1: *> \brief \b ZHER
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 ZHER(UPLO,N,ALPHA,X,INCX,A,LDA)
12: *
13: * .. Scalar Arguments ..
14: * DOUBLE PRECISION ALPHA
15: * INTEGER INCX,LDA,N
16: * CHARACTER UPLO
17: * ..
18: * .. Array Arguments ..
19: * COMPLEX*16 A(LDA,*),X(*)
20: * ..
21: *
22: *
23: *> \par Purpose:
24: * =============
25: *>
26: *> \verbatim
27: *>
28: *> ZHER performs the hermitian rank 1 operation
29: *>
30: *> A := alpha*x*x**H + A,
31: *>
32: *> where alpha is a real scalar, x is an n element vector and A is an
33: *> n 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 DOUBLE PRECISION.
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,out] A
82: *> \verbatim
83: *> A is COMPLEX*16 array, dimension ( LDA, N )
84: *> Before entry with UPLO = 'U' or 'u', the leading n by n
85: *> upper triangular part of the array A must contain the upper
86: *> triangular part of the hermitian matrix and the strictly
87: *> lower triangular part of A is not referenced. On exit, the
88: *> upper triangular part of the array A is overwritten by the
89: *> upper triangular part of the updated matrix.
90: *> Before entry with UPLO = 'L' or 'l', the leading n by n
91: *> lower triangular part of the array A must contain the lower
92: *> triangular part of the hermitian matrix and the strictly
93: *> upper triangular part of A is not referenced. On exit, the
94: *> lower triangular part of the array A is overwritten by the
95: *> lower triangular part of the updated matrix.
96: *> Note that the imaginary parts of the diagonal elements need
97: *> not be set, they are assumed to be zero, and on exit they
98: *> are set to zero.
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. LDA must be at least
106: *> max( 1, n ).
107: *> \endverbatim
108: *
109: * Authors:
110: * ========
111: *
112: *> \author Univ. of Tennessee
113: *> \author Univ. of California Berkeley
114: *> \author Univ. of Colorado Denver
115: *> \author NAG Ltd.
116: *
117: *> \date December 2016
118: *
119: *> \ingroup complex16_blas_level2
120: *
121: *> \par Further Details:
122: * =====================
123: *>
124: *> \verbatim
125: *>
126: *> Level 2 Blas routine.
127: *>
128: *> -- Written on 22-October-1986.
129: *> Jack Dongarra, Argonne National Lab.
130: *> Jeremy Du Croz, Nag Central Office.
131: *> Sven Hammarling, Nag Central Office.
132: *> Richard Hanson, Sandia National Labs.
133: *> \endverbatim
134: *>
135: * =====================================================================
136: SUBROUTINE ZHER(UPLO,N,ALPHA,X,INCX,A,LDA)
137: *
138: * -- Reference BLAS level2 routine (version 3.7.0) --
139: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
140: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
141: * December 2016
142: *
143: * .. Scalar Arguments ..
144: DOUBLE PRECISION ALPHA
145: INTEGER INCX,LDA,N
146: CHARACTER UPLO
147: * ..
148: * .. Array Arguments ..
149: COMPLEX*16 A(LDA,*),X(*)
150: * ..
151: *
152: * =====================================================================
153: *
154: * .. Parameters ..
155: COMPLEX*16 ZERO
156: PARAMETER (ZERO= (0.0D+0,0.0D+0))
157: * ..
158: * .. Local Scalars ..
159: COMPLEX*16 TEMP
160: INTEGER I,INFO,IX,J,JX,KX
161: * ..
162: * .. External Functions ..
163: LOGICAL LSAME
164: EXTERNAL LSAME
165: * ..
166: * .. External Subroutines ..
167: EXTERNAL XERBLA
168: * ..
169: * .. Intrinsic Functions ..
170: INTRINSIC DBLE,DCONJG,MAX
171: * ..
172: *
173: * Test the input parameters.
174: *
175: INFO = 0
176: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
177: INFO = 1
178: ELSE IF (N.LT.0) THEN
179: INFO = 2
180: ELSE IF (INCX.EQ.0) THEN
181: INFO = 5
182: ELSE IF (LDA.LT.MAX(1,N)) THEN
183: INFO = 7
184: END IF
185: IF (INFO.NE.0) THEN
186: CALL XERBLA('ZHER ',INFO)
187: RETURN
188: END IF
189: *
190: * Quick return if possible.
191: *
192: IF ((N.EQ.0) .OR. (ALPHA.EQ.DBLE(ZERO))) RETURN
193: *
194: * Set the start point in X if the increment is not unity.
195: *
196: IF (INCX.LE.0) THEN
197: KX = 1 - (N-1)*INCX
198: ELSE IF (INCX.NE.1) THEN
199: KX = 1
200: END IF
201: *
202: * Start the operations. In this version the elements of A are
203: * accessed sequentially with one pass through the triangular part
204: * of A.
205: *
206: IF (LSAME(UPLO,'U')) THEN
207: *
208: * Form A when A is stored in upper triangle.
209: *
210: IF (INCX.EQ.1) THEN
211: DO 20 J = 1,N
212: IF (X(J).NE.ZERO) THEN
213: TEMP = ALPHA*DCONJG(X(J))
214: DO 10 I = 1,J - 1
215: A(I,J) = A(I,J) + X(I)*TEMP
216: 10 CONTINUE
217: A(J,J) = DBLE(A(J,J)) + DBLE(X(J)*TEMP)
218: ELSE
219: A(J,J) = DBLE(A(J,J))
220: END IF
221: 20 CONTINUE
222: ELSE
223: JX = KX
224: DO 40 J = 1,N
225: IF (X(JX).NE.ZERO) THEN
226: TEMP = ALPHA*DCONJG(X(JX))
227: IX = KX
228: DO 30 I = 1,J - 1
229: A(I,J) = A(I,J) + X(IX)*TEMP
230: IX = IX + INCX
231: 30 CONTINUE
232: A(J,J) = DBLE(A(J,J)) + DBLE(X(JX)*TEMP)
233: ELSE
234: A(J,J) = DBLE(A(J,J))
235: END IF
236: JX = JX + INCX
237: 40 CONTINUE
238: END IF
239: ELSE
240: *
241: * Form A when A is stored in lower triangle.
242: *
243: IF (INCX.EQ.1) THEN
244: DO 60 J = 1,N
245: IF (X(J).NE.ZERO) THEN
246: TEMP = ALPHA*DCONJG(X(J))
247: A(J,J) = DBLE(A(J,J)) + DBLE(TEMP*X(J))
248: DO 50 I = J + 1,N
249: A(I,J) = A(I,J) + X(I)*TEMP
250: 50 CONTINUE
251: ELSE
252: A(J,J) = DBLE(A(J,J))
253: END IF
254: 60 CONTINUE
255: ELSE
256: JX = KX
257: DO 80 J = 1,N
258: IF (X(JX).NE.ZERO) THEN
259: TEMP = ALPHA*DCONJG(X(JX))
260: A(J,J) = DBLE(A(J,J)) + DBLE(TEMP*X(JX))
261: IX = JX
262: DO 70 I = J + 1,N
263: IX = IX + INCX
264: A(I,J) = A(I,J) + X(IX)*TEMP
265: 70 CONTINUE
266: ELSE
267: A(J,J) = DBLE(A(J,J))
268: END IF
269: JX = JX + INCX
270: 80 CONTINUE
271: END IF
272: END IF
273: *
274: RETURN
275: *
276: * End of ZHER .
277: *
278: END
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