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
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
|
SUBROUTINE SGETRFNP( M, N, A, LDA, INFO )
!
! -- LAPACK computational routine (version 3.4.0) --
! -- LAPACK is a software package provided by Univ. of Tennessee, --
! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! November 2011
!
! .. Scalar Arguments ..
INTEGER INFO, LDA, M, N
! ..
! .. Array Arguments ..
REAL*4 A( LDA, * )
! ..
!
! =====================================================================
!
! .. Parameters ..
REAL*4 ONE, ZERO
PARAMETER ( ONE = 1.0+0, ZERO = 0.0+0 )
! ..
! .. Local Scalars ..
REAL*4 SFMIN
INTEGER I, J, JP
! ..
! .. External Functions ..
REAL*4 SLAMCH
INTEGER IDAMAX
EXTERNAL SLAMCH, IDAMAX
! ..
! .. External Subroutines ..
EXTERNAL SGER, SSCAL, SSWAP, XERBLA
! ..
! .. Intrinsic Functions ..
INTRINSIC MAX, MIN
! ..
! .. Executable Statements ..
!
! Test the input parameters.
!
INFO = 0
IF( M.LT.0 ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
INFO = -4
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SGETRFNP', -INFO )
RETURN
END IF
!
! Quick return if possible
!
IF( M.EQ.0 .OR. N.EQ.0 ) RETURN
!
! Compute machine safe minimum
!
SFMIN = SLAMCH('S')
!
DO 10 J = 1, MIN ( M, N )
JP = J
IF( A( JP, J ).NE.ZERO ) THEN
!
! Compute elements J+1:M of J-th column.
!
IF( J.LT.M ) THEN
IF( ABS(A( J, J )) .GE. SFMIN ) THEN
CALL SSCAL( M-J, ONE / A( J, J ), A( J+1, J ), 1 )
ELSE
DO 20 I = 1, M-J
A( J+I, J ) = A( J+I, J ) / A( J, J )
20 CONTINUE
END IF
END IF
!
ELSE IF( INFO.EQ.0 ) THEN
!
INFO = J
END IF
!
IF( J.LT.MIN( M, N ) ) THEN
!
! Update trailing submatrix.
!
CALL SGER( M-J, N-J, -ONE, A( J+1, J ), 1,&
A( J, J+1 ),LDA,A( J+1, J+1 ), LDA )
END IF
10 CONTINUE
RETURN
!
! End of SGETRFNP
!
END
SUBROUTINE SGETRF( M, N, A, LDA, IPIV, INFO )
!
! -- LAPACK computational routine (version 3.4.0) --
! -- LAPACK is a software package provided by Univ. of Tennessee, --
! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! November 2011
!
! .. Scalar Arguments ..
INTEGER INFO, LDA, M, N
! ..
! .. Array Arguments ..
INTEGER IPIV( * )
REAL*4 A( LDA, * )
! ..
!
! =====================================================================
!
! .. Parameters ..
REAL*4 ONE
PARAMETER ( ONE = 1.0E+0 )
! ..
! .. Local Scalars ..
INTEGER I, IINFO, J, JB, NB
! ..
! .. External Subroutines ..
EXTERNAL SGEMM, SGETF2, SLASWP, STRSM, XERBLA
! ..
! .. External Functions ..
INTEGER ILAENV
EXTERNAL ILAENV
! ..
! .. Intrinsic Functions ..
INTRINSIC MAX, MIN
! ..
! .. Executable Statements ..
!
! Test the input parameters.
!
INFO = 0
IF( M.LT.0 ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
INFO = -4
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SGETRF', -INFO )
RETURN
END IF
!
! Quick return if possible
!
IF( M.EQ.0 .OR. N.EQ.0 ) RETURN
!
! Determine the block size for this environment.
!
NB = ILAENV( 1, 'SGETRF', ' ', M, N, -1, -1 )
IF( NB.LE.1 .OR. NB.GE.MIN( M, N ) ) THEN
!
! Use unblocked code.
!
CALL SGETF2( M, N, A, LDA, IPIV, INFO )
ELSE
!
! Use blocked code.
!
DO 20 J = 1, MIN( M, N ), NB
JB = MIN( MIN( M, N )-J+1, NB )
!
! Factor diagonal and subdiagonal blocks and test for exact
! singularity.
