LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
zlauu2.f
Go to the documentation of this file.
1 *> \brief \b ZLAUU2 computes the product UUH or LHL, where U and L are upper or lower triangular matrices (unblocked algorithm).
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
10 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlauu2.f">
11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlauu2.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlauu2.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZLAUU2( UPLO, N, A, LDA, INFO )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER UPLO
25 * INTEGER INFO, LDA, N
26 * ..
27 * .. Array Arguments ..
28 * COMPLEX*16 A( LDA, * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> ZLAUU2 computes the product U * U**H or L**H * L, where the triangular
38 *> factor U or L is stored in the upper or lower triangular part of
39 *> the array A.
40 *>
41 *> If UPLO = 'U' or 'u' then the upper triangle of the result is stored,
42 *> overwriting the factor U in A.
43 *> If UPLO = 'L' or 'l' then the lower triangle of the result is stored,
44 *> overwriting the factor L in A.
45 *>
46 *> This is the unblocked form of the algorithm, calling Level 2 BLAS.
47 *> \endverbatim
48 *
49 * Arguments:
50 * ==========
51 *
52 *> \param[in] UPLO
53 *> \verbatim
54 *> UPLO is CHARACTER*1
55 *> Specifies whether the triangular factor stored in the array A
56 *> is upper or lower triangular:
57 *> = 'U': Upper triangular
58 *> = 'L': Lower triangular
59 *> \endverbatim
60 *>
61 *> \param[in] N
62 *> \verbatim
63 *> N is INTEGER
64 *> The order of the triangular factor U or L. N >= 0.
65 *> \endverbatim
66 *>
67 *> \param[in,out] A
68 *> \verbatim
69 *> A is COMPLEX*16 array, dimension (LDA,N)
70 *> On entry, the triangular factor U or L.
71 *> On exit, if UPLO = 'U', the upper triangle of A is
72 *> overwritten with the upper triangle of the product U * U**H;
73 *> if UPLO = 'L', the lower triangle of A is overwritten with
74 *> the lower triangle of the product L**H * L.
75 *> \endverbatim
76 *>
77 *> \param[in] LDA
78 *> \verbatim
79 *> LDA is INTEGER
80 *> The leading dimension of the array A. LDA >= max(1,N).
81 *> \endverbatim
82 *>
83 *> \param[out] INFO
84 *> \verbatim
85 *> INFO is INTEGER
86 *> = 0: successful exit
87 *> < 0: if INFO = -k, the k-th argument had an illegal value
88 *> \endverbatim
89 *
90 * Authors:
91 * ========
92 *
93 *> \author Univ. of Tennessee
94 *> \author Univ. of California Berkeley
95 *> \author Univ. of Colorado Denver
96 *> \author NAG Ltd.
97 *
98 *> \date September 2012
99 *
100 *> \ingroup complex16OTHERauxiliary
101 *
102 * =====================================================================
103  SUBROUTINE zlauu2( UPLO, N, A, LDA, INFO )
104 *
105 * -- LAPACK auxiliary routine (version 3.4.2) --
106 * -- LAPACK is a software package provided by Univ. of Tennessee, --
107 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
108 * September 2012
109 *
110 * .. Scalar Arguments ..
111  CHARACTER UPLO
112  INTEGER INFO, LDA, N
113 * ..
114 * .. Array Arguments ..
115  COMPLEX*16 A( lda, * )
116 * ..
117 *
118 * =====================================================================
119 *
120 * .. Parameters ..
121  COMPLEX*16 ONE
122  parameter ( one = ( 1.0d+0, 0.0d+0 ) )
123 * ..
124 * .. Local Scalars ..
125  LOGICAL UPPER
126  INTEGER I
127  DOUBLE PRECISION AII
128 * ..
129 * .. External Functions ..
130  LOGICAL LSAME
131  COMPLEX*16 ZDOTC
132  EXTERNAL lsame, zdotc
133 * ..
134 * .. External Subroutines ..
135  EXTERNAL xerbla, zdscal, zgemv, zlacgv
136 * ..
137 * .. Intrinsic Functions ..
138  INTRINSIC dble, dcmplx, max
139 * ..
140 * .. Executable Statements ..
141 *
142 * Test the input parameters.
143 *
144  info = 0
145  upper = lsame( uplo, 'U' )
146  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
147  info = -1
148  ELSE IF( n.LT.0 ) THEN
149  info = -2
150  ELSE IF( lda.LT.max( 1, n ) ) THEN
151  info = -4
152  END IF
153  IF( info.NE.0 ) THEN
154  CALL xerbla( 'ZLAUU2', -info )
155  RETURN
156  END IF
157 *
158 * Quick return if possible
159 *
160  IF( n.EQ.0 )
161  \$ RETURN
162 *
163  IF( upper ) THEN
164 *
165 * Compute the product U * U**H.
166 *
167  DO 10 i = 1, n
168  aii = a( i, i )
169  IF( i.LT.n ) THEN
170  a( i, i ) = aii*aii + dble( zdotc( n-i, a( i, i+1 ), lda,
171  \$ a( i, i+1 ), lda ) )
172  CALL zlacgv( n-i, a( i, i+1 ), lda )
173  CALL zgemv( 'No transpose', i-1, n-i, one, a( 1, i+1 ),
174  \$ lda, a( i, i+1 ), lda, dcmplx( aii ),
175  \$ a( 1, i ), 1 )
176  CALL zlacgv( n-i, a( i, i+1 ), lda )
177  ELSE
178  CALL zdscal( i, aii, a( 1, i ), 1 )
179  END IF
180  10 CONTINUE
181 *
182  ELSE
183 *
184 * Compute the product L**H * L.
185 *
186  DO 20 i = 1, n
187  aii = a( i, i )
188  IF( i.LT.n ) THEN
189  a( i, i ) = aii*aii + dble( zdotc( n-i, a( i+1, i ), 1,
190  \$ a( i+1, i ), 1 ) )
191  CALL zlacgv( i-1, a( i, 1 ), lda )
192  CALL zgemv( 'Conjugate transpose', n-i, i-1, one,
193  \$ a( i+1, 1 ), lda, a( i+1, i ), 1,
194  \$ dcmplx( aii ), a( i, 1 ), lda )
195  CALL zlacgv( i-1, a( i, 1 ), lda )
196  ELSE
197  CALL zdscal( i, aii, a( i, 1 ), lda )
198  END IF
199  20 CONTINUE
200  END IF
201 *
202  RETURN
203 *
204 * End of ZLAUU2
205 *
206  END
subroutine zgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
ZGEMV
Definition: zgemv.f:160
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine zdscal(N, DA, ZX, INCX)
ZDSCAL
Definition: zdscal.f:54
subroutine zlauu2(UPLO, N, A, LDA, INFO)
ZLAUU2 computes the product UUH or LHL, where U and L are upper or lower triangular matrices (unblock...
Definition: zlauu2.f:104
subroutine zlacgv(N, X, INCX)
ZLACGV conjugates a complex vector.
Definition: zlacgv.f:76