LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ ctfsm()

 subroutine ctfsm ( character transr, character side, character uplo, character trans, character diag, integer m, integer n, complex alpha, complex, dimension( 0: * ) a, complex, dimension( 0: ldb-1, 0: * ) b, integer ldb )

CTFSM solves a matrix equation (one operand is a triangular matrix in RFP format).

Download CTFSM + dependencies [TGZ] [ZIP] [TXT]

Purpose:
``` Level 3 BLAS like routine for A in RFP Format.

CTFSM solves the matrix equation

op( A )*X = alpha*B  or  X*op( A ) = alpha*B

where alpha is a scalar, X and B are m by n matrices, A is a unit, or
non-unit,  upper or lower triangular matrix  and  op( A )  is one  of

op( A ) = A   or   op( A ) = A**H.

A is in Rectangular Full Packed (RFP) Format.

The matrix X is overwritten on B.```
Parameters
 [in] TRANSR ``` TRANSR is CHARACTER*1 = 'N': The Normal Form of RFP A is stored; = 'C': The Conjugate-transpose Form of RFP A is stored.``` [in] SIDE ``` SIDE is CHARACTER*1 On entry, SIDE specifies whether op( A ) appears on the left or right of X as follows: SIDE = 'L' or 'l' op( A )*X = alpha*B. SIDE = 'R' or 'r' X*op( A ) = alpha*B. Unchanged on exit.``` [in] UPLO ``` UPLO is CHARACTER*1 On entry, UPLO specifies whether the RFP matrix A came from an upper or lower triangular matrix as follows: UPLO = 'U' or 'u' RFP A came from an upper triangular matrix UPLO = 'L' or 'l' RFP A came from a lower triangular matrix Unchanged on exit.``` [in] TRANS ``` TRANS is CHARACTER*1 On entry, TRANS specifies the form of op( A ) to be used in the matrix multiplication as follows: TRANS = 'N' or 'n' op( A ) = A. TRANS = 'C' or 'c' op( A ) = conjg( A' ). Unchanged on exit.``` [in] DIAG ``` DIAG is CHARACTER*1 On entry, DIAG specifies whether or not RFP A is unit triangular as follows: DIAG = 'U' or 'u' A is assumed to be unit triangular. DIAG = 'N' or 'n' A is not assumed to be unit triangular. Unchanged on exit.``` [in] M ``` M is INTEGER On entry, M specifies the number of rows of B. M must be at least zero. Unchanged on exit.``` [in] N ``` N is INTEGER On entry, N specifies the number of columns of B. N must be at least zero. Unchanged on exit.``` [in] ALPHA ``` ALPHA is COMPLEX On entry, ALPHA specifies the scalar alpha. When alpha is zero then A is not referenced and B need not be set before entry. Unchanged on exit.``` [in] A ``` A is COMPLEX array, dimension (N*(N+1)/2) NT = N*(N+1)/2. On entry, the matrix A in RFP Format. RFP Format is described by TRANSR, UPLO and N as follows: If TRANSR='N' then RFP A is (0:N,0:K-1) when N is even; K=N/2. RFP A is (0:N-1,0:K) when N is odd; K=N/2. If TRANSR = 'C' then RFP is the Conjugate-transpose of RFP A as defined when TRANSR = 'N'. The contents of RFP A are defined by UPLO as follows: If UPLO = 'U' the RFP A contains the NT elements of upper packed A either in normal or conjugate-transpose Format. If UPLO = 'L' the RFP A contains the NT elements of lower packed A either in normal or conjugate-transpose Format. The LDA of RFP A is (N+1)/2 when TRANSR = 'C'. When TRANSR is 'N' the LDA is N+1 when N is even and is N when is odd. See the Note below for more details. Unchanged on exit.``` [in,out] B ``` B is COMPLEX array, dimension (LDB,N) Before entry, the leading m by n part of the array B must contain the right-hand side matrix B, and on exit is overwritten by the solution matrix X.``` [in] LDB ``` LDB is INTEGER On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. LDB must be at least max( 1, m ). Unchanged on exit.```
Further Details:
```  We first consider Standard Packed Format when N is even.
We give an example where N = 6.

AP is Upper             AP is Lower

00 01 02 03 04 05       00
11 12 13 14 15       10 11
22 23 24 25       20 21 22
33 34 35       30 31 32 33
44 45       40 41 42 43 44
55       50 51 52 53 54 55

Let TRANSR = 'N'. RFP holds AP as follows:
For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
three columns of AP upper. The lower triangle A(4:6,0:2) consists of
conjugate-transpose of the first three columns of AP upper.
For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
three columns of AP lower. The upper triangle A(0:2,0:2) consists of
conjugate-transpose of the last three columns of AP lower.
To denote conjugate we place -- above the element. This covers the
case N even and TRANSR = 'N'.

