numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/TESTING/LIN/ztbt06.f | 5640B | -rw-r--r-- |
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*> \brief \b ZTBT06 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZTBT06( RCOND, RCONDC, UPLO, DIAG, N, KD, AB, LDAB, * RWORK, RAT ) * * .. Scalar Arguments .. * CHARACTER DIAG, UPLO * INTEGER KD, LDAB, N * DOUBLE PRECISION RAT, RCOND, RCONDC * .. * .. Array Arguments .. * DOUBLE PRECISION RWORK( * ) * COMPLEX*16 AB( LDAB, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZTBT06 computes a test ratio comparing RCOND (the reciprocal *> condition number of a triangular matrix A) and RCONDC, the estimate *> computed by ZTBCON. 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. *> \endverbatim * * Arguments: * ========== * *> \param[in] RCOND *> \verbatim *> 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)) ). *> \endverbatim *> *> \param[in] RCONDC *> \verbatim *> RCONDC is DOUBLE PRECISION *> The estimate of the reciprocal condition number computed by *> ZTBCON. *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER *> Specifies whether the matrix A is upper or lower triangular. *> = 'U': Upper triangular *> = 'L': Lower triangular *> \endverbatim *> *> \param[in] DIAG *> \verbatim *> DIAG is CHARACTER *> Specifies whether or not the matrix A is unit triangular. *> = 'N': Non-unit triangular *> = 'U': Unit triangular *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] KD *> \verbatim *> KD is INTEGER *> The number of superdiagonals or subdiagonals of the *> triangular band matrix A. KD >= 0. *> \endverbatim *> *> \param[in] AB *> \verbatim *> AB is COMPLEX*16 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). *> \endverbatim *> *> \param[in] LDAB *> \verbatim *> LDAB is INTEGER *> The leading dimension of the array AB. LDAB >= KD+1. *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is DOUBLE PRECISION array, dimension (N) *> \endverbatim *> *> \param[out] RAT *> \verbatim *> 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. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup complex16_lin * * ===================================================================== SUBROUTINE ZTBT06( RCOND, RCONDC, UPLO, DIAG, N, KD, AB, LDAB, $ RWORK, RAT ) * * -- 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 DOUBLE PRECISION RAT, RCOND, RCONDC * .. * .. Array Arguments .. DOUBLE PRECISION RWORK( * ) COMPLEX*16 AB( LDAB, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. DOUBLE PRECISION ANORM, BIGNUM, EPS, RMAX, RMIN * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, ZLANTB EXTERNAL DLAMCH, ZLANTB * .. * .. 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. * BIGNUM = ONE / DLAMCH( 'Safe minimum' ) ANORM = ZLANTB( 'M', UPLO, DIAG, N, KD, AB, LDAB, RWORK ) * RAT = RMAX*( MIN( BIGNUM / MAX( ONE, ANORM ), ONE / EPS ) ) END IF * RETURN * * End of ZTBT06 * END