LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
cher.f
Go to the documentation of this file.
1 *> \brief \b CHER
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 CHER(UPLO,N,ALPHA,X,INCX,A,LDA)
12 *
13 * .. Scalar Arguments ..
14 * REAL ALPHA
15 * INTEGER INCX,LDA,N
16 * CHARACTER UPLO
17 * ..
18 * .. Array Arguments ..
19 * COMPLEX A(LDA,*),X(*)
20 * ..
21 *
22 *
23 *> \par Purpose:
24 * =============
25 *>
26 *> \verbatim
27 *>
28 *> CHER 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 REAL
63 *> On entry, ALPHA specifies the scalar alpha.
64 *> \endverbatim
65 *>
66 *> \param[in] X
67 *> \verbatim
68 *> X is COMPLEX 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 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 *> \ingroup complex_blas_level2
118 *
119 *> \par Further Details:
120 * =====================
121 *>
122 *> \verbatim
123 *>
124 *> Level 2 Blas routine.
125 *>
126 *> -- Written on 22-October-1986.
127 *> Jack Dongarra, Argonne National Lab.
128 *> Jeremy Du Croz, Nag Central Office.
129 *> Sven Hammarling, Nag Central Office.
130 *> Richard Hanson, Sandia National Labs.
131 *> \endverbatim
132 *>
133 * =====================================================================
134  SUBROUTINE cher(UPLO,N,ALPHA,X,INCX,A,LDA)
135 *
136 * -- Reference BLAS level2 routine --
137 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
138 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
139 *
140 * .. Scalar Arguments ..
141  REAL ALPHA
142  INTEGER INCX,LDA,N
143  CHARACTER UPLO
144 * ..
145 * .. Array Arguments ..
146  COMPLEX A(LDA,*),X(*)
147 * ..
148 *
149 * =====================================================================
150 *
151 * .. Parameters ..
152  COMPLEX ZERO
153  parameter(zero= (0.0e+0,0.0e+0))
154 * ..
155 * .. Local Scalars ..
156  COMPLEX TEMP
157  INTEGER I,INFO,IX,J,JX,KX
158 * ..
159 * .. External Functions ..
160  LOGICAL LSAME
161  EXTERNAL lsame
162 * ..
163 * .. External Subroutines ..
164  EXTERNAL xerbla
165 * ..
166 * .. Intrinsic Functions ..
167  INTRINSIC conjg,max,real
168 * ..
169 *
170 * Test the input parameters.
171 *
172  info = 0
173  IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
174  info = 1
175  ELSE IF (n.LT.0) THEN
176  info = 2
177  ELSE IF (incx.EQ.0) THEN
178  info = 5
179  ELSE IF (lda.LT.max(1,n)) THEN
180  info = 7
181  END IF
182  IF (info.NE.0) THEN
183  CALL xerbla('CHER ',info)
184  RETURN
185  END IF
186 *
187 * Quick return if possible.
188 *
189  IF ((n.EQ.0) .OR. (alpha.EQ.real(zero))) RETURN
190 *
191 * Set the start point in X if the increment is not unity.
192 *
193  IF (incx.LE.0) THEN
194  kx = 1 - (n-1)*incx
195  ELSE IF (incx.NE.1) THEN
196  kx = 1
197  END IF
198 *
199 * Start the operations. In this version the elements of A are
200 * accessed sequentially with one pass through the triangular part
201 * of A.
202 *
203  IF (lsame(uplo,'U')) THEN
204 *
205 * Form A when A is stored in upper triangle.
206 *
207  IF (incx.EQ.1) THEN
208  DO 20 j = 1,n
209  IF (x(j).NE.zero) THEN
210  temp = alpha*conjg(x(j))
211  DO 10 i = 1,j - 1
212  a(i,j) = a(i,j) + x(i)*temp
213  10 CONTINUE
214  a(j,j) = real(a(j,j)) + real(x(j)*temp)
215  ELSE
216  a(j,j) = real(a(j,j))
217  END IF
218  20 CONTINUE
219  ELSE
220  jx = kx
221  DO 40 j = 1,n
222  IF (x(jx).NE.zero) THEN
223  temp = alpha*conjg(x(jx))
224  ix = kx
225  DO 30 i = 1,j - 1
226  a(i,j) = a(i,j) + x(ix)*temp
227  ix = ix + incx
228  30 CONTINUE
229  a(j,j) = real(a(j,j)) + real(x(jx)*temp)
230  ELSE
231  a(j,j) = real(a(j,j))
232  END IF
233  jx = jx + incx
234  40 CONTINUE
235  END IF
236  ELSE
237 *
238 * Form A when A is stored in lower triangle.
239 *
240  IF (incx.EQ.1) THEN
241  DO 60 j = 1,n
242  IF (x(j).NE.zero) THEN
243  temp = alpha*conjg(x(j))
244  a(j,j) = real(a(j,j)) + real(temp*x(j))
245  DO 50 i = j + 1,n
246  a(i,j) = a(i,j) + x(i)*temp
247  50 CONTINUE
248  ELSE
249  a(j,j) = real(a(j,j))
250  END IF
251  60 CONTINUE
252  ELSE
253  jx = kx
254  DO 80 j = 1,n
255  IF (x(jx).NE.zero) THEN
256  temp = alpha*conjg(x(jx))
257  a(j,j) = real(a(j,j)) + real(temp*x(jx))
258  ix = jx
259  DO 70 i = j + 1,n
260  ix = ix + incx
261  a(i,j) = a(i,j) + x(ix)*temp
262  70 CONTINUE
263  ELSE
264  a(j,j) = real(a(j,j))
265  END IF
266  jx = jx + incx
267  80 CONTINUE
268  END IF
269  END IF
270 *
271  RETURN
272 *
273 * End of CHER
274 *
275  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine cher(UPLO, N, ALPHA, X, INCX, A, LDA)
CHER
Definition: cher.f:135