1: *> \brief \b ZSYRK
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 ZSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
12: *
13: * .. Scalar Arguments ..
14: * COMPLEX*16 ALPHA,BETA
15: * INTEGER K,LDA,LDC,N
16: * CHARACTER TRANS,UPLO
17: * ..
18: * .. Array Arguments ..
19: * COMPLEX*16 A(LDA,*),C(LDC,*)
20: * ..
21: *
22: *
23: *> \par Purpose:
24: * =============
25: *>
26: *> \verbatim
27: *>
28: *> ZSYRK performs one of the symmetric rank k operations
29: *>
30: *> C := alpha*A*A**T + beta*C,
31: *>
32: *> or
33: *>
34: *> C := alpha*A**T*A + beta*C,
35: *>
36: *> where alpha and beta are scalars, C is an n by n symmetric matrix
37: *> and A is an n by k matrix in the first case and a k by n matrix
38: *> in the second case.
39: *> \endverbatim
40: *
41: * Arguments:
42: * ==========
43: *
44: *> \param[in] UPLO
45: *> \verbatim
46: *> UPLO is CHARACTER*1
47: *> On entry, UPLO specifies whether the upper or lower
48: *> triangular part of the array C is to be referenced as
49: *> follows:
50: *>
51: *> UPLO = 'U' or 'u' Only the upper triangular part of C
52: *> is to be referenced.
53: *>
54: *> UPLO = 'L' or 'l' Only the lower triangular part of C
55: *> is to be referenced.
56: *> \endverbatim
57: *>
58: *> \param[in] TRANS
59: *> \verbatim
60: *> TRANS is CHARACTER*1
61: *> On entry, TRANS specifies the operation to be performed as
62: *> follows:
63: *>
64: *> TRANS = 'N' or 'n' C := alpha*A*A**T + beta*C.
65: *>
66: *> TRANS = 'T' or 't' C := alpha*A**T*A + beta*C.
67: *> \endverbatim
68: *>
69: *> \param[in] N
70: *> \verbatim
71: *> N is INTEGER
72: *> On entry, N specifies the order of the matrix C. N must be
73: *> at least zero.
74: *> \endverbatim
75: *>
76: *> \param[in] K
77: *> \verbatim
78: *> K is INTEGER
79: *> On entry with TRANS = 'N' or 'n', K specifies the number
80: *> of columns of the matrix A, and on entry with
81: *> TRANS = 'T' or 't', K specifies the number of rows of the
82: *> matrix A. K must be at least zero.
83: *> \endverbatim
84: *>
85: *> \param[in] ALPHA
86: *> \verbatim
87: *> ALPHA is COMPLEX*16
88: *> On entry, ALPHA specifies the scalar alpha.
89: *> \endverbatim
90: *>
91: *> \param[in] A
92: *> \verbatim
93: *> A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is
94: *> k when TRANS = 'N' or 'n', and is n otherwise.
95: *> Before entry with TRANS = 'N' or 'n', the leading n by k
96: *> part of the array A must contain the matrix A, otherwise
97: *> the leading k by n part of the array A must contain the
98: *> matrix A.
99: *> \endverbatim
100: *>
101: *> \param[in] LDA
102: *> \verbatim
103: *> LDA is INTEGER
104: *> On entry, LDA specifies the first dimension of A as declared
105: *> in the calling (sub) program. When TRANS = 'N' or 'n'
106: *> then LDA must be at least max( 1, n ), otherwise LDA must
107: *> be at least max( 1, k ).
108: *> \endverbatim
109: *>
110: *> \param[in] BETA
111: *> \verbatim
112: *> BETA is COMPLEX*16
113: *> On entry, BETA specifies the scalar beta.
114: *> \endverbatim
115: *>
116: *> \param[in,out] C
117: *> \verbatim
118: *> C is COMPLEX*16 array, dimension ( LDC, N )
119: *> Before entry with UPLO = 'U' or 'u', the leading n by n
120: *> upper triangular part of the array C must contain the upper
121: *> triangular part of the symmetric matrix and the strictly
122: *> lower triangular part of C is not referenced. On exit, the
123: *> upper triangular part of the array C is overwritten by the
124: *> upper triangular part of the updated matrix.
