LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
zhemm.f
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1 *> \brief \b ZHEMM
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 ZHEMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
12 *
13 * .. Scalar Arguments ..
14 * COMPLEX*16 ALPHA,BETA
15 * INTEGER LDA,LDB,LDC,M,N
16 * CHARACTER SIDE,UPLO
17 * ..
18 * .. Array Arguments ..
19 * COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*)
20 * ..
21 *
22 *
23 *> \par Purpose:
24 * =============
25 *>
26 *> \verbatim
27 *>
28 *> ZHEMM performs one of the matrix-matrix operations
29 *>
30 *> C := alpha*A*B + beta*C,
31 *>
32 *> or
33 *>
34 *> C := alpha*B*A + beta*C,
35 *>
36 *> where alpha and beta are scalars, A is an hermitian matrix and B and
37 *> C are m by n matrices.
38 *> \endverbatim
39 *
40 * Arguments:
41 * ==========
42 *
43 *> \param[in] SIDE
44 *> \verbatim
45 *> SIDE is CHARACTER*1
46 *> On entry, SIDE specifies whether the hermitian matrix A
47 *> appears on the left or right in the operation as follows:
48 *>
49 *> SIDE = 'L' or 'l' C := alpha*A*B + beta*C,
50 *>
51 *> SIDE = 'R' or 'r' C := alpha*B*A + beta*C,
52 *> \endverbatim
53 *>
54 *> \param[in] UPLO
55 *> \verbatim
56 *> UPLO is CHARACTER*1
57 *> On entry, UPLO specifies whether the upper or lower
58 *> triangular part of the hermitian matrix A is to be
59 *> referenced as follows:
60 *>
61 *> UPLO = 'U' or 'u' Only the upper triangular part of the
62 *> hermitian matrix is to be referenced.
63 *>
64 *> UPLO = 'L' or 'l' Only the lower triangular part of the
65 *> hermitian matrix is to be referenced.
66 *> \endverbatim
67 *>
68 *> \param[in] M
69 *> \verbatim
70 *> M is INTEGER
71 *> On entry, M specifies the number of rows of the matrix C.
72 *> M must be at least zero.
73 *> \endverbatim
74 *>
75 *> \param[in] N
76 *> \verbatim
77 *> N is INTEGER
78 *> On entry, N specifies the number of columns of the matrix C.
79 *> N must be at least zero.
80 *> \endverbatim
81 *>
82 *> \param[in] ALPHA
83 *> \verbatim
84 *> ALPHA is COMPLEX*16
85 *> On entry, ALPHA specifies the scalar alpha.
86 *> \endverbatim
87 *>
88 *> \param[in] A
89 *> \verbatim
90 *> A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is
91 *> m when SIDE = 'L' or 'l' and is n otherwise.
92 *> Before entry with SIDE = 'L' or 'l', the m by m part of
93 *> the array A must contain the hermitian matrix, such that
94 *> when UPLO = 'U' or 'u', the leading m by m upper triangular
95 *> part of the array A must contain the upper triangular part
96 *> of the hermitian matrix and the strictly lower triangular
97 *> part of A is not referenced, and when UPLO = 'L' or 'l',
98 *> the leading m by m lower triangular part of the array A
99 *> must contain the lower triangular part of the hermitian
100 *> matrix and the strictly upper triangular part of A is not
101 *> referenced.
102 *> Before entry with SIDE = 'R' or 'r', the n by n part of
103 *> the array A must contain the hermitian matrix, such that
104 *> when UPLO = 'U' or 'u', the leading n by n upper triangular
105 *> part of the array A must contain the upper triangular part
106 *> of the hermitian matrix and the strictly lower triangular
107 *> part of A is not referenced, and when UPLO = 'L' or 'l',
108 *> the leading n by n lower triangular part of the array A
109 *> must contain the lower triangular part of the hermitian
110 *> matrix and the strictly upper triangular part of A is not
111 *> referenced.
112 *> Note that the imaginary parts of the diagonal elements need
113 *> not be set, they are assumed to be zero.
114 *> \endverbatim
115 *>
116 *> \param[in] LDA
117 *> \verbatim
118 *> LDA is INTEGER
119 *> On entry, LDA specifies the first dimension of A as declared
120 *> in the calling (sub) program. When SIDE = 'L' or 'l' then
121 *> LDA must be at least max( 1, m ), otherwise LDA must be at
122 *> least max( 1, n ).
