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
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