/**
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* @license
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* Copyright 2021 Google LLC. 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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import { assert } from '../util_base';
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const ARROW = '->';
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const ARROW_REGEX = /->/g;
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const COMMA = ',';
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const ELLIPSIS = '...';
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/**
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* Parse an equation for einsum.
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*
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* @param equation The einsum equation (e.g., "ij,jk->ik").
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* @param numTensors Number of tensors provided along with `equation`. Used to
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* check matching number of input tensors.
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* @returns An object consisting of the following fields:
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* - allDims: all dimension names as strings.
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* - summedDims: a list of all dimensions being summed over, as indices to
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* the elements of `allDims`.
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* - idDims: indices of the dimensions in each input tensor, as indices to
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* the elements of `allDims.
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*/
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export function decodeEinsumEquation(equation, numTensors) {
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equation = equation.replace(/\s/g, ''); // Remove witespace in equation.
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const numArrows = (equation.length - equation.replace(ARROW_REGEX, '').length) /
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ARROW.length;
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if (numArrows < 1) {
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throw new Error('Equations without an arrow are not supported.');
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}
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else if (numArrows > 1) {
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throw new Error(`Equation must contain exactly one arrow ("${ARROW}").`);
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}
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const [inputString, outputString] = equation.split(ARROW);
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assert(inputString.indexOf(ELLIPSIS) === -1, () => `The ellipsis notation ("${ELLIPSIS}") is not supported yet.`);
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const inputTerms = inputString.split(COMMA);
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const numInputs = inputTerms.length;
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if (numTensors !== numInputs) {
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throw new Error(`Expected ${numInputs} input tensors, received ${numTensors}`);
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}
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if (numInputs > 2) {
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throw new Error('Support for more than 2 input tensors is not implemented yet.');
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}
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const allDims = [];
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for (let i = 0; i < outputString.length; ++i) {
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const dimName = outputString[i];
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if (!inputTerms.some(inputTerm => inputTerm.indexOf(dimName) !== -1)) {
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throw new Error(`Output subscripts contain the label ${dimName} ` +
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`not present in the input subscripts.`);
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}
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if (allDims.indexOf(dimName) === -1) {
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allDims.push(dimName);
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}
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}
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for (let i = 0; i < inputString.length; ++i) {
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const dimName = inputString[i];
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if (allDims.indexOf(dimName) === -1 && dimName !== COMMA) {
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allDims.push(dimName);
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}
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}
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const idDims = new Array(inputTerms.length);
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for (let i = 0; i < numInputs; ++i) {
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if (new Set(inputTerms[i].split('')).size !== inputTerms[i].length) {
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throw new Error(`Found duplicate axes in input component ${inputTerms[i]}. ` +
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`Support for duplicate axes in input is not implemented yet.`);
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}
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idDims[i] = [];
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for (let j = 0; j < inputTerms[i].length; ++j) {
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idDims[i].push(allDims.indexOf(inputTerms[i][j]));
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}
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}
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const numDims = allDims.length; // Number of unique dimensions.
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const numOutDims = outputString.length; // Number of output dimensions.
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const summedDims = []; // Dimensions being summed over.
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for (let i = numOutDims; i < numDims; ++i) {
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summedDims.push(i);
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}
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return { allDims, summedDims, idDims };
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}
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/**
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* Get the permutation for a given input tensor.
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*
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* @param nDims Total number of dimension of all tensors involved in the einsum
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* operation.
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* @param idDims Dimension indices involve in the tensor in question.
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* @returns An object consisting of the following fields:
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* - permutationIndices: Indices to permute the axes of the tensor with.
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* - expandDims: Indices to the dimension that need to be expanded from the
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* tensor after permutation.
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*/
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export function getEinsumPermutation(nDims, idDims) {
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let permutationIndices = new Array(nDims);
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permutationIndices.fill(-1);
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for (let i = 0; i < idDims.length; ++i) {
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permutationIndices[idDims[i]] = i;
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}
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const expandDims = [];
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for (let i = 0; i < nDims; ++i) {
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if (permutationIndices[i] === -1) {
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expandDims.push(i);
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}
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}
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permutationIndices = permutationIndices.filter(d => d !== -1);
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return { permutationIndices, expandDims };
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}
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/**
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* Checks that the dimension sizes from different input tensors match the
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* equation.
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*/
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export function checkEinsumDimSizes(nDims, idDims, tensors) {
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const dimSizes = new Array(nDims);
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for (let i = 0; i < tensors.length; ++i) {
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const shape = tensors[i].shape;
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for (let j = 0; j < idDims[i].length; ++j) {
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if (dimSizes[idDims[i][j]] === undefined) {
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dimSizes[idDims[i][j]] = shape[j];
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}
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else {
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assert(dimSizes[idDims[i][j]] === shape[j], () => `Expected dimension ${dimSizes[idDims[i][j]]} at axis ${j} ` +
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`of input shaped ${JSON.stringify(shape)}, ` +
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`but got dimension ${shape[j]}`);
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}
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}
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}
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}
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/**
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* Gets path of computation for einsum.
