef UNARY
#undef UNARY_REAL
#undef UNARY_COMPLEX
REGISTER_OP("IsNan")
.Input("x: T")
.Output("y: bool")
.Attr("T: {half, float, double}")
.SetShapeFn(shape_inference::UnchangedShape)
.Doc(R"doc(
Returns which elements of x are NaN.
@compatibility(numpy)
Equivalent to np.isnan
@end_compatibility
)doc");
REGISTER_OP("IsInf")
.Input("x: T")
.Output("y: bool")
.Attr("T: {half, float, double}")
.SetShapeFn(shape_inference::UnchangedShape)
.Doc(R"doc(
Returns which elements of x are Inf.
@compatibility(numpy)
Equivalent to np.isinf
@end_compatibility
)doc");
REGISTER_OP("IsFinite")
.Input("x: T")
.Output("y: bool")
.Attr("T: {half, float, double}")
.SetShapeFn(shape_inference::UnchangedShape)
.Doc(R"doc(
Returns which elements of x are finite.
@compatibility(numpy)
Equivalent to np.isfinite
@end_compatibility
)doc");
REGISTER_OP("Sign")
.Input("x: T")
.Output("y: T")
.Attr("T: {half, float, double, int32, int64, complex64, complex128}")
.SetShapeFn(shape_inference::UnchangedShape)
.Doc(R"doc(
Returns an element-wise indication of the sign of a number.
`y = sign(x) = -1` if `x < 0`; 0 if `x == 0`; 1 if `x > 0`.
For complex numbers, `y = sign(x) = x / |x|` if `x != 0`, otherwise `y = 0`.
)doc");
REGISTER_OP("Floor")
.Input("x: T")
.Output("y: T")
.Attr("T: {half, float, double}")
.SetShapeFn(shape_inference::UnchangedShape)
.Doc(R"doc(
Returns element-wise largest integer not greater than x.
)doc");
REGISTER_OP("Ceil")
.Input("x: T")
.Output("y: T")
.Attr("T: {half, float, double}")
.SetShapeFn(shape_inference::UnchangedShape)
.Doc(R"doc(
Returns element-wise smallest integer in not less than x.
)doc");
REGISTER_OP("Rint")
.Input("x: T")
.Output("y: T")
.Attr("T: {float, double}")
.SetShapeFn(shape_inference::UnchangedShape)
.Doc(R"doc(
Returns element-wise integer closest to x.
If the result is midway between two representable values,
the even representable is chosen.
For example:
```
rint(-1.5) ==> -2.0
rint(0.5000001) ==> 1.0
rint([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0]) ==> [-2., -2., -0., 0., 2., 2., 2.]
```
)doc");
// Declares cwise binary operations signature: 't, 't -> 't.
#define BINARY_MORE() \
Input("x: T").Input("y: T").Output("z: T").Attr( \
"T: {half, float, double, uint8, int8, uint16, int16, int32, int64, complex64, complex128}")
#define BINARY_FEWER() \
Input("x: T").Input("y: T").Output("z: T").Attr( \
"T: {half, float, double, int32, int64, complex64, complex128}")
// TODO(mrry): Restore `SetIsCommutative()` for non-string types.
REGISTER_OP("Add")
.Input("x: T")
.Input("y: T")
.Output("z: T")
.Attr(
"T: {half, float, double, uint8, int8, int16, int32, int64, complex64, "
"complex128, string}")
.SetShapeFn(shape_inference::BroadcastBinaryOpShapeFn)
.Doc(R"doc(
Returns x + y element-wise.
*NOTE*: `Add` supports broadcasting. `AddN` does not. More about broadcasting
[here](http://docs.scipy.org/doc/numpy/user/basics.broadcasting.html)
)doc");
REGISTER_OP("Sub")
.BINARY_FEWER()
.SetShapeFn(shape_inference::BroadcastBinaryOpShapeFn)
.Doc(R"doc(
Returns x - y element-wise.