!
CALL SGETF2( M-J+1, JB, A( J, J ), LDA, IPIV( J ), IINFO )
!
! Adjust INFO and the pivot indices.
!
IF( INFO.EQ.0 .AND. IINFO.GT.0 ) INFO = IINFO + J - 1
DO 10 I = J, MIN( M, J+JB-1 )
IPIV( I ) = J - 1 + IPIV( I )
10 CONTINUE
!
! Apply interchanges to columns 1:J-1.
!
CALL SLASWP( J-1, A, LDA, J, J+JB-1, IPIV, 1 )
!
IF( J+JB.LE.N ) THEN
!
! Apply interchanges to columns J+JB:N.
!
CALL SLASWP( N-J-JB+1, A( 1, J+JB ), LDA, J, J+JB-1,&
IPIV, 1 )
!
! Compute block row of U.
!
CALL STRSM( 'Left', 'Lower', 'No transpose', 'Unit', JB,&
N-J-JB+1, ONE, A( J, J ), LDA, A( J, J+JB ),&
LDA )
IF( J+JB.LE.M ) THEN
!
! Update trailing submatrix.
!
CALL SGEMM( 'No transpose', 'No transpose', M-J-JB+1,&
N-J-JB+1, JB, -ONE, A( J+JB, J ), LDA,&
A( J, J+JB ), LDA, ONE, A( J+JB, J+JB ),&
LDA )
END IF
END IF
20 CONTINUE
END IF
RETURN
!
! End of SGETRF
!
END
SUBROUTINE SGETF2( M, N, A, LDA, IPIV, INFO )
!
! -- LAPACK computational routine (version 3.4.0) --
! -- LAPACK is a software package provided by Univ. of Tennessee, --
! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! November 2011
!
! .. Scalar Arguments ..
INTEGER INFO, LDA, M, N
! ..
! .. Array Arguments ..
INTEGER IPIV( * )
REAL*4 A( LDA, * )
! ..
!
! =====================================================================
!
! .. Parameters ..
REAL*4 ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
! ..
! .. Local Scalars ..
REAL*4 SFMIN
INTEGER I, J, JP
! ..
! .. External Functions ..
REAL*4 SLAMCH
INTEGER IDAMAX
EXTERNAL SLAMCH, IDAMAX
! ..
! .. External Subroutines ..
EXTERNAL SGER, SSCAL, SSWAP, XERBLA
! ..
! .. Intrinsic Functions ..
INTRINSIC MAX, MIN
! ..
! .. Executable Statements ..
!
! Test the input parameters.
!
INFO = 0
IF( M.LT.0 ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
INFO = -4
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SGETF2', -INFO )
RETURN
END IF
!
! Quick return if possible
!
IF( M.EQ.0 .OR. N.EQ.0 ) RETURN
!
! Compute machine safe minimum
!
SFMIN = SLAMCH('S')
!
DO 10 J = 1, MIN( M, N )
!
! Find pivot and test for singularity.
!
JP = J - 1 + IDAMAX( M-J+1, A( J, J ), 1 )
IPIV( J ) = JP
IF( A( JP, J ).NE.ZERO ) THEN
!
! Apply the interchange to columns 1:N.
!
IF(JP.NE.J) CALL SSWAP( N, A( J, 1 ), LDA, A( JP, 1 ), LDA )
!
! Compute elements J+1:M of J-th column.
!
IF( J.LT.M ) THEN
IF( ABS(A( J, J )) .GE. SFMIN ) THEN
CALL SSCAL( M-J, ONE / A( J, J ), A( J+1, J ), 1 )
ELSE
DO 20 I = 1, M-J
A( J+I, J ) = A( J+I, J ) / A( J, J )
20 CONTINUE
END IF
END IF
!
ELSE IF( INFO.EQ.0 ) THEN
!
INFO = J
END IF
!
IF( J.LT.MIN( M, N ) ) THEN
!
! Update trailing submatrix.
!
CALL SGER( M-J, N-J, -ONE, A( J+1, J ), 1, A( J, J+1 ), &
LDA, A( J+1, J+1 ), LDA )
END IF
10 CONTINUE
RETURN
!
! End of SGETF2
!
END
SUBROUTINE SLASWP( N, A, LDA, K1, K2, IPIV, INCX )
!
