zlarge.f

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*> \brief \b ZLARGE
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
*  Definition:
*  ===========
*
*       SUBROUTINE ZLARGE( N, A, LDA, ISEED, WORK, INFO )
* 
*       .. Scalar Arguments ..
*       INTEGER            INFO, LDA, N
*       ..
*       .. Array Arguments ..
*       INTEGER            ISEED( 4 )
*       COMPLEX*16         A( LDA, * ), WORK( * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> ZLARGE pre- and post-multiplies a complex general n by n matrix A
*> with a random unitary matrix: A = U*D*U'.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*>          A is COMPLEX*16 array, dimension (LDA,N)
*>          On entry, the original n by n matrix A.
*>          On exit, A is overwritten by U*A*U' for some random
*>          unitary matrix U.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= N.
*> \endverbatim
*>
*> \param[in,out] ISEED
*> \verbatim
*>          ISEED is INTEGER array, dimension (4)
*>          On entry, the seed of the random number generator; the array
*>          elements must be between 0 and 4095, and ISEED(4) must be
*>          odd.
*>          On exit, the seed is updated.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is COMPLEX*16 array, dimension (2*N)
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>          = 0: successful exit
*>          < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date November 2011
*
*> \ingroup complex16_matgen
*
*  =====================================================================
      SUBROUTINE zlarge( N, A, LDA, ISEED, WORK, INFO )
*
*  -- LAPACK auxiliary routine (version 3.4.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2011
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDA, N
*     ..
*     .. Array Arguments ..
      INTEGER            ISEED( 4 )
      COMPLEX*16         A( lda, * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      COMPLEX*16         ZERO, ONE
      parameter                ( zero = ( 0.0d+0, 0.0d+0 ),
     $                   one = ( 1.0d+0, 0.0d+0 ) )
*     ..
*     .. Local Scalars ..
      INTEGER            I
      DOUBLE PRECISION   WN
      COMPLEX*16         TAU, WA, WB
*     ..
*     .. External Subroutines ..
      EXTERNAL           xerbla, zgemv, zgerc, zlarnv, zscal
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, dble, max
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   DZNRM2
      EXTERNAL           dznrm2
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      info = 0
      IF( n.LT.0 ) THEN
         info = -1
      ELSE IF( lda.LT.max( 1, n ) ) THEN
         info = -3
      END IF
      IF( info.LT.0 ) THEN
         CALL xerbla( 'ZLARGE', -info )
         RETURN
      END IF
*
*     pre- and post-multiply A by random unitary matrix
*
      DO 10 i = n, 1, -1
*
*        generate random reflection
*
         CALL zlarnv( 3, iseed, n-i+1, work )
         wn = dznrm2( n-i+1, work, 1 )
         wa = ( wn / abs( work( 1 ) ) )*work( 1 )
         IF( wn.EQ.zero ) THEN
            tau = zero
         ELSE
            wb = work( 1 ) + wa
            CALL zscal( n-i, one / wb, work( 2 ), 1 )
            work( 1 ) = one
            tau = dble( wb / wa )
         END IF
*
*        multiply A(i:n,1:n) by random reflection from the left
*
         CALL zgemv( 'Conjugate transpose', n-i+1, n, one, a( i, 1 ),
     $               lda, work, 1, zero, work( n+1 ), 1 )
         CALL zgerc( n-i+1, n, -tau, work, 1, work( n+1 ), 1, a( i, 1 ),
     $               lda )
*
*        multiply A(1:n,i:n) by random reflection from the right
*
         CALL zgemv( 'No transpose', n, n-i+1, one, a( 1, i ), lda,
     $               work, 1, zero, work( n+1 ), 1 )
         CALL zgerc( n, n-i+1, -tau, work( n+1 ), 1, work, 1, a( 1, i ),
     $               lda )
   10 CONTINUE
      RETURN
*
*     End of ZLARGE
*
      END