RFP A                   RFP A

-- -- --
03 04 05                33 43 53
-- --
13 14 15                00 44 54
--
23 24 25                10 11 55

33 34 35                20 21 22
--
00 44 45                30 31 32
-- --
01 11 55                40 41 42
-- -- --
02 12 22                50 51 52

Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
transpose of RFP A above. One therefore gets:

RFP A                   RFP A

-- -- -- --                -- -- -- -- -- --
03 13 23 33 00 01 02    33 00 10 20 30 40 50
-- -- -- -- --                -- -- -- -- --
04 14 24 34 44 11 12    43 44 11 21 31 41 51
-- -- -- -- -- --                -- -- -- --
05 15 25 35 45 55 22    53 54 55 22 32 42 52

We next  consider Standard Packed Format when N is odd.
We give an example where N = 5.

AP is Upper                 AP is Lower

00 01 02 03 04              00
11 12 13 14              10 11
22 23 24              20 21 22
33 34              30 31 32 33
44              40 41 42 43 44

Let TRANSR = 'N'. RFP holds AP as follows:
For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
three columns of AP upper. The lower triangle A(3:4,0:1) consists of
conjugate-transpose of the first two   columns of AP upper.
For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
three columns of AP lower. The upper triangle A(0:1,1:2) consists of
conjugate-transpose of the last two   columns of AP lower.
To denote conjugate we place -- above the element. This covers the
case N odd  and TRANSR = 'N'.

RFP A                   RFP A

-- --
02 03 04                00 33 43
--
12 13 14                10 11 44

22 23 24                20 21 22
--
00 33 34                30 31 32
-- --
01 11 44                40 41 42

Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
transpose of RFP A above. One therefore gets:

RFP A                   RFP A

-- -- --                   -- -- -- -- -- --
02 12 22 00 01             00 10 20 30 40 50
-- -- -- --                   -- -- -- -- --
03 13 23 33 11             33 11 21 31 41 51
-- -- -- -- --                   -- -- -- --
04 14 24 34 44             43 44 22 32 42 52```

Definition at line 296 of file ctfsm.f.

