LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
ctfsm.f
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1 *> \brief \b CTFSM solves a matrix equation (one operand is a triangular matrix in RFP format).
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download CTFSM + dependencies
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11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ctfsm.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ctfsm.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CTFSM( TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A,
22 * B, LDB )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER TRANSR, DIAG, SIDE, TRANS, UPLO
26 * INTEGER LDB, M, N
27 * COMPLEX ALPHA
28 * ..
29 * .. Array Arguments ..
30 * COMPLEX A( 0: * ), B( 0: LDB-1, 0: * )
31 * ..
32 *
33 *
34 *> \par Purpose:
35 * =============
36 *>
37 *> \verbatim
38 *>
39 *> Level 3 BLAS like routine for A in RFP Format.
40 *>
41 *> CTFSM solves the matrix equation
42 *>
43 *> op( A )*X = alpha*B or X*op( A ) = alpha*B
44 *>
45 *> where alpha is a scalar, X and B are m by n matrices, A is a unit, or
46 *> non-unit, upper or lower triangular matrix and op( A ) is one of
47 *>
48 *> op( A ) = A or op( A ) = A**H.
49 *>
50 *> A is in Rectangular Full Packed (RFP) Format.
51 *>
52 *> The matrix X is overwritten on B.
53 *> \endverbatim
54 *
55 * Arguments:
56 * ==========
57 *
58 *> \param[in] TRANSR
59 *> \verbatim
60 *> TRANSR is CHARACTER*1
61 *> = 'N': The Normal Form of RFP A is stored;
62 *> = 'C': The Conjugate-transpose Form of RFP A is stored.
63 *> \endverbatim
64 *>
65 *> \param[in] SIDE
66 *> \verbatim
67 *> SIDE is CHARACTER*1
68 *> On entry, SIDE specifies whether op( A ) appears on the left
69 *> or right of X as follows:
70 *>
71 *> SIDE = 'L' or 'l' op( A )*X = alpha*B.
72 *>
73 *> SIDE = 'R' or 'r' X*op( A ) = alpha*B.
74 *>
75 *> Unchanged on exit.
76 *> \endverbatim
77 *>
78 *> \param[in] UPLO
79 *> \verbatim
80 *> UPLO is CHARACTER*1
81 *> On entry, UPLO specifies whether the RFP matrix A came from
82 *> an upper or lower triangular matrix as follows:
83 *> UPLO = 'U' or 'u' RFP A came from an upper triangular matrix
84 *> UPLO = 'L' or 'l' RFP A came from a lower triangular matrix
85 *>
86 *> Unchanged on exit.
87 *> \endverbatim
88 *>
89 *> \param[in] TRANS
90 *> \verbatim
91 *> TRANS is CHARACTER*1
92 *> On entry, TRANS specifies the form of op( A ) to be used
93 *> in the matrix multiplication as follows:
94 *>
95 *> TRANS = 'N' or 'n' op( A ) = A.
96 *>
97 *> TRANS = 'C' or 'c' op( A ) = conjg( A' ).
98 *>
99 *> Unchanged on exit.
100 *> \endverbatim
101 *>
102 *> \param[in] DIAG
103 *> \verbatim
104 *> DIAG is CHARACTER*1
105 *> On entry, DIAG specifies whether or not RFP A is unit
106 *> triangular as follows:
107 *>
108 *> DIAG = 'U' or 'u' A is assumed to be unit triangular.
109 *>
110 *> DIAG = 'N' or 'n' A is not assumed to be unit
111 *> triangular.
112 *>
113 *> Unchanged on exit.
114 *> \endverbatim
115 *>
116 *> \param[in] M
117 *> \verbatim
118 *> M is INTEGER
119 *> On entry, M specifies the number of rows of B. M must be at
120 *> least zero.
121 *> Unchanged on exit.
122 *> \endverbatim
123 *>
124 *> \param[in] N
125 *> \verbatim
126 *> N is INTEGER
127 *> On entry, N specifies the number of columns of B. N must be
128 *> at least zero.
129 *> Unchanged on exit.
130 *> \endverbatim
131 *>
132 *> \param[in] ALPHA
133 *> \verbatim
134 *> ALPHA is COMPLEX
135 *> On entry, ALPHA specifies the scalar alpha. When alpha is
136 *> zero then A is not referenced and B need not be set before
137 *> entry.
138 *> Unchanged on exit.
139 *> \endverbatim
140 *>
141 *> \param[in] A
142 *> \verbatim
143 *> A is COMPLEX array, dimension (N*(N+1)/2)
144 *> NT = N*(N+1)/2. On entry, the matrix A in RFP Format.
145 *> RFP Format is described by TRANSR, UPLO and N as follows:
146 *> If TRANSR='N' then RFP A is (0:N,0:K-1) when N is even;
147 *> K=N/2. RFP A is (0:N-1,0:K) when N is odd; K=N/2. If
148 *> TRANSR = 'C' then RFP is the Conjugate-transpose of RFP A as
149 *> defined when TRANSR = 'N'. The contents of RFP A are defined
150 *> by UPLO as follows: If UPLO = 'U' the RFP A contains the NT
151 *> elements of upper packed A either in normal or
152 *> conjugate-transpose Format. If UPLO = 'L' the RFP A contains
153 *> the NT elements of lower packed A either in normal or
154 *> conjugate-transpose Format. The LDA of RFP A is (N+1)/2 when
155 *> TRANSR = 'C'. When TRANSR is 'N' the LDA is N+1 when N is
156 *> even and is N when is odd.
