ctrt01()

subroutine ctrt01	(	character	uplo,
		character	diag,
		integer	n,
		complex, dimension( lda, * )	a,
		integer	lda,
		complex, dimension( ldainv, * )	ainv,
		integer	ldainv,
		real	rcond,
		real, dimension( * )	rwork,
		real	resid
	)

CTRT01

Purpose:

 CTRT01 computes the residual for a triangular matrix A times its
 inverse:
    RESID = norm( A*AINV - I ) / ( N * norm(A) * norm(AINV) * EPS ),
 where EPS is the machine epsilon.

Parameters

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular
[in]	DIAG	DIAG is CHARACTER*1 Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular = 'U': Unit triangular
[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in]	A	A is COMPLEX array, dimension (LDA,N) The triangular matrix A. If UPLO = 'U', the leading n by n upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
[in]	AINV	AINV is COMPLEX array, dimension (LDAINV,N) On entry, the (triangular) inverse of the matrix A, in the same storage format as A. On exit, the contents of AINV are destroyed.
[in]	LDAINV	LDAINV is INTEGER The leading dimension of the array AINV. LDAINV >= max(1,N).
[out]	RCOND	RCOND is REAL The reciprocal condition number of A, computed as 1/(norm(A) * norm(AINV)).
[out]	RWORK	RWORK is REAL array, dimension (N)
[out]	RESID	RESID is REAL norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 123 of file ctrt01.f.

*
*  -- LAPACK test routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          DIAG, UPLO
      INTEGER            LDA, LDAINV, N
      REAL               RCOND, RESID
*     ..
*     .. Array Arguments ..
      REAL               RWORK( * )
      COMPLEX            A( LDA, * ), AINV( LDAINV, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO, ONE
      parameter( zero = 0.0e+0, one = 1.0e+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            J
      REAL               AINVNM, ANORM, EPS
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      REAL               CLANTR, SLAMCH
      EXTERNAL           lsame, clantr, slamch
*     ..
*     .. External Subroutines ..
      EXTERNAL           ctrmv
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          real
*     ..
*     .. Executable Statements ..
*
*     Quick exit if N = 0
*
      IF( n.LE.0 ) THEN
         rcond = one
         resid = zero
         RETURN
      END IF
*
*     Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
*
      eps = slamch( 'Epsilon' )
      anorm = clantr( '1', uplo, diag, n, n, a, lda, rwork )
      ainvnm = clantr( '1', uplo, diag, n, n, ainv, ldainv, rwork )
      IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
         rcond = zero
         resid = one / eps
         RETURN
      END IF
      rcond = ( one / anorm ) / ainvnm
*
*     Set the diagonal of AINV to 1 if AINV has unit diagonal.
*
      IF( lsame( diag, 'U' ) ) THEN
         DO 10 j = 1, n
            ainv( j, j ) = one
   10    CONTINUE
      END IF
*
*     Compute A * AINV, overwriting AINV.
*
      IF( lsame( uplo, 'U' ) ) THEN
         DO 20 j = 1, n
            CALL ctrmv( 'Upper', 'No transpose', diag, j, a, lda,
     $                  ainv( 1, j ), 1 )
   20    CONTINUE
      ELSE
         DO 30 j = 1, n
            CALL ctrmv( 'Lower', 'No transpose', diag, n-j+1, a( j, j ),
     $                  lda, ainv( j, j ), 1 )
   30    CONTINUE
      END IF
*
*     Subtract 1 from each diagonal element to form A*AINV - I.
*
      DO 40 j = 1, n
         ainv( j, j ) = ainv( j, j ) - one
   40 CONTINUE
*
*     Compute norm(A*AINV - I) / (N * norm(A) * norm(AINV) * EPS)
*
      resid = clantr( '1', uplo, 'Non-unit', n, n, ainv, ldainv, rwork )
*
      resid = ( ( resid*rcond ) / real( n ) ) / eps
*
      RETURN
*
*     End of CTRT01
*

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