*> \brief \b DTBCON * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DTBCON + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK, * IWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER DIAG, NORM, UPLO * INTEGER INFO, KD, LDAB, N * DOUBLE PRECISION RCOND * .. * .. Array Arguments .. * INTEGER IWORK( * ) * DOUBLE PRECISION AB( LDAB, * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DTBCON 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 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). *> 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 DOUBLE PRECISION array, dimension (3*N) *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER 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. * *> \date December 2016 * *> \ingroup doubleOTHERcomputational * * ===================================================================== SUBROUTINE DTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK, \$ IWORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER DIAG, NORM, UPLO INTEGER INFO, KD, LDAB, N DOUBLE PRECISION RCOND * .. * .. Array Arguments .. INTEGER IWORK( * ) DOUBLE PRECISION 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 * .. * .. Local Arrays .. INTEGER ISAVE( 3 ) * .. * .. External Functions .. LOGICAL LSAME INTEGER IDAMAX DOUBLE PRECISION DLAMCH, DLANTB EXTERNAL LSAME, IDAMAX, DLAMCH, DLANTB * .. * .. External Subroutines .. EXTERNAL DLACN2, DLATBS, DRSCL, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, MAX * .. * .. 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( 'DTBCON', -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( 1, N ) ) * * Compute the norm of the triangular matrix A. * ANORM = DLANTB( NORM, UPLO, DIAG, N, KD, AB, LDAB, WORK ) * * Continue only if ANORM > 0. * IF( ANORM.GT.ZERO ) THEN * * Estimate the 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 DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE ) IF( KASE.NE.0 ) THEN IF( KASE.EQ.KASE1 ) THEN * * Multiply by inv(A). * CALL DLATBS( UPLO, 'No transpose', DIAG, NORMIN, N, KD, \$ AB, LDAB, WORK, SCALE, WORK( 2*N+1 ), INFO ) ELSE * * Multiply by inv(A**T). * CALL DLATBS( UPLO, 'Transpose', DIAG, NORMIN, N, KD, AB, \$ LDAB, WORK, SCALE, WORK( 2*N+1 ), INFO ) END IF NORMIN = 'Y' * * Multiply by 1/SCALE if doing so will not cause overflow. * IF( SCALE.NE.ONE ) THEN IX = IDAMAX( N, WORK, 1 ) XNORM = ABS( WORK( IX ) ) IF( SCALE.LT.XNORM*SMLNUM .OR. SCALE.EQ.ZERO ) \$ GO TO 20 CALL DRSCL( 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 DTBCON * END