! -- LAPACK auxiliary routine (version 3.4.0) --
! -- LAPACK is a software package provided by Univ. of Tennessee, --
! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! November 2011
!
! .. Scalar Arguments ..
INTEGER INCX, K1, K2, LDA, N
! ..
! .. Array Arguments ..
INTEGER IPIV( * )
REAL*4 A( LDA, * )
! ..
!
! =====================================================================
!
! .. Local Scalars ..
INTEGER I, I1, I2, INC, IP, IX, IX0, J, K, N32
REAL*4 TEMP
! ..
! .. Executable Statements ..
!
! Interchange row I with row IPIV(I) for each of rows K1 through K2.
!
IF( INCX.GT.0 ) THEN
IX0 = K1
I1 = K1
I2 = K2
INC = 1
ELSE IF( INCX.LT.0 ) THEN
IX0 = 1 + ( 1-K2 )*INCX
I1 = K2
I2 = K1
INC = -1
ELSE
RETURN
END IF
!
N32 = ( N / 32 )*32
IF( N32.NE.0 ) THEN
DO 30 J = 1, N32, 32
IX = IX0
DO 20 I = I1, I2, INC
IP = IPIV( IX )
IF( IP.NE.I ) THEN
DO 10 K = J, J + 31
TEMP = A( I, K )
A( I, K ) = A( IP, K )
A( IP, K ) = TEMP
10 CONTINUE
END IF
IX = IX + INCX
20 CONTINUE
30 CONTINUE
END IF
IF( N32.NE.N ) THEN
N32 = N32 + 1
IX = IX0
DO 50 I = I1, I2, INC
IP = IPIV( IX )
IF( IP.NE.I ) THEN
DO 40 K = N32, N
TEMP = A( I, K )
A( I, K ) = A( IP, K )
A( IP, K ) = TEMP
40 CONTINUE
END IF
IX = IX + INCX
50 CONTINUE
END IF
!
RETURN
!
! End of SLASWP
!
END
SUBROUTINE STRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
!
! -- Reference BLAS level3 routine (version 3.4.0) --
! -- Reference BLAS is a software package provided by Univ. of Tennessee, --
! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! November 2011
!
! .. Scalar Arguments ..
REAL*4 ALPHA
INTEGER LDA,LDB,M,N
CHARACTER DIAG,SIDE,TRANSA,UPLO
! ..
! .. Array Arguments ..
REAL*4 A(LDA,*),B(LDB,*)
! ..
!
! =====================================================================
!
! .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
! ..
! .. External Subroutines ..
EXTERNAL XERBLA
! ..
! .. Intrinsic Functions ..
INTRINSIC MAX
! ..
! .. Local Scalars ..
REAL*4 TEMP
INTEGER I,INFO,J,K,NROWA
LOGICAL LSIDE,NOUNIT,UPPER
! ..
! .. Parameters ..
REAL*4 ONE,ZERO
PARAMETER (ONE=1.0E+0,ZERO=0.0E+0)
! ..
!
! Test the input parameters.
!
LSIDE = LSAME(SIDE,'L')
IF (LSIDE) THEN
NROWA = M
ELSE
NROWA = N
END IF
NOUNIT = LSAME(DIAG,'N')
UPPER = LSAME(UPLO,'U')
!
INFO = 0
IF ((.NOT.LSIDE) .AND. (.NOT.LSAME(SIDE,'R'))) THEN
INFO = 1
ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
INFO = 2
ELSE IF ((.NOT.LSAME(TRANSA,'N')) .AND. &
(.NOT.LSAME(TRANSA,'T')) .AND. &
(.NOT.LSAME(TRANSA,'C'))) THEN
INFO = 3
ELSE IF ((.NOT.LSAME(DIAG,'U')) .AND. (.NOT.LSAME(DIAG,'N'))) THEN
INFO = 4
ELSE IF (M.LT.0) THEN
INFO = 5
ELSE IF (N.LT.0) THEN
INFO = 6
ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
INFO = 9
ELSE IF (LDB.LT.MAX(1,M)) THEN
INFO = 11
END IF
IF (INFO.NE.0) THEN
CALL XERBLA('STRSM ',INFO)
RETURN
END IF
!
! Quick return if possible.
!
IF (M.EQ.0 .OR. N.EQ.0) RETURN
!
