forked from pytorch/pytorch
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathBatchLinearAlgebra.cpp
4032 lines (3487 loc) · 161 KB
/
BatchLinearAlgebra.cpp
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
#define TORCH_ASSERT_ONLY_METHOD_OPERATORS
#include <ATen/core/Tensor.h>
#include <ATen/core/grad_mode.h>
#include <ATen/Dispatch.h>
#include <ATen/Parallel.h>
#include <ATen/TensorMeta.h>
#include <ATen/TensorOperators.h>
#include <ATen/TensorSubclassLikeUtils.h>
#include <ATen/native/BatchLinearAlgebra.h>
#include <ATen/native/LinearAlgebraUtils.h>
#include <ATen/native/Resize.h>
#include <ATen/native/cpu/zmath.h>
#include <c10/util/irange.h>
#include <utility>
#include <vector>
#ifndef AT_PER_OPERATOR_HEADERS
#include <ATen/Functions.h>
#include <ATen/NativeFunctions.h>
#else
#include <ATen/ops/_cholesky_solve_helper.h>
#include <ATen/ops/_cholesky_solve_helper_native.h>
#include <ATen/ops/_linalg_check_errors.h>
#include <ATen/ops/_linalg_check_errors_native.h>
#include <ATen/ops/_linalg_eigh.h>
#include <ATen/ops/_linalg_eigh_meta.h>
#include <ATen/ops/_linalg_eigh_native.h>
#include <ATen/ops/_linalg_eigvals.h>
#include <ATen/ops/_linalg_eigvals_native.h>
#include <ATen/ops/_linalg_solve_ex.h>
#include <ATen/ops/_linalg_solve_ex_meta.h>
#include <ATen/ops/_linalg_solve_ex_native.h>
#include <ATen/ops/_linalg_svd.h>
#include <ATen/ops/_linalg_svd_meta.h>
#include <ATen/ops/_linalg_svd_native.h>
#include <ATen/ops/_lu_with_info_native.h>
#include <ATen/ops/all.h>
#include <ATen/ops/arange.h>
#include <ATen/ops/cat.h>
#include <ATen/ops/cholesky.h>
#include <ATen/ops/cholesky_inverse.h>
#include <ATen/ops/cholesky_inverse_native.h>
#include <ATen/ops/cholesky_native.h>
#include <ATen/ops/cholesky_solve.h>
#include <ATen/ops/cholesky_solve_native.h>
#include <ATen/ops/clone.h>
#include <ATen/ops/complex.h>
#include <ATen/ops/cumprod.h>
#include <ATen/ops/empty.h>
#include <ATen/ops/empty_like.h>
#include <ATen/ops/geqrf.h>
#include <ATen/ops/geqrf_native.h>
#include <ATen/ops/inverse_native.h>
#include <ATen/ops/linalg_cholesky_ex.h>
#include <ATen/ops/linalg_cholesky_ex_meta.h>
#include <ATen/ops/linalg_cholesky_ex_native.h>
#include <ATen/ops/linalg_cholesky_native.h>
#include <ATen/ops/linalg_eig.h>
#include <ATen/ops/linalg_eig_native.h>
#include <ATen/ops/linalg_eigh_native.h>
#include <ATen/ops/linalg_eigvals.h>
#include <ATen/ops/linalg_eigvals_native.h>
#include <ATen/ops/linalg_eigvalsh_native.h>
#include <ATen/ops/linalg_householder_product.h>
#include <ATen/ops/linalg_householder_product_native.h>
#include <ATen/ops/linalg_inv.h>
#include <ATen/ops/linalg_inv_ex.h>
#include <ATen/ops/linalg_inv_ex_native.h>
#include <ATen/ops/linalg_inv_native.h>
#include <ATen/ops/linalg_ldl_factor_ex.h>
#include <ATen/ops/linalg_ldl_factor_ex_meta.h>
#include <ATen/ops/linalg_ldl_factor_ex_native.h>
#include <ATen/ops/linalg_ldl_factor_native.h>
#include <ATen/ops/linalg_ldl_solve_meta.h>
#include <ATen/ops/linalg_ldl_solve_native.h>
#include <ATen/ops/linalg_lstsq.h>
#include <ATen/ops/linalg_lstsq_native.h>
#include <ATen/ops/linalg_lu_factor_ex.h>
#include <ATen/ops/linalg_lu_factor_ex_meta.h>
#include <ATen/ops/linalg_lu_factor_ex_native.h>
#include <ATen/ops/linalg_lu_factor_native.h>
#include <ATen/ops/linalg_lu_meta.h>
#include <ATen/ops/linalg_lu_native.h>
#include <ATen/ops/linalg_lu_solve.h>
#include <ATen/ops/linalg_lu_solve_meta.h>
#include <ATen/ops/linalg_lu_solve_native.h>
#include <ATen/ops/linalg_qr.h>
#include <ATen/ops/linalg_qr_meta.h>
#include <ATen/ops/linalg_qr_native.h>
#include <ATen/ops/linalg_solve_ex.h>
#include <ATen/ops/linalg_solve_ex_native.h>
#include <ATen/ops/linalg_solve_native.h>
#include <ATen/ops/linalg_solve_triangular_native.h>
#include <ATen/ops/linalg_svd.h>
#include <ATen/ops/linalg_svd_native.h>
#include <ATen/ops/linalg_svdvals.h>
#include <ATen/ops/linalg_svdvals_native.h>
#include <ATen/ops/linalg_vander_native.h>
#include <ATen/ops/linalg_vecdot_native.h>
#include <ATen/ops/lu_solve_native.h>
#include <ATen/ops/lu_unpack.h>
#include <ATen/ops/lu_unpack_meta.h>
#include <ATen/ops/lu_unpack_native.h>
#include <ATen/ops/orgqr_native.h>
#include <ATen/ops/ormqr_native.h>
#include <ATen/ops/qr_native.h>
#include <ATen/ops/real.h>
#include <ATen/ops/resize_as_native.h>
#include <ATen/ops/sum.h>
#include <ATen/ops/svd_native.h>
#include <ATen/ops/triangular_solve_meta.h>
#include <ATen/ops/triangular_solve_native.h>
#include <ATen/ops/tril.h>
#include <ATen/ops/triu.h>
#include <ATen/ops/vdot.h>
#include <ATen/ops/zeros.h>
#endif
// First the required LAPACK implementations are registered here.