123 *> \endverbatim
124 *>
125 *> \param[in] B
126 *> \verbatim
127 *> B is COMPLEX*16 array, dimension ( LDB, N )
128 *> Before entry, the leading m by n part of the array B must
129 *> contain the matrix B.
130 *> \endverbatim
131 *>
132 *> \param[in] LDB
133 *> \verbatim
134 *> LDB is INTEGER
135 *> On entry, LDB specifies the first dimension of B as declared
136 *> in the calling (sub) program. LDB must be at least
137 *> max( 1, m ).
138 *> \endverbatim
139 *>
140 *> \param[in] BETA
141 *> \verbatim
142 *> BETA is COMPLEX*16
143 *> On entry, BETA specifies the scalar beta. When BETA is
144 *> supplied as zero then C need not be set on input.
145 *> \endverbatim
146 *>
147 *> \param[in,out] C
148 *> \verbatim
149 *> C is COMPLEX*16 array, dimension ( LDC, N )
150 *> Before entry, the leading m by n part of the array C must
151 *> contain the matrix C, except when beta is zero, in which
152 *> case C need not be set on entry.
153 *> On exit, the array C is overwritten by the m by n updated
154 *> matrix.
155 *> \endverbatim
156 *>
157 *> \param[in] LDC
158 *> \verbatim
159 *> LDC is INTEGER
160 *> On entry, LDC specifies the first dimension of C as declared
161 *> in the calling (sub) program. LDC must be at least
162 *> max( 1, m ).
163 *> \endverbatim
164 *
165 * Authors:
166 * ========
167 *
168 *> \author Univ. of Tennessee
169 *> \author Univ. of California Berkeley
170 *> \author Univ. of Colorado Denver
171 *> \author NAG Ltd.
172 *
173 *> \ingroup complex16_blas_level3
174 *
175 *> \par Further Details:
176 * =====================
177 *>
178 *> \verbatim
179 *>
180 *> Level 3 Blas routine.
181 *>
182 *> -- Written on 8-February-1989.
183 *> Jack Dongarra, Argonne National Laboratory.
184 *> Iain Duff, AERE Harwell.
185 *> Jeremy Du Croz, Numerical Algorithms Group Ltd.
186 *> Sven Hammarling, Numerical Algorithms Group Ltd.
187 *> \endverbatim
188 *>
189 * =====================================================================
190  SUBROUTINE zhemm(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
191 *
192 * -- Reference BLAS level3 routine --
193 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
194 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
195 *
196 * .. Scalar Arguments ..
197  COMPLEX*16 ALPHA,BETA
198  INTEGER LDA,LDB,LDC,M,N
199  CHARACTER SIDE,UPLO
200 * ..
201 * .. Array Arguments ..
202  COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*)
203 * ..
204 *
205 * =====================================================================
206 *
207 * .. External Functions ..
208  LOGICAL LSAME
209  EXTERNAL lsame
210 * ..
211 * .. External Subroutines ..
212  EXTERNAL xerbla
213 * ..
214 * .. Intrinsic Functions ..
215  INTRINSIC dble,dconjg,max
216 * ..
217 * .. Local Scalars ..
218  COMPLEX*16 TEMP1,TEMP2
219  INTEGER I,INFO,J,K,NROWA
220  LOGICAL UPPER
221 * ..
222 * .. Parameters ..
223  COMPLEX*16 ONE
224  parameter(one= (1.0d+0,0.0d+0))
225  COMPLEX*16 ZERO
226  parameter(zero= (0.0d+0,0.0d+0))
227 * ..
228 *
229 * Set NROWA as the number of rows of A.
230 *
231  IF (lsame(side,'L')) THEN
232  nrowa = m
233  ELSE
234  nrowa = n
235  END IF
236  upper = lsame(uplo,'U')
237 *
238 * Test the input parameters.
