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, 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, 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, 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*> \ingroup complex16_blas_level3
178*
179*> \par Further Details:
180*  =====================
181*>
182*> \verbatim
183*>
184*>  Level 3 Blas routine.
185*>
186*>  -- Written on 8-February-1989.
187*>     Jack Dongarra, Argonne National Laboratory.
188*>     Iain Duff, AERE Harwell.
189*>     Jeremy Du Croz, Numerical Algorithms Group Ltd.
190*>     Sven Hammarling, Numerical Algorithms Group Ltd.
191*>
192*>  -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1.
193*>     Ed Anderson, Cray Research Inc.
194*> \endverbatim
195*>
196*  =====================================================================
197      SUBROUTINE ZHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
198*
199*  -- Reference BLAS level3 routine --
200*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
201*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
202*
203*     .. Scalar Arguments ..
204      COMPLEX*16 ALPHA
205      DOUBLE PRECISION BETA
206      INTEGER K,LDA,LDB,LDC,N
207      CHARACTER TRANS,UPLO
208*     ..
209*     .. Array Arguments ..
210      COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*)
211*     ..
212*
213*  =====================================================================
214*
215*     .. External Functions ..
216      LOGICAL LSAME
217      EXTERNAL LSAME
218*     ..
219*     .. External Subroutines ..
220      EXTERNAL XERBLA
221*     ..
222*     .. Intrinsic Functions ..
223      INTRINSIC DBLE,DCONJG,MAX
224*     ..
225*     .. Local Scalars ..
226      COMPLEX*16 TEMP1,TEMP2
227      INTEGER I,INFO,J,L,NROWA
228      LOGICAL UPPER
229*     ..
230*     .. Parameters ..
231      DOUBLE PRECISION ONE
232      PARAMETER (ONE=1.0D+0)
233      COMPLEX*16 ZERO
234      PARAMETER (ZERO= (0.0D+0,0.0D+0))
235*     ..
236*
237*     Test the input parameters.
238*
239      IF (LSAME(TRANS,'N')) THEN
240          NROWA = N
241      ELSE
242          NROWA = K
243      END IF
244      UPPER = LSAME(UPLO,'U')
245*
246      INFO = 0
247      IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
248          INFO = 1
249      ELSE IF ((.NOT.LSAME(TRANS,'N')) .AND.
250     +         (.NOT.LSAME(TRANS,'C'))) THEN
251          INFO = 2
252      ELSE IF (N.LT.0) THEN
253          INFO = 3
254      ELSE IF (K.LT.0) THEN
255          INFO = 4
256      ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
257          INFO = 7
258      ELSE IF (LDB.LT.MAX(1,NROWA)) THEN
259          INFO = 9
260      ELSE IF (LDC.LT.MAX(1,N)) THEN
261          INFO = 12
262      END IF
263      IF (INFO.NE.0) THEN
264          CALL XERBLA('ZHER2K',INFO)
265          RETURN
266      END IF
267*
268*     Quick return if possible.
269*
270      IF ((N.EQ.0) .OR. (((ALPHA.EQ.ZERO).OR.
271     +    (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN
272*
273*     And when  alpha.eq.zero.
274*
275      IF (ALPHA.EQ.ZERO) THEN
276          IF (UPPER) THEN
277              IF (BETA.EQ.DBLE(ZERO)) THEN
278                  DO 20 J = 1,N
279                      DO 10 I = 1,J
280                          C(I,J) = ZERO
281   10                 CONTINUE
282   20             CONTINUE
283              ELSE
284                  DO 40 J = 1,N
285                      DO 30 I = 1,J - 1
286                          C(I,J) = BETA*C(I,J)
287   30                 CONTINUE
288                      C(J,J) = BETA*DBLE(C(J,J))
289   40             CONTINUE
290              END IF
291          ELSE
292              IF (BETA.EQ.DBLE(ZERO)) THEN
293                  DO 60 J = 1,N
294                      DO 50 I = J,N
295                          C(I,J) = ZERO
296   50                 CONTINUE
297   60             CONTINUE
298              ELSE
299                  DO 80 J = 1,N
300                      C(J,J) = BETA*DBLE(C(J,J))
301                      DO 70 I = J + 1,N
302                          C(I,J) = BETA*C(I,J)
303   70                 CONTINUE
304   80             CONTINUE
305              END IF
306          END IF
307          RETURN
308      END IF
309*
310*     Start the operations.
311*
312      IF (LSAME(TRANS,'N')) THEN
313*
314*        Form  C := alpha*A*B**H + conjg( alpha )*B*A**H +
315*                   C.
