"use strict";
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/**
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* @license
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* Copyright 2018 Google Inc. All Rights Reserved.
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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* =============================================================================
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*/
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Object.defineProperty(exports, "__esModule", { value: true });
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var tensor_util_env_1 = require("../tensor_util_env");
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var util_1 = require("../util");
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var axis_util = require("./axis_util");
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var operation_1 = require("./operation");
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var tensor_ops_1 = require("./tensor_ops");
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/**
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* Computes the norm of scalar, vectors, and matrices.
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* This function can compute several different vector norms (the 1-norm, the
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* Euclidean or 2-norm, the inf-norm, and in general the p-norm for p > 0)
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* and matrix norms (Frobenius, 1-norm, and inf-norm).
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*
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* ```js
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* const x = tf.tensor1d([1, 2, 3, 4]);
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*
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* x.norm().print(); // or tf.norm(x)
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* ```
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*
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* @param x The input array.
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* @param ord Optional. Order of the norm. Supported norm types are
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* following:
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*
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* | ord | norm for matrices | norm for vectors
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* |------------|---------------------------|---------------------
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* |'euclidean' |Frobenius norm |2-norm
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* |'fro' |Frobenius norm |
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* |Infinity |max(sum(abs(x), axis=1)) |max(abs(x))
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* |-Infinity |min(sum(abs(x), axis=1)) |min(abs(x))
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* |1 |max(sum(abs(x), axis=0)) |sum(abs(x))
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* |2 | |sum(abs(x)^2)^1/2*
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*
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* @param axis Optional. If axis is null (the default), the input is
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* considered a vector and a single vector norm is computed over the entire
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* set of values in the Tensor, i.e. norm(x, ord) is equivalent
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* to norm(x.reshape([-1]), ord). If axis is a integer, the input
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* is considered a batch of vectors, and axis determines the axis in x
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* over which to compute vector norms. If axis is a 2-tuple of integer it is
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* considered a batch of matrices and axis determines the axes in NDArray
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* over which to compute a matrix norm.
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* @param keepDims Optional. If true, the norm have the same dimensionality
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* as the input.
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*/
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/** @doc {heading: 'Operations', subheading: 'Matrices'} */
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function norm_(x, ord, axis, keepDims) {
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if (ord === void 0) { ord = 'euclidean'; }
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if (axis === void 0) { axis = null; }
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if (keepDims === void 0) { keepDims = false; }
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x = tensor_util_env_1.convertToTensor(x, 'x', 'norm');
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var norm = normImpl(x, ord, axis);
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var keepDimsShape = norm.shape;
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if (keepDims) {
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var axes = util_1.parseAxisParam(axis, x.shape);
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keepDimsShape = axis_util.expandShapeToKeepDim(norm.shape, axes);
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}
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return norm.reshape(keepDimsShape);
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}
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function normImpl(x, p, axis) {
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if (axis === void 0) { axis = null; }
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if (x.rank === 0) {
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return x.abs();
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}
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// consider vector when no axis is specified
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if (x.rank !== 1 && axis === null) {
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return normImpl(x.reshape([-1]), p, axis);
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}
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// vector
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if (x.rank === 1 || typeof axis === 'number' ||
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Array.isArray(axis) && axis.length === 1) {
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if (p === 1) {
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return x.abs().sum(axis);
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}
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if (p === Infinity) {
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return x.abs().max(axis);
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}
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if (p === -Infinity) {
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return x.abs().min(axis);
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}
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if (p === 'euclidean' || p === 2) {
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// norm(x, 2) = sum(abs(xi) ^ 2) ^ 1/2
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return x.abs().pow(tensor_ops_1.scalar(2, 'int32')).sum(axis).sqrt();
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}
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throw new Error("Error in norm: invalid ord value: " + p);
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}
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// matrix (assumption axis[0] < axis[1])
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if (Array.isArray(axis) && axis.length === 2) {
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if (p === 1) {
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return x.abs().sum(axis[0]).max(axis[1] - 1);
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}
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if (p === Infinity) {
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return x.abs().sum(axis[1]).max(axis[0]);
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}
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if (p === -Infinity) {
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return x.abs().sum(axis[1]).min(axis[0]);
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}
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if (p === 'fro' || p === 'euclidean') {
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// norm(x) = sqrt(sum(pow(x, 2)))
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return x.square().sum(axis).sqrt();
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}
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throw new Error("Error in norm: invalid ord value: " + p);
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}
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throw new Error("Error in norm: invalid axis: " + axis);
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}
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exports.norm = operation_1.op({ norm_: norm_ });
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//# sourceMappingURL=norm.js.map
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