LAPACK  3.7.0 LAPACK: Linear Algebra PACKage
zsymm.f
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1 *> \brief \b ZSYMM
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 ZSYMM(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 *> ZSYMM 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 a symmetric 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 symmetric 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 symmetric matrix A is to be
59 *> referenced as follows:
60 *>
61 *> UPLO = 'U' or 'u' Only the upper triangular part of the
62 *> symmetric matrix is to be referenced.
63 *>
64 *> UPLO = 'L' or 'l' Only the lower triangular part of the
65 *> symmetric 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 of 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 symmetric 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 symmetric 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 symmetric
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 symmetric 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 symmetric 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 symmetric
110 *> matrix and the strictly upper triangular part of A is not
111 *> referenced.
112 *> \endverbatim
113 *>
114 *> \param[in] LDA
115 *> \verbatim
116 *> LDA is INTEGER
117 *> On entry, LDA specifies the first dimension of A as declared
118 *> in the calling (sub) program. When SIDE = 'L' or 'l' then
119 *> LDA must be at least max( 1, m ), otherwise LDA must be at
120 *> least max( 1, n ).
121 *> \endverbatim
122 *>
123 *> \param[in] B
124 *> \verbatim
125 *> B is COMPLEX*16 array of DIMENSION ( LDB, n ).
126 *> Before entry, the leading m by n part of the array B must
127 *> contain the matrix B.
128 *> \endverbatim
129 *>
130 *> \param[in] LDB
131 *> \verbatim
132 *> LDB is INTEGER
133 *> On entry, LDB specifies the first dimension of B as declared
134 *> in the calling (sub) program. LDB must be at least
135 *> max( 1, m ).
136 *> \endverbatim
137 *>
138 *> \param[in] BETA
139 *> \verbatim
140 *> BETA is COMPLEX*16
141 *> On entry, BETA specifies the scalar beta. When BETA is
142 *> supplied as zero then C need not be set on input.
143 *> \endverbatim
144 *>
145 *> \param[in,out] C
146 *> \verbatim
147 *> C is COMPLEX*16 array of DIMENSION ( LDC, n ).
148 *> Before entry, the leading m by n part of the array C must
149 *> contain the matrix C, except when beta is zero, in which
150 *> case C need not be set on entry.
151 *> On exit, the array C is overwritten by the m by n updated
152 *> matrix.
153 *> \endverbatim
154 *>
155 *> \param[in] LDC
156 *> \verbatim
157 *> LDC is INTEGER
158 *> On entry, LDC specifies the first dimension of C as declared
159 *> in the calling (sub) program. LDC must be at least
160 *> max( 1, m ).
161 *> \endverbatim
162 *
163 * Authors:
164 * ========
165 *
166 *> \author Univ. of Tennessee
167 *> \author Univ. of California Berkeley
168 *> \author Univ. of Colorado Denver
169 *> \author NAG Ltd.
170 *
171 *> \date December 2016
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 zsymm(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
191 *
192 * -- Reference BLAS level3 routine (version 3.7.0) --
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 * December 2016
196 *
197 * .. Scalar Arguments ..
198  COMPLEX*16 ALPHA,BETA
199  INTEGER LDA,LDB,LDC,M,N
200  CHARACTER SIDE,UPLO
201 * ..
202 * .. Array Arguments ..
203  COMPLEX*16 A(lda,*),B(ldb,*),C(ldc,*)
204 * ..
205 *
206 * =====================================================================
207 *
208 * .. External Functions ..
209  LOGICAL LSAME
210  EXTERNAL lsame
211 * ..
212 * .. External Subroutines ..
213  EXTERNAL xerbla
214 * ..
215 * .. Intrinsic Functions ..
216  INTRINSIC max
217 * ..
218 * .. Local Scalars ..
219  COMPLEX*16 TEMP1,TEMP2
220  INTEGER I,INFO,J,K,NROWA
221  LOGICAL UPPER
222 * ..
223 * .. Parameters ..
224  COMPLEX*16 ONE
225  parameter(one= (1.0d+0,0.0d+0))
226  COMPLEX*16 ZERO
227  parameter(zero= (0.0d+0,0.0d+0))
228 * ..
229 *
230 * Set NROWA as the number of rows of A.
231 *
232  IF (lsame(side,'L')) THEN
233  nrowa = m
234  ELSE
235  nrowa = n
236  END IF
237  upper = lsame(uplo,'U')
238 *
239 * Test the input parameters.