// A comment above the registered LAPACK routine suggest which batched
// linear algebra function uses that routine
#if AT_BUILD_WITH_LAPACK()
// getrf
extern "C" void zgetrf_(int *m, int *n, std::complex<double> *a, int *lda, int *ipiv, int *info);
extern "C" void cgetrf_(int *m, int *n, std::complex<float> *a, int *lda, int *ipiv, int *info);
extern "C" void dgetrf_(int *m, int *n, double *a, int *lda, int *ipiv, int *info);
extern "C" void sgetrf_(int *m, int *n, float *a, int *lda, int *ipiv, int *info);
// potrs
extern "C" void zpotrs_(char *uplo, int *n, int *nrhs, std::complex<double> *a, int *lda, std::complex<double> *b, int *ldb, int *info);
extern "C" void cpotrs_(char *uplo, int *n, int *nrhs, std::complex<float> *a, int *lda, std::complex<float> *b, int *ldb, int *info);
extern "C" void dpotrs_(char *uplo, int *n, int *nrhs, double *a, int *lda, double *b, int *ldb, int *info);
extern "C" void spotrs_(char *uplo, int *n, int *nrhs, float *a, int *lda, float *b, int *ldb, int *info);
// potrf
extern "C" void zpotrf_(char *uplo, int *n, std::complex<double> *a, int *lda, int *info);
extern "C" void cpotrf_(char *uplo, int *n, std::complex<float> *a, int *lda, int *info);
extern "C" void dpotrf_(char *uplo, int *n, double *a, int *lda, int *info);
extern "C" void spotrf_(char *uplo, int *n, float *a, int *lda, int *info);
// potri
extern "C" void zpotri_(char *uplo, int *n, std::complex<double> *a, int *lda, int *info);
extern "C" void cpotri_(char *uplo, int *n, std::complex<float> *a, int *lda, int *info);
extern "C" void dpotri_(char *uplo, int *n, double *a, int *lda, int *info);
extern "C" void spotri_(char *uplo, int *n, float *a, int *lda, int *info);
// sytrf
extern "C" void dsytrf_(
char* uplo,
int* n,
double* a,
int* lda,
int* ipiv,
double* work,
int* lwork,
int* info);
extern "C" void ssytrf_(
char* uplo,
int* n,
float* a,
int* lda,
int* ipiv,
float* work,
int* lwork,
int* info);
extern "C" void zsytrf_(
char* uplo,
int* n,
std::complex<double>* a,
int* lda,
int* ipiv,
std::complex<double>* work,
int* lwork,
int* info);
extern "C" void csytrf_(
char* uplo,
int* n,
std::complex<float>* a,
int* lda,
int* ipiv,
std::complex<float>* work,
int* lwork,
int* info);
// hetrf
extern "C" void zhetrf_(
char* uplo,
int* n,
std::complex<double>* a,
int* lda,
int* ipiv,
std::complex<double>* work,
int* lwork,
int* info);
extern "C" void chetrf_(
char* uplo,
int* n,
std::complex<float>* a,
int* lda,
int* ipiv,
std::complex<float>* work,
int* lwork,
int* info);
// sytrs
extern "C" void dsytrs_(
char* uplo,
int* n,
int* nrhs,
double* a,
int* lda,
int* ipiv,
double* b,
int* ldb,
int* info);
extern "C" void ssytrs_(
char* uplo,
int* n,
int* nrhs,
float* a,
int* lda,
int* ipiv,
float* b,
int* ldb,
int* info);
extern "C" void zsytrs_(
char* uplo,
int* n,
int* nrhs,
std::complex<double>* a,
int* lda,
int* ipiv,
std::complex<double>* b,
int* ldb,
int* info);
extern "C" void csytrs_(
char* uplo,
int* n,
int* nrhs,
std::complex<float>* a,
int* lda,
int* ipiv,
std::complex<float>* b,
int* ldb,
int* info);
// hetrs
extern "C" void zhetrs_(
char* uplo,
int* n,
int* nrhs,
std::complex<double>* a,
int* lda,
int* ipiv,
std::complex<double>* b,
int* ldb,
int* info);
extern "C" void chetrs_(
char* uplo,
int* n,
int* nrhs,
std::complex<float>* a,
int* lda,
int* ipiv,
std::complex<float>* b,
int* ldb,
int* info);
// geqrf
extern "C" void zgeqrf_(int *m, int *n, std::complex<double> *a, int *lda, std::complex<double> *tau, std::complex<double> *work, int *lwork, int *info);
extern "C" void cgeqrf_(int *m, int *n, std::complex<float> *a, int *lda, std::complex<float> *tau, std::complex<float> *work, int *lwork, int *info);
extern "C" void dgeqrf_(int *m, int *n, double *a, int *lda, double *tau, double *work, int *lwork, int *info);
extern "C" void sgeqrf_(int *m, int *n, float *a, int *lda, float *tau, float *work, int *lwork, int *info);
// orgqr
extern "C" void zungqr_(int *m, int *n, int *k, std::complex<double> *a, int *lda, std::complex<double> *tau, std::complex<double> *work, int *lwork, int *info);
extern "C" void cungqr_(int *m, int *n, int *k, std::complex<float> *a, int *lda, std::complex<float> *tau, std::complex<float> *work, int *lwork, int *info);
extern "C" void dorgqr_(int *m, int *n, int *k, double *a, int *lda, double *tau, double *work, int *lwork, int *info);
extern "C" void sorgqr_(int *m, int *n, int *k, float *a, int *lda, float *tau, float *work, int *lwork, int *info);
// ormqr
extern "C" void zunmqr_(char *side, char *trans, int *m, int *n, int *k, std::complex<double> *a, int *lda, std::complex<double> *tau, std::complex<double> *c, int *ldc, std::complex<double> *work, int *lwork, int *info);
extern "C" void cunmqr_(char *side, char *trans, int *m, int *n, int *k, std::complex<float> *a, int *lda, std::complex<float> *tau, std::complex<float> *c, int *ldc, std::complex<float> *work, int *lwork, int *info);
extern "C" void dormqr_(char *side, char *trans, int *m, int *n, int *k, double *a, int *lda, double *tau, double *c, int *ldc, double *work, int *lwork, int *info);
extern "C" void sormqr_(char *side, char *trans, int *m, int *n, int *k, float *a, int *lda, float *tau, float *c, int *ldc, float *work, int *lwork, int *info);
// syevd
extern "C" void zheevd_(char *jobz, char *uplo, int *n, std::complex<double> *a, int *lda, double *w, std::complex<double> *work, int *lwork, double *rwork, int *lrwork, int *iwork, int *liwork, int *info);
extern "C" void cheevd_(char *jobz, char *uplo, int *n, std::complex<float> *a, int *lda, float *w, std::complex<float> *work, int *lwork, float *rwork, int *lrwork, int *iwork, int *liwork, int *info);
