faer/linalg/qr/no_pivoting/
factor.rs

1use crate::assert;
2use crate::internal_prelude::*;
3use linalg::householder::{self};
4/// information about the resulting $QR$ factorization.
5#[derive(Copy, Clone, Debug)]
6pub struct QrInfo {
7	/// estimated rank of the matrix.
8	pub rank: usize,
9}
10
11fn qr_in_place_unblocked<T: ComplexField>(
12	A: MatMut<'_, T>,
13	H: RowMut<'_, T>,
14	row_start: usize,
15	col_start: usize,
16) -> usize {
17	let mut A = A;
18	let mut H = H;
19	let (m, n) = A.shape();
20	let size = H.ncols();
21	let mut col = col_start;
22	let mut row = row_start;
23
24	while row < Ord::min(size, m) && col < n {
25		let norm = A.rb().col(col).get(..row).norm_l2();
26		let (mut A00, A01, A10, A11) =
27			A.rb_mut().split_at_mut(row + 1, col + 1);
28
29		let (mut A10l, A10r) = A10.split_at_col_mut(col);
30		let mut A10r = A10r.col_mut(0);
31
32		let A01 = A01.row_mut(row);
33		let A00 = &mut A00[(row, col)];
34
35		let (info, v) = if row == col {
36			let info =
37				householder::make_householder_in_place(A00, A10r.rb_mut());
38			(info, A10r.rb())
39		} else {
40			let info = householder::make_householder_out_of_place(
41				A00,
42				A10l.rb_mut().col_mut(row),
43				A10r.rb(),
44			);
45			let nrows = A10r.nrows();
46			A10r.rb_mut()
47				.get_mut(..Ord::min(nrows, col - row))
48				.fill(zero());
49			(info, A10l.rb().col(row))
50		};
51
52		let norm = &info.norm.hypot(norm);
53		let eps = &eps::<T::Real>();
54		let leeway = &from_f64::<T::Real>((m - row) as f64 * 16.0);
55		let threshold = eps * leeway * norm;
56
57		let tau_inv = &info.tau.recip();
58		H[row] = info.tau.to_cplx();
59
60		if *tau_inv < min_positive() {
61			if info.norm > zero() {
62				row += 1;
63			}
64		} else if info.norm > threshold {
65			for (head, tail) in
66				core::iter::zip(A01.iter_mut(), A11.col_iter_mut())
67			{
68				let dot = &*head
69					+ linalg::matmul::dot::inner_prod(
70						v.transpose(),
71						Conj::Yes,
72						tail.rb(),
73						Conj::No,
74					);
75				let k = &-dot.mul_real(tau_inv);
76				*head += k;
77				z!(tail, v).for_each(|uz!(dst, src)| {
78					*dst += k * src;
79				});
80			}
81			row += 1;
82		}
83		col += 1;
84	}
85	row
86}
87
88/// the recommended block size to use for a $QR$ decomposition of a matrix with
89/// the given shape.
90#[inline]
91pub fn recommended_block_size<T: ComplexField>(
92	nrows: usize,
93	ncols: usize,
94) -> usize {
95	let prod = nrows * ncols;
96	let size = nrows.min(ncols);
97	(if prod > 8192 * 8192 {
98		256
99	} else if prod > 2048 * 2048 {
100		128
101	} else if prod > 1024 * 1024 {
102		64
103	} else if prod > 512 * 512 {
104		48
105	} else if prod > 128 * 128 {
106		32
107	} else if prod > 32 * 32 {
108		8
109	} else if prod > 16 * 16 {
110		4
111	} else {
112		1
113	})
114	.min(size)
115	.max(1)
116}
117/// $QR$ factorization tuning parameters.