240 *
241  info = 0
242  IF ((.NOT.lsame(side,'L')) .AND. (.NOT.lsame(side,'R'))) THEN
243  info = 1
244  ELSE IF ((.NOT.upper) .AND. (.NOT.lsame(uplo,'L'))) THEN
245  info = 2
246  ELSE IF (m.LT.0) THEN
247  info = 3
248  ELSE IF (n.LT.0) THEN
249  info = 4
250  ELSE IF (lda.LT.max(1,nrowa)) THEN
251  info = 7
252  ELSE IF (ldb.LT.max(1,m)) THEN
253  info = 9
254  ELSE IF (ldc.LT.max(1,m)) THEN
255  info = 12
256  END IF
257  IF (info.NE.0) THEN
258  CALL xerbla('ZSYMM ',info)
259  RETURN
260  END IF
261 *
262 * Quick return if possible.
263 *
264  IF ((m.EQ.0) .OR. (n.EQ.0) .OR.
265  + ((alpha.EQ.zero).AND. (beta.EQ.one))) RETURN
266 *
267 * And when alpha.eq.zero.
268 *
269  IF (alpha.EQ.zero) THEN
270  IF (beta.EQ.zero) THEN
271  DO 20 j = 1,n
272  DO 10 i = 1,m
273  c(i,j) = zero
274  10 CONTINUE
275  20 CONTINUE
276  ELSE
277  DO 40 j = 1,n
278  DO 30 i = 1,m
279  c(i,j) = beta*c(i,j)
280  30 CONTINUE
281  40 CONTINUE
282  END IF
283  RETURN
284  END IF
285 *
286 * Start the operations.
287 *
288  IF (lsame(side,'L')) THEN
289 *
290 * Form C := alpha*A*B + beta*C.
291 *
292  IF (upper) THEN
293  DO 70 j = 1,n
294  DO 60 i = 1,m
295  temp1 = alpha*b(i,j)
296  temp2 = zero
297  DO 50 k = 1,i - 1
298  c(k,j) = c(k,j) + temp1*a(k,i)
299  temp2 = temp2 + b(k,j)*a(k,i)
300  50 CONTINUE
301  IF (beta.EQ.zero) THEN
302  c(i,j) = temp1*a(i,i) + alpha*temp2
303  ELSE
304  c(i,j) = beta*c(i,j) + temp1*a(i,i) +
305  + alpha*temp2
306  END IF
307  60 CONTINUE
308  70 CONTINUE
309  ELSE
310  DO 100 j = 1,n
311  DO 90 i = m,1,-1
312  temp1 = alpha*b(i,j)
313  temp2 = zero
314  DO 80 k = i + 1,m
315  c(k,j) = c(k,j) + temp1*a(k,i)
316  temp2 = temp2 + b(k,j)*a(k,i)
317  80 CONTINUE
318  IF (beta.EQ.zero) THEN
319  c(i,j) = temp1*a(i,i) + alpha*temp2
320  ELSE
321  c(i,j) = beta*c(i,j) + temp1*a(i,i) +
322  + alpha*temp2
323  END IF
324  90 CONTINUE
325  100 CONTINUE
326  END IF
327  ELSE
328 *
329 * Form C := alpha*B*A + beta*C.
330 *
331  DO 170 j = 1,n
332  temp1 = alpha*a(j,j)
333  IF (beta.EQ.zero) THEN
334  DO 110 i = 1,m
335  c(i,j) = temp1*b(i,j)
336  110 CONTINUE
337  ELSE
338  DO 120 i = 1,m
339  c(i,j) = beta*c(i,j) + temp1*b(i,j)
340  120 CONTINUE
341  END IF
342  DO 140 k = 1,j - 1
343  IF (upper) THEN
344  temp1 = alpha*a(k,j)
345  ELSE
346  temp1 = alpha*a(j,k)
347  END IF
348  DO 130 i = 1,m
349  c(i,j) = c(i,j) + temp1*b(i,k)
350  130 CONTINUE
351  140 CONTINUE
352  DO 160 k = j + 1,n
353  IF (upper) THEN
354  temp1 = alpha*a(j,k)
355  ELSE
356  temp1 = alpha*a(k,j)
357  END IF
358  DO 150 i = 1,m
359  c(i,j) = c(i,j) + temp1*b(i,k)
360  150 CONTINUE
361  160 CONTINUE
362  170 CONTINUE
363  END IF
364 *
365  RETURN
366 *
367 * End of ZSYMM .
368 *
369  END
subroutine zsymm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZSYMM
Definition: zsymm.f:191
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62