298*
299* -- LAPACK computational routine --
300* -- LAPACK is a software package provided by Univ. of Tennessee, --
301* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
302*
303* .. Scalar Arguments ..
304 CHARACTER TRANSR, DIAG, SIDE, TRANS, UPLO
305 INTEGER LDB, M, N
306 COMPLEX ALPHA
307* ..
308* .. Array Arguments ..
309 COMPLEX A( 0: * ), B( 0: LDB-1, 0: * )
310* ..
311*
312* =====================================================================
313* ..
314* .. Parameters ..
315 COMPLEX CONE, CZERO
316 parameter( cone = ( 1.0e+0, 0.0e+0 ),
317 \$ czero = ( 0.0e+0, 0.0e+0 ) )
318* ..
319* .. Local Scalars ..
320 LOGICAL LOWER, LSIDE, MISODD, NISODD, NORMALTRANSR,
321 \$ NOTRANS
322 INTEGER M1, M2, N1, N2, K, INFO, I, J
323* ..
324* .. External Functions ..
325 LOGICAL LSAME
326 EXTERNAL lsame
327* ..
328* .. External Subroutines ..
329 EXTERNAL xerbla, cgemm, ctrsm
330* ..
331* .. Intrinsic Functions ..
332 INTRINSIC max, mod
333* ..
334* .. Executable Statements ..
335*
336* Test the input parameters.
337*
338 info = 0
339 normaltransr = lsame( transr, 'N' )
340 lside = lsame( side, 'L' )
341 lower = lsame( uplo, 'L' )
342 notrans = lsame( trans, 'N' )
343 IF( .NOT.normaltransr .AND. .NOT.lsame( transr, 'C' ) ) THEN
344 info = -1
345 ELSE IF( .NOT.lside .AND. .NOT.lsame( side, 'R' ) ) THEN
346 info = -2
347 ELSE IF( .NOT.lower .AND. .NOT.lsame( uplo, 'U' ) ) THEN
348 info = -3
349 ELSE IF( .NOT.notrans .AND. .NOT.lsame( trans, 'C' ) ) THEN
350 info = -4
351 ELSE IF( .NOT.lsame( diag, 'N' ) .AND. .NOT.lsame( diag, 'U' ) )
352 \$ THEN
353 info = -5
354 ELSE IF( m.LT.0 ) THEN
355 info = -6
356 ELSE IF( n.LT.0 ) THEN
357 info = -7
358 ELSE IF( ldb.LT.max( 1, m ) ) THEN
359 info = -11
360 END IF
361 IF( info.NE.0 ) THEN
362 CALL xerbla( 'CTFSM ', -info )
363 RETURN
364 END IF
365*
366* Quick return when ( (N.EQ.0).OR.(M.EQ.0) )
367*
368 IF( ( m.EQ.0 ) .OR. ( n.EQ.0 ) )
369 \$ RETURN
370*
371* Quick return when ALPHA.EQ.(0E+0,0E+0)
372*
373 IF( alpha.EQ.czero ) THEN
374 DO 20 j = 0, n - 1
375 DO 10 i = 0, m - 1
376 b( i, j ) = czero
377 10 CONTINUE
378 20 CONTINUE
379 RETURN
380 END IF
381*
382 IF( lside ) THEN
383*
384* SIDE = 'L'
385*
386* A is M-by-M.
387* If M is odd, set NISODD = .TRUE., and M1 and M2.
388* If M is even, NISODD = .FALSE., and M.
389*
390 IF( mod( m, 2 ).EQ.0 ) THEN
391 misodd = .false.
392 k = m / 2
393 ELSE
394 misodd = .true.
395 IF( lower ) THEN
396 m2 = m / 2
397 m1 = m - m2
398 ELSE
399 m1 = m / 2
400 m2 = m - m1
401 END IF
402 END IF
403*
404 IF( misodd ) THEN
405*
406* SIDE = 'L' and N is odd
407*
408 IF( normaltransr ) THEN
409*
410* SIDE = 'L', N is odd, and TRANSR = 'N'
411*
412 IF( lower ) THEN
413*
414* SIDE ='L', N is odd, TRANSR = 'N', and UPLO = 'L'
415*
416 IF( notrans ) THEN
417*
418* SIDE ='L', N is odd, TRANSR = 'N', UPLO = 'L', and
419* TRANS = 'N'
420*
421 IF( m.EQ.1 ) THEN
422 CALL ctrsm( 'L', 'L', 'N', diag, m1, n, alpha,
423 \$ a, m, b, ldb )
424 ELSE
425 CALL ctrsm( 'L', 'L', 'N', diag, m1, n, alpha,
426 \$ a( 0 ), m, b, ldb )
427 CALL cgemm( 'N', 'N', m2, n, m1, -cone, a( m1 ),