extern "C" void dsyevd_(char *jobz, char *uplo, int *n, double *a, int *lda, double *w, double *work, int *lwork, int *iwork, int *liwork, int *info);
extern "C" void ssyevd_(char *jobz, char *uplo, int *n, float *a, int *lda, float *w, float *work, int *lwork, int *iwork, int *liwork, int *info);
// geev
extern "C" void dgeev_(char *jobvl, char *jobvr, int *n, double *a, int *lda, double *wr, double *wi, double* vl, int *ldvl, double *vr, int *ldvr, double *work, int *lwork, int *info);
extern "C" void sgeev_(char *jobvl, char *jobvr, int *n, float *a, int *lda, float *wr, float *wi, float* vl, int *ldvl, float *vr, int *ldvr, float *work, int *lwork, int *info);
extern "C" void cgeev_(char *jobvl, char *jobvr, int *n,
std::complex<float> *a, int *lda,
std::complex<float> *w,
std::complex<float> *vl, int *ldvl,
std::complex<float> *vr, int *ldvr,
std::complex<float> *work, int *lwork,
float *rwork,
int *info);
extern "C" void zgeev_(char *jobvl, char *jobvr, int *n,
std::complex<double> *a, int *lda,
std::complex<double> *w,
std::complex<double> *vl, int *ldvl,
std::complex<double> *vr, int *ldvr,
std::complex<double> *work, int *lwork,
double *rwork,
int *info);
// gesdd
extern "C" void zgesdd_(char *jobz, int *m, int *n, std::complex<double> *a, int *lda,
double *s, std::complex<double> *u, int *ldu, std::complex<double> *vt, int *ldvt, std::complex<double> *work, int *lwork, double *rwork, int *iwork, int *info);
extern "C" void cgesdd_(char *jobz, int *m, int *n, std::complex<float> *a, int *lda,
float *s, std::complex<float> *u, int *ldu, std::complex<float> *vt, int *ldvt, std::complex<float> *work, int *lwork, float *rwork, int *iwork, int *info);
extern "C" void dgesdd_(char *jobz, int *m, int *n, double *a, int *lda,
double *s, double *u, int *ldu, double *vt, int *ldvt, double *work, int *lwork, int *iwork, int *info);
extern "C" void sgesdd_(char *jobz, int *m, int *n, float *a, int *lda,
float *s, float *u, int *ldu, float *vt, int *ldvt, float *work, int *lwork, int *iwork, int *info);
// getrs
extern "C" void zgetrs_(char *trans, int *n, int *nrhs, std::complex<double> *a, int *lda, int *ipiv, std::complex<double> *b, int *ldb, int *info);
extern "C" void cgetrs_(char *trans, int *n, int *nrhs, std::complex<float> *a, int *lda, int *ipiv, std::complex<float> *b, int *ldb, int *info);
extern "C" void dgetrs_(char *trans, int *n, int *nrhs, double *a, int *lda, int *ipiv, double *b, int *ldb, int *info);
extern "C" void sgetrs_(char *trans, int *n, int *nrhs, float *a, int *lda, int *ipiv, float *b, int *ldb, int *info);
// gels
extern "C" void zgels_(char *trans, int *m, int *n, int *nrhs,
std::complex<double> *a, int *lda, std::complex<double> *b, int *ldb,
std::complex<double> *work, int *lwork, int *info);
extern "C" void cgels_(char *trans, int *m, int *n, int *nrhs,
std::complex<float> *a, int *lda, std::complex<float> *b, int *ldb,
std::complex<float> *work, int *lwork, int *info);
extern "C" void dgels_(char *trans, int *m, int *n, int *nrhs,
double *a, int *lda, double *b, int *ldb,
double *work, int *lwork, int *info);
extern "C" void sgels_(char *trans, int *m, int *n, int *nrhs,
float *a, int *lda, float *b, int *ldb,
float *work, int *lwork, int *info);
// gelsd
extern "C" void zgelsd_(int *m, int *n, int *nrhs,
std::complex<double> *a, int *lda, std::complex<double> *b, int *ldb,
double *s, double *rcond, int *rank,
std::complex<double> *work, int *lwork, double *rwork, int *iwork, int *info);
extern "C" void cgelsd_(int *m, int *n, int *nrhs,
std::complex<float> *a, int *lda, std::complex<float> *b, int *ldb,
float *s, float *rcond, int *rank,
std::complex<float> *work, int *lwork, float *rwork, int *iwork, int *info);
extern "C" void dgelsd_(int *m, int *n, int *nrhs,
double *a, int *lda, double *b, int *ldb,
double *s, double *rcond, int *rank,
double *work, int *lwork, int *iwork, int *info);
extern "C" void sgelsd_(int *m, int *n, int *nrhs,
float *a, int *lda, float *b, int *ldb,
float *s, float *rcond, int *rank,
float *work, int *lwork, int *iwork, int *info);
// gelsy
extern "C" void zgelsy_(int *m, int *n, int *nrhs,
std::complex<double> *a, int *lda, std::complex<double> *b, int *ldb,
int *jpvt, double *rcond, int *rank,
std::complex<double> *work, int *lwork,
double *rwork, int *info);
extern "C" void cgelsy_(int *m, int *n, int *nrhs,
std::complex<float> * a, int *lda, std::complex<float> *b, int *ldb,
int *jpvt, float *rcond, int *rank,
std::complex<float> *work, int *lwork,
float *rwork, int *info);
extern "C" void dgelsy_(int *m, int *n, int *nrhs,
double *a, int *lda, double *b, int *ldb,
int *jpvt, double *rcond, int *rank,
double *work, int *lwork, int *info);
extern "C" void sgelsy_(int *m, int *n, int *nrhs,
float *a, int *lda, float *b, int *ldb,
int *jpvt, float *rcond, int *rank,
float *work, int *lwork, int *info);
// gelss
extern "C" void zgelss_(int *m, int *n, int *nrhs,
std::complex<double> *a, int *lda, std::complex<double> *b, int *ldb,
double *s, double *rcond, int *rank,
std::complex<double> *work, int *lwork,
double *rwork, int *info);
extern "C" void cgelss_(int *m, int *n, int *nrhs,
std::complex<float> *a, int *lda, std::complex<float> *b, int *ldb,
float *s, float *rcond, int *rank,
std::complex<float> *work, int *lwork,
float *rwork, int *info);
extern "C" void dgelss_(int *m, int *n, int *nrhs,
double *a, int *lda, double *b, int *ldb,
double *s, double *rcond, int *rank,
double *work, int *lwork, int *info);
extern "C" void sgelss_(int *m, int *n, int *nrhs,
float *a, int *lda, float *b, int *ldb,
float *s, float *rcond, int *rank,
float *work, int *lwork, int *info);
#endif
#if AT_BUILD_WITH_BLAS()
// trsm
