LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ zlauu2()

 subroutine zlauu2 ( character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA, integer INFO )

ZLAUU2 computes the product UUH or LHL, where U and L are upper or lower triangular matrices (unblocked algorithm).

Purpose:
``` ZLAUU2 computes the product U * U**H or L**H * L, where the triangular
factor U or L is stored in the upper or lower triangular part of
the array A.

If UPLO = 'U' or 'u' then the upper triangle of the result is stored,
overwriting the factor U in A.
If UPLO = 'L' or 'l' then the lower triangle of the result is stored,
overwriting the factor L in A.

This is the unblocked form of the algorithm, calling Level 2 BLAS.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the triangular factor stored in the array A is upper or lower triangular: = 'U': Upper triangular = 'L': Lower triangular``` [in] N ``` N is INTEGER The order of the triangular factor U or L. N >= 0.``` [in,out] A ``` A is COMPLEX*16 array, dimension (LDA,N) On entry, the triangular factor U or L. On exit, if UPLO = 'U', the upper triangle of A is overwritten with the upper triangle of the product U * U**H; if UPLO = 'L', the lower triangle of A is overwritten with the lower triangle of the product L**H * L.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -k, the k-th argument had an illegal value```

Definition at line 101 of file zlauu2.f.

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*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zdscal(N, DA, ZX, INCX)
ZDSCAL
Definition: zdscal.f:78
complex *16 function zdotc(N, ZX, INCX, ZY, INCY)
ZDOTC
Definition: zdotc.f:83
subroutine zgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
ZGEMV
Definition: zgemv.f:158
subroutine zlacgv(N, X, INCX)
ZLACGV conjugates a complex vector.
Definition: zlacgv.f:74
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