157 *> See the Note below for more details. Unchanged on exit.
158 *> \endverbatim
159 *>
160 *> \param[in,out] B
161 *> \verbatim
162 *> B is COMPLEX array, dimension (LDB,N)
163 *> Before entry, the leading m by n part of the array B must
164 *> contain the right-hand side matrix B, and on exit is
165 *> overwritten by the solution matrix X.
166 *> \endverbatim
167 *>
168 *> \param[in] LDB
169 *> \verbatim
170 *> LDB is INTEGER
171 *> On entry, LDB specifies the first dimension of B as declared
172 *> in the calling (sub) program. LDB must be at least
173 *> max( 1, m ).
174 *> Unchanged on exit.
175 *> \endverbatim
176 *
177 * Authors:
178 * ========
179 *
180 *> \author Univ. of Tennessee
181 *> \author Univ. of California Berkeley
182 *> \author Univ. of Colorado Denver
183 *> \author NAG Ltd.
184 *
185 *> \ingroup complexOTHERcomputational
186 *
187 *> \par Further Details:
188 * =====================
189 *>
190 *> \verbatim
191 *>
192 *> We first consider Standard Packed Format when N is even.
193 *> We give an example where N = 6.
194 *>
195 *> AP is Upper AP is Lower
196 *>
197 *> 00 01 02 03 04 05 00
198 *> 11 12 13 14 15 10 11
199 *> 22 23 24 25 20 21 22
200 *> 33 34 35 30 31 32 33
201 *> 44 45 40 41 42 43 44
202 *> 55 50 51 52 53 54 55
203 *>
204 *>
205 *> Let TRANSR = 'N'. RFP holds AP as follows:
206 *> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
207 *> three columns of AP upper. The lower triangle A(4:6,0:2) consists of
208 *> conjugate-transpose of the first three columns of AP upper.
209 *> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
210 *> three columns of AP lower. The upper triangle A(0:2,0:2) consists of
211 *> conjugate-transpose of the last three columns of AP lower.
212 *> To denote conjugate we place -- above the element. This covers the
213 *> case N even and TRANSR = 'N'.
214 *>
215 *> RFP A RFP A
216 *>
217 *> -- -- --
218 *> 03 04 05 33 43 53
219 *> -- --
220 *> 13 14 15 00 44 54
221 *> --
222 *> 23 24 25 10 11 55
223 *>
224 *> 33 34 35 20 21 22
225 *> --
226 *> 00 44 45 30 31 32
227 *> -- --
228 *> 01 11 55 40 41 42
229 *> -- -- --
230 *> 02 12 22 50 51 52
231 *>
232 *> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
233 *> transpose of RFP A above. One therefore gets:
234 *>
235 *>
236 *> RFP A RFP A
237 *>
238 *> -- -- -- -- -- -- -- -- -- --
239 *> 03 13 23 33 00 01 02 33 00 10 20 30 40 50
240 *> -- -- -- -- -- -- -- -- -- --
241 *> 04 14 24 34 44 11 12 43 44 11 21 31 41 51
242 *> -- -- -- -- -- -- -- -- -- --
243 *> 05 15 25 35 45 55 22 53 54 55 22 32 42 52
244 *>
245 *>
246 *> We next consider Standard Packed Format when N is odd.
247 *> We give an example where N = 5.
248 *>
249 *> AP is Upper AP is Lower
250 *>
251 *> 00 01 02 03 04 00
252 *> 11 12 13 14 10 11
253 *> 22 23 24 20 21 22
254 *> 33 34 30 31 32 33
255 *> 44 40 41 42 43 44
256 *>
257 *>
258 *> Let TRANSR = 'N'. RFP holds AP as follows:
259 *> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
260 *> three columns of AP upper. The lower triangle A(3:4,0:1) consists of
261 *> conjugate-transpose of the first two columns of AP upper.
262 *> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
263 *> three columns of AP lower. The upper triangle A(0:1,1:2) consists of
264 *> conjugate-transpose of the last two columns of AP lower.
265 *> To denote conjugate we place -- above the element. This covers the
266 *> case N odd and TRANSR = 'N'.
267 *>
268 *> RFP A RFP A
269 *>
270 *> -- --
271 *> 02 03 04 00 33 43
272 *> --
273 *> 12 13 14 10 11 44
274 *>
275 *> 22 23 24 20 21 22
276 *> --
277 *> 00 33 34 30 31 32
278 *> -- --
279 *> 01 11 44 40 41 42
280 *>
281 *> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
282 *> transpose of RFP A above. One therefore gets:
283 *>
284 *>
285 *> RFP A RFP A
286 *>
287 *> -- -- -- -- -- -- -- -- --
288 *> 02 12 22 00 01 00 10 20 30 40 50
289 *> -- -- -- -- -- -- -- -- --
290 *> 03 13 23 33 11 33 11 21 31 41 51
291 *> -- -- -- -- -- -- -- -- --
292 *> 04 14 24 34 44 43 44 22 32 42 52
293 *> \endverbatim
294 *>
295 * =====================================================================
296  SUBROUTINE ctfsm( TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A,
297  $ B, LDB )
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 *
1023  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:187
subroutine ctrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
CTRSM
Definition: ctrsm.f:180
subroutine ctfsm(TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, B, LDB)
CTFSM solves a matrix equation (one operand is a triangular matrix in RFP format).
Definition: ctfsm.f:298