LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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cher2k.f
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1*> \brief \b CHER2K
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 CHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
12*
13* .. Scalar Arguments ..
14* COMPLEX ALPHA
15* REAL BETA
16* INTEGER K,LDA,LDB,LDC,N
17* CHARACTER TRANS,UPLO
18* ..
19* .. Array Arguments ..
20* COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
21* ..
22*
23*
24*> \par Purpose:
25* =============
26*>
27*> \verbatim
28*>
29*> CHER2K 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
93*> On entry, ALPHA specifies the scalar alpha.
94*> \endverbatim
95*>
96*> \param[in] A
97*> \verbatim
98*> A is COMPLEX 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 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*> \endverbatim
133*>
134*> \param[in] BETA
135*> \verbatim
136*> BETA is REAL
137*> On entry, BETA specifies the scalar beta.
138*> \endverbatim
139*>
140*> \param[in,out] C
141*> \verbatim
142*> C is COMPLEX array, dimension ( LDC, N )
143*> Before entry with UPLO = 'U' or 'u', the leading n by n
144*> upper triangular part of the array C must contain the upper
145*> triangular part of the hermitian matrix and the strictly
146*> lower triangular part of C is not referenced. On exit, the
147*> upper triangular part of the array C is overwritten by the
148*> upper triangular part of the updated matrix.
149*> Before entry with UPLO = 'L' or 'l', the leading n by n
150*> lower triangular part of the array C must contain the lower
151*> triangular part of the hermitian matrix and the strictly
152*> upper triangular part of C is not referenced. On exit, the
153*> lower triangular part of the array C is overwritten by the
154*> lower triangular part of the updated matrix.
155*> Note that the imaginary parts of the diagonal elements need
156*> not be set, they are assumed to be zero, and on exit they
157*> are set to zero.
158*> \endverbatim
159*>
160*> \param[in] LDC
161*> \verbatim
162*> LDC is INTEGER
163*> On entry, LDC specifies the first dimension of C as declared
164*> in the calling (sub) program. LDC must be at least
165*> max( 1, n ).
166*> \endverbatim
167*
168* Authors:
169* ========
170*
171*> \author Univ. of Tennessee
172*> \author Univ. of California Berkeley
173*> \author Univ. of Colorado Denver
174*> \author NAG Ltd.
175*
176*> \ingroup her2k
177*
178*> \par Further Details:
179* =====================
180*>
181*> \verbatim
182*>
183*> Level 3 Blas routine.
184*>
185*> -- Written on 8-February-1989.
186*> Jack Dongarra, Argonne National Laboratory.
187*> Iain Duff, AERE Harwell.
188*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
189*> Sven Hammarling, Numerical Algorithms Group Ltd.
190*>
191*> -- Modified 8-Nov-93 to set C(J,J) to REAL( C(J,J) ) when BETA = 1.
192*> Ed Anderson, Cray Research Inc.
193*> \endverbatim
194*>
195* =====================================================================
196 SUBROUTINE cher2k(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
197*
198* -- Reference BLAS level3 routine --
199* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
200* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
201*
202* .. Scalar Arguments ..
203 COMPLEX ALPHA
204 REAL BETA
205 INTEGER K,LDA,LDB,LDC,N
206 CHARACTER TRANS,UPLO
207* ..
208* .. Array Arguments ..
209 COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
210* ..
211*
212* =====================================================================
213*
214* .. External Functions ..
215 LOGICAL LSAME
216 EXTERNAL lsame
217* ..
218* .. External Subroutines ..
219 EXTERNAL xerbla
220* ..
221* .. Intrinsic Functions ..
222 INTRINSIC conjg,max,real
223* ..
224* .. Local Scalars ..
225 COMPLEX TEMP1,TEMP2
226 INTEGER I,INFO,J,L,NROWA
227 LOGICAL UPPER
228* ..
229* .. Parameters ..
230 REAL ONE
231 parameter(one=1.0e+0)
232 COMPLEX ZERO
233 parameter(zero= (0.0e+0,0.0e+0))
234* ..
235*
236* Test the input parameters.
237*
238 IF (lsame(trans,'N')) THEN
239 nrowa = n
240 ELSE
241 nrowa = k
242 END IF
243 upper = lsame(uplo,'U')
244*
245 info = 0
246 IF ((.NOT.upper) .AND. (.NOT.lsame(uplo,'L'))) THEN
247 info = 1
248 ELSE IF ((.NOT.lsame(trans,'N')) .AND.
249 + (.NOT.lsame(trans,'C'))) THEN
250 info = 2
251 ELSE IF (n.LT.0) THEN
252 info = 3
253 ELSE IF (k.LT.0) THEN
254 info = 4
255 ELSE IF (lda.LT.max(1,nrowa)) THEN
256 info = 7
257 ELSE IF (ldb.LT.max(1,nrowa)) THEN
258 info = 9
259 ELSE IF (ldc.LT.max(1,n)) THEN
260 info = 12
261 END IF
262 IF (info.NE.0) THEN
263 CALL xerbla('CHER2K',info)
264 RETURN
265 END IF
266*
267* Quick return if possible.
268*
269 IF ((n.EQ.0) .OR. (((alpha.EQ.zero).OR.
270 + (k.EQ.0)).AND. (beta.EQ.one))) RETURN
271*
272* And when alpha.eq.zero.
