ztrt01()

subroutine ztrt01	(	character	UPLO,
		character	DIAG,
		integer	N,
		complex*16, dimension( lda, * )	A,
		integer	LDA,
		complex*16, dimension( ldainv, * )	AINV,
		integer	LDAINV,
		double precision	RCOND,
		double precision, dimension( * )	RWORK,
		double precision	RESID
	)

ZTRT01

Purpose:

 ZTRT01 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*16 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*16 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 DOUBLE PRECISION The reciprocal condition number of A, computed as 1/(norm(A) * norm(AINV)).
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (N)
[out]	RESID	RESID is DOUBLE PRECISION norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date

December 2016

Definition at line 127 of file ztrt01.f.

*
*  -- LAPACK test routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
*     .. Scalar Arguments ..
      CHARACTER          DIAG, UPLO
      INTEGER            LDA, LDAINV, N
      DOUBLE PRECISION   RCOND, RESID
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   RWORK( * )
      COMPLEX*16         A( LDA, * ), AINV( LDAINV, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      parameter( zero = 0.0d+0, one = 1.0d+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            J
      DOUBLE PRECISION   AINVNM, ANORM, EPS
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      DOUBLE PRECISION   DLAMCH, ZLANTR
      EXTERNAL           lsame, dlamch, zlantr
*     ..
*     .. External Subroutines ..
      EXTERNAL           ztrmv
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          dble
*     ..
*     .. 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 = dlamch( 'Epsilon' )
      anorm = zlantr( '1', uplo, diag, n, n, a, lda, rwork )
      ainvnm = zlantr( '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 ztrmv( 'Upper', 'No transpose', diag, j, a, lda,
     $                  ainv( 1, j ), 1 )
   20    CONTINUE
      ELSE
         DO 30 j = 1, n
            CALL ztrmv( '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 = zlantr( '1', uplo, 'Non-unit', n, n, ainv, ldainv, rwork )
*
      resid = ( ( resid*rcond ) / dble( n ) ) / eps
*
      RETURN
*
*     End of ZTRT01
*

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