428 \$ m, b, ldb, alpha, b( m1, 0 ), ldb )
429 CALL ctrsm( 'L', 'U', 'C', diag, m2, n, cone,
430 \$ a( m ), m, b( m1, 0 ), ldb )
431 END IF
432*
433 ELSE
434*
435* SIDE ='L', N is odd, TRANSR = 'N', UPLO = 'L', and
436* TRANS = 'C'
437*
438 IF( m.EQ.1 ) THEN
439 CALL ctrsm( 'L', 'L', 'C', diag, m1, n, alpha,
440 \$ a( 0 ), m, b, ldb )
441 ELSE
442 CALL ctrsm( 'L', 'U', 'N', diag, m2, n, alpha,
443 \$ a( m ), m, b( m1, 0 ), ldb )
444 CALL cgemm( 'C', 'N', m1, n, m2, -cone, a( m1 ),
445 \$ m, b( m1, 0 ), ldb, alpha, b, ldb )
446 CALL ctrsm( 'L', 'L', 'C', diag, m1, n, cone,
447 \$ a( 0 ), m, b, ldb )
448 END IF
449*
450 END IF
451*
452 ELSE
453*
454* SIDE ='L', N is odd, TRANSR = 'N', and UPLO = 'U'
455*
456 IF( .NOT.notrans ) THEN
457*
458* SIDE ='L', N is odd, TRANSR = 'N', UPLO = 'U', and
459* TRANS = 'N'
460*
461 CALL ctrsm( 'L', 'L', 'N', diag, m1, n, alpha,
462 \$ a( m2 ), m, b, ldb )
463 CALL cgemm( 'C', 'N', m2, n, m1, -cone, a( 0 ), m,
464 \$ b, ldb, alpha, b( m1, 0 ), ldb )
465 CALL ctrsm( 'L', 'U', 'C', diag, m2, n, cone,
466 \$ a( m1 ), m, b( m1, 0 ), ldb )
467*
468 ELSE
469*
470* SIDE ='L', N is odd, TRANSR = 'N', UPLO = 'U', and
471* TRANS = 'C'
472*
473 CALL ctrsm( 'L', 'U', 'N', diag, m2, n, alpha,
474 \$ a( m1 ), m, b( m1, 0 ), ldb )
475 CALL cgemm( 'N', 'N', m1, n, m2, -cone, a( 0 ), m,
476 \$ b( m1, 0 ), ldb, alpha, b, ldb )
477 CALL ctrsm( 'L', 'L', 'C', diag, m1, n, cone,
478 \$ a( m2 ), m, b, ldb )
479*
480 END IF
481*
482 END IF
483*
484 ELSE
485*
486* SIDE = 'L', N is odd, and TRANSR = 'C'
487*
488 IF( lower ) THEN
489*
490* SIDE ='L', N is odd, TRANSR = 'C', and UPLO = 'L'
491*
492 IF( notrans ) THEN
493*
494* SIDE ='L', N is odd, TRANSR = 'C', UPLO = 'L', and
495* TRANS = 'N'
496*
497 IF( m.EQ.1 ) THEN
498 CALL ctrsm( 'L', 'U', 'C', diag, m1, n, alpha,
499 \$ a( 0 ), m1, b, ldb )
500 ELSE
501 CALL ctrsm( 'L', 'U', 'C', diag, m1, n, alpha,
502 \$ a( 0 ), m1, b, ldb )
503 CALL cgemm( 'C', 'N', m2, n, m1, -cone,
504 \$ a( m1*m1 ), m1, b, ldb, alpha,
505 \$ b( m1, 0 ), ldb )
506 CALL ctrsm( 'L', 'L', 'N', diag, m2, n, cone,
507 \$ a( 1 ), m1, b( m1, 0 ), ldb )
508 END IF
509*
510 ELSE
511*
512* SIDE ='L', N is odd, TRANSR = 'C', UPLO = 'L', and
513* TRANS = 'C'
514*
515 IF( m.EQ.1 ) THEN
516 CALL ctrsm( 'L', 'U', 'N', diag, m1, n, alpha,
517 \$ a( 0 ), m1, b, ldb )
518 ELSE
519 CALL ctrsm( 'L', 'L', 'C', diag, m2, n, alpha,
520 \$ a( 1 ), m1, b( m1, 0 ), ldb )
521 CALL cgemm( 'N', 'N', m1, n, m2, -cone,
522 \$ a( m1*m1 ), m1, b( m1, 0 ), ldb,
523 \$ alpha, b, ldb )
524 CALL ctrsm( 'L', 'U', 'N', diag, m1, n, cone,
525 \$ a( 0 ), m1, b, ldb )
526 END IF
527*
528 END IF
529*
530 ELSE
531*
532* SIDE ='L', N is odd, TRANSR = 'C', and UPLO = 'U'
533*
534 IF( .NOT.notrans ) THEN
535*
536* SIDE ='L', N is odd, TRANSR = 'C', UPLO = 'U', and
537* TRANS = 'N'
538*
539 CALL ctrsm( 'L', 'U', 'C', diag, m1, n, alpha,
540 \$ a( m2*m2 ), m2, b, ldb )
541 CALL cgemm( 'N', 'N', m2, n, m1, -cone, a( 0 ), m2,
542 \$ b, ldb, alpha, b( m1, 0 ), ldb )
543 CALL ctrsm( 'L', 'L', 'N', diag, m2, n, cone,
544 \$ a( m1*m2 ), m2, b( m1, 0 ), ldb )
