LAPACK  3.10.0 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```

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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