1*> \brief \b ZHER2K
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
8*  Definition:
9*  ===========
10*
11*       SUBROUTINE ZHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
12*
13*       .. Scalar Arguments ..
14*       COMPLEX*16 ALPHA
15*       DOUBLE PRECISION BETA
16*       INTEGER K,LDA,LDB,LDC,N
17*       CHARACTER TRANS,UPLO
18*       ..
19*       .. Array Arguments ..
20*       COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*)
21*       ..
22*
23*
24*> \par Purpose:
25*  =============
26*>
27*> \verbatim
28*>
29*> ZHER2K  performs one of the hermitian rank 2k operations
30*>
31*>    C := alpha*A*B**H + conjg( alpha )*B*A**H + beta*C,
32*>
33*> or
34*>
35*>    C := alpha*A**H*B + conjg( alpha )*B**H*A + beta*C,
36*>
37*> where  alpha and beta  are scalars with  beta  real,  C is an  n by n
38*> hermitian matrix and  A and B  are  n by k matrices in the first case
39*> and  k by n  matrices in the second case.
40*> \endverbatim
41*
42*  Arguments:
43*  ==========
44*
45*> \param[in] UPLO
46*> \verbatim
47*>          UPLO is CHARACTER*1
48*>           On  entry,   UPLO  specifies  whether  the  upper  or  lower
49*>           triangular  part  of the  array  C  is to be  referenced  as
50*>           follows:
51*>
52*>              UPLO = 'U' or 'u'   Only the  upper triangular part of  C
53*>                                  is to be referenced.
54*>
55*>              UPLO = 'L' or 'l'   Only the  lower triangular part of  C
56*>                                  is to be referenced.
57*> \endverbatim
58*>
59*> \param[in] TRANS
60*> \verbatim
61*>          TRANS is CHARACTER*1
62*>           On entry,  TRANS  specifies the operation to be performed as
63*>           follows:
64*>
65*>              TRANS = 'N' or 'n'    C := alpha*A*B**H          +
66*>                                         conjg( alpha )*B*A**H +
67*>                                         beta*C.
68*>
69*>              TRANS = 'C' or 'c'    C := alpha*A**H*B          +
70*>                                         conjg( alpha )*B**H*A +
71*>                                         beta*C.
72*> \endverbatim
73*>
74*> \param[in] N
75*> \verbatim
76*>          N is INTEGER
77*>           On entry,  N specifies the order of the matrix C.  N must be
78*>           at least zero.
79*> \endverbatim
80*>
81*> \param[in] K
82*> \verbatim
83*>          K is INTEGER
84*>           On entry with  TRANS = 'N' or 'n',  K  specifies  the number
85*>           of  columns  of the  matrices  A and B,  and on  entry  with
86*>           TRANS = 'C' or 'c',  K  specifies  the number of rows of the
87*>           matrices  A and B.  K must be at least zero.
88*> \endverbatim
89*>
90*> \param[in] ALPHA
91*> \verbatim
92*>          ALPHA is COMPLEX*16 .
93*>           On entry, ALPHA specifies the scalar alpha.
94*> \endverbatim
95*>
96*> \param[in] A
97*> \verbatim
98*>          A is COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is
99*>           k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
100*>           Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
101*>           part of the array  A  must contain the matrix  A,  otherwise
102*>           the leading  k by n  part of the array  A  must contain  the
103*>           matrix A.
104*> \endverbatim
105*>
106*> \param[in] LDA
107*> \verbatim
108*>          LDA is INTEGER
109*>           On entry, LDA specifies the first dimension of A as declared
110*>           in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
111*>           then  LDA must be at least  max( 1, n ), otherwise  LDA must
112*>           be at least  max( 1, k ).
113*> \endverbatim
114*>
115*> \param[in] B
116*> \verbatim
117*>          B is COMPLEX*16 array of DIMENSION ( LDB, kb ), where kb is
118*>           k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
119*>           Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
120*>           part of the array  B  must contain the matrix  B,  otherwise
121*>           the leading  k by n  part of the array  B  must contain  the
122*>           matrix B.
