LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ 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```
Date
December 2016

Definition at line 104 of file zlauu2.f.

104 *
105 * -- LAPACK auxiliary routine (version 3.7.0) --
106 * -- LAPACK is a software package provided by Univ. of Tennessee, --
107 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
108 * December 2016
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 *
subroutine zlacgv(N, X, INCX)
ZLACGV conjugates a complex vector.
Definition: zlacgv.f:76
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
complex *16 function zdotc(N, ZX, INCX, ZY, INCY)
ZDOTC
Definition: zdotc.f:85
subroutine zdscal(N, DA, ZX, INCX)
ZDSCAL
Definition: zdscal.f:80
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine zgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
ZGEMV
Definition: zgemv.f:160
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