545*
546 ELSE
547*
548* SIDE ='L', N is odd, TRANSR = 'C', UPLO = 'U', and
549* TRANS = 'C'
550*
551 CALL ctrsm( 'L', 'L', 'C', diag, m2, n, alpha,
552 \$ a( m1*m2 ), m2, b( m1, 0 ), ldb )
553 CALL cgemm( 'C', 'N', m1, n, m2, -cone, a( 0 ), m2,
554 \$ b( m1, 0 ), ldb, alpha, b, ldb )
555 CALL ctrsm( 'L', 'U', 'N', diag, m1, n, cone,
556 \$ a( m2*m2 ), m2, b, ldb )
557*
558 END IF
559*
560 END IF
561*
562 END IF
563*
564 ELSE
565*
566* SIDE = 'L' and N is even
567*
568 IF( normaltransr ) THEN
569*
570* SIDE = 'L', N is even, and TRANSR = 'N'
571*
572 IF( lower ) THEN
573*
574* SIDE ='L', N is even, TRANSR = 'N', and UPLO = 'L'
575*
576 IF( notrans ) THEN
577*
578* SIDE ='L', N is even, TRANSR = 'N', UPLO = 'L',
579* and TRANS = 'N'
580*
581 CALL ctrsm( 'L', 'L', 'N', diag, k, n, alpha,
582 \$ a( 1 ), m+1, b, ldb )
583 CALL cgemm( 'N', 'N', k, n, k, -cone, a( k+1 ),
584 \$ m+1, b, ldb, alpha, b( k, 0 ), ldb )
585 CALL ctrsm( 'L', 'U', 'C', diag, k, n, cone,
586 \$ a( 0 ), m+1, b( k, 0 ), ldb )
587*
588 ELSE
589*
590* SIDE ='L', N is even, TRANSR = 'N', UPLO = 'L',
591* and TRANS = 'C'
592*
593 CALL ctrsm( 'L', 'U', 'N', diag, k, n, alpha,
594 \$ a( 0 ), m+1, b( k, 0 ), ldb )
595 CALL cgemm( 'C', 'N', k, n, k, -cone, a( k+1 ),
596 \$ m+1, b( k, 0 ), ldb, alpha, b, ldb )
597 CALL ctrsm( 'L', 'L', 'C', diag, k, n, cone,
598 \$ a( 1 ), m+1, b, ldb )
599*
600 END IF
601*
602 ELSE
603*
604* SIDE ='L', N is even, TRANSR = 'N', and UPLO = 'U'
605*
606 IF( .NOT.notrans ) THEN
607*
608* SIDE ='L', N is even, TRANSR = 'N', UPLO = 'U',
609* and TRANS = 'N'
610*
611 CALL ctrsm( 'L', 'L', 'N', diag, k, n, alpha,
612 \$ a( k+1 ), m+1, b, ldb )
613 CALL cgemm( 'C', 'N', k, n, k, -cone, a( 0 ), m+1,
614 \$ b, ldb, alpha, b( k, 0 ), ldb )
615 CALL ctrsm( 'L', 'U', 'C', diag, k, n, cone,
616 \$ a( k ), m+1, b( k, 0 ), ldb )
617*
618 ELSE
619*
620* SIDE ='L', N is even, TRANSR = 'N', UPLO = 'U',
621* and TRANS = 'C'
622 CALL ctrsm( 'L', 'U', 'N', diag, k, n, alpha,
623 \$ a( k ), m+1, b( k, 0 ), ldb )
624 CALL cgemm( 'N', 'N', k, n, k, -cone, a( 0 ), m+1,
625 \$ b( k, 0 ), ldb, alpha, b, ldb )
626 CALL ctrsm( 'L', 'L', 'C', diag, k, n, cone,
627 \$ a( k+1 ), m+1, b, ldb )
628*
629 END IF
630*
631 END IF
632*
633 ELSE
634*
635* SIDE = 'L', N is even, and TRANSR = 'C'
636*
637 IF( lower ) THEN
638*
639* SIDE ='L', N is even, TRANSR = 'C', and UPLO = 'L'
640*
641 IF( notrans ) THEN
642*
643* SIDE ='L', N is even, TRANSR = 'C', UPLO = 'L',
644* and TRANS = 'N'
645*
646 CALL ctrsm( 'L', 'U', 'C', diag, k, n, alpha,
647 \$ a( k ), k, b, ldb )
648 CALL cgemm( 'C', 'N', k, n, k, -cone,
649 \$ a( k*( k+1 ) ), k, b, ldb, alpha,
650 \$ b( k, 0 ), ldb )
651 CALL ctrsm( 'L', 'L', 'N', diag, k, n, cone,
652 \$ a( 0 ), k, b( k, 0 ), ldb )
653*
654 ELSE
655*
656* SIDE ='L', N is even, TRANSR = 'C', UPLO = 'L',
657* and TRANS = 'C'
658*
659 CALL ctrsm( 'L', 'L', 'C', diag, k, n, alpha,
660 \$ a( 0 ), k, b( k, 0 ), ldb )
661 CALL cgemm( 'N', 'N', k, n, k, -cone,
662 \$ a( k*( k+1 ) ), k, b( k, 0 ), ldb,
663 \$ alpha, b, ldb )