*NOTE*: `Sub` supports broadcasting. More about broadcasting
[here](http://docs.scipy.org/doc/numpy/user/basics.broadcasting.html)
)doc");
REGISTER_OP("Mul")
.BINARY_MORE()
.SetIsCommutative()
.SetShapeFn(shape_inference::BroadcastBinaryOpShapeFn)
.Doc(R"doc(
Returns x * y element-wise.
*NOTE*: `Mul` supports broadcasting. More about broadcasting
[here](http://docs.scipy.org/doc/numpy/user/basics.broadcasting.html)
)doc");
REGISTER_OP("Div")
.BINARY_MORE()
.SetShapeFn(shape_inference::BroadcastBinaryOpShapeFn)
.Doc(R"doc(
Returns x / y element-wise.
*NOTE*: `Div` supports broadcasting. More about broadcasting
[here](http://docs.scipy.org/doc/numpy/user/basics.broadcasting.html)
)doc");
REGISTER_OP("FloorDiv")
.BINARY_MORE()
.SetShapeFn(shape_inference::BroadcastBinaryOpShapeFn)
.Doc(R"doc(
Returns x // y element-wise.
*NOTE*: `FloorDiv` supports broadcasting. More about broadcasting
[here](http://docs.scipy.org/doc/numpy/user/basics.broadcasting.html)
)doc");
REGISTER_OP("TruncateDiv")
.BINARY_MORE()
.SetShapeFn(shape_inference::BroadcastBinaryOpShapeFn)
.Doc(R"doc(
Returns x / y element-wise for integer types.
Truncation designates that negative numbers will round fractional quantities
toward zero. I.e. -7 / 5 = 1. This matches C semantics but it is different
than Python semantics. See `FloorDiv` for a division function that matches
Python Semantics.
*NOTE*: `TruncateDiv` supports broadcasting. More about broadcasting
[here](http://docs.scipy.org/doc/numpy/user/basics.broadcasting.html)
)doc");
REGISTER_OP("RealDiv")
.BINARY_MORE()
.SetShapeFn(shape_inference::BroadcastBinaryOpShapeFn)
.Doc(R"doc(
Returns x / y element-wise for real types.
If `x` and `y` are reals, this will return the floating-point division.
*NOTE*: `Div` supports broadcasting. More about broadcasting
[here](http://docs.scipy.org/doc/numpy/user/basics.broadcasting.html)
)doc");
REGISTER_OP("SquaredDifference")
.BINARY_FEWER()
.SetIsCommutative()
.SetShapeFn(shape_inference::BroadcastBinaryOpShapeFn)
.Doc(R"doc(
Returns (x - y)(x - y) element-wise.
*NOTE*: `SquaredDifference` supports broadcasting. More about broadcasting
[here](http://docs.scipy.org/doc/numpy/user/basics.broadcasting.html)
)doc");
#undef BINARY_FEWER
#undef BINARY_MORE
REGISTER_OP("Maximum")
.Input("x: T")
.Input("y: T")
.Output("z: T")
.Attr("T: {half, float, double, int32, int64}")
.SetIsCommutative()
.SetShapeFn(shape_inference::BroadcastBinaryOpShapeFn)
.Doc(R"doc(
Returns the max of x and y (i.e. x > y ? x : y) element-wise.
*NOTE*: `Maximum` supports broadcasting. More about broadcasting
[here](http://docs.scipy.org/doc/numpy/user/basics.broadcasting.html)
)doc");
REGISTER_OP("Minimum")
.Input("x: T")
.Input("y: T")
.Output("z: T")
.Attr("T: {half, float, double, int32, int64}")
.SetIsCommutative()
.SetShapeFn(shape_inference::BroadcastBinaryOpShapeFn)
.Doc(R"doc(
Returns the min of x and y (i.e. x < y ? x : y) element-wise.
*NOTE*: `Minimum` supports broadcasting. More about broadcasting
[here](http://docs.scipy.org/doc/numpy/user/basics.broadcasting.html)
)doc");
REGISTER_OP("Mod")
.Input("x: T")
.Input("y: T")
.Output("z: T")
.Attr("T: {int32, int64, float, double}")
.SetShapeFn(shape_inference::BroadcastBinaryOpShapeFn)
.Doc(R"doc(
Returns element-wise remainder of division.
