numeric-linalg

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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.
*
*> \ingroup complex16_matgen
*
*  =====================================================================
      SUBROUTINE ZLARGE( N, A, LDA, ISEED, WORK, INFO )
*
*  -- LAPACK auxiliary routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. 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