extern "C" void ztrsm_(char *side, char *uplo, char *trans, char *diag, int *n, int *nrhs, std::complex<double> *alpha, std::complex<double> *a, int *lda, std::complex<double> *b, int *ldb);
extern "C" void ctrsm_(char *side, char *uplo, char *trans, char *diag, int *n, int *nrhs, std::complex<float> *alpha, std::complex<float> *a, int *lda, std::complex<float> *b, int *ldb);
extern "C" void dtrsm_(char *side, char *uplo, char *trans, char *diag, int *n, int *nrhs, double *alpha, double *a, int *lda, double *b, int *ldb);
extern "C" void strsm_(char *side, char *uplo, char *trans, char *diag, int *n, int *nrhs, float *alpha, float *a, int *lda, float *b, int *ldb);
#endif
namespace at::meta {
TORCH_META_FUNC(linalg_ldl_factor_ex)
(const Tensor& self, bool hermitian, bool check_errors) {
at::native::squareCheckInputs(self, "torch.linalg.ldl_factor_ex");
at::native::checkFloatingOrComplex(self, "torch.linalg.ldl_factor_ex");
auto shape = self.sizes();
auto ndim = shape.size();
// prefer column major strides
auto ld_strides = at::native::batched_matrix_contiguous_strides(shape, /*f-contig=*/true);
set_output_strided(0, shape, ld_strides, self.options(), {}); // LD
set_output_contiguous(
1, shape.slice(0, ndim - 1), self.options().dtype(ScalarType::Int)); // pivots
set_output_contiguous(
2, shape.slice(0, ndim - 2), self.options().dtype(ScalarType::Int)); // info
}
TORCH_META_FUNC(linalg_ldl_solve)
(const Tensor& LD,
const Tensor& pivots,
const Tensor& B,
bool hermitian) {
at::native::squareCheckInputs(LD, "torch.linalg.ldl_solve");
at::native::checkFloatingOrComplex(LD, "torch.linalg.ldl_solve");
at::native::linearSolveCheckInputs(B, LD, "torch.linalg.ldl_solve");
TORCH_CHECK(
B.dim() >= 2,
"torch.linalg.ldl_solve: Expected B to have at least 2 dimensions, but it has ",
B.dim(),
" dimensions instead");
auto expected_pivots_shape = LD.sizes().slice(0, LD.dim() - 1);
TORCH_CHECK(
expected_pivots_shape.equals(pivots.sizes()),
"torch.linalg.ldl_solve: Expected LD.shape[:-1] and pivots.shape to be the same, but got pivots with shape ",
pivots.sizes(),
" instead");
// pivots is allowed to be any integer type
// LAPACK we use is 32-bit interface while cuSOLVER uses 64-bit interface for integers
TORCH_CHECK(
at::isIntegralType(pivots.scalar_type(), /*includeBool=*/false),
"torch.linalg.ldl_solve: Expected pivots to be integers. Got ",
pivots.scalar_type());
TORCH_CHECK(
LD.scalar_type() == B.scalar_type(),
"torch.linalg.ldl_solve: ",
"LD dtype",
LD.scalar_type(),
" does not match b dtype ",
B.scalar_type());
auto [B_broadcast_size, _] = at::native::_linalg_broadcast_batch_dims(B, LD);
// prefer column major strides
auto result_strides = at::native::batched_matrix_contiguous_strides(B_broadcast_size, /*f_contig=*/true);
set_output_strided(0, B_broadcast_size, result_strides, B.options(), {});
}
TORCH_META_FUNC(triangular_solve)(const Tensor& self, const Tensor& A, bool upper, bool transpose, bool unitriangular) {
TORCH_CHECK(self.dim() >= 2,
"torch.triangular_solve: Expected b to have at least 2 dimensions, but it has ", self.dim(), " dimensions instead");
TORCH_CHECK(A.dim() >= 2,
"torch.triangular_solve: Expected A to have at least 2 dimensions, but it has ", A.dim(), " dimensions instead");
at::native::linearSolveCheckInputs(self, A, "triangular_solve");
if (A.layout() == Layout::Strided) {
auto [self_broadcast_size, A_broadcast_size] = at::native::_linalg_broadcast_batch_dims(self, A);
// make column major strides for BLAS
const auto solution_strides = at::native::batched_matrix_contiguous_strides(self_broadcast_size, /*f-contig=*/true);
set_output_raw_strided(0, self_broadcast_size, solution_strides, self.options(), {});
// make column major strides for BLAS
auto clone_A_strides = at::native::batched_matrix_contiguous_strides(A_broadcast_size, /*f_contig=*/true);
set_output_raw_strided(1, A_broadcast_size, clone_A_strides, A.options(), {});
} else if (A.layout() == Layout::SparseCsr || A.layout() == Layout::SparseBsr) {
// no broadcasting for non-strided layout
set_output_raw_strided(0, self.sizes(), {}, self.options(), {}); // make row major strides for Sparse BLAS
set_output_raw_strided(1, {0}, {}, self.options(), {}); // return 0-sized tensor
} else {
TORCH_INTERNAL_ASSERT(false, "triangular_solve: Got an unexpected layout.");
}
}
TORCH_META_FUNC(_linalg_solve_ex)(const Tensor& A,
const Tensor& B,
bool left,
bool check_errors) {
// dtype
at::native::checkFloatingOrComplex(A, "linalg.solve");
TORCH_CHECK(A.scalar_type() == B.scalar_type(),
"linalg.solve: Expected A and B to have the same dtype, but found A of type ",
A.scalar_type(), " and B of type ", B.scalar_type(), " instead");
// NumPy compat: Two types of 'B' tensors are supported:
// - 1D tensor or batch of 1D tensors (vector case)
// - 2D tensor or batch of 2D tensors (matrix case)
const bool vector_case = at::native::linalg_solve_is_vector_rhs(A, B);
auto B_ = vector_case ? B.unsqueeze(-1) : B;
// matrix shapes
at::native::checkInputsSolver(A, B_, /*left=*/left, "linalg.solve");
// Check that B can be broadcasted to the shape of A
auto B_broad_shape = std::get<0>(at::native::_linalg_broadcast_batch_dims(B_, A));
// We disallow the broadcasting of B as a vector when left=False as, in that case, A.shape = (*, 1, 1)
TORCH_CHECK(left || !vector_case, "linalg.solve: Vector broadcasting of the left hand side is not supported for left=False. In this case linalg.solve is equivalent to B / A.squeeze(-1)");
auto result_shape = vector_case ? IntArrayRef(B_broad_shape.data(), B_broad_shape.size() - 1)
: B_broad_shape;
auto result_strides = at::native::batched_matrix_contiguous_strides(result_shape, /*f_contig=*/left);