664 CALL ctrsm( 'L', 'U', 'N', diag, k, n, cone,
665 \$ a( k ), k, b, ldb )
666*
667 END IF
668*
669 ELSE
670*
671* SIDE ='L', N is even, TRANSR = 'C', and UPLO = 'U'
672*
673 IF( .NOT.notrans ) THEN
674*
675* SIDE ='L', N is even, TRANSR = 'C', UPLO = 'U',
676* and TRANS = 'N'
677*
678 CALL ctrsm( 'L', 'U', 'C', diag, k, n, alpha,
679 \$ a( k*( k+1 ) ), k, b, ldb )
680 CALL cgemm( 'N', 'N', k, n, k, -cone, a( 0 ), k, b,
681 \$ ldb, alpha, b( k, 0 ), ldb )
682 CALL ctrsm( 'L', 'L', 'N', diag, k, n, cone,
683 \$ a( k*k ), k, b( k, 0 ), ldb )
684*
685 ELSE
686*
687* SIDE ='L', N is even, TRANSR = 'C', UPLO = 'U',
688* and TRANS = 'C'
689*
690 CALL ctrsm( 'L', 'L', 'C', diag, k, n, alpha,
691 \$ a( k*k ), k, b( k, 0 ), ldb )
692 CALL cgemm( 'C', 'N', k, n, k, -cone, a( 0 ), k,
693 \$ b( k, 0 ), ldb, alpha, b, ldb )
694 CALL ctrsm( 'L', 'U', 'N', diag, k, n, cone,
695 \$ a( k*( k+1 ) ), k, b, ldb )
696*
697 END IF
698*
699 END IF
700*
701 END IF
702*
703 END IF
704*
705 ELSE
706*
707* SIDE = 'R'
708*
709* A is N-by-N.
710* If N is odd, set NISODD = .TRUE., and N1 and N2.
711* If N is even, NISODD = .FALSE., and K.
712*
713 IF( mod( n, 2 ).EQ.0 ) THEN
714 nisodd = .false.
715 k = n / 2
716 ELSE
717 nisodd = .true.
718 IF( lower ) THEN
719 n2 = n / 2
720 n1 = n - n2
721 ELSE
722 n1 = n / 2
723 n2 = n - n1
724 END IF
725 END IF
726*
727 IF( nisodd ) THEN
728*
729* SIDE = 'R' and N is odd
730*
731 IF( normaltransr ) THEN
732*
733* SIDE = 'R', N is odd, and TRANSR = 'N'
734*
735 IF( lower ) THEN
736*
737* SIDE ='R', N is odd, TRANSR = 'N', and UPLO = 'L'
738*
739 IF( notrans ) THEN
740*
741* SIDE ='R', N is odd, TRANSR = 'N', UPLO = 'L', and
742* TRANS = 'N'
743*
744 CALL ctrsm( 'R', 'U', 'C', diag, m, n2, alpha,
745 \$ a( n ), n, b( 0, n1 ), ldb )
746 CALL cgemm( 'N', 'N', m, n1, n2, -cone, b( 0, n1 ),
747 \$ ldb, a( n1 ), n, alpha, b( 0, 0 ),
748 \$ ldb )
749 CALL ctrsm( 'R', 'L', 'N', diag, m, n1, cone,
750 \$ a( 0 ), n, b( 0, 0 ), ldb )
751*
752 ELSE
753*
754* SIDE ='R', N is odd, TRANSR = 'N', UPLO = 'L', and
755* TRANS = 'C'
756*
757 CALL ctrsm( 'R', 'L', 'C', diag, m, n1, alpha,
758 \$ a( 0 ), n, b( 0, 0 ), ldb )
759 CALL cgemm( 'N', 'C', m, n2, n1, -cone, b( 0, 0 ),
760 \$ ldb, a( n1 ), n, alpha, b( 0, n1 ),
761 \$ ldb )
762 CALL ctrsm( 'R', 'U', 'N', diag, m, n2, cone,
763 \$ a( n ), n, b( 0, n1 ), ldb )
764*
765 END IF
766*
767 ELSE
768*
769* SIDE ='R', N is odd, TRANSR = 'N', and UPLO = 'U'
770*
771 IF( notrans ) THEN
772*
773* SIDE ='R', N is odd, TRANSR = 'N', UPLO = 'U', and
774* TRANS = 'N'
775*
776 CALL ctrsm( 'R', 'L', 'C', diag, m, n1, alpha,
777 \$ a( n2 ), n, b( 0, 0 ), ldb )
778 CALL cgemm( 'N', 'N', m, n2, n1, -cone, b( 0, 0 ),
779 \$ ldb, a( 0 ), n, alpha, b( 0, n1 ),
780 \$ ldb )
781 CALL ctrsm( 'R', 'U', 'N', diag, m, n2, cone,
782 \$ a( n1 ), n, b( 0, n1 ), ldb )
783*
784 ELSE
785*
786* SIDE ='R', N is odd, TRANSR = 'N', UPLO = 'U', and
787* TRANS = 'C'
788*
789 CALL ctrsm( 'R', 'U', 'C', diag, m, n2, alpha,
790 \$ a( n1 ), n, b( 0, n1 ), ldb )
791 CALL cgemm( 'N', 'C', m, n1, n2, -cone, b( 0, n1 ),
792 \$ ldb, a( 0 ), n, alpha, b( 0, 0 ), ldb )
