subroutine dtrt01	(	character	UPLO,
		character	DIAG,
		integer	N,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( ldainv, * )	AINV,
		integer	LDAINV,
		double precision	RCOND,
		double precision, dimension( * )	WORK,
		double precision	RESID
	)

DTRT01

Purpose:

 DTRT01 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 DOUBLE PRECISION 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,out]	AINV	AINV is DOUBLE PRECISION 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]	WORK	WORK 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

November 2011

Definition at line 126 of file dtrt01.f.

*
*  -- LAPACK test 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 ..
      CHARACTER          diag, uplo
      INTEGER            lda, ldainv, n
      DOUBLE PRECISION   rcond, resid
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   a( lda, * ), ainv( ldainv, * ), work( * )
*     ..
*
*  =====================================================================
*
*     .. 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, dlantr
      EXTERNAL           lsame, dlamch, dlantr
*     ..
*     .. External Subroutines ..
      EXTERNAL           dtrmv
*     ..
*     .. 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 = dlantr( '1', uplo, diag, n, n, a, lda, work )
      ainvnm = dlantr( '1', uplo, diag, n, n, ainv, ldainv, work )
      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 dtrmv( 'Upper', 'No transpose', diag, j, a, lda,
     $                  ainv( 1, j ), 1 )
   20    CONTINUE
      ELSE
         DO 30 j = 1, n
            CALL dtrmv( '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 = dlantr( '1', uplo, 'Non-unit', n, n, ainv, ldainv, work )
*
      resid = ( ( resid*rcond ) / dble( n ) ) / eps
*
      RETURN
*
*     End of DTRT01
*

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