123*> \endverbatim
124*>
125*> \param[in] LDB
126*> \verbatim
127*>          LDB is INTEGER
128*>           On entry, LDB specifies the first dimension of B as declared
129*>           in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
130*>           then  LDB must be at least  max( 1, n ), otherwise  LDB must
131*>           be at least  max( 1, k ).
132*>           Unchanged on exit.
133*> \endverbatim
134*>
135*> \param[in] BETA
136*> \verbatim
137*>          BETA is DOUBLE PRECISION .
138*>           On entry, BETA specifies the scalar beta.
139*> \endverbatim
140*>
141*> \param[in,out] C
142*> \verbatim
143*>          C is COMPLEX*16 array of DIMENSION ( LDC, n ).
144*>           Before entry  with  UPLO = 'U' or 'u',  the leading  n by n
145*>           upper triangular part of the array C must contain the upper
146*>           triangular part  of the  hermitian matrix  and the strictly
147*>           lower triangular part of C is not referenced.  On exit, the
148*>           upper triangular part of the array  C is overwritten by the
149*>           upper triangular part of the updated matrix.
150*>           Before entry  with  UPLO = 'L' or 'l',  the leading  n by n
151*>           lower triangular part of the array C must contain the lower
152*>           triangular part  of the  hermitian matrix  and the strictly
153*>           upper triangular part of C is not referenced.  On exit, the
154*>           lower triangular part of the array  C is overwritten by the
155*>           lower triangular part of the updated matrix.
156*>           Note that the imaginary parts of the diagonal elements need
157*>           not be set,  they are assumed to be zero,  and on exit they
158*>           are set to zero.
159*> \endverbatim
160*>
161*> \param[in] LDC
162*> \verbatim
163*>          LDC is INTEGER
164*>           On entry, LDC specifies the first dimension of C as declared
165*>           in  the  calling  (sub)  program.   LDC  must  be  at  least
166*>           max( 1, n ).
167*> \endverbatim
168*
169*  Authors:
170*  ========
171*
172*> \author Univ. of Tennessee
173*> \author Univ. of California Berkeley
174*> \author Univ. of Colorado Denver
175*> \author NAG Ltd.
176*
177*> \date November 2011
178*
179*> \ingroup complex16_blas_level3
180*
181*> \par Further Details:
182*  =====================
183*>
184*> \verbatim
185*>
186*>  Level 3 Blas routine.
187*>
188*>  -- Written on 8-February-1989.
189*>     Jack Dongarra, Argonne National Laboratory.
190*>     Iain Duff, AERE Harwell.
191*>     Jeremy Du Croz, Numerical Algorithms Group Ltd.
192*>     Sven Hammarling, Numerical Algorithms Group Ltd.
193*>
194*>  -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1.
195*>     Ed Anderson, Cray Research Inc.
196*> \endverbatim
197*>
198*  =====================================================================
199      SUBROUTINE ZHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
200*
201*  -- Reference BLAS level3 routine (version 3.4.0) --
202*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
203*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
204*     November 2011
205*
206*     .. Scalar Arguments ..
207      COMPLEX*16 ALPHA
208      DOUBLE PRECISION BETA
209      INTEGER K,LDA,LDB,LDC,N
210      CHARACTER TRANS,UPLO
211*     ..
212*     .. Array Arguments ..
213      COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*)
214*     ..
215*
216*  =====================================================================
217*
218*     .. External Functions ..
219      LOGICAL LSAME
220      EXTERNAL LSAME
221*     ..
222*     .. External Subroutines ..
223      EXTERNAL XERBLA
224*     ..
225*     .. Intrinsic Functions ..
226      INTRINSIC DBLE,DCONJG,MAX
227*     ..
228*     .. Local Scalars ..
229      COMPLEX*16 TEMP1,TEMP2
230      INTEGER I,INFO,J,L,NROWA
231      LOGICAL UPPER
232*     ..
233*     .. Parameters ..