793 CALL ctrsm( 'R', 'L', 'N', diag, m, n1, cone,
794 \$ a( n2 ), n, b( 0, 0 ), ldb )
795*
796 END IF
797*
798 END IF
799*
800 ELSE
801*
802* SIDE = 'R', N is odd, and TRANSR = 'C'
803*
804 IF( lower ) THEN
805*
806* SIDE ='R', N is odd, TRANSR = 'C', and UPLO = 'L'
807*
808 IF( notrans ) THEN
809*
810* SIDE ='R', N is odd, TRANSR = 'C', UPLO = 'L', and
811* TRANS = 'N'
812*
813 CALL ctrsm( 'R', 'L', 'N', diag, m, n2, alpha,
814 \$ a( 1 ), n1, b( 0, n1 ), ldb )
815 CALL cgemm( 'N', 'C', m, n1, n2, -cone, b( 0, n1 ),
816 \$ ldb, a( n1*n1 ), n1, alpha, b( 0, 0 ),
817 \$ ldb )
818 CALL ctrsm( 'R', 'U', 'C', diag, m, n1, cone,
819 \$ a( 0 ), n1, b( 0, 0 ), ldb )
820*
821 ELSE
822*
823* SIDE ='R', N is odd, TRANSR = 'C', UPLO = 'L', and
824* TRANS = 'C'
825*
826 CALL ctrsm( 'R', 'U', 'N', diag, m, n1, alpha,
827 \$ a( 0 ), n1, b( 0, 0 ), ldb )
828 CALL cgemm( 'N', 'N', m, n2, n1, -cone, b( 0, 0 ),
829 \$ ldb, a( n1*n1 ), n1, alpha, b( 0, n1 ),
830 \$ ldb )
831 CALL ctrsm( 'R', 'L', 'C', diag, m, n2, cone,
832 \$ a( 1 ), n1, b( 0, n1 ), ldb )
833*
834 END IF
835*
836 ELSE
837*
838* SIDE ='R', N is odd, TRANSR = 'C', and UPLO = 'U'
839*
840 IF( notrans ) THEN
841*
842* SIDE ='R', N is odd, TRANSR = 'C', UPLO = 'U', and
843* TRANS = 'N'
844*
845 CALL ctrsm( 'R', 'U', 'N', diag, m, n1, alpha,
846 \$ a( n2*n2 ), n2, b( 0, 0 ), ldb )
847 CALL cgemm( 'N', 'C', m, n2, n1, -cone, b( 0, 0 ),
848 \$ ldb, a( 0 ), n2, alpha, b( 0, n1 ),
849 \$ ldb )
850 CALL ctrsm( 'R', 'L', 'C', diag, m, n2, cone,
851 \$ a( n1*n2 ), n2, b( 0, n1 ), ldb )
852*
853 ELSE
854*
855* SIDE ='R', N is odd, TRANSR = 'C', UPLO = 'U', and
856* TRANS = 'C'
857*
858 CALL ctrsm( 'R', 'L', 'N', diag, m, n2, alpha,
859 \$ a( n1*n2 ), n2, b( 0, n1 ), ldb )
860 CALL cgemm( 'N', 'N', m, n1, n2, -cone, b( 0, n1 ),
861 \$ ldb, a( 0 ), n2, alpha, b( 0, 0 ),
862 \$ ldb )
863 CALL ctrsm( 'R', 'U', 'C', diag, m, n1, cone,
864 \$ a( n2*n2 ), n2, b( 0, 0 ), ldb )
865*
866 END IF
867*
868 END IF
869*
870 END IF
871*
872 ELSE
873*
874* SIDE = 'R' and N is even
875*
876 IF( normaltransr ) THEN
877*
878* SIDE = 'R', N is even, and TRANSR = 'N'
879*
880 IF( lower ) THEN
881*
882* SIDE ='R', N is even, TRANSR = 'N', and UPLO = 'L'
883*
884 IF( notrans ) THEN
885*
886* SIDE ='R', N is even, TRANSR = 'N', UPLO = 'L',
887* and TRANS = 'N'
888*
889 CALL ctrsm( 'R', 'U', 'C', diag, m, k, alpha,
890 \$ a( 0 ), n+1, b( 0, k ), ldb )
891 CALL cgemm( 'N', 'N', m, k, k, -cone, b( 0, k ),
892 \$ ldb, a( k+1 ), n+1, alpha, b( 0, 0 ),
893 \$ ldb )
894 CALL ctrsm( 'R', 'L', 'N', diag, m, k, cone,
895 \$ a( 1 ), n+1, b( 0, 0 ), ldb )
896*
897 ELSE
898*
899* SIDE ='R', N is even, TRANSR = 'N', UPLO = 'L',
900* and TRANS = 'C'
901*
902 CALL ctrsm( 'R', 'L', 'C', diag, m, k, alpha,
903 \$ a( 1 ), n+1, b( 0, 0 ), ldb )
904 CALL cgemm( 'N', 'C', m, k, k, -cone, b( 0, 0 ),
905 \$ ldb, a( k+1 ), n+1, alpha, b( 0, k ),
906 \$ ldb )
907 CALL ctrsm( 'R', 'U', 'N', diag, m, k, cone,
908 \$ a( 0 ), n+1, b( 0, k ), ldb )
909*
910 END IF
911*
912 ELSE
913*
914* SIDE ='R', N is even, TRANSR = 'N', and UPLO = 'U'