118#[derive(Debug, Copy, Clone)]
119pub struct QrParams {
120	/// threshold at which blocking algorithms should be disabled
121	pub blocking_threshold: usize,
122	/// threshold at which the parallelism should be disabled
123	pub par_threshold: usize,
124	#[doc(hidden)]
125	pub non_exhaustive: NonExhaustive,
126}
127impl<T: ComplexField> Auto<T> for QrParams {
128	#[inline]
129	fn auto() -> Self {
130		Self {
131			blocking_threshold: 48 * 48,
132			par_threshold: 192 * 256,
133			non_exhaustive: NonExhaustive(()),
134		}
135	}
136}
137fn qr_in_place_blocked<T: ComplexField>(
138	A: MatMut<'_, T>,
139	H: MatMut<'_, T>,
140	row_start: usize,
141	col_start: usize,
142	par: Par,
143	stack: &mut MemStack,
144	params: Spec<QrParams, T>,
145) -> usize {
146	let params = params.config;
147	let (m, n) = A.shape();
148	let size = Ord::min(m, n);
149	let block_size = H.nrows();
150	assert!(block_size > 0);
151	if block_size == 1 {
152		return qr_in_place_unblocked(A, H.row_mut(0), row_start, col_start);
153	}
154	let sub_block_size = if m * n < params.blocking_threshold {
155		1
156	} else {
157		block_size / 2
158	};
159	let mut A = A;
160	let mut H = H;
161	let mut col = col_start;
162	let mut row = row_start;
163	while row < size && col < n {
164		let block_size = Ord::min(block_size, Ord::min(size - row, n - col));
165		let sub_block_size = Ord::min(block_size, sub_block_size);
166		let mut A = A.rb_mut();
167		let mut H = H.rb_mut();
168		let start = row;
169		let mut offset = 0;
170		while offset < block_size && col < n {
171			let block_size = Ord::min(n - col, block_size - offset);
172			let sub_block_size = Ord::min(block_size, sub_block_size);
173			let new_row = qr_in_place_blocked(
174				A.rb_mut().subcols_mut(0, col + block_size),
175				H.rb_mut().subrows_mut(offset, sub_block_size),
176				row,
177				col,
178				par,
179				stack,
180				params.into(),
181			);
182			let local = new_row - row;
183			if local > 0 {
184				let mut k = 0;
185				while k < local {
186					let sub_block_size = Ord::min(sub_block_size, local - k);
187					if k > 0 {
188						let mut H = H
189							.rb_mut()
190							.get_mut(offset.., ..)
191							.subcols_mut(row + k, sub_block_size);
192						let (H0, H1) = H.rb_mut().split_at_row_mut(k);
193						let H0 = H0.rb().subrows(0, sub_block_size);
194						let H1 = H1.subrows_mut(0, sub_block_size);
195						{ H1 }.copy_from_triangular_upper(H0);
196					}
197					k += sub_block_size;
198				}
199				householder::upgrade_householder_factor(
200					H.rb_mut()
201						.get_mut(offset..offset + local, row..row + local),
202					A.rb().get(row.., row..row + local),
203					local,
204					sub_block_size,
205					par,
206				);
207				if offset > 0 {
208					use crate::linalg::matmul::triangular::{
209						self, BlockStructure,
210					};
211					let mut H = H.rb_mut().get_mut(
212						..offset + local,
213						start..start + offset + local,
214					);
215					let A = A.rb().get(start.., start..start + offset + local);
216					let (A0, A1) = A.split_at_row(offset + local);
217					triangular::matmul(
218						H.rb_mut(),
219						BlockStructure::UnitTriangularUpper,
220						Accum::Replace,
221						A0.adjoint(),
222						BlockStructure::UnitTriangularUpper,
223						A0,
224						BlockStructure::UnitTriangularLower,
225						one(),
226						par,
227					);
228					triangular::matmul(
229						H.rb_mut(),
230						BlockStructure::UnitTriangularUpper,
231						Accum::Add,
232						A1.adjoint(),
233						BlockStructure::Rectangular,
234						A1,
235						BlockStructure::Rectangular,
236						one(),
237						par,
238					);
239				}
240			}
241			let (Q0, A1) = A
242				.rb_mut()
243				.get_mut(row.., ..)