234      DOUBLE PRECISION ONE
235      PARAMETER (ONE=1.0D+0)
236      COMPLEX*16 ZERO
237      PARAMETER (ZERO= (0.0D+0,0.0D+0))
238*     ..
239*
240*     Test the input parameters.
241*
242      IF (LSAME(TRANS,'N')) THEN
243          NROWA = N
244      ELSE
245          NROWA = K
246      END IF
247      UPPER = LSAME(UPLO,'U')
248*
249      INFO = 0
250      IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
251          INFO = 1
252      ELSE IF ((.NOT.LSAME(TRANS,'N')) .AND.
253     +         (.NOT.LSAME(TRANS,'C'))) THEN
254          INFO = 2
255      ELSE IF (N.LT.0) THEN
256          INFO = 3
257      ELSE IF (K.LT.0) THEN
258          INFO = 4
259      ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
260          INFO = 7
261      ELSE IF (LDB.LT.MAX(1,NROWA)) THEN
262          INFO = 9
263      ELSE IF (LDC.LT.MAX(1,N)) THEN
264          INFO = 12
265      END IF
266      IF (INFO.NE.0) THEN
267          CALL XERBLA('ZHER2K',INFO)
268          RETURN
269      END IF
270*
271*     Quick return if possible.
272*
273      IF ((N.EQ.0) .OR. (((ALPHA.EQ.ZERO).OR.
274     +    (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN
275*
276*     And when  alpha.eq.zero.
277*
278      IF (ALPHA.EQ.ZERO) THEN
279          IF (UPPER) THEN
280              IF (BETA.EQ.DBLE(ZERO)) THEN
281                  DO 20 J = 1,N
282                      DO 10 I = 1,J
283                          C(I,J) = ZERO
284   10                 CONTINUE
285   20             CONTINUE
286              ELSE
287                  DO 40 J = 1,N
288                      DO 30 I = 1,J - 1
289                          C(I,J) = BETA*C(I,J)
290   30                 CONTINUE
291                      C(J,J) = BETA*DBLE(C(J,J))
292   40             CONTINUE
293              END IF
294          ELSE
295              IF (BETA.EQ.DBLE(ZERO)) THEN
296                  DO 60 J = 1,N
297                      DO 50 I = J,N
298                          C(I,J) = ZERO
299   50                 CONTINUE
300   60             CONTINUE
301              ELSE
302                  DO 80 J = 1,N
303                      C(J,J) = BETA*DBLE(C(J,J))
304                      DO 70 I = J + 1,N
305                          C(I,J) = BETA*C(I,J)
306   70                 CONTINUE
307   80             CONTINUE
308              END IF
309          END IF
310          RETURN
311      END IF
312*
313*     Start the operations.
314*
315      IF (LSAME(TRANS,'N')) THEN
316*
317*        Form  C := alpha*A*B**H + conjg( alpha )*B*A**H +
318*                   C.
319*
320          IF (UPPER) THEN
321              DO 130 J = 1,N
322                  IF (BETA.EQ.DBLE(ZERO)) THEN
323                      DO 90 I = 1,J
324                          C(I,J) = ZERO
325   90                 CONTINUE
326                  ELSE IF (BETA.NE.ONE) THEN
327                      DO 100 I = 1,J - 1
328                          C(I,J) = BETA*C(I,J)
329  100                 CONTINUE
330                      C(J,J) = BETA*DBLE(C(J,J))
331                  ELSE
332                      C(J,J) = DBLE(C(J,J))
333                  END IF
334                  DO 120 L = 1,K
335                      IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN
336                          TEMP1 = ALPHA*DCONJG(B(J,L))
337                          TEMP2 = DCONJG(ALPHA*A(J,L))
338                          DO 110 I = 1,J - 1
339                              C(I,J) = C(I,J) + A(I,L)*TEMP1 +
340     +                                 B(I,L)*TEMP2
341  110                     CONTINUE
342                          C(J,J) = DBLE(C(J,J)) +
343     +                             DBLE(A(J,L)*TEMP1+B(J,L)*TEMP2)
344                      END IF
345  120             CONTINUE
346  130         CONTINUE
347          ELSE
348              DO 180 J = 1,N
349                  IF (BETA.EQ.DBLE(ZERO)) THEN
350                      DO 140 I = J,N
351                          C(I,J) = ZERO
