1: *> \brief \b ZHER2
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 ZHER2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA)
12: *
13: * .. Scalar Arguments ..
14: * COMPLEX*16 ALPHA
15: * INTEGER INCX,INCY,LDA,N
16: * CHARACTER UPLO
17: * ..
18: * .. Array Arguments ..
19: * COMPLEX*16 A(LDA,*),X(*),Y(*)
20: * ..
21: *
22: *
23: *> \par Purpose:
24: * =============
25: *>
26: *> \verbatim
27: *>
28: *> ZHER2 performs the hermitian rank 2 operation
29: *>
30: *> A := alpha*x*y**H + conjg( alpha )*y*x**H + A,
31: *>
32: *> where alpha is a scalar, x and y are n element vectors and A is an n
33: *> by n hermitian matrix.
34: *> \endverbatim
35: *
36: * Arguments:
37: * ==========
38: *
39: *> \param[in] UPLO
40: *> \verbatim
41: *> UPLO is CHARACTER*1
42: *> On entry, UPLO specifies whether the upper or lower
43: *> triangular part of the array A is to be referenced as
44: *> follows:
45: *>
46: *> UPLO = 'U' or 'u' Only the upper triangular part of A
47: *> is to be referenced.
48: *>
49: *> UPLO = 'L' or 'l' Only the lower triangular part of A
50: *> is to be referenced.
51: *> \endverbatim
52: *>
53: *> \param[in] N
54: *> \verbatim
55: *> N is INTEGER
56: *> On entry, N specifies the order of the matrix A.
57: *> N must be at least zero.
58: *> \endverbatim
59: *>
60: *> \param[in] ALPHA
61: *> \verbatim
62: *> ALPHA is COMPLEX*16
63: *> On entry, ALPHA specifies the scalar alpha.
64: *> \endverbatim
65: *>
66: *> \param[in] X
67: *> \verbatim
68: *> X is COMPLEX*16 array, dimension at least
69: *> ( 1 + ( n - 1 )*abs( INCX ) ).
70: *> Before entry, the incremented array X must contain the n
71: *> element vector x.
72: *> \endverbatim
73: *>
74: *> \param[in] INCX
75: *> \verbatim
76: *> INCX is INTEGER
77: *> On entry, INCX specifies the increment for the elements of
78: *> X. INCX must not be zero.
79: *> \endverbatim
80: *>
81: *> \param[in] Y
82: *> \verbatim
83: *> Y is COMPLEX*16 array, dimension at least
84: *> ( 1 + ( n - 1 )*abs( INCY ) ).
85: *> Before entry, the incremented array Y must contain the n
86: *> element vector y.
87: *> \endverbatim
88: *>
89: *> \param[in] INCY
90: *> \verbatim
91: *> INCY is INTEGER
92: *> On entry, INCY specifies the increment for the elements of
93: *> Y. INCY must not be zero.
94: *> \endverbatim
95: *>
96: *> \param[in,out] A
97: *> \verbatim
98: *> A is COMPLEX*16 array, dimension ( LDA, N )
99: *> Before entry with UPLO = 'U' or 'u', the leading n by n
100: *> upper triangular part of the array A must contain the upper
101: *> triangular part of the hermitian matrix and the strictly
102: *> lower triangular part of A is not referenced. On exit, the
103: *> upper triangular part of the array A is overwritten by the
104: *> upper triangular part of the updated matrix.
105: *> Before entry with UPLO = 'L' or 'l', the leading n by n
106: *> lower triangular part of the array A must contain the lower
107: *> triangular part of the hermitian matrix and the strictly
108: *> upper triangular part of A is not referenced. On exit, the
109: *> lower triangular part of the array A is overwritten by the
110: *> lower triangular part of the updated matrix.
111: *> Note that the imaginary parts of the diagonal elements need
112: *> not be set, they are assumed to be zero, and on exit they
113: *> are set to 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. LDA must be at least
121: *> max( 1, n ).
122: *> \endverbatim
123: *
124: * Authors:
125: * ========
126: *
127: *> \author Univ. of Tennessee
128: *> \author Univ. of California Berkeley
129: *> \author Univ. of Colorado Denver
130: *> \author NAG Ltd.
131: *
132: *> \ingroup complex16_blas_level2
133: *
134: *> \par Further Details:
135: * =====================
136: *>
137: *> \verbatim
138: *>
139: *> Level 2 Blas routine.
140: *>
141: *> -- Written on 22-October-1986.
142: *> Jack Dongarra, Argonne National Lab.
143: *> Jeremy Du Croz, Nag Central Office.
144: *> Sven Hammarling, Nag Central Office.
145: *> Richard Hanson, Sandia National Labs.
146: *> \endverbatim
147: *>
148: * =====================================================================
149: SUBROUTINE ZHER2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA)
150: *
151: * -- Reference BLAS level2 routine --
152: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
153: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
154: *
155: * .. Scalar Arguments ..
156: COMPLEX*16 ALPHA
157: INTEGER INCX,INCY,LDA,N
158: CHARACTER UPLO
159: * ..
160: * .. Array Arguments ..