set_output_strided(0, result_shape, result_strides, B.options(), {});
auto shape = A.sizes();
auto ndim = shape.size();
// LU
auto LU_strides = at::native::batched_matrix_contiguous_strides(shape, /*f-contig*=*/true);
set_output_strided(1, shape, LU_strides, A.options(), {});
// pivots
set_output_contiguous(2, shape.slice(0, ndim - 1), A.options().dtype(kInt));
// info
set_output_contiguous(3, shape.slice(0, ndim - 2), A.options().dtype(kInt));
}
TORCH_META_FUNC(linalg_inv_ex)(const Tensor& A, bool check_errors) {
at::native::squareCheckInputs(A, "linalg.inv");
at::native::checkFloatingOrComplex(A, "linalg.inv", /*allow_low_precision_dtypes*/false);
auto shape = A.sizes();
auto result_strides = at::native::batched_matrix_contiguous_strides(shape, /*f-contig*=*/true);
set_output_strided(0, shape, result_strides, A.options(), {});
set_output_contiguous(
1, shape.slice(0, shape.size() - 2), A.options().dtype(ScalarType::Int)); // info
}
TORCH_META_FUNC(linalg_lu_factor_ex)(const Tensor& A, bool pivot, bool check_errors) {
TORCH_CHECK(A.dim() >= 2, "torch.lu_factor: Expected tensor with 2 or more dimensions. Got size: ", A.sizes(), " instead");
auto sizes = A.sizes().vec();
const auto m = sizes.cend()[-2];
const auto n = sizes.cend()[-1];
// make column major strides for BLAS
auto LU_strides = at::native::batched_matrix_contiguous_strides(sizes, /*f-contig*=*/true);
set_output_strided(0, sizes, LU_strides, A.options(), {});
// Set sizes to the size of pivots
sizes.pop_back();
sizes.back() = std::min(m, n);
set_output_contiguous(1, sizes, A.options().dtype(kInt), {});
// Set sizes to the size of info
sizes.pop_back();
set_output_contiguous(2, sizes, A.options().dtype(kInt), {});
}
TORCH_META_FUNC(linalg_lu_solve)(const Tensor& LU,
const Tensor& pivots,
const Tensor& B,
bool left,
bool adjoint) {
// dtype
at::native::checkFloatingOrComplex(LU, "torch.linalg.lu_solve");
TORCH_CHECK(LU.scalar_type() == B.scalar_type(),
"linalg.lu_solve: Expected LU and B to have the same dtype, but found LU of type ",
LU.scalar_type(), " and B of type ", B.scalar_type(), " instead");
TORCH_CHECK(pivots.dtype() == at::kInt,
"linalg.lu_solve: pivots should be a Tensor of scalar type torch.int32");
// matrix shapes
at::native::squareCheckInputs(LU, "torch.linalg.lu_solve");
at::native::checkInputsSolver(LU, B, left, "linalg.lu_solve");
//
TORCH_CHECK(LU.size(-1) == pivots.size(-1),
"linalg.lu_solve: Number of pivots per batch should be same as the dimension of the matrix");
// batches
TORCH_CHECK(
LU.sizes().slice(0, LU.dim() - 1).equals(pivots.sizes()),
"linalg.lu_solve: Expected LU.shape[:-1] and pivots.shape to be the same, but got pivots with shape ",
pivots.sizes(), " instead");
// This one checks that B can be broadcasted to the shape of A
auto B_broadcast_size = std::get<0>(at::native::_linalg_broadcast_batch_dims(B, LU));
auto result_strides = at::native::batched_matrix_contiguous_strides(B_broadcast_size, /*f_contig=*/left);
set_output_strided(0, B_broadcast_size, result_strides, B.options(), {});
}
TORCH_META_FUNC(linalg_cholesky_ex)(const Tensor& A,
bool upper,
bool check_errors) {
at::native::squareCheckInputs(A, "linalg.cholesky");
at::native::checkFloatingOrComplex(A, "linalg.cholesky");
auto A_shape = A.sizes();
auto ndim = A_shape.size();
// L
auto L_strides = at::native::batched_matrix_contiguous_strides(A_shape, /*f-contig*=*/true);
set_output_strided(0, A_shape, L_strides, A.options(), {});
// info
set_output_contiguous(1, A_shape.slice(0, ndim - 2), A.options().dtype(ScalarType::Int));
}
TORCH_META_FUNC(linalg_qr)(const Tensor& A,
c10::string_view mode) {
at::native::checkIsMatrix(A, "linalg.qr");
at::native::checkFloatingOrComplex(A, "linalg.qr");
auto [compute_q, reduced_mode] = at::native::_parse_qr_mode(mode);
auto A_shape = A.sizes().vec();
const auto m = A_shape.cend()[-2];
const auto n = A_shape.cend()[-1];
const auto k = std::min(m, n);
if (compute_q) {
auto Q_shape = A_shape;
Q_shape.end()[-1] = reduced_mode ? k : m;
auto Q_strides = at::native::batched_matrix_contiguous_strides(Q_shape, /*f-contig*=*/true);
set_output_strided(0, Q_shape, Q_strides, A.options(), {});
} else {
set_output_raw_strided(0, {0}, {}, A.options(), {});
}
// For readability
auto R_shape = std::move(A_shape);
R_shape.end()[-2] = (reduced_mode || !compute_q) ? k : m;
auto R_strides = at::native::batched_matrix_contiguous_strides(R_shape, /*f-contig*=*/true);
set_output_strided(1, R_shape, R_strides, A.options(), {});
}
TORCH_META_FUNC(_linalg_svd)(const Tensor& A,
bool full_matrices,
bool compute_uv,
std::optional<c10::string_view> driver) {
at::native::checkIsMatrix(A, "linalg.svd");
at::native::checkFloatingOrComplex(A, "linalg.svd");
auto sizes = A.sizes().vec();
const auto m = sizes.cend()[-2];
const auto n = sizes.cend()[-1];
const auto k = std::min(m, n);
// Prepare sizes for U
if (compute_uv) {
sizes.back() = full_matrices ? m : k;
auto U_strides = at::native::batched_matrix_contiguous_strides(sizes, /*f-contig*=*/true);
set_output_strided(0, sizes, U_strides, A.options(), {});
// Prepare sizes for Vh
sizes.end()[-2] = full_matrices ? n : k;
sizes.end()[-1] = n;
// We need to distinguish the cuSOLVER case, as the cuSOLVER algorithms we use
// expect F-contig matrices, but they compute V rather than Vh
const bool use_cusolver = at::native::svd_uses_cusolver(A);
auto Vh_strides = at::native::batched_matrix_contiguous_strides(sizes, /*f-contig*=*/!use_cusolver);
set_output_strided(2, sizes, Vh_strides, A.options(), {});
} else {
set_output_raw_strided(0, {0}, {}, A.options(), {});
set_output_raw_strided(2, {0}, {}, A.options(), {});
}
// Prepare sizes for S. S is always real, even when A is complex.
