LAPACK  3.10.0
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, 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, 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, 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 *> \ingroup complex16_blas_level3
172 *
173 *> \par Further Details:
174 * =====================
175 *>
176 *> \verbatim
177 *>
178 *> Level 3 Blas routine.
179 *>
180 *> -- Written on 8-February-1989.
181 *> Jack Dongarra, Argonne National Laboratory.
182 *> Iain Duff, AERE Harwell.
183 *> Jeremy Du Croz, Numerical Algorithms Group Ltd.
184 *> Sven Hammarling, Numerical Algorithms Group Ltd.
185 *> \endverbatim
186 *>
187 * =====================================================================
188  SUBROUTINE zsymm(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
189 *
190 * -- Reference BLAS level3 routine --
191 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
192 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
193 *
194 * .. Scalar Arguments ..
195  COMPLEX*16 ALPHA,BETA
196  INTEGER LDA,LDB,LDC,M,N
197  CHARACTER SIDE,UPLO
198 * ..
199 * .. Array Arguments ..
200  COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*)
201 * ..
202 *
203 * =====================================================================
204 *
205 * .. External Functions ..
206  LOGICAL LSAME
207  EXTERNAL lsame
208 * ..
209 * .. External Subroutines ..
210  EXTERNAL xerbla
211 * ..
212 * .. Intrinsic Functions ..
213  INTRINSIC max
214 * ..
215 * .. Local Scalars ..
216  COMPLEX*16 TEMP1,TEMP2
217  INTEGER I,INFO,J,K,NROWA
218  LOGICAL UPPER
219 * ..
220 * .. Parameters ..
221  COMPLEX*16 ONE
222  parameter(one= (1.0d+0,0.0d+0))
223  COMPLEX*16 ZERO
224  parameter(zero= (0.0d+0,0.0d+0))
225 * ..
226 *
227 * Set NROWA as the number of rows of A.
228 *
229  IF (lsame(side,'L')) THEN
230  nrowa = m
231  ELSE
232  nrowa = n
233  END IF
234  upper = lsame(uplo,'U')
235 *
236 * Test the input parameters.
237 *
238  info = 0
239  IF ((.NOT.lsame(side,'L')) .AND. (.NOT.lsame(side,'R'))) THEN
240  info = 1
241  ELSE IF ((.NOT.upper) .AND. (.NOT.lsame(uplo,'L'))) THEN
242  info = 2
243  ELSE IF (m.LT.0) THEN
244  info = 3
245  ELSE IF (n.LT.0) THEN
246  info = 4
247  ELSE IF (lda.LT.max(1,nrowa)) THEN
248  info = 7
249  ELSE IF (ldb.LT.max(1,m)) THEN
250  info = 9
251  ELSE IF (ldc.LT.max(1,m)) THEN
252  info = 12
253  END IF
254  IF (info.NE.0) THEN
255  CALL xerbla('ZSYMM ',info)
256  RETURN
257  END IF
258 *
259 * Quick return if possible.
260 *
261  IF ((m.EQ.0) .OR. (n.EQ.0) .OR.
262  + ((alpha.EQ.zero).AND. (beta.EQ.one))) RETURN
263 *
264 * And when alpha.eq.zero.
265 *
266  IF (alpha.EQ.zero) THEN
267  IF (beta.EQ.zero) THEN
268  DO 20 j = 1,n
269  DO 10 i = 1,m
270  c(i,j) = zero
271  10 CONTINUE
272  20 CONTINUE
273  ELSE
274  DO 40 j = 1,n
275  DO 30 i = 1,m
276  c(i,j) = beta*c(i,j)
277  30 CONTINUE
278  40 CONTINUE
279  END IF
280  RETURN
281  END IF
282 *
283 * Start the operations.
284 *
285  IF (lsame(side,'L')) THEN
286 *
287 * Form C := alpha*A*B + beta*C.
288 *
289  IF (upper) THEN
290  DO 70 j = 1,n
291  DO 60 i = 1,m
292  temp1 = alpha*b(i,j)
293  temp2 = zero
294  DO 50 k = 1,i - 1
295  c(k,j) = c(k,j) + temp1*a(k,i)
296  temp2 = temp2 + b(k,j)*a(k,i)
297  50 CONTINUE
298  IF (beta.EQ.zero) THEN
299  c(i,j) = temp1*a(i,i) + alpha*temp2
300  ELSE
301  c(i,j) = beta*c(i,j) + temp1*a(i,i) +
302  + alpha*temp2
303  END IF
304  60 CONTINUE
305  70 CONTINUE
306  ELSE
307  DO 100 j = 1,n
308  DO 90 i = m,1,-1
309  temp1 = alpha*b(i,j)
310  temp2 = zero
311  DO 80 k = i + 1,m
312  c(k,j) = c(k,j) + temp1*a(k,i)
313  temp2 = temp2 + b(k,j)*a(k,i)
314  80 CONTINUE
315  IF (beta.EQ.zero) THEN
316  c(i,j) = temp1*a(i,i) + alpha*temp2
317  ELSE
318  c(i,j) = beta*c(i,j) + temp1*a(i,i) +
319  + alpha*temp2
320  END IF
321  90 CONTINUE
322  100 CONTINUE
323  END IF
324  ELSE
325 *
326 * Form C := alpha*B*A + beta*C.
327 *
328  DO 170 j = 1,n
329  temp1 = alpha*a(j,j)
330  IF (beta.EQ.zero) THEN
331  DO 110 i = 1,m
332  c(i,j) = temp1*b(i,j)
333  110 CONTINUE
334  ELSE
335  DO 120 i = 1,m
336  c(i,j) = beta*c(i,j) + temp1*b(i,j)
337  120 CONTINUE
338  END IF
339  DO 140 k = 1,j - 1
340  IF (upper) THEN
341  temp1 = alpha*a(k,j)
342  ELSE
343  temp1 = alpha*a(j,k)
344  END IF
345  DO 130 i = 1,m
346  c(i,j) = c(i,j) + temp1*b(i,k)
347  130 CONTINUE
348  140 CONTINUE
349  DO 160 k = j + 1,n
350  IF (upper) THEN
351  temp1 = alpha*a(j,k)
352  ELSE
353  temp1 = alpha*a(k,j)
354  END IF
355  DO 150 i = 1,m
356  c(i,j) = c(i,j) + temp1*b(i,k)
357  150 CONTINUE
358  160 CONTINUE
359  170 CONTINUE
360  END IF
361 *
362  RETURN
363 *
364 * End of ZSYMM
365 *
366  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zsymm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZSYMM
Definition: zsymm.f:189