161: COMPLEX*16 A(LDA,*),X(*),Y(*)
162: * ..
163: *
164: * =====================================================================
165: *
166: * .. Parameters ..
167: COMPLEX*16 ZERO
168: PARAMETER (ZERO= (0.0D+0,0.0D+0))
169: * ..
170: * .. Local Scalars ..
171: COMPLEX*16 TEMP1,TEMP2
172: INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY
173: * ..
174: * .. External Functions ..
175: LOGICAL LSAME
176: EXTERNAL LSAME
177: * ..
178: * .. External Subroutines ..
179: EXTERNAL XERBLA
180: * ..
181: * .. Intrinsic Functions ..
182: INTRINSIC DBLE,DCONJG,MAX
183: * ..
184: *
185: * Test the input parameters.
186: *
187: INFO = 0
188: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
189: INFO = 1
190: ELSE IF (N.LT.0) THEN
191: INFO = 2
192: ELSE IF (INCX.EQ.0) THEN
193: INFO = 5
194: ELSE IF (INCY.EQ.0) THEN
195: INFO = 7
196: ELSE IF (LDA.LT.MAX(1,N)) THEN
197: INFO = 9
198: END IF
199: IF (INFO.NE.0) THEN
200: CALL XERBLA('ZHER2 ',INFO)
201: RETURN
202: END IF
203: *
204: * Quick return if possible.
205: *
206: IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN
207: *
208: * Set up the start points in X and Y if the increments are not both
209: * unity.
210: *
211: IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN
212: IF (INCX.GT.0) THEN
213: KX = 1
214: ELSE
215: KX = 1 - (N-1)*INCX
216: END IF
217: IF (INCY.GT.0) THEN
218: KY = 1
219: ELSE
220: KY = 1 - (N-1)*INCY
221: END IF
222: JX = KX
223: JY = KY
224: END IF
225: *
226: * Start the operations. In this version the elements of A are
227: * accessed sequentially with one pass through the triangular part
228: * of A.
229: *
230: IF (LSAME(UPLO,'U')) THEN
231: *
232: * Form A when A is stored in the upper triangle.
233: *
234: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
235: DO 20 J = 1,N
236: IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
237: TEMP1 = ALPHA*DCONJG(Y(J))
238: TEMP2 = DCONJG(ALPHA*X(J))
239: DO 10 I = 1,J - 1
240: A(I,J) = A(I,J) + X(I)*TEMP1 + Y(I)*TEMP2
241: 10 CONTINUE
242: A(J,J) = DBLE(A(J,J)) +
243: + DBLE(X(J)*TEMP1+Y(J)*TEMP2)
244: ELSE
245: A(J,J) = DBLE(A(J,J))
246: END IF
247: 20 CONTINUE
248: ELSE
249: DO 40 J = 1,N
250: IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
251: TEMP1 = ALPHA*DCONJG(Y(JY))
252: TEMP2 = DCONJG(ALPHA*X(JX))
253: IX = KX
254: IY = KY
255: DO 30 I = 1,J - 1
256: A(I,J) = A(I,J) + X(IX)*TEMP1 + Y(IY)*TEMP2
257: IX = IX + INCX
258: IY = IY + INCY
259: 30 CONTINUE
260: A(J,J) = DBLE(A(J,J)) +
261: + DBLE(X(JX)*TEMP1+Y(JY)*TEMP2)
262: ELSE
263: A(J,J) = DBLE(A(J,J))
264: END IF
265: JX = JX + INCX
266: JY = JY + INCY
267: 40 CONTINUE
268: END IF
269: ELSE
270: *
271: * Form A when A is stored in the lower triangle.
272: *
273: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
274: DO 60 J = 1,N
275: IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
276: TEMP1 = ALPHA*DCONJG(Y(J))
277: TEMP2 = DCONJG(ALPHA*X(J))
278: A(J,J) = DBLE(A(J,J)) +
279: + DBLE(X(J)*TEMP1+Y(J)*TEMP2)
280: DO 50 I = J + 1,N
281: A(I,J) = A(I,J) + X(I)*TEMP1 + Y(I)*TEMP2
282: 50 CONTINUE
283: ELSE
284: A(J,J) = DBLE(A(J,J))
285: END IF
286: 60 CONTINUE
287: ELSE
288: DO 80 J = 1,N
289: IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
290: TEMP1 = ALPHA*DCONJG(Y(JY))
291: TEMP2 = DCONJG(ALPHA*X(JX))
292: A(J,J) = DBLE(A(J,J)) +
293: + DBLE(X(JX)*TEMP1+Y(JY)*TEMP2)
294: IX = JX
295: IY = JY
296: DO 70 I = J + 1,N
297: IX = IX + INCX
298: IY = IY + INCY
299: A(I,J) = A(I,J) + X(IX)*TEMP1 + Y(IY)*TEMP2
300: 70 CONTINUE
301: ELSE
302: A(J,J) = DBLE(A(J,J))
303: END IF
304: JX = JX + INCX
305: JY = JY + INCY
306: 80 CONTINUE
307: END IF
308: END IF
309: *
310: RETURN
311: *
312: * End of ZHER2
313: *
314: END
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