zget01.f

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      SUBROUTINE zget01( M, N, A, LDA, AFAC, LDAFAC, IPIV, RWORK,
     $                   resid )
*
*  -- LAPACK test routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
      INTEGER            lda, ldafac, m, n
      DOUBLE PRECISION   resid
*     ..
*     .. Array Arguments ..
      INTEGER            ipiv( * )
      DOUBLE PRECISION   rwork( * )
      COMPLEX*16         a( lda, * ), afac( ldafac, * )
*     ..
*
*  Purpose
*  =======
*
*  ZGET01 reconstructs a matrix A from its L*U factorization and
*  computes the residual
*     norm(L*U - A) / ( N * norm(A) * EPS ),
*  where EPS is the machine epsilon.
*
*  Arguments
*  ==========
*
*  M       (input) INTEGER
*          The number of rows of the matrix A.  M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix A.  N >= 0.
*
*  A       (input) COMPLEX*16 array, dimension (LDA,N)
*          The original M x N matrix A.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= max(1,M).
*
*  AFAC    (input/output) COMPLEX*16 array, dimension (LDAFAC,N)
*          The factored form of the matrix A.  AFAC contains the factors
*          L and U from the L*U factorization as computed by ZGETRF.
*          Overwritten with the reconstructed matrix, and then with the
*          difference L*U - A.
*
*  LDAFAC  (input) INTEGER
*          The leading dimension of the array AFAC.  LDAFAC >= max(1,M).
*
*  IPIV    (input) INTEGER array, dimension (N)
*          The pivot indices from ZGETRF.
*
*  RWORK   (workspace) DOUBLE PRECISION array, dimension (M)
*
*  RESID   (output) DOUBLE PRECISION
*          norm(L*U - A) / ( N * norm(A) * EPS )
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   zero, one
      parameter( zero = 0.0d+0, one = 1.0d+0 )
      COMPLEX*16         cone
      parameter( cone = ( 1.0d+0, 0.0d+0 ) )
*     ..
*     .. Local Scalars ..
      INTEGER            i, j, k
      DOUBLE PRECISION   anorm, eps
      COMPLEX*16         t
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   dlamch, zlange
      COMPLEX*16         zdotu
      EXTERNAL           dlamch, zlange, zdotu
*     ..
*     .. External Subroutines ..
      EXTERNAL           zgemv, zlaswp, zscal, ztrmv
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          dble, min
*     ..
*     .. Executable Statements ..
*
*     Quick exit if M = 0 or N = 0.
*
      IF( m.LE.0 .OR. n.LE.0 ) THEN
         resid = zero
         return
      END IF
*
*     Determine EPS and the norm of A.
*
      eps = dlamch( 'Epsilon' )
      anorm = zlange( '1', m, n, a, lda, rwork )
*
*     Compute the product L*U and overwrite AFAC with the result.
*     A column at a time of the product is obtained, starting with
*     column N.
*
      DO 10 k = n, 1, -1
         IF( k.GT.m ) THEN
            CALL ztrmv( 'Lower', 'No transpose', 'Unit', m, afac,
     $                  ldafac, afac( 1, k ), 1 )
         ELSE
*
*           Compute elements (K+1:M,K)
*
            t = afac( k, k )
            IF( k+1.LE.m ) THEN
               CALL zscal( m-k, t, afac( k+1, k ), 1 )
               CALL zgemv( 'No transpose', m-k, k-1, cone,
     $                     afac( k+1, 1 ), ldafac, afac( 1, k ), 1,
     $                     cone, afac( k+1, k ), 1 )
            END IF
*
*           Compute the (K,K) element
*
            afac( k, k ) = t + zdotu( k-1, afac( k, 1 ), ldafac,
     $                     afac( 1, k ), 1 )
*
*           Compute elements (1:K-1,K)
*
            CALL ztrmv( 'Lower', 'No transpose', 'Unit', k-1, afac,
     $                  ldafac, afac( 1, k ), 1 )
         END IF
   10 continue
      CALL zlaswp( n, afac, ldafac, 1, min( m, n ), ipiv, -1 )
*
*     Compute the difference  L*U - A  and store in AFAC.
*
      DO 30 j = 1, n
         DO 20 i = 1, m
            afac( i, j ) = afac( i, j ) - a( i, j )
   20    continue
   30 continue
*
*     Compute norm( L*U - A ) / ( N * norm(A) * EPS )
*
      resid = zlange( '1', m, n, afac, ldafac, rwork )
*
      IF( anorm.LE.zero ) THEN
         IF( resid.NE.zero )
     $      resid = one / eps
      ELSE
         resid = ( ( resid / dble( n ) ) / anorm ) / eps
      END IF
*
      return
*
*     End of ZGET01
*
      END