! And when alpha.eq.zero.
!
IF (ALPHA.EQ.ZERO) THEN
DO 20 J = 1,N
DO 10 I = 1,M
B(I,J) = ZERO
10 CONTINUE
20 CONTINUE
RETURN
END IF
!
! Start the operations.
!
IF (LSIDE) THEN
IF (LSAME(TRANSA,'N')) THEN
!
! Form B := alpha*inv( A )*B.
!
IF (UPPER) THEN
DO 60 J = 1,N
IF (ALPHA.NE.ONE) THEN
DO 30 I = 1,M
B(I,J) = ALPHA*B(I,J)
30 CONTINUE
END IF
DO 50 K = M,1,-1
IF (B(K,J).NE.ZERO) THEN
IF (NOUNIT) B(K,J) = B(K,J)/A(K,K)
DO 40 I = 1,K - 1
B(I,J) = B(I,J) - B(K,J)*A(I,K)
40 CONTINUE
END IF
50 CONTINUE
60 CONTINUE
ELSE
DO 100 J = 1,N
IF (ALPHA.NE.ONE) THEN
DO 70 I = 1,M
B(I,J) = ALPHA*B(I,J)
70 CONTINUE
END IF
DO 90 K = 1,M
IF (B(K,J).NE.ZERO) THEN
IF (NOUNIT) B(K,J) = B(K,J)/A(K,K)
DO 80 I = K + 1,M
B(I,J) = B(I,J) - B(K,J)*A(I,K)
80 CONTINUE
END IF
90 CONTINUE
100 CONTINUE
END IF
ELSE
!
! Form B := alpha*inv( A**T )*B.
!
IF (UPPER) THEN
DO 130 J = 1,N
DO 120 I = 1,M
TEMP = ALPHA*B(I,J)
DO 110 K = 1,I - 1
TEMP = TEMP - A(K,I)*B(K,J)
110 CONTINUE
IF (NOUNIT) TEMP = TEMP/A(I,I)
B(I,J) = TEMP
120 CONTINUE
130 CONTINUE
ELSE
DO 160 J = 1,N
DO 150 I = M,1,-1
TEMP = ALPHA*B(I,J)
DO 140 K = I + 1,M
TEMP = TEMP - A(K,I)*B(K,J)
140 CONTINUE
IF (NOUNIT) TEMP = TEMP/A(I,I)
B(I,J) = TEMP
150 CONTINUE
160 CONTINUE
END IF
END IF
ELSE
IF (LSAME(TRANSA,'N')) THEN
!
! Form B := alpha*B*inv( A ).
!
IF (UPPER) THEN
DO 210 J = 1,N
IF (ALPHA.NE.ONE) THEN
DO 170 I = 1,M
B(I,J) = ALPHA*B(I,J)
170 CONTINUE
END IF
DO 190 K = 1,J - 1
IF (A(K,J).NE.ZERO) THEN
DO 180 I = 1,M
B(I,J) = B(I,J) - A(K,J)*B(I,K)
180 CONTINUE
END IF
190 CONTINUE
IF (NOUNIT) THEN
TEMP = ONE/A(J,J)
DO 200 I = 1,M
B(I,J) = TEMP*B(I,J)
200 CONTINUE
END IF
210 CONTINUE
ELSE
DO 260 J = N,1,-1
IF (ALPHA.NE.ONE) THEN
DO 220 I = 1,M
B(I,J) = ALPHA*B(I,J)
220 CONTINUE
END IF
DO 240 K = J + 1,N
IF (A(K,J).NE.ZERO) THEN
DO 230 I = 1,M
B(I,J) = B(I,J) - A(K,J)*B(I,K)
230 CONTINUE
END IF
240 CONTINUE
IF (NOUNIT) THEN
TEMP = ONE/A(J,J)
DO 250 I = 1,M
B(I,J) = TEMP*B(I,J)
250 CONTINUE
END IF
260 CONTINUE
END IF
ELSE
!
! Form B := alpha*B*inv( A**T ).
!