273*
274 IF (alpha.EQ.zero) THEN
275 IF (upper) THEN
276 IF (beta.EQ.real(zero)) THEN
277 DO 20 j = 1,n
278 DO 10 i = 1,j
279 c(i,j) = zero
280 10 CONTINUE
281 20 CONTINUE
282 ELSE
283 DO 40 j = 1,n
284 DO 30 i = 1,j - 1
285 c(i,j) = beta*c(i,j)
286 30 CONTINUE
287 c(j,j) = beta*real(c(j,j))
288 40 CONTINUE
289 END IF
290 ELSE
291 IF (beta.EQ.real(zero)) THEN
292 DO 60 j = 1,n
293 DO 50 i = j,n
294 c(i,j) = zero
295 50 CONTINUE
296 60 CONTINUE
297 ELSE
298 DO 80 j = 1,n
299 c(j,j) = beta*real(c(j,j))
300 DO 70 i = j + 1,n
301 c(i,j) = beta*c(i,j)
302 70 CONTINUE
303 80 CONTINUE
304 END IF
305 END IF
306 RETURN
307 END IF
308*
309* Start the operations.
310*
311 IF (lsame(trans,'N')) THEN
312*
313* Form C := alpha*A*B**H + conjg( alpha )*B*A**H +
314* C.
315*
316 IF (upper) THEN
317 DO 130 j = 1,n
318 IF (beta.EQ.real(zero)) THEN
319 DO 90 i = 1,j
320 c(i,j) = zero
321 90 CONTINUE
322 ELSE IF (beta.NE.one) THEN
323 DO 100 i = 1,j - 1
324 c(i,j) = beta*c(i,j)
325 100 CONTINUE
326 c(j,j) = beta*real(c(j,j))
327 ELSE
328 c(j,j) = real(c(j,j))
329 END IF
330 DO 120 l = 1,k
331 IF ((a(j,l).NE.zero) .OR. (b(j,l).NE.zero)) THEN
332 temp1 = alpha*conjg(b(j,l))
333 temp2 = conjg(alpha*a(j,l))
334 DO 110 i = 1,j - 1
335 c(i,j) = c(i,j) + a(i,l)*temp1 +
336 + b(i,l)*temp2
337 110 CONTINUE
338 c(j,j) = real(c(j,j)) +
339 + real(a(j,l)*temp1+b(j,l)*temp2)
340 END IF
341 120 CONTINUE
342 130 CONTINUE
343 ELSE
344 DO 180 j = 1,n
345 IF (beta.EQ.real(zero)) THEN
346 DO 140 i = j,n
347 c(i,j) = zero
348 140 CONTINUE
349 ELSE IF (beta.NE.one) THEN
350 DO 150 i = j + 1,n
351 c(i,j) = beta*c(i,j)
352 150 CONTINUE
353 c(j,j) = beta*real(c(j,j))
354 ELSE
355 c(j,j) = real(c(j,j))
356 END IF
357 DO 170 l = 1,k
358 IF ((a(j,l).NE.zero) .OR. (b(j,l).NE.zero)) THEN
359 temp1 = alpha*conjg(b(j,l))
360 temp2 = conjg(alpha*a(j,l))
361 DO 160 i = j + 1,n
362 c(i,j) = c(i,j) + a(i,l)*temp1 +
363 + b(i,l)*temp2
364 160 CONTINUE
365 c(j,j) = real(c(j,j)) +
366 + real(a(j,l)*temp1+b(j,l)*temp2)
367 END IF
368 170 CONTINUE
369 180 CONTINUE
370 END IF
371 ELSE
372*
373* Form C := alpha*A**H*B + conjg( alpha )*B**H*A +
374* C.
375*
376 IF (upper) THEN
377 DO 210 j = 1,n
378 DO 200 i = 1,j
379 temp1 = zero
380 temp2 = zero
381 DO 190 l = 1,k
382 temp1 = temp1 + conjg(a(l,i))*b(l,j)
383 temp2 = temp2 + conjg(b(l,i))*a(l,j)
384 190 CONTINUE
385 IF (i.EQ.j) THEN
386 IF (beta.EQ.real(zero)) THEN
387 c(j,j) = real(alpha*temp1+
388 + conjg(alpha)*temp2)
389 ELSE
390 c(j,j) = beta*real(c(j,j)) +
391 + real(alpha*temp1+
392 + conjg(alpha)*temp2)
393 END IF
394 ELSE
395 IF (beta.EQ.real(zero)) THEN
396 c(i,j) = alpha*temp1 + conjg(alpha)*temp2
397 ELSE
398 c(i,j) = beta*c(i,j) + alpha*temp1 +
399 + conjg(alpha)*temp2
400 END IF
401 END IF
402 200 CONTINUE
403 210 CONTINUE
404 ELSE
405 DO 240 j = 1,n
406 DO 230 i = j,n
407 temp1 = zero
408 temp2 = zero
409 DO 220 l = 1,k
410 temp1 = temp1 + conjg(a(l,i))*b(l,j)
411 temp2 = temp2 + conjg(b(l,i))*a(l,j)
412 220 CONTINUE
413 IF (i.EQ.j) THEN
414 IF (beta.EQ.real(zero)) THEN
415 c(j,j) = real(alpha*temp1+
416 + conjg(alpha)*temp2)
417 ELSE
418 c(j,j) = beta*real(c(j,j)) +
419 + real(alpha*temp1+
420 + conjg(alpha)*temp2)
421 END IF
422 ELSE
423 IF (beta.EQ.real(zero)) THEN
424 c(i,j) = alpha*temp1 + conjg(alpha)*temp2
425 ELSE
426 c(i,j) = beta*c(i,j) + alpha*temp1 +
427 + conjg(alpha)*temp2
428 END IF
429 END IF
430 230 CONTINUE
431 240 CONTINUE
432 END IF
433 END IF
434*
435 RETURN
436*
437* End of CHER2K
438*
439 END
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
cher2k
subroutine cher2k(uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
CHER2K
Definition cher2k.f:197