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1.1 bertrand 1: SUBROUTINE ZHEMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
2: * .. Scalar Arguments ..
3: DOUBLE COMPLEX ALPHA,BETA
4: INTEGER LDA,LDB,LDC,M,N
5: CHARACTER SIDE,UPLO
6: * ..
7: * .. Array Arguments ..
8: DOUBLE COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
9: * ..
10: *
11: * Purpose
12: * =======
13: *
14: * ZHEMM performs one of the matrix-matrix operations
15: *
16: * C := alpha*A*B + beta*C,
17: *
18: * or
19: *
20: * C := alpha*B*A + beta*C,
21: *
22: * where alpha and beta are scalars, A is an hermitian matrix and B and
23: * C are m by n matrices.
24: *
25: * Arguments
26: * ==========
27: *
28: * SIDE - CHARACTER*1.
29: * On entry, SIDE specifies whether the hermitian matrix A
30: * appears on the left or right in the operation as follows:
31: *
32: * SIDE = 'L' or 'l' C := alpha*A*B + beta*C,
33: *
34: * SIDE = 'R' or 'r' C := alpha*B*A + beta*C,
35: *
36: * Unchanged on exit.
37: *
38: * UPLO - CHARACTER*1.
39: * On entry, UPLO specifies whether the upper or lower
40: * triangular part of the hermitian matrix A is to be
41: * referenced as follows:
42: *
43: * UPLO = 'U' or 'u' Only the upper triangular part of the
44: * hermitian matrix is to be referenced.
45: *
46: * UPLO = 'L' or 'l' Only the lower triangular part of the
47: * hermitian matrix is to be referenced.
48: *
49: * Unchanged on exit.
50: *
51: * M - INTEGER.
52: * On entry, M specifies the number of rows of the matrix C.
53: * M must be at least zero.
54: * Unchanged on exit.
55: *
56: * N - INTEGER.
57: * On entry, N specifies the number of columns of the matrix C.
58: * N must be at least zero.
59: * Unchanged on exit.
60: *
61: * ALPHA - COMPLEX*16 .
62: * On entry, ALPHA specifies the scalar alpha.
63: * Unchanged on exit.
64: *
65: * A - COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is
66: * m when SIDE = 'L' or 'l' and is n otherwise.
67: * Before entry with SIDE = 'L' or 'l', the m by m part of
68: * the array A must contain the hermitian matrix, such that
69: * when UPLO = 'U' or 'u', the leading m by m upper triangular
70: * part of the array A must contain the upper triangular part
71: * of the hermitian matrix and the strictly lower triangular
72: * part of A is not referenced, and when UPLO = 'L' or 'l',
73: * the leading m by m lower triangular part of the array A
74: * must contain the lower triangular part of the hermitian
75: * matrix and the strictly upper triangular part of A is not
76: * referenced.
77: * Before entry with SIDE = 'R' or 'r', the n by n part of
78: * the array A must contain the hermitian matrix, such that
79: * when UPLO = 'U' or 'u', the leading n by n upper triangular
80: * part of the array A must contain the upper triangular part
81: * of the hermitian matrix and the strictly lower triangular
82: * part of A is not referenced, and when UPLO = 'L' or 'l',
83: * the leading n by n lower triangular part of the array A
84: * must contain the lower triangular part of the hermitian
85: * matrix and the strictly upper triangular part of A is not
86: * referenced.
87: * Note that the imaginary parts of the diagonal elements need
88: * not be set, they are assumed to be zero.
89: * Unchanged on exit.
90: *
91: * LDA - INTEGER.
92: * On entry, LDA specifies the first dimension of A as declared
93: * in the calling (sub) program. When SIDE = 'L' or 'l' then
94: * LDA must be at least max( 1, m ), otherwise LDA must be at
95: * least max( 1, n ).
96: * Unchanged on exit.
97: *
98: * B - COMPLEX*16 array of DIMENSION ( LDB, n ).
99: * Before entry, the leading m by n part of the array B must
100: * contain the matrix B.
101: * Unchanged on exit.
102: *
103: * LDB - INTEGER.
104: * On entry, LDB specifies the first dimension of B as declared
105: * in the calling (sub) program. LDB must be at least
106: * max( 1, m ).
107: * Unchanged on exit.
108: *
109: * BETA - COMPLEX*16 .
110: * On entry, BETA specifies the scalar beta. When BETA is
111: * supplied as zero then C need not be set on input.
112: * Unchanged on exit.
113: *
114: * C - COMPLEX*16 array of DIMENSION ( LDC, n ).
115: * Before entry, the leading m by n part of the array C must
116: * contain the matrix C, except when beta is zero, in which
117: * case C need not be set on entry.
118: * On exit, the array C is overwritten by the m by n updated
119: * matrix.
120: *
121: * LDC - INTEGER.
122: * On entry, LDC specifies the first dimension of C as declared
123: * in the calling (sub) program. LDC must be at least
124: * max( 1, m ).
125: * Unchanged on exit.
126: *
127: * Further Details
128: * ===============
129: *
130: * Level 3 Blas routine.
131: *
132: * -- Written on 8-February-1989.
133: * Jack Dongarra, Argonne National Laboratory.
134: * Iain Duff, AERE Harwell.
135: * Jeremy Du Croz, Numerical Algorithms Group Ltd.
136: * Sven Hammarling, Numerical Algorithms Group Ltd.
137: *
138: * =====================================================================
139: *
140: * .. External Functions ..
141: LOGICAL LSAME
142: EXTERNAL LSAME
143: * ..
144: * .. External Subroutines ..
145: EXTERNAL XERBLA
146: * ..
147: * .. Intrinsic Functions ..
