From a5252f841c53f5a7db2c69b313c7518e0c45d86c Mon Sep 17 00:00:00 2001 From: LTLA Date: Fri, 7 Apr 2023 06:45:36 +0000 Subject: [PATCH] =?UTF-8?q?Deploying=20to=20gh-pages=20from=20@=20LTLA/Cpp?= =?UTF-8?q?Irlba@d23a4c12b95563907cf8ca7584b7bb6625ff886b=20=F0=9F=9A=80?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- docs/classirlba_1_1Irlba.html | 23 +- docs/graph_legend.png | Bin 22655 -> 22761 bytes docs/irlba_8hpp__incl.png | Bin 43571 -> 43699 bytes docs/irlba_8hpp_source.html | 448 +++++++++++++++--------------- docs/lanczos_8hpp__dep__incl.png | Bin 3653 -> 3673 bytes docs/lanczos_8hpp__incl.png | Bin 23646 -> 23700 bytes docs/parallel_8hpp__incl.png | Bin 14508 -> 14606 bytes docs/utils_8hpp__dep__incl.png | Bin 16673 -> 16652 bytes docs/utils_8hpp__incl.png | Bin 9457 -> 9561 bytes docs/wrappers_8hpp__dep__incl.png | Bin 5911 -> 5950 bytes docs/wrappers_8hpp__incl.png | Bin 13336 -> 13339 bytes 11 files changed, 228 insertions(+), 243 deletions(-) diff --git a/docs/classirlba_1_1Irlba.html b/docs/classirlba_1_1Irlba.html index c6c6816..3d2d7df 100644 --- a/docs/classirlba_1_1Irlba.html +++ b/docs/classirlba_1_1Irlba.html @@ -204,7 +204,7 @@

Template Parameters
- +
MMatrix class, typically from the Eigen matrix manipulation library. However, other classes are also supported, see the other run() methods for details.
MMatrix class, typically from the Eigen matrix manipulation library. However, other classes are also supported, see wrappers.hpp for details.
EngineA (pseudo-)random number generator class, returning a randomly sampled value when called as a functor with no arguments.
@@ -283,7 +283,7 @@

Template Parameters
- +
MMatrix class, most typically from the Eigen matrix manipulation library. However, other classes are also supported, see the other run() methods for details.
MMatrix class, most typically from the Eigen matrix manipulation library. However, other classes are also supported, see wrappers.hpp for details.
EngineA (pseudo-)random number generator class, returning a randomly sampled value when called as a functor with no arguments.
@@ -346,7 +346,7 @@

run() method for more details.

Template Parameters
- +
MMatrix class, most typically from the Eigen matrix manipulation library. However, other classes are also supported, see the other run() methods for details.
MMatrix class, most typically from the Eigen matrix manipulation library. However, other classes are also supported, see wrappers.hpp for details.
EngineA (pseudo-)random number generator class, returning a randomly sampled value when called as a functor with no arguments.
@@ -442,22 +442,7 @@

Returns
A pair where the first entry indicates whether the algorithm converged, and the second entry indicates the number of restart iterations performed.

-

Custom classes can be used to define modified matrices that cannot be efficiently realized into the standard Eigen classes. We expect:

    -
  • A rows() method that returns the number of rows.
  • -
  • A cols() method that returns the number of columns.
  • -
  • One of the following for matrix-vector multiplication:
      -
    • multiply(rhs, out), which should compute the product of the matrix with rhs, a Eigen::VectorXd-equivalent of length equal to the number of columns; and stores the result in out, an Eigen::VectorXd of length equal to the number of rows.
    • -
    • A * method where the right-hand side is an Eigen::VectorXd (or equivalent expression) of length equal to the number of columsn, and returns an Eigen::VectorXd-equivalent of length equal to the number of rows.
    • -
    -
  • -
  • One of the following for matrix transpose-vector multiplication:
      -
    • adjoint_multiply(rhs, out), which should compute the product of the matrix transpose with rhs, a Eigen::VectorXd-equivalent of length equal to the number of rows; and stores the result in out, an Eigen::VectorXd of length equal to the number of columns.
    • -
    • An adjoint() method that returns an instance of any class that has a * method for matrix-vector multiplication. The method should accept an Eigen::VectorXd-equivalent of length equal to the number of rows, and return an Eigen::VectorXd-equvialent of length equal to the number of columns.
    • -
    -
  • -
  • A realize() method that returns an Eigen::MatrixXd object representing the modified matrix. This can be omitted if an Eigen::MatrixXd can be copy-constructed from the class.
  • -
-

See the Centered and Scaled classes for more details.