sizes.pop_back();
sizes.end()[-1] = k;
set_output_contiguous(1, sizes, A.options().dtype(c10::toRealValueType(A.scalar_type())), {});
}
TORCH_META_FUNC(lu_unpack)(const Tensor& LU, const Tensor& pivots, bool unpack_data, bool unpack_pivots) {
TORCH_CHECK(LU.dim() >= 2, "torch.lu_unpack: Expected tensor with 2 or more dimensions. Got size: ", LU.sizes(), " instead");
if (unpack_pivots) {
TORCH_CHECK(pivots.scalar_type() == at::kInt,
"torch.lu_unpack: LU_pivots is expected to be a contiguous tensor of torch.int32 dtype.\n"
"Note: this function is intended to be used with the output produced by torch.linalg.lu_factor");
}
auto sizes = LU.sizes().vec();
const auto m = sizes.cend()[-2];
const auto n = sizes.cend()[-1];
const auto k = std::min(m, n);
// P.shape[-2:] == (m, m) (or size zero if pivot == False)
sizes.end()[-1] = m;
if (unpack_pivots) {
set_output_raw_strided(0, sizes, {}, LU.options(), {});
} else {
set_output_raw_strided(0, {0}, {}, LU.options(), {});
}
if (unpack_data) {
// L.shape[-2:] == (m, k)
sizes.end()[-1] = k;
set_output_raw_strided(1, sizes, {}, LU.options(), {});
// U.shape[-2:] == (k, n)
sizes.end()[-2] = k;
sizes.end()[-1] = n;
set_output_raw_strided(2, sizes, {}, LU.options(), {});
} else {
set_output_raw_strided(1, {0}, {}, LU.options(), {});
set_output_raw_strided(2, {0}, {}, LU.options(), {});
}
}
TORCH_META_FUNC(_linalg_eigh)(const Tensor& A,
c10::string_view uplo,
bool compute_v) {
at::native::squareCheckInputs(A, "linalg.eigh");
at::native::checkUplo(uplo);
auto shape = A.sizes().vec();
if (compute_v) {
// eigenvectors
auto V_strides = at::native::batched_matrix_contiguous_strides(shape, /*f-contig*=*/true);
set_output_strided(1, shape, V_strides, A.options(), {});
} else {
set_output_raw_strided(1, {0}, {}, A.options(), {});
}
// eigenvalues
shape.pop_back();
set_output_contiguous(0, shape, A.options().dtype(c10::toRealValueType(A.scalar_type())), {});
}
TORCH_META_FUNC(linalg_lu)(const Tensor& A, bool pivot) {
TORCH_CHECK(A.dim() >= 2, "linalg.lu: Expected tensor with 2 or more dimensions. Got size: ", A.sizes(), " instead");
auto sizes = A.sizes().vec();
const auto m = sizes.cend()[-2];
const auto n = sizes.cend()[-1];
const auto k = std::min(m, n);
// P.shape[-2:] == (m, m) (or size zero if pivot == False)
sizes.end()[-1] = m;
if (pivot) {
set_output_raw_strided(0, sizes, {}, A.options(), {});
} else {
set_output_raw_strided(0, {0}, {}, A.options(), {});
}
// L.shape[-2:] == (m, k)
sizes.end()[-1] = k;
set_output_raw_strided(1, sizes, {}, A.options(), {});
// U.shape[-2:] == (k, n)
sizes.end()[-2] = k;
sizes.end()[-1] = n;
set_output_raw_strided(2, sizes, {}, A.options(), {});
}
} // namespace at::meta
namespace at::native {
#if AT_BUILD_WITH_LAPACK()
// Define the per-batch functions to be used in the main implementation of the batched
// linear algebra operations
template<class scalar_t>
void lapackCholeskySolve(char uplo, int n, int nrhs, scalar_t *a, int lda, scalar_t *b, int ldb, int *info);
template<class scalar_t, class value_t=scalar_t>
void lapackSymeig(char jobz, char uplo, int n, scalar_t *a, int lda, value_t *w, scalar_t *work, int lwork, value_t *rwork, int *info);
template<> void lapackLu<c10::complex<double>>(int m, int n, c10::complex<double> *a, int lda, int *ipiv, int *info) {
zgetrf_(&m, &n, reinterpret_cast<std::complex<double>*>(a), &lda, ipiv, info);
}
template<> void lapackLu<c10::complex<float>>(int m, int n, c10::complex<float> *a, int lda, int *ipiv, int *info) {
cgetrf_(&m, &n, reinterpret_cast<std::complex<float>*>(a), &lda, ipiv, info);
}
template<> void lapackLu<double>(int m, int n, double *a, int lda, int *ipiv, int *info) {
dgetrf_(&m, &n, a, &lda, ipiv, info);
}
template<> void lapackLu<float>(int m, int n, float *a, int lda, int *ipiv, int *info) {
sgetrf_(&m, &n, a, &lda, ipiv, info);
}
template<> void lapackCholeskySolve<c10::complex<double>>(char uplo, int n, int nrhs, c10::complex<double> *a, int lda, c10::complex<double> *b, int ldb, int *info) {
zpotrs_(&uplo, &n, &nrhs, reinterpret_cast<std::complex<double>*>(a), &lda, reinterpret_cast<std::complex<double>*>(b), &ldb, info);
}
template<> void lapackCholeskySolve<c10::complex<float>>(char uplo, int n, int nrhs, c10::complex<float> *a, int lda, c10::complex<float> *b, int ldb, int *info) {
cpotrs_(&uplo, &n, &nrhs, reinterpret_cast<std::complex<float>*>(a), &lda, reinterpret_cast<std::complex<float>*>(b), &ldb, info);
}
template<> void lapackCholeskySolve<double>(char uplo, int n, int nrhs, double *a, int lda, double *b, int ldb, int *info) {
dpotrs_(&uplo, &n, &nrhs, a, &lda, b, &ldb, info);
}
template<> void lapackCholeskySolve<float>(char uplo, int n, int nrhs, float *a, int lda, float *b, int ldb, int *info) {
spotrs_(&uplo, &n, &nrhs, a, &lda, b, &ldb, info);
}
template<> void lapackCholesky<c10::complex<double>>(char uplo, int n, c10::complex<double> *a, int lda, int *info) {
zpotrf_(&uplo, &n, reinterpret_cast<std::complex<double>*>(a), &lda, info);
}
