/**
 * @license
 * Copyright 2018 Google Inc. 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.
 * =============================================================================
 */
import { CustomGradientFunc } from './engine';
import { Scalar, Tensor, Variable } from './tensor';
import { NamedTensorMap } from './tensor_types';
import { TensorLike } from './types';
/**
 * Provided `f(x)`, returns another function `g(x, dy?)`, which gives the
 * gradient of `f(x)` with respect to `x`.
 *
 * If `dy` is provided, the gradient of `f(x).mul(dy).sum()` with respect to
 * `x` is computed instead. `f(x)` must take a single tensor `x` and return a
 * single tensor `y`. If `f()` takes multiple inputs, use `tf.grads` instead.
 *
 * ```js
 * // f(x) = x ^ 2
 * const f = x => x.square();
 * // f'(x) = 2x
 * const g = tf.grad(f);
 *
 * const x = tf.tensor1d([2, 3]);
 * g(x).print();
 * ```
 *
 * ```js
 * // f(x) = x ^ 3
 * const f = x => x.pow(tf.scalar(3, 'int32'));
 * // f'(x) = 3x ^ 2
 * const g = tf.grad(f);
 * // f''(x) = 6x
 * const gg = tf.grad(g);
 *
 * const x = tf.tensor1d([2, 3]);
 * gg(x).print();
 * ```
 *
 * @param f The function f(x), to compute gradient for.
 */
/** @doc {heading: 'Training', subheading: 'Gradients'} */
declare function grad(f: (x: Tensor) => Tensor): (x: TensorLike | Tensor, dy?: TensorLike | Tensor) => Tensor;
/**
 * Provided `f(x1, x2,...)`, returns another function `g([x1, x2,...], dy?)`,
 * which gives an array of gradients of `f()` with respect to each input
 * [`x1`,`x2`,...].
 *
 * If `dy` is passed when calling `g()`, the gradient of
 * `f(x1,...).mul(dy).sum()` with respect to each input is computed instead.
 * The provided `f` must take one or more tensors and return a single tensor
 * `y`. If `f()` takes a single input, we recommend using `tf.grad` instead.
 *
 * ```js
 * // f(a, b) = a * b
 * const f = (a, b) => a.mul(b);
 * // df / da = b, df / db = a
 * const g = tf.grads(f);
 *
 * const a = tf.tensor1d([2, 3]);
 * const b = tf.tensor1d([-2, -3]);
 * const [da, db] = g([a, b]);
 * console.log('da');
 * da.print();
 * console.log('db');
 * db.print();
 * ```
 *
 * @param f The function `f(x1, x2,...)` to compute gradients for.
 */
/** @doc {heading: 'Training', subheading: 'Gradients'} */
declare function grads(f: (...args: Tensor[]) => Tensor): (args: Array<Tensor | TensorLike>, dy?: Tensor | TensorLike) => Tensor[];
/**
 * Like `tf.grad`, but also returns the value of `f()`. Useful when `f()`
 * returns a metric you want to show.
 *
 * The result is a rich object with the following properties:
 * - grad: The gradient of `f(x)` w.r.t `x` (result of `tf.grad`).
 * - value: The value returned by `f(x)`.
 *
 * ```js
 * // f(x) = x ^ 2
 * const f = x => x.square();
 * // f'(x) = 2x
 * const g = tf.valueAndGrad(f);
 *
 * const x = tf.tensor1d([2, 3]);
 * const {value, grad} = g(x);
 *
 * console.log('value');
 * value.print();
 * console.log('grad');
 * grad.print();
 * ```
 */
/** @doc {heading: 'Training', subheading: 'Gradients'} */
declare function valueAndGrad<I extends Tensor, O extends Tensor>(f: (x: I) => O): (x: I, dy?: O) => {
    value: O;
    grad: I;
};
/**
 * Like `tf.grads`, but returns also the value of `f()`. Useful when `f()`
 * returns a metric you want to show.
 *
 * The result is a rich object with the following properties:
 * - grads: The gradients of `f()` w.r.t each input (result of `tf.grads`).
 * - value: The value returned by `f(x)`.