*NOTE*: `Mod` supports broadcasting. More about broadcasting
[here](http://docs.scipy.org/doc/numpy/user/basics.broadcasting.html)
)doc");
REGISTER_OP("FloorMod")
.Input("x: T")
.Input("y: T")
.Output("z: T")
.Attr("T: {int32, int64, float, double}")
.SetShapeFn(shape_inference::BroadcastBinaryOpShapeFn)
.Doc(R"doc(
Returns element-wise remainder of division. When `x < 0` xor `y < 0` is
true, this follows Python semantics in that the result here is consistent
with a flooring divide. E.g. `floor(x / y) * y + mod(x, y) = x`.
*NOTE*: `FloorMod` supports broadcasting. More about broadcasting
[here](http://docs.scipy.org/doc/numpy/user/basics.broadcasting.html)
)doc");
REGISTER_OP("TruncateMod")
.Input("x: T")
.Input("y: T")
.Output("z: T")
.Attr("T: {int32, int64, float, double}")
.SetShapeFn(shape_inference::BroadcastBinaryOpShapeFn)
.Doc(R"doc(
Returns element-wise remainder of division. This emulates C semantics where
true, this follows C semantics in that the result here is consistent
with a flooring divide. E.g. `floor(x / y) * y + mod(x, y) = x`.
*NOTE*: `Mod` supports broadcasting. More about broadcasting
[here](http://docs.scipy.org/doc/numpy/user/basics.broadcasting.html)
)doc");
REGISTER_OP("Pow")
.Input("x: T")
.Input("y: T")
.Output("z: T")
.Attr("T: {half, float, double, int32, int64, complex64, complex128}")
.SetShapeFn(shape_inference::BroadcastBinaryOpShapeFn)
.Doc(R"doc(
Computes the power of one value to another.
Given a tensor `x` and a tensor `y`, this operation computes \\(x^y\\) for
corresponding elements in `x` and `y`. For example:
```
# tensor 'x' is [[2, 2]], [3, 3]]
# tensor 'y' is [[8, 16], [2, 3]]
tf.pow(x, y) ==> [[256, 65536], [9, 27]]
```
)doc");
REGISTER_OP("Igammac")
.Input("a: T")
.Input("x: T")
.Output("z: T")
.Attr("T: {float, double}")
.SetShapeFn(shape_inference::BroadcastBinaryOpShapeFn)
.Doc(R"doc(
Compute the upper regularized incomplete Gamma function `Q(a, x)`.
The upper regularized incomplete Gamma function is defined as:
```
Q(a, x) = Gamma(a, x) / Gamma(a) = 1 - P(a, x)
```
where
```
Gamma(a, x) = int_{x}^{\infty} t^{a-1} exp(-t) dt
```
is the upper incomplete Gama function.
Note, above `P(a, x)` (`Igamma`) is the lower regularized complete
Gamma function.
)doc");
REGISTER_OP("Igamma")
.Input("a: T")
.Input("x: T")
.Output("z: T")
.Attr("T: {float, double}")
.SetShapeFn(shape_inference::BroadcastBinaryOpShapeFn)
.Doc(R"doc(
Compute the lower regularized incomplete Gamma function `Q(a, x)`.
The lower regularized incomplete Gamma function is defined as:
```
P(a, x) = gamma(a, x) / Gamma(a) = 1 - Q(a, x)
```
where
```
gamma(a, x) = int_{0}^{x} t^{a-1} exp(-t) dt
```
is the lower incomplete Gamma function.
Note, above `Q(a, x)` (`Igammac`) is the upper regularized complete
Gamma function.
)doc");
REGISTER_OP("Zeta")
.Input("x: T")
.Input("q: T")
.Output("z: T")
.Attr("T: {float, double}")
.SetShapeFn(shape_inference::BroadcastBinaryOpShapeFn)
.Doc(R"doc(
Compute the Hurwitz zeta function \\(\zeta(x, q)\\).