IF (UPPER) THEN
DO 310 K = N,1,-1
IF (NOUNIT) THEN
TEMP = ONE/A(K,K)
DO 270 I = 1,M
B(I,K) = TEMP*B(I,K)
270 CONTINUE
END IF
DO 290 J = 1,K - 1
IF (A(J,K).NE.ZERO) THEN
TEMP = A(J,K)
DO 280 I = 1,M
B(I,J) = B(I,J) - TEMP*B(I,K)
280 CONTINUE
END IF
290 CONTINUE
IF (ALPHA.NE.ONE) THEN
DO 300 I = 1,M
B(I,K) = ALPHA*B(I,K)
300 CONTINUE
END IF
310 CONTINUE
ELSE
DO 360 K = 1,N
IF (NOUNIT) THEN
TEMP = ONE/A(K,K)
DO 320 I = 1,M
B(I,K) = TEMP*B(I,K)
320 CONTINUE
END IF
DO 340 J = K + 1,N
IF (A(J,K).NE.ZERO) THEN
TEMP = A(J,K)
DO 330 I = 1,M
B(I,J) = B(I,J) - TEMP*B(I,K)
330 CONTINUE
END IF
340 CONTINUE
IF (ALPHA.NE.ONE) THEN
DO 350 I = 1,M
B(I,K) = ALPHA*B(I,K)
350 CONTINUE
END IF
360 CONTINUE
END IF
END IF
END IF
!
RETURN
!
! End of STRSM .
!
END
SUBROUTINE SGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
!
! -- Reference BLAS level3 routine (version 3.4.0) --
! -- Reference BLAS is a software package provided by Univ. of Tennessee, --
! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! November 2011
!
! .. Scalar Arguments ..
REAL*4 ALPHA,BETA
INTEGER K,LDA,LDB,LDC,M,N
CHARACTER TRANSA,TRANSB
! ..
! .. Array Arguments ..
REAL*4 A(LDA,*),B(LDB,*),C(LDC,*)
! ..
!
! =====================================================================
!
! .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
! ..
! .. External Subroutines ..
EXTERNAL XERBLA
! ..
! .. Intrinsic Functions ..
INTRINSIC MAX
! ..
! .. Local Scalars ..
REAL*4 TEMP
INTEGER I,INFO,J,L,NCOLA,NROWA,NROWB
LOGICAL NOTA,NOTB
! ..
! .. Parameters ..
REAL*4 ONE,ZERO
PARAMETER (ONE=1.0E+0,ZERO=0.0E+0)
! ..
!
! Set NOTA and NOTB as true if A and B respectively are not
! transposed and set NROWA, NCOLA and NROWB as the number of rows
! and columns of A and the number of rows of B respectively.
!
NOTA = LSAME(TRANSA,'N')
NOTB = LSAME(TRANSB,'N')
IF (NOTA) THEN
NROWA = M
NCOLA = K
ELSE
NROWA = K
NCOLA = M
END IF
IF (NOTB) THEN
NROWB = K
ELSE
NROWB = N
END IF
!
! Test the input parameters.
!
INFO = 0
IF ((.NOT.NOTA) .AND. (.NOT.LSAME(TRANSA,'C')) .AND. &
(.NOT.LSAME(TRANSA,'T'))) THEN
INFO = 1
ELSE IF ((.NOT.NOTB) .AND. (.NOT.LSAME(TRANSB,'C')) .AND. &
(.NOT.LSAME(TRANSB,'T'))) THEN
INFO = 2
ELSE IF (M.LT.0) THEN
INFO = 3
ELSE IF (N.LT.0) THEN
INFO = 4
ELSE IF (K.LT.0) THEN
INFO = 5
ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
INFO = 8
ELSE IF (LDB.LT.MAX(1,NROWB)) THEN
INFO = 10
ELSE IF (LDC.LT.MAX(1,M)) THEN
INFO = 13
END IF
IF (INFO.NE.0) THEN
CALL XERBLA('SGEMM ',INFO)
RETURN
END IF
!
! Quick return if possible.
!
IF ((M.EQ.0) .OR. (N.EQ.0) .OR. &
(((ALPHA.EQ.ZERO).OR. (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN
!
! And if alpha.eq.zero.
!
IF (ALPHA.EQ.ZERO) THEN
IF (BETA.EQ.ZERO) THEN
DO 20 J = 1,N
DO 10 I = 1,M
C(I,J) = ZERO
10 CONTINUE
20 CONTINUE
ELSE
DO 40 J = 1,N
DO 30 I = 1,M
C(I,J) = BETA*C(I,J)
30 CONTINUE
40 CONTINUE
END IF
RETURN
END IF
!
