dtpt06()

subroutine dtpt06	(	double precision	rcond,
		double precision	rcondc,
		character	uplo,
		character	diag,
		integer	n,
		double precision, dimension( * )	ap,
		double precision, dimension( * )	work,
		double precision	rat )

DTPT06

Purpose:

!>
!> DTPT06 computes a test ratio comparing RCOND (the reciprocal
!> condition number of a triangular matrix A) and RCONDC, the estimate
!> computed by DTPCON.  Information about the triangular matrix A is
!> used if one estimate is zero and the other is non-zero to decide if
!> underflow in the estimate is justified.
!> 

Parameters

[in]	RCOND	!> RCOND is DOUBLE PRECISION !> The estimate of the reciprocal condition number obtained by !> forming the explicit inverse of the matrix A and computing !> RCOND = 1/( norm(A) * norm(inv(A)) ). !>
[in]	RCONDC	!> RCONDC is DOUBLE PRECISION !> The estimate of the reciprocal condition number computed by !> DTPCON. !>
[in]	UPLO	!> UPLO is CHARACTER !> Specifies whether the matrix A is upper or lower triangular. !> = 'U': Upper triangular !> = 'L': Lower triangular !>
[in]	DIAG	!> DIAG is CHARACTER !> 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]	AP	!> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2) !> The upper or lower triangular matrix A, packed columnwise in !> a linear array. The j-th column of A is stored in the array !> AP as follows: !> if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j; !> if UPLO = 'L', !> AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n. !>
[out]	WORK	!> WORK is DOUBLE PRECISION array, dimension (N) !>
[out]	RAT	!> RAT is DOUBLE PRECISION !> The test ratio. If both RCOND and RCONDC are nonzero, !> RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1. !> If RAT = 0, the two estimates are exactly the same. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 110 of file dtpt06.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            N
      DOUBLE PRECISION   RAT, RCOND, RCONDC
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   AP( * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      parameter( zero = 0.0d+0, one = 1.0d+0 )
*     ..
*     .. Local Scalars ..
      DOUBLE PRECISION   ANORM, BIGNUM, EPS, RMAX, RMIN, SMLNUM
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   DLAMCH, DLANTP
      EXTERNAL           dlamch, dlantp
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max, min
*     ..
*     .. Executable Statements ..
*
      eps = dlamch( 'Epsilon' )
      rmax = max( rcond, rcondc )
      rmin = min( rcond, rcondc )
*
*     Do the easy cases first.
*
      IF( rmin.LT.zero ) THEN
*
*        Invalid value for RCOND or RCONDC, return 1/EPS.
*
         rat = one / eps
*
      ELSE IF( rmin.GT.zero ) THEN
*
*        Both estimates are positive, return RMAX/RMIN - 1.
*
         rat = rmax / rmin - one
*
      ELSE IF( rmax.EQ.zero ) THEN
*
*        Both estimates zero.
*
         rat = zero
*
      ELSE
*
*        One estimate is zero, the other is non-zero.  If the matrix is
*        ill-conditioned, return the nonzero estimate multiplied by
*        1/EPS; if the matrix is badly scaled, return the nonzero
*        estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
*        element in absolute value in A.
*
         smlnum = dlamch( 'Safe minimum' )
         bignum = one / smlnum
         anorm = dlantp( 'M', uplo, diag, n, ap, work )
*
         rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
      END IF
*
      RETURN
*
*     End of DTPT06
*

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