244				.split_at_col_mut(col + block_size);
245			let Q0 = Q0.rb().get(.., row..row + local);
246			let H = H.rb().get(offset..offset + local, row..row + local);
247			if A1.ncols() > 0 {
248				householder::apply_block_householder_transpose_on_the_left_in_place_with_conj(Q0.rb(), H.rb(), Conj::Yes, A1, par, stack);
249			}
250			offset += local;
251			row += local;
252			col += block_size;
253		}
254	}
255	row
256}
257#[track_caller]
258pub fn qr_in_place<T: ComplexField>(
259	A: MatMut<'_, T>,
260	Q_coeff: MatMut<'_, T>,
261	par: Par,
262	stack: &mut MemStack,
263	params: Spec<QrParams, T>,
264) -> QrInfo {
265	let block_size = Q_coeff.nrows();
266	assert!(all(
267		block_size > 0,
268		Q_coeff.ncols() == Ord::min(A.nrows(), A.ncols()),
269	));
270	#[cfg(feature = "perf-warn")]
271	if A.row_stride().unsigned_abs() != 1 && crate::__perf_warn!(QR_WARN) {
272		if A.col_stride().unsigned_abs() == 1 {
273			log::warn!(
274				target : "faer_perf",
275				"QR prefers column-major matrix. Found row-major matrix."
276			);
277		} else {
278			log::warn!(
279				target : "faer_perf",
280				"QR prefers column-major matrix. Found matrix with generic strides."
281			);
282		}
283	}
284	let mut Q_coeff = Q_coeff;
285	let rank =
286		qr_in_place_blocked(A, Q_coeff.rb_mut(), 0, 0, par, stack, params);
287	Q_coeff.rb_mut().get_mut(.., rank..).fill(zero());
288	let mut col = rank / block_size * block_size;
289	let n = Q_coeff.ncols();
290	while col < n {
291		let block_size = Ord::min(block_size, n - col);
292		let start = Ord::max(rank, col);
293		Q_coeff
294			.rb_mut()
295			.get_mut(start - col.., start..col + block_size)
296			.diagonal_mut()
297			.fill(infinity());
298		col += block_size;
299	}
300	QrInfo { rank }
301}
302/// computes the layout of required workspace for performing a qr
303/// decomposition with no pivoting
304#[inline]
305pub fn qr_in_place_scratch<T: ComplexField>(
306	nrows: usize,
307	ncols: usize,
308	block_size: usize,
309	par: Par,
310	params: Spec<QrParams, T>,
311) -> StackReq {
312	let _ = par;
313	let _ = nrows;
314	let _ = &params;
315	temp_mat_scratch::<T>(block_size, ncols)
316}
317#[cfg(test)]
318mod tests {
319	use super::*;
320	use crate::linalg::solvers::DenseSolveCore;
321	use crate::stats::prelude::*;
322	use crate::utils::approx::*;
323	use crate::{Mat, Row, assert, c64};
324	use dyn_stack::MemBuffer;
325
326	#[test]
327	fn test_qr() {
328		let rng = &mut StdRng::seed_from_u64(0);
329		for rank in [1, 2, 3, 4, 5, 100, usize::MAX] {
330			for par in [Par::Seq, Par::rayon(8)] {
331				for n in [2, 4, 8, 16, 24, 32, 127, 128, 257] {
332					let rank = Ord::min(n, rank);
333					let approx_eq = CwiseMat(ApproxEq {
334						abs_tol: 1e-10,
335						rel_tol: 1e-10,
336					});
337					let A0 = CwiseMatDistribution {
338						nrows: n,
339						ncols: rank,
340						dist: ComplexDistribution::new(
341							StandardNormal,
342							StandardNormal,
343						),
344					}
345					.rand::<Mat<c64>>(rng);
346					let A1 = CwiseMatDistribution {
347						nrows: rank,
348						ncols: n,
349						dist: ComplexDistribution::new(
350							StandardNormal,
351							StandardNormal,
352						),
353					}
354					.rand::<Mat<c64>>(rng);
355					let A = &A0 * &A1;
356					let A = A.as_ref();
357					let mut QR = A.cloned();