316*
317          IF (UPPER) THEN
318              DO 130 J = 1,N
319                  IF (BETA.EQ.DBLE(ZERO)) THEN
320                      DO 90 I = 1,J
321                          C(I,J) = ZERO
322   90                 CONTINUE
323                  ELSE IF (BETA.NE.ONE) THEN
324                      DO 100 I = 1,J - 1
325                          C(I,J) = BETA*C(I,J)
326  100                 CONTINUE
327                      C(J,J) = BETA*DBLE(C(J,J))
328                  ELSE
329                      C(J,J) = DBLE(C(J,J))
330                  END IF
331                  DO 120 L = 1,K
332                      IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN
333                          TEMP1 = ALPHA*DCONJG(B(J,L))
334                          TEMP2 = DCONJG(ALPHA*A(J,L))
335                          DO 110 I = 1,J - 1
336                              C(I,J) = C(I,J) + A(I,L)*TEMP1 +
337     +                                 B(I,L)*TEMP2
338  110                     CONTINUE
339                          C(J,J) = DBLE(C(J,J)) +
340     +                             DBLE(A(J,L)*TEMP1+B(J,L)*TEMP2)
341                      END IF
342  120             CONTINUE
343  130         CONTINUE
344          ELSE
345              DO 180 J = 1,N
346                  IF (BETA.EQ.DBLE(ZERO)) THEN
347                      DO 140 I = J,N
348                          C(I,J) = ZERO
349  140                 CONTINUE
350                  ELSE IF (BETA.NE.ONE) THEN
351                      DO 150 I = J + 1,N
352                          C(I,J) = BETA*C(I,J)
353  150                 CONTINUE
354                      C(J,J) = BETA*DBLE(C(J,J))
355                  ELSE
356                      C(J,J) = DBLE(C(J,J))
357                  END IF
358                  DO 170 L = 1,K
359                      IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN
360                          TEMP1 = ALPHA*DCONJG(B(J,L))
361                          TEMP2 = DCONJG(ALPHA*A(J,L))
362                          DO 160 I = J + 1,N
363                              C(I,J) = C(I,J) + A(I,L)*TEMP1 +
364     +                                 B(I,L)*TEMP2
365  160                     CONTINUE
366                          C(J,J) = DBLE(C(J,J)) +
367     +                             DBLE(A(J,L)*TEMP1+B(J,L)*TEMP2)
368                      END IF
369  170             CONTINUE
370  180         CONTINUE
371          END IF
372      ELSE
373*
374*        Form  C := alpha*A**H*B + conjg( alpha )*B**H*A +
375*                   C.
376*
377          IF (UPPER) THEN
378              DO 210 J = 1,N
379                  DO 200 I = 1,J
380                      TEMP1 = ZERO
381                      TEMP2 = ZERO
382                      DO 190 L = 1,K
383                          TEMP1 = TEMP1 + DCONJG(A(L,I))*B(L,J)
384                          TEMP2 = TEMP2 + DCONJG(B(L,I))*A(L,J)
385  190                 CONTINUE
386                      IF (I.EQ.J) THEN
387                          IF (BETA.EQ.DBLE(ZERO)) THEN
388                              C(J,J) = DBLE(ALPHA*TEMP1+
389     +                                 DCONJG(ALPHA)*TEMP2)
390                          ELSE
391                              C(J,J) = BETA*DBLE(C(J,J)) +
392     +                                 DBLE(ALPHA*TEMP1+
393     +                                 DCONJG(ALPHA)*TEMP2)
394                          END IF
395                      ELSE
396                          IF (BETA.EQ.DBLE(ZERO)) THEN
397                              C(I,J) = ALPHA*TEMP1 + DCONJG(ALPHA)*TEMP2
398                          ELSE
399                              C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 +
400     +                                 DCONJG(ALPHA)*TEMP2
401                          END IF
402                      END IF
403  200             CONTINUE
404  210         CONTINUE
405          ELSE
406              DO 240 J = 1,N
407                  DO 230 I = J,N
408                      TEMP1 = ZERO
409                      TEMP2 = ZERO
410                      DO 220 L = 1,K
411                          TEMP1 = TEMP1 + DCONJG(A(L,I))*B(L,J)
412                          TEMP2 = TEMP2 + DCONJG(B(L,I))*A(L,J)
413  220                 CONTINUE
414                      IF (I.EQ.J) THEN
415                          IF (BETA.EQ.DBLE(ZERO)) THEN
416                              C(J,J) = DBLE(ALPHA*TEMP1+
417     +                                 DCONJG(ALPHA)*TEMP2)
418                          ELSE
419                              C(J,J) = BETA*DBLE(C(J,J)) +
420     +                                 DBLE(ALPHA*TEMP1+
421     +                                 DCONJG(ALPHA)*TEMP2)
422                          END IF
423                      ELSE
424                          IF (BETA.EQ.DBLE(ZERO)) THEN
425                              C(I,J) = ALPHA*TEMP1 + DCONJG(ALPHA)*TEMP2
426                          ELSE
427                              C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 +
428     +                                 DCONJG(ALPHA)*TEMP2
429                          END IF
430                      END IF
431  230             CONTINUE
432  240         CONTINUE
433          END IF
434      END IF
435*
436      RETURN
437*
438*     End of ZHER2K
439*
440      END
441