template<> void lapackCholesky<c10::complex<float>>(char uplo, int n, c10::complex<float> *a, int lda, int *info) {
cpotrf_(&uplo, &n, reinterpret_cast<std::complex<float>*>(a), &lda, info);
}
template<> void lapackCholesky<double>(char uplo, int n, double *a, int lda, int *info) {
dpotrf_(&uplo, &n, a, &lda, info);
}
template<> void lapackCholesky<float>(char uplo, int n, float *a, int lda, int *info) {
spotrf_(&uplo, &n, a, &lda, info);
}
template<> void lapackCholeskyInverse<c10::complex<double>>(char uplo, int n, c10::complex<double> *a, int lda, int *info) {
zpotri_(&uplo, &n, reinterpret_cast<std::complex<double>*>(a), &lda, info);
}
template<> void lapackCholeskyInverse<c10::complex<float>>(char uplo, int n, c10::complex<float> *a, int lda, int *info) {
cpotri_(&uplo, &n, reinterpret_cast<std::complex<float>*>(a), &lda, info);
}
template<> void lapackCholeskyInverse<double>(char uplo, int n, double *a, int lda, int *info) {
dpotri_(&uplo, &n, a, &lda, info);
}
template<> void lapackCholeskyInverse<float>(char uplo, int n, float *a, int lda, int *info) {
spotri_(&uplo, &n, a, &lda, info);
}
template<> void lapackGeqrf<c10::complex<double>>(int m, int n, c10::complex<double> *a, int lda, c10::complex<double> *tau, c10::complex<double> *work, int lwork, int *info) {
zgeqrf_(&m, &n, reinterpret_cast<std::complex<double>*>(a), &lda, reinterpret_cast<std::complex<double>*>(tau), reinterpret_cast<std::complex<double>*>(work), &lwork, info);
}
template<> void lapackGeqrf<c10::complex<float>>(int m, int n, c10::complex<float> *a, int lda, c10::complex<float> *tau, c10::complex<float> *work, int lwork, int *info) {
cgeqrf_(&m, &n, reinterpret_cast<std::complex<float>*>(a), &lda, reinterpret_cast<std::complex<float>*>(tau), reinterpret_cast<std::complex<float>*>(work), &lwork, info);
}
template<> void lapackGeqrf<double>(int m, int n, double *a, int lda, double *tau, double *work, int lwork, int *info) {
dgeqrf_(&m, &n, a, &lda, tau, work, &lwork, info);
}
template<> void lapackGeqrf<float>(int m, int n, float *a, int lda, float *tau, float *work, int lwork, int *info) {
sgeqrf_(&m, &n, a, &lda, tau, work, &lwork, info);
}
template<> void lapackOrgqr<c10::complex<double>>(int m, int n, int k, c10::complex<double> *a, int lda, c10::complex<double> *tau, c10::complex<double> *work, int lwork, int *info) {
zungqr_(&m, &n, &k, reinterpret_cast<std::complex<double>*>(a), &lda, reinterpret_cast<std::complex<double>*>(tau), reinterpret_cast<std::complex<double>*>(work), &lwork, info);
}
template<> void lapackOrgqr<c10::complex<float>>(int m, int n, int k, c10::complex<float> *a, int lda, c10::complex<float> *tau, c10::complex<float> *work, int lwork, int *info) {
cungqr_(&m, &n, &k, reinterpret_cast<std::complex<float>*>(a), &lda, reinterpret_cast<std::complex<float>*>(tau), reinterpret_cast<std::complex<float>*>(work), &lwork, info);
}
template<> void lapackOrgqr<double>(int m, int n, int k, double *a, int lda, double *tau, double *work, int lwork, int *info) {
dorgqr_(&m, &n, &k, a, &lda, tau, work, &lwork, info);
}
template<> void lapackOrgqr<float>(int m, int n, int k, float *a, int lda, float *tau, float *work, int lwork, int *info) {
sorgqr_(&m, &n, &k, a, &lda, tau, work, &lwork, info);
}
template<> void lapackOrmqr<c10::complex<double>>(char side, char trans, int m, int n, int k, c10::complex<double> *a, int lda, c10::complex<double> *tau, c10::complex<double> *c, int ldc, c10::complex<double> *work, int lwork, int *info) {
zunmqr_(&side, &trans, &m, &n, &k, reinterpret_cast<std::complex<double>*>(a), &lda, reinterpret_cast<std::complex<double>*>(tau), reinterpret_cast<std::complex<double>*>(c), &ldc, reinterpret_cast<std::complex<double>*>(work), &lwork, info);
}
template<> void lapackOrmqr<c10::complex<float>>(char side, char trans, int m, int n, int k, c10::complex<float> *a, int lda, c10::complex<float> *tau, c10::complex<float> *c, int ldc, c10::complex<float> *work, int lwork, int *info) {
cunmqr_(&side, &trans, &m, &n, &k, reinterpret_cast<std::complex<float>*>(a), &lda, reinterpret_cast<std::complex<float>*>(tau), reinterpret_cast<std::complex<float>*>(c), &ldc, reinterpret_cast<std::complex<float>*>(work), &lwork, info);
}
template<> void lapackOrmqr<double>(char side, char trans, int m, int n, int k, double *a, int lda, double *tau, double *c, int ldc, double *work, int lwork, int *info) {
dormqr_(&side, &trans, &m, &n, &k, a, &lda, tau, c, &ldc, work, &lwork, info);
}
template<> void lapackOrmqr<float>(char side, char trans, int m, int n, int k, float *a, int lda, float *tau, float *c, int ldc, float *work, int lwork, int *info) {
sormqr_(&side, &trans, &m, &n, &k, a, &lda, tau, c, &ldc, work, &lwork, info);
}
template<> void lapackSyevd<c10::complex<double>, double>(char jobz, char uplo, int n, c10::complex<double> *a, int lda, double *w, c10::complex<double> *work, int lwork, double *rwork, int lrwork, int *iwork, int liwork, int *info) {
zheevd_(&jobz, &uplo, &n, reinterpret_cast<std::complex<double>*>(a), &lda, w, reinterpret_cast<std::complex<double>*>(work), &lwork, rwork, &lrwork, iwork, &liwork, info);
