LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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zlauu2.f
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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
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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*> \ingroup complex16OTHERauxiliary
99*
100* =====================================================================
101 SUBROUTINE zlauu2( UPLO, N, A, LDA, INFO )
102*
103* -- LAPACK auxiliary routine --
104* -- LAPACK is a software package provided by Univ. of Tennessee, --
105* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
106*
107* .. Scalar Arguments ..
108 CHARACTER UPLO
109 INTEGER INFO, LDA, N
110* ..
111* .. Array Arguments ..
112 COMPLEX*16 A( LDA, * )
113* ..
114*
115* =====================================================================
116*
117* .. Parameters ..
118 COMPLEX*16 ONE
119 parameter( one = ( 1.0d+0, 0.0d+0 ) )
120* ..
121* .. Local Scalars ..
122 LOGICAL UPPER
123 INTEGER I
124 DOUBLE PRECISION AII
125* ..
126* .. External Functions ..
127 LOGICAL LSAME
128 COMPLEX*16 ZDOTC
129 EXTERNAL lsame, zdotc
130* ..
131* .. External Subroutines ..
132 EXTERNAL xerbla, zdscal, zgemv, zlacgv
133* ..
134* .. Intrinsic Functions ..
135 INTRINSIC dble, dcmplx, max
136* ..
137* .. Executable Statements ..
138*
139* Test the input parameters.
140*
141 info = 0
142 upper = lsame( uplo, 'U' )
143 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
144 info = -1
145 ELSE IF( n.LT.0 ) THEN
146 info = -2
147 ELSE IF( lda.LT.max( 1, n ) ) THEN
148 info = -4
149 END IF
150 IF( info.NE.0 ) THEN
151 CALL xerbla( 'ZLAUU2', -info )
152 RETURN
153 END IF
154*
155* Quick return if possible
156*
157 IF( n.EQ.0 )
158 \$ RETURN
159*
160 IF( upper ) THEN
161*
162* Compute the product U * U**H.
163*
164 DO 10 i = 1, n
165 aii = dble( a( i, i ) )
166 IF( i.LT.n ) THEN
167 a( i, i ) = aii*aii + dble( zdotc( n-i, a( i, i+1 ), lda,
168 \$ a( i, i+1 ), lda ) )
169 CALL zlacgv( n-i, a( i, i+1 ), lda )
170 CALL zgemv( 'No transpose', i-1, n-i, one, a( 1, i+1 ),
171 \$ lda, a( i, i+1 ), lda, dcmplx( aii ),
172 \$ a( 1, i ), 1 )
173 CALL zlacgv( n-i, a( i, i+1 ), lda )
174 ELSE
175 CALL zdscal( i, aii, a( 1, i ), 1 )
176 END IF
177 10 CONTINUE
178*
179 ELSE
180*
181* Compute the product L**H * L.
182*
183 DO 20 i = 1, n
184 aii = dble( a( i, i ) )
185 IF( i.LT.n ) THEN
186 a( i, i ) = aii*aii + dble( zdotc( n-i, a( i+1, i ), 1,
187 \$ a( i+1, i ), 1 ) )
188 CALL zlacgv( i-1, a( i, 1 ), lda )
189 CALL zgemv( 'Conjugate transpose', n-i, i-1, one,
190 \$ a( i+1, 1 ), lda, a( i+1, i ), 1,
191 \$ dcmplx( aii ), a( i, 1 ), lda )
192 CALL zlacgv( i-1, a( i, 1 ), lda )
193 ELSE
194 CALL zdscal( i, aii, a( i, 1 ), lda )
195 END IF
196 20 CONTINUE
197 END IF
198*
199 RETURN
200*
201* End of ZLAUU2
202*
203 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zdscal(N, DA, ZX, INCX)
ZDSCAL
Definition: zdscal.f:78
subroutine zgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
ZGEMV
Definition: zgemv.f:158
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:102
subroutine zlacgv(N, X, INCX)
ZLACGV conjugates a complex vector.
Definition: zlacgv.f:74