The Hurwitz zeta function is defined as:
```
\zeta(x, q) = \sum_{n=0}^{\infty} (q + n)^{-x}
```
)doc");
REGISTER_OP("Polygamma")
.Input("a: T")
.Input("x: T")
.Output("z: T")
.Attr("T: {float, double}")
.SetShapeFn(shape_inference::BroadcastBinaryOpShapeFn)
.Doc(R"doc(
Compute the polygamma function \\(\psi^{(n)}(x)\\).
The polygamma function is defined as:
```
\psi^{(n)}(x) = \frac{d^n}{dx^n} \psi(x)
```
where \\(\psi(x)\\) is the digamma function.
)doc");
REGISTER_OP("Betainc")
.Input("a: T")
.Input("b: T")
.Input("x: T")
.Output("z: T")
.Attr("T: {float, double}")
.SetShapeFn([](InferenceContext* c) {
const int num_inputs = 3;
ShapeHandle output = c->UnknownShape();
int num_scalars = 0;
ShapeHandle some_non_scalar;
for (int i = 0; i < num_inputs; ++i) {
ShapeHandle in = c->input(i);
if (!c->RankKnown(in)) {
some_non_scalar = in;
// An input with unknown rank could be either a scalar (to be
// broadcast) or some other shape.
} else if (c->Rank(in) == 0) {
// Input is a scalar, it will be broadcast to the output shape.
++num_scalars;
} else {
TF_RETURN_IF_ERROR(c->Merge(output, in, &output));
some_non_scalar = output;
}
}
if (num_scalars == num_inputs - 1) {
// If all but one input is known to be a scalar, then output is the
// remaining input.
output = some_non_scalar;
} else if (num_scalars == num_inputs) {
// If all are scalars, output is scalar; pick the first one arbitrarily.
output = c->input(0);
}
c->set_output(0, output);
return Status::OK();
})
.Doc(R"doc(
Compute the regularized incomplete beta integral \\(I_x(a, b)\\).
The regularized incomplete beta integral is defined as:
```
I_x(a, b) = \frac{B(x; a, b)}{B(a, b)}
```
where
```
B(x; a, b) = \int_0^x t^{a-1} (1 - t)^{b-1} dt
```
is the incomplete beta function and \\(B(a, b)\\) is the *complete*
beta function.
)doc");
// --------------------------------------------------------------------------
// Declares cwise binary comparison operations signature: 't, 't -> bool,
// where 't has a natural total order.
#define COMPARISON() \
Input("x: T") \
.Input("y: T") \
.Output("z: bool") \
.Attr("T: realnumbertype") \
.SetShapeFn(shape_inference::BroadcastBinaryOpShapeFn)
REGISTER_OP("Less")
.COMPARISON()
.Doc(R"doc(
Returns the truth value of (x < y) element-wise.
*NOTE*: `Less` supports broadcasting. More about broadcasting
[here](http://docs.scipy.org/doc/numpy/user/basics.broadcasting.html)
)doc");
REGISTER_OP("LessEqual")
.COMPARISON()
.Doc(R"doc(
Returns the truth value of (x <= y) element-wise.
*NOTE*: `LessEqual` supports broadcasting. More about broadcasting
[here](http://docs.scipy.org/doc/numpy/user/basics.broadcasting.html)
)doc");
REGISTER_OP("Greater")
.COMPARISON()
.Doc(R"doc(
Returns the truth value of (x > y) element-wise.
*NOTE*: `Greater` supports broadcasting. More about broadcasting
[here](http://docs.scipy.org/doc/numpy/user/basics.broadcasting.html)
)doc");
REGISTER_OP("GreaterEqual")
.COMPARISON()
.Doc(R"doc(
Returns the truth value of (x >= y) element-wise.