+

Custom classes can be used to define modified matrices that cannot be efficiently realized into the standard Eigen classes. See the wrappers.hpp file for more details, along with the Centered and Scaled classes.

If the smallest dimension of mat is below 6, this method falls back to performing an exact SVD.

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251 }
252
-
299 template<class Matrix, class Engine = std::mt19937_64>
-
300 std::pair<bool, int> run(
-
301 const Matrix& mat,
-
302 Eigen::MatrixXd& outU,
-
303 Eigen::MatrixXd& outV,
-
304 Eigen::VectorXd& outD,
-
305 Engine* eng = null_rng(),
-
306 Eigen::VectorXd* init = NULL)
-
307 const {
-
308 if (eng == NULL) {
-
309 std::mt19937_64 rng(seed);
-
310 return run_internal(mat, rng, outU, outV, outD, init);
-
311 } else {
-
312 return run_internal(mat, *eng, outU, outV, outD, init);
-
313 }
-
314 }
-
315
-
316private:
-
317 template<class M, class Engine>
-
318 std::pair<bool, int> run_internal(
-
319 const M& mat,
-
320 Engine& eng,
-
321 Eigen::MatrixXd& outU,
-
322 Eigen::MatrixXd& outV,
-
323 Eigen::VectorXd& outD,
-
324 Eigen::VectorXd* init)
-
325 const {
-
326 const int smaller = std::min(mat.rows(), mat.cols());
-
327 if (number >= smaller) {
-
328 throw std::runtime_error("requested number of singular values must be less than smaller matrix dimension");
-
329 }
-
330
-
331 // Falling back to an exact SVD for small matrices.
-
332 if (smaller < 6) {
-
333 exact(mat, outU, outV, outD);
-
334 return std::make_pair(true, 0);
-
335 }
+
282 template<class Matrix, class Engine = std::mt19937_64>
+
283 std::pair<bool, int> run(
+
284 const Matrix& mat,
+
285 Eigen::MatrixXd& outU,
+
286 Eigen::MatrixXd& outV,
+
287 Eigen::VectorXd& outD,
+
288 Engine* eng = null_rng(),
+
289 Eigen::VectorXd* init = NULL)
+
290 const {
+
291 if (eng == NULL) {
+
292 std::mt19937_64 rng(seed);
+
293 return run_internal(mat, rng, outU, outV, outD, init);
+
294 } else {
+
295 return run_internal(mat, *eng, outU, outV, outD, init);
+
296 }
+
297 }
+
298
+
299private:
+
300 template<class M, class Engine>
+
301 std::pair<bool, int> run_internal(
+
302 const M& mat,
+
303 Engine& eng,
+
304 Eigen::MatrixXd& outU,
+
305 Eigen::MatrixXd& outV,
+
306 Eigen::VectorXd& outD,
+
307 Eigen::VectorXd* init)
+
308 const {
+
309 const int smaller = std::min(mat.rows(), mat.cols());
+
310 if (number >= smaller) {
+
311 throw std::runtime_error("requested number of singular values must be less than smaller matrix dimension");
+
312 }
+
313
+
314 // Falling back to an exact SVD for small matrices.
+
315 if (smaller < 6) {
+
316 exact(mat, outU, outV, outD);
+
317 return std::make_pair(true, 0);
+
318 }
+
319
+
320 const int work = std::min(number + extra_work, smaller);
+
321
+
322 Eigen::MatrixXd V(mat.cols(), work);
+
323 if (init) {
+
324 if (init->size() != V.rows()) {
+
325 throw std::runtime_error("initialization vector does not have expected number of rows");
+
326 }
+
327 V.col(0) = *init;
+
328 } else {
+
329 fill_with_random_normals(V, 0, eng);
+
330 }
+
331 V.col(0) /= V.col(0).norm();
+
332
+
333 bool converged = false;
+
334 int iter = 0, k =0;
+
335 Eigen::JacobiSVD<Eigen::MatrixXd> svd(work, work, Eigen::ComputeThinU | Eigen::ComputeThinV);
336
-
337 const int work = std::min(number + extra_work, smaller);
+
337 auto lptmp = lp.initialize(mat);
338
-
339 Eigen::MatrixXd V(mat.cols(), work);
-
340 if (init) {
-
341 if (init->size() != V.rows()) {
-
