*> \brief \b ZTBCON
*
* =========== DOCUMENTATION ===========
*
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*
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*
* Definition:
* ===========
*
* SUBROUTINE ZTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK,
* RWORK, INFO )
*
* .. Scalar Arguments ..
* CHARACTER DIAG, NORM, UPLO
* INTEGER INFO, KD, LDAB, N
* DOUBLE PRECISION RCOND
* ..
* .. Array Arguments ..
* DOUBLE PRECISION RWORK( * )
* COMPLEX*16 AB( LDAB, * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZTBCON estimates the reciprocal of the condition number of a
*> triangular band matrix A, in either the 1-norm or the infinity-norm.
*>
*> The norm of A is computed and an estimate is obtained for
*> norm(inv(A)), then the reciprocal of the condition number is
*> computed as
*> RCOND = 1 / ( norm(A) * norm(inv(A)) ).
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] NORM
*> \verbatim
*> NORM is CHARACTER*1
*> Specifies whether the 1-norm condition number or the
*> infinity-norm condition number is required:
*> = '1' or 'O': 1-norm;
*> = 'I': Infinity-norm.
*> \endverbatim
*>
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> = 'U': A is upper triangular;
*> = 'L': A is lower triangular.
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*> DIAG is CHARACTER*1
*> = 'N': A is non-unit triangular;
*> = 'U': A is 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).
*> If DIAG = 'U', the diagonal elements of A are not referenced
*> and are assumed to be 1.
*> \endverbatim
*>
*> \param[in] LDAB
*> \verbatim
*> LDAB is INTEGER
*> The leading dimension of the array AB. LDAB >= KD+1.
*> \endverbatim
*>
*> \param[out] RCOND
*> \verbatim
*> RCOND is DOUBLE PRECISION
*> The reciprocal of the condition number of the matrix A,
*> computed as RCOND = 1/(norm(A) * norm(inv(A))).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX*16 array, dimension (2*N)
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (N)
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complex16OTHERcomputational
*
* =====================================================================
SUBROUTINE ZTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK,
$ RWORK, INFO )
*
* -- LAPACK computational 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, NORM, UPLO
INTEGER INFO, KD, LDAB, N
DOUBLE PRECISION RCOND
* ..
* .. Array Arguments ..
DOUBLE PRECISION RWORK( * )
COMPLEX*16 AB( LDAB, * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
LOGICAL NOUNIT, ONENRM, UPPER
CHARACTER NORMIN
INTEGER IX, KASE, KASE1
DOUBLE PRECISION AINVNM, ANORM, SCALE, SMLNUM, XNORM
COMPLEX*16 ZDUM
* ..
* .. Local Arrays ..
INTEGER ISAVE( 3 )
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER IZAMAX
DOUBLE PRECISION DLAMCH, ZLANTB
EXTERNAL LSAME, IZAMAX, DLAMCH, ZLANTB
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, ZDRSCL, ZLACN2, ZLATBS
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, DIMAG, MAX
* ..
* .. Statement Functions ..
DOUBLE PRECISION CABS1
* ..
* .. Statement Function definitions ..
CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
UPPER = LSAME( UPLO, 'U' )
ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
NOUNIT = LSAME( DIAG, 'N' )
*
IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
INFO = -1
ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -2
ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
INFO = -3
ELSE IF( N.LT.0 ) THEN
INFO = -4
ELSE IF( KD.LT.0 ) THEN
INFO = -5
ELSE IF( LDAB.LT.KD+1 ) THEN
INFO = -7
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZTBCON', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 ) THEN
RCOND = ONE
RETURN
END IF
*
RCOND = ZERO
SMLNUM = DLAMCH( 'Safe minimum' )*DBLE( MAX( N, 1 ) )
*
* Compute the 1-norm of the triangular matrix A or A**H.
*
ANORM = ZLANTB( NORM, UPLO, DIAG, N, KD, AB, LDAB, RWORK )
*
* Continue only if ANORM > 0.
*
IF( ANORM.GT.ZERO ) THEN
*
* Estimate the 1-norm of the inverse of A.
*
AINVNM = ZERO
NORMIN = 'N'
IF( ONENRM ) THEN
KASE1 = 1
ELSE
KASE1 = 2
END IF
KASE = 0
10 CONTINUE
CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
IF( KASE.NE.0 ) THEN
IF( KASE.EQ.KASE1 ) THEN
*
* Multiply by inv(A).
*
CALL ZLATBS( UPLO, 'No transpose', DIAG, NORMIN, N, KD,
$ AB, LDAB, WORK, SCALE, RWORK, INFO )
ELSE
*
* Multiply by inv(A**H).
*
CALL ZLATBS( UPLO, 'Conjugate transpose', DIAG, NORMIN,
$ N, KD, AB, LDAB, WORK, SCALE, RWORK, INFO )
END IF
NORMIN = 'Y'
*
* Multiply by 1/SCALE if doing so will not cause overflow.
*
IF( SCALE.NE.ONE ) THEN
IX = IZAMAX( N, WORK, 1 )
XNORM = CABS1( WORK( IX ) )
IF( SCALE.LT.XNORM*SMLNUM .OR. SCALE.EQ.ZERO )
$ GO TO 20
CALL ZDRSCL( N, SCALE, WORK, 1 )
END IF
GO TO 10
END IF
*
* Compute the estimate of the reciprocal condition number.
*
IF( AINVNM.NE.ZERO )
$ RCOND = ( ONE / ANORM ) / AINVNM
END IF
*
20 CONTINUE
RETURN
*
* End of ZTBCON
*
END