! Start the operations.
!
IF (NOTB) THEN
IF (NOTA) THEN
!
! Form C := alpha*A*B + beta*C.
!
DO 90 J = 1,N
IF (BETA.EQ.ZERO) THEN
DO 50 I = 1,M
C(I,J) = ZERO
50 CONTINUE
ELSE IF (BETA.NE.ONE) THEN
DO 60 I = 1,M
C(I,J) = BETA*C(I,J)
60 CONTINUE
END IF
DO 80 L = 1,K
IF (B(L,J).NE.ZERO) THEN
TEMP = ALPHA*B(L,J)
DO 70 I = 1,M
C(I,J) = C(I,J) + TEMP*A(I,L)
70 CONTINUE
END IF
80 CONTINUE
90 CONTINUE
ELSE
!
! Form C := alpha*A**T*B + beta*C
!
DO 120 J = 1,N
DO 110 I = 1,M
TEMP = ZERO
DO 100 L = 1,K
TEMP = TEMP + A(L,I)*B(L,J)
100 CONTINUE
IF (BETA.EQ.ZERO) THEN
C(I,J) = ALPHA*TEMP
ELSE
C(I,J) = ALPHA*TEMP + BETA*C(I,J)
END IF
110 CONTINUE
120 CONTINUE
END IF
ELSE
IF (NOTA) THEN
!
! Form C := alpha*A*B**T + beta*C
!
DO 170 J = 1,N
IF (BETA.EQ.ZERO) THEN
DO 130 I = 1,M
C(I,J) = ZERO
130 CONTINUE
ELSE IF (BETA.NE.ONE) THEN
DO 140 I = 1,M
C(I,J) = BETA*C(I,J)
140 CONTINUE
END IF
DO 160 L = 1,K
IF (B(J,L).NE.ZERO) THEN
TEMP = ALPHA*B(J,L)
DO 150 I = 1,M
C(I,J) = C(I,J) + TEMP*A(I,L)
150 CONTINUE
END IF
160 CONTINUE
170 CONTINUE
ELSE
!
! Form C := alpha*A**T*B**T + beta*C
!
DO 200 J = 1,N
DO 190 I = 1,M
TEMP = ZERO
DO 180 L = 1,K
TEMP = TEMP + A(L,I)*B(J,L)
180 CONTINUE
IF (BETA.EQ.ZERO) THEN
C(I,J) = ALPHA*TEMP
ELSE
C(I,J) = ALPHA*TEMP + BETA*C(I,J)
END IF
190 CONTINUE
200 CONTINUE
END IF
END IF
!
RETURN
!
! End of SGEMM .
!
END
SUBROUTINE SSWAP(N,SX,INCX,SY,INCY)
!
! -- Reference BLAS level1 routine (version 3.4.0) --
! -- Reference BLAS is a software package provided by Univ. of Tennessee, --
! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! November 2011
!
! .. Scalar Arguments ..
INTEGER INCX,INCY,N
! ..
! .. Array Arguments ..
REAL SX(*),SY(*)
! ..
!
! =====================================================================
!
! .. Local Scalars ..
REAL STEMP
INTEGER I,IX,IY,M,MP1
! ..
! .. Intrinsic Functions ..
INTRINSIC MOD
! ..
IF (N.LE.0) RETURN
IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN
!
! code for both increments equal to 1
!
!
! clean-up loop
!
M = MOD(N,3)
IF (M.NE.0) THEN
DO I = 1,M
STEMP = SX(I)
SX(I) = SY(I)
SY(I) = STEMP
END DO
IF (N.LT.3) RETURN
END IF
MP1 = M + 1
DO I = MP1,N,3
STEMP = SX(I)
SX(I) = SY(I)
SY(I) = STEMP
STEMP = SX(I+1)
SX(I+1) = SY(I+1)
SY(I+1) = STEMP
STEMP = SX(I+2)
SX(I+2) = SY(I+2)
SY(I+2) = STEMP
END DO
ELSE
!
! code for unequal increments or equal increments not equal
! to 1
!
