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: *> \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
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