358					let mut H = Row::zeros(n);
359					let mut params: QrParams = auto!(c64);
360					params.blocking_threshold = usize::MAX;
361					let params = params.into();
362					let computed_rank = qr_in_place(
363						QR.as_mut(),
364						H.as_mat_mut(),
365						Par::Seq,
366						MemStack::new(&mut MemBuffer::new(
367							qr_in_place_scratch::<c64>(
368								n,
369								n,
370								1,
371								Par::Seq,
372								params,
373							),
374						)),
375						params,
376					);
377					assert!(computed_rank.rank >= rank);
378					let mut Q = Mat::<c64>::zeros(n, n);
379					let mut R = QR.as_ref().cloned();
380					for j in 0..n {
381						Q[(j, j)] = c64::ONE;
382					}
383					householder::apply_block_householder_sequence_on_the_left_in_place_with_conj(
384						QR.as_ref(),
385						H.as_mat(),
386						Conj::No,
387						Q.as_mut(),
388						Par::Seq,
389						MemStack::new(&mut MemBuffer::new(
390							householder::apply_block_householder_sequence_transpose_on_the_left_in_place_scratch::<c64>(n, 1, n),
391						)),
392					);
393					for j in 0..n {
394						for i in j + 1..n {
395							R[(i, j)] = c64::ZERO;
396						}
397					}
398					assert!(Q * R ~ A);
399				}
400				for n in [2, 3, 4, 8, 16, 24, 32, 128, 255, 256, 257, 512] {
401					let bs = 15;
402					let rank = Ord::min(n, rank);
403					let approx_eq = CwiseMat(ApproxEq {
404						abs_tol: 1e-10,
405						rel_tol: 1e-10,
406					});
407					let A0 = CwiseMatDistribution {
408						nrows: n,
409						ncols: rank,
410						dist: ComplexDistribution::new(
411							StandardNormal,
412							StandardNormal,
413						),
414					}
415					.rand::<Mat<c64>>(rng);
416					let A1 = CwiseMatDistribution {
417						nrows: rank,
418						ncols: n,
419						dist: ComplexDistribution::new(
420							StandardNormal,
421							StandardNormal,
422						),
423					}
424					.rand::<Mat<c64>>(rng);
425					let A = &A0 * &A1;
426					let A = A.as_ref();
427					let mut QR = A.cloned();
428					let mut H = Mat::zeros(bs, n);
429					let computed_rank = qr_in_place(
430						QR.as_mut(),
431						H.as_mut(),
432						par,
433						MemStack::new(&mut MemBuffer::new(
434							qr_in_place_scratch::<c64>(
435								n,
436								n,
437								bs,
438								par,
439								default(),
440							),
441						)),
442						default(),
443					);
444					assert!(computed_rank.rank >= rank);
445					let mut Q = Mat::<c64>::zeros(n, n);
446					let mut R = QR.as_ref().cloned();
447					for j in 0..n {
448						Q[(j, j)] = c64::ONE;
449					}
450					householder::apply_block_householder_sequence_on_the_left_in_place_with_conj(
451						QR.as_ref(),
452						H.as_ref(),
453						Conj::No,
454						Q.as_mut(),
455						Par::Seq,
456						MemStack::new(&mut MemBuffer::new(
457							householder::apply_block_householder_sequence_on_the_left_in_place_scratch::<c64>(n, bs, n),
458						)),
459					);
460					for j in 0..n {
461						for i in j + 1..n {
462							R[(i, j)] = c64::ZERO;
463						}
464					}
465					assert!(Q * R ~ A);
466				}
467				let n = 20;
468				for m in [2, 3, 4, 8, 16, 24, 32, 128, 255, 256, 257, 512] {
469					let size = Ord::min(m, n);
470					let bs = 15;
471					let rank = Ord::min(size, rank);
472					let approx_eq = CwiseMat(ApproxEq {
473						abs_tol: 1e-10,
