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2025-02-12 ea42ff3ebee1eeb3fb29423aa848a249441db81c

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/**
 * @license
 * Copyright 2020 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 { ENGINE } from '../../engine';
import { assert } from '../../util';
import { div } from '../div';
import { mul } from '../mul';
import { norm } from '../norm';
import { op } from '../operation';
import { split } from '../split';
import { squeeze } from '../squeeze';
import { stack } from '../stack';
import { sub } from '../sub';
import { sum } from '../sum';
/**
 * Gram-Schmidt orthogonalization.
 *
 * ```js
 * const x = tf.tensor2d([[1, 2], [3, 4]]);
 * let y = tf.linalg.gramSchmidt(x);
 * y.print();
 * console.log('Orthogonalized:');
 * y.dot(y.transpose()).print();  // should be nearly the identity matrix.
 * console.log('First row direction maintained:');
 * const data = await y.array();
 * console.log(data[0][1] / data[0][0]);  // should be nearly 2.
 * ```
 *
 * @param xs The vectors to be orthogonalized, in one of the two following
 *   formats:
 *   - An Array of `tf.Tensor1D`.
 *   - A `tf.Tensor2D`, i.e., a matrix, in which case the vectors are the rows
 *     of `xs`.
 *   In each case, all the vectors must have the same length and the length
 *   must be greater than or equal to the number of vectors.
 * @returns The orthogonalized and normalized vectors or matrix.
 *   Orthogonalization means that the vectors or the rows of the matrix
 *   are orthogonal (zero inner products). Normalization means that each
 *   vector or each row of the matrix has an L2 norm that equals `1`.
 *
 * @doc {heading:'Operations', subheading:'Linear Algebra', namespace:'linalg'}
 */
function gramSchmidt_(xs) {
    let inputIsTensor2D;
    if (Array.isArray(xs)) {
        inputIsTensor2D = false;
        assert(xs != null && xs.length > 0, () => 'Gram-Schmidt process: input must not be null, undefined, or ' +
            'empty');
        const dim = xs[0].shape[0];
        for (let i = 1; i < xs.length; ++i) {
            assert(xs[i].shape[0] === dim, () => 'Gram-Schmidt: Non-unique lengths found in the input vectors: ' +
                `(${xs[i].shape[0]} vs. ${dim})`);
        }
    }
    else {
        inputIsTensor2D = true;
        xs = split(xs, xs.shape[0], 0).map(x => squeeze(x, [0]));
    }
    assert(xs.length <= xs[0].shape[0], () => `Gram-Schmidt: Number of vectors (${xs.length}) exceeds ` +
        `number of dimensions (${xs[0].shape[0]}).`);
    const ys = [];
    const xs1d = xs;
    for (let i = 0; i < xs.length; ++i) {
        ys.push(ENGINE.tidy(() => {
            let x = xs1d[i];
            if (i > 0) {
                for (let j = 0; j < i; ++j) {
                    const proj = mul(sum(mul(ys[j], x)), ys[j]);
                    x = sub(x, proj);
                }
            }
            return div(x, norm(x, 'euclidean'));
        }));
    }
    if (inputIsTensor2D) {
        return stack(ys, 0);
    }
    else {
        return ys;
    }
}
export const gramSchmidt = /* @__PURE__ */ op({ gramSchmidt_ });
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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 {ENGINE} from '../../engine';\nimport {Tensor1D, Tensor2D} from '../../tensor';\nimport {assert} from '../../util';\n\nimport {div} from '../div';\nimport {mul} from '../mul';\nimport {norm} from '../norm';\nimport {op} from '../operation';\nimport {split} from '../split';\nimport {squeeze} from '../squeeze';\nimport {stack} from '../stack';\nimport {sub} from '../sub';\nimport {sum} from '../sum';\n\n/**\n * Gram-Schmidt orthogonalization.\n *\n * ```js\n * const x = tf.tensor2d([[1, 2], [3, 4]]);\n * let y = tf.linalg.gramSchmidt(x);\n * y.print();\n * console.log('Orthogonalized:');\n * y.dot(y.transpose()).print();  // should be nearly the identity matrix.\n * console.log('First row direction maintained:');\n * const data = await y.array();\n * console.log(data[0][1] / data[0][0]);  // should be nearly 2.\n * ```\n *\n * @param xs The vectors to be orthogonalized, in one of the two following\n *   formats:\n *   - An Array of `tf.Tensor1D`.\n *   - A `tf.Tensor2D`, i.e., a matrix, in which case the vectors are the rows\n *     of `xs`.\n *   In each case, all the vectors must have the same length and the length\n *   must be greater than or equal to the number of vectors.\n * @returns The orthogonalized and normalized vectors or matrix.\n *   Orthogonalization means that the vectors or the rows of the matrix\n *   are orthogonal (zero inner products). Normalization means that each\n *   vector or each row of the matrix has an L2 norm that equals `1`.\n *\n * @doc {heading:'Operations', subheading:'Linear Algebra', namespace:'linalg'}\n */\nfunction gramSchmidt_(xs: Tensor1D[]|Tensor2D): Tensor1D[]|Tensor2D {\n  let inputIsTensor2D: boolean;\n  if (Array.isArray(xs)) {\n    inputIsTensor2D = false;\n    assert(\n        xs != null && xs.length > 0,\n        () => 'Gram-Schmidt process: input must not be null, undefined, or ' +\n            'empty');\n    const dim = xs[0].shape[0];\n    for (let i = 1; i < xs.length; ++i) {\n      assert(\n          xs[i].shape[0] === dim,\n          () =>\n              'Gram-Schmidt: Non-unique lengths found in the input vectors: ' +\n              `(${(xs as Tensor1D[])[i].shape[0]} vs. ${dim})`);\n    }\n  } else {\n    inputIsTensor2D = true;\n    xs = split(xs, xs.shape[0], 0).map(x => squeeze(x, [0]));\n  }\n\n  assert(\n      xs.length <= xs[0].shape[0],\n      () => `Gram-Schmidt: Number of vectors (${\n                (xs as Tensor1D[]).length}) exceeds ` +\n          `number of dimensions (${(xs as Tensor1D[])[0].shape[0]}).`);\n\n  const ys: Tensor1D[] = [];\n  const xs1d = xs;\n  for (let i = 0; i < xs.length; ++i) {\n    ys.push(ENGINE.tidy(() => {\n      let x = xs1d[i];\n      if (i > 0) {\n        for (let j = 0; j < i; ++j) {\n          const proj = mul(sum(mul(ys[j], x)), ys[j]);\n          x = sub(x, proj);\n        }\n      }\n      return div(x, norm(x, 'euclidean'));\n    }));\n  }\n\n  if (inputIsTensor2D) {\n    return stack(ys, 0) as Tensor2D;\n  } else {\n    return ys;\n  }\n}\n\nexport const gramSchmidt = /* @__PURE__ */ op({gramSchmidt_});\n"]}