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SUBROUTINE DTBT06( RCOND, RCONDC, UPLO, DIAG, N, KD, AB, LDAB,
$ WORK, RAT )
*
* -- LAPACK test routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* February 29, 1992
*
* .. Scalar Arguments ..
CHARACTER DIAG, UPLO
INTEGER KD, LDAB, N
DOUBLE PRECISION RAT, RCOND, RCONDC
* ..
* .. Array Arguments ..
DOUBLE PRECISION AB( LDAB, * ), WORK( * )
* ..
*
* Purpose
* =======
*
* DTBT06 computes a test ratio comparing RCOND (the reciprocal
* condition number of a triangular matrix A) and RCONDC, the estimate
* computed by DTBCON. 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.
*
* Arguments
* =========
*
* RCOND (input) 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)) ).
*
* RCONDC (input) DOUBLE PRECISION
* The estimate of the reciprocal condition number computed by
* DTBCON.
*
* UPLO (input) CHARACTER
* Specifies whether the matrix A is upper or lower triangular.
* = 'U': Upper triangular
* = 'L': Lower triangular
*
* DIAG (input) CHARACTER
* Specifies whether or not the matrix A is unit triangular.
* = 'N': Non-unit triangular
* = 'U': Unit triangular
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* KD (input) INTEGER
* The number of superdiagonals or subdiagonals of the
* triangular band matrix A. KD >= 0.
*
* AB (input) DOUBLE PRECISION 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).
*
* LDAB (input) INTEGER
* The leading dimension of the array AB. LDAB >= KD+1.
*
* WORK (workspace) DOUBLE PRECISION array, dimension (N)
*
* RAT (output) 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.
*
* =====================================================================
*
* .. 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, DLANTB
EXTERNAL DLAMCH, DLANTB
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. External Subroutines ..
EXTERNAL DLABAD
* ..
* .. 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
CALL DLABAD( SMLNUM, BIGNUM )
ANORM = DLANTB( 'M', UPLO, DIAG, N, KD, AB, LDAB, WORK )
*
RAT = RMAX*( MIN( BIGNUM / MAX( ONE, ANORM ), ONE / EPS ) )
END IF
*
RETURN
*
* End of DTBT06
*
END
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