@tensorflow/tfjs-core/src/ops/norm.ts

Hardware-accelerated JavaScript library for machine intelligence

/**
 * @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() as Tensor;
    }

    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_});