/**
|
* @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 { dispose } from '../../globals';
|
import { assert } from '../../util';
|
import { clone } from '../clone';
|
import { concat } from '../concat';
|
import { div } from '../div';
|
import { eye } from '../eye';
|
import { greater } from '../greater';
|
import { matMul } from '../mat_mul';
|
import { mul } from '../mul';
|
import { neg } from '../neg';
|
import { norm } from '../norm';
|
import { op } from '../operation';
|
import { reshape } from '../reshape';
|
import { slice } from '../slice';
|
import { stack } from '../stack';
|
import { sub } from '../sub';
|
import { tensor2d } from '../tensor2d';
|
import { transpose } from '../transpose';
|
import { unstack } from '../unstack';
|
import { where } from '../where';
|
/**
|
* Compute QR decomposition of m-by-n matrix using Householder transformation.
|
*
|
* Implementation based on
|
* [http://www.cs.cornell.edu/~bindel/class/cs6210-f09/lec18.pdf]
|
* (http://www.cs.cornell.edu/~bindel/class/cs6210-f09/lec18.pdf)
|
*
|
* ```js
|
* const a = tf.tensor2d([[1, 2], [3, 4]]);
|
* let [q, r] = tf.linalg.qr(a);
|
* console.log('Q');
|
* q.print();
|
* console.log('R');
|
* r.print();
|
* console.log('Orthogonalized');
|
* q.dot(q.transpose()).print() // should be nearly the identity matrix.
|
* console.log('Reconstructed');
|
* q.dot(r).print(); // should be nearly [[1, 2], [3, 4]];
|
* ```
|
*
|
* @param x The `tf.Tensor` to be QR-decomposed. Must have rank >= 2. Suppose
|
* it has the shape `[..., M, N]`.
|
* @param fullMatrices An optional boolean parameter. Defaults to `false`.
|
* If `true`, compute full-sized `Q`. If `false` (the default),
|
* compute only the leading N columns of `Q` and `R`.
|
* @returns An `Array` of two `tf.Tensor`s: `[Q, R]`. `Q` is a unitary matrix,
|
* i.e., its columns all have unit norm and are mutually orthogonal.
|
* If `M >= N`,
|
* If `fullMatrices` is `false` (default),
|
* - `Q` has a shape of `[..., M, N]`,
|
* - `R` has a shape of `[..., N, N]`.
|
* If `fullMatrices` is `true` (default),
|
* - `Q` has a shape of `[..., M, M]`,
|
* - `R` has a shape of `[..., M, N]`.
|
* If `M < N`,
|
* - `Q` has a shape of `[..., M, M]`,
|
* - `R` has a shape of `[..., M, N]`.
|
* @throws If the rank of `x` is less than 2.
|
*
|
* @doc {heading:'Operations',
|
* subheading:'Linear Algebra',
|
* namespace:'linalg'}
|
*/
|
function qr_(x, fullMatrices = false) {
|
assert(x.rank >= 2, () => `qr() requires input tensor to have a rank >= 2, but got rank ${x.rank}`);
|
if (x.rank === 2) {
|
return qr2d(x, fullMatrices);
|
}
|
else {
|
// Rank > 2.
|
// TODO(cais): Below we split the input into individual 2D tensors,
|
// perform QR decomposition on them and then stack the results back
|
// together. We should explore whether this can be parallelized.
|
const outerDimsProd = x.shape.slice(0, x.shape.length - 2)
|
.reduce((value, prev) => value * prev);
|
const x2ds = unstack(reshape(x, [
|
outerDimsProd, x.shape[x.shape.length - 2],
|
x.shape[x.shape.length - 1]
|
]), 0);
|
const q2ds = [];
|
const r2ds = [];
|
x2ds.forEach(x2d => {
|
const [q2d, r2d] = qr2d(x2d, fullMatrices);
|
q2ds.push(q2d);
|
r2ds.push(r2d);
|
});
|
const q = reshape(stack(q2ds, 0), x.shape);
|
const r = reshape(stack(r2ds, 0), x.shape);
|
return [q, r];
|
}
|
}
|
function qr2d(x, fullMatrices = false) {
|
return ENGINE.tidy(() => {
|
assert(x.shape.length === 2, () => `qr2d() requires a 2D Tensor, but got a ${x.shape.length}D Tensor.`);
|
const m = x.shape[0];
|
const n = x.shape[1];
|
let q = eye(m); // Orthogonal transform so far.
