stbt06()

subroutine stbt06	(	real	RCOND,
		real	RCONDC,
		character	UPLO,
		character	DIAG,
		integer	N,
		integer	KD,
		real, dimension( ldab, * )	AB,
		integer	LDAB,
		real, dimension( * )	WORK,
		real	RAT
	)

STBT06

Purpose:

 STBT06 computes a test ratio comparing RCOND (the reciprocal
 condition number of a triangular matrix A) and RCONDC, the estimate
 computed by STBCON.  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 REAL 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 REAL The estimate of the reciprocal condition number computed by STBCON.
[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]	KD	KD is INTEGER The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0.
[in]	AB	AB is REAL array, dimension (LDAB,N) The upper or lower triangular band matrix A, stored in the first kd+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
[in]	LDAB	LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1.
[out]	WORK	WORK is REAL array, dimension (N)
[out]	RAT	RAT is REAL 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 123 of file stbt06.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            KD, LDAB, N
      REAL               RAT, RCOND, RCONDC
*     ..
*     .. Array Arguments ..
      REAL               AB( LDAB, * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO, ONE
      parameter( zero = 0.0e+0, one = 1.0e+0 )
*     ..
*     .. Local Scalars ..
      REAL               ANORM, BIGNUM, EPS, RMAX, RMIN, SMLNUM
*     ..
*     .. External Functions ..
      REAL               SLAMCH, SLANTB
      EXTERNAL           slamch, slantb
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max, min
*     ..
*     .. External Subroutines ..
      EXTERNAL           slabad
*     ..
*     .. Executable Statements ..
*
      eps = slamch( '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 = slamch( 'Safe minimum' )
         bignum = one / smlnum
         CALL slabad( smlnum, bignum )
         anorm = slantb( 'M', uplo, diag, n, kd, ab, ldab, work )
*
         rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
      END IF
*
      RETURN
*
*     End of STBT06
*

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