915*
916 IF( notrans ) THEN
917*
918* SIDE ='R', N is even, TRANSR = 'N', UPLO = 'U',
919* and TRANS = 'N'
920*
921 CALL ctrsm( 'R', 'L', 'C', diag, m, k, alpha,
922 \$ a( k+1 ), n+1, b( 0, 0 ), ldb )
923 CALL cgemm( 'N', 'N', m, k, k, -cone, b( 0, 0 ),
924 \$ ldb, a( 0 ), n+1, alpha, b( 0, k ),
925 \$ ldb )
926 CALL ctrsm( 'R', 'U', 'N', diag, m, k, cone,
927 \$ a( k ), n+1, b( 0, k ), ldb )
928*
929 ELSE
930*
931* SIDE ='R', N is even, TRANSR = 'N', UPLO = 'U',
932* and TRANS = 'C'
933*
934 CALL ctrsm( 'R', 'U', 'C', diag, m, k, alpha,
935 \$ a( k ), n+1, b( 0, k ), ldb )
936 CALL cgemm( 'N', 'C', m, k, k, -cone, b( 0, k ),
937 \$ ldb, a( 0 ), n+1, alpha, b( 0, 0 ),
938 \$ ldb )
939 CALL ctrsm( 'R', 'L', 'N', diag, m, k, cone,
940 \$ a( k+1 ), n+1, b( 0, 0 ), ldb )
941*
942 END IF
943*
944 END IF
945*
946 ELSE
947*
948* SIDE = 'R', N is even, and TRANSR = 'C'
949*
950 IF( lower ) THEN
951*
952* SIDE ='R', N is even, TRANSR = 'C', and UPLO = 'L'
953*
954 IF( notrans ) THEN
955*
956* SIDE ='R', N is even, TRANSR = 'C', UPLO = 'L',
957* and TRANS = 'N'
958*
959 CALL ctrsm( 'R', 'L', 'N', diag, m, k, alpha,
960 \$ a( 0 ), k, b( 0, k ), ldb )
961 CALL cgemm( 'N', 'C', m, k, k, -cone, b( 0, k ),
962 \$ ldb, a( ( k+1 )*k ), k, alpha,
963 \$ b( 0, 0 ), ldb )
964 CALL ctrsm( 'R', 'U', 'C', diag, m, k, cone,
965 \$ a( k ), k, b( 0, 0 ), ldb )
966*
967 ELSE
968*
969* SIDE ='R', N is even, TRANSR = 'C', UPLO = 'L',
970* and TRANS = 'C'
971*
972 CALL ctrsm( 'R', 'U', 'N', diag, m, k, alpha,
973 \$ a( k ), k, b( 0, 0 ), ldb )
974 CALL cgemm( 'N', 'N', m, k, k, -cone, b( 0, 0 ),
975 \$ ldb, a( ( k+1 )*k ), k, alpha,
976 \$ b( 0, k ), ldb )
977 CALL ctrsm( 'R', 'L', 'C', diag, m, k, cone,
978 \$ a( 0 ), k, b( 0, k ), ldb )
979*
980 END IF
981*
982 ELSE
983*
984* SIDE ='R', N is even, TRANSR = 'C', and UPLO = 'U'
985*
986 IF( notrans ) THEN
987*
988* SIDE ='R', N is even, TRANSR = 'C', UPLO = 'U',
989* and TRANS = 'N'
990*
991 CALL ctrsm( 'R', 'U', 'N', diag, m, k, alpha,
992 \$ a( ( k+1 )*k ), k, b( 0, 0 ), ldb )
993 CALL cgemm( 'N', 'C', m, k, k, -cone, b( 0, 0 ),
994 \$ ldb, a( 0 ), k, alpha, b( 0, k ), ldb )
995 CALL ctrsm( 'R', 'L', 'C', diag, m, k, cone,
996 \$ a( k*k ), k, b( 0, k ), ldb )
997*
998 ELSE
999*
1000* SIDE ='R', N is even, TRANSR = 'C', UPLO = 'U',
1001* and TRANS = 'C'
1002*
1003 CALL ctrsm( 'R', 'L', 'N', diag, m, k, alpha,
1004 \$ a( k*k ), k, b( 0, k ), ldb )
1005 CALL cgemm( 'N', 'N', m, k, k, -cone, b( 0, k ),
1006 \$ ldb, a( 0 ), k, alpha, b( 0, 0 ), ldb )
1007 CALL ctrsm( 'R', 'U', 'C', diag, m, k, cone,
1008 \$ a( ( k+1 )*k ), k, b( 0, 0 ), ldb )
1009*
1010 END IF
1011*
1012 END IF
1013*
1014 END IF
1015*
1016 END IF
1017 END IF
1018*
1019 RETURN
1020*
1021* End of CTFSM
1022*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine cgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
CGEMM
Definition cgemm.f:188
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine ctrsm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
CTRSM
Definition ctrsm.f:180
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