|
let r = clone(x); // Transformed matrix so far.
|
const one2D = tensor2d([[1]], [1, 1]);
|
let w = clone(one2D);
|
const iters = m >= n ? n : m;
|
for (let j = 0; j < iters; ++j) {
|
// This tidy within the for-loop ensures we clean up temporary
|
// tensors as soon as they are no longer needed.
|
const rTemp = r;
|
const wTemp = w;
|
const qTemp = q;
|
[w, r, q] = ENGINE.tidy(() => {
|
// Find H = I - tau * w * w', to put zeros below R(j, j).
|
const rjEnd1 = slice(r, [j, j], [m - j, 1]);
|
const normX = norm(rjEnd1);
|
const rjj = slice(r, [j, j], [1, 1]);
|
// The sign() function returns 0 on 0, which causes division by zero.
|
const s = where(greater(rjj, 0), tensor2d([[-1]]), tensor2d([[1]]));
|
const u1 = sub(rjj, mul(s, normX));
|
const wPre = div(rjEnd1, u1);
|
if (wPre.shape[0] === 1) {
|
w = clone(one2D);
|
}
|
else {
|
w = concat([
|
one2D,
|
slice(wPre, [1, 0], [wPre.shape[0] - 1, wPre.shape[1]])
|
], 0);
|
}
|
const tau = neg(div(matMul(s, u1), normX));
|
// -- R := HR, Q := QH.
|
const rjEndAll = slice(r, [j, 0], [m - j, n]);
|
const tauTimesW = mul(tau, w);
|
const wT = transpose(w);
|
if (j === 0) {
|
r = sub(rjEndAll, matMul(tauTimesW, matMul(wT, rjEndAll)));
|
}
|
else {
|
const rTimesTau = sub(rjEndAll, matMul(tauTimesW, matMul(wT, rjEndAll)));
|
r = concat([slice(r, [0, 0], [j, n]), rTimesTau], 0);
|
}
|
const tawTimesWT = transpose(tauTimesW);
|
const qAllJEnd = slice(q, [0, j], [m, q.shape[1] - j]);
|
if (j === 0) {
|
q = sub(qAllJEnd, matMul(matMul(qAllJEnd, w), tawTimesWT));
|
}
|
else {
|
const qTimesTau = sub(qAllJEnd, matMul(matMul(qAllJEnd, w), tawTimesWT));
|
q = concat([slice(q, [0, 0], [m, j]), qTimesTau], 1);
|
}
|
return [w, r, q];
|
});
|
dispose([rTemp, wTemp, qTemp]);
|
}
|
if (!fullMatrices && m > n) {
|
q = slice(q, [0, 0], [m, n]);
|
r = slice(r, [0, 0], [n, n]);
|
}
|
return [q, r];
|
});
|
}
|
export const qr = /* @__PURE__ */ op({ qr_ });
|
//# sourceMappingURL=data:application/json;base64,{"version":3,"file":"qr.js","sourceRoot":"","sources":["../../../../../../../tfjs-core/src/ops/linalg/qr.ts"],"names":[],"mappings":"AAAA;;;;;;;;;;;;;;;GAeG;AACH,OAAO,EAAC,MAAM,EAAC,MAAM,cAAc,CAAC;AACpC,OAAO,EAAC,OAAO,EAAC,MAAM,eAAe,CAAC;AAEtC,OAAO,EAAC,MAAM,EAAC,MAAM,YAAY,CAAC;AAElC,OAAO,EAAC,KAAK,EAAC,MAAM,UAAU,CAAC;AAC/B,OAAO,EAAC,MAAM,EAAC,MAAM,WAAW,CAAC;AACjC,OAAO,EAAC,GAAG,EAAC,MAAM,QAAQ,CAAC;AAC3B,OAAO,EAAC,GAAG,EAAC,MAAM,QAAQ,CAAC;AAC3B,OAAO,EAAC,OAAO,EAAC,