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
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