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*
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* @param summedDims indices to the dimensions being summed over.
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* @param idDims A look up table for the dimensions present in each input
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* tensor. Each consituent array contains indices for the dimensions in the
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* corresponding input tensor.
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*
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* @return A map with two fields:
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* - path: The path of computation, with each element indicating the dimension
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* being summed over after the element-wise multiplication in that step.
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* - steps: With the same length as `path`. Each element contains the indices
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* to the input tensors being used for element-wise multiplication in the
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* corresponding step.
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*/
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export function getEinsumComputePath(summedDims, idDims) {
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const path = summedDims;
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const steps = [];
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let nSteps = 0;
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if (summedDims.length === 0) {
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// Einsum that involes no summing: e.g., transpose and outer product.
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path.push(-1);
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}
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nSteps = summedDims.length + 1;
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for (let i = 0; i < nSteps; ++i) {
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steps.push([]);
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}
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const computedTermIndices = [];
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for (let i = 0; i < path.length; ++i) {
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const summedDim = path[i];
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const termIndices = findTermsWithDim(idDims, summedDim);
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for (const termIndex of termIndices) {
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if (computedTermIndices.indexOf(termIndex) === -1) {
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steps[i].push(termIndex);
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computedTermIndices.push(termIndex);
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}
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}
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}
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return { path, steps };
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}
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/** Determines if an axes permutation is the identity permutation. */
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export function isIdentityPermutation(perm) {
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return perm.every((dim, index) => dim === index);
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}
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function findTermsWithDim(idDims, dim) {
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const termIndices = [];
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for (let i = 0; i < idDims.length; ++i) {
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if (idDims[i].length === 0 || idDims[i].indexOf(dim) !== -1 || dim === -1) {
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termIndices.push(i);
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}
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}
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return termIndices;
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}
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* @license\n * Copyright 2021 Google LLC. 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\n/**\n * Utility functions for computing einsum (tensor contraction and summation\n * based on Einstein summation.)\n */\n\nimport {Tensor} from '../tensor';\nimport {assert} from '../util_base';\n\nconst ARROW = '->';\nconst ARROW_REGEX = /->/g;\nconst COMMA = ',';\nconst ELLIPSIS = '...';\n\n/**\n * Parse an equation for einsum.\n *\n * @param equation The einsum equation (e.g., \"ij,jk->ik\").\n * @param numTensors Number of tensors provided along with `equation`. Used to\n *   check matching number of input tensors.\n * @returns An object consisting of the following fields:\n *   - allDims: all dimension names as strings.\n *   - summedDims: a list of all dimensions being summed over, as indices to\n *     the elements of `allDims`.\n *   - idDims: indices of the dimensions in each input tensor, as indices to\n *     the elements of `allDims.\n */\nexport function decodeEinsumEquation(equation: string, numTensors: number): {\n  allDims: string[],\n  summedDims: number[],\n  idDims: number[][],\n} {\n  equation = equation.replace(/\\s/g, '');  // Remove witespace in equation.\n  const numArrows =\n      (equation.length - equation.replace(ARROW_REGEX, '').length) /\n      ARROW.length;\n  if (numArrows < 1) {\n    throw new Error('Equations without an arrow are not supported.');\n  } else if (numArrows > 1) {\n    throw new Error(`Equation must contain exactly one arrow (\"${ARROW}\").