MAAM,YAAY,CAAC;AACnC,OAAO,EAAC,MAAM,EAAC,MAAM,YAAY,CAAC;AAClC,OAAO,EAAC,GAAG,EAAC,MAAM,QAAQ,CAAC;AAC3B,OAAO,EAAC,GAAG,EAAC,MAAM,QAAQ,CAAC;AAC3B,OAAO,EAAC,IAAI,EAAC,MAAM,SAAS,CAAC;AAC7B,OAAO,EAAC,EAAE,EAAC,MAAM,cAAc,CAAC;AAChC,OAAO,EAAC,OAAO,EAAC,MAAM,YAAY,CAAC;AACnC,OAAO,EAAC,KAAK,EAAC,MAAM,UAAU,CAAC;AAC/B,OAAO,EAAC,KAAK,EAAC,MAAM,UAAU,CAAC;AAC/B,OAAO,EAAC,GAAG,EAAC,MAAM,QAAQ,CAAC;AAC3B,OAAO,EAAC,QAAQ,EAAC,MAAM,aAAa,CAAC;AACrC,OAAO,EAAC,SAAS,EAAC,MAAM,cAAc,CAAC;AACvC,OAAO,EAAC,OAAO,EAAC,MAAM,YAAY,CAAC;AACnC,OAAO,EAAC,KAAK,EAAC,MAAM,UAAU,CAAC;AAE/B;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;GA0CG;AACH,SAAS,GAAG,CAAC,CAAS,EAAE,YAAY,GAAG,KAAK;IAC1C,MAAM,CACF,CAAC,CAAC,IAAI,IAAI,CAAC,EACX,GAAG,EAAE,CAAC,gEACF,CAAC,CAAC,IAAI,EAAE,CAAC,CAAC;IAElB,IAAI,CAAC,CAAC,IAAI,KAAK,CAAC,EAAE;QAChB,OAAO,IAAI,CAAC,CAAa,EAAE,YAAY,CAAC,CAAC;KAC1C;SAAM;QACL,YAAY;QACZ,mEAAmE;QACnE,qEAAqE;QACrE,kEAAkE;QAClE,MAAM,aAAa,GAAG,CAAC,CAAC,KAAK,CAAC,KAAK,CAAC,CAAC,EAAE,CAAC,CAAC,KAAK,CAAC,MAAM,GAAG,CAAC,CAAC;aAC/B,MAAM,CAAC,CAAC,KAAK,EAAE,IAAI,EAAE,EAAE,CAAC,KAAK,GAAG,IAAI,CAAC,CAAC;QACjE,MAAM,IAAI,GAAG,OAAO,CAChB,OAAO,CACH,CAAC,EACD;YACE,aAAa,EAAE,CAAC,CAAC,KAAK,CAAC,CAAC,CAAC,KAAK,CAAC,MAAM,GAAG,CAAC,CAAC;YAC1C,CAAC,CAAC,KAAK,CAAC,CAAC,CAAC,KAAK,CAAC,MAAM,GAAG,CAAC,CAAC;SAC5B,CAAC,EACN,CAAC,CAAC,CAAC;QACP,MAAM,IAAI,GAAe,EAAE,CAAC;QAC5B,MAAM,IAAI,GAAe,EAAE,CAAC;QAC5B,IAAI,CAAC,OAAO,CAAC,GAAG,CAAC,EAAE;YACjB,MAAM,CAAC,GAAG,EAAE,GAAG,CAAC,GAAG,IAAI,CAAC,GAAe,EAAE,YAAY,CAAC,CAAC;YACvD,IAAI,CAAC,IAAI,CAAC,GAAG,CAAC,CAAC;YACf,IAAI,CAAC,IAAI,CAAC,GAAG,CAAC,CAAC;QACjB,CAAC,CAAC,CAAC;QACH,MAAM,CAAC,GAAG,OAAO,CAAC,KAAK,CAAC,IAAI,EAAE,CAAC,CAAC,EAAE,CAAC,CAAC,KAAK,CAAC,CAAC;QAC3C,MAAM,CAAC,GAAG,OAAO,CAAC,KAAK,CAAC,IAAI,EAAE,CAAC,CAAC,EAAE,CAAC,CAAC,KAAK,CAAC,CAAC;QAC3C,OAAO,CAAC,CAAC,EAAE,CAAC,CAAC,CAAC;KACf;AACH,CAAC;AAED,SAAS,IAAI,CAAC,CAAW,EAAE,YAAY,GAAG,KAAK;IAC7C,OAAO,MAAM,CAAC,IAAI,CAAC,GAAG,EAAE;QACtB,MAAM,CACF,CAAC,CAAC,KAAK,CAAC,MAAM,KAAK,CAAC,EACpB,GAAG,EAAE,CAAC,0CACF,CAAC,CAAC,KAAK,CAAC,MAAM,WAAW,CAAC,CAAC;QAEnC,MAAM,CAAC,GAAG,CAAC,CAAC,KAAK,CAAC,CAAC,CAAC,CAAC;QACrB,MAAM,CAAC,GAAG,CAAC,CAAC,KAAK,CAAC,CAAC,CAAC,CAAC;QAErB,IAAI,CAAC,GAAG,GAAG,CAAC,CAAC,CAAC,CAAC,CAAI,+BAA+B;QAClD,IAAI,CAAC,GAAG,KAAK,CAAC,CAAC,CAAC,CAAC,CAAE,6BAA6B;QAEhD,MAAM,KAAK,GAAG,QAAQ,CAAC,CAAC,CAAC,CAAC,CAAC,CAAC,EAAE,CAAC,CAAC,EAAE,CAAC,CAAC,CAAC,CAAC;QACtC,IAAI,CAAC,GAAa,KAAK,CAAC,KAAK,CAAC,CAAC;QAE/B,MAAM,KAAK,GAAG,CAAC,IAAI,CAAC,CAAC,