342 throw std::runtime_error("initialization vector does not have expected number of rows");
-
343 }
-
344 V.col(0) = *init;
-
345 } else {
-
346 fill_with_random_normals(V, 0, eng);
-
347 }
-
348 V.col(0) /= V.col(0).norm();
+
339 Eigen::MatrixXd W(mat.rows(), work);
+
340 Eigen::MatrixXd Wtmp(mat.rows(), work);
+
341 Eigen::MatrixXd Vtmp(mat.cols(), work);
+
342
+
343 Eigen::MatrixXd B(work, work);
+
344 B.setZero(work, work);
+
345 Eigen::VectorXd res(work);
+
346 Eigen::VectorXd F(mat.cols());
+
347
+
348 Eigen::VectorXd prevS(work);
349
-
350 bool converged = false;
-
351 int iter = 0, k =0;
-
352 Eigen::JacobiSVD<Eigen::MatrixXd> svd(work, work, Eigen::ComputeThinU | Eigen::ComputeThinV);
-
353
-
354 auto lptmp = lp.initialize(mat);
+
350 for (; iter < maxit; ++iter) {
+
351 // Technically, this is only a 'true' Lanczos bidiagonalization
+
352 // when k = 0. All other times, we're just recycling the machinery,
+
353 // see the text below Equation 3.11 in Baglama and Reichel.
+
354 lp.run(mat, W, V, B, eng, lptmp, k);
355
-
356 Eigen::MatrixXd W(mat.rows(), work);
-
357 Eigen::MatrixXd Wtmp(mat.rows(), work);
-
358 Eigen::MatrixXd Vtmp(mat.cols(), work);
-
359
-
360 Eigen::MatrixXd B(work, work);
-
361 B.setZero(work, work);
-
362 Eigen::VectorXd res(work);
-
363 Eigen::VectorXd F(mat.cols());
-
364
-
365 Eigen::VectorXd prevS(work);
+
356// if (iter < 2) {
+
357// std::cout << "B is currently:\n" << B << std::endl;
+
358// std::cout << "W is currently:\n" << W << std::endl;
+
359// std::cout << "V is currently:\n" << V << std::endl;
+
360// }
+
361
+
362 svd.compute(B);
+
363 const auto& BS = svd.singularValues();
+
364 const auto& BU = svd.matrixU();
+
365 const auto& BV = svd.matrixV();
366
-
367 for (; iter < maxit; ++iter) {
-
368 // Technically, this is only a 'true' Lanczos bidiagonalization
-
369 // when k = 0. All other times, we're just recycling the machinery,
-
370 // see the text below Equation 3.11 in Baglama and Reichel.
-
371 lp.run(mat, W, V, B, eng, lptmp, k);
+
367 // Checking for convergence.
+
368 if (B(work-1, work-1) == 0) { // a.k.a. the final value of 'S' from the Lanczos iterations.
+
369 converged = true;
+
370 break;
+
371 }
372
-
373// if (iter < 2) {
-
374// std::cout << "B is currently:\n" << B << std::endl;
-
375// std::cout << "W is currently:\n" << W << std::endl;
-
376// std::cout << "V is currently:\n" << V << std::endl;
-
377// }
-
378
-
379 svd.compute(B);
-
380 const auto& BS = svd.singularValues();
-
381 const auto& BU = svd.matrixU();
-
382 const auto& BV = svd.matrixV();
-
383
-
384 // Checking for convergence.
-
385 if (B(work-1, work-1) == 0) { // a.k.a. the final value of 'S' from the Lanczos iterations.
-
386 converged = true;
-
387 break;
+
373 F = lptmp.residuals();
+
374 double R_F = F.norm();
+
375 F /= R_F;
+
376
+
377 // Computes the convergence criterion defined in on the LHS of Equation 2.13 of Baglama and Riechel.
+
378 // We expose it here as we will be re-using the same values to update B, see below.
+
379 res = R_F * BU.row(work - 1);
+
380
+
381 int n_converged = 0;
+
382 if (iter > 0) {
+
383 n_converged = convtest.run(BS, res, prevS);
+
384 if (n_converged >= number) {
+
385 converged = true;
+
386 break;
+
387 }
388 }
-
389
-
390 F = lptmp.residuals();
-
391 double R_F = F.norm();
-
392 F /= R_F;
-
393
-
394 // Computes the convergence criterion defined in on the LHS of Equation 2.13 of Baglama and Riechel.
-