}
template<> void lapackSyevd<c10::complex<float>, float>(char jobz, char uplo, int n, c10::complex<float> *a, int lda, float *w, c10::complex<float> *work, int lwork, float *rwork, int lrwork, int *iwork, int liwork, int *info) {
cheevd_(&jobz, &uplo, &n, reinterpret_cast<std::complex<float>*>(a), &lda, w, reinterpret_cast<std::complex<float>*>(work), &lwork, rwork, &lrwork, iwork, &liwork, info);
}
template<> void lapackSyevd<double>(char jobz, char uplo, int n, double *a, int lda, double *w, double *work, int lwork, double *rwork, int lrwork, int *iwork, int liwork, int *info) {
(void)rwork; // unused
(void)lrwork; // unused
dsyevd_(&jobz, &uplo, &n, a, &lda, w, work, &lwork, iwork, &liwork, info);
}
template<> void lapackSyevd<float>(char jobz, char uplo, int n, float *a, int lda, float *w, float *work, int lwork, float *rwork, int lrwork, int *iwork, int liwork, int *info) {
(void)rwork; // unused
(void)lrwork; // unused
ssyevd_(&jobz, &uplo, &n, a, &lda, w, work, &lwork, iwork, &liwork, info);
}
template<> void lapackEig<double>(char jobvl, char jobvr, int n, double *a, int lda, double *w, double* vl, int ldvl, double *vr, int ldvr, double *work, int lwork, double *rwork, int *info) {
// lapack [sd]geev wants to separate output arrays: wr and wi for the real
// and imaginary parts
double *wr = w;
double *wi = w ? w + n : nullptr;
(void)rwork; // unused
dgeev_(&jobvl, &jobvr, &n, a, &lda, wr, wi, vl, &ldvl, vr, &ldvr, work, &lwork, info);
}
template<> void lapackEig<float>(char jobvl, char jobvr, int n, float *a, int lda, float *w, float* vl, int ldvl, float *vr, int ldvr, float *work, int lwork, float *rwork, int *info) {
// lapack [sd]geev wants to separate output arrays: wr and wi for the real
// and imaginary parts
float *wr = w;
float *wi = w ? w + n : nullptr;
(void)rwork; // unused
sgeev_(&jobvl, &jobvr, &n, a, &lda, wr, wi, vl, &ldvl, vr, &ldvr, work, &lwork, info);
}
template<> void lapackEig<c10::complex<double>, double>(char jobvl, char jobvr, int n, c10::complex<double> *a, int lda, c10::complex<double> *w, c10::complex<double> *vl, int ldvl, c10::complex<double> *vr, int ldvr, c10::complex<double> *work, int lwork, double *rwork, int *info) {
zgeev_(&jobvl, &jobvr, &n,
reinterpret_cast<std::complex<double>*>(a), &lda,
reinterpret_cast<std::complex<double>*>(w),
reinterpret_cast<std::complex<double>*>(vl), &ldvl,
reinterpret_cast<std::complex<double>*>(vr), &ldvr,
reinterpret_cast<std::complex<double>*>(work), &lwork,
rwork, info);
}
template<> void lapackEig<c10::complex<float>, float>(char jobvl, char jobvr, int n, c10::complex<float> *a, int lda, c10::complex<float> *w, c10::complex<float> *vl, int ldvl, c10::complex<float> *vr, int ldvr, c10::complex<float> *work, int lwork, float *rwork, int *info) {
cgeev_(&jobvl, &jobvr, &n,
reinterpret_cast<std::complex<float>*>(a), &lda,
reinterpret_cast<std::complex<float>*>(w),
reinterpret_cast<std::complex<float>*>(vl), &ldvl,
reinterpret_cast<std::complex<float>*>(vr), &ldvr,
reinterpret_cast<std::complex<float>*>(work), &lwork,
rwork, info);
}
template<> void lapackSvd<c10::complex<double>, double>(char jobz, int m, int n, c10::complex<double> *a, int lda,
double *s, c10::complex<double> *u, int ldu, c10::complex<double> *vt, int ldvt, c10::complex<double> *work, int lwork, double *rwork, int *iwork, int *info) {
zgesdd_(&jobz, &m, &n, reinterpret_cast<std::complex<double>*>(a), &lda, s, reinterpret_cast<std::complex<double>*>(u), &ldu,
reinterpret_cast<std::complex<double>*>(vt), &ldvt, reinterpret_cast<std::complex<double>*>(work), &lwork, rwork, iwork, info);
}
template<> void lapackSvd<c10::complex<float>, float>(char jobz, int m, int n, c10::complex<float> *a, int lda,
float *s, c10::complex<float> *u, int ldu, c10::complex<float> *vt, int ldvt, c10::complex<float> *work, int lwork, float *rwork, int *iwork, int *info) {
cgesdd_(&jobz, &m, &n, reinterpret_cast<std::complex<float>*>(a), &lda, s, reinterpret_cast<std::complex<float>*>(u), &ldu,
reinterpret_cast<std::complex<float>*>(vt), &ldvt, reinterpret_cast<std::complex<float>*>(work), &lwork, rwork, iwork, info);
}
template<> void lapackSvd<double>(char jobz, int m, int n, double *a, int lda,
double *s, double *u, int ldu, double *vt, int ldvt, double *work, int lwork, double *rwork, int *iwork, int *info) {
dgesdd_(&jobz, &m, &n, a, &lda, s, u, &ldu, vt, &ldvt, work, &lwork, iwork, info);
}
template<> void lapackSvd<float>(char jobz, int m, int n, float *a, int lda,
float *s, float *u, int ldu, float *vt, int ldvt, float *work, int lwork, float *rwork, int *iwork, int *info) {
sgesdd_(&jobz, &m, &n, a, &lda, s, u, &ldu, vt, &ldvt, work, &lwork, iwork, info);
}
template <>
void lapackLdlSymmetric<double>(
char uplo,
int n,
double* a,
int lda,
int* ipiv,
double* work,
int lwork,
int* info) {
dsytrf_(&uplo, &n, a, &lda, ipiv, work, &lwork, info);
}
template <>
void lapackLdlSymmetric<float>(
char uplo,
int n,
float* a,
int lda,