474						rel_tol: 1e-10,
475					});
476					let A0 = CwiseMatDistribution {
477						nrows: m,
478						ncols: rank,
479						dist: ComplexDistribution::new(
480							StandardNormal,
481							StandardNormal,
482						),
483					}
484					.rand::<Mat<c64>>(rng);
485					let A1 = CwiseMatDistribution {
486						nrows: rank,
487						ncols: n,
488						dist: ComplexDistribution::new(
489							StandardNormal,
490							StandardNormal,
491						),
492					}
493					.rand::<Mat<c64>>(rng);
494					let A = &A0 * &A1;
495					let A = A.as_ref();
496					let mut QR = A.cloned();
497					let mut H = Mat::zeros(bs, size);
498					let computed_rank = qr_in_place(
499						QR.as_mut(),
500						H.as_mut(),
501						par,
502						MemStack::new(&mut MemBuffer::new(
503							qr_in_place_scratch::<c64>(
504								m,
505								n,
506								bs,
507								par,
508								default(),
509							),
510						)),
511						default(),
512					);
513					assert!(computed_rank.rank >= rank);
514					let mut Q = Mat::<c64, _, _>::zeros(m, m);
515					let mut R = QR.as_ref().cloned();
516					for j in 0..m {
517						Q[(j, j)] = c64::ONE;
518					}
519					householder::apply_block_householder_sequence_on_the_left_in_place_with_conj(
520						QR.as_ref().subcols(0, size),
521						H.as_ref(),
522						Conj::No,
523						Q.as_mut(),
524						Par::Seq,
525						MemStack::new(&mut MemBuffer::new(
526							householder::apply_block_householder_sequence_on_the_left_in_place_scratch::<c64>(m, bs, m),
527						)),
528					);
529					for j in 0..n {
530						for i in j + 1..m {
531							R[(i, j)] = c64::ZERO;
532						}
533					}
534					assert!(Q * R ~ A);
535				}
536			}
537		}
538	}
539	#[test]
540	fn test_rank_deficient() {
541		let i = c64::new(0.0, 1.0);
542		let A = mat![
543			[
544				-42.63301571125646 + 12.332799004481444 * i,
545				22.14792539952694 + 34.88980973191775 * i,
546				17.08833097340157 - 35.73642756638833 * i,
547				16.46359410465419 - 42.92839086211859 * i,
548				-51.764730444742824 + 81.65328924776695 * i,
549				16.26315772194988 + 101.5902862344418 * i,
550				32.77410298966414 - 29.760957827435675 * i,
551				54.439294321277174 - 19.079738442315318 * i,
552				-13.472034925473565 - 13.943573427112455 * i,
553				-37.92130013603088 - 5.7926798723257775 * i,
554				11.194976295897504 - 31.928468357395335 * i,
555				22.006669976718612 + 3.3819587127690625 * i,
556				-6.674280620224554 + 3.387564723853501 * i,
557				-27.293486814495225 + 15.784839382140262 * i,
558				-70.1443517961362 + 45.51634877173214 * i,
559				8.181229285208616 + 11.577617946683347 * i,
560				91.36331153456992 + 5.978813469385237 * i,
561				9.984370037964844 - 46.821962088062065 * i,
562				-7.961599724739131 + 24.482176731342236 * i,
563				-2.3944781784861675 + 59.88090585477201 * i,
564				-30.59313953515538 + 26.04745441455745 * i,
565				-23.2138559332029 + 71.42630235367764 * i,
566				22.210550339117574 - 8.41265667708069 * i,
567				-11.395416853480953 - 21.12459074171425 * i,
568				53.214674012253 - 115.94154857087852 * i,
569				-73.57661533181208 - 26.388545645959155 * i,
570				-7.090193099053337 + 25.72478190092928 * i,
571				69.88086414991596 - 61.87734406117171 * i,
572				1.7746488531197873 + 22.338809391772543 * i,
573				53.17879024337897 + 3.0434791244725403 * i,