395 // We expose it here as we will be re-using the same values to update B, see below.
-
396 res = R_F * BU.row(work - 1);
-
397
-
398 int n_converged = 0;
-
399 if (iter > 0) {
-
400 n_converged = convtest.run(BS, res, prevS);
-
401 if (n_converged >= number) {
-
402 converged = true;
-
403 break;
-
404 }
-
405 }
-
406 prevS = BS;
-
407
-
408 // Setting 'k'. This looks kinda weird, but this is deliberate,
-
409 // see the text below Algorithm 3.1 of Baglama and Reichel.
-
410 if (n_converged + number > k) {
-
411 k = n_converged + number;
-
412 }
-
413 if (k > work - 3) {
-
414 k = work - 3;
-
415 }
-
416 if (k < 1) {
-
417 k = 1;
-
418 }
-
419
-
420 // Updating B, W and V.
-
421 Vtmp.leftCols(k).noalias() = V * BV.leftCols(k);
-
422 V.leftCols(k) = Vtmp.leftCols(k);
-
423
-
424 V.col(k) = F; // See Equation 3.2 of Baglama and Reichel, where our 'V' is
-
425 // their 'P', and our 'F' is their 'p_{m+1}' (2.2).
-
426 // 'F' was orthogonal to the old 'V' and it so it
-
427 // should still be orthogonal to the new left-most
-
428 // columns of 'V'; the input expectations of 'lp'
-
429 // are still met.
-
430
-
431 Wtmp.leftCols(k).noalias() = W * BU.leftCols(k);
-
432 W.leftCols(k) = Wtmp.leftCols(k);
-
433
-
434 B.setZero(work, work);
-
435 for (int l = 0; l < k; ++l) {
-
436 B(l, l) = BS[l];
-
437 B(l, k) = res[l]; // this looks weird but is deliberate, see
-
438 // Equation 3.6 of Baglama and Reichel.
-
439 // By happy coincidence, this is the same
-
440 // value used to determine convergence in
-
441 // 2.13, so we can just re-use it.
-
442 }
-
443 }
-
444
-
445 // See Equation 2.11 of Baglama and Reichel for how to get from B's
-
446 // singular triplets to mat's singular triplets.
-
447 outD.resize(number);
-
448 outD = svd.singularValues().head(number);
-
449
-
450 outU.resize(mat.rows(), number);
-
451 outU.noalias() = W * svd.matrixU().leftCols(number);
-
452
-
453 outV.resize(mat.cols(), number);
-
454 outV.noalias() = V * svd.matrixV().leftCols(number);
-
455
-
456 return std::make_pair(converged, iter + 1);
-
457 }
+
389 prevS = BS;
+
390
+
391 // Setting 'k'. This looks kinda weird, but this is deliberate,
+
392 // see the text below Algorithm 3.1 of Baglama and Reichel.
+
393 if (n_converged + number > k) {
+
394 k = n_converged + number;
+
395 }
+
396 if (k > work - 3) {
+
397 k = work - 3;
+
398 }
+
399 if (k < 1) {
+
400 k = 1;
+
401 }
+
402
+
403 // Updating B, W and V.
+
404 Vtmp.leftCols(k).noalias() = V * BV.leftCols(k);
+
405 V.leftCols(k) = Vtmp.leftCols(k);
+
406
+
407 V.col(k) = F; // See Equation 3.2 of Baglama and Reichel, where our 'V' is
+
408 // their 'P', and our 'F' is their 'p_{m+1}' (2.2).
+
409 // 'F' was orthogonal to the old 'V' and it so it
+
410 // should still be orthogonal to the new left-most
+
411 // columns of 'V'; the input expectations of 'lp'
+
412 // are still met.
+
413
+
414 Wtmp.leftCols(k).noalias() = W * BU.leftCols(k);
+
415 W.leftCols(k) = Wtmp.leftCols(k);
+
416
+
417 B.setZero(work, work);
+
418 for (int l = 0; l < k; ++l) {
+
419 B(l, l) = BS[l];
+
420 B(l, k) = res[l]; // this looks weird but is deliberate, see
+
421 // Equation 3.6 of Baglama and Reichel.
+
422 // By happy coincidence, this is the same
+
423 // value used to determine convergence in
+
424 // 2.13, so we can just re-use it.
+
425 }
+
426 }
+
427
+
428 // See Equation 2.11 of Baglama and Reichel for how to get from B's
+
429 // singular triplets to mat's singular triplets.
+
