LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ clauu2()

subroutine clauu2 ( character  UPLO,
integer  N,
complex, dimension( lda, * )  A,
integer  LDA,
integer  INFO 
)

CLAUU2 computes the product UUH or LHL, where U and L are upper or lower triangular matrices (unblocked algorithm).

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Purpose:
 CLAUU2 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 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
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 101 of file clauu2.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 A( LDA, * )
113 * ..
114 *
115 * =====================================================================
116 *
117 * .. Parameters ..
118  COMPLEX ONE
119  parameter( one = ( 1.0e+0, 0.0e+0 ) )
120 * ..
121 * .. Local Scalars ..
122  LOGICAL UPPER
123  INTEGER I
124  REAL AII
125 * ..
126 * .. External Functions ..
127  LOGICAL LSAME
128  COMPLEX CDOTC
129  EXTERNAL lsame, cdotc
130 * ..
131 * .. External Subroutines ..
132  EXTERNAL cgemv, clacgv, csscal, xerbla
133 * ..
134 * .. Intrinsic Functions ..
135  INTRINSIC cmplx, max, real
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( 'CLAUU2', -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 = real( a( i, i ) )
166  IF( i.LT.n ) THEN
167  a( i, i ) = aii*aii + real( cdotc( n-i, a( i, i+1 ), lda,
168  $ a( i, i+1 ), lda ) )
169  CALL clacgv( n-i, a( i, i+1 ), lda )
170  CALL cgemv( 'No transpose', i-1, n-i, one, a( 1, i+1 ),
171  $ lda, a( i, i+1 ), lda, cmplx( aii ),
172  $ a( 1, i ), 1 )
173  CALL clacgv( n-i, a( i, i+1 ), lda )
174  ELSE
175  CALL csscal( 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 = real( a( i, i ) )
185  IF( i.LT.n ) THEN
186  a( i, i ) = aii*aii + real( cdotc( n-i, a( i+1, i ), 1,
187  $ a( i+1, i ), 1 ) )
188  CALL clacgv( i-1, a( i, 1 ), lda )
189  CALL cgemv( 'Conjugate transpose', n-i, i-1, one,
190  $ a( i+1, 1 ), lda, a( i+1, i ), 1,
191  $ cmplx( aii ), a( i, 1 ), lda )
192  CALL clacgv( i-1, a( i, 1 ), lda )
193  ELSE
194  CALL csscal( i, aii, a( i, 1 ), lda )
195  END IF
196  20 CONTINUE
197  END IF
198 *
199  RETURN
200 *
201 * End of CLAUU2
202 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
complex function cdotc(N, CX, INCX, CY, INCY)
CDOTC
Definition: cdotc.f:83
subroutine csscal(N, SA, CX, INCX)
CSSCAL
Definition: csscal.f:78
subroutine cgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
CGEMV
Definition: cgemv.f:158
subroutine clacgv(N, X, INCX)
CLACGV conjugates a complex vector.
Definition: clacgv.f:74
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