574				17.11701506186965 + 8.310347464005673 * i,
575				-1.4446985641791343 - 8.302085605445917 * i,
576				31.01042486753896 - 7.032023465838279 * i,
577				50.529023639015065 - 30.432756878940538 * i,
578				31.20832359612237 - 18.42527233678696 * i,
579				-11.219592741413372 + 7.966456895330857 * i,
580				-29.972014970412957 + 14.566825708553516 * i,
581				0.29786829050329544 - 60.43731329910441 * i,
582				68.20619173666897 + 61.4177082555907 * i,
583				38.18522457770308 + 39.84442487790024 * i,
584			],
585			[
586				12.392666547455747 + 8.598469521105585 * i,
587				-4.989137989279129 - 33.00917260871823 * i,
588				-36.3778560847675 + 33.965754531979854 * i,
589				-14.186892703037756 + 7.8005444248189235 * i,
590				40.14774343578466 - 37.073977200615204 * i,
591				20.515112381381726 - 39.67019203209179 * i,
592				-11.247367898035563 - 24.867001222923307 * i,
593				-49.7400862432402 + 41.41428057951588 * i,
594				-3.7213275390216154 + 51.57768254492541 * i,
595				-6.345081010580628 + 53.304858550561896 * i,
596				-11.529781103419339 + 2.902201112665864 * i,
597				-19.346649644440838 + 7.461276014085186 * i,
598				-28.718472256689964 - 2.8043513041184553 * i,
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2012			],
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4664				91.1918363550727 - 24.09689836725063 * i,
4665				83.4549967540554 - 20.34134879703427 * i,
4666				14.845553062520082 - 17.329688701627873 * i,
4667				-57.79299873582244 - 61.6190659268681 * i,
4668				-11.341895639832885 - 29.389275980068188 * i,
4669				-6.103606129159111 + 2.6732605138042516 * i,
4670				-30.639674305109082 + 38.30047965862747 * i,
4671				-32.52405690925754 - 1.147975907681655 * i,
4672				-60.91464903420922 + 3.3569835263393486 * i,
4673				0.9465373318364527 - 12.319332957187953 * i,
4674				74.55664621734081 - 18.56283082736708 * i,
4675				17.803562763968827 - 23.82546060059542 * i,
4676				-51.806669208246944 - 30.915651046889167 * i,
4677				-62.162718932301345 - 32.517877652384755 * i,
4678				36.98331909299938 - 8.453357560368715 * i,
4679				25.670062202629836 + 14.042422507005398 * i,
4680				21.722934057138772 + 12.849989979431058 * i,
4681				40.15558451876862 + 12.329157892817022 * i,
4682				-9.139517533292345 - 25.743989625176226 * i,
4683				-4.468120791789221 - 13.755867478499477 * i,
4684				-69.01712528118367 + 8.639846913771777 * i,
4685				10.839156913536948 + 75.26051799617554 * i,
4686				-37.746419555778104 - 15.850150517077978 * i,
4687				-68.64741450018217 - 20.527021740042183 * i,
4688				-15.434262576161444 - 28.137900034870583 * i,
4689				13.210389026964918 + 4.156278279710207 * i,
4690				-45.62063377733667 + 31.0877877497326 * i,
4691				-26.1631431584863 - 12.079306214684529 * i,
4692				-78.11257536327938 - 2.0945118991163714 * i,
4693				-48.602415683300734 - 50.252561412350786 * i,
4694				-36.63139136867553 - 10.753264854693908 * i,
4695				-4.413610245696162 + 48.86992836326893 * i,
4696				-9.688690027055344 + 55.27630347193527 * i,
4697				-49.44780929458748 + 8.589562480583625 * i,
4698				81.94654000279007 - 97.13615598710763 * i,
4699				1.9811020394914598 - 53.536238319414494 * i,
4700			],
4701			[
4702				-52.26002756952291 - 12.420745406989852 * i,