430 outD.resize(number);
+
431 outD = svd.singularValues().head(number);
+
432
+
433 outU.resize(mat.rows(), number);
+
434 outU.noalias() = W * svd.matrixU().leftCols(number);
+
435
+
436 outV.resize(mat.cols(), number);
+
437 outV.noalias() = V * svd.matrixV().leftCols(number);
+
438
+
439 return std::make_pair(converged, iter + 1);
+
440 }
+
441
+
442private:
+
443 template<class M>
+
444 void exact(const M& mat, Eigen::MatrixXd& outU, Eigen::MatrixXd& outV, Eigen::VectorXd& outD) const {
+
445 Eigen::BDCSVD<Eigen::MatrixXd> svd(mat.rows(), mat.cols(), Eigen::ComputeThinU | Eigen::ComputeThinV);
+
446
+
447 if constexpr(std::is_same<M, Eigen::MatrixXd>::value) {
+
448 svd.compute(mat);
+
449 } else {
+
450 if constexpr(has_realize_method<M>::value) {
+
451 Eigen::MatrixXd adjusted = mat.realize();
+
452 svd.compute(adjusted);
+
453 } else {
+
454 Eigen::MatrixXd adjusted(mat);
+
455 svd.compute(adjusted);
+
456 }
+
457 }
458
-
459private:
-
460 template<class M>
-
461 void exact(const M& mat, Eigen::MatrixXd& outU, Eigen::MatrixXd& outV, Eigen::VectorXd& outD) const {
-
462 Eigen::BDCSVD<Eigen::MatrixXd> svd(mat.rows(), mat.cols(), Eigen::ComputeThinU | Eigen::ComputeThinV);
-
463
-
464 if constexpr(std::is_same<M, Eigen::MatrixXd>::value) {
-
465 svd.compute(mat);
-
466 } else {
-
467 if constexpr(has_realize_method<M>::value) {
-
468 Eigen::MatrixXd adjusted = mat.realize();
-
469 svd.compute(adjusted);
-
470 } else {
-
471 Eigen::MatrixXd adjusted(mat);
-
472 svd.compute(adjusted);
-
473 }
-
474 }
-
475
-
476 outD.resize(number);
-
477 outD = svd.singularValues().head(number);
-
478
-
479 outU.resize(mat.rows(), number);
-
480 outU = svd.matrixU().leftCols(number);
-
481
-
482 outV.resize(mat.cols(), number);
-
483 outV = svd.matrixV().leftCols(number);
-
484
-
485 return;
-
486 }
-
487
-
488public:
-
492 struct Results {
-
498 Eigen::MatrixXd U;
-
499
-
505 Eigen::MatrixXd V;
+
459 outD.resize(number);
+
460 outD = svd.singularValues().head(number);
+
461
+
462 outU.resize(mat.rows(), number);
+
463 outU = svd.matrixU().leftCols(number);
+
464
+
465 outV.resize(mat.cols(), number);
+
466 outV = svd.matrixV().leftCols(number);
+
467
+
468 return;
+
469 }
+
470
+
471public:
+
475 struct Results {
+
481 Eigen::MatrixXd U;
+
482
+
488 Eigen::MatrixXd V;
+
489
+
494 Eigen::VectorXd D;
+
495
+ +
500
+ +
505 };
506
-
511 Eigen::VectorXd D;
-
512
- -
517
- -
522 };
-
523
-
541 template<class M, class Engine = std::mt19937_64>
-
542 Results run(const M& mat, bool center, bool scale, Engine* eng = null_rng(), Eigen::VectorXd* init = NULL) const {
-
543 Results output;
-
544 auto stats = run(mat, center, scale, output.U, output.V, output.D, eng, init);
-
545 output.converged = stats.first;
-
546 output.iterations = stats.second;
-
547 return output;
-
548 }
-
549
-
565 template<class M, class Engine = std::mt19937_64>
-
566 Results run(const M& mat, Engine* eng = null_rng(), Eigen::VectorXd* init = NULL) const {
-
567 Results output;
-
568 auto stats = run(mat, output.U, output.V, output.D, eng, init);
-
569 output.converged = stats.first;
-
570 output.iterations = stats.second;
-
571 return output;
-
572 }
-
573};
-
574
-
575}
-
576
-
577#endif
+
524 template<class M, class Engine = std::mt19937_64>
+
525 Results run(const M& mat, bool center, bool scale, Engine* eng = null_rng(), Eigen::VectorXd* init = NULL) const {
+
526 Results output;
+
527 auto stats = run(mat, center, scale, output.U, output.V, output.D, eng, init);