CAAC,CAAC,CAAC,CAAC,CAAC,CAAC,CAAC,CAAC;QAC7B,KAAK,IAAI,CAAC,GAAG,CAAC,EAAE,CAAC,GAAG,KAAK,EAAE,EAAE,CAAC,EAAE;YAC9B,8DAA8D;YAC9D,gDAAgD;YAChD,MAAM,KAAK,GAAG,CAAC,CAAC;YAChB,MAAM,KAAK,GAAG,CAAC,CAAC;YAChB,MAAM,KAAK,GAAG,CAAC,CAAC;YAChB,CAAC,CAAC,EAAE,CAAC,EAAE,CAAC,CAAC,GAAG,MAAM,CAAC,IAAI,CAAC,GAAmC,EAAE;gBAC3D,yDAAyD;gBACzD,MAAM,MAAM,GAAG,KAAK,CAAC,CAAC,EAAE,CAAC,CAAC,EAAE,CAAC,CAAC,EAAE,CAAC,CAAC,GAAG,CAAC,EAAE,CAAC,CAAC,CAAC,CAAC;gBAC5C,MAAM,KAAK,GAAG,IAAI,CAAC,MAAM,CAAC,CAAC;gBAC3B,MAAM,GAAG,GAAG,KAAK,CAAC,CAAC,EAAE,CAAC,CAAC,EAAE,CAAC,CAAC,EAAE,CAAC,CAAC,EAAE,CAAC,CAAC,CAAC,CAAC;gBAErC,qEAAqE;gBACrE,MAAM,CAAC,GAAG,KAAK,CAAC,OAAO,CAAC,GAAG,EAAE,CAAC,CAAC,EAAE,QAAQ,CAAC,CAAC,CAAC,CAAC,CAAC,CAAC,CAAC,CAAC,EAAE,QAAQ,CAAC,CAAC,CAAC,CAAC,CAAC,CAAC,CAAC,CAAC,CAAC;gBAEpE,MAAM,EAAE,GAAG,GAAG,CAAC,GAAG,EAAE,GAAG,CAAC,CAAC,EAAE,KAAK,CAAC,CAAC,CAAC;gBACnC,MAAM,IAAI,GAAG,GAAG,CAAC,MAAM,EAAE,EAAE,CAAC,CAAC;gBAC7B,IAAI,IAAI,CAAC,KAAK,CAAC,CAAC,CAAC,KAAK,CAAC,EAAE;oBACvB,CAAC,GAAG,KAAK,CAAC,KAAK,CAAC,CAAC;iBAClB;qBAAM;oBACL,CAAC,GAAG,MAAM,CACN;wBACE,KAAK;wBACL,KAAK,CAAC,IAAI,EAAE,CAAC,CAAC,EAAE,CAAC,CAAC,EAAE,CAAC,IAAI,CAAC,KAAK,CAAC,CAAC,CAAC,GAAG,CAAC,EAAE,IAAI,CAAC,KAAK,CAAC,CAAC,CAAC,CAAC,CAC1C;qBACb,EACD,CAAC,CAAC,CAAC;iBACR;gBACD,MAAM,GAAG,GAAG,GAAG,CAAC,GAAG,CAAC,MAAM,CAAC,CAAC,EAAE,EAAE,CAAC,EAAE,KAAK,CAAC,CAAa,CAAC;gBAEvD,uBAAuB;gBACvB,MAAM,QAAQ,GAAG,KAAK,CAAC,CAAC,EAAE,CAAC,CAAC,EAAE,CAAC,CAAC,EAAE,CAAC,CAAC,GAAG,CAAC,EAAE,CAAC,CAAC,CAAC,CAAC;gBAC9C,MAAM,SAAS,GAAa,GAAG,CAAC,GAAG,EAAE,CAAC,CAAC,CAAC;gBACxC,MAAM,EAAE,GAAa,SAAS,CAAC,CAAC,CAAC,CAAC;gBAClC,IAAI,CAAC,KAAK,CAAC,EAAE;oBACX,CAAC,GAAG,GAAG,CAAC,QAAQ,EAAE,MAAM,CAAC,SAAS,EAAE,MAAM,CAAC,EAAE,EAAE,QAAQ,CAAC,CAAC,CAAC,CAAC;iBAC5D;qBAAM;oBACL,MAAM,SAAS,GACX,GAAG,CAAC,QAAQ,EAAE,MAAM,CAAC,SAAS,EAAE,MAAM,CAAC,EAAE,EAAE,QAAQ,CAAC,CAAC,CAAC,CAAC;oBAC3D,CAAC,GAAG,MAAM,CAAC,CAAC,KAAK,CAAC,CAAC,EAAE,CAAC,CAAC,EAAE,CAAC,CAAC,EAAE,CAAC,CAAC,EAAE,CAAC,CAAC,CAAC,EAAE,SAAS,CAAC,EAAE,CAAC,CAAC,CAAC;iBACtD;gBACD,MAAM,UAAU,GAAa,SAAS,CAAC,SAAS,CAAC,CAAC;gBAClD,MAAM,QAAQ,GAAG,KAAK,CAAC,CAAC,EAAE,CAAC,CAAC,EAAE,CAAC,CAAC,EAAE,CAAC,CAAC,EAAE,CAAC,CAAC,KAAK,CAAC,CAAC,CAAC,GAAG,CAAC,CAAC,CAAC,CAAC;gBACvD,IAAI,CAAC,KAAK,CAAC,EAAE;oBACX,CAAC,GAAG,GAAG,CAAC,QAAQ,EAAE,MAAM,CAAC,MAAM,CAAC,QAAQ,EAAE,CAAC,CAAC,EAAE,UAAU,CAAC,CAAC,CAAC;iBAC5D;qBAAM;oBACL,MAAM,SAAS,GACX,GAAG,CAAC,QAAQ,EAAE,MAAM,CAAC,MAAM,CAAC,QAAQ,EAAE,CAAC,CAAC,EAAE,UAAU,CAAC,CAAC,CAAC;oBAC3D,CAAC,GAAG,MAAM,CAAC,CAAC,KAAK,CAAC,CAAC,EAAE,CAAC,CAAC,EAAE,CAAC,CAAC,EAAE,CAAC,CAAC,EAAE,CAAC,CAAC,CAAC,EAAE,SAAS,CAAC,EAAE,CAAC,CAAC,CAAC;iBACtD;gBACD,OAAO,CAAC,CAAC,EAAE,CAAC,EAAE,CAAC,CAAC,CAAC;YACnB,CAAC,CAAC,CAAC;YACH,OAAO,CAAC,CAAC,KAAK,EAAE,KAAK,EAAE,KAAK,CAAC,CAAC,CAAC;SAChC;QAED,IAAI,CAAC,YAAY,IAAI,CAAC,GAAG,CAAC,EAAE;YAC1B,CAAC,GAAG,KAAK,CAAC,CAAC,EAAE,CAAC,CAAC,EAAE,CAAC,CAAC,EAAE,CAAC,CAAC,EAAE,CAAC,CAAC,CAAC,CAAC;YAC7B,CAAC,GAAG,KAAK,CAAC,CAAC,EAAE,CAAC,CAAC,EAAE,CAAC,CAAC,EAAE,CAAC,CAAC,EAAE,CAAC,CAAC,CAAC,CAAC;SAC9B;QAED,OAAO,CAAC,CAAC,EAAE,CAAC,CAAC,CAAC;IAChB,CAAC,CAAyB,CAAC;AAC7B,CAAC;AAED,MAAM,CAAC,MAAM,EAAE,GAAG,eAAe,CAAC,EAAE,CAAC,EAAC,GAAG,EAAC,CAAC,CAAC","sourcesContent":["/**\n * @license\n * Copyright 2020 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 */\nimport {ENGINE} from '../../engine';\nimport {dispose} from '../../globals';\nimport {Tensor, Tensor2D} from '../../tensor';\nimport {assert} from '../../util';\n\nimport {clone} from '../clone';\nimport {concat} from '../concat';\nimport {div} from '../div';\nimport {eye} from '../eye';\nimport {greater} from '../greater';\nimport {matMul} from '../mat_mul';\nimport {mul} from '../mul';\nimport {neg} from '../neg';\nimport {norm} from '../norm';\nimport {op} from '../operation';\nimport {reshape} from '../reshape';\nimport {slice} from '../slice';\nimport {stack} from '../stack';\nimport {sub} from '../sub';\nimport {tensor2d} from '../tensor2d';\nimport {transpose} from '../transpose';\nimport {unstack} from '../unstack';\nimport {where} from '../where';\n\n/**\n * Compute QR decomposition of m-by-n matrix using Householder transformation.\n *\n * Implementation based on\n *   [http://www.cs.cornell.edu/~bindel/class/cs6210-f09/lec18.pdf]\n * (http://www.cs.cornell.edu/~bindel/class/cs6210-f09/lec18.pdf)\n *\n * ```js\n * const a = tf.tensor2d([[1, 2], [3, 4]]);\n * let [q, r] = tf.linalg.qr(a);\n * console.log('Q');\n * q.print();\n * console.log('R');\n * r.print();\n * console.log('Orthogonalized');\n * q.dot(q.transpose()).print()  // should be nearly the identity matrix.\n * console.log('Reconstructed');\n * q.dot(r).print(); // should be nearly [[1, 2], [3, 4]];\n * ```\n *\n * @param x The `tf.Tensor` to be QR-decomposed. Must have rank >= 2. Suppose\n *   it has the shape `[..., M, N]`.\n * @param fullMatrices An optional boolean parameter. Defaults to `false`.