125: *> Before entry with UPLO = 'L' or 'l', the leading n by n
126: *> lower triangular part of the array C must contain the lower
127: *> triangular part of the symmetric matrix and the strictly
128: *> upper triangular part of C is not referenced. On exit, the
129: *> lower triangular part of the array C is overwritten by the
130: *> lower triangular part of the updated matrix.
131: *> \endverbatim
132: *>
133: *> \param[in] LDC
134: *> \verbatim
135: *> LDC is INTEGER
136: *> On entry, LDC specifies the first dimension of C as declared
137: *> in the calling (sub) program. LDC must be at least
138: *> max( 1, n ).
139: *> \endverbatim
140: *
141: * Authors:
142: * ========
143: *
144: *> \author Univ. of Tennessee
145: *> \author Univ. of California Berkeley
146: *> \author Univ. of Colorado Denver
147: *> \author NAG Ltd.
148: *
149: *> \date December 2016
150: *
151: *> \ingroup complex16_blas_level3
152: *
153: *> \par Further Details:
154: * =====================
155: *>
156: *> \verbatim
157: *>
158: *> Level 3 Blas routine.
159: *>
160: *> -- Written on 8-February-1989.
161: *> Jack Dongarra, Argonne National Laboratory.
162: *> Iain Duff, AERE Harwell.
163: *> Jeremy Du Croz, Numerical Algorithms Group Ltd.
164: *> Sven Hammarling, Numerical Algorithms Group Ltd.
165: *> \endverbatim
166: *>
167: * =====================================================================
168: SUBROUTINE ZSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
169: *
170: * -- Reference BLAS level3 routine (version 3.7.0) --
171: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
172: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
173: * December 2016
174: *
175: * .. Scalar Arguments ..
176: COMPLEX*16 ALPHA,BETA
177: INTEGER K,LDA,LDC,N
178: CHARACTER TRANS,UPLO
179: * ..
180: * .. Array Arguments ..
181: COMPLEX*16 A(LDA,*),C(LDC,*)
182: * ..
183: *
184: * =====================================================================
185: *
186: * .. External Functions ..
187: LOGICAL LSAME
188: EXTERNAL LSAME
189: * ..
190: * .. External Subroutines ..
191: EXTERNAL XERBLA
192: * ..
193: * .. Intrinsic Functions ..
194: INTRINSIC MAX
195: * ..
196: * .. Local Scalars ..
197: COMPLEX*16 TEMP
198: INTEGER I,INFO,J,L,NROWA
199: LOGICAL UPPER
200: * ..
201: * .. Parameters ..
202: COMPLEX*16 ONE
203: PARAMETER (ONE= (1.0D+0,0.0D+0))
204: COMPLEX*16 ZERO
205: PARAMETER (ZERO= (0.0D+0,0.0D+0))
206: * ..
207: *
208: * Test the input parameters.
209: *
210: IF (LSAME(TRANS,'N')) THEN
211: NROWA = N
212: ELSE
213: NROWA = K
214: END IF
215: UPPER = LSAME(UPLO,'U')
216: *
217: INFO = 0
218: IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
219: INFO = 1
220: ELSE IF ((.NOT.LSAME(TRANS,'N')) .AND.
221: + (.NOT.LSAME(TRANS,'T'))) THEN
222: INFO = 2
223: ELSE IF (N.LT.0) THEN
224: INFO = 3
225: ELSE IF (K.LT.0) THEN
226: INFO = 4
227: ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
228: INFO = 7
229: ELSE IF (LDC.LT.MAX(1,N)) THEN
230: INFO = 10
231: END IF
232: IF (INFO.NE.0) THEN
233: CALL XERBLA('ZSYRK ',INFO)
234: RETURN
235: END IF
236: *
237: * Quick return if possible.
238: *
239: IF ((N.EQ.0) .OR. (((ALPHA.EQ.ZERO).OR.
240: + (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN
241: *
242: * And when alpha.eq.zero.