+
528 output.converged = stats.first;
+
529 output.iterations = stats.second;
+
530 return output;
+
531 }
+
532
+
548 template<class M, class Engine = std::mt19937_64>
+
549 Results run(const M& mat, Engine* eng = null_rng(), Eigen::VectorXd* init = NULL) const {
+
550 Results output;
+
551 auto stats = run(mat, output.U, output.V, output.D, eng, init);
+
552 output.converged = stats.first;
+
553 output.iterations = stats.second;
+
554 return output;
+
555 }
+
556};
+
557
+
558}
+
559
+
560#endif
Run IRLBA on an input matrix.
Definition: irlba.hpp:31
Irlba & set_singular_value_ratio_tolerance(double t=ConvergenceTest::Defaults::svtol)
Definition: irlba.hpp:150
-
std::pair< bool, int > run(const Matrix &mat, Eigen::MatrixXd &outU, Eigen::MatrixXd &outV, Eigen::VectorXd &outD, Engine *eng=null_rng(), Eigen::VectorXd *init=NULL) const
Definition: irlba.hpp:300
+
std::pair< bool, int > run(const Matrix &mat, Eigen::MatrixXd &outU, Eigen::MatrixXd &outV, Eigen::VectorXd &outD, Engine *eng=null_rng(), Eigen::VectorXd *init=NULL) const
Definition: irlba.hpp:283
Irlba & set_work(int w=Defaults::extra_work)
Definition: irlba.hpp:114
Irlba & set_invariant_tolerance(double e=LanczosBidiagonalization::Defaults::epsilon)
Definition: irlba.hpp:126
Irlba & set_seed(uint64_t s=Defaults::seed)
Definition: irlba.hpp:101
std::pair< bool, int > run(const M &mat, bool center, bool scale, Eigen::MatrixXd &outU, Eigen::MatrixXd &outV, Eigen::VectorXd &outD, Engine *eng=null_rng(), Eigen::VectorXd *init=NULL) const
Definition: irlba.hpp:188
Irlba & set_number(int n=Defaults::number)
Definition: irlba.hpp:76
-
Results run(const M &mat, bool center, bool scale, Engine *eng=null_rng(), Eigen::VectorXd *init=NULL) const
Definition: irlba.hpp:542
+
Results run(const M &mat, bool center, bool scale, Engine *eng=null_rng(), Eigen::VectorXd *init=NULL) const
Definition: irlba.hpp:525
Irlba & set_convergence_tolerance(double t=ConvergenceTest::Defaults::tol)
Definition: irlba.hpp:138
Irlba & set_maxit(int m=Defaults::maxit)
Definition: irlba.hpp:89
-
Results run(const M &mat, Engine *eng=null_rng(), Eigen::VectorXd *init=NULL) const
Definition: irlba.hpp:566
+
Results run(const M &mat, Engine *eng=null_rng(), Eigen::VectorXd *init=NULL) const
Definition: irlba.hpp:549
Perform Lanczos bidiagonalization on an input matrix.
Definition: lanczos.hpp:21
LanczosBidiagonalization & set_epsilon(double e=Defaults::epsilon)
Definition: lanczos.hpp:40
Intermediates< M > initialize(const M &mat) const
Definition: lanczos.hpp:91
@@ -470,12 +470,12 @@
static constexpr int number
Definition: irlba.hpp:40
static constexpr int extra_work
Definition: irlba.hpp:45
static constexpr int maxit
Definition: irlba.hpp:50
-
Result of the IRLBA-based decomposition.
Definition: irlba.hpp:492
-
int iterations
Definition: irlba.hpp:516
-
Eigen::MatrixXd U
Definition: irlba.hpp:498
-
Eigen::VectorXd D
Definition: irlba.hpp:511
-
Eigen::MatrixXd V
Definition: irlba.hpp:505
-
bool converged
Definition: irlba.hpp:521
+
Result of the IRLBA-based decomposition.
Definition: irlba.hpp:475
+
int iterations
Definition: irlba.hpp:499
+
Eigen::MatrixXd U
Definition: irlba.hpp:481
+
Eigen::VectorXd D
Definition: irlba.hpp:494
+
Eigen::MatrixXd V
Definition: irlba.hpp:488
+
bool converged
Definition: irlba.hpp:504
Wrapper for a scaled matrix.
Definition: wrappers.hpp:283
Various utility functions.
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