4703				-48.649220026936035 + 7.357476578955215 * i,
4704				38.787613829805125 + 10.060178851506798 * i,
4705				66.73096163304089 - 29.035248735396436 * i,
4706				-61.64298521757553 - 18.69502418563181 * i,
4707				-29.453498465992812 + 17.273712641503778 * i,
4708				-23.978289374625334 + 5.426227955442368 * i,
4709				-22.187325339436626 + 7.616246279667706 * i,
4710				0.23983491995083472 + 29.039311850170208 * i,
4711				-23.98539518469839 + 22.208046420756617 * i,
4712				-21.949181055868166 - 6.377838450298583 * i,
4713				-3.7265685887609905 + 37.45221650597609 * i,
4714				-4.143690915425717 + 24.28814333995993 * i,
4715				31.38920960676393 + 12.194486215746437 * i,
4716				-79.51417920753015 - 16.50518165970584 * i,
4717				32.71507304910372 - 11.776944279561476 * i,
4718				17.17306580323782 - 14.977922134779789 * i,
4719				6.885898385994769 - 10.98778009512454 * i,
4720				-8.275369291448726 - 1.9605494472583729 * i,
4721				19.48762176513239 - 54.32936286437996 * i,
4722				44.357911062016996 - 3.9032778083657718 * i,
4723				-44.97315666672529 - 6.184203147927221 * i,
4724				-6.058516855245614 + 27.83425935490075 * i,
4725				-2.050191134621514 - 16.210824046071107 * i,
4726				-60.30984541807075 + 73.2259570501726 * i,
4727				17.61949960977492 - 35.141160821726814 * i,
4728				5.115244950064259 + 10.874296478175332 * i,
4729				55.83189663550353 + 10.363015579614597 * i,
4730				-24.990503094223847 - 21.874177365821854 * i,
4731				-10.097267728879046 - 8.658355090659887 * i,
4732				17.767114705732443 + 39.570479820025625 * i,
4733				29.577401265203108 - 25.912819592353227 * i,
4734				57.09539968262975 + 82.31124802224056 * i,
4735				30.92321422368017 - 3.8563763701881157 * i,
4736				8.845784787148993 + 37.3323860605405 * i,
4737				5.002676757558589 - 7.182096583667285 * i,
4738				-51.886884166861805 + 16.09726666941668 * i,
4739				47.074640241096716 - 32.6760384906439 * i,
4740				-16.303505294511297 - 13.412914880672735 * i,
4741				43.70182473837136 - 32.15973260778437 * i,
4742			],
4743		];
4744		let (m, n) = A.shape();
4745		let mut QR = A.clone();
4746		let mut H = Mat::zeros(20, A.ncols());
4747		qr_in_place(
4748			QR.rb_mut(),
4749			H.rb_mut(),
4750			Par::Seq,
4751			MemStack::new(&mut MemBuffer::new(qr_in_place_scratch::<c64>(
4752				A.nrows(),
4753				A.ncols(),
4754				20,
4755				Par::Seq,
4756				default(),
4757			))),
4758			default(),
4759		);
4760		let approx_eq = CwiseMat(ApproxEq {
4761			abs_tol: 1e-10,
4762			rel_tol: 1e-10,
4763		});
4764		let mut Q = Mat::<c64>::zeros(m, m);
4765		let mut R = QR.as_ref().cloned();
4766		for j in 0..m {
4767			Q[(j, j)] = c64::ONE;
4768		}
4769		householder::apply_block_householder_sequence_on_the_left_in_place_with_conj(
4770			QR.rb(),
4771			H.rb(),
4772			Conj::No,
4773			Q.as_mut(),
4774			Par::Seq,
4775			MemStack::new(&mut MemBuffer::new(
4776				householder::apply_block_householder_sequence_transpose_on_the_left_in_place_scratch::<c64>(m, 20, m),
4777			)),
4778		);
4779		for j in 0..n {
4780			for i in j + 1..m {
4781				R[(i, j)] = c64::ZERO;
4782			}
4783		}
4784		assert!(Q * R ~ A);
4785		let QR = A.qr().reconstruct();
4786		assert!(QR ~ A);
4787	}
4788}
faer/linalg/qr/no_pivoting/factor.rs

faer/linalg/qr/no_pivoting/
factor.rs