243: *
244: IF (ALPHA.EQ.ZERO) THEN
245: IF (UPPER) THEN
246: IF (BETA.EQ.ZERO) THEN
247: DO 20 J = 1,N
248: DO 10 I = 1,J
249: C(I,J) = ZERO
250: 10 CONTINUE
251: 20 CONTINUE
252: ELSE
253: DO 40 J = 1,N
254: DO 30 I = 1,J
255: C(I,J) = BETA*C(I,J)
256: 30 CONTINUE
257: 40 CONTINUE
258: END IF
259: ELSE
260: IF (BETA.EQ.ZERO) THEN
261: DO 60 J = 1,N
262: DO 50 I = J,N
263: C(I,J) = ZERO
264: 50 CONTINUE
265: 60 CONTINUE
266: ELSE
267: DO 80 J = 1,N
268: DO 70 I = J,N
269: C(I,J) = BETA*C(I,J)
270: 70 CONTINUE
271: 80 CONTINUE
272: END IF
273: END IF
274: RETURN
275: END IF
276: *
277: * Start the operations.
278: *
279: IF (LSAME(TRANS,'N')) THEN
280: *
281: * Form C := alpha*A*A**T + beta*C.
282: *
283: IF (UPPER) THEN
284: DO 130 J = 1,N
285: IF (BETA.EQ.ZERO) THEN
286: DO 90 I = 1,J
287: C(I,J) = ZERO
288: 90 CONTINUE
289: ELSE IF (BETA.NE.ONE) THEN
290: DO 100 I = 1,J
291: C(I,J) = BETA*C(I,J)
292: 100 CONTINUE
293: END IF
294: DO 120 L = 1,K
295: IF (A(J,L).NE.ZERO) THEN
296: TEMP = ALPHA*A(J,L)
297: DO 110 I = 1,J
298: C(I,J) = C(I,J) + TEMP*A(I,L)
299: 110 CONTINUE
300: END IF
301: 120 CONTINUE
302: 130 CONTINUE
303: ELSE
304: DO 180 J = 1,N
305: IF (BETA.EQ.ZERO) THEN
306: DO 140 I = J,N
307: C(I,J) = ZERO
308: 140 CONTINUE
309: ELSE IF (BETA.NE.ONE) THEN
310: DO 150 I = J,N
311: C(I,J) = BETA*C(I,J)
312: 150 CONTINUE
313: END IF
314: DO 170 L = 1,K
315: IF (A(J,L).NE.ZERO) THEN
316: TEMP = ALPHA*A(J,L)
317: DO 160 I = J,N
318: C(I,J) = C(I,J) + TEMP*A(I,L)
319: 160 CONTINUE
320: END IF
321: 170 CONTINUE
322: 180 CONTINUE
323: END IF
324: ELSE
325: *
326: * Form C := alpha*A**T*A + beta*C.
327: *
328: IF (UPPER) THEN
329: DO 210 J = 1,N
330: DO 200 I = 1,J
331: TEMP = ZERO
332: DO 190 L = 1,K
333: TEMP = TEMP + A(L,I)*A(L,J)
334: 190 CONTINUE
335: IF (BETA.EQ.ZERO) THEN
336: C(I,J) = ALPHA*TEMP
337: ELSE
338: C(I,J) = ALPHA*TEMP + BETA*C(I,J)
339: END IF
340: 200 CONTINUE
341: 210 CONTINUE
342: ELSE
343: DO 240 J = 1,N
344: DO 230 I = J,N
345: TEMP = ZERO
346: DO 220 L = 1,K
347: TEMP = TEMP + A(L,I)*A(L,J)
348: 220 CONTINUE
349: IF (BETA.EQ.ZERO) THEN
350: C(I,J) = ALPHA*TEMP
351: ELSE
352: C(I,J) = ALPHA*TEMP + BETA*C(I,J)
353: END IF
354: 230 CONTINUE
355: 240 CONTINUE
356: END IF
357: END IF
358: *
359: RETURN
360: *
361: * End of ZSYRK .
362: *
363: END
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