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chenyc

2025-02-12 ea42ff3ebee1eeb3fb29423aa848a249441db81c

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