\n *   If `true`, compute full-sized `Q`. If `false` (the default),\n *   compute only the leading N columns of `Q` and `R`.\n * @returns An `Array` of two `tf.Tensor`s: `[Q, R]`. `Q` is a unitary matrix,\n *   i.e., its columns all have unit norm and are mutually orthogonal.\n *   If `M >= N`,\n *     If `fullMatrices` is `false` (default),\n *       - `Q` has a shape of `[..., M, N]`,\n *       - `R` has a shape of `[..., N, N]`.\n *     If `fullMatrices` is `true` (default),\n *       - `Q` has a shape of `[..., M, M]`,\n *       - `R` has a shape of `[..., M, N]`.\n *   If `M < N`,\n *     - `Q` has a shape of `[..., M, M]`,\n *     - `R` has a shape of `[..., M, N]`.\n * @throws If the rank of `x` is less than 2.\n *\n * @doc {heading:'Operations',\n *       subheading:'Linear Algebra',\n *       namespace:'linalg'}\n */\nfunction qr_(x: Tensor, fullMatrices = false): [Tensor, Tensor] {\n  assert(\n      x.rank >= 2,\n      () => `qr() requires input tensor to have a rank >= 2, but got rank ${\n          x.rank}`);\n\n  if (x.rank === 2) {\n    return qr2d(x as Tensor2D, fullMatrices);\n  } else {\n    // Rank > 2.\n    // TODO(cais): Below we split the input into individual 2D tensors,\n    //   perform QR decomposition on them and then stack the results back\n    //   together. We should explore whether this can be parallelized.\n    const outerDimsProd = x.shape.slice(0, x.shape.length - 2)\n                              .reduce((value, prev) => value * prev);\n    const x2ds = unstack(\n        reshape(\n            x,\n            [\n              outerDimsProd, x.shape[x.shape.length - 2],\n              x.shape[x.shape.length - 1]\n            ]),\n        0);\n    const q2ds: Tensor2D[] = [];\n    const r2ds: Tensor2D[] = [];\n    x2ds.forEach(x2d => {\n      const [q2d, r2d] = qr2d(x2d as Tensor2D, fullMatrices);\n      q2ds.push(q2d);\n      r2ds.push(r2d);\n    });\n    const q = reshape(stack(q2ds, 0), x.shape);\n    const r = reshape(stack(r2ds, 0), x.shape);\n    return [q, r];\n  }\n}\n\nfunction qr2d(x: Tensor2D, fullMatrices = false): [Tensor2D, Tensor2D] {\n  return ENGINE.tidy(() => {\n    assert(\n        x.shape.length === 2,\n        () => `qr2d() requires a 2D Tensor, but got a ${\n            x.shape.length}D Tensor.`);\n\n    const m = x.shape[0];\n    const n = x.shape[1];\n\n    let q = eye(m);    // Orthogonal transform so far.\n    let r = clone(x);  // Transformed matrix so far.