352  140                 CONTINUE
353                  ELSE IF (BETA.NE.ONE) THEN
354                      DO 150 I = J + 1,N
355                          C(I,J) = BETA*C(I,J)
356  150                 CONTINUE
357                      C(J,J) = BETA*DBLE(C(J,J))
358                  ELSE
359                      C(J,J) = DBLE(C(J,J))
360                  END IF
361                  DO 170 L = 1,K
362                      IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN
363                          TEMP1 = ALPHA*DCONJG(B(J,L))
364                          TEMP2 = DCONJG(ALPHA*A(J,L))
365                          DO 160 I = J + 1,N
366                              C(I,J) = C(I,J) + A(I,L)*TEMP1 +
367     +                                 B(I,L)*TEMP2
368  160                     CONTINUE
369                          C(J,J) = DBLE(C(J,J)) +
370     +                             DBLE(A(J,L)*TEMP1+B(J,L)*TEMP2)
371                      END IF
372  170             CONTINUE
373  180         CONTINUE
374          END IF
375      ELSE
376*
377*        Form  C := alpha*A**H*B + conjg( alpha )*B**H*A +
378*                   C.
379*
380          IF (UPPER) THEN
381              DO 210 J = 1,N
382                  DO 200 I = 1,J
383                      TEMP1 = ZERO
384                      TEMP2 = ZERO
385                      DO 190 L = 1,K
386                          TEMP1 = TEMP1 + DCONJG(A(L,I))*B(L,J)
387                          TEMP2 = TEMP2 + DCONJG(B(L,I))*A(L,J)
388  190                 CONTINUE
389                      IF (I.EQ.J) THEN
390                          IF (BETA.EQ.DBLE(ZERO)) THEN
391                              C(J,J) = DBLE(ALPHA*TEMP1+
392     +                                 DCONJG(ALPHA)*TEMP2)
393                          ELSE
394                              C(J,J) = BETA*DBLE(C(J,J)) +
395     +                                 DBLE(ALPHA*TEMP1+
396     +                                 DCONJG(ALPHA)*TEMP2)
397                          END IF
398                      ELSE
399                          IF (BETA.EQ.DBLE(ZERO)) THEN
400                              C(I,J) = ALPHA*TEMP1 + DCONJG(ALPHA)*TEMP2
401                          ELSE
402                              C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 +
403     +                                 DCONJG(ALPHA)*TEMP2
404                          END IF
405                      END IF
406  200             CONTINUE
407  210         CONTINUE
408          ELSE
409              DO 240 J = 1,N
410                  DO 230 I = J,N
411                      TEMP1 = ZERO
412                      TEMP2 = ZERO
413                      DO 220 L = 1,K
414                          TEMP1 = TEMP1 + DCONJG(A(L,I))*B(L,J)
415                          TEMP2 = TEMP2 + DCONJG(B(L,I))*A(L,J)
416  220                 CONTINUE
417                      IF (I.EQ.J) THEN
418                          IF (BETA.EQ.DBLE(ZERO)) THEN
419                              C(J,J) = DBLE(ALPHA*TEMP1+
420     +                                 DCONJG(ALPHA)*TEMP2)
421                          ELSE
422                              C(J,J) = BETA*DBLE(C(J,J)) +
423     +                                 DBLE(ALPHA*TEMP1+
424     +                                 DCONJG(ALPHA)*TEMP2)
425                          END IF
426                      ELSE
427                          IF (BETA.EQ.DBLE(ZERO)) THEN
428                              C(I,J) = ALPHA*TEMP1 + DCONJG(ALPHA)*TEMP2
429                          ELSE
430                              C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 +
431     +                                 DCONJG(ALPHA)*TEMP2
432                          END IF
433                      END IF
434  230             CONTINUE
435  240         CONTINUE
436          END IF
437      END IF
438*
439      RETURN
440*
441*     End of ZHER2K.
442*
443      END
444