`);\n  }\n  const [inputString, outputString] = equation.split(ARROW);\n  assert(\n      inputString.indexOf(ELLIPSIS) === -1,\n      () => `The ellipsis notation (\"${ELLIPSIS}\") is not supported yet.`);\n  const inputTerms = inputString.split(COMMA);\n  const numInputs = inputTerms.length;\n  if (numTensors !== numInputs) {\n    throw new Error(\n        `Expected ${numInputs} input tensors, received ${numTensors}`);\n  }\n  if (numInputs > 2) {\n    throw new Error(\n        'Support for more than 2 input tensors is not implemented yet.');\n  }\n\n  const allDims: string[] = [];\n  for (let i = 0; i < outputString.length; ++i) {\n    const dimName = outputString[i];\n    if (!inputTerms.some(inputTerm => inputTerm.indexOf(dimName) !== -1)) {\n      throw new Error(\n          `Output subscripts contain the label ${dimName} ` +\n          `not present in the input subscripts.`);\n    }\n    if (allDims.indexOf(dimName) === -1) {\n      allDims.push(dimName);\n    }\n  }\n  for (let i = 0; i < inputString.length; ++i) {\n    const dimName = inputString[i];\n    if (allDims.indexOf(dimName) === -1 && dimName !== COMMA) {\n      allDims.push(dimName);\n    }\n  }\n\n  const idDims: number[][] = new Array<number[]>(inputTerms.length);\n  for (let i = 0; i < numInputs; ++i) {\n    if (new Set(inputTerms[i].split('')).size !== inputTerms[i].length) {\n      throw new Error(\n          `Found duplicate axes in input component ${inputTerms[i]}. ` +\n          `Support for duplicate axes in input is not implemented yet.`);\n    }\n    idDims[i] = [];\n    for (let j = 0; j < inputTerms[i].length; ++j) {\n      idDims[i].push(allDims.indexOf(inputTerms[i][j]));\n    }\n  }\n\n  const numDims = allDims.length;          // Number of unique dimensions.\n  const numOutDims = outputString.length;  // Number of output dimensions.\n  const summedDims: number[] = [];         // Dimensions being summed over.\n  for (let i = numOutDims; i < numDims; ++i) {\n    summedDims.push(i);\n  }\n  return {allDims, summedDims, idDims};\n}\n\n/**\n * Get the permutation for a given input tensor.\n *\n * @param nDims Total number of dimension of all tensors involved in the einsum\n *   operation.\n * @param idDims Dimension indices involve in the tensor in question.\n * @returns An object consisting of the following fields:\n *   - permutationIndices: Indices to permute the axes of the tensor with.\n *   - expandDims: Indices to the dimension that need to be expanded from the\n *     tensor after permutation.\n */\nexport function getEinsumPermutation(nDims: number, idDims: number[]):\n    {permutationIndices: number[], expandDims: number[]} {\n  let permutationIndices: number[] = new Array<number>(nDims);\n  permutationIndices.fill(-1);\n  for (let i = 0; i < idDims.length; ++i) {\n    permutationIndices[idDims[i]] = i;\n  }\n  const expandDims: number[] = [];\n  for (let i = 0; i < nDims; ++i) {\n    if (permutationIndices[i] === -1) {\n      expandDims.push(i);\n    }\n  }\n  permutationIndices = permutationIndices.filter(d => d !== -1);\n  return {permutationIndices, expandDims};\n}\n\n/**\n * Checks that the dimension sizes from different input tensors match the\n * equation.\n */\nexport function checkEinsumDimSizes(\n    nDims: number, idDims: number[][], tensors: Tensor[]) {\n  const dimSizes: number[] = new Array<number>(nDims);\n  for (let i = 0; i < tensors.length; ++i) {\n    const shape: number[] = tensors[i].shape;\n    for (let j = 0; j < idDims[i].length; ++j) {\n      if (dimSizes[idDims[i][j]] === undefined) {\n        dimSizes[idDims[i][j]] = shape[j];\n      } else {\n        assert(\n            dimSizes[idDims[i][j]] === shape[j],\n            () => `Expected dimension ${dimSizes[idDims[i][j]]} at axis ${j} ` +\n                `of input shaped ${JSON.stringify(shape)}, ` +\n                `but got dimension ${shape[j]}`);\n      }\n    }\n  }\n}\n\n/**\n * Gets path of computation for einsum.\n *\n * @param summedDims indices to the dimensions being summed over.\n * @param idDims A look up table for the dimensions present in each input\n *     tensor. Each consituent array contains indices for the dimensions in the\n *     corresponding input tensor.\n *\n * @return A map with two fields:\n *   - path: The path of computation, with each element indicating the dimension\n *     being summed over after the element-wise multiplication in that step.\n *   - steps: With the same length as `path`. Each element contains the indices\n *     to the input tensors being used for element-wise multiplication in the\n *     corresponding step.\n */\nexport function getEinsumComputePath(summedDims: number[], idDims: number[][]):\n    {path: number[], steps: number[][]} {\n  const path: number[] = summedDims;\n  const steps: number[][] = [];\n  let nSteps = 0;\n  if (summedDims.length === 0) {\n    // Einsum that involes no summing: e.g., transpose and outer product.\n    path.push(-1);\n  }\n  nSteps = summedDims.length + 1;\n  for (let i = 0; i < nSteps; ++i) {\n    steps.push([]);\n  }\n  const computedTermIndices: number[] = [];\n  for (let i = 0; i < path.length; ++i) {\n    const summedDim = path[i];\n    const termIndices = findTermsWithDim(idDims, summedDim);\n    for (const termIndex of termIndices) {\n      if (computedTermIndices.indexOf(termIndex) === -1) {\n        steps[i].push(termIndex);\n        computedTermIndices.push(termIndex);\n      }\n    }\n  }\n  return {path, steps};\n}\n\n/** Determines if an axes permutation is the identity permutation. */\nexport function isIdentityPermutation(perm: number[]): boolean {\n  return perm.every((dim: number, index: number) => dim === index);\n}\n\nfunction findTermsWithDim(idDims: number[][], dim: number): number[] {\n  const termIndices: number[] = [];\n  for (let i = 0; i < idDims.length; ++i) {\n    if (idDims[i].length === 0 || idDims[i].indexOf(dim) !== -1 || dim === -1) {\n      termIndices.push(i);\n    }\n  }\n  return termIndices;\n}\n"]}
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