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
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