148: INTRINSIC DBLE,DCONJG,MAX
149: * ..
150: * .. Local Scalars ..
151: DOUBLE COMPLEX TEMP1,TEMP2
152: INTEGER I,INFO,J,K,NROWA
153: LOGICAL UPPER
154: * ..
155: * .. Parameters ..
156: DOUBLE COMPLEX ONE
157: PARAMETER (ONE= (1.0D+0,0.0D+0))
158: DOUBLE COMPLEX ZERO
159: PARAMETER (ZERO= (0.0D+0,0.0D+0))
160: * ..
161: *
162: * Set NROWA as the number of rows of A.
163: *
164: IF (LSAME(SIDE,'L')) THEN
165: NROWA = M
166: ELSE
167: NROWA = N
168: END IF
169: UPPER = LSAME(UPLO,'U')
170: *
171: * Test the input parameters.
172: *
173: INFO = 0
174: IF ((.NOT.LSAME(SIDE,'L')) .AND. (.NOT.LSAME(SIDE,'R'))) THEN
175: INFO = 1
176: ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
177: INFO = 2
178: ELSE IF (M.LT.0) THEN
179: INFO = 3
180: ELSE IF (N.LT.0) THEN
181: INFO = 4
182: ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
183: INFO = 7
184: ELSE IF (LDB.LT.MAX(1,M)) THEN
185: INFO = 9
186: ELSE IF (LDC.LT.MAX(1,M)) THEN
187: INFO = 12
188: END IF
189: IF (INFO.NE.0) THEN
190: CALL XERBLA('ZHEMM ',INFO)
191: RETURN
192: END IF
193: *
194: * Quick return if possible.
195: *
196: IF ((M.EQ.0) .OR. (N.EQ.0) .OR.
197: + ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
198: *
199: * And when alpha.eq.zero.
200: *
201: IF (ALPHA.EQ.ZERO) THEN
202: IF (BETA.EQ.ZERO) THEN
203: DO 20 J = 1,N
204: DO 10 I = 1,M
205: C(I,J) = ZERO
206: 10 CONTINUE
207: 20 CONTINUE
208: ELSE
209: DO 40 J = 1,N
210: DO 30 I = 1,M
211: C(I,J) = BETA*C(I,J)
212: 30 CONTINUE
213: 40 CONTINUE
214: END IF
215: RETURN
216: END IF
217: *
218: * Start the operations.
219: *
220: IF (LSAME(SIDE,'L')) THEN
221: *
222: * Form C := alpha*A*B + beta*C.
223: *
224: IF (UPPER) THEN
225: DO 70 J = 1,N
226: DO 60 I = 1,M
227: TEMP1 = ALPHA*B(I,J)
228: TEMP2 = ZERO
229: DO 50 K = 1,I - 1
230: C(K,J) = C(K,J) + TEMP1*A(K,I)
231: TEMP2 = TEMP2 + B(K,J)*DCONJG(A(K,I))
232: 50 CONTINUE
233: IF (BETA.EQ.ZERO) THEN
234: C(I,J) = TEMP1*DBLE(A(I,I)) + ALPHA*TEMP2
235: ELSE
236: C(I,J) = BETA*C(I,J) + TEMP1*DBLE(A(I,I)) +
237: + ALPHA*TEMP2
238: END IF
239: 60 CONTINUE
240: 70 CONTINUE
241: ELSE
242: DO 100 J = 1,N
243: DO 90 I = M,1,-1
244: TEMP1 = ALPHA*B(I,J)
245: TEMP2 = ZERO
246: DO 80 K = I + 1,M
247: C(K,J) = C(K,J) + TEMP1*A(K,I)
248: TEMP2 = TEMP2 + B(K,J)*DCONJG(A(K,I))
249: 80 CONTINUE
250: IF (BETA.EQ.ZERO) THEN
251: C(I,J) = TEMP1*DBLE(A(I,I)) + ALPHA*TEMP2
252: ELSE
253: C(I,J) = BETA*C(I,J) + TEMP1*DBLE(A(I,I)) +
254: + ALPHA*TEMP2
255: END IF
256: 90 CONTINUE
257: 100 CONTINUE
258: END IF
259: ELSE
260: *
261: * Form C := alpha*B*A + beta*C.
262: *
263: DO 170 J = 1,N
264: TEMP1 = ALPHA*DBLE(A(J,J))
265: IF (BETA.EQ.ZERO) THEN
266: DO 110 I = 1,M
267: C(I,J) = TEMP1*B(I,J)
268: 110 CONTINUE
269: ELSE
270: DO 120 I = 1,M
271: C(I,J) = BETA*C(I,J) + TEMP1*B(I,J)
272: 120 CONTINUE
273: END IF
274: DO 140 K = 1,J - 1
275: IF (UPPER) THEN
276: TEMP1 = ALPHA*A(K,J)
277: ELSE
278: TEMP1 = ALPHA*DCONJG(A(J,K))
279: END IF
280: DO 130 I = 1,M
281: C(I,J) = C(I,J) + TEMP1*B(I,K)
282: 130 CONTINUE
283: 140 CONTINUE
284: DO 160 K = J + 1,N
285: IF (UPPER) THEN
286: TEMP1 = ALPHA*DCONJG(A(J,K))
287: ELSE
288: TEMP1 = ALPHA*A(K,J)
289: END IF
290: DO 150 I = 1,M
291: C(I,J) = C(I,J) + TEMP1*B(I,K)
292: 150 CONTINUE
293: 160 CONTINUE
294: 170 CONTINUE
295: END IF
296: *
297: RETURN
298: *
299: * End of ZHEMM .
300: *
301: END