IX = 1
IY = 1
IF (INCX.LT.0) IX = (-N+1)*INCX + 1
IF (INCY.LT.0) IY = (-N+1)*INCY + 1
DO I = 1,N
STEMP = SX(IX)
SX(IX) = SY(IY)
SY(IY) = STEMP
IX = IX + INCX
IY = IY + INCY
END DO
END IF
RETURN
END
SUBROUTINE SSCAL(N,SA,SX,INCX)
!
! -- Reference BLAS level1 routine (version 3.4.0) --
! -- Reference BLAS is a software package provided by Univ. of Tennessee, --
! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! November 2011
!
! .. Scalar Arguments ..
REAL SA
INTEGER INCX,N
! ..
! .. Array Arguments ..
REAL SX(*)
! ..
!
! =====================================================================
!
! .. Local Scalars ..
INTEGER I,M,MP1,NINCX
! ..
! .. Intrinsic Functions ..
INTRINSIC MOD
! ..
IF (N.LE.0 .OR. INCX.LE.0) RETURN
IF (INCX.EQ.1) THEN
!
! code for increment equal to 1
!
!
! clean-up loop
!
M = MOD(N,5)
IF (M.NE.0) THEN
DO I = 1,M
SX(I) = SA*SX(I)
END DO
IF (N.LT.5) RETURN
END IF
MP1 = M + 1
DO I = MP1,N,5
SX(I) = SA*SX(I)
SX(I+1) = SA*SX(I+1)
SX(I+2) = SA*SX(I+2)
SX(I+3) = SA*SX(I+3)
SX(I+4) = SA*SX(I+4)
END DO
ELSE
!
! code for increment not equal to 1
!
NINCX = N*INCX
DO I = 1,NINCX,INCX
SX(I) = SA*SX(I)
END DO
END IF
RETURN
END
SUBROUTINE SGER(M,N,ALPHA,X,INCX,Y,INCY,A,LDA)
!
! -- Reference BLAS level2 routine (version 3.4.0) --
! -- Reference BLAS is a software package provided by Univ. of Tennessee, --
! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! November 2011
!
! .. Scalar Arguments ..
REAL ALPHA
INTEGER INCX,INCY,LDA,M,N
! ..
! .. Array Arguments ..
REAL A(LDA,*),X(*),Y(*)
! ..
!
! =====================================================================
!
! .. Parameters ..
REAL ZERO
PARAMETER (ZERO=0.0E+0)
! ..
! .. Local Scalars ..
REAL TEMP
INTEGER I,INFO,IX,J,JY,KX
! ..
! .. External Subroutines ..
EXTERNAL XERBLA
! ..
! .. Intrinsic Functions ..
INTRINSIC MAX
! ..
!
! Test the input parameters.
!
INFO = 0
IF (M.LT.0) THEN
INFO = 1
ELSE IF (N.LT.0) THEN
INFO = 2
ELSE IF (INCX.EQ.0) THEN
INFO = 5
ELSE IF (INCY.EQ.0) THEN
INFO = 7
ELSE IF (LDA.LT.MAX(1,M)) THEN
INFO = 9
END IF
IF (INFO.NE.0) THEN
CALL XERBLA('SGER ',INFO)
RETURN
END IF
!
! Quick return if possible.
!
IF ((M.EQ.0) .OR. (N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN
!
! Start the operations. In this version the elements of A are
! accessed sequentially with one pass through A.
!
IF (INCY.GT.0) THEN
JY = 1
ELSE
JY = 1 - (N-1)*INCY
END IF
IF (INCX.EQ.1) THEN
DO 20 J = 1,N
IF (Y(JY).NE.ZERO) THEN
TEMP = ALPHA*Y(JY)
DO 10 I = 1,M
A(I,J) = A(I,J) + X(I)*TEMP
10 CONTINUE
END IF
JY = JY + INCY
20 CONTINUE
ELSE
IF (INCX.GT.0) THEN
KX = 1
ELSE
KX = 1 - (M-1)*INCX
END IF
DO 40 J = 1,N
IF (Y(JY).NE.ZERO) THEN
TEMP = ALPHA*Y(JY)
IX = KX
DO 30 I = 1,M
A(I,J) = A(I,J) + X(IX)*TEMP
IX = IX + INCX
30 CONTINUE
END IF
JY = JY + INCY
40 CONTINUE
END IF
!
RETURN
!
! End of SGER .
!