 *
 * ```js
 * // f(a, b) = a * b
 * const f = (a, b) => a.mul(b);
 * // df/da = b, df/db = a
 * const g = tf.valueAndGrads(f);
 *
 * const a = tf.tensor1d([2, 3]);
 * const b = tf.tensor1d([-2, -3]);
 * const {value, grads} = g([a, b]);
 *
 * const [da, db] = grads;
 *
 * console.log('value');
 * value.print();
 *
 * console.log('da');
 * da.print();
 * console.log('db');
 * db.print();
 * ```
 */
/** @doc {heading: 'Training', subheading: 'Gradients'} */
declare function valueAndGrads<O extends Tensor>(f: (...args: Tensor[]) => O): (args: Tensor[], dy?: O) => {
    grads: Tensor[];
    value: O;
};
/**
 * Computes and returns the gradient of f(x) with respect to the list of
 * trainable variables provided by `varList`. If no list is provided, it
 * defaults to all trainable variables.
 *
 * ```js
 * const a = tf.variable(tf.tensor1d([3, 4]));
 * const b = tf.variable(tf.tensor1d([5, 6]));
 * const x = tf.tensor1d([1, 2]);
 *
 * // f(a, b) = a * x ^ 2 + b * x
 * const f = () => a.mul(x.square()).add(b.mul(x)).sum();
 * // df/da = x ^ 2, df/db = x
 * const {value, grads} = tf.variableGrads(f);
 *
 * Object.keys(grads).forEach(varName => grads[varName].print());
 * ```
 *
 * @param f The function to execute. f() should return a scalar.
 * @param varList The list of variables to compute the gradients with respect
 *     to. Defaults to all trainable variables.
 * @returns An object with the following keys and values:
 *   - `value`: The value of the function `f`.
 *   - `grads`: A map from the names of the variables to the gradients.
 *     If the `varList` argument is provided explicitly and contains a subset of
 *     non-trainable variables, this map in the return value will contain keys
 *     that map the names of the non-trainable variables to `null`.
 */
/** @doc {heading: 'Training', subheading: 'Gradients'} */
declare function variableGrads(f: () => Scalar, varList?: Variable[]): {
    value: Scalar;
    grads: NamedTensorMap;
};
/**
 * Overrides the gradient computation of a function `f`.
 *
 * Takes a function
 * `f(...inputs, save) => {value: Tensor, gradFunc: (dy, saved) => Tensor[]}`
 * and returns another function `g(...inputs)` which takes the same inputs as
 * `f`. When called, `g` returns `f().value`. In backward mode, custom gradients
 * with respect to each input of `f` are computed using `f().gradFunc`.
 *
 * The `save` function passsed to `f` should be used for saving tensors needed
 * in the gradient. And the `saved` passed to the `gradFunc` is a
 * `NamedTensorMap`, which contains those saved tensor.
 *
 * ```js
 * const customOp = tf.customGrad((x, save) => {
 *   // Save x to make sure it's available later for the gradient.
 *   save([x]);
 *   // Override gradient of our custom x ^ 2 op to be dy * abs(x);
 *   return {
 *     value: x.square(),
 *     // Note `saved.x` which points to the `x` we saved earlier.
 *     gradFunc: (dy, saved) => [dy.mul(saved[0].abs())]
 *   };
 * });
 *
 * const x = tf.tensor1d([-1, -2, 3]);
 * const dx = tf.grad(x => customOp(x));
 *
 * console.log(`f(x):`);
 * customOp(x).print();
 * console.log(`f'(x):`);
 * dx(x).print();
 * ```
 *
 * @param f The function to evaluate in forward mode, which should return
 *     `{value: Tensor, gradFunc: (dy, saved) => Tensor[]}`, where `gradFunc`
 *     returns the custom gradients of `f` with respect to its inputs.
 */
/** @doc {heading: 'Training', subheading: 'Gradients'} */
declare function customGrad<T extends Tensor>(f: CustomGradientFunc<T>): (...args: Tensor[]) => T;
export { customGrad, variableGrads, valueAndGrad, valueAndGrads, grad, grads, };