\n\n    const one2D = tensor2d([[1]], [1, 1]);\n    let w: Tensor2D = clone(one2D);\n\n    const iters = m >= n ? n : m;\n    for (let j = 0; j < iters; ++j) {\n      // This tidy within the for-loop ensures we clean up temporary\n      // tensors as soon as they are no longer needed.\n      const rTemp = r;\n      const wTemp = w;\n      const qTemp = q;\n      [w, r, q] = ENGINE.tidy((): [Tensor2D, Tensor2D, Tensor2D] => {\n        // Find H = I - tau * w * w', to put zeros below R(j, j).\n        const rjEnd1 = slice(r, [j, j], [m - j, 1]);\n        const normX = norm(rjEnd1);\n        const rjj = slice(r, [j, j], [1, 1]);\n\n        // The sign() function returns 0 on 0, which causes division by zero.\n        const s = where(greater(rjj, 0), tensor2d([[-1]]), tensor2d([[1]]));\n\n        const u1 = sub(rjj, mul(s, normX));\n        const wPre = div(rjEnd1, u1);\n        if (wPre.shape[0] === 1) {\n          w = clone(one2D);\n        } else {\n          w = concat(\n              [\n                one2D,\n                slice(wPre, [1, 0], [wPre.shape[0] - 1, wPre.shape[1]]) as\n                    Tensor2D\n              ],\n              0);\n        }\n        const tau = neg(div(matMul(s, u1), normX)) as Tensor2D;\n\n        // -- R := HR, Q := QH.\n        const rjEndAll = slice(r, [j, 0], [m - j, n]);\n        const tauTimesW: Tensor2D = mul(tau, w);\n        const wT: Tensor2D = transpose(w);\n        if (j === 0) {\n          r = sub(rjEndAll, matMul(tauTimesW, matMul(wT, rjEndAll)));\n        } else {\n          const rTimesTau: Tensor2D =\n              sub(rjEndAll, matMul(tauTimesW, matMul(wT, rjEndAll)));\n          r = concat([slice(r, [0, 0], [j, n]), rTimesTau], 0);\n        }\n        const tawTimesWT: Tensor2D = transpose(tauTimesW);\n        const qAllJEnd = slice(q, [0, j], [m, q.shape[1] - j]);\n        if (j === 0) {\n          q = sub(qAllJEnd, matMul(matMul(qAllJEnd, w), tawTimesWT));\n        } else {\n          const qTimesTau: Tensor2D =\n              sub(qAllJEnd, matMul(matMul(qAllJEnd, w), tawTimesWT));\n          q = concat([slice(q, [0, 0], [m, j]), qTimesTau], 1);\n        }\n        return [w, r, q];\n      });\n      dispose([rTemp, wTemp, qTemp]);\n    }\n\n    if (!fullMatrices && m > n) {\n      q = slice(q, [0, 0], [m, n]);\n      r = slice(r, [0, 0], [n, n]);\n    }\n\n    return [q, r];\n  }) as [Tensor2D, Tensor2D];\n}\n\nexport const qr = /* @__PURE__ */ op({qr_});\n"]}
|