*NOTE*: `GreaterEqual` supports broadcasting. More about broadcasting
[here](http://docs.scipy.org/doc/numpy/user/basics.broadcasting.html)
)doc");
#undef COMPARISON
// --------------------------------------------------------------------------
#define EQUALITY_COMPARISON() \
Input("x: T") \
.Input("y: T") \
.Output("z: bool") \
.SetIsCommutative() \
.Attr( \
"T: {half, float, double, uint8, int8, int16, int32, int64, " \
"complex64, " \
"quint8, qint8, qint32, string, bool, complex128}") \
.SetShapeFn(shape_inference::BroadcastBinaryOpShapeFn)
REGISTER_OP("Equal")
.EQUALITY_COMPARISON()
.Doc(R"doc(
Returns the truth value of (x == y) element-wise.
*NOTE*: `Equal` supports broadcasting. More about broadcasting
[here](http://docs.scipy.org/doc/numpy/user/basics.broadcasting.html)
)doc");
REGISTER_OP("NotEqual")
.EQUALITY_COMPARISON()
.Doc(R"doc(
Returns the truth value of (x != y) element-wise.
*NOTE*: `NotEqual` supports broadcasting. More about broadcasting
[here](http://docs.scipy.org/doc/numpy/user/basics.broadcasting.html)
)doc");
#undef EQUALITY_COMPARISON
// --------------------------------------------------------------------------
REGISTER_OP("LogicalNot")
.Input("x: bool")
.Output("y: bool")
.SetShapeFn(shape_inference::UnchangedShape)
.Doc(R"doc(
Returns the truth value of NOT x element-wise.
)doc");
#define BINARY_LOGICAL() \
Input("x: bool") \
.Input("y: bool") \
.Output("z: bool") \
.SetIsCommutative() \
.SetShapeFn(shape_inference::BroadcastBinaryOpShapeFn)
REGISTER_OP("LogicalAnd")
.BINARY_LOGICAL()
.Doc(R"doc(
Returns the truth value of x AND y element-wise.
*NOTE*: `LogicalAnd` supports broadcasting. More about broadcasting
[here](http://docs.scipy.org/doc/numpy/user/basics.broadcasting.html)
)doc");
REGISTER_OP("LogicalOr")
.BINARY_LOGICAL()
.Doc(R"doc(
Returns the truth value of x OR y element-wise.
*NOTE*: `LogicalOr` supports broadcasting. More about broadcasting
[here](http://docs.scipy.org/doc/numpy/user/basics.broadcasting.html)
)doc");
#undef BINARY_LOGICAL
// --------------------------------------------------------------------------
REGISTER_OP("Select")
.Input("condition: bool")
.Input("t: T")
.Input("e: T")
.Output("output: T")
.Attr("T: type")
.SetShapeFn([](InferenceContext* c) {
// Merge handle shape and dtype if applicable.
if (c->input_handle_dtype(1) != c->input_handle_dtype(2)) {
// TODO(apassos) resolve this in the manner of b/32476923
return errors::InvalidArgument(
"Trying to merge handles pointing to different dtypes.");
}
c->set_output_handle_dtype(0, c->input_handle_dtype(1));
ShapeHandle output_handle_shape;
TF_RETURN_IF_ERROR(c->Merge(c->input_handle_shape(1),
c->input_handle_shape(2),
&output_handle_shape));
c->set_output_handle_shape(0, output_handle_shape);
// The inputs 'then' and 'else' must have the same shape.
ShapeHandle data = c->input(1);
ShapeHandle other = c->input(2);
TF_RETURN_IF_ERROR(c->Merge(data, other, &data));
// The input 'cond' must either have the same shape as 'then' and
// 'else', or be a vector if 'then' and 'else' are at least vectors.
ShapeHandle cond = c->input(0);
if (!c->RankKnown(cond) || !c->RankKnown(data)) {
c->set_output(0, data);
return Status::OK();
}
// rank of shape and data is known.
const int32 cond_rank = c->Rank(cond);
const int32 data_rank = c->Rank(data);
if (cond_rank == 0){
// The rank of 'cond' is a scalar.
// t and e can have any shape.
c->set_output(0, data);
return Status::OK();
}
if (cond_rank != 1) {
// If 'cond' is not a vector, and not a scalar,
// then shape must match 'then' and 'else'
TF_RETURN_IF_ERROR(c->Merge(data, cond, &data));