/**
|
* @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 {Tensor} from '../tensor';
|
import {convertToTensor} from '../tensor_util_env';
|
import {TensorLike} from '../types';
|
import {parseAxisParam} from '../util';
|
|
import * as axis_util from './axis_util';
|
import {op} from './operation';
|
import {scalar} from './tensor_ops';
|
|
/**
|
* Computes the norm of scalar, vectors, and matrices.
|
* This function can compute several different vector norms (the 1-norm, the
|
* Euclidean or 2-norm, the inf-norm, and in general the p-norm for p > 0)
|
* and matrix norms (Frobenius, 1-norm, and inf-norm).
|
*
|
* ```js
|
* const x = tf.tensor1d([1, 2, 3, 4]);
|
*
|
* x.norm().print(); // or tf.norm(x)
|
* ```
|
*
|
* @param x The input array.
|
* @param ord Optional. Order of the norm. Supported norm types are
|
* following:
|
*
|
* | ord | norm for matrices | norm for vectors
|
* |------------|---------------------------|---------------------
|
* |'euclidean' |Frobenius norm |2-norm
|
* |'fro' |Frobenius norm |
|
* |Infinity |max(sum(abs(x), axis=1)) |max(abs(x))
|
* |-Infinity |min(sum(abs(x), axis=1)) |min(abs(x))
|
* |1 |max(sum(abs(x), axis=0)) |sum(abs(x))
|
* |2 | |sum(abs(x)^2)^1/2*
|
*
|
* @param axis Optional. If axis is null (the default), the input is
|
* considered a vector and a single vector norm is computed over the entire
|
* set of values in the Tensor, i.e. norm(x, ord) is equivalent
|
* to norm(x.reshape([-1]), ord). If axis is a integer, the input
|
* is considered a batch of vectors, and axis determines the axis in x
|
* over which to compute vector norms. If axis is a 2-tuple of integer it is
|
* considered a batch of matrices and axis determines the axes in NDArray
|
* over which to compute a matrix norm.
|
* @param keepDims Optional. If true, the norm have the same dimensionality
|
* as the input.
|
*/
|
/** @doc {heading: 'Operations', subheading: 'Matrices'} */
|
function norm_(
|
x: Tensor|TensorLike, ord: number|'euclidean'|'fro' = 'euclidean',
|
axis: number|number[] = null, keepDims = false): Tensor {
|
x = convertToTensor(x, 'x', 'norm');
|
|
const norm = normImpl(x, ord, axis);
|
let keepDimsShape = norm.shape;
|
if (keepDims) {
|
const axes = parseAxisParam(axis, x.shape);
|
keepDimsShape = axis_util.expandShapeToKeepDim(norm.shape, axes);
|
}
|
return norm.reshape(keepDimsShape);
|
}
|
|
function normImpl(
|
x: Tensor, p: number|string, axis: number|number[] = null): Tensor {
|
if (x.rank === 0) {
|
return x.abs();
|
}
|
|
// consider vector when no axis is specified
|
if (x.rank !== 1 && axis === null) {
|
return normImpl(x.reshape([-1]), p, axis);
|
}
|
|
// vector
|
if (x.rank === 1 || typeof axis === 'number' ||
|
Array.isArray(axis) && axis.length === 1) {
|
if (p === 1) {
|
return x.abs().sum(axis);
|
}
|
if (p === Infinity) {
|
return x.abs().max(axis);
|
}
|
if (p === -Infinity) {
|
return x.abs().min(axis);
|
}
|
if (p === 'euclidean' || p === 2) {
|
// norm(x, 2) = sum(abs(xi) ^ 2) ^ 1/2
|
return x.abs().pow(scalar(2, 'int32')).sum(axis).sqrt();
|
}
|
|
throw new Error(`Error in norm: invalid ord value: ${p}`);
|
}
|
|
// matrix (assumption axis[0] < axis[1])
|
if (Array.isArray(axis) && axis.length === 2) {
|
if (p === 1) {
|
return x.abs().sum(axis[0]).max(axis[1] - 1);
|
}
|
if (p === Infinity) {
|
return x.abs().sum(axis[1]).max(axis[0]);
|
}
|
if (p === -Infinity) {
|
return x.abs().sum(axis[1]).min(axis[0]);
|
}
|
if (p === 'fro' || p === 'euclidean') {
|
// norm(x) = sqrt(sum(pow(x, 2)))
|
return x.square().sum(axis).sqrt();
|
}
|
|
throw new Error(`Error in norm: invalid ord value: ${p}`);
|
}
|
|
throw new Error(`Error in norm: invalid axis: ${axis}`);
|
}
|
|
export const norm = op({norm_});
|