239 *
240  info = 0
241  IF ((.NOT.lsame(side,'L')) .AND. (.NOT.lsame(side,'R'))) THEN
242  info = 1
243  ELSE IF ((.NOT.upper) .AND. (.NOT.lsame(uplo,'L'))) THEN
244  info = 2
245  ELSE IF (m.LT.0) THEN
246  info = 3
247  ELSE IF (n.LT.0) THEN
248  info = 4
249  ELSE IF (lda.LT.max(1,nrowa)) THEN
250  info = 7
251  ELSE IF (ldb.LT.max(1,m)) THEN
252  info = 9
253  ELSE IF (ldc.LT.max(1,m)) THEN
254  info = 12
255  END IF
256  IF (info.NE.0) THEN
257  CALL xerbla('ZHEMM ',info)
258  RETURN
259  END IF
260 *
261 * Quick return if possible.
262 *
263  IF ((m.EQ.0) .OR. (n.EQ.0) .OR.
264  + ((alpha.EQ.zero).AND. (beta.EQ.one))) RETURN
265 *
266 * And when alpha.eq.zero.
267 *
268  IF (alpha.EQ.zero) THEN
269  IF (beta.EQ.zero) THEN
270  DO 20 j = 1,n
271  DO 10 i = 1,m
272  c(i,j) = zero
273  10 CONTINUE
274  20 CONTINUE
275  ELSE
276  DO 40 j = 1,n
277  DO 30 i = 1,m
278  c(i,j) = beta*c(i,j)
279  30 CONTINUE
280  40 CONTINUE
281  END IF
282  RETURN
283  END IF
284 *
285 * Start the operations.
286 *
287  IF (lsame(side,'L')) THEN
288 *
289 * Form C := alpha*A*B + beta*C.
290 *
291  IF (upper) THEN
292  DO 70 j = 1,n
293  DO 60 i = 1,m
294  temp1 = alpha*b(i,j)
295  temp2 = zero
296  DO 50 k = 1,i - 1
297  c(k,j) = c(k,j) + temp1*a(k,i)
298  temp2 = temp2 + b(k,j)*dconjg(a(k,i))
299  50 CONTINUE
300  IF (beta.EQ.zero) THEN
301  c(i,j) = temp1*dble(a(i,i)) + alpha*temp2
302  ELSE
303  c(i,j) = beta*c(i,j) + temp1*dble(a(i,i)) +
304  + alpha*temp2
305  END IF
306  60 CONTINUE
307  70 CONTINUE
308  ELSE
309  DO 100 j = 1,n
310  DO 90 i = m,1,-1
311  temp1 = alpha*b(i,j)
312  temp2 = zero
313  DO 80 k = i + 1,m
314  c(k,j) = c(k,j) + temp1*a(k,i)
315  temp2 = temp2 + b(k,j)*dconjg(a(k,i))
316  80 CONTINUE
317  IF (beta.EQ.zero) THEN
318  c(i,j) = temp1*dble(a(i,i)) + alpha*temp2
319  ELSE
320  c(i,j) = beta*c(i,j) + temp1*dble(a(i,i)) +
321  + alpha*temp2
322  END IF
323  90 CONTINUE
324  100 CONTINUE
325  END IF
326  ELSE
327 *
328 * Form C := alpha*B*A + beta*C.
329 *
330  DO 170 j = 1,n
331  temp1 = alpha*dble(a(j,j))
332  IF (beta.EQ.zero) THEN
333  DO 110 i = 1,m
334  c(i,j) = temp1*b(i,j)
335  110 CONTINUE
336  ELSE
337  DO 120 i = 1,m
338  c(i,j) = beta*c(i,j) + temp1*b(i,j)
339  120 CONTINUE
340  END IF
341  DO 140 k = 1,j - 1
342  IF (upper) THEN
343  temp1 = alpha*a(k,j)
344  ELSE
345  temp1 = alpha*dconjg(a(j,k))
346  END IF
347  DO 130 i = 1,m
348  c(i,j) = c(i,j) + temp1*b(i,k)
349  130 CONTINUE
350  140 CONTINUE
351  DO 160 k = j + 1,n
352  IF (upper) THEN
353  temp1 = alpha*dconjg(a(j,k))
354  ELSE
355  temp1 = alpha*a(k,j)
356  END IF
357  DO 150 i = 1,m
358  c(i,j) = c(i,j) + temp1*b(i,k)
359  150 CONTINUE
360  160 CONTINUE
361  170 CONTINUE
362  END IF
363 *
364  RETURN
365 *
366 * End of ZHEMM
367 *
368  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zhemm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZHEMM
Definition: zhemm.f:191