@tensorflow/tfjs-core
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Hardware-accelerated JavaScript library for machine intelligence
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JavaScript
/**
* @license
* Copyright 2018 Google LLC. 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 { convertToTensor } from '../tensor_util_env';
import { parseAxisParam } from '../util';
import { abs } from './abs';
import * as axis_util from './axis_util';
import { max } from './max';
import { min } from './min';
import { op } from './operation';
import { pow } from './pow';
import { reshape } from './reshape';
import { scalar } from './scalar';
import { sqrt } from './sqrt';
import { square } from './square';
import { sum } from './sum';
/**
* 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, ord = 'euclidean', axis = null, keepDims = false) {
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 reshape(norm, keepDimsShape);
}
function normImpl(x, p, axis = null) {
if (x.rank === 0) {
return abs(x);
}
// consider vector when no axis is specified
if (x.rank !== 1 && axis === null) {
return normImpl(reshape(x, [-1]), p, axis);
}
// vector
if (x.rank === 1 || typeof axis === 'number' ||
Array.isArray(axis) && axis.length === 1) {
if (p === 1) {
return sum(abs(x), axis);
}
if (p === Infinity) {
return max(abs(x), axis);
}
if (p === -Infinity) {
return min(abs(x), axis);
}
if (p === 'euclidean' || p === 2) {
// norm(x, 2) = sum(abs(xi) ^ 2) ^ 1/2
return sqrt(sum(pow(abs(x), scalar(2, 'int32')), axis));
}
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 max(sum(abs(x), axis[0]), axis[1] - 1);
}
if (p === Infinity) {
return max(sum(abs(x), axis[1]), axis[0]);
}
if (p === -Infinity) {
return min(sum(abs(x), axis[1]), axis[0]);
}
if (p === 'fro' || p === 'euclidean') {
// norm(x) = sqrt(sum(pow(x, 2)))
return sqrt(sum(square(x), axis));
}
throw new Error(`Error in norm: invalid ord value: ${p}`);
}
throw new Error(`Error in norm: invalid axis: ${axis}`);
}
export const norm = op({ norm_ });
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