END
INTEGER FUNCTION ISAMAX(N,SX,INCX)
!
! -- Reference BLAS level1 routine (version 3.4.0) --
! -- Reference BLAS is a software package provided by Univ. of Tennessee, --
! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! November 2011
!
! .. Scalar Arguments ..
INTEGER INCX,N
! ..
! .. Array Arguments ..
REAL SX(*)
! ..
!
! =====================================================================
!
! .. Local Scalars ..
REAL SMAX
INTEGER I,IX
! ..
! .. Intrinsic Functions ..
INTRINSIC ABS
! ..
ISAMAX = 0
IF (N.LT.1 .OR. INCX.LE.0) RETURN
ISAMAX = 1
IF (N.EQ.1) RETURN
IF (INCX.EQ.1) THEN
!
! code for increment equal to 1
!
SMAX = ABS(SX(1))
DO I = 2,N
IF (ABS(SX(I)).GT.SMAX) THEN
ISAMAX = I
SMAX = ABS(SX(I))
END IF
END DO
ELSE
!
! code for increment not equal to 1
!
IX = 1
SMAX = ABS(SX(1))
IX = IX + INCX
DO I = 2,N
IF (ABS(SX(IX)).GT.SMAX) THEN
ISAMAX = I
SMAX = ABS(SX(IX))
END IF
IX = IX + INCX
END DO
END IF
RETURN
END
REAL FUNCTION SLAMCH( CMACH )
!
! -- LAPACK auxiliary routine (version 3.4.0) --
! -- LAPACK is a software package provided by Univ. of Tennessee, --
! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! November 2011
!
! .. Scalar Arguments ..
CHARACTER CMACH
! ..
!
! =====================================================================
!
! .. Parameters ..
REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
! ..
! .. Local Scalars ..
REAL RND, EPS, SFMIN, SMALL, RMACH
! ..
! .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
! ..
! .. Intrinsic Functions ..
INTRINSIC DIGITS, EPSILON, HUGE, MAXEXPONENT
INTRINSIC MINEXPONENT, RADIX, TINY
! ..
! .. Executable Statements ..
!
!
! Assume rounding, not chopping. Always.
!
RND = ONE
!
IF( ONE.EQ.RND ) THEN
EPS = EPSILON(ZERO) * 0.5
ELSE
EPS = EPSILON(ZERO)
END IF
!
IF( LSAME( CMACH, 'E' ) ) THEN
RMACH = EPS
ELSE IF( LSAME( CMACH, 'S' ) ) THEN
SFMIN = TINY(ZERO)
SMALL = ONE / HUGE(ZERO)
IF( SMALL.GE.SFMIN ) THEN
!
! Use SMALL plus a bit, to avoid the possibility of rounding
! causing overflow when computing 1/sfmin.
!
SFMIN = SMALL*( ONE+EPS )
END IF
RMACH = SFMIN
ELSE IF( LSAME( CMACH, 'B' ) ) THEN
RMACH = RADIX(ZERO)
ELSE IF( LSAME( CMACH, 'P' ) ) THEN
RMACH = EPS * RADIX(ZERO)
ELSE IF( LSAME( CMACH, 'N' ) ) THEN
RMACH = DIGITS(ZERO)
ELSE IF( LSAME( CMACH, 'R' ) ) THEN
RMACH = RND
ELSE IF( LSAME( CMACH, 'M' ) ) THEN
RMACH = MINEXPONENT(ZERO)
ELSE IF( LSAME( CMACH, 'U' ) ) THEN
RMACH = tiny(zero)
ELSE IF( LSAME( CMACH, 'L' ) ) THEN
RMACH = MAXEXPONENT(ZERO)
ELSE IF( LSAME( CMACH, 'O' ) ) THEN
RMACH = HUGE(ZERO)
ELSE
RMACH = ZERO
END IF
!
SLAMCH = RMACH
RETURN
!
! End of SLAMCH
!
END
REAL FUNCTION SLAMC3( A, B )
!
! -- LAPACK auxiliary routine (version 3.4.0) --
! Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
! November 2010
!
! .. Scalar Arguments ..
REAL A, B
! ..
! =====================================================================
!
! .. Executable Statements ..
!
SLAMC3 